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AWorld Bank Publication I

I I I I THE HIGHWAY DESIGN AND MAINTENANCE STANDARDS SERIES

Vehicle Operating Costs Evidence from Developing Countries

Andrew Chesher and Robert Harrison

Publishedfor The WorldBank The Johns Hopkins University Press Baltimore and London © 1987 The International Bank for Reconstruction and Development / The World Bank 1818 H Street, N.W., Washington, D.C. 20433, U.S.A.

The Johns Hopkins University Press Baltimore, Maryland 21211 First printing December 1987

The findings, interpretations, and conclusions expressed in this study are the results of research supported by the World Bank, but they are entirely those of the authors and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they represent.

Library of Congress Cataloging-in-PublicationData

Chesher, Andrew, 1948- Vehicle Operating Costs: evidence from developing countries by Andrew Chesher and Robert Harrison. p. cm. - (The Highway design and maintenance standards series)

Bibliography:p. 1. Motor vehicles-Developing countries-Cost of operation. I. Harrison, Robert, 1943- . II. Title. III. Series. TL151.5.C48 1987 361.6'1'072-dcl9 87-22178 ISBN 0-8018-3588-7 Foreword

An effective road transportation network is an important factor in economic and social development. It is also costly. Road construction and maintenance consume a large proportion of the national budget, while the costs borne by the road-using public for vehicle operation and depreciation are even greater. It is therefore vitally important that policies be pursued which, within financial and other constraints, minimize total transport costs for the individual road links and for the road network as a whole. To do this meaningfully, particularly when dealing with large and diverse road networks, alternatives must be compared and the tradeoffs between them carefully assessed. This in turn requires the ability to quantify and predict performance and cost functions for the desired period of analysis. Because of the need for such quantitative functions, the World Bank initiated a study in 1969 that later became a large-scale program of collaborative research with leading research institutions and road agencies in several countries. This Highway Design and Maintenance Standards Study (HDM) has focused both on the rigorous empirical quantification of the tradeoffs between the costs of road construction, road maintenance, and vehicle operation and on the development of planning models incorporating total life-cyclecost simulation as a basis for highways decisionmaking. This volume is one in a series that documents the results of the HDM study. The other volumes are:

Vehicle Speeds and Operating Costs Models for Road Planning and Management

Road Deterioration and Maintenance Effects Models for Planning and Management

The Highway Design and Maintenance Standards Model Volume 1. Description of the HDM-III Model

The Highway Design and Maintenance Standards Model Volume 2. User's Manual for the HDM-III Model

Road-user costs are by far the largest cost element in road transport. Improvements in road conditions, although costly, can yet pay substantial dividends by reducing vehicle operating costs and hence generate large net benefits to the national economy as a whole. Thus, expressing vehicle operating costs in relation to road characteristics-geometry and pavement condition-is the logical approach. For certain cost components, especially fuel consumption, the required data can be obtained through controlled experiments, whereas for others, especially vehicle maintenance costs, extensive road user surveys are needed. Both approaches were used in the HDM studies in Kenya, Brazil, and India and in the study in the Caribbean sponsored by the British Transport and Road Research Laboratory. The resulting body of knowledge on road-user costs is enormous. It covers conditions on three continents, with diverse highway conditions, and in radically different economic environments. This volume considers vehicle operating cost equations in an economic context and analyzes experimental and survey data through statistical means. The findings are interpreted not only in the mechanistic sense, but also in the sense of understanding how economic influences bear on a firm's operating decisions. Firms' responses to highway conditions depend not only on vehicle design and performance, but also on the costs incurred under alternative operating policies and thus on the prices of inputs and on the nature of the competitive market in which transport services are sold. These considerations are of crucial importance when the cost relationships are applied in new environments with different price configurations. A particularly important application of this principle is in the evaluation of depreciation and interest costs. These costs are difficult to determine through experimentation and surveys, but they can be assessed through judicious use of data on maintenance and other costs, as well as in light of factors such as tariffs, taxes, and legislation.

iii This volume is to some extent a companion to Vehicle Speeds and Operating Costs:Models for Road Planning and Management, which is based on an aggregate-mechanistic methodology that considers vehicle operating cost equations essentially in a mechanistic context. These two approaches are complementary and elucidate different aspects and different components of the road-user cost complex. Most of the relationships described in this volume are included in the HDM-III model, sometimes as alternatives to relationships derived on a different basis. But they can also be used on their own and are particularly helpful for comparing the relationships in the various studies that were derived on different premises. In this sense, they help to explain such differences and the technical, economic, political, and other factors that caused them.

Clell G. Harral Per E. Fossberg Principal Transport Economist Highways Adviser

iv Contents

Preface ix

Part I. Vehicle Operating Costs: Background, Theory, and Estimation I Chapter 1. Vehicle Operating Cost Studies 3 Chapter 2. Vehicle Operating Costs: Theory and Estimation 11 2.1 VehicleOperating Costs: Theory 13 2.1.1 Choice of scrapping date 17 2.1.2 Choice of utilisation and fleet size 23 2.1.3 The effect of highway conditions on the cost of provision of transportation 25 2.2 Statistical Analysis of User Cost Data 28 Appendix. A Model for VehicleOperating Costs 34 A2.1 Optimal replacement policy, vehicle value, depreciation, and interest costs 35 A2.2 Choice of utilisation and fleet size 38 A2.3 The sensitivity of costs to highway conditions 39 Part II. Estimates of Cost Components 43 Chapter 3. The User Cost Studies 45 3.1 The Background to the Studies 45 3.2 Research Organisation 57 3.2.1 The Kenyan study,1971-75 57 3.2.2 The Brazilian study, 1975-82 58 3.2.3 The Caribbean study, 1977-82 60 3.2.4 TheIndianstudy, 1977-82 62 3.3 Data Collection 65 3.3.1 Usercostdata 65 3.3.2 The measurement of highway characteristics 68 Chapter 4. Vehicle Speeds 75 4.1 The Brazil Speed Model 76 4.2 Car and Light Goods VehicleSpeeds 79 4.3 Bus Speeds 88 4.4 Truck Speeds 89 4.4.1 Medium trucks 92 4.4.2 Heavy and articulated trucks 95 4.5 Concluding Remarks 95 Appendix. VehicleSpeed Equations 100 A4.1 Kenya 100 A4.2 Caribbean 102 A4.3 Brazil 103 A4.4 India 113

V Chapter 5. Fuel and Lubricant Costs 117 5.1 Fuel Consumption Models 118 5.2 Fuel Consumption Equations and Predictions: Cars and Light Goods Vehicles 121 5.3 Fuel Consumption Equations and Predictions: Buses and Trucks 129 5.4 Fuel Consumption: Concluding Remarks 142 5.5 Lubricant Costs 142 Appendix A. Fuel Consumption Equations as Reported by the Four Studies 146 A5.1 Kenya 146 A5.2 Caribbean 148 A5.3 Brazil 150 A5.4 India 155 Appendix B. Engine Oil Consumption Equations as Reported by the Four Studies 161 B5.1 Kenya and Caribbean 161 B5.2 Brazil 161 B5.3 India 162 Appendix C. Tables of Speed and Fuel Consumption Predictions 165 Chapter 6. Tire Costs 193 6.1 TireCostData 196 6.2 EstimationofTireCostEquations 198 6.3 Tire Consumption: Cars and Light Goods Vehicles 200 6.4 Tire Costs: Buses and Trucks 204 6.5 Concluding Remarks 215 Appendix. Tire Equations as Reported in the Four Studies 217 A6.1 Kenya 217 A6.2 Caribbean 218 A6.3 Brazil 219 A6.4 India 222 Chapter 7. Maintenance Costs 227 7.1 Collection of Maintenance Cost Data 230 7.2 Statistical Analysisof Maintenance Cost Data 232 7.3 Maintenance Parts Costs: Estimated Equations 233 7.3.1 Maintenance parts costs: cars and light goods vehicles 234 7.3.2 Maintenance parts costs: buses 242 7.3.3 Maintenance parts costs: trucks 247 7.4 Maintenance Labor Costs: Estimated Equations 255 7.5 The Effect of Highway Geometry on Maintenance Costs 260 7.6 Concluding Remarks 266 Appendix A. Maintenance Parts Equations as Reported by the Four Studies 270 A7.1 Kenya 270 A7.2 Caribbean 272 A7.3 Brazil 273 A7.4 India 277

vi Appendix B. Maintenance Labor Equations as Reported by the Four Studies 281 B7.1 Kenya 281 B7.2 Caribbean 282 B7.3 Brazil 282 B7.4 India 283 Part III. Total Vehicle Operating Costs 287

Chapter 8. The Calculation of Transport Costs 289 8.1 Relationships between VehicleValue and VehicleAge 291 8.2 VehicleUtilisation 298 8.3 Depreciation, Interest, andMaintenanceCosts 301 Appendix A. Relationships between VehicleValues and VehicleAge 310 A8.1 Kenya 310 A8.2 Caribbean 310 A8.3 Brazil 311 A8.4 India 312 Appendix B. OptimalVehicle Lives 313 Chapter 9. The Costs of Transport Services 317 9.1 Costs of Provision of Transport Services 317 9.2 Transferability and Use of Cost Equations 330 Appendix. Tablesof Total Costs andTheir Components 335 Cost tables calculated by the VAmethod 338 Cost tables calculated by the OL method 348 Annex. Accidents 357 References 369

vii Acknowledgments

Many individuals and organizations have provided us with assistance and encouragement both during the writing of this book and earlier while we were singly or jointly employed as consultants to the World Bank, the United Nations Development Programme, and the Texas Research and Development Foundation and contributing to the research whose results are reported here. We are grateful to them all for their help. We should like to thank particularly Henry Hide of the United Kingdom Transport and Road Research Laboratory; L. R. Kadayali, formerly of the Central Road Research Institute of India and now Chief Engineer, Planning, of the Ministry of Shipping and Transport of India; and the staff of Empresa Brasileira de Planejamento de Transportes, GEIPOT, Brazil, all of whom have responded quickly and helpfully to the numerous questions that we have put to them. We are grateful to Alan Walters, whose advice when he was economic adviser to the World Bank's Transportation Department influenced us greatly, and to W. Ronald Hudson and Bertell C. Butler for their advice and encouragement during our involvement in the research in Brazil. Our debt to Mari Dhokai, Val Harvey, Mary Harthan, and Pat Shaw, who typed, laid out, and revised a difficult manuscript quickly and accurately is enormous. Sabine Shive provided excellent editorial advice and directed the final preparation of the camera-ready copy. Finally, we record our thanks to the World Bank and particularly to C. G. Harral, who saw the need for this book and who asked us to write it.

viii Preface

This book presents information concerning the relationships between vehicle operating costs and highway conditions derived from four studies performed in Kenya, the Caribbean, Brazil, and India in the 1970s and early 1980s. The levels of transport costs and the amounts by which they are altered when highway conditions change depend on two main factors. The first is the production technology facing firms, in particular, the types and designs of vehicles to which firms have access. The second is the economic environment that firms face, in particular, relative prices of inputs to the production of transportation, such as fuel, tires, labor, and vehicles, and the nature of the transport markets that firms serve. The first part of this book sets out an economic model of firms managing vehicle fleets within which these influences can be examined. This model is an aid to understanding the results of the studies' research into vehicle operating costs reported in Part II and provides a framework within which to consider the statistical analysis of vehicle operating costs data, which typically comes from firms using vehicles in competitive business environments. The second part of this book reports and interprets the results of the four major research projects which were designed to study the influences on vehicle operating costs. It opens with Chapter 3, which describes the enviromnents in which the studies were performed and the ways in which their research was organized and their data collected. Chapter 4 contains the studies' estimates of relationships between vehicle speeds and highway characteristics. The equations presented there relate to free flow speeds and were mostly obtained from roadside observation of the speeds of vehicles under normal operating conditions. In each study estimates of the effects on speeds of surface roughness, gradient, and curvature were obtained. There are some similarities in the studies' results, but speed levels do differ somewhat across the four countries, as is to be expected given their differing economic environments and the differences in the specifications of vehicles found in the four countries. The speed equations provide an input to the fuel consumption equations, presented in Chapter 5. The extensive fuel consumption equations were for the most part obtained from experiments conducted over diverse types of highway using instrumented fleets of specially purchased test vehicles. The vehicles considered range from cars to 40-ton articulated trucks, and the equations obtained allow the effects on fuel consumption of surface roughness, gradient, and in some cases curvature to be predicted with high accuracy. Differences in vehicle specifications lead to differences in the fuel consumption equations across studies, but broad similarities come through. All the studies' equations write fuel consumption as a function of vehicle speed, and, to predict fuel consumption, the speed models of Chapter 4 can be used. Chapter 6 contains equations with which to predict tire costs. Tire costs and maintenance costs, considered in Chapter 7, present the greatest difficulties for the analyst attempting to produce robust, reliable equations. Firms can choose the amount of maintenance that they perform, trading off maintenance expenditures against depreciation costs, and their choice of policy can be expected to be influenced by the prices of inputs to maintenance activities and by the price at which vehicles are purchased. The equations presented in Chapters 6 and 7 were obtained using data gathered in large- scale surveys of commercial road users carried out over periods ranging from one to three years. Estimates of the effects on tire and maintenance costs of vehicle age and surface roughness are presented, and, for some vehicles classes, estimates of the effects of highway geometry are included. The third part of this book examines total vehicle operating costs. To compute these it is necessary to consider expenditures associated with vehicle purchase and replacement. Fleets of vehicles are major investments, and funds devoted to their purchase could be used in alternative profitable activities. In

ix providing transport services, vehicles deteriorate and their value declines, though the decline is offset to some extent by maintenance expenditures. The consequent interest and depreciation costs are important components of the cost of provision of transport services, but the studies provide rather little direct evidence on these costs. Chapter 8, which opens Part III, examines ways in which they can be calculated, exploiting the model developed in Chapter 2. The final Chapter 9 contains illustrative calculations of the costs of provision of transport services per unit distance, thus bringing together the results contained in Part II, the methods described in Chapter 8, and information on prices of inputs, where possible gross and net of taxes. The studies' predictions of the effects of highway conditions on total costs are compared and evaluated, and some guidance is given concerning which of the studies' many equations to use in what circumstances. The problem of applying the studies' results in new environments is also considered.

x PART I Vehicle Operating Costs: Background, Theory, and Estimation I~ ~~~~~~~~~ Il CHAPTER1 Vehicle Operating Cost Studies

This book provides information concerning the costs of transportation on non-urban highways and the relationships between these costs and characteristics of highways like surface roughness, and vertical and horizontal geometry. The sources of the information presented here are four major road user cost studies performed between 1970 and 1982 in Kenya, the Caribbean, Brazil, and India. In these studies road user costs were investigated in considerable depth. Surveys of commercial road users were performed, surveys on a far larger scale than had been conducted prior to the 1970s. Large scale experiments were undertaken, aimed at determining the fuel consumption of cars, buses and light and heavy goods vehicles under alternative highway conditions, and considerable effort was devoted to obtaining data on vehicle speeds and their responses to highway conditions. The resulting body of knowledge concerning road users' costs is enormous, spanning three continents, diverse highway conditions and radically different economic environments.

The studies were performed in order to provide information to use In benefit cost analysis of highway investment projects and many of their results are Incorporated in the Highway Design and Maintenance Model (HDM Ill), developed by the World Bank, designed to aid In evaluating highway investments and described In a companion volume in this series (Watanatada et al. 1987).

Benefit cost analyses of highway investments proceed by calculating streams of costs associated with highway construction and maintenance and streams of benefits that arise in consequence of the investments. Most of these benefits come about as a result of reductions in the costs per unit output of provision of transportation which affect the supply side of markets for transport services. Other benefits arise from Improvements in the quality of transportation. These affect the demand side of the market for transport services and are particularly important in passenger transportation, demand for which may be increased quite substantially as a result of reductions In journey times and improved comfort and safety. Most of the results obtained In the four country studles bear on the changes in vehicle operating costs attendant on highway Improvements and thus on the supply side of transport markets. The studies provide Information concerning vehicle speeds which Is useful in coming to conclusions concerning time savings but the questlon of valuing such savings and similar Issues relevant to the demand side of transport markets are not considered In this book.

Highway engineers have, for many years, been concerned to discover the relationships between highway design, condition and road user costs - Indeed, vehicle operating costs for horse drawn vehicles were

3 4 VEHICLE OPERATING COST STUDIES published over one hundred years ago (Law and Klnnear-Clark 1881). Motor vehicles' costs first received attention In North America after the First World War, when Agg studled the performance of a small test fleet fitted with fuel flowmeters and chart distance recorders. Agg's work (Agg 1923), Influenced both the design and reporting of subsequent fuel consumption experiments, and his appointment as Director of the Iowa State College Engineering Station initiated a series of vehicle cost studies. By 1935, Its staff had reported on the effect of geometry on operating costs (Agg and Carter 1928), on truck operations In Iowa (Winfrey 1933), on tractive resistance and road surface types (PaustIan 1934), and on tire skidding characteristics, surface types and safety (Moyer 1934).

One of the earliest surveys of operating costs was reported by Moyer and Winfrey (1939), who examined the fuel, oil, maintenance and tire costs of rural mall carriers and Moyer and Tesdall (1945) complemented this study with the results from tire wear experiments. The period to 1960 saw North American and European research concentrated on the relationships between highway geometry, vehicle performance and costs. Saal (1942) extended his experimental fuel consumption data using survey Information - an Important development - while Coquand (1958), Sawhill and Firey (1960) and Claffey (1960) developed models and reported results of speed and fuel experiments Incorporating highway and vehicle characteristics. Interest In total operating cost levels and In tire, maintenance and depreclation costs stimulated road user surveys, Including Kent (1960) and Stevens (1961). Surveys of users in developing countries Include those reported by the Indian Roads Congress (1961, 1971) and Bonney and Stevens (1967) whose data were obtained In East Africa.

In the early 1950s, the first appraisal manual Incorporating road user costs was produced by the American Associatlon of State Highway Officlals (AASHO 1952). Although it gave data only for passenger cars In rural areas, and some limited Information on truck costs, It did help to establish the economic evaluation of highway Improvements at a planning level. However, many of the technical relationships became obsolete and Its usefulness was limited by the 1960s despite an update In 1959 incorporating new unit prices. It was ultimately Winfrey (1963) who synthesized the available experimental and survey operating cost data to produce a pubilcation which profoundly Influenced highway planning In the United States and the developing world over the next 15 years.

Winfrey's comprehensive review of the American vehicle operating cost literature revealed considerable gaps and deficiencies which were filled by data from his own records on vehicle costs, discussions wlth speciallsts In the motor industry, and by judicious use of theoretical reasoning concerning operating costs. Winfrey's main sources of Information are given In Table 1.1 The baslc work was revised in 1969 to include a section on accident costs.

Despite the considerable efforts devoted to collecting U.S. and European vehicle operating cost Information, by 1965 only fuel consumption could be predicted at all accurately and most of the information avallable was not well sulted to use outside North America and Western Europe. The growing need for economic appraisal of highway projects in developing VEHICLE OPERATING COST STUDIES 5

Table 1.1: Data Sources for Wlnfrey (1963)

Item Primary Sources OtherSources

Fuel Clafbey (1960) Sawhill andFirey (1960) Winfrey (peonal test) Sawhill (1962) Correspondencewith speciait in car companies Moyer (1939)

Engine Oil Moyer (1939) Wintrey (1962) Kent (1962) Stevens (1961)

Maintenance Stevens (1961) Wlntrey (judgement)

Tires Moyer and Tesdall (1945) Wintrey (judgemen based on power requirements Kent (1962) for curves andgrades) Gough (1966) Gough and Shearer (1966) Hershey (1957)

Depreciation Stevens (1961) Wintrey (judgement)

Gravel Adjustments Moyer (1939) Wlntrey (judgement) Claffey (1960) Sawhill (1962)

Source: Hide (1976). 6 VEHICLE OPERATING COST STUDIES regions led the World Bank to sponsor a literature review and the preparation of cost tables. The results were published by de Weille (1966) whose main sources are given In Table 1.2.

It Is evident that Winfrey's (1963) text was a major source and using this and other, mainly the American research, de Weilie was able to assemble a set of basic tables with a common structure. Tables were prepared for seven vehicle types, three cars and four trucks and accompanied by indicative prices. No data concerning buses were provided, an Important omission for most highway studies In developing countries. The largest car and all the trucks were those used by Winfrey, the small car was a Volkswagen 1200 and the "average" car was a "composite" of the other two car types. Costs were given for these vehicles operating at a series of constant or "benchmark" speeds on paved, gravel and earth surfaces. Using the indicative prices, costs for fuel and oil consumption, tire wear, depreciation and interest, maintenance parts, maintenance labour and occupants time were given for each combination of speed and surface type.

After the publication of de Weille's work It was clear that results based on American vehicles and environment, many of them out of date, were Inadequate for evaluating highway Investment projects in developing countries and that the only way to correct the deficiency was to conduct a program of user cost research outside the United States.

In 1969 the World Bank initiated a program of research to develop models relevant to conditions in developing countries with which to examine the trade-offs between Initial construction costs, future maintenance expenditures and road user costs for alternative highway design and maintenance strategies. The results concerning vehicle operating costs are the primary focus of this book.

Phase 1 of the program was carried out by staff of the Massachusetts Institute of Technology, the World Bank, and the British Transport and Road Research Laboratory (TRRL). The report covering this phase (Moavenzadeh et al. 1971) gave a structure within which construction, malntenance and road user costs could be interrelated In order to evaluate the costs and benefits associated with alternative highway design and maintenance strategies. The report concluded that t available engineering relationships with which to predict highway deterioration, and the economic relationships with which to predict road user costs were Inadequate for use In developing countries and Phase II of the program was designed to remedy these deficiencies. Research institutions In developing countries were encouraged to support research Into user costs and, where possible, pavement deterioration. The result was the series of studies undertaken In Kenya, Brazil, the Eastern Caribbean and India between 1971 and 1982 whose results concerning vehicle operating costs are the subject of this book. The studies are described In Chapter 3 and Part 11 presents many of their results.

Since 1970 other vehicle operating cost results have been reported which are relevant to low volume roads although they are not easily compared with the results reported here because of differences In the measurement of highway characteristics, particularly roughness. VEHICLE OPERATINGCOST STUDIES 7

Table 1.2: Data Sources for de WeIlle (1966)1

Item Primary Sources Other Sources

Speed MSHO Red Book (1959) Odier (1962) Moyer (1939) Saal (1950) Winfrey

Fuel - speed Winfrey - rise + fall Winfrey - curvature Winfrey - surface type Winfrey Odier (1962)

Oil - speed Winfrey - surface type Doyen (1960)

Tires - speed Wintrey - surface type Winfrey Doyen (1960)

Deprecation de Weille (judgement using - speed Winfrey and United States othicial data, e.g. U.S. Bureau of the Census (1962) and Liston and Allen (1964))

Maintenance - speed Winfrey -surface type Winfrey | Doyen (1960)

Notes:

1. All references to Winfrey are to Winfrey (1963).

2. See table 1.4 for Winfrey's sources.

Source: de Weille (1966). 8 VEHICLE OPERATING COST STUDIES

Abelson (1973) examined de Weille's work, and identified four areas in which supplementary data and relationships were needed to make the findings applicable to developing countries. These areas were the effect of the market economy (especially wages and prices) on operating cost levels, the calibration of technical relatlonships to local conditions, the value of time savings and accident and overhead costs and they were discussed with reference to Thailand and Illustrated with user cost data from Thailand and from other countries. Daniels (1974) reported the measurement of vehicle operating costs in Africa by the Economist Intelligence Unit of the United Kingdom, mostly in the late 1960s. Particular attention was directed towards how operating costs are best collected, the determination of maintenance and depreciation costs, and of vehicle service life and utilisatlon.

Australian research in the field of vehicle operating costs during the 1970s was directed towards relating vehicle characteristics to pavement damage as well as vehicle operating costs to highway characteristics. Lack (1968) provided one of the earliest models, which influenced subsequent formulation of the World Bank models. Soloman (1970) reported on optimum axle loads for Australlan roads and stimulated research on the broader question of commercial vehicle (particularly truck) designs, (Fry et al. 1974, 1975, 1976). Vehicle operating costs were studied between 1968 and 1976, first by Pelensky et al. (1968; 1970) for cars, then by Soloman and Conroy (1974) for commercial vehicles and Ker (1976), who estimated truck operating costs from fleet data.

The second edition of the United States Forest Service Vehicle Operating Cost Model (Sullivan 1977) influenced the speed and fuel modelling carried out using the Brazilian data in the early 1980s, described In Chapters 4 and 5. The model simulates vehicle travel along a route and requires a detailed road description together with extensive information on vehicle characteristics. It contains constraints on vehicle performance derived from physical principles and assumptions concerning what "prudent" drivers will do when faced with different combinations of highway characteristics. Times for acceleration, braking or coasting are determined and the associated speeds, travel times, forces and energy requirements are calculated. These energy requirements are converted to instantaneous fuel consumption and tire wear and with other operating cost components to give predictions of total vehicle costs.

In 1981, an updated version of the Federal Highway Authority Vehicle Operating Cost and Pavement Type manual was published (Zaniewskl et al. 1981) revising the earlier version based on Winfrey (1969) and Claffey's work (1971). Look-up tables reported operating costs for a range of vehicle types at constant speeds, and over speed cycles. Zaniewski conducted a series of fuel experiments on paved roads using a test fleet of four cars, a pickup and three trucks. He also modelled tire wear using the procedures developed by Barreire et al. (1974) and Delia Moretta (1974) for use In the Forest Service Model (Sullivan 1977).

This book Is concerned with operating costs for motorized vehicles but it should be recognised that the evaluation of design and maintenance strategies must take account of the local modes in use on the highway network being studied. In some developing countries, traffic flows consist of small engined vehicles or animal powered vehicles which were not covered VEHICLE OPERATING COST STUDIES 9

In the four country studles. Rogers (1983) reports productivity rates and costs per passenger or tonne kilometer for a variety of such modes In Indonesia. Some Informatlon on low powered vehicles is provided by the Indian study but not reported here.

Chapter 2 which follows concludes Part I. It sets out on economic structure within which to Interpret the studies' results, given in Part Ii, Estimates of Cost Components. It also provides a framework within which the problem of computing total vehicle operating costs, including costs associated with vehicle purchase and replacement, can be considered and It will be exploited In Part ill, Total Vehicle Operating Costs, In which these Issues arise. I I CHAPTER 2 Vehicle Operating Costs: Theory and Estimation

Most of this book is concerned with estimates of vehicle operating costs and their relationship to highway characteristics, obtained during the four user cost studles carried out between 1972 and 1982 in Kenya, the Caribbean, Brazil, and India. The relationships are presented In Part 11 of this book and in Part III we examine how the equations can be combined to obtain estimates of total operating costs and we compare the studies' predlctions of the effects of highway conditions on these total costs. In this Chapter, which concludes Part 1, we describe the methods used to analyse the studies' data and we set the operating cost equations that the studies estimated In the context of an economic theory of the transport firm.

The statistical procedures used to produce the studies' results are described here because If the procedures and their limitations are not understood then the results which occupy Part 11 may be misinterpreted. The usefulness of setting vehicle operating cost equatlons In an economic context may be less obvious - certainly such considerations are not to the fore In de Weille's (1966) predecessor to this volume, nor In the reports of the four studles - but we believe that the exercise Is essential, for the following reasons.

Most vehicle operating cost data (fuel consumption data are the only Important exception) are collected from firms that operate vehicles during the course of their normal business activities. Firms' responses to highway conditlons are dependent on vehicle design and performance, but also on costs Incurred under alternative operating policies and thus on prices of Inputs to the provislon of transportation. Thus speed and loading decisions and choices of vehicle specification are determined in part by prices of vehicles, fuel, malntenance,labour, and so forth. In order to place correct Interpretations on vehicle operating cost data gathered from firms, to choose suitable procedures with which to analyse the data, and to understand the limitations of such data it Is necessary to understand how economic Influences bear on firms' operating decisions. These considerations become crucially Important when one tries to apply cost relationships In new environments In which firms face different price configurations and vehicle designs. The structure developed In this chapter will be useful when we examine the problem of transferring cost relationships In Part 111.

There is another reason for considering vehicle operating cost equations In an economic context. The four studies provide little Information on depreciation and Interest costs which are Important components of the cost of provision of transportation. By working within the framework of an economic model of the transport firm It Is possible to

11 12 THEORY AND ESTIMATION find ways of remedying this deficiency, exploiting Information on maintenance and other costs to deduce the magnitude of depreciation and interest costs and their sensitivity to highway conditions.

We should also note that the vehicle operating cost equations reported in Part 11 are derived for use In economic appraisal of the benefits arlsing from highway Investments. The way In which the studles' results bear on concepts that arise In such appralsals Is therefore of Interest and to conclude this introductory section we consider this briefly.

In economic appraisals of highway investments the impact of highway conditions on costs of transport services per unit output Is of central Interest. Where transport services are purchased In markets supplied by transport firms, transport costs per unit output can be expected to be closely related to prices at which transport services are sold. In competitive markets, transport services will be sold at a price equal to their marginal cost of production. If transport firms have monopoly power then the relationship between costs per unit output and prices will be less direct, prices and amounts of transportation provided being determined by the equality of marginal revenue and marginal cost. in both cases, and more generally, knowledge of the relationships between highway conditions and costs per unit output of the provision of transport services in helpful In determining the responses of prices of transport services to changes In highway conditions brought about by highway Investments. It Is through such price changes that many of the benefits arising from highway Investments flow for, in general, changes in transport prices lead to changes in prices of goods and services In the production of which transport services are an Input and to changes In volumes of trade.

Similar considerations arise when transportation Is provided by firms on their own account, as Is common In many countries, especially where general haulage Is subject to governmental regulation. Such firms, which operate fleets of vehicles dedicated to their own needs, will experience transport cost changes as a result of highway Investments and these will generally lead to changes In prices of the firms' products and the amounts of those products that are traded. Private Individuals can purchase transport from transport firms but they can also provide transportation on their own account, using private cars rather than purchasing services from bus and taxi companies. Here transport cost changes lead to changes In welfare as a result of alterations to budget constraints and there may be changes In the amount of transportation employed and the mode of transport used.

The results reported in Part 11 concern the Influence of highway conditions on transport costs. To determine the benefits that result from highway Investments that change transport costs, knowledge of the demand side of transport markets is required. This Is not provided by the four studies whose results are the focus of this book and we shall not be concerned with the demand for transportation. However, It should be noted that highway Investments can result In changes In the "quality" of transport services. Thus travel may be faster and more comfortable and there may be a lower rlsk of accident after a highway Improvement. These THEORY AND ESTIMATION 13

"quality" changes affect the demand for transport services and the supply side oriented studies that we report in Part II paid little attention to these effects. Limited results are available on accident rates and these are brlefly summarized In an annex to the book.

An important consideration arising from the preceding discussion that Is relevant to the results in Part II, and to their application Is the measurement of the flow of transport services and thus of the output of transport firms. Since output is a flow it has to be measured on a per time period basis, and since vehicle owners can use vehicles of different capacities and, with any given vehicle, can vary loads carried, one will usually want to measure the flow of output in tonne, volume, or passenger kilometers per time period, depending on the nature of the transport service provided. In the four studies operating costs were calculated on a per vehicle, per kilometer basis and adjustments will generally be required to allow for loads carried and for vehicles' capacities.

To determine costs per unit output for any given output flow we require to know the flow of output per vehicle per time period. This is because the flow of costs associated with the capital embodied In the firm depends on the number of vehicles It operates and on the other capital resources it uses. When large numbers of vehicles are used to produce a flow of output, so that output per vehicle per time period is low, Interest costs will be high, but the correspondingly low rates of utilisation per vehicle will usually lead to lower fuel and other costs. How firms determine utilisation and fleet size Is considered in the next section. in calculating costs per unit output in Part IlIlwe use information on speed responses to changes in highway conditions produced by the four studies. It is important to note that the rate of flow of output per time period does not appear as an influence on operating costs in the studies' results, nor in our calculation of costs per unit output in Part ill. Some of the statistical procedures described In the concluding section of this chapter preclude the appearance of such effects since they Involve only wlthin company comparisons of costs and highway conditions. It may be that, when the scale of a firm's operations Is large, costs per unit output are low, because of economies of scale in, for example, the provislon of maintenance facilities. However, the studles' results provide us with no evidence on this Issue and In the model we Introduce now we proceed assuming that costs per unit output are Independent of the rate of flow of output per time period; equivalently that average and marginal costs of production of transport services are, at least in the long run, equal.

2.1 VEHICLE OPERATING COSTS: THEORY

The analysis of this section Is based on the Idea that firms seek to minimise the cost of production of transport services, and is carried out largely without reference to the demand side of the market for transport services. Consequently much of the analysis is applicable to firms that operate fleets of vehicles but whose main business Is not the provision of transport services, and to fIrms with a degree of monopoly power in their output markets or who operate in markets in which prices or output are regulated. 14 THEORY AND ESTIMATION

Firms have considerable discretion concerning the way In which they produce transport services. In the short run they are constrained to some extent by historic choices that are expensive to alter quickly and which anyway they may wish to leave unaltered because of uncertainty regarding the permanence of short run changes in demand conditions and in factors affecting their costs. Thus in the short run firms may be unwilling to alter the size of their fleet or the specification of the vehicles that they run. However they can quickly change utilisation which we define as output per time period per vehicle, by altering loads carried, speed of travel, and hours of operation per time period and they can advance or delay vehicle scrapping. In the long run firms can adjust fleet size and vehicle specification, purchasing more or less robust, or powerful, or more or less capacious vehicles, generally, of course, facing different purchase prices for vehicles of different specifications. We regard firms as making these policy decisions with a view to minimising the cost of production of transport services.

When highway conditions change then it Is likely that new policles will emerge. Faced with a highway deterioration, firms will react so as to minimise the impact of the deterioration on their costs. In the short run there may be little that they can do If fleet size Is not variable, though there may be output responses, but In the long run speeds and loads can be varied, fleet size being adjusted accordingly and the firm has the option of purchasing more robust vehicles, trading off a higher vehicle purchase price against reduced maintenance costs. Faced with a highway Improvement, cost minimising firms will, at any level of output, seek to maximise the benefit they can obtain through lowering costs. So, on improved roads higher speeds and, perhaps, heavier loads may be observed. Indeed some running costs, for example fuel costs per kilometer, may rise - even maintenance costs may not fall greatly after an improvement. This Is of little concern to the vehicle owner who, in consequence of increased utilisatlon, experiences for example lower interest and wage costs per kilometer. One of the results to emerge from the analysis below is that, In the long run, running costs per unit output, excluding costs associated with vehicle replacement and the opportunity cost of the capital employed by the enterprise, may actually fall as highways worsen. This has Important implications for the Interpretation of the results of user cost studies and will be discussed further later.

The distinction between short and long run adjustments to highway conditions Is Important because in user cost surveys, in which emphasis Is often placed on finding companies with well-organised records, and companies operating vehicles on fixed homogeneous routes, there is a tendency to find companies that are well adjusted to the highway conditlons that they face. We can therefore expect the relationships between vehicle running costs and highway characteristics obtained from user surveys to reflect more the long run responses of vehicle owners to highway conditions than the short run responses. The situation is represented In Figure 2.1 In which the line LL shows the "long run" relationship between per unit output costs of provision of transport services and "highway conditions."

Starting well adjusted to highway conditions h1 the firm faces the short run relationship between costs per unit output and highway THEORY AND ESTIMATION 15 conditions, s11s. DeterioratlonsIn highway conditions result In short run Increases In costs along the relativelysteep function s1s1 but In the long run cost reductions can be achleved,bringing the firm back down on to the long run relationship LL. Highway improvements lead to llmitedcost reductionsalong the relatively flat part of the relationships1s, In the short run but In the long run to further cost reductionswhich bring the firm back down on to LL. Starting well adjusted to highway conditions h2 the firm faces the short run relationship s2s2 in Figure 2.1 and we see that the long run relationshipLL is the envelope of the set of short run relationshipsnecessarily belng "less convex" than those relationships.

Some of the user cost relationships obtained In the studles and reported In Part II were obtained by "experimental"methods. The essence of these methods is that many features of vehicle operation are held fixed

Figure 2.1: Short and Long Run Vehicle Operating Cost Relationships

Cost of provision of transport services per unit output

h2 hI highway conditions

"high" "poor" quality quality 16 THEORY AND ESTIMATION so that the effect of highway conditions can be Isolated. These relationships tend to approximate short run cost relationships because, as they stand, they do not capture vehicle owner's optimal responses to highway conditions. In using these relationships some care is needed in modelling vehicle owners' responses to highway conditions. For example, speed of travel Is obviously influenced by the physical limitations of vehicles, but a driver's speed reduction on encountering a rough route is essentially a response to the (possibly very large) increase in running costs that he would experience were he to maintain his original speed. Were malntenance labour and parts free, the driver might be less careful when encountering poor quality roads, as anyone who has driven a hire car on poor quality roads (and paid the hire charge) will appreciate.

In the next subsection we develop a simple model of the cost minimising transport firm to aid the interpretation of vehicle operating cost equations and to provide a framework within which to consider the problems Involved in using such equations in Investment appraisals. In considerlng this latter Issue the role played by reiative prices of inputs to transportation Is of Interest because cost minimising firms' responses to changes In highway conditions will generally depend upon the relative prices of different inputs to vehicle operation. Where fuel is cheap, fuel cost will not weigh so heavy in the firms' considerations and speeds may be higher, particularly where vehicles are expensive to purchase. Highway Improvements may lead to higher speeds in some countries, but in others, where maintenance labour and parts are very expensive relative to new vehicles, the owner may take the opportunity provided by a highway Improvement to reduce maintenance costs per kilometer, accepting only a small reduction per kilometer In time related costs such as interest charges. The studies reported later in this book have concentrated on estimating vehicle operating cost relationships for distinct cost components, sometimes trying to model physical consumptions of inputs to vehicle operation, on the basis that the resulting equations can then be freely applied outside the environments in which they were obtained, applying unit prices relevant to the new environment, and adding up to produce a total vehicle operating cost relationship which Is intended to have wide validity. Expressing consumptions of Inputs in physical units and modelling consumptions of Inputs separately removes prices from the cost equations but the Influence of prices of inputs to vehicle operation Is embodied In the data obtained In user cost studies. Consequently application of the results In very different economic environments requires some care.

In most developing countries the transport industry is capital Intensive. Expensive vehicles, often imported and purchased with scarce foreign exchange, are used to move goods and people and the successful transport firms are those that manage effic;ently the large capital Investment that the firms' vehicles represent. Improperly used, vehicles deteriorate and, unless maintenance Is performed, they will soon fail to provide the service for which they were bought. But maintenance Is costly to perform, particularly In countries where maintenance labour wage rates are high or where good quality spare parts are expensive, or in short supply, and there comes a point In a vehicle's life when It is optimal either to scrap It or to sell It to another firm. THEORY AND ESTIMATION 17

Firms' decisions concerning when to scrap vehicles are important for they determine both the dates at which expensive vehicle purchases have to be made and the magnitude of maintenance expenditures. Delaying scrapping Increases maintenance costs since these rise through the life of a vehicle, but puts back the date at which a new vehicle must be bought. We start our analysis of firms' policy with regard to the provision of transport services by examining, in the next subsection, vehicle scrapping decisions. The results obtained there are important In tying down the concepts of depreciation and Interest costs and they will be used In Part liI when we come to consider combining the results concerning cost components given in Part II. In the subsequent subsections we consider utilisation and fleet size decisions and finally the Influence of highway conditions on firms' policies and thus on costs. The notation used in this chapter and the more technical derivations are given In the appendix to this chapter.

In reality scrapping decisions are made jointly with decisions concerning utilisation, fleet size and the optimal time path of maintenance expenditures through the vehicle's life. Some flavor of the complexity of this Joint decision can be obtained from Nickell's (1978) analysis of replacement, maintenance and depreciation. Here we start by abstracting from many of thsse problems by supposing that utillsation, fleet size and the time path of maintenance expenditures are given. Under these circumstances when should a cost minimising firm scrap a vehicle?

2.1.1 Choice of Scrapping Date

We suppose that a firm is to produce q units of output per time period, for example, q passenger kilometers per year, or q tonne or cubic meter kilometers per year, or, on fixed routes, perhaps q tonne or passenger trips per year. If the price at which the firm sells Its output Is constant and equal to p then its stream of revenue is constant, equal to pq per time period and at a discount rate r, the present value of Its revenue stream is:

(1) PVR(q) - pq/r.

Here and later we use continuous discounting.

The firm's expenditure stream Is typically not constant because at discrete points in time It has to make vehicle purchases. We let PVC(q) denote the present value of the expenditure stream associated with the production of q units of output per time period in perpetuity and define C as the constant expenditure stream whose present value Is PCV(q). The relationship between C and PVC(q) is:

(2) PVC(q) - C(q)/r. 18 THEORY AND ESTIMATION

The firm Is assumed to minimise the present value of the cost of production of whatever output stream it actually produces, and we suppose that at any point in time it operates a fleet of N vehicles each producing a constant flow of output equal to u units of output per time period. We shall often talk of "u" as utilisation but it should not be confused with a common usage of the word signifying kilometers travelled per year. Of course more kilometers per year may lead to higher values of 'u" but so can Increases In passengers or goods carried per kilometer. The simple relationship between output per time period, q, fleet size, N, and utilisatlon per vehicle, u, is:

(3) q - Nu.

In practice the firm will alter fleet size (N) and utilisation (u) to suit the conditions that It faces and we investigate Its cost minimising policy In this regard In the next subsection. For the moment N and u are regarded as fixed and the firm's optimal policy regarding vehicle scrapping Is examined.

The vehicles that the firm uses are assumed to be identical, purchased new at a price VP and scrapped s time periods after purchase. We proceed assuming that the complete fleet Is scrapped every s time periods, giving, for the present value of the stream of vehicle replacement expenditures under continuous discounting: N.VP/(C1e-rs). In reality firms will operate vehicles of different ages at any point In time but for most of the analysis we can proceed as if the fleet were purchased and scrapped en masse without altering our conclusions and benefiting from the resulting simplicity in notation.

The other costs the firm Incurs per vehicle per time period are assumed to depend upon vehicle age, t, and, for a vehicle t time periods old we write the rate of flow per time period of these costs as m(t). We refer to these costs as "running costs." Since m(t) Is a rate of flow, the running costs Incurred in the Interval Et1 , t2] of a vehicle's life t2 are given by J m(t)dt. In general m(t) will be Increasing In t - Indeed

If it Is not then, In a stationary environment, vehicles will never be scrapped. A typical time path for these running costs Is shown In Figure 2.2 which exhibits a "saw toothed" pattern, the rate of flow of costs dropping at fleet replacements which occur every s time periods.

The function m(t) encompasses fuel, lubricant and tire costs, maintenance costs, the wages of drivers - all the costs Incurred per vehicle except vehicle replacement costs. The four studies focussed almost exclusively on these "running costs." Generally m(O) will be non-zero, for, of course, new vehicles require for example fuel, tires, and drivers. The function m(t) rlses as vehicles age because of increases In malntenance costs and perhaps because older vehicles consume more fuel, Incur higher THEORY AND ESTIMATION 19

Figure 2.2: Time Path of Flow of Running Costs

Rate of flow of running costs ner time period

m(t)

0 s 2s 3s time

tire costs and so forth. An Important influence on m(t) will be the amount of use to which a vehicle is put, for m(t) gives the rate of flow of costs per time period per vehicle, which must be higher for vehicles producing more output per time period (e.g., travelling more kilometers per time period or carrying heavier loads per trip). In the next subsection we consider firms' optimal choice of vehicle utilisation which must be dependent upon the sensitivity of m(t) to changes in output per time period per vehicle.

The present value of the stream of running costs, the Initial part of which is pictured for a single vehicle in Figure 2.2, Is:

s 1-eNJ m(t)e-rtdt

lers 20 THEORY AND ESTIMATION and adding this to the present value of the stream of vehicle purchase costs gives PVC(q), the present value of the stream of costs incurred In producing q units of output per time period (see, e.g., Nash 1976):

(4) PVC(q) 1 N-r 5 Vp + J m(t)ert dt

Cost minimising firms choose vehicle lives, s, to minimise (4) and If the function m(t) is well-behaved then firms' optimal scrapping policy can be determined by examining the first order condition obtained by setting the first derivative of PVC(q) with respect to s equal to zero.

In the appendix to this chapter we show that vehicle lives, s, satisfy:

(5) Nm(s) - rPVC(q) which has a finite solution for s so long as the rate of flow of running costs Increases sufficiently fast as vehicles age. The right hand side of (5) Is equal to the constant (over time) flow of costs, C(q), whose present value Is PVC(q) and we can regard rPVC(q) as the cost of production per time period. The condition (5) requires the owner to scrap the fleet at the date when Its per time period running cost rises to be equal to the per time period cost of production. Delaying scrapping past this date Increases per time period running costs by introducing higher than optimal running costs. Advancing scrapping before this date increases per time period costs of production by bringing forward the dates at which vehicle purchases have to be made.

Of course in reality scrapping decisions are more complicated than this because firms are uncertain about the future and because the running cost time path Is often discontinuous, In which case the simple calculus techniques used above are not appropriate. The function m(t) contains elements due to maintenance expenditures and in practice at certain times in a vehicle's life its owner may choose to make a significant reinvestment In the vehicle by carrying out a major overhaul and even a partial reconstruction of the vehicle. At such times the rate of flow of running costs per time period, m(t), Is very high, far exceeding the rate of flow of revenues per time period, but the owner's action Is sensible If after this overhaul he experiences a sufficiently reduced stream of running costs. Roughly speaking such overhaul expenditures will be made If the present value of subsequent net cost reductions exceeds the current cost of the overhaul, and scrapping will occur when all such possibilities have been exhausted. Despite - or perhaps because of its simplicity, the model outlined above does allow us to get a flavor of the optimal scrapping decision and to see revealed the influences on this decision. THEORY AND ESTIMATION 21

The four studies whose results are presented In Part II provide only limited direct Information concerning depreciation and Interest costs. However, in some applications these costs can be calculated using equation (4). The term NVP/(1-e-rs) in (4) gives the present value of the stream of vehicle purchase and replacement costs and this is equivalent to a constant per time period flow at the rate:

(6) Dl (q) - rNVP/(1 - erS).

At a zero discount rate this simplifies to NVP/s which Is a per time period flow of depreciation costs and when there is no scrapping (i.e., equation (5) has no finite solution) DT(q) simplifies to rNVP which Is the per time period flow of Interest costs on the initial (and only) fleet purchase. In other cases DT(q) can be interpreted as the constant per time period flow of depreciation and interest costs, whose present value Is equal to the present value of the vehicle purchase and replacement cost stream. It can be calculated If we know vehicle prices, the discount rate and vehicle lives.

Information on vehicle lives can be difficult to obtain, particularly if we wish to know how vehicle lives vary with highway conditions. The four studies provide no direct Information on this. The analysis so far allows us to deduce optimal vehicle lives given Information on the time path of running costs, m(t), vehicle prices, VP, and the discount rate. In the appendix we show that condition (5) Is equivalent to:

f - (t)rt (7) VP = W(i(s)- m(t))e dt 0

which can be solved for optimal vehicle life s. It Is then possible to calculate the smoothed flow of depreciation and Interest costs, Dl(q) or to calculate these cost flows as a function of vehicle age.

The latter Is achieved by using (7) to define the value, V(0), of a new vehicle and defining the value of a t time period old vehicle, V(t) by:

(8) Vt) -rt f (ms) - m(w))e rw dw. t

V(t) Is the value of a t time period old vehicle In the sense that It Is a lower bound on the price at which a cost minimising vehicle owner would be prepared to sell a t time period old vehicle and an upper bound on the price at which he would buy such a vehicle (see the following appendix).

Defining the rate of flow of depreciation costs as the negative of the rate of change of a vehicle's value, D(t) - -dV(t)/dt, differentlating 22 THEORY AND ESTIMATION

(8) and Identifying l(t) - rV(t) as the rate of flow of Interest costs we have the decompositlon:

(9) m(s) rPVC(q) , C) _ D(t) + l(t) + m(t). rn(s)-N N

This equation tells us how to combine depreciation, Interest and running costs to produce total costs, and, given a solutlon for vehicle life, obtained as described above, and knowledge of the time path of running costs, It allows us to calculate depreciation and Interest costs as functions of vehicle age. We consider this further In Part Ill.

Figure 2.3 Illustrates the determination of optimal vehicle lives. The increasing, curved llne In Figure 2.3 depicts the time path of running costs, m(t). By virtue of equatlon (7), the shaded area which falls above m(t) and below m(s), when discounted, equals new vehicle price. High vehicle prices cause m(s) - C(q)/N to be high and lead to relatively long vehicle lives.

Figure 2.3: Vehicle Value and Running Cost Flows

Costs per time unit

mn(s) - m(t)

O s time THEORY AND ESTIMATION 23

Conversely factors leading to high running costs, like high maintenance labour wage rates will tend to lead to short vehicle lives. Of course, highway conditions are a major Influence on the time path of running costs, m(t), and we can expect running costs to rise as highway conditions worsen. In the absence of any other response this would lead to shorter vehicle lives, but other responses are likely to occur to offset this effect. To some extent firms can respond by adjusting maintenance strategies in the face of changes in highway conditions, changing not just the level but the path of m(t) through time. Formal analysis of this response Is very difficult (see Nickell 1978), and will not be attempted here. A response which Is easier to analyse, and which is likely to be of more importance in practice, involves changing utilisation - either vehicle speeds or loads, or both. Of course, the penalty for lowering utilisation in the face of worsening highway conditions while maintaining output is the necessity to run a larger fieet of vehicles. However, if lowering utilisation drops the running cost stream sufficiently then such a policy is worthwhile. Changes in utilisation in response to changes in highway conditions are Important in Interpreting and applying vehicle operating cost equations, and in comparing experimental and survey based results. In the next subsection we consider the joint utilisation and scrapping decision, holding highway conditions fixed, subsequently considering responses to changes In highway conditions.

2.1.2. Choice of Utillsatlon and Fleet Size

When deciding how to produce any given flow of output, the firm can elect to use few vehicles at a high level of utilisation or many vehicles at a low level of utilisatlon. The equation q - Nu, describes the choices available. It Is clear that m(t) Increases with utilisation - that Is that running costs per time period per vehicle Increase as output per time period per vehicle increases. More kilometers travelled per time period means higher fuel costs and tire and maintenance costs per time period. To the extent that util5satlon increases are brought about by Increases In running speeds or loads carried then we can expect m(t)/u to Increase with utilisation as well, this ratio being running costs per unit output per vehicle. It Is this ratio, or something close to It, that Is modelled in the four user cost studies whose results are reported In Part 11. The major focus of the studles Is the relationship between expenditure flows per unit output, like m(t)/u, and highway characteristics. To examine utilisation decisions, we proceed with the model used earlier, making the dependence on utilisation explicit by rewriting m(t) as m(u,t), and examine the conditions governing optimal utilisation, fleet size, and scrapping. It might appear at first sight that scrapping decisions are Independent of the utilisation and fleet size decision but in general this Is not the case.

In what follows, utilisatlon Is assumed to be constant through the life of a vehicle. This is a major simplifying assumption which Is perhaps not too far from the truth. Vehicles In the Brazilian survey showed fairly constant utilisation over the major part of their lives when compared within companies. We also proceed regarding fleet size, N, as continuously variable. In practice It must take Integer values but as long as the scale of production of transportation Is reasonably large, the simplifying I

24 THEORY AND ESTIMATION assumption that N Is continuous Is Innocuous. Replacing fleet size, N In (4) by q/u gives the present value of the cost of producing the flow of output q:

(10) PVC(q) q 1 |VP + m(u,t)e rtdt

This Is to be regarded as a long run cost function - fleet size Is varlable - but any fixed costs flowing at a constant rate FC per time period can be Included by adding to (10) the term FC/r which is the present value of such costs, and economies or diseconomies of scale related to fleet size could be Introduced by making FC a function of fleet size, N.

The firm's optimal utilisation, u, and vehicle life, s, are obtained by minimising PVC(q) In (10) with respect to u and s, fleet size being obtained using N - q/u. Assuming the function PVC(q) Is well behaved the conditions governing u and s are obtained as solutions to the first order conditions glven by setting the derivatives of (10) with respect to u and s equal to zero. The resulting conditions require:

r -rt (11) PVC(q) 1 mu (u,t)e dt q 1- -rs O

(12) uPVC(q) m(u, s) q r the latter being the optimal scrapping condition derived earlier with fleet size N, replaced by q/u. Vehicle lives are now determined Jolntly with utillsation as a solution to (11) and (12) and In general the scrapping and utilisation decisions cannot be made Independently. Some Intuition on this can be gained by Imagining what happens If utilisatlon Is lowered. Recall that In this cost minimisation problem output Is fixed - so low utilisation means operating a larger fleet. But this In turn requires greater capital expenditures when vehicles are replaced. Thus lowering utilisation may make delaying scrapping optimal even though higher running costs are experienced, because, by delaying scrapping, the date at which expensive vehicle purchases have to be made Is put forward Into the future. Were vehicles cheap to purchase, lowering utilisation might lead to advancing of scrapping dates.

We have Introduced utilisatlon Into the model because we can expect firms' responses to changes In highway conditlons to Involve significant adjustments In utilisation. It Is this Issue which we examine In the next subsection. THEORY AND ESTIMATION 25

2.1.3 The Effect of Highway Conditions on the Cost of Provislon of Transportation

In this section we examine how changes in highway conditions affect the costs of the cost minimising firm. Of particular Interest are the responses that firms make In order to avoid excessive cost increases when highways deteriorate and the influences that prices have on these responses. The first of these Issues Is of concern because most of the results reported In Part II are obtained from firms which are well adjusted to the highway conditions that they face. The second Issue is of interest when we come, In Part liI, to consider the transferability of vehicle operatIng cost equations.

Highway conditions enter the model developed In the preceding subsections through the function m(u,t) which describes the path of running costs (fuel, tire, maintenance costs and so forth) through a vehicle's life under alternative rates of utillsation. Deterioration In highways leads to an Increase In running costs If utilisation Is held fixed and generally to an Increase in running costs per unit output per vehicle, m(u,t)/u. But faced with a deterioration or an Improvement In highway conditions, firms are likely to react by changing utilisation (thus altering fleet size) and by advancing or delaying vehicle scrapping.

To examine the effect of changing highway characteristics on fIrm's policy we totally dIfferentiate the first order conditions that define optimal utilisation and scrapping policy, given In the following appendix, requiring these conditions tc hold before and after the change in highway conditions, first Introducing the additional variable "h" Into the running cost function m(u,t). The variable "h" represents highway conditions, large values of h being taken to Indicate poor quality highways and higher costs per unit time period per vehicle at any age or utilisation. In practice "h" might be taken to Indicate surface condition or highway geometry - Indeed one might wish to regard "h" as a vector of highway characteristics. Here we leave "h" loosely defined and regard it as scalar.

in order to obtain results that are more easily understood we now Introduce a simplification, requirlng m(u,t) to be a product of functlons of utilisation and age. Many of the vehicle running cost equations estimated In the four studies and presented In Part II have this form. Further, we write that component of running costs that depends on vehicle age as uf(u,h) where f(u,h) is measured per unit of output so that uf(u,h) is measured per unit time period. Thus we have:

(13) m(u,t) - uf(u,h)a(t).

Here a(t), taken to be an Increasing functlon of vehicle age, determines the "shape" of the time path of running costs. It Is shifted multiplicatively up or down as utilisation or highway conditions alter, by an amount depending upon the function f(u,h). In fact the function f(u,h) a(t) Is 26 THEORY AND ESTIMATION very close to the per vehicle per kilometer cost relationships reported In Part Ii.

Since poor quality highways are associated with high costs per unit output we assume fh(u,h) - 5f(u,h)/6h > 0 and we also assume that fu(u,h) - 5f(u,h)/6u > 0, that Is, that Increasing output per time period results In Increases in running costs per unit output. Later we will 2 assume that fuh(u,h) - 6 f(u,h)/5u6h > 0 arguing that the Increment to per unit output running costs from increasing output per time period Increases as highways worsen.

With this additional structure, the present value of the cost of producing the output stream q is:

(14) PVC(q) - 1 - VP u f(u,h) A(s) u l -rs IS +

where A(s) - f a(t)e dt. The equations whose solution gives optimal utilisatlon and vehicle lives are developed In the following appendix. They are:

2 (15) VP - u fu(u,h) A(s)

(16) VP - u f(u,h) B(s)

where B(s) - f (a(s) - a(t))e dt. 0

As highway conditions (h) alter, utilisatlon (u) and vehicle lives (s) alter so as to maintain equality in (15) and (16). We show In the appendix that, as highway conditions worsen, either utillsation falls or vehicle lives are reduced or both. Stronger statements are not possible without stronger assumptions but In practice we can expect utillsation to fall as highway conditions deteriorate, with some adjustment In vehicle lives, and this has important implications when we come to consider the interpretation of the results reported In Part II. There are a number of Issues to be considered here.

First, consider the results on fuel consumption, which are obtained largely from experimental data. Fuel costs, expressed per unit distance are a component of per unit output running costs, f(u,h), If distance travelled per time period Is taken to measure output per vehicle THEORY AND ESTIMATION 27 per time period. The experiment based equations Include vehicle speed as an explanatory variable, sometimes vehicle load as well, factors which were controlled when the experIments were performed. Thus the equations that the studies report for fuel consumption and its relation to highway conditions are Informative about the simple partial derivative(s) fh(u,h).

The equations In Part II relating to vehicle speeds were obtained by analysing data derived from roadside observation of vehicles. Speed is an Important determinant of utilisation, along with load carried and hours of operation per time period, and we can expect observed speeds to be Influenced by economic factors. This suggests that speed models should be applied In new environments with care, for speed predictions obtained using the studies equations may be unreliable If relative prices are very different from those observed In the four studies. The problem is easily seen In a very simple model In which vehicles are regarded as generating just fuel and Interest costs.

If we use the sort of fuel consumption model estimated in Kenya, the Caribbean and India, then costs per kilometer per vehicle at speed V kilometers per hour, for vehicles operating H hours per year are:

a V)+rVP 1 2 C - Pfa +- -+ a2V + VH

Here ao, a1 and a2 are coefficients (see Chapter 5 In Part II for typical values), pf is the unit price of fuel, VP is the price of a new vehicle and r Is the per time period discount rate. Cost minimising speed is:

rVP 11/3 V - pf-H+ a1

, 2a2 and we see that vehicle speeds are a concave, Increasing function of the relative price of vehicles and fuel. Even In the absence of differences In vehicle design and fuel quality we can expect to see different speeds where relative prices are substantially different.

The lubricant, tire and maintenance cost results reported in Part 11 were developed from survey data obtained from firms who were generally well adjusted to the highway conditions that they face. Thus we can expect these data to reflect costs after adjustment of utilisatlon and other aspects of company policy along the lines described earlier. The equations do not Include vehicle speeds as explanatory variables nor, except in a very few cases, vehicle loads. We have to conclude that these survey based equations relating costs per vehicle per kilometer of components of running costs to highway conditions are informative about components of the derivative: df(u,h)dh after allowance for adjustments In utilisation, vehicle lives and so forth. Since: 28 THEORY AND ESTIMATION

df d Th- (u,h) -fU(U,h)Uh + fh(u,h) and since we can generally expect du/dh to be negative, we can expect to see smaller effects for highway conditions in survey data than In experimentaldata (df(u,h)/dh< fh(u,h)). Indeed, It Is even possible for df(u,h)/dh to be negative If utilisation responses are sufficlently large and It Is certainly possible for components of running costs to show apparentlyperverse relationshipswith highway conditions. For example, a highway Improvementwhich causes speeds and loads to increasesubstantially may well lead to an Increase in fuel costs per unit output with reductions In maintenance and capital related costs per unit output outweighing the increase. These arguments suggest that It may be naive to expect to see substantialeffects for highway conditlons on all elements of running costs in data derived from surveys of firms. As we will see in Part 11 many elements of running costs are relatively Insensitiveto highway geometry. However, speeds are sensitive to geometry and poor geometric design undoubtedly leads to higher costs per unit output, the effect passing In large part through capital related costs.

We have consideredhow running costs vary with highway conditions and how firms might respond to changes In highway conditions by adjusting utilisation, fleet size and vehicle lives. In the final section of this chapter we describe the procedures used to analyse the four studies' data. The preceding discusslon will be relevant there, and when we come In Part 11 to consider the results that the studies reported.

2.2 STATISTICAL ANALYSIS OF USER COST DATA

In the four user cost studies carried out in India, Brazil, the Caribbean and Kenya most cost Items were studied using data obtained from companies participating In road user surveys. Though survey data on fuel costs were obtained In all four studies, the primary sources of fuel consumption data were series of experiments performed using Instrumented vehicles. In the Brazilian study survey data on vehicles' annual kilometerageswere investigated and, In the Indian study, data on the operating speeds of survey vehicle were obtalned from timetables and schedules. However, In all four studies the major source of Informationon vehicle speeds was data obtained by roadside observation of passing vehicles. In this section we examine some of the problems that arise in analysing experimentalfuel, roadside speed and user survey cost data and describe the statistical methods that were used. Survey data present different and more substantialproblems than do either the experimentally obtained fuel consumptiondata or the roadside speed data. Consequently, most of this section Is devoted to a discussionof the analysis of survey data. First we comment briefly on the statisticalmethods applied to the experimentalfuel and roadside speed data.

In the Kenyan study all the fuel experimentaland speed data were analysed using ordinary least squares applied to quite simple relationships while In the Caribbean study welghted least squares estimates were calculated. In the Indian study, ordinary and weighted least squares THEORY AND ESTIMATION 29 estimates were produced. In the Kenyan, Caribbean, and Indian studies vehicle speed was included In fuel consumption equations In non-linear form, fuel consumptlon being written as a function of the inverse of speed and speed squared but the resulting relationship Is linear In parameters and is estimated by ordinary or weighted least squares.

A variety of summary statistics accompany the studies' ordinary least squares estimates, those avallable In any particular case depending on the reporting style of the study concerned. Generally goodness of fit statistics are reported, along with standard errors, that Is, estimates of standard deviations of estimated coefficients. Where available these statistics are reported in appendices to the chapters in Part II In which results are presented. Additionally, an estimate of the standard deviation of the disturbance or error term (denoted s) Is usually reported, this error term belng the deviation of the dependent variable from its regression function.

In the Brazilian study the equation relating vehicle speed to highway characterlstics Is non-ilnear In parameters and was estimated by non-linear least squares. The methods used are discussed In Chapter 4 where vehicle speed equations are presented. Non-linear least squares estimators are biased in small samples but the bias Is generally small In large samples. Also It Is only In large samples that standard errors provide good estimates of standard deviations of estimated coefficients. Where ordinary least squares methods are used coefficient estimators are unbiased and efficient as long as standard conditions are satisfied (see e.g. Judge et al. 1980).

Writing a typical equation as:

(17) c x f + e

where c Is a cost Item or consumption of some Input, x Is a vector containing measurements of highway characteristics, p is a vector of coefficients to be estimated and e Is a disturbance, the standard conditions require e to be uncorrelated wlth x, wlth zero mean, to have constant variance Independent of x and to be serially uncorrelated. As far as fuel experimental and roadside speed data are concerned these conditions are apparently approxlmately met in practice, perhaps after some transformation of the dependent variable. In practice, we may find that the disturbance variance Is dependent on x, often the variance being larger for disturbances associated wlth values of x leading to large costs or consumptions. One way to combat this problem Is to estimate p by weighted least squares. However, a commonly adopted solution Is to replace c In (17) by log(c) which has the effect of stabilizing the variance of the error term and often results In a better representation of the data as a consequence of the change In functional form.

We now turn to the statistical analysis of survey data. The first matter that requires consideration Is the Impact of survey design on the properties of estimators. In user surveys a two-stage sampling procedure Is used. At the first stage companies are selected. In the four country 30 THEORY AND ESTIMATION studies, companies were sought whose vehicles operated on fixed routes and on routes within which there was little variation on highway characteristics, so called "homogeneous routes." In practice this aim was generally only partially fulfilled. The advantage of selecting companies with vehicles on fixed, homogeneous routes Is that good ranges for highway characteristics are then more easily obtained. Were companies to be selected whose vehicles did not operate on such routes then highway conditions experienced by the survey vehicles would be pulled towards mean highway conditions for the country, as a result of averaging. Of course companies whose vehicles do operate fixed homogeneous routes can be expected to be well adjusted to the highway conditions that they face, having purchased vehicles built to appropriate specifications and so forth.

The disadvantage of selecting companies whose vehicles operate on fixed homogeneous routes is that, following this policy, we tend to obtain much of the variation In highway characteristics at the company level rather than at the vehicle level - often obtaining wide variation In highway characteristics mainly by choosing companies operating in distinct geographical regions. The problem then is that it is at least possible that not all the across company variation in costs is due to variations In highway characteristics, for some may be due to unmeasured differences in conditions in the regions in which companies operate. Companies differ in the type of transport service that they provide - particularly in goods transportation - so that we can expect across company variation In costs, even under identical highway conditions. In user surveys the number of companies surveyed is relatively small. If there is substantial across company variation in costs not due to differences in highway characteristics then there is a danger of spuriously attributing to highway characteristics, cost variatlons that are In fact due to other causes. There is even the possibility that there are across company cost variations associated with variations In highway characteristics but not due to them. To examine these Issues further it is useful to extend the notation Introduced earlier.

Recognising the two-stage sampling procedure employed in user surveys we index c, the cost item or consumption, x, the vector of highway characteristics and the disturbance, e, with two indices: "f" indicating the company or firm generating the observation, and "v" Indicating the vehicle generating the observation. Thus cfv denotes a cost observation for the vehicle indexed "v" in the company indexed "f." Then (17) can be rewritten:

(18) cfv x +fv*l Ef.

Across company variation in costs is captured by rewriting Efv as:

(19) Efv uf +wfv, where uf is an error term specific to company f and wfv Is an error term specific to vehicle v in company f. The model described by (18) and (19) THEORY AND ESTIMATION 31

is known in the statistical literature as an "error components" model. There are good reasons for expecting it to be applicable to user survey data and there Is substantial empirical evidence for the presence of the company specific error component Uf In user survey data. Estimates obtained using Brazilian and Indian survey data, which relate to survey periods of around 18 months, suggest that, for many cost components, variation In Uf Is of a similar order of magnitude to variation in wvf.

The presence of the company specific error term Uf In (19) ensures that the disturbance efv Is serially correlated. As a result estimates obtained by applying ordinary least squares to (18) are Inefficient and accompanying summary statistics, calculated Ignoring the presence of Uf are misleading. One solution Is to apply generalized least squares, first estimating au2 , the variance of uf and Ofw2, the variance of wfv. in practice this Is achieved by transforming the data prior to application of ordinary least squares using estimates su2 and sw2 of aU2 and aw2. In the analysis of the Brazilian study data and In the re-analysis of the Indian study data (Chesher 1983) generalized least squares estimators were calculated for many cost components, estimates being obtalned using the procedure described by Fuller and Battese (1973) which uses unblased estimators of vu2 and oW2. The square roots, su and sw, of the unbiased variance estimates are reported with generalized least squares estimates as results are presented In the chapters that follow In Part II.

The resulting estimators of the coefficients, O, are unbiased as long as the error distributions involved are symmetric with zero means, and they are efficient relative to ordinary least squares estimators, at least In large samples. Since the generalized least squares estimates (GLS) are not ordinary least squares estimates (OLS) the fit of the GLS equations is not as "good" as that of the equations produced by OLS. This highlights a deficiency of "RI" type statistics which are sensitive to the scale on which the dependent varlable Is measured and which anyway are not Interesting In themselves. The aim of user survey analysts should be to obtain good, usable estimates of the coefficients, f not necessarily to "explain" large amounts of the variation In the dependent variable. Sometimes In-sample "fit" has to be sacrificed in order to obtain useful estimates.

A possibility that has to be allowed for in analysing user survey data is that the company specific error term, uf In (19), Is correlated with the highway characteristics measured by x. If it is then both OLS and GLS estimators will be biased, the estimated coefficients picking up variation In uf and assigning It Incorrectly to elements of the observable vector x.

One argument for such a correlation requires us to Imagine that companies differ In their ability to minimise the costs of production. On high volume routes where there Is fierce competition companies must succeed at keeping costs down, or perish, for customers will not pay higher prices 32 THEORY AND ESTIMATION than are necessary and companies cannot operate at a loss for long. But on low volume routes where a company may have some degree of monopoly power, market forces may not drive the high cost company out of business, at least not so fast as on high volume routes. High volume routes tend to be high quality routes built to good geometric standards, with a high quality surface, but low volume roads are often of lower quality, because of historic planning decislons and Improvement policies. In this scenario companies with high values for uf tend to fall on routes with poor quality surfaces, maybe with lower geometric design standards, and uf and x are correlated. Then ordinary least squares and generalized least squares give misleading estimates of the effects of highway characterlstics on costs. Misleading because, on Improving highways the cost reductions predicted using such estimates may not materialize unless Improved low quality routes are, or become, high volume routes. In this situation there will be a tendency to overestimate coefficlents on measures of highway quality.

Suppose the company specific error uf is correlated with the highway characteristics, x, then how can we derive estimates of the coefficients, 0, unaffected by the correlation? The answer Is obtained by considering the equation that results when we express equation (18) In terms of deviations about company means, cf., Xf. and wf., thus:

(20) cfv - cf - (xfv - Xf )VP + wfv - wf

In this equation the company specific error does not appear. Estimating (20), which under standard conditlons can be done efficiently by ordinary least squares, we obtain an estimator of P Insensitive to the behaviour of uf, an estimator free of company effects. Estimating equatlon (20) Involves regressing deviations of vehicle costs from company average costs on deviations of highway characteristics experienced by Individual vehicles from company averages of these same characteristics. Clearly Information Is thrown away If this procedure Is used since only within company variation In costs and highway characteristics Is explolted, across company variation being Ignored. However, evidence arising from within company comparisons of costs and highway characteristics Is In our opinion more convincing than evidence coming from comparisons of costs across companies.

Unfortunately there are occasions when (20) does not produce usable estimates because of Insufficient variation In highway characteristics within companies. This Is likely to be a problem when variation In highway characteristics has been obtained by sampling companies In distinct geographical regions with distinctive topography. Then there may be no alternative but to exploit across company cost and highway characteristic variation to obtain estimates of ,, though the Influence of company effects can be lessened to some extent by including additional explanatory variables descrlbing company characteristics so that uf Is partially explained. An alternative Is to proceed with (20) but to group companies so far as possible Into homogeneous groups, redefining cf and so forth as company group averages. THEORY AND ESTIMATION 33

The estimator produced by applying ordinary least squares to (20) can also be obtained by Introducing binary Indlcators Identifying companies, rewriting (18) as:

(21) cfV EufDf + xfv P + fv-

Here Df Is one for observations arising from company f and Is zero otherwise. Equations (18) and (21) are Just two ways of writing the same relationship and applying ordinary least squares to (21) produces estimates of the uf's (as coefficients on the Df's) and, for p, an estimator algebraically Identical to that obtained by applying ordinary least squares to (20). The resulting estimator Is known as a "fixed effects" estimator In the statistical literature and we use this terminology later when results are presented. Using (21) one obtains as many Intercept terms as there are companies whereas using (20) there Is no estimated Intercept since (20) necessarily passes through the origin. In practice users will want to calibrate user cost equations so that predicted cost levels accord with those found In new environments. However, for the purpose of presenting results it Is useful to report a single Intercept. In the case of ti,e Indian survey results, Intercepts have been provided by the Study Director In a personal communication to the authors. Where the Indian data has been reanalysed and In the case of the Brazilian study a single Intercept Is reported which Is a weighted average of the company Intercepts, with weights given by the number of vehicles sampled per company.

The existence of two estimators, the fixed effects estimator and the generalized least squares estimator, one Insensitive, the other sensitive to correlations between uf and x, leads to a method for detecting such correlations due to Hausman and Taylor (1981) which Involves comparing the vector of differences between the two estimators with an estimate of the variance of the sampling distribution of this difference. This "Hausman" test was applied extensively In the analysis of the Brazilian survey data and In the authors' analysis of the Indian survey data to help In deciding which estimator to use.

User survey designers and designers of user cost experiments strive to obtaln Information on vehicles travelling over wide ranges of highway conditions but In practice they have mixed success. Then It is tempting to extrapolate the fitted user cost equations outside the range of conditions experienced in the studies, but extrapolatlon should be practiced only with extreme caution, for there Is generally no guarantee that the functional forms fitted to the data over the ranges of highway conditions experienced will apply far outside those ranges. In reporting predictions In the following chapters, we have endeavoured not to push the equations far, If at all, beyond the range of experience In the relevant studies. The Transport and Road Research Laboratory, cognizant of the problem that extrapolation poses, have fitted to the Kenyan and Caribbean data S-shaped curves, which flatten to asymptotes when extrapolated to extreme high or low qualIty highways. These curves are not reported later, In part because to have done so would have substantlally Increased the 34 THEORY AND ESTIMATION volume of results to be treated. More fundamentally, It Is not evident from graphs of most of the Kenyan and Caribbean studies' data that an S- shaped curve Is appropriate - indeed It seems quite likely that costs do continue to Increase as highways worsen; what Is doubtful Is whether they Increase exponentially or even quadratically. We doubt whether the data obtained in user surveys contain significant Information concerning upper and lower bounds on costs and therefore choose to report equations as originally derived, stressing the need for care If extrapolatlon Is contemplated.

Finally, before proceeding to examine the results obtained In the four studies we address some Issues that arise because of non-linearities In some of the cost-highway characteristic relationships. A number of the user survey equations are obtained using the logarithm of some cost Item as the dependent variable. Upon exponentlating the fitted equation we obtained a non-linear equation with which to predict the cost Item, but the resulting predictions are biased. Using the equation as fitted In logarithmic form one obtains unbiased predictions of the logarithm of costs but since the exponential function Is convex and the expectation of a convex function of a variate exceeds the convex function of Its expectation, exponentiated predictions of log (costs) tend to lie below average values for costs. In reporting equations originally estimated using log (costs) as the dependent variable we Introduce a correction obtained assuming that the error distribution using the logarithmic transformation Is normal wlth mean zero and variance a2. The expected value of the exponentlated error is then exp (a2/2) (see e.g. Aitchinson and Brown 1957) and the correction Involves multiplying predictions through by exp (s2/2) 2 1 where s2 Is an unbiased estimate of the variance of the error term using the logarithmic transformation.

APPENDIX. A MODEL FOR VEHICLE OPERATING COSTS

Notation

Policy Variables

q : output per firm per time period u : output per vehicle per time period N : fleet size, I.e. vehicles per firm s : vehicle life (number of time periods)

Prices, etc.

VP : new vehicle price r : per time period continuous discount rate. THEORYAND ESTIMATION 35

Costs, etc.

PVC(q) : present value of cost of production of q In perpetuity C(q) : constant per time period flow with present value PVC(q)

PVR(q) : present value of revenues accruing from sale of q in perpetuity

R(q) : constant per time period flow with present value PVR(q)

PVAC(q) : present value of the average cost of product of q In perpetuity- PVC(q)/q

PVMC(q) : present value of the marginal cost of productionof q in perpetuity - dPVC(q)/dq

m(t) rate of flow of costs per vehicle per time period, other than vehicle replacement costs for a t time period old vehicle.

Other Variables

t : vehicle age (time periods) h : highway characteristics.

A2.1 Optimal ReplacementPolicy, Vehicle Value, Depreciationand Interest Costs

A firm produces an output stream of q units of transportservices per time period using N vehicles at utilisationu per vehicle. Thus:

(A2.1) q - Nu.

Vehicles are scrapped s time periods after purchase and replaced at a price VP per vehicle. The present value of the stream of replacementcosts for a fleet of N vehicles Is thus NVP/(1-e-rS)where r Is the continuous per time period discount rate. Vehicles Incur other costs ("running" costs) flowing at the rate m(t) per vehicle per time period for a t time period old vehicle. These costs depend upon u - q/N but for the moment the notatlon does not make the dependence explicit. The present value of the stream of running costs Incurredwhen the output stream q Is produced In perpetuity Is:

(A2.2) N fsm(w)erJ-rw + J2sm(w-s)e-rwdw+ f3sm(w-2s)e-rwdw )

N- ftm(t)ertdt 1-e-sf 36 THEORY AND ESTIMATION

Adding replacement and running costs and assuming no other costs of production, the present value of the total cost of producing q in perpetuity Is:

(A2.3) PVC(q) - Nrs (VP + fOm(t)e dt} 1-e

Note that economies or diseconomies of scale associated with fleet size could be captured by adding to (A2.3) a function of N, or by making m(t) depend on N.

Differentiating (A2.3) with respect to s gives the first order condition for optimal vehicle lives:

dPVCCq) , e -rs { -rPVC(q) + Nm(s) ) - O dS 11-e-rs which Impiles:

(A2.4) Nm(S) - rPVC(q) - C(q) where C(q) Is the constant flow of costs whose present value Is PVC(q).

The second order condition for a minimum requires:

(A2.5) Nmt(s)/(ers - 1) > 0 where mt(s) - dm(t)/dt evaluated at t-s, the solution to (A2.4).

Equation (A2.4) may have no finite solution If m(t) Is eventually Increasing not at all, or only slowly with vehicle age. If there Is a finite solution then (A2.5) shows that m(t) must be Increasing at the date of scrapping. In practice m(t) may not be monotonic because of large scale vehicle refurbishments In which case there may be multiple solutlons to (A2.4).

Since:

1-e rs -rt r m(s) - m(s)e dt equation (A2.3) can be rewritten as: THEORYAND ESTIMATION 37

(A2.6) VP - J (m(s) - m(t))e dt. 0

DefineV(t) by:

(A2.7) V(t) = Ws) - m(w+t))e rwdw

- ert{ (m(s) - m(x))e rxdx t and note that V(O) - VP.

We now show that V(t) can be interpretedas the valueof a t time periodold vehicle. Considera firm wlth a vehicleaged t time periods. Runningthe vehicleuntil Itsoptimal scrappingdate and then replacingit with a sequence of new vehicle, the present value of the costsof productlon associated with the vehicle, excluding costs associated with ownershipof the used vehicleIs, If the vehicleIs kept:

rtS -rw e-r(s-t) s rw CA2.8) ck ertmCw)er dw l rs + fJmCw)e'"dw

Using the definitionof V(t) In (A2.7)and the optimalscrapping condition this can be rewrittenas:

Ck - -V(t)+ m(s)/r. If the firm sells the t time period old vehicle for an amountSP, purchasinga new vehicle so as to maintainproduction, then the present valueof the costsassociated wlth the vehicleis:

*A2.9)c - SP + 1 - VP + m(w)e-rWdw s ~~1-ers

- - SP + m(s)/r exploitingthe optimalscrapping condition. Sincea cost minimislngfirm sells If and only If Cs < ck, we concludethat a t time periodold vehicle will be sold If and only if SP > V(t). FurtherIt will be optimalfor the firm to purchaset time periodold vehiclesIf they are offeredat a price 38 THEORY AND ESTIMATION below SP. It Is In this sense that V(t) defines the value of a t time period old vehicle. The present value of the costs associated with a t time period old vehicle, including the opportunity cost arising because the vehicle is not sold, Is ck + V(t) - m(s)/r which Is Independent of vehicle age. Thus costs of production are Independent of the age distribution of the firm's fleet.

Having defined the concept of vehicle value It Is now possible to define depreciation and interest cost flows. Depreciation costs arise because of the reduction In a vehicle's value as It ages. These costs flow at the rate D(t) - -dV(t)/dt per time period. Interest costs, l(t), flow at a rate proportional to vehicle value, thus: I(t) - rV(t).

Differentiating (A2.7), which defines vehicle value, gives:

(A2.10) dV(t) - -O(t) rV(t) (m(s) dt - - - m(t)) and on rearranging:

(A2.11) m(s) - D(t) + I(t) + m(t).

The optimal scrapping condition requires m(s) - C(q)/N, which Is total per vehicle per time period costs so that

(A2.12) C(q)/N - D(t) + I(t) + m(t) which decomposes vehicle operating costs Into their components.

A2.2 Choice of Utillsatlon and Fleet Size

The dependence of running costs on utilisation s now made explicit by writing m(t) as m(u,t) where u Is output per vehicle per time period. Partial derivatives are denoted by mu(u,t), mut(u,t) and so forth, and mu(u,t), mt(u,t) are assumed to be positive. The present value of the cost of producing q Is, substituting N - q/u Into (A2.3):

q 1 (A2.13) PVC(q) u rs r P + Jm(ut)ertdtJ

Fleet size, N, Is now variable, but determined by u since, In this analysis of the cost minimising fIrm, q Is fixed. Cost minimising fIrms choose u and s to minimise (A2.13). Note that we could add FC/r to (A2.10) to allow THEORY AND ESTIMATION 39 for fixed costs flowing at the rate FC per time period and FC could depend on fleet size which would allow the possibility of economies or diseconomies of scale.

The first order conditions for optimal utlilsatlon and vehicle lives are:

(A2.14) - | VP Im(uu,t)e rtdt u + u

(A2.15) -rs {VP + Im(u,t)e rtdt} _ mru,s)

which can be rewritten as:

(A2.16) PVC(q) _ PVAC(g) PVMC(q) - 1 _-(urs rt)edt q 1-e-rsf

m(u's) (A2.17) uPVC(q)q uPVAC(q) - uPVMC(q) r where PVAC(q) and PVMC(q) are the present values of, respectively, the average and marginal costs of producing q. These are constant for variations In q because, as noted earlier, there are neither economies nor diseconomles of scale in this model.

The second order conditions sufficient to ensure that a solution to (A2.16-17) corresponds to a cost minimum are not straightforward to interpret. Two necessary conditions that are easy to interpret are that, at a solution to (A2.16-17):

Jmu(u,t)e tdt > 0

which relates to the convexity of the running cost stream as a function of utillsation and:

mt(u,s) > 0

which has been encountered earlier.

A2.3 The Sensitivity of Costs to Highway Conditions

Changes In highway conditlons alter the flow of running costs, m(u, t) and this leads to changes In utlilsation and vehicle lives. 40 THEORY AND ESTIMATION

Equations (A2.16-17) will be satisfied before and after the change so that the sensitivity to highway conditions of utilisation, vehicle lives and thus of costs of production can be examined by totally differentiating these equations. We simplify by writing m(u,t) In the multiplicatively separable form:

m(u, t) - uf(u,h) a (t) where h denotes highway conditions, large h being taken to Indicate poor highways, and we assume a(t) Is Increasing In t, fh(u,h) > 0, fu(u,h) > 0 and fuu(u,h) > 0. Defining:

A(s) - I (t)ert dt O we then have, for the present value of the cost of producing q:

CA2.18) PVC(q) - u 1_,.rs1 P + ufuhAC)uf(u,h)A(s) and for the conditions governing optimal utilisation and scrapping, equivalent to (A2.16-17):

(A2.19) VP - u 2 fu(u,h)A(s)

(A2.20) VP - uf(u,h)B(s)

where B(s) - J(a(s)- C(t))ert dt.

Totally differentiating (A2.19-20), allowing u, s and h to alter glVes:

(A2.21) [_d+ u 1 u + d log B(s) ds h au+ f(u,h) dh L ds dh f(u,h)

2 fuu(u,h) ) du (d log A(s)) ds ffuh(u,h) (A2.22) au+ fu(u,h) dh ds dh fu(u,h) THEORY AND ESTIMATION 41 which determine the optimal response of utilisation and scrapping dates to changes In highway conditions. Note that this is In a sense a "long run" analysis since we are allowing fleet size to adjust.

The four coefficients on du/dh and ds/dh In (A2.21-22) can be expected to be positive and the two right hand side terms can be expected to be negative. Consequently without further restrictions It Is not possible to sign dsu/dh and ds/dh Individually. Note though that If du/dh > 0 then ds/dh < 0 and If ds/dh > 0 then du/dh < 0. Thus deterioratlons In highway conditions lead to reductlons In utilisatlon or shortening of vehicle lives, or both.

The effects of highway conditions on costs are easier to determine. We can expect prices charged to purchasers of transport services to be closely related to the present value of the marginal cost of productlon. We have:

(A.23) PVMC(q) - PVC(q) - 1 u [VP + uf(u,h)A(s)]. q 1-e-rs) u

Dlfferentiating with respect to h and allowing for adjustments In utilisation and vehicle lives gives:

dPVMC(q) _ 1 | dPVC(q) du dPVC(q) dsl h A(s) (A2.24) dh q du dh ds hdh]hCu )1 e-rs

-- *f(u,h) . A(s) h le1huh) rs since the braced term Is zero by virtue of the conditions governing optimal utilisatlon and scrapping. Since fh(u,h) > 0, dPVMC(q)/dh Is unambiguously positive. The constant flow with present value equal to that given by (A2.24) Is fh(u,h) rA(s)/1-e-rS). When r-0, rA(s)/(1-e-rs) - A(s)/s (applying L'H6pital's rule) and rA(s)/(1-erS) Is a kind of across time average of the time varying factor affecting running costs. I I PART II Estimates of Cost Components

In Part 11 the user cost equatlons developed In the Kenyan, Caribbean, Brazilian, and Indian studles are presented and compared. Chapter 3 sets the scene, presentIng Information concerning the environments In which the studles were performed and giving brief details of the organisation of the studies and of the ways In which data were collected. In Chapters 4-7, the results concerning vehicle speeds, fuel and lubricant costs, tire costs and maintenance costs are examined. In the main text of these chapters the results are recorded in a common notation and they are accompanied by extensive tables and graphs. Appendices give cost equations In the forms reported by the studies with summary statistics and ranges for explanatory variables and they contain commentary regarding statistical properties of the estimates and details of modifications Introduced In order to achieve the common reporting style of the main text. Tables and figures for which sources are not provided were assembled by the authors using the studies reports and the results of their own analyses of the studies' data.

43 I I I CHAPTER 3 The User Cost Studies

This chapter provides essential background informatlon concerning the four user cost studies conducted between 1971 and 1982 In Indla, Brazil, the Caribbean and Kenya. The next section gives details of the environments in which the studies were performed, knowledge of which is essential If the results of the studies are to be Interpreted and applied correctly. Of particular Importance are the structure of the transport Industry, the types of vehicles In operation at the times of the studies and the economic conditions facing transport firms. The World Tables (World Bank 1985) and the United Nations Statistical Yearbook (1982) have been used as the main source of the national data reported In Sectlon 3.1. Unless otherwise stated prices are recorded In local currency. Where US dollar prices are given they are obtained by applying offIcial exchange rates for the reported year.

The last two sections of this chapter describe the organisation of the four studies and the methods used to collect data. Section 3.2 deals with the four studies In turn and in Section 3.3, first cost data, and then the collection of data on highway characteristics are described.

3.1 THE BACKGROUND TO THE STUDIES

The four studies covered an enormous range of physical and economic conditions, matched by considerable variations In highway conditions and vehicle fleet design and composition. In this section some of the Important features of the environments In which the studies were performed are described. It Is Important to understand the conditions prevailing when the studies were performed If the results presented In the succeeding chapters In Part II are not to be misinterpreted.

Tables 3.1 and 3.2 provide data concerning the four study regions. The climatic Information In Table 3.1 shows considerable variations within and across countries and In some cases across seasons. The conditlons found In India were particularly variable, ranging from the relatively cool province of Kashmir with Its moderate rainfall to the oppressively hot and humid West Coast areas In which, for example, Bombay Is located, experiencing Intense monsoon rains. Much of the Brazilian study was performed In the Brazilian plateau region In the states of Golas, Minas Gerais, Mato Grosso, Mato Grosso do Sul and Sao Paulo. In much of this area the winter months are dry but even In the south frosts are rare and temperatures vary little over the year.

Much of the Kenyan research was carried out In the Kenyan highlands which experience only moderate rainfall, peaking In the period from March to May (see the data for Nairobi and Kisumu in Table 3.1). This

45 TablIe3. 1: Average DaIlIy Temperatures CT : C, Max and M I ) and Average monthlIyRa Inf al CR : MU)

KENYA _____ BRAZIL BARBADOS ST. LUCIA INDIA

Kisumu Mombasa Nairobi Goiis ParanA1 Rio de Bridgetown Soufri bre Hyderabad Srinagar Delhi Bomibay M Janeiro 0 N T T R T T R T T R T T R T T R T T R T T R T T R T T R T T R T T R T T R T H max mini max mini max min max mini max mini max mini max mini max mini max min max mini max mini max mini

iJ29 18 48 31 24 25 25 12 38 30 17 317 32 14 287 29 23 125 28 21 66 28 21 135 29 16 8 5 -2 74 21 7 23 28 19 3

F 29 19 8 31 24 18 26 13 64 32 17 251 32 15 236 29 23 122 28 2:28 28 21 91 32 18 10 7 -1 71 24 9 18 28 19 3

'M 28 1.9140 31 25 64 25 14 125 32 17 259 32 15 239 28 22 130 29 21 33 29 21 97 36 21 13 14 3 91 31 14 13 30 22 3

*A28 18 191 30 24 196 24 14 211 33 17 117 32 14 102 27 21 107 30 22 36 31 22 86 38 24 31 19 7 94 36 20 8 32 24 0

*M27 18 155 28 23 320 22 13 158 33 16 10 33 12 13 25 19 79 31 23 58 31 23 150 40 27 28 24 11 61 41 26 13 33 27 18

iJ27 17 84 28 23 119 21 12 46 32 13 8 33 9 0 24 18 53 31 23 42 31 23 218 35 24 112 29 14 36 39 28 74 32 26 485

J 27 17 58 27 22 89 21 11 15 32 13 0 33 9 3 24 17 41 30 23 147 31 23 236 31 23 152 31 18 58 36 27 180 29 25617

A 27 17 76 27 22 64 21 11 23 34 15 8 34 10 5 24 18 43 31 23 147 31 23 249 31 23 135 3118S61 34 26 173 29 24340

S 28 17 64 28 22 64 24 11 31 34 18 58 35 13 28 24 18 66 31 23 170 31 23 252 31 22 165 28 12 38 34 24 117 29 24 264

0 29 18 56 29 23 86 24 13 53 34 17 135 34 14 127 25 19 79 30 23 178 31 22 236 31 21 64 22 5 31 3418a10 32 24 64

N 29 18 86 29 24 97 23 13 109 32 17 239 33 14 231 26 20 104 29 23 206 29 22 231 29 17 28 16 -1 10 29 11 3 32 23 13

D 29 18 102 30 24 61 23 13 86 31 17 241 32 14 310 28 22 137 28 22 97 28 21 198 28 15 8 9 -2 33 33 8 10 31 21 3

Source: The World Weather Guide (PearceA Smith 1984). USER COST STUDIES 47

Is the most densely populated part of Kenya and it contains the most productive agricultural land. Temperatures vary little through the year and are only moderate because of the altitude of this region (Kisumu Is 1,148m above sea level, Nairobi, 1,820m).

The Islands studied In the Caribbean research have climates typical of the Caribbean region with high rainfall during the hurricane season from July to November and with little seasonal variation in temperature. Barbados is less hilly than Dominica, St. Lucia, and St. Vincent and receives less rainfall.

Table 3.2 provides additional physical and some economic data. Brazil Is by far the largest of the countries studied with a surface area more than twice that of India. Brazil's terrain, like much of India's Is flat or rolling with few mountainous areas. Although Brazil's population was relatively small (116 million) leading to the lowest populatlon density of any of the regions studied, more than 60 percent of the population lived In urban areas, and demand for Inter urban transport services was high. Brazil, with Industrial output constituting around a quarter of GDP at factor cost, had been experiencing a high growth rate and was untypical of developing countries In the 1970's. However the rural economy was Important, and in the mid-1970s agricultural products generated 60 percent of export earnings. India's population was 632 millon In 1977, only 21 percent of whom lived In urban areas. In spite of its growing Industrial sector, at the time of the user cost research the country had a predominantly agrarian and rural based economy with agricultural production accounting for almost 60 percent of GDP.

Kenya, the largest East African country, has a surface area less than a fifth of India's and when the study began In 1971 had around 12 million Inhabitants, 11 percent of whom lived In urban areas. The rapid urbanisation evident In the late 1970s and early 1980s had not yet got underway. Agriculture accounted for over 70 percent of export earning and 30 percent of GDP at factor cost, while manufacturing made up 12 percent of GDP. It Is Important to note that the Kenyan study was carried out before the large oil price rise of the mid-1970s, hence the distinctive import composition and small rate of change of retail prices shown In Table 3.2.

Kenya was making large investments In the transport and communications sector at the time the study was conducted. Improvement in both surface quality and geometric design standards of the national highway system accounted for most of the highway funding, reducing Journey times and vehicle wear (for trucks the Journey from Nalrobi to Mombasa was reduced from over one day to just a few hours), and such Investments probably made a significant contribution to the 6 percent growth In GDP achleved during 1965-71. Kenya's 2,600 kilometers of railway provided a frelght rather than passenger service and was used largely for moving agricultural products and for cargo shipments from neighbouring countries.

The Caribbean study focussed on four countries, Barbados and the Wlndward Islands of St. Vincent, St. Lucla and Dominica. These islands are extremely small, their combined surface area Is less than 1 percent of that of Kenya, and their Inhabitants are concentrated in valleys giving high 48 USER COST STUDIES

Table 3.2: Selected Data for Kenya, Barbados, Brazil and India1

Indicr wid Unis Ke rbado Brazi Indx"

Poputbn, 103 innhatnts 12122 247 116100 631726

Popuation, % urban 11 367 64 22

Popubfton Osty, inhabitants per eq.khm 20 577 14 192

GNP 2 . per capita. $ US 166 20076 1570 163

GoP 3 . $US, 106 1842 388 137121 91370

C3oP3 , by Industry, per cent. Agriculture 33 11 12 40 Manufacture 12 11 23 16 Trade/Finance 15 22 20 15 Transport/Communctions 6 8 5 6 Mining I 1 Construction 7 8 6 6

-mport ComposIton, per cent Fuel and Lubrkants 12 13 34 26 Food 6 23 7 16 Machinery/Equipment 34 19 26 19 Othr Manufactures 34 42 26 24

Eport Composition, per cent Food, beverages So 39 62 32 Miwala, metals 16 13 10 9 Machinery/Equipment 2 12 12 6 Other Manufactures 16 26 26 50

Currency Vaiue 4 7.142 2.006 14.144 8.563

etail Price Index, Annual Rat* of Change, per cent 5 2.1 16.9 25.9 9.0

140TES :

1. Md-isurvey date, 1972 or Kenya, 1977 for other studies. 2. Current market prices, xcpt Brzil : current factor cost. 3. Current factor cost. 4. Kenyan shillings, Babadan dollars, Brazilian cruzeiros and Indian rupee per US dollar at mid-survey date. S. 1960/1970 for Kenya. 1970/1977 for other studies. 6. Dominlca : $US 444, St. Lucia : $ US 469, St. Vincent and the Grenadines: $US 283 7. Dominica, St. Lucia, St. Vincent and the Gronadines, 100% rural

Source: World Tables, U.N. Statistical Yearbook and World Bank internal sources. USER COST STUDIES 49 population density. Most of the data In Table 3.2 relate to Barbados, by far the richest of Islands studied. Agriculture and manufactured goods were equally Important contributors to GDP and to exports. The other Caribbean Islands were less prosperous, their GDP per capita being around a quarter of that of Barbados or less, and they were highly dependent on their fruit exports to generate foreign earnings. The Caribbean Islands had small road systems and no railways. For example, Barbados had 1,640 kilometers of roads while Dominica had just 752 kilometers. Roads were narrow, generally as a result of hilly terrain, and mostly paved.

Transport Infrastructure in Brazil and Indla was different In all respects from that of the Caribbean islands, principally because of the need to link diverse population centers spread over enormous distances and to support rapidly growing industrial and export earning sectors. Table 3.3 gives a breakdown of non-urban highway categories for these countries. Data are not available in this form for the other studies. It is notable that only 6 percent of the total Brazilian network was paved In 1977 and even within the small federal system this figure was only 40 percent. Much of this largely unpaved system, which was crucial to the economic prosperity of the country, was constructed to high geometric design standards and Investment strategies focussed on changing grading frequencies or timing the paving of road surfaces. In 1977 In Brazil road transport accounted for 90 percent of passenger kilometers and 70 percent of freight tonne kilometers. The railway network was around 30,000 kilometers long, Including urban corridors In the metropolitan cities, but Its contribution to transport movements was limited to export commodities like soya, and minerals, and to urban commuting trips. Road transport remained the main mode of transport In Brazil and this Is reflected In the size of the national vehicle fleet.

India, on the other hand, relied significantly on its railway system for both passenger and freight movements (particularly between states) and was the only one of the four countries studies to possess a large and protected rail system. Road Infrastructure had received limited Investment with emphasis on making road surfaces all-weather, rather than on Improving geometric design standards. However, most federal and state highways In India were paved (see Table 3.3) though many to very low standards. By International standards Indlan highways were extremely narrow, with many vehicles being forced to leave the pavement when overtaking or meeting other traffic.

The degree of regulation within the road haulage sector varied considerably across the countries where the studies were conducted. The Caribbean islands had free entry to most services (the exception being Barbados where passenger services were franchised) and a commercial vehicle license was Issued on production of driver license, Insurance and vehicle construction and use documents. In Kenya, road transport was highly regulated at the time of the study, In a manner similar to that practiced In the United Klngdom prior to the mid-1960s. In Brazil, entry to the freight sector was unrestricted and there were a large number of owner- drivers, particularly In the medium to heavy truck categories. Passenger transport was highly regulated and each state was responsible for fixing schedules and fares on routes within Its boundaries. Comparisons made 50 USER COST STUDIES

Table 3.3: Non-Urban Brazillan and Indian Highway Categories In 1978

India Brazil

Clss Length Per cent Paved Length Per cent Paved 103 km 103 kM

NationalHighways 29.3 99 84.8 54

State Highways 94.1 94 113.2 26

Municipal or DistrictRoads 701,0 15 1116.4 1

Villge Roads (India only) 675.5 11 - _

TOTAL 1499.9 37 1314.4 6

Sources: Brazil, Annuarlo Estatistico, GEIPOT (1982); India, CRRI (1982).

between actual fares and estimates of total vehicle operating costs (GEIPOT 1981) suggested that bus operations were very profitable, especially on unpaved routes. In India, there was a very restrictive licensing system covering both passenger and freight services whose prime obJective was to protect the rail network. In an effort to ratlonalIse this system, a Transport Development Council was appointed In the mld-1970s, but progress In removing restrictions was slow and for the duration of the Indian user cost study the road transport sector was strictly regulated.

In India public ownership of buses and trucks was more extensive than In the other three countries studied. Road passenger operatlons were evenly divided between public and private enterprises although some states had wholly nationallsed services. Forty-eight state enterprises owned 52 percent of the total registered bus fleet In 1977 while truck operations were dominated by owner-drivers who accounted for 90 percent of trucks registered In 1977. There were few large trucking companies, In part due to regulation and licensing.

In all the countries studied vehicle speeds and loads were regulated. Table 3.3a shows speed llmits and axle load limits and weight restrictions are given In Table 3.3b. In Brazil, the speed limit of 80 km/h was Imposed (and strictly enforced) just after the start of the study which necessitated restarting the collection of vehicle speed data. USER COST STUDIES 51

Table 3.3a: Maximum Permitted Speeds (km/h)

Country Cars r Buses and Trucks |

Kenya 100 65 Brazil 80 80 India no limit 60 St. Lucia 50 50 Barbados 56(1) 56(1)

Notes : (1) 80 km/h on the East Coast highway.

Source: World Bank Internalsources.

Table 3.3b: Axle Load and Vehicle Weight Restrictlonsat 1981

Axle Loads Maximum Gross Weight (tonne/axle) (tonne) Country Axle Configuration(') Single Tandem axle axle 2 3 3S2

Kenya 8 9.8- 14.5 10.5 15.4 26.2 Brazil 10 17 15 22 45

India 12.5 - 20 - -

Barbados n.r. n.r. 11.2 _ _

St. Lucia n.r. n.r. 8.3 _ _

Notes : (1) 2 : 2 axle rigid 3 : 3 axle rigid 3S2 : Tractor : 3 axle, Semitrailer : 2 axle. n.r. not regulated - not available or not applicable Source: Limits of Motor Vehicle Sizes and Weights, InternationalRoad Federation (1981). 52 USER COST STUDIES

Axle loads were not restricted In St. Lucia or Barbados but vehicle weights were very strictly limited. Elsewhere axle load restrictions were Imposed but enforcement was rather variable. In Brazil enforcement was strict and there were qulte frequent weigh stations on Interstate highways, but In India overloading was common.

Compositions of registered national fleets when the research studies were performed are given in Table 3.4. Kenya and Brazil alone had a full range of vehicle types, from passenger cars, to super heavy trucks whose gross vehicle weight exceeded 30 tonnes. The Kenyan data relate to the early 1970s and the number of passenger cars doubled by 1977 while in Brazil car ownership grew by 12 percent per year from 1977 to 1982. The Kenyan natlonal fleet contained many light goods vehicles, reflecting the Importance of Jeeps and other dual-purpose vehicles In the Kenyan economy at that time. The Caribbean data relate to all the Islands - the relatively large numbers of cars is note worthy. The buses recorded for the Carlbbean Include a significant proportion of minl-buses, large buses being confined mainly to urban use. Many truck owners In the Caribbean fitted rudimentary seating and provided passenger services when business was slack, or between harvests. The Indian data reveal limited passenger car ownership and large numbers of two and three wheeled vehicles, substitutes for the passenger car which was expensive to purchase. The range of motorized vehicles was extremely limited In India and there were many non-motorized vehicles, resulting in much traffic interaction.

Table 3.4: Compositlon of Registered Vehicle Fleets at Time of the Studies (Thousands of Vehicles)

1 Vehi CleGln KWs Caribbean Brazil India 1970 1977 1977 197

Car*2 63.7 (42) 32.8 (80) 5789.8 (74) 675.9 (21)

Taxis N.A. N.A. 156.4 (2) 76.8 (2)

Light Goods Vehice 40.8 (27) 4.1 (10) 735.6 (10) 105.0 (3)

Trucks 20.4 (14) 2.9 (7) 8l2.5 (10) 375.3 (11)

Bus 3.0 (2) 1.1 (3) 102.7 (1) 119.5 (4)

Two and Three Wheles 9.9 (7) N.A. 202.3 (3) 1550.3 (47)

Others 12.5 (8) N.A. N.A. 400.3 (12)

TOTALS 150.3 (100) 40.9 (100) 7768.9 (100) 3303.1 (100)

NOTES

1. Cribbean dats are the combined figures from Barbodos. St. Vincont. St. Lucia and Dominica.

2. Kenyan and Carbbean figures include Taxis.

Source: World Bank internal sources. USER COST STUDIES 53

The vehicle designs available In the four countries differed substantially. The Kenyan vehicles were Imported, in "knockdown" kits, and assembled locally, while Caribbean vehicles were Imported as assembled units. India and Brazil had extensive local vehicle manufacturing Industries and vehicle Importation was prohibited.

The vehicles observed in Kenya at the time of the study were purchased when fuel was relatively cheap and designed using the technology of the 1960s. Generally they were not fuel efficient, but relatively heavily bulit and robust. The Ford Cortina (no longer manufactured) with a 1.6-liter, 4-cylinder engine was typical of the cars available, while the Volkswagen Kombi with a 1.5-liter, 4-cylinder alr-cooled rear engine and the all-wheel drive Land Rover with a 2.3-liter, 4-cylinder engine were typical of vehicles In the light goods or utility class. Bus chassis were Imported, chiefly from Europe, and fitted with locally made bodles. The Alblon (manufacturer now defunct) CD 23, 6-cylinder, 6.3-liter diesel engined model was typical of this category. Multi-axled articulated 'vehicles were rarely seen at the time of the study and the largest vehicles were two or three axied trucks pulling two or three axled drawbar trailers, with up to 40 tonnes gross vehicle weight. Turbo-charged diesel engines were uncommon and the super heavy trucks, for example the Flat (now part of Iveco) 682, were powered by a normally aspirated engine of around 11.5 liters displacement, producing around 200 horsepower SAE. Compared to vehicle types now seen in developing countries, we would expect the vehicles In the Kenyan study to be long lived, simple to maintain and rebuild, with a relatively modest level of performance.

The vehicles In the Caribbean study were confined to two broad types, passenger cars and two axle trucks from 3 to 10 tonnes gross vehicle weight. These were of more modern design than those found In the Kenyan study although the smallness of the Islands rarely permitted advantages to appear. Some care should be taken In applying Caribbean operating cost data In new environments because of the special conditions prevailing on the small Islands. Annual utilisation and lifetime kilometerage were low and proximity to the sea exposed vehicles to corrosion. Spare parts were Imported and not easy to obtain.

Details of Brazil's and India's vehicle production In 1977 are given In Tab3e 3.5a. In India, four manufacturers dominated both the passenger car and bus and truck markets producing only a small selection of model types. The Ambassador and Premier Padmini were the only cars available. Though based on out-moded European designs they were very sturdy and apparently well suited to Indian conditions. The truck and bus markets were led by Tata, a company producing vehicles originally based on Mercedes-Benz designs and technologies, whose most popular model was similar to the Brazilian 1111/1113 types. Ashok Leyland held around 20 percent of the market, producing vehicles that had a reputation for rugged design and long life. Almost all trucks were two axle models and the typical truck observed during the research period was a two-axle, 12-tonne gross vehicle weight, forward control model powered by a 125 horsepower (SAE) engine. Indian buses had a construction similar to that of the trucks and there were no monocoque or platform rear engined buses operating In the late 1970s. Bus bodies were locally bullt to a variety of simple designs on "stretched" truck chassis supplied by the main natlonal 54 USER COST STUDIES manufacturers. In the late 1970s in India there was excess demand for trucks and manufacturers showed little Inclination to develop new models. It was only in the early 1980s that some three axled and articulated vehicles and turbo-charged diesel engines became available. At the time of the study Indian vehicles, like Kenyan vehicles, were robust, of simple construction, and designed to carry significant overloads on poorly surfaced roads at low speeds.

Table 3.5a: Brazilian and Indian Vehicle Production In 1977

Numbers of Vehicles

Fuel Vehicle Class Brazil india

G"oline Cars 769700 37900 (60) (54)

Light Goods Vehicles 3220 N.A.

Disel Light Goods Vehicles 27W 9600

Buses 3800 N.A. (90)

Trucl:

Light 16600 {41700 (56) Medium/Large 7070 (43)

H"vy 6900 N.C.

Total Trucks 96200 41700

Annual Total 9166082

NOTIES:

1. Figures in parenthesesindicate the perocntage market share of the leading manutacturer.

2. N. A. indicatesdate not available;N.C. indicatesnot constructed.

3. Indian Manufacturen produced 245200 two-whoieed and 19300 three-wheld vehicls during this period. In Brazil, les then 2500 such vehicles were made.

Sources: Brazil, Annuarlo Estatistico, GEIPOT (1982); India, CRRI (1982). USERCOST STUDIES 55

Brazil, with a total annual productionof around one millon units (see Table 3.5a), was one of the top ten centers for vehicle manufacture In the world. The largesttruck and bus manufacturerwas Mercedes-Benzwhose truck range Includedover 30 basic models and who took over 40 percent of the popular medium to large truck class. FNM was a Brazilian company building heavy truck chassis to 1960s Flat designs. The Scania trucks were more technicallyadvanced and turbo-charged and intercooledengines were available for line haul work. However, these models were not as efficient as their European counterpartsand this has impilcationsfor the prediction of fuel consumption for this vehicle class. The lightertruck market, containing trucks of the size of those typical In India, was very competitive and was shared between Ford, Mercedes-Benz,and Chevrolet. A feature of Brazilian truck design in the 1970s was the developmentof engine efficlency and chassis/suspensiondesigns so that payloads could be Improvedwlthout exceeding gross vehicle weight and axle load limits. By 1980, there was a range of engines from 95 to 370 horsepower (SAE) which could run on a variety of gasoline, gasohol, and diesel fuels. Consequently,vehicle owners were able to match truck specificationsto the type of service they wished to provide. Throughout the study period, the most widely used inter-urbantruck in Brazil was a three axle rigid vehicle with a non-driven trailing axle, grossing between 18 to 22 tonnes and powered by a 147 horsepower (SAE) engine.

The bus market In Brazil was dominated by Mercedes-Benzwho offered 11 basic models ranging from integral (monocoque)and platform, rear engined vehicles, for paved road operatlons, to traditionalfront engined, ladder-typechassis versions for use on unpaved routes. There were a number of companies building bus bodies, ranging from robust designs for unpaved roads to designs with air suspension and air conditioningfor long distance inter-city paved operations. All buses crossing state boundaries or travelling routes longer than 300 kilometers within a state had to be fitted wlth a tachograph and rules governing speed limits and driving hours were strictly enforced.

Car designs changed substantially during the course of the Brazilian study. When the study began, In 1975, designs reflected 1960s European and American designs. The most popular car, the Volkswagen 1300, was even more elderly as its basic design went back to 1937. The Increase in oil prices in the 1970s, together with the developmentof "world car designs" by the multinational manufacturers produced dramatic changes in Brazilian car designs and by the end of the study they were little different from those found elsewhere in the world. By 1982 complete passenger cars were being exported to the Middle East and North Africa, trucks to North America, and engine and transmission units were being shipped to European manufacturingcenters. Details of vehicle exports and imports are given In Table 3.5b. Apart from Brazil, only India exported significant numbers of vehicles and neither country Importedvehicles to any extent. In Kenya and the Caribbean all vehicles were Imported.

Typical prices of inputs to transportatlon at the times when the four studles were performedare shown In Table 3.6 in U.S. dollars. A more extensive table of prices In local currencies together with exchange rates 56 USER COST STUDIES

Table 3.5b: Numbers of Vehicles Imported and Exported

Cars Buses, Coaches, Goods Vehicles

Imports Exports Imports Exports

Kenya 1973 5400 _ 3300 _ 1974 9400 _ 5800 _ 1975 5000 - 5500 _

Brazil 1976 - 67000 - 9000 1977 5600 59000 1039 11000 1978 - 96000(1) - see cars 1979 - 87000 - 18000 1980 - 136000 75 21000

India 1977 - 370 _ 2850 1978 - 670 _ 5800 1979 - 630 _ 5900 1980 - 2200 _ 9950

Barbados 1978 1230 - 700 _

Dominica 1980 350 - 440 _

St. Lucia 1976 570(l) - see cars _ 1977 870(1) - see cars _ 1 1978 1060( ) - see cars _ 1979 970(1) - see cars _

St. Vincent 1977 250(1) - see cars _ 1978 380(1) - see cars _ 1979 380(1) - see cars

Notes : (1) all vehicles combined - zero or negligible

Sources: Kenya, Brazil, India: World Bank Statistics (1977-1985); Caribbean: World Bank/IMF internal sources. USER COST STUDIES 57

Table 3.6: Typical Prices of Inputs to Transportation. Gross of Tax, at Study Dates

Kenya Buaced. Br 21 Ind.

1S72 1978.r 197S Isis1S718

Gasoline. $ UStlibte .15 .15 .35 .40

Oesel. $USs/br . .13 .11 .18 20

Engine Oil, $ US/ltre .63 .55 .85 .1

Laborl. $US/hour 3.50 6.50 1.42 0.26i

2 Tir Cost , $ US:

Cas 22 40 36 NA. Light Good. Vehicle 13? N.A. 161 NA, truck 13S 238 225 217 Bus 115 N .A. 213 N.A.

3 Ne. Vehicle Prks . $US:

CW 2S1 3964 3488 71536 Light Goods Vehicle 49101 4525 41Q 1744 Two-axe Trk 7843 115 15150 2151h Sm 16317 N.A. 34710 21012

NO res:

1. Data to, Knyo and Barbeds r rates charged by garages whil thos for Brazil and India are bad o company workhop nitorn,tioo.

2 Conei,tiona1 tirs, bi ply costrusct".

3. R*tail dots.

4. N. A. : ot ,nlable.

Source: Study reports and personal communication with studies' staff. can be found In Chapter 9 In Part lii. The relatively low price of labour relative to other prices in Brazil and especially Indla, and the high relatlve price of fuel In India are noteworthy.

3.2 RESEARCH ORGANISATION

3.2.1 The Kenyan Study, 1971-75

The Transport and Road Research Laboratory's study team were based In Nairobi and consisted of six U.K. staff and 30 local employees.

The fuel study used three Instrumented vehicles, a car, a light goods vehicle and a medium truck. Details of the vehicles are given in Section 3.3. The test vehicles ran over 95 experimental sections (42 paved, 49 gravel, and 4 earth) representing typical combinatlons of Kenyan environmental and highway conditions. Speed data were collected from passing traffic at the same sites. The effect on fuel consumption of speed cycle changes during normal driving was determined by running the vehicles over two long (8.4km unpaved, 15.4km paved) sections. An adjustment was reported to convert fuel cohsumptlon predicted at constant speeds to values appropriate to normal operating conditions.

The user survey collected data from vehicle operators between 1971 and 1973. The sample Included some small firms but most data came from medium and large companies, some engaged In own account transportation. 58 USER COST STUDIES

The survey data analyzed relate to the calendar year 1972 and the adoption of a 12-month reporting period was a characteristic of this and subsequent TRRL vehicle operating cost surveys. The reported survey data were obtained from 43 cars, 47 light goods vehicles, 78 medium/heavy trucks (5 to 26 tonnes payload) and 121 large buses (more than 30 seats). These observations were combined, where this was considered appropriate, to form averages, 6 for cars, 7 for light goods vehicles, 21 for trucks and 19 for buses. The route network used by these vehicles was around 9,300 kilometers in length.

Detalls of the highway conditions experienced by the Kenyan survey vehicles are given in Table 3.7. Roughness was measured using a car mounted bump integrater calibrated by a towed 5th wheel as described in Section 3.3. For user survey routes geometry was taken from maps with additional information coming from instrumented vehicles. No vehicles were observed operating for substantial periods of the survey over very rough routes and the largest roughness value recorded for a survey vehicle was 7,000mm/km (9.0 I.R.I.). Similarly, only limited ranges were observed for highway geometry and as we will see later In Part II, It Is difficult to detect the effect of highway geometry on costs recorded In the user survey.

The experimental fuel and roadside speed studies covered wider ranges of roughness and geometry (the latter measured with surveying instruments), but no test sections had curvature exceeding 2000 /km or gradient exceeding 8.6 percent.

TRRL staff returned to the United Kingdom In 1974 and the final analyses and report writing were done at their headquarters In Crowthorne. The results of the vehicle operating cost investigations were reported by Hide et al. (1975) and the relatlonships were Incorporated Into a Road Transport and Investment Model, RTIM (Robinson 1975) and the World Bank's Highway Design and Maintenance Model, HDM Ill.

3.2.2 The Brazilian Study. 1975-82

The Brazilian study team were based In Brasilla and consisted of over 150 personnel Including 11 International staff and thelr Brazilian counterparts. The Brazilian study was wider In scope and more expensive to conduct than the other studies dealt wlth In this volume. An overview can be found In Butler et al. (1979). Considerable resources were expended on developing pavement deterioration models, and extensive fuel consumption experiments and programs of roadside speed observation were conducted. As in the other studies maintenance, tire cost and other data were obtained from a survey of road users. The intention was to establish vehicle operating costs for the main vehicle types found on low-volume, non-urban roads In Brazil.

A fleet of 10 specially purchased vehicles was used to conduct fuel consumption experIments, examining constant speed fuel consumption, the effects of acceleration and deceleration and the influence of horizontal and sag curves. Details of the experiment fleet are given In Section 3.3 where the vehicles used in all the studies' experiments are compared. USER COST STUDIES 59

Table 3.7: Highway CharacteristicsIn the Kenyan Study1

| -Roughness Rise & Fall Rise Fall Curvature EN IRI (mlkm) (mJkm) (m/km) ( 0 /km) (mm/kin) (imkmi)

All Experiment:

Mean 3985 5.1 _ 14 14 46 Min 1429 2.1 _0 0 0 max 20600 22.1 _ 86 86 198

Car Survey:

Mean 1 3740 4.8 n.a. _ _ n.s. Min 2440 3.3 n.a. _ _ n.a. Max | 6400 7.8 n.a. _ _ n.a.

Bus Survey:

Mean J 3228 4.3 33 - - 11 hWn | 2440 3.3 17 _ - 2 max 5000 6.3 69 _ - 50

TrickSurvey:

mean 2954 3.9 17 - - 32 Min 2550 3.4 15 - - 8 Max 7500 9.0 66 - - 45

1. Average values for survey vehicles, weighted by number of vehicles. 2. n.a. = notavailable.

Source: Hide et al. (1975). 60 USER COST STUDIES

Vehicle speeds were measured using hidden radar equlpment. DurIng the course of the study the government Imposed and strictly enforced a nationwide 80 kilometer per hour speed limit. The speed models reported In Chapter 4 use data obtained subsequent to this regulatory change. Relationships between vehicle speeds and highway and vehicle characteristics were Investigated in eleven substudles In the speed observation program. Data on free speeds and speeds under deceleration were obtained by observing vehicles In the normal vehicle population traversing the test sections. Data concerning speeds under acceleration were obtained using vehicles In the fuel experiment test fleet. More than 100,000 free speeds were obtained at 176 test sites.

Most of the user survey data were collected between 1976 and 1979 and the majority of the analysis was performed between 1979 to 1981 during which period many technical reports were published. A basic file of over 2,500 vehicle cost histories was reduced to 1,675 vehicle records sultable for analysis, collected from 147 companies, 75 of which were owner-drivers. It was not possible to collect data on all operating cost components for all vehicles so each vehicle's record contains a variety of Information and there Is considerable across vehicle variation In the number of months of data available. Data relating to only short periods of operation were not entered In analysis files and In consequence sample sizes for analysis vary by cost component. Tire data were difficult to collect. The other studies gathered tire data using a vehicle as the basic unit of observatlon but this was not the practice adopted In the Brazil study In which data were recorded on an Individual tire basis. The basic tire file contalned Information on 20,800 tire changes, around 6,800 tire lives. For analysis, vehicles were grouped Into five classes: cars, light goods vehicles, medium and heavy trucks, and buses.

Highway characteristics were measured using a car mounted response-type roughness device, the Maysmeter, calibrated by the GMR Profilometer. Experimental sections were surveyed to determine highway geometry while an Instrumented vehicle travelled user survey vehicles' routes measuring both roughness and geometry. Table 3.8 provides some Information concerning ranges and averages of highway conditions encountered In the Brazilian road user survey. The wide ranges of roughness observed for buses and trucks are notable but the ranges of highway geometry are disappointingly narrow. These figures reflect the rolling terrain of much of Brazil, particularly the ancient central highlands where much of the data were obtained. Technical reports were Issued at the end of the first phase (TRDF 1980) and the second phase (GEIPOT 1981). The World Bank sponsored research Into the modelling of vehicle speed, fuel consumption, and tire wear, which was begun In Brasilia In 1981 and was eventually completed In Washington D.C. during 1985.

3.2.3 The Caribbean Study, 1977-82

The Caribbean study, conducted by the Transport and Road Research Laboratory, Investigated road user costs In Barbados and In the Windward Islands of St. Vincent, St. Lucia, and Dominica. The Islands were chosen In part because of their wide variation In geometry, Barbados having USER COST STUDIES 81

Table 3.8: Highway Characteristics In the Brazil Survey for a Selection of Cost Components

VehlcbaCompont R _oubnea Rbie + Fall Cvatwe 1 Rl tmJI ,) (on") (mnulkm) (rn/i)

Cara/Partsmm Lab.

Man 3648 4.7 23 46 MAn 22W 3.0 12 11 Max I1 9.2 38 202

lSuaa/Parta and Lor

Man 4786 6.0 24 41 Mn 1265 1.8 10 6 x f I lf 13.3 3S 148

Madium Truaba/Pata an Labor

Men 3178 4.2 34 75 Min 160 1.9 25 7 man 78 8.6 48 294

Suau and Trucks/Tirea

Man 4801 5.8 29 66 Min 1t6 1.9 10 S max 12 14.9 48 234

Source: GEIPOT (1981).

generally flat to rolling terrain with only a small hilly area, the other Islands being more mountainous.

All the fuel experiment and roadside speed data were gathered In St. Lucia. A test fieet of three Instrumented vehicles, described In Section 3.3, was used to measure fuel consumptlon. It was not possible to select a series of test sections of equal length that were homogeneous In terms of geometry, due to the sinuous nature of St. Lucia's road network. Therefore, six routes were surveyed and their vertical profiles plotted so that sections of road with uniform gradients but of varying length could be selected. This enabled an experimental design to be constructed covering the full range of combinations of vertical and horizontal geometry sought by the study. The test sections had gradients ranging from zero to 14 percent, average degrees of curvature from zero to 1,600 degrees per kilometer, widths of from 4.3 to 8.5 meters and surface roughness ranging from 1,400 to 14,800 mm per kilometer. Free speeds were obtained for three classes of vehicles: cars, light goods vehicles, and trucks, by observing traffic In normal conditions running over 28 test sites. Trucks were weighed some distance after their speeds were recorded. Averages by vehicle class of space mean speeds were obtained for cars and light goods vehicles at each test site while individual vehicle speeds were retalned for trucks because gross vehicle weight was to be related to truck speed In analysis. 62 USER COST STUDIES

The road user survey, based In Barbados, collected data on all four Islands. Collection of cost data was difficult as many vehicle owners had no cost recording system and ad hoc arrangements were made to obtain invoices and to question drivers and owners about Items of consumptlon. User cost data were collected for four classes of vehicle: cars, light goods vehicles (under 3 tonnes gross vehicle weight), trucks (greater than 3 tonnes gross vehicle weight), and buses (greater than 40 seats). Results were reported only for two vehicle classes - cars and light goods vehicles combined, and trucks - there being insufficient data relating to bus costs. The first group consisted of 40 vehicles, data on nine of which were averaged to give 32 observations. These vehicles were typically gasoline engined with a displacement of between 1.6 and 2 liters. Data were obtained for 96 trucks. Some of the truck data obtained on Barbados and St. Vincent were averaged and 28 observations were used in the statistical analyses. Typical of these trucks is a two-axled vehicle with a gross vehicle weight of ten tonnes (six tonne pay load) powered by a six cylinder, 100 BHP (SAE), diesel engine. Vehicle utilisation was very low, with trucks in the survey recording an annual average of 13,000 kilometers and cars and light goods around 16,000 kilometers. The methods used to measure highway conditions were similar to those employed In Kenya. As the team had hoped wide variation in highway geometry was found, with average gradients over the survey period as high as 8.2 percent and average curvature as high as 1,0800 /km being recorded. All user survey routes were paved. Table 3.9 provides more detail.

As in the Kenyan study, the data analyzed relate to vehicle operations over a 12-month period and this corresponds to the calendar year 1978. Final analyses and report writing were completed in the United Kingdom. The results were published in two reports in 1982 - Hide (1982) and Morosluk and Abaynayaka (1972).

3.2.4 The Indian Study, 1977-82

The Indian study was based at the Central Road Research Institute headquarters In New Delhi and employed over 120 staff. The Indian study was broad ranging, examining time valuation and accident rates and costs, as well as the Items treated in the other studies. As In the other studies fuel consumption was measured In a series of experiments, vehicle speeds In a program of roadside speed observation, and maintenance, tire and other costs In a road user survey.

In the fuel consumption study the Indian team used two cars, a diesel engined jeep and a medium and a heavy truck. As in the Kenyan and Caribbean studies the Intention was to predict bus fuel consumption by applying suitable adjustments to medium trucks' fuel relationships. The vehicles are described in Section 3.3. Fuel experiments were also performed using two and three wheeled vehicles but the results are not reported In this volume. Roadside speed data were collected at 76 sites, time and space mean speeds being calculated by observers who used stopwatches, noting numberplates and using radar equipment. Over 114,000 free speeds were recorded.

Highway conditions were measured using procedures similar to those employed In Kenya and the Caribbean. Table 3.10 shows ranges of highway USER COST STUDIES 63

Table 3.9: Ranges of Average Route Highway Characterlstics In the Caribbean Road User Survey

Island Average Degrees Rise plus _Ru _ Rjhness of Curvature Fall Bi IRI (0/kJn) {m/km) (mm/ksm) (mtkm)

Barbados 90- 390 8 - 60 2600 - 5600 3.5 - 6.9

St Vincent 520 - 810 37 - 78 3200 - 8000 4.2 - 9.5

St Lucia 160 - 730 17 - 82 3300 - 7600 4.3 - 9.1

Dominirca 180 -1040 19 - S8 3800 - 9800 4.9 - 11.4

Source: Hide (1982).

conditions observed at the test sites. These were all paved, with surfaces varying from asphaltic concrete to waterbound macadam, and covered wide ranges of highway geometry.

The user survey team of 46 staff collected a full range of operating cost data for 939 vehicles - 640 buses, 232 trucks and 67 cars and jeeps. Of the trucks and buses, 62 percent were manufactured by Tata, 29 percent by Ashok Leyland. Most of the data were provided by large companies. Of the 121 companies recruited, 54 percent had fleets exceeding 50 vehicles and 78 percent had fleets exceeding 25 vehicles.

As In the other studies the survey team attempted to find vehicles covering wide ranges of highway conditions. The ranges given In Table 3.10 show that they had some success, especially In finding vehicles operating over sinuous routes and on rough routes. Unfortunately, much of the data relating to high levels of curvature Is obtained In mountainous terrain and the difficulties In disentangling gradient and curvature effects are substantial. Many Indian roads have bi-directional single lane 3.8-meter wide pavements and a major preoccupation of the road authorities was the benefits to highway widening. Thus the Indian study Is notable in providing more Information on pavement width than the other studies.

The Indian study reported In 1982 after only a short period of analysis. We are fortunate to have had access to the data and where particular difficulties arise with the relationships reported at the conclusion of the study we have attempted to provide alternative results which will serve better In applications. 64 USERCOST STUDIES

Table 3.10: HIghway Characteristics In the Indian Study

Roughnes Rise plus T Ribem Fall |Curvature Pavement Fl IRI Fall (m/km) (rnmk.) (1uk'n) Wkith (nmm/km) (m/km) (m/km) (m)

Fuel Experiments:

Mn 2130 2.9 _ 0 0 - - mmx 10o10o(1) 11.7 _ 50 _ _

RoadsideSpeed:

Mean 444 5.7 - I 1.5 11.5 274 5.4 M*n 2050 | 2.8 _0 0 1 3.5 Me 152150(2) 16.9 _ 91 91 1243 7.0

Cars, Survey:

Mean 4987 6.2 10 - - 107 6.2 min 3416 4.5 3 - - 9 4.7 ax 69a5 8.4 36 - - 690 7.0

euss, survey:

Mean 85g3 7.3 15 - - 149 5.2 KMI 2925 3.9 1 - - 5 3.7 mx 12072 13.7 50 - - 1021 7.2

Trucks, Survey:

Mean 3t31 7.3 13 - - 137 6.0 MIn 29E0 3.9 1 - - 8 3.8 max 15600 17.2 58 - - 1215 7.0

1. Value for DIes Jeep. Car, Bus and Truck Muaimum Is 8200

2. Only two tea sections exceed 7120 mm/km (8.6 minkm. IRI).

Source: CRRI (1982). USER COST STUDIES 65

3.3 DATA COLLECTION

3.3.1 User Cost Data

Information on user costs can be obtained from a variety of sources - from vehicle and component manufacturers, and from vehicle dealers and distributors. For certain cost Items whose consumption can be measured continuously, like fuel, Information can be obtained from experiments using Instrumented test vehicles. But experiments are expensive to conduct and the data that they produce do not provide Information concerning owners' and drivers' responses to highway conditions and to the business environment that they face, so that In order to use data obtained from experlments one has to attempt to model these responses. Cost items like tire and maintenance costs are particularly difficult to study using experiments because their consumption is only apparent at distinct and sometimes distantly separated points In time.

In the roadside speed studies, road sections were selected with the intentlon of obtaining good coverage of ranges and combinations of highway characteristics of Interest. Highway gradient, curvature, roughness and surface type received special attention and, In the Indian study, much attention was also devoted to road width. Trucks' load condition has an Important influence on speeds and a difficulty with roadside speed observation Is that It is costly to obtain accurate estimates of loads carried. In fact only In the Caribbean study were accurate vehicle load data obtained, gross vehicle weights being determined at weigh stations some way beyond the sites at which speed observations were made. In the Brazilian study vehicle loads were estimated visually where possible, and vehicles were recorded as empty, half loaded or full. In neither the Kenyan nor the Indian studies were data obtained on the loads of vehicles observed In speed studies. A study into the effect of gross vehicle weight on vehicle speeds was carried out In Ethiopia subsequent to the Kenyan study (Abaynayaka et al. 1977), and the results were used to introduce weight effects Into the Kenyan equations.

In all the studies fuel consumption data were obtained by observing Instrumented test vehicles driven In a controlled manner over road sections chosen to cover ranges and combinations of highway characteristics of Interest. Generally the test sections were one kilometer long with half kilometer long transition sectlons, to allow test vehicles to attain the required speeds and gear selections prior to enterlng the test sections.

Details of the vehicles used In the studies' fuel consumption experiments are given In Table 3.11. The Kenyan and Caribbean studles' vehicles were purchased In Britain and shipped to the study regions. Vehicle designs were modified steadily between 1971, when the Kenyan study vehicles were purchased, and 1977, when vehicles were obtained for the Caribbean study. Thus the 1977 version of the Ford Cortina used in the Caribbean had a redesigned, "economy" carburetter. The Kenyan and Caribbean studies' Bedford and Ford, normal controlled, or "cab-over," truck models are likely to be 66 USER COST STUDIES

Table 3.11: Experimental Test Vehicle Characteristics1

Vehicle class Study Fuel BHP(SAE)RPM Tire Number/Size GVW

'Car r Kenya t Gasoline 1 71/ 5000 I 4/ 165*13 892

Caribbean Gasoline 64/ 4750 4/ 165*13 1115

Brazil Gasoline 49/ 4600 4/ 560*15/4 ply I 1200

India Gasoline 50/ 4200 4/ 590*15/4 ply 1528

Kenya Gasoline I 85/ 4500 4/ 750*16 1705

-~ ~~~- 1 ~--- -.- I ---- Light Goods Vehicle Caribbean Gasoline 70/ 4500 4/ 185*14 2600

Brazil I Gasoline 61/ 4600 4/ 700-14/8 ply 2100

India Diesel 38/ 2300 4/ 600*16/10 ply 1200

Light Truck Kenya Diesel 107/ 2800 1 6/ 825*20 8420

Caribbean Diesel 113/ 2600 6/ 825*20 8420

Bra_zil Diesel I 103/ 3000 6t 700*16/10 ply 6100

Mtedium Trucki Brazil Diesel 149/ 2800 6/ 900*20/12 ply 15000

India Die"se 112/ 2800 6/ 900*20/14 ply I 12180

_ -__ ----- _ -I-1 ~ t------Heavy Truck2 Brazil Diesel 149/ 2800 10/ 1000*20/14 ply 18500

__India Diesel 180/1 2200 6/ 1100*20/16 ply 16260

Articulated Truck Brazil Diesel 1 289/ 2200 18/ 1100*22/14 ply 1 40000

Bus Brazil Diesel 149/ 2800 6/ 900*20/12 ply 11500

1. The large Brazilian experimental fleet also included a medium and a large passenger car, together with a gasoline engined light truck not included here. See Watanatada (1986) for details.

2. SAE Horsepower, GVW is gross vehicle weight in kilograms.

Source: Studies' reports. USER COST STUDIES 67 useful for predicting fuel consumption of normally aspirated dlesel engined trucks of around 12 tonnes gross vehicle weight, and the Caribbean Ford Transit model Is likely to be useful In predicting fuel consumption of light goods vehicles with petrol engines. However, even this popular model has been totally redesigned recently and Its fuel efficiency has Increased. Small diesel fuelled light goods vehicles are now being used In many developing countries and their fuel consumption cannot be predicted using any of the studies' experimental results. The Land Rover, used In the Kenyan study Is a 4-wheel drive vehicle with unusually high fuel consumption for a light goods vehicle. The Indian test vehicles were locally produced models and their fuel consumption data are unilkely, with the exception of the two axled trucks, to transfer well to other environments. In fact, radically new car designs are to be Introduced In the Indian market shortly so that the passenger car data obtained during the study may soon not be appropriate even in India.

The Brazilian study data would seem to offer the best prospect for predicting fuel consumption In the 1980s and beyond, because of the range of vehicles used In the experiments and their relatively modern design. However, the experimental vehicles were purchased In 1975 and therefore did not benefit either from the adjustments to engines that followed the steep oil price Increases of the 1970s or from developments in alternative fuels and Improvements to design and manufacturing technologies which took place after 1976. This can be seen by considering the three passenger cars used for fuel experiments (only one Is shown in Table 3.11).

The small engined car, a Volkswagen, was based on a 1930s design and was well suited to hard use and Brazilian conditions while fuel was cheap and road surfaces rough. However It was costly to manufacture, and Its cramped interior and high fuel consumption combined to cause a loss in popularity and market share after 1975. In 1985 Brazil was the only country In the world to manufacture this air-cooled, rear engined model and even that was modified to use local alcohol fuels rather than gasoline. The medium car, a GM Opala, was unfortunately fitted with a 6-cylinder gasoline engine which was unusually large and produced fuel consumption figures between 50 to 80 percent higher than most vehicles in the car class. The large car was a V8 engined Chrysler, a typical "gas-guzzler" of the late 1960s and early 1970s and Is of a type now little used in developing countries. The Brazilian light goods vehicle, an air-cooled, rear engined, gasoline powered Volkswagen Kombi, Is not typical of light goods vehicles used now and there Is some question about the performance of the Scania super heavy tractor. This heavy truck had very high fuel consumption compared with similar European versions from the same manufacturer, particularly when it was running loaded on grades. Recent investigations have revealed that the vehicle was fitted with a low speed differential which may be partly responsible. This was not realized when the vehicle's fuel data were collected and analyzed. Prospective users of the Brazilian fuel study's results should use predictions for this vehicle type with caution and check them against data from vehicle operators In the environments In which the results are appiled.

The four studies' user cost surveys varied considerably In size but their structure was qulte similar. The aim of all the studies was to determine the Influences of highway characteristics on user costs, so that, 68 USER COST STUDIES

In selecting companies to appear In the surveys, adequate coverage of ranges and combinations of highway conditions was sought. The road user surveys were not designed to be representative surveys of commercial vehicle operations In the countries In which they performed. Indeed, In order to obtain data on vehicles working on extreme highway conditlons, Information was on occasions acquired from quite atypical companies. Consequently the surveys cannot be expected to provide particularly accurate information on general levels of costs. They were designed to provide Information on cost differentials associated with alternative highway conditions and users of the equations reported later will need to calibrate the equations for the environments that they face.

In order to obtain accurate estimates of costs associated with maintenance activities occurring at discrete Intervals, vehicles were monitored for substantial periods of time - In Kenya and the Caribbean for two years, In Brazil for up to thirty-six months with an average survey period of eighteen months, and In India for up to two years with an average survey period of seventeen months. The data analyzed In the Kenyan and Caribbean studles relate to twelve month periods of vehicle operation.

In the analysis of user cost data vehicles' costs are related to the characteristics of the highways that vehicles travel. For user survey vehicles these are averages of highway characterlstics over the route(s) travelled during the survey period. In the final part of this chapter we describe how highway characteristics were measured In the four studies.

3.3.2 The Measurement of Highway Characteristics

In all the studies It was necessary to record considerable quantities of Information descrlbing the permanent features of the roadway, like Its geometric alignment, together with variable conditions like surface roughness. The measurement programs Included experimental road sections from one to two kilometers long and commercial road users' routes that could be many hundreds of kilometers In length - Table 3.12 shows the lengths of the survey route networks. While It was possible to employ traditional surveying techniques on experimental sections, the determination of highway geometry on survey routes could not be accomplished In the time available using such methods.

In the Kenyan study, surveying techniques were used to measure experimental sites and maps were employed to derive measures of highway geometry for survey vehicles' routes. An instrumented vehicle was equipped to measure road surface roughness at experimental sites and for measuring survey vehicles' routes, and a number of modifications were made to this vehicle towards the end of the study to test the feasibility of recording geometry Information dynamically. Though such tests were broadly successful, they came too late to be fully incorporated Into the Kenya survey results.

As a result of these activities and of further research In the United Kingdom, the TRRL published a description of the Instruments which could be fitted to a light vehicle and used to measure highway characteristics In developing countries (Abaynayaka 1976). The Ideas In this document formed the basis for the Instrumented vehicles used In the Table 3.12: Summary of Instruments Used to Measure Geometry. Width and Roughness

Highway Characteristics Pave t Gometry GeomRoghnessSurvey Rout ountry Pa"ment j Vertical Horizontal Surfaej Network Length Width G ometry t3metmry |(k9he tm)

r~~~~~~~~~~~ _ - ______

Brszil Experimental fuel, Tape Rod & level Compas !Mameterin cars and Roadside speed sections j Survey station wagons calibrated 3600o by GMR proffilometer and Uar Survey Routes Estimated Linear Gyrocompss Quarter-car Index Progran. I by eye Accelerometer

Kenya Experimental fuel. TaeO Rod & Level Compass Bump integrator mounted Roadside speed sections Survey i in station wagons gm ______-______|__ calibratedby TRRL towed ffth wheel) Usr Survey Routes - Map Mal

jCaribbean Experimental tuel. Tape Rod & level Gyrocomss Bump integrator mounted India 42000 and India Roadside speed sections Survey i in station wagons (cars in ! ______-______- - - ____---- I India) calibratedby TRRL Caribbean not Usr Survey Routes Estimated ! Gradometer Gyrocompas towed fith wheel) avaiable by ey (India) ' i i 70 USER COST STUDIES

subsequentCaribbean and Indian studies. By the time the TRRL published Its report, the Brazilian study had developed Its own Instrumentedsurvey vehicle, after fabricatingmuch of the equipment and spending considerable time developing instrumentsappropriate to the needs of the study (GEIPOT 1981). A summary of the equipment used in the studies to measure horizontal geometry, vertical geometry, width and surface roughness Is given In Table 3.12.

To measure vertical geometry the Carlbbean and Indian studies used a TRRL designed Gradometer consisting of a weighted pendulum, dampened to lessen the Influence of vibration and acceleration. The Brazilian study utillsed an electronic linear accelerometer. Whether equipped with a pendulum or accelerometer, an Instrumented vehicle must be driven at a constant speed If gradients are to be recorded accurately. In the Carlbbean and Indian studies the measurement speed was fixed at 32 km per hour. In the Brazilian study the measurement speed was 50 km per hour for unpaved roads and 80 km per hour for paved roads. The output of these Instrumentstogether with data on the locationof measurements enabled a vertical profile of the route to be made. At test sites where fuel and speed data were collected, vertical and horizontal profiles were produced using surveying methods and vertical profiles were processed to produce two measures of vertical geometry, meters of rise per kilometer and meters of fall per kilometer, both expressed as positive quantities. Most vehicles In user surveys make round trips, passing along routes In both directions, so In the analysis of user survey data a single measure of vertical geometry was used, meters of rise plus fall per kilometer, equal to the sum of the positive quantities - meters of rise and meters of fall - expressed on a per kilometer basis.

Horizontal geometry was measured using maps In the Kenyan study and In all the other studies using an aircraft directionalgyrocompass. For use In analysis of user survey data horizontal profiles were processed to give a single measure of horizontal geometry - average degrees of curvature. This measure is obtained by adding all the angular movements recorded on a route and dividing the sum by route length.

Road widths were measured at fuel and speed test sites In all the studies using measuring and walking tapes. Widths of survey routes were assessed visually. In the Brazilian study the instrumentedvt 'cle made one pass over a route segment to measure roughness and another to measure geometry and assess width. In the Indian study all measurementswere taken In a single pass.

Road surface roughnesswas known to exert a considerable Influence on road user costs from early research conducted In the United States (Moyer and Winfrey 1939) and the results of the four country studies reported in the remainderof Part II all confirm the Importance of surface condition. A variety of systems were available to measure roughness Includingresponse type Instruments, direct profile measuring systems, indirect profile measuring systems and subjective panel assessments.

All response type instrumentslike the Bureau of Public Roads (BPR) Roughmeter, the TRRL towed fifth wheel, the TRRL bump Integratorunit and the Ralnhard Mays Ride Meter measure the displacement of a wheel suspension USER COST STUDIES 71 relative to a vehicle body or towing frame. The first two of these instruments are single wheeled devices that are towed behind a vehicle. The latter two devices are directly mounted in the rear of a light vehicle (usually a car or station wagon) and measure the cumulative movement of the rear axle relative to the vehicle body. The data produced by these vehicle mounted systems are affected by several factors In addition to surface roughness, notably vehicle speed, suspension mechanisms (which deteriorate), tire pressure, uneven tire wear and vehicle weight. To give an example of the sorts of effects involved, It was found in the Brazilian study that a change of 5 percent In vehicle weight or of 1 percent In tire pressure changed the response measurement count by around 2 percent. The trailer mounted units are more stable over time than vehicle mounted devices but because of their slow operating speed they are not normally used for extensive measurement programs.

In the Kenyan, Caribbean, and Indian studies the Instrumented vehicles (station wagons, except in India where cars were used) carried Bump Integrator Units. In Brazil Mays-Ride-Meters, producing a digital display of the cumulated displacement of the rear axle every 320 meters were employed. It was common to find more than one instrumented vehicle belng used to measure surface roughness and because of response variations across time and across vehicles the response type Instruments were regularly calibrated against a standard roughness measurement.

On the road sections In Brazil that were chosen as calibratlon sections, profiles were measured using a Profilometer which Is an Indirect profile measuring device utilising an accelerometer to provide the reference datum while the datum to ground information is given by a follower wheel equipped with a potentiometer. In the other studies a towed fifth wheel equipped with a Bump Integrator Unit was used to obtain information against which to calibrate vehicle mounted roughness measurement systems.

An absolute measure of roughness can be obtained by processing the proflle of vertical devlations of a road surface in wheel paths. Typically the profile has a complex structure which can be decomposed into different wave-lengths and amplitudes, this decomposition varying somewhat with the type of surfacing. Different vehicles are affected by surface roughness in different ways and for the purposes of determining the effects of surface roughness on user costs It would be useful to have a multidimensional measure of roughness capturing the various Important features of the road's vertical profile. However, none of the studies used such a measure. Instead unidimensional measures were employed, these being chose to capture the primary influence of surface roughness on a moving vehicle. In the Brazilian study, vertical profiles were processed through a computer program that described the behaviour of a body mass, a single tire, shock absorber and spring system, and the simulated movements of the body relative to the axle were aggregated as the recorded profile was traversed. The resulting index, measured per unit distance, was known as a quarter-car Index (QI) and In all the Brazilian study, roughness measurements were recorded In Qi units. The Kenyan, Caribbean, and Indian studies recorded roughness in millimeters per kilometer of vertical displacement as measured by the towed Bump Integrator Units. 72 USER COST STUDIES

Table 3.13: StandardisedRelationship between the lnternational Roughness Index (IRI) and Bump Integrator(Bl) Scales

Bi IRI (mm/km) (m/km)

0 0 2000 2.8 4000 5. 1 6000 7.4 8000 9.5 10000 12.0 12000 14.0 14000 16.0 16000 18.0 18000 20.0

Source: Paterson (1986).

Because of the use by three of the four studies of the Bump Integrator based, Bl, mm/km roughness measure and in the absence, at the time of original writing, of any international standard scale for roughness measurement, we have chosen to present in the main text the results of all four studies expressed In Bi units. Brazilian study equations and predictions originally expressed In Ql units have been converted using a relationship recommended by Paterson et al. (1984):

1 Qi unit - 55 mn/km BI.

Paterson reports that this conversion - while adequate for paved and gravel roads, should be amended for earth or parched-clay-gravel roads, to 1QI - 73BI. However he notes that these latter surface types were uncommon In the Brazil study. These conversions are the result of an international road roughness experiment coordinated by the World Bank and conducted In Brazil In mid-1982. The experiment reported by Sayers et al. (1986) was sponsored by the World Bank, GEIPOT and the Road Research Institute (IPR) In Brazil and supported by research and road Institutions from the United Kingdom, the United States, Australia and France.

Since completing the major part of this text an International Roughness Index (IRI) has been proposed. This Is measured In meter per kilometer units and Is a unidimensional profile summary statistic USER COST STUDIES 73

Table 3.14: Descriptions of the IRI and BI Roughness Scales

BI (mm/km) IRI (m/kmn) Descriptors

0-1100 0 - 1.6 Extremely high-quality new asphalt concrete or slipform portland cement conrete pavement for high speed motorways and airport runways, uncommon for highways. Undulations barely perceptible at 100 km/h. Depressions 0-2 mm/3 m.

1100-1800 1.6 - 2.5 Typical high-quality asphalt concrete or very high-quality surface treatment pavements; unpaved roads of excellent protile with fine-gravel or recently- bladed earth surface. Depressions 3-5 mm/3 m. Undulations barely perceptible at 80 km/h.

2200-3800 3 - 5 Asphalt pavements usually showing signs of deterioriation (may include wide range of defects from 0 to 100% cracking, occasional patches, shallow depressions or occasional shallow pot-holes), or defect-free surface treatment pavements of moderate to fair shape-quality, or unpaved roads of good quality. Depressions or unevenness are just visually perceptible, e.g. 10-25 mm/3 m. Sharp movements or undulations perceptible at 80 km/h. Travel speeds less than 100 km/h.

4200-5600 5.5 - 7 Pavements with visible irregularities and shape defects (often with extensive severe cracking or uneven patching over 20 to 50% of area), or defect- free surface treatment of very poor shape. Moderate depressions, 20-40 mm/3 m. Unpaved roads with shallow-moderate depressions, minor potholes, shallow corrugations (6-20 mm/1.5 m), or coarse gravel (stone size greater than 60 mm) on well-shaped surface. Sharp movements and undulations perceptible at 60 km/h, travel speeds less than 80 km/h.

6500-8300 8 - 10 Exceptional for paved roads, extreme deterioration, frequent depressions, extensive patching and unavoidable potholes, travel speeds less than 60 km/h. Unpaved roads: clearly visible frequent transverse depressions (20-40 mm/3 m), strong corrugations (10-30 mm/0.7-1.5 m) or occasional deep depressions (40-80 mm/3 m) or pot-holes; travel speeds less than 80 to 60 km/h.

10000-18000 12 - 20 Unpaved roads: unavoidable deep depressions (40-80 mm/1-3 m) or occasional very deep depressions/potholes (more than 80 mm, deep), frequent transverse or diagonal erosion gullies. Travel speeds generally less than 50 km/h, and at 20 m/km generally less than 35 km/h.

Source: Paterson (1986). 74 USER COST STUDIES representing cumulative relative axle-body displacement In a standardized quarter car simulation, of the sort used In Brazil to obtain the Ql index. The International Roughness Index is described In Paterson (1986). In subsequent chapters, where predictions are presented In tables and graphs, information concerning IRI m/km values corresponding to BI mm/km values is provided. The relationship between the Bi and IRI scales Is shown in Table 3.13. The conversions between the BI and IRI scales are achieved using:

IRI - 0.0032(BI)0 .89

1 1 2 Bi - 630(iRI) . .

Note that the relationship between the two indices is non-linear so that, were graphs of predictions given later in Part II to be redrawn using the IRI measure, the curvature of the plotted lines would alter. Table 3.14 gives a description of the surface conditions that yield particular roughness measurements (Bi and IRI).

Routes travelled by user survey vehicles were divided Into links and average rise + fall, degrees of curvature and surface roughness for measured links were combined by kilometer welghted averaging to produce route averages. Frequencies with which routes were travelled were obtained for all survey vehicles and route averages were combined, again using kilometer weighted averaging, to produce averages of highway conditions experienced by survey vehicles during the survey period. Since the IRI Index Is related non-linearly to the BI measure, average survey period IRI cannot be reproduced accurately Just from knowledge of average BI or 01. CHAPIER 4 Vehicle Speeds

The first of the studies' results to be presented are those concerning vehicle speed. The prediction of vehicle speed Is central to the prediction of road user costs in the methodology adopted in the user cost studies in India, Brazil, the Caribbean, and Kenya. Vehicle speeds determine Journey times so that predictions of speeds before and after highway Improvements are required If travel time savings are to be evaluated. Depreciation, Interest, and crew costs are generally avallable on a per time period basis and to convert them to the per unit output basis that is relevant for cost benefit analysis of highway Investments, kilometers travelled per time period has to be predicted. Given hours driven per time period, kilometers travelled is proportional to vehicle speed so that vehicle speed predictions play a role In determining depreciation, Interest, and crew costs. And, since in all four studies fuel consumption is written as a function of highway characteristics and of vehicle speed, to predict fuel consumption, predictions of vehicle speed are required.

In all four user cost studies speeds were obtained from roadside observation of vehicles about their normal business on short sections of road selected to cover wide ranges of highway conditlons. The methods used have been described In Chapter 3 and differ only slightly from study to study. The data used to estimate the equations reported In this chapter are free flow speeds on road sections, along the length of which highway conditions were uniform. In the Indian study speeds on congested highways were studied and the Influence of slow moving (e.g., animal powered) traffic was examined. Preliminary results are given in CRRI (1982). In the Brazilian study roadside speed data obtained at short test sections were supplemented by speeds recorded at longer (2 km) sections and by Information collected from operating schedules and tachograph records during the road user survey. In the Indian study data on vehicle speeds were obtained from time tables or operating schedules for all vehicles participating in the user survey.

In Sections 4.2, 4.3, and 4.4 results obtained using roadside and survey speed data concerning respectively cars and light goods vehicles, buses and trucks are presented. Details of estimation methods, summary statistics, means and ranges of explanatory variables and so forth are given in the appendix to this chapter. An appendix to Chapter 5 provides tables of speed predictions for combinations of highway roughness, vertical and horizontal geometry.

The speed models available from the Kenyan, Caribbean and Indian studies write speed as simple linear functions of highway characteristics such as average rise + fall, average degrees of curvature and surface

75 76 VEHICLE SPEEDS roughness. The Brazilian speed model Is substantially more complex and before proceeding to consider the predictions that It produces It is necessary to explain its structure. This is the subject of the next section.

4.1 THE BRAZILSPEED MODEL

The relative complexity of the Brazil study speed model arises because in the model an attempt is made to allow for Interactions amongst and non-linearities in the effects on vehicle speed of highway and vehicle characteristics. This is achieved by regarding attalned speeds as the minimum of constraining or maximum allowable velocities (M.A.V.'s), most of which are associated with distinct highway features, and by modelling these M.A.V.'s by reference to vehicle characteristics and the constraints upon vehicle performance that are Imposed by highway conditions. Models of this sort have been used by Guenther (1969) and Sullivan (1977).

At the heart of the Brazil study speed model are the relationships between maximum allowable velocities and vehicle and highway characteristics. The relationships are Intended to describe the behaviour of vehicles In steady state, that Is when highway conditions are constant, and have been experienced for sufficient time to ensure that speed Is not changing. Consequently, they were estimated using data relatlng to vehicles believed to be In steady state and using road sections where attaining steady state speed was possible.

Of course In practice vehicles at times travel at other than steady state speeds. To predict Journey speeds when such considerations are Important there Is a version of the Brazil speed model, known as the "micro-transitional" model, In which speed change cycles are modelled. Details can be found In Watanatada et al. (1987). In this chapter we describe and present estimates of the version of the model Intended for use In large scale highway planning exercises In which transitional effects and the heterogeneity of highway conditlons are not modelled. In this "aggregate" model, highways are regarded as homogeneous with respect to highway conditions, with highway characteristics measured by the distance weighted averages of their values along the length of the highway.

In the model maximum allowable velocities are associated with curvature (Vc) and surface roughness (VR) and there are two velocities associated with gradient (VOR and VBR), although only one of these Is a potential constraining velocity at any point In time. The velocity VDR Is associated wlth the driving power of the vehicle. The velocity VBR Is associated with Its braking capability and does not act to constrain attained speed on positive gradlents or on negative gradients for which gradient exceeds the vehicle's coefficient of roliing resistance. A fifth constraining velocity, VDE, Is Interpreted as maximum "desired speed" and Is Intended to represent an ultimate upper limit on speed of travel.

The maximum allowable velocities are thought of as varying from vehicle to vehicle and from section to section, variation being only In VEHICLE SPEEDS 77 part attributable to variation in observed vehicle and highway characterlstics. The average, or expected values of the M.A.V.'s, denoted by VDR, VBR, VC% VR and VDE are specified as functionsof observed vehicle and highway characteristics. A vehicle travelling over a road section generates realisations of the maximum allowable velocities, vDR, vBR, vC, vR, and vDE, and, since vehicle speed is assumed to be maximised, but constrained by the maximum allowable velocities, attained speed v Is related to the maximum allowable velocities by

(1) v - min (VDR, VBR, vC, vR, vDE)

The attained speed v Is regarded as a realisation of a variable V - min (VDR, VBR, VC' VR, VDE) which has expectationV. Watanatada et al. (1987) give formulae for the means, VDR, VBR, VC VR as functions of vehicle and highway characteristics and they provide values for VDE. These are reproduced in the appendix to this chapter.

In order to predict average speed, V, as a function of average maximum allowable velocities (VDR,VBR, VC, VR, VDE) and thus as a function of highway and vehicle characteristics, assumptions concerning the jolnt probability distribution of the maximum allowable velocities must be Imposed. In the Brazilian speed model these velocities are assumed to have. independent Welbull distributions with common shape parameter equal to p (see e.g. Johnson and Kotz (1970) for a survey of the propertles of Welbull distributions). Under this assumption the probability that, say, VC exceeds some value vC is given by:

(2) P[VC > vcJ - exp{- OC vC1/p) VC > 0,

and the expected value of VC, VC, Is related to OC and fl by:

(3) E(VC) - VC - prcp)eC,

where r(fl) Is the Gamma function, xN e xdx.

Attained speed V Is the minimum of the maxlmum allowable velocities so that:

P[V > VI - PEVDR > v n VBR > v n Vc > v n VR > v n VDE > v] 78 VEHICLE SPEEDS and the Independence of maximum allowable velocities allows us to write this as:

(4) P[V > v] - PEVDR v] P[VBR > v] P[VC > v] PEVR > v] PEVDE > v]

0 - exp { - E DR + OBR + OC + OR + ODE] v 'Pi so that V also has a Welbull distribution with shape parameter I.If the Independence assumption Is not valid or If the distributions of the maximum allowable velocities do not have common shape parameters then equation (4) does not hold. The independence assumption falls to hold, if for example vehicles with relatively low maximum allowable velocities associated with, say, gradient tend to have relatively low maximum allowable velocities associated with, say, roughness. Shape parameters will vary If the dispersions of the log maximum allowable velocities are not all equal.

From equations (3) and (4) we have the following relationship between expected attained speed V - E(V) and the expected maximum allowable velocities associated with each feature of the highway:

(5) V - U(V )D + (VBR)-'/ + (Vc) + (VR + (vDE

Speed predictions are obtained by calculating average maximum allowable velocities associated with gradient (VDR, VBR), with curvature (VC), wlth roughness (VR) and the average maximum "desired" speed (VDE), using the formulae and parameter estimates given in Table A4.1 in the appendix and appropriate values for gradient, curvature and roughness. Having obtained predicted average maximum allowable velocities, predicted average attained speed Is then calculated using equation (5) and the estimated values of P (which are vehicle class specific) which are given in the appendix. Finally, an approximately unbiased speed prediction is obtained by multiplying through by a factor exp (uf2/2) using values for a2 given in Table A4.1.

In the aggregate speed model average values for highway characteristics are entered into these formulae and, Initially, separate predictions are obtained for speed of uphill and downhill travel, the model being applied once with gradient specified as positive and once with gradient specified as negative. Journey speed Is obtained as the harmonic mean of the two speed predictions that result.

The three graphs in Figure 4.1 Illustrate the operation of the model for a heavy truck carrying a net load of 6 tonnes on a paved surface. Each graph shows the response of predicted speed to changes in a specific VEHICLE SPEEDS 79

highway characteristic. Flgure 4.1a shows the effect of surface roughness for a relatively straight downhill section. The predicted speed and the predicted constraining velocity associated with the varying factor are graphed as solid lines and the other predicted constraining velocities are graphed as dashed lines. In Figure 4.1a the maximum desired speed Is relatively Influential on smooth routes but Its effect virtually disappears as roughness Increases. VC and VDE are Independent of roughness but roughness affects VDR and VBR through the coefficient of rolling resistance. Figure 4.1b shows the effect of gradient and again we see that VDE has appreciable influence only on relatively flat routes. Gradient has no effect on VDE, VC or VR. Figure 4.1c shows the effect of varying curvature - note that the predicted speed here Is to be regarded as that attained_on a curve sufficiently long for speed to be constant. VDE, VBR, VDR and VR are all independent of horizontal alignment.

Watanatada et al. (1987) report the results of limited Investigation Into the predictive accuracy of the aggregate model In the Brazilian environment using speed data obtained from roadside observation of vehicles at six road sections ranging In length from 2 km to 4.2 km. Observed speeds, averaged by vehicle classes, were regressed against speeds predicted using the "aggregate" model described above. For all vehicle classes the fitted lines have positive Intercepts and slopes less than one, ranging from 0.66 to 0.90, with R2 statistics ranging from 0.47 to 0.72. Thus there Is some indication of underprediction of speeds at low speeds and overprediction of speeds at high speeds, but the sample of sectlons used In this exercise Is very small and It would be unwise to draw any general conclusions.

Watanatada et al. (1987) also report comparisons of predicted speeds obtained using the "aggregate" model with speeds derived from bus tachograph records obtained during the Brazilian study's road user survey. These data are average round trip, space mean speeds for 41 bus routes and are perhaps not ideal for use in assessing the predictive accuracy of the "aggregate" speed model In which transitional effects are not modelled, because some of the bus routes Involve qulte frequent stops. Indeed for these data the squared correlation between observed and predicted speeds is 0.51, lower than most of the correlations found In the analysis of data from relatively short test sections described above, and marginally lower than the squared coefficient of multiple correlation (0.56) obtained when the observed bus tachograph speeds are related linearly to the recorded values (see Watanatada et al. 1987) of average rise + fall, average degrees of curvature and surface roughness.

Further details concerning the Brazilian study speed model are given In the appendix. In the next three sectlons the results obtalned In all four studies are presented and compared.

4.2 CAR AND LIGHT GOODS VEHICLE SPEEDS

Speed equations as reported In the four studies are presented in the appendix, together with summary statistics and comments concerning the Figure 4.1: Effect of Constraining Factors on Predicted Steady-State Speed

(a) SuWbcIimgulrly (b) VeEIedAigment (c) HodzontalAlignment

Speed(km/h) Speed(km/h) Speed(km/h) 30D0 VBRAK 300 -300

270 - 3270- VCURVE 270 VBRAKE VCURVE 240 - 240 240

210 210 210 VROUGHVRLHVOG

180 \ 180 .180------

150 _…\VDRIrVE 150 _VDRVE 150 VDRIVE

120 - 120 120 VCURVE VDESIR VDESIR VDESIR 0090.-...... 90 - - - 90.. 0 60 60 60

30 -30 30

X 0 I I I I I0 I I I I 0 25 50 75 100 125 -10 -8 -6 -4 -2 0 2 4 6 8 10 0 200 400 600 800 1,000 Roughness(Qi) Gradient (%) Curvature(degrees/km)

Curvature=25degrees/km; grodlent=-3.5% Roughness=40Ql; curvature=25degrees/km Roughness=40QI; grodient=-3.5%

V=Predlctedsteody-state speed VEHICLE SPEEDS 81 data used and estimation procedures. The equations are summarized In Table 4.1 below. The Brazilian speed model estimated using roadside speed data is too complex to present in this section and details are given in the appendix. Most of the equations given In Table 4.1 derive from roadside speed data but two of the equations were obtained using data from user survey companies. In both cases no accurate estimates of the effect of road curvature on vehicle speed could be found, largely because of high correlations among geometry measures In the data sets. It should be borne In mind that the coefficients on rise + fall obtained using survey data may be inflated as a result of omitting curvature.

The designs of the cars found in the studies differed greatly, as noted In Chapter 3, and we can expect ambient speeds to differ across countries In consequence. Further, we might expect to find relatively high speeds In Brazil, where journeys exceeding 200 km are common, and relatively lower speeds In the Caribbean where Journeys around the small Islands are necessarily short. Finally, to the extent that speed of travel is Influenced by economic conditions, speeds can be expected to vary across countries because of differences in relative prices.

Inspecting Table 4.1 It can be seen that measures of rise, fall, curvature, and surface roughness take negative coefficlents but that the magnitudes obtained vary quite considerably. The Indian roadside speed equation Includes pavement width as an explanatory variable though the width effect Is rather small, every one meter reduction In width being associated with a I km/hr reduction In speed. The Kenyan, Caribbean, and Brazilian studies all recommend adjustments to vehicle speed predictlons to allow for pavement widths narrower than 5 meters. The adjustment factors reported In the Kenyan and Caribbean studies Imply a speed reduction of around 7.5 km/hr for every 1 m reduction in width below 5 m.

The equations are graphed for all vehicle classes, once against curvature, once against rise + fall, and once against surface roughness In Figures 4.2 - 4.5. The graphs show speed varying as highway characteristics are changed one at a time and other variables that appear In the equations are set to values, recorded In notes accompanying the graphs, chosen to be close to average values observed in the studies. In the graphs the measure of vertical geometry used Is average rise + fall (RF) rather than rise or fall, so as to maintain consistency with user survey results given later which all use rise + fall. In practice users will often want to predict round trip speed In which case rise + fall Is relevant. In most of the graphs that appear In this book the extent of the plotted lines give a rough Indication of the range of the explanatory variable observed In the study generating the equation. In this and the following chapter this convention has been broken on occasions since there seems to be some consensus that equations obtained from experimental fuel and roadside speed data can be extrapolated to a llmited extent.

In developing predictlons for the Brazilian study model the default formula relating superelevation to average degrees of curvature given In Appendix A4.3.1 has been applied. This has a dramatic effect on predicted speeds. If superelevation Is not adjusted as curvature Is altered as described In A4.3.1 then the model can predict curvature effects 82 VEHICLE SPEEDS

Table 4.1: Equations for Vehicle Speed (km/h): Cars and Light Goods Vehicles

Coefflcients on Vehicle Country Type of Road Clas Study Surface Intercept Rise Fall Curvature Roughness Other Varables(l) CmCkm) (m/km) (0/k) B1 (mm/km) Cars India Roadside Mostly Paved 60.6 -. -. 18 -. 0078 -. 0036 +1 O5W

Cars India SurveyX2 ) Mostly Paved 58.7 -. 40 -. 0023

Cars Brazil Survey(2) Paved and 66.2 -. 27 -. 0040 +7.26T + .068D Unpaved

cars Kenya Roadside Paved 102.6 -. 37 -. 08 -. 111 -. 0049A

Cars Kenya Roadside Unpaved 84.2 -. 21 -. 07 -. 118 -. 00089 -. 131 - . 19RD

Cars Caribbean Roadside Paved 67.6 -. 08 -. 07 -. 024 -. 00067

Light Kenya Roadside Paved 86.9 -. 42 -. 05 -. 074 -. 0028a Goods

Light Kenya Roadside Unpaved 81.2 -. 32 -. 059 -. 097 -0005 -. 29M - .20RD Goods

Ught Caribbean Roadside Paved 62.6 -.09 -.07 -. 022 -.00066 Goods

Notes

Equations for vehicle speed are linear in explanatory variables with coefficients as given above.

(1) Other variables defined as follows: W = pavement width (m) T = number of trips per day D = one way route distance (km) A = Altitude (m) M = Moisture content I%) RD = rut depth (mm)

(2) In survey equations vertical geometry is measured by average rise plus fall. Coeffident In column headed "rise" is coefficient on average rise plus fall for survey equations. VEHICLE SPEEDS 83

Figure 4.2: Vehicle Speed (V) versus Rise + Fall (RF): Cars

70-

K B 60 __

40v

30 I

__ _ _X _ __3- ______...... _...... RF

0 10 20 30 40 s0 60 70 80 90

Ecuations: B = Brazil Medium Cars K = Kenya Cars C = Caribbean : Cars I = India Cars

Units: V = Speed (kmth) RF = Rise plus Fall (m/km) C = Curvature (0/km) R = RoughnessBI (mm/km), IRI (m/km)

Variables not Plotted: C = Curvature = 500/km R = Roughness= 5500 BI (mm/km), 6.8 IRI (m/km) M = Moisture Content (Kenya only) = 2.6% RD = Rut Depth (Kenya only) = 18.9 mm. W = Width (India only) = 7 m. ALT = Attitude (Brazil only) = 0 GVW = Gross Vehicle Weight (Brazil only) = 1.4 tonnes For other Brazilian speed model variables not plotted, see default values in the Appendix. 84 VEHICLE SPEEDS

Figure 4.3: Vehicle Speed (V) versus Curvature (C): Cars

60i

70 \

60 -

aD- -- -~~~~~~~~- - - - - ~ ~- ~ ~~ ~~ ~ ~ ------

40 - --- C

0 200 400 600 600 1000 1200

Vehicle Speed (V) versus Roughness (R): Cars

60 ___ _ -

B (pav.d)

40 -

,~ ~~ ~ ~ ~ ~~~~~~,B 20-

0 2000 4000 60oo 6000 10000 12000

2. 51 --- . R, IRI 2.8 5.1 7.4 9. 5 12.0 14.o VEHICLE SPEEDS 85

Figure 4.4: Vehicle Speed (V) versus Rise + Fall (RF): Light Goods Vehicles and Utilities

v 70

511- 8w'-s------~~~----- C

40_

. ~~~...... ~ ...,, ...... ,,, ...... RF 0 10 20 30 40 50 60 70 80 Z0

Equations: B = Brazil Utility Vehicle K = Kenya Light Goods Vehice C = Caribbean Light Goods Vehide

Units: V = Speed (km/h) RF = Rise plus Fall (mr/km) C = Curvature (0/km) R = Roughness, Bi (mm/km). IRI (m/mk)

Variables not Plotted: C = Curvature = 500/km R = Roughness= 5500 S1 (mm/km), 6.8 IRI Cm/km) M = Moisture Content (Kenya onlY) = 2.6% RD = Rut Depth (Kenya only) = 16.9 mm. ALT = Altitude (Brazil only) = 0 GVW = Gross Vehice Weight (Brazil only) = 2.1 tonnes For other Brazilianspeed model variablesnot plotted,see defaultvalues In theAppendix. 86 VEHICLE SPEEDS

Figure 4.5: Vehicle Speed (V) versus Curvature (C): Light Goods Vehicles and Utilities

v 70

40 ',

3040 *~"C-.

20-

o~~~~~~~~~~~~~~~~~~~~~~

0] 200 400 Sao Bo0 1000 1200

Vehicle Speed (V) versus Roughness (R): Light Goods Vehicles and Utlilties

ZpB (paved)

40 B (uOpav-d)

20-

a 2000.00 4000 9000 120000 12000

2.8 5.1 7.A 9.5 12.0 14.0 VEHICLE SPEEDS 87 which are much larger than those reported below. Users should take care to ensure that the formula used here Is applicable In environments in which they apply the model.

Considering first car speeds, and the equations derived from roadside speed data, the graphs show quite clearly that car speeds vary substantially across countries. Predicted speeds are generally lowest using the Indian study model and highest for the Brazilian study model. It should be noted that the Brazilian model was estimated using data only on vehicles which, In the judgement of the analysts, had attained steady state speed. The Brazilian speed equations graphed here refer to the "average" sized passenger car (see Table A4.2) with a gross vehicle weight of 1.4 tonnes.

All the studies give speed as linear functions of curvature, rise + fall and roughness except the Brazilian study. The Caribbean and particularly the Brazilian study equations show very small effects for rise + fall, vehicle speeds being predicted by the Brazilian study model to be virtually constant until average rise + fall exceeds 60 m/km, which represents quite severe vertical geometry on a long route. Very pronounced curvature effects are predicted by the Kenyan and Brazilian models at low levels of curvature. The Kenyan model predicts speed reductions of the order of 35-40 percent as curvature Increases from 00 /km to 2500/km. The effects are somewhat smaller in the Brazilian model and become less marked as curvature Increases. Assumptions concerning superelevation are critical here. The effect of roughness varies across the studies too. The Indian and Brazilian models predict quite sharp reductions In speed once roughness exceeds 4,000 mm/km and the Brazilian model predicts different speeds at the same roughness level on paved and unpaved routes.

In the Kenyan study also, separate relationships are given for paved and unpaved routes. However, no roughness effect Is reported for paved routes so In Figure 4.3 only the equation for unpaved routes Is drawn. Where speed Is graphed against rise + fall or curvature the equations drawn for the Kenyan and Brazillan studies are those for unpaved routes. At any given level of roughness, speeds are predicted to be lower on unpaved than on paved routes. This is possibly due in part to different responses to surface texture produced by the roughness measuring Instruments. However, if unpaved routes show greater variation in roughness along their length then we would expect average speeds to be lower on unpaved routes than on paved routes with the same average roughness. First, because drivers may travel slower on unpaved routes to avoid excessive damage to vehicles should an unusually rough section be suddenly encountered. Second, because of the manner in which average speeds are calculated. If we regard a road section as composed of a number of equal length subsections then average speed over the road section Is the harmonic mean of speeds along the subsections. Since, In the harmonic mean, more "weight" Is given to the slower speed, average speed over the whole section will be lower than speed over the average roughness subsections of the section if speed Is a linear or concave function of roughness over the relevant range.

Predictions obtained using the user survey speed equations are lower than those obtained from roadside speed equations. This Is to be 88 VEHICLE SPEEDS expected since the user survey speed data relate to average speeds over long Journeys during which vehicles accelerate and decelerate and on occasions encounter congestion and delays.

Speed equations for utilities and light goods vehicles obtained In the Brazilian, Caribbean, and Kenyan studies are graphed In Figures 4.4 - 4.5. The Indian study did not report equations for this vehicle class. Here there is much more agreement across the studies concerning speed levels. As for cars, the Kenyan and Brazilian study equatlons predict large curvature effects at low levels of curvature. The Caribbean study results are notable In predicting low sensitivityof speeds to variations In roughness and rise + fall. In fact only the Brazilian study predicts substantial reductions In speed on Increasing surface roughness for this vehicle class. Appendix C to Chapter 5 contains tables of predicted speeds for cars and light goods vehicles.

4.3 BUS SPEEDS

Bus speed equations as reported In the studies are given In the, appendix and, with the exception of the Brazillan speed model, they are summarized In Table 4.2. Predictions from all the models are graphed In Figures 4.6 and 4.7, and are given In tables In Appendix C to Chapter 5. For the Brazilian model graphs of speed agalnst roughness show relationshipsfor paved and for unpaved surfaces. The graph derived from the Kenyan study model relates to speeds on unpaved surfaces.

Bus speeds vary across countrles, as Is to be expected, In part because of the differences In vehicle type described In Chapter 3. On good quality paved routes the Brazilian model predicts higher speeds than the Kenyan and Indian models. On unpaved surfaces with high geometric standards the Brazilian and Kenyan models predict rather similar speeds. There Is some agreement on the effect of gradient on bus speeds, the Brazilian, Kenyan, and Indian models predicting a 20-30 percent reduction In speed on Increasinggradient on good quality paved roads from lOm/km. Power to weight ratlos for the typical loaded bus were similar In all three studies (around 8.5 km/tonne).

Figure 4.7 shows the relatively large curvature effects predicted by the Kenyan and Brazilian speed models as curvature Increaseson relativelystraight routes. Again assumptionsconcerning superelevatIon are critical In the Brazil study model. The curvature effect predicted by the Indian study models Is much smaller, approaching that predicted by the Brazilian model on very sinuous routes. It should be noted that none of the test sections used In the Kenyan study had curvature exceeding 2000/km whereas In the Indian study curvature up to 1,2430/km was recorded and in Brazil, 2,8660/km. Figure 4.7 shows vehicle speed plotted against roughness for routes of reasonably good geometry. The Kenyan model shows very small roughness effects compared with the Indian model throughout the roughness range, quite similar to those predicted by the Brazilian model for relatively smooth routes. In both the Kenyan and Brazilian models speeds are predicted to be higher on paved than on unpaved routes with Identicalmeasured roughness. VEHICLE SPEEDS 89

Table 4.2: Equatlons for Vehicle Speed (km/h): Buses

Coeffcents on Country Typ of Ro.d Study Road Intercept Rb Fal raturv Roughns Xher Variabls(1) Studysudwe ~ ~ Im/ktm)rn/in) (m/bn{Xu rnkm (*/kun) Bi1tm2 (mm/kinm

India Roadside yMostyPayed 55.0 -. 301 -. 228 - 0077 -. 02 +.0.61W

India Survey(21 MostlyPaved 30.6 -. 315 -. 0004 +2.29W

Brazil Survey Paved and 64.1 -. 0616 -003 +.o18D unpaved

Kenye Roadside Paved 72.5 -526 067 - .066 - 0042A

Kenya Roadside Unpaved 62.6 -. 492 .010 - 046 -. 00036 -. 16M -. ORD

Nogjg Equationsfor vehicespeeds are linw in explanatoryvariables with coefficientsas given above (1). (2) see Table 4.1.

Predictions of bus speeds obtained using equations derived from Brazilian and Indian study user survey data are substantially lower than the predictions given by the corresponding models derived from roadside speed data.

4.4 TRUCK SPEEDS

Truck speeds equations as reported In the four studies are given In the appendix and the results from the Kenyan, Caribbean, and Indian studles are summarized In Table 4.3. Speed equations for all models are graphed In Figures 4.8 and 4.9, and predicted speeds are given In tables In Appendix C to Chapter 5.

Speed equatlons for medium sized trucks with two axles up to 15 tonnes gross vehicle weight, are reported In all four studies. Larger trucks than these were uncommon In St. Lucia and Indla and no results for these heavier vehicle types were reported In either study. Heavier trucks were operating In Kenya but there were Insufficient speed data to allow an equation to be derived for these vehicles. Two main types of larger truck were found In Brazil, a three axle rigid vehicle grossing around 20 tonnes and a five axle articulated vehicle with a gross vehicle weight of 40 tonnes. There were other types of heavy vehicle but these two can be regarded as representative of the group. The three axle rigid truck shared the same engine as the medium truck and so had a much lower power to weight ratlo and Inferior performance on gradients. The heavy articulated truck had a turbocharged diesel engine producing good performance even when fully loaded. We consider first the medium truck speed results and then those for the heavy and articulated Brazillan vehicles. 90 VEHICLE SPEEDS

Figure 4.6: Vehicle Speed (V) versus Rlse + Fall (RF): Buses

v 50-

.,KB 30 "

...... -- 1-...... l ...... RF 0 10 20 a0 40 S0 s0 70 80 g0

Equations: B = Brazil: Bums K = Kenya: Buses I= India : Buses

Unfit: V Speed (kmhh) RF = Rise plus Fall (m/km) C = Curvature (0/km) R = Roughness, Bi (mm/khn), IRI (mtkm)

Variables not Plotted: C = Curvature = 5OO/km R = Roughness= 5500 BI (mm/km), 6.8 IRI (m/km) M = Moisture Content (Kenya only) = 2.6% RD = Rut Depth (Kenya only) = 18.9 mm. W = Width (India only) = 7 m. ALT = Altitude (Brazil only) = 0 GVW = Gross Vehile Weight (Brazil only) = 11 tonnes

For other Brazilian speed model variables not plotted, see default values in the Appendix. VEHICLE SPEEDS 91

Figure 4.7: Vehicle Speed (V) versus Curvature (C): Buses

451

40" - -- -\ - 0 KK____ ----

B 40~~~~~~,~ ~ ,_ __ ~ ~ ~ ~ ~ ~ ~ ~ ------

3 0 … …B E

20-

15-

O ___r______TTTT ___T __T____ '__'__,_____,_,__,__C

0 200 400 500 sOC 1000 1200

VehicleSpeed (V) versus Roughness (R): Buses

70-

4050-

sol- ~ -,-s,-----s

20- . R_ ......

30- ~ 2. . 95 1.0 1.

12000 0 2000 4000 6000 B0D0 10000

'.B 5.19.5 7.4 12.0 4.0R , 92 VEHICLE SPEEDS

Table 4.3: Equations for Vehicle Speed (km/h): Trucks

Coefficients on Country Truck Type Type of Road - r- Study Surace Intercept Rise P.Fall Curvature Roughness Other l i (mlkm)l (m/km) (0 /km) B1 (mmtkm) Variables( 1 ).

India Mostly 2-axle Roadside Mostly 47.3 -. 269 1-.265 -. 010 1 -. 0019 +1.06W -upto 16t GVW Paved ; .

India Mostly 2-axle User(2) Mostly 31.4 -. 307 +1.48W up to 16t GVW Survey Paved

_ _ _ _|------Caribbean Mostly 2-axle Roadside Paved 51. 9 -. 222 -I122 -. 017 i -. 0011 +.559PW up to 12t GVW

Kenya Medium Roadside Paved 68.1 -. 519 +.030 - 058 I -. 0004A and Heavy I

Kenya Medium Roadside Unpaved 69.3 -. 433 t tlO4 -.061 -. 00060 -. 22M -,27RD and Heavy l l _

Notes Equations for vehice speeds are linear in explanatory variables with coefficients as given above. (1). (2) see Table 4.3-

4.4.1 Medium Trucks

Considerable variation in truck speed levels across countries is to be expected, even for similar sized vehicles, due to the nature of the service provided by owners and variations In the Incidence of overloading. There seems to be no clear pattern in predicted speed levels except that Kenyan trucks are generally the fastest over the observed range of highway characteristics and Indian trucks are the slowest. Relatively low truck speeds are predicted by the Indian model. These are unlikely to be due to the presence of slow moving and animal traffic on Indian roads because roadside speed data are normally obtained under free flow conditions. The overloading reported In CRRI (1982) may have some influence on Indian speeds. The Brazilian model predicts large effects for all highway characteristics so that relatively high speed levels on well designed roads fall rapidly as the geometric design worsens or surface condition deteriorates.

Figure 4.8 shows predictlons of the effects of gradient on medium truck speeds and these are quite similar across the four studies. The Caribbean and Kenyan studies predict the smallest effects, speeds Increasing by 11 percent (Carlbbean) and 18 percent (Kenya) as rise + fall drops from 50m/km to 20m/km. The Brazilian and Indian study models predict speed Increases of around 25 percent In this situation. The predicted effects of curvature are graphed in Figure 4.9. As for other vehicle classes the Brazil study model predicts relatively large curvature effects for curvature changes on relatively straight routes. The Kenyan study model, estimated using data over only a limited range of curvature also predicts large effects. VEHICLE SPEEDS 93

Flgure 4.8: Vehicle Speed (V) versus Rlse + Fall (RF): Medium Trucks

v 590

45-

40 ".

25- ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 5

O- ...... lE§|zlES4...... ,1. , R Ff 0 10 20 30 40 so so 70 ea 9t

-quations: B = Brazil: Medium Trucks K = Kenya Medium Trucks C = Caribbean : Medium Trucks I India: Medium Trucks

Units: V = Speed (km/h) RF = Rise plus Fall (mrkin) C = Curvature (0 /km) R = Roughness, Bi (mm/km). IRI (m/km)

Variables not Plotted: C = Curvature = 500/km R = Roughness = 5500 Bi (mm/km), 6.8 IRI Cm/km) M = Moisture Content (Kenya only) = 2.6% RD Rut Depth (Kenya only) = 18.9 mm. W = Width (India only) = 7 m. ALT = Altitude (Brazil only) = 0 GVW = Gross Vehicle Weight (Brazil only) = 14 tonnes PW = Power to Weight ratio (Caribbeanonly) 9.3 Bhp/tonne

For other Brazilianspeed model variablesnot plotted,see defaultvalues in the Appendix. 94 VEHICLE SPEEDS

Figure 4.9: Vehicle Speed (V) versus Curvature (C): Medium Trucks

v 55

45 -

40 K0 4I

35 ~~~~~~~~~------…- 10 305 __-c ---

a 200 400 5000 BOO 1000 1200

Vehicle Speed (V) versus Roughness (R): Medium Trucks

V 55-

50 -

40N

;5.B (paved)

30 B (unpaved)

o-a a ...... ,,,,,,R,Bs 0 2000 4000 .000 8000 10000 12000 R, IRI

2.8 5.1 7.4 9.5 12.0 14.0 VEHICLE SPEEDS 95

Figure 4.9 shows predicted roughness effects. The Brazil study model predicts the largestroughness effects, once roughnessexceeds around 4,000mm/km. The Kenyan model (drawn in Figure 4.13 for unpaved surfaces) shows rather llttle sensitivity to roughness, speeds being predlcted to Increase by only 2 percent as surface roughness falls from 7,000mm/km to 4,000mm/kmon highways built to good geometric design standards. For the same roughness change the Indian study model predicts speed Increasesof around 16 percent.

4.4.2 Heavy and ArticulatedTrucks

In the Kenyan study, heavy vehicles were combined with medium trucks for the estimation of speed equations and only In the Brazillan study is a separate model for the speeds of heavy and articulatedvehicles estimated. The equation Is graphed for a three axle, 20 tonne rigid truck- and a five axle, 40 tonne articulatedvehicle in Figures 4.10 and 4.11. In calculatingpredictions these vehicles are taken to be fully laden at all times, and this may result In predicted average speeds somewhat lower than average speeds actually attained under normal operating conditions. The power to weight ratios of these two vehicle types are similar, 4.8 and 5.3 km/tonne for the fully loaded 3 and 5 axle trucks respectively. The effect of rise + fall on average speed Is graphed In Figure 4.10 and the two vehicles show similar responses for average gradients greater than 30 m/km. Large speed differencesare only present for gradlents up to 1 percent and thereafterthe curves converge rapidly and Intersect when rise + fall equals 70 m/km.

Figure 4.11 shows the effect of curvature on the predicted average speeds of heavy vehicles. With the assumptions concerning superelevatlon adopted throughout this and the subsequent chapter, the effects are very small.

Figure 4.12 shows the effects of roughnesson predicted speeds for both vehicle types on paved and unpaved highways. In fact, It Is uncommon to find large articulatedvehicles running on rough unpaved routes. High tire costs and the difficulties in achieving sufficient traction severely limit such operations and businesses plying rough unpaved routes will typicallyuse smaller rigid vehicles. Only one company In the Brazillan road user survey employed articulated vehicles extensively on unpaved routes, but the highways Involved were owned by the company who made substantial investmentsto ensure that the unpaved surfaced were of high quality.

In many countries, and Indeed in parts of Brazil, articulated vehicle speeds are high on good quality routes, rather higher than the 50- 60 km/hr predicted by the model presented here.

4.5 CONCLUDING REMARKS

The results presented in the previous three sectlons suggest quite substantlal differences in speeds and In speed responses to highway conditions for the vehicles and drivers observed In the four studies. Some 96 VEHICLE SPEEDS

Figure 4.10: Vehicle Speod (V) versus Rise + Fall (RF): Heavy and ArticulatedTrucks

v 55

50__

'S 45-' 45 B (heavy)

40 " 'S

B (Artic) ' ' 35 -"S"

S.~~S ''

25 S*

.,~~~~~~~~~~~~~~~~.~

35-

n-T,--- f....----- ... - -,r, - RF

a 20 30 40 - so so 70 so go

Ecuationm B(Atic) 2Brazil, articulated truck. unpaved road. BtHeavyl = Brazil, heavy truck. unpaved ra

YAM:s V = Speed (krn/h) RF = Ris plus Fall tm/km) C = Curvatur (0/kmn) R = Roughness, Bl (mm/km), IRI tm/km)

Vanotbi FlotbdM C = Curvature = 50°/km R = Roughness= 5500 Bl tmm/km), 6.8 IRI tmJkm) ALT = Altitude = o CVW = Gros Vehicle Weight = 20 tonnes Heavy, 40 tonnes Articulated For other Brazillianspeed model Variables not plotted, see default values In the Appendix to Chapter 4. VEHICLE SPEEDS 97

Figure 4.11: Vehicle Speed (V) versus Curvature (C): Heavy and ArticulatedTrucks

i -

B (heavy)

______-

B (Aret.O)

25-

20-

15-

10-

B~~~~~~~~~~~~~~~~~~~~~~

0 200 400 BOO SDO 1000 1200

Vehicle Speed (V) versus Roughness (R): Heavy and ArticulatedTrucks

40-

- _

- N NNN N N~ ~ ~ ~ ~~~~(~tc- aVd

is~~~~~~~~ N N N> B theavy- upaved)

NNBi cri - paved) 25-

B (Attic - urnpaveG)

10-15-

0 2000 4000 05 8000o0000aco 12000

2.&2. 5.1. 7.47 9.5 12.0 14.0 R, IRI 98 VEHICLE SPEEDS of these differences may be due to the model forms employed. For example, the Brazilian model ties roughness effects to gradient effects through the specification of rolling resistance and it specifies distinctive non-linear forms for the effects of highway conditions.

So far as speed levels are concerned, the Indian study predicts by far the lowest speeds. The other three studles predict fairly similar speed levels, with the Brazil study uniformly higher than the rest. Both the Brazilian and the Kenyan models predict large effects for highway curvature. The Kenyan curvature effects are obtained using data In which only a narrow range of curvature was observed (O 0 /km - 200 0/km) and it would be unwise to extrapolate the Kenyan estimates to high levels of curvature. The Brazilian data contain a much wider range of curvature but the Brazilian model's predictions concerning curvature are very sensitive to the specification of superelevation. In producing the graphs In the last three sections we have used the default formulae recommended by Watanatada et al. (1987) and this may be responsible for the noticeable flattening out of the curvature effect once curvature exceeds about 300 0 /km. The sharpest response to curvature In the Brazillan model occurs In the range 0 0 /km - 250 0 /km. This is not a transitional effect because the model Is constructed to describe, and estimated using steady state, free flow speed data.

The studies agree quite closely on the effects of gradient on speeds. So far as roughness is concerned a variety of effects are predicted, with the Brazilian model generally yielding the largest responses.

Data collectlon methods were quite similar In all the studies and while differences In model form may be partly responsible for the differences in the results, It seems likely that there are other Important contributory factors. One of these must be vehicle design. We have described the sorts of vehicles observed durlng the studies and features of thelr designs In Chapter 3, which opened Part II. The low power to weight ratio of typical Indian vehicles relative to those found In the other studies must be partly responsible for the low speeds found In India. Perhaps differences In vehicle designs are responsible for some of the differences In responses to highway conditions, but there Is little hard Informatlon to help us here.

One factor that may be responsible Is differences In prices. Fuel was relatively expensive In India, which would lead Indian firms to schedule vehicles to travel closer to fuel cost minimising speeds and might lead to overloading which would further encourage fuel conservation. The results reported In the next chapter show that Indian vehicles have an unusually pronounced U-shaped fuel consumption-vehicle speed relationship, bottoming out at rather low speeds. The penaltles for departing from fuel cost minimising speeds are larger for Indian vehicles than for any of the vehicles observed In the other studies.

It Is notable that only one of the studies (Brazil) attempts to model vehicle speeds In terms of vehicle characterIstics and that none of the studies model the influence of fuel, vehicle, and other prices. As we will see In Part lii, this complicates the task of transferrlng the VEHICLE SPEEDS 99 studies' relationships to new environments. The Brazilian model does incorporate a behavioural assumption, but it Is an implausible one - namely that firms schedule vehicles to maximise speed. If cost components expressed per unit of output (e.g., per kilometer) like fuel and tire costs rise as vehicles approach maximum allowable velocities then It will be optimal to travel at speeds below maximum allowable velocities to an extent that depends on the relative prices of cost components and the value of time, which, for commercial transport firms, enters largely through Interest and depreciatlon costs, I.e., vehicle purchase and replacement costs.

The full force of the speed maximisation assumption is lessened by the Inclusion In the Brazilian model of a limiting velocity "maximum desired speed," VDE, which reflects maximum speeds for unimpeded traffic on good quality routes. However, as the discussion of Section 4.1 makes clear, VDE only has a small impact on speeds when speeds are largely constrained by other maximum allowable velocities. Thus, the level of VDE Is not Influential in determining speeds on poor quality routes, but It Is on such routes that cost considerations and the Influence of prices may be most Important.

It Is tempting to use VDE to calibrate the Brazilian model for new environments but great care should be taken If this approach is adopted, for the following reason. Reducing or Increasing VDE will have substantial Impact on predicted speeds on good quality routes, but only a small Impact on predicted speeds on poor quality routes. In a typical highway investment appraisal, one wishes to compare predicted speeds before and after an Improvement and by adjusting VDE this speed difference can be made large or small at will.

Users should take care to ensure that any speed model chosen from those reported here Is appropriate for the environment In which they are working. Even In the case of the relatively flexible Brazil study model caution Is required. Though the user can adjust certain vehicle characteristics many features of vehicle and engine design are not considered In the model and no attentlon Is paid to the Influence of prices and costs. One potentially important cost is fuel cost. It Is to the studies' results concerning fuel costs that we turn In the next chapter. 100 VEHICLE SPEEDS

APPENDIX. VEHICLE SPEED EQUATIONS

A4.1 Kenya

Hide et al. (1975) report separate equations for paved and unpaved road surfaces. Notation Is as follows:

V - vehicle speed (km/hr) RS - rise (m/km) FL - fall (m/km) C - curvature (0/km) A - altitude (m) R - surface roughness (mm/km) M - moisture content (%) RD - rut depth (mm) L - depth of loose material (mm) W - pavement width (m).

The equations are given below. Figures In parentheses are ratios of coefficients to standard errors.

Cars, paved roads

V - 102.6 - .372RS - .076FL - .111C - .0049A (-20.3) (-4.1) (-14.5) (-7.8)

R2 . .73, S - 6.57, 468 observations.

Cars, unpaved roads

V - 84.2 - .21ORS - .070FL - .118C - .00089 R - .13M - .19RD (-9.53) (-3.1) (-17.6) (-7.4) (-1.3) (-6.2)

R2 _ .67, S - 5.23, 307 observatlons.

Light goods vehicles, paved roads

V - 86.9 - .418RS - .050FL - .074C - .0028A (-26.7) (-3.1) (-11.3) (-5.1)

R2 _ .77, S - 5.50, 453 observations.

Light goods vehicles, unpaved roads

V - 81.2 - .317RS - .059FL - .097C - .00095R - .29M - .20RD (-15.6) (-2.9) (-15.5) (-8.7) (-3.0) (-6.8)

R2 _ .72, S - 4.96, 327 observations. VEHICLE SPEEDS 101

Medium and heavy goods vehicles, paved roads

V - 68.1 - .519RS + .030FL - .058C - .0004A (-33.2) (2.0) (-9.0) (-0.8)

R2 _ .83, S - 5.35, 453 observations.

Medlum and heavy goods vehicles, unpaved roads

V - 69.3 - .433RS + .004FL - .061C - .00060R - .22M - .27RD (-19.9) (.20) (-8.9) (-5.5) (-2.4) (-9.2)

R2 _ .75, S - 5.03, 309 observations.

Buses, paved roads

V - 72.5 - .526RS + .067FL - .066C - .0042A (-17.1) (2.2) (-5.0) (-4.2)

R2 _ .55, S - 11.08, 532 observations.

Buses, unpaved roads

V - 62.6 - .492RS + .01OFL - .046C - .00036R - .16M - .09RD (-12.6) (0.3) (-3.6) (-1.8) (-1.0) (-1.8)

R- _ .42, S - 9.46, 355 observations.

Approximate Means and Ranges of Explanatory Variables

Paved Unpaved

Variable Min Max Mean Min Max Mean

RS(m/km) 0 86 14 0 55 13 FL(m/km) 0 86 15 0 55 13 C(0 /km) 0 157 47 0 198 45 A(m) 180 2,300 1,282 R(mm/km) 2,200 20,600 5,984 M(M) 0 25 3 RD(mm) 0 67 19 L(mm) 0 13 1

Source: Hide et al. (1975).

Hide et al. (1975) report correction factors to be added to predicted speeds for use on roads less than 5m wide, as follows. 102 VEHICLE SPEEDS

Adjustments for Road Width Less Than 5m. Add Terms below to Predicted Speeds

Vehicle Class Paved Unpaved

Cars and light goods -max (7.31(5-W),O) -max (4.32(5-W),O)

Buses and medium and heavy goods -max (3.29(5-W),O) -max (6.36(5-W),O)

Source: Hide et al. (1975).

Remarks

Vehicle speeds were sampled at 95 1-kilometer long test sections, 49 of which were paved, 42 gravel and 4 earth. Vehicles' Journey times were recorded using two observers with synchronized stopwatches who recorded registration numbers and times at which vehicles passed. Journey times were converted to space mean speeds for analysis. Observation continued at test sections until adequate numbers of vehicles had been recorded. None of the test sections experienced traffic flows exceeding 1,500 vehicles per day and the majority carried 150 vehicles per day or less. The data were apparently averaged prior to analysis but each section-direction produces more than one average. The numbers of observations producing each average are not reported. The equatlons are obtained by ordinary least squares. No effect was found for surface type on paved roads nor could effects for road width on paved or unpaved roads or for surface roughness on paved roads be obtained. Adjustments to apply to roads narrower than 5 meters are given, obtained from earlier work In Kenya (Abaynayaka et al. 1974).

A4.2 Caribbean

The equations reported In Morosluk and Abaynayaka (1982) for roads of all widths are shown below. Symbols are as In A4.1 and additionally:

PW - Power to gross vehicle weight ratio (bhp/tonne).

Passenger cars

V - 67.6 - 0.078RS - 0.067FL - 0.024C - 0.00087R (45.1) (-4.6) (-3.8) (-10.3) (-4.4)

R2 _ 0.90, 56 averages from 20,523 vehicles.

Light goods vehicles

V - 62.6 - 0.085RS - 0.067FL - 0.022C - 0.00066R (47.8) (-6.1) (-4.4) (-11.1) (-4.3)

R2 - 0.91, 56 averages from 13,713 vehicles. VEHICLE SPEEDS 103

Trucks

V - 51.9 - 0.222RS - 0.122FL - 0.017C - 0.00106R + 0.559PW (92.0) (-37.3) (-20.2) (-20.4) (-12.3) (20.0)

R2 _ 0.49, 4,812 data points.

Approximate Means and Ranges of Explanatory Variables

Variable Min Max Mean

RS(m/km) 0 110.8 53.3 FL(m/km) 0 110.8 53.3 C (0 /km) 0 1,099 395 R (mm/km) 1,329 12,928 4,612 PW (bhp/tonne) 6.5 20 15.9

Source: Morosiuk and Abaynayaka (1982).

Morosluk and Abaynayaka (1982) report correction factors for use on roads less than 5 meters wide as follows:

Cars Add: -8.1 max (5-W,0)

Light Vehicles Add: -7.0 max (5-W,0)

Trucks Add: -6.2 max (5-W,0).

Remarks

Data were collected using similar procedures to those used in the Kenyan study reported above. Additionally trucks' weights were measured In axle load surveys carried out a few kilometers away from test sections. The truck speed equation is obtained by ordinary least squares applied to individual truck speeds, the car and light vehicle equations by weighted least squares applied to averages taken by test section. All test sections are paved and no roughness effects are reported. The R2 statistic is lower for the truck speed equation than for the car or light goods vehicle equations. Presumably this reflects the use of averages In fitting the latter equations - the discussion In Chapter 6 Is relevant.

A4.3 Brazil

The Brazilian study reports equations obtained using roadside speed data and user survey data. The model estimated using roadside speed data Is presented first. 104 VEHICLE SPEEDS

A4.3.1 Brazil: model estimated using roadside speed data

The vehicle speed model estimated in the Brazilian study Is rather different In character from that estimated in the Kenyan, Caribbean, and Indlan studies. In this subsection the data and the estimation procedure employed are briefly described. For further details the reader Is referred to Watanatada et al. (1987).

Vehicle speeds were obtained from around 200 road sections using radar speedometers. In all around 100,000 observations were obtained but observations made with radar exposed were deleted. The speed model fitted uses the concept of "steady state speed" which Is the speed that a vehicle would eventually attain on a long road section which has the same characteristics (curvature, gradient, roughness, etc.) as the relatively short test sections on which observations were taken. Before estimatlon spot speeds were plotted against distance, each observation station (3-5 per section) contrlbuting a point to the graph. Data on vehicles that did not appear to have attalned steady state speed were eliminated. For the purposes of estimation speed observations were averaged, after taking logarithms, by vehicle class and, for trucks, by load state (which was estimated visually).

As explalned In the main text, the vehicle speed model estimated in the Brazilian study Is constructed using the Idea of constraining velocities, one associated with each of a number of highway features. In particular gradients, curvature, and roughness are Isolated for attention. Associated with a given gradient and vehicle driving power is a speed (VDR) which would be attained on such a grade were the road stralght and smooth. Similarly associated with a given grade and vehicle braking capacity there Is a speed (VBR) attained as a steady state velocity by a vehicle on such a grade on a smooth straight road of Indefinite length. Of course these constraining velocities, VDR and VBR are vehicle class specific as Is VC, the constralning velocity associated with a curve, defined as the speed attained by a vehicle on a flat smooth road of Indefinite length with curvature equal to that of the curve of Interest. VR defines a constraining velocity associated with roughness, attained by vehicles on straight flat roads of given roughness. The final constraining velocity Is denoted by VDE which is to be Interpreted as "maximum desired speed." This Is meant to represent the maximum speed at which a vehicle of given class (car, bus, truck) would travel on a flat, straight, smooth road of Indefinite length. In the report on the Brazilian speed model these constraining velocitles are referred to as "maximum allowable speeds" and their relatlonships to gradient, curvature, roughness, and vehicle characteristics are obtained by examining the maximum performance attainable from a vehicle as determined by Its engine power, capability for braking, skid resistance, and so forth. The constraining velocities (except VDE) are Intended to represent speeds attainable when vehicles are pushed to their limits.

In practice, a road section of Interest will have combinations of gradient, curvature, and roughness. The speed attained on such a road Is defined In the model as the minimum of VDE and the constraining velocities associated with each of the highway features. The Idea Is that drivers drive as fast as their vehicles will allow, within the constraint Imposed by VDE- VEHICLE SPEEDS 105

In practice, speeds of Identical vehicles on the same stretch of road can differ and In order to model speeds the constraining velocitles are regarded as random variables wlth average values referred to In the maln text as VDR, VBR, VC, VR, and VDE. In Watanatada et al. (1987) these averages are denoted respectively VDRIVE, VBRAKE, VCURVE, VROUGH, and VDESIR. They are written as functions of vehicle and highway characteristics, as follows:

(a) VDRIVE

VDRIVE - (HG + HA)1 /3 - (HG - HA)1 /3 , HG real

- MAX (v1, v2 , v3 ) HG complex

where: HG - (HA2 + (MG/3 AIR)3 )1 /2

MG - 1000 (GVW)(g)(CR + GR)

AIR - 0.5 (RHO)(CD)(AR)

HA - 736 HPDRIVE/(2 AIR)

v, - Rcos(z)

v2 - Rcos(z+211/3)

v 3 _ Rcos(z+411/3)

R - 2( -MG/3AIR)1/2

z - (1/3) arc cos (-2HA/(R MG/3AIR))

and: HPDRIVE - maximum used driving power (metric hp)

GVW - gross vehicle weight (tonnes)

- TARE (tare weight, tonnes)

+ LOAD (payload, tonnes)

g - gravitational constant - 9.81 m/s2

GR - signed vertical gradient (fraction)

CR ^ coefficient of rolling resistance (dimensionless)

- .0218 + .0000467QI for cars and utilities

- .0139 + .0000198QI for buses and trucks 106 VEHICLE SPEEDS

Table A4.1: Parameter Estimates and Default Settings for Brazilian Speed Model

Vehicle [ c Lrear Utility Bus Light Trucks Trucks Small lwlediumt Large Large gas [diesel Medium Hvy Articulated

Parameters m A

Drag coefficient, CO 0.45 0.S0 0.45 0,46 0.65 0.70 0.70 0.85 | 0.85 0.63

Frontal area, AR(m2) 1.80 2.06 2.20 2. 72 6.30 3.25 3.25 5.20 5.20 5,75

TARE (tonnes) 1.0 1.2 1.7 1.3 8.1 3.1 3.3 5.4 6.6 14.7

LOAD (tonnes) 0.2 0.3 0.2 0.8 3.4 3.0 2.8 9.6 11.9 25.3

______-______' _ _. _ . .. HPDRIVE (metric hp) 30.0 70.0 85.0 40.0 100.0 80.0 60,0 100.0 100.0 210.0

HPBRAKE (metric hp) 17.0 21.0 27.0 30.0 160.0 100.04 100.0 250.0 250.0 500.0

FRAnoo (tonne-1 ) t Paved roads 0.268 0.268 0.268 0.221 0.233 0.253 0.253 1 0.22 0.292 0.170 Unpaved roads 0.124 0.124 0.124 0.117 0.095 0.099 0.099 0.067 0.087 0,040

1 FRATIO1 (tonne' ) , I Paved roads 0 0 0 0 0 0.0128 0.0128 10.0094 0.0093 0.0023 Unpaved roads 0 0 0 0 0 0 O 0 0 0 .______. .__ s______.....______. ______...... ____ _.__ ...______-I...... AMVMAX(mm/s) 259.7 259.7 259.7 239.7 212.8 194.0 194.0 177.7 177.7 130.9 ARMA (kmm's) 96.'3949 - VOESIRO(km/h) Paved roads 98.3 98.3 1 98.3 94.9 93.4 81.6 88.8 88.8 84.1 Unpaved roads 82.2 82.2 82.2 76.3 68.4 71.9 71.9 72.1 72.1 49.6

3w (km(h/m) Paved roads 7.31 7.31 7.31 7.31 3.29 3.29 ! 3.29 3.29 3.29 3.29 Unpaved roads 4.32 4.32 4.32 4.32 6.36 6.36 6.36 6.36 6.36 6.36

1 13 0.274 0.274 0.274 0.306 0.273 0.304 1 0.304 0.310 0.310 0.244

I a2 0.0289 0,0289 0.0289 0,0436 0.0524 0.05 62 0.0627| 0.0627 0.0724

Source: Watanatada et al. (1987). VEHICLE SPEEDS 107

Where Ql - road roughness (Ql* units) RHO - mass density of air (kg/m3) - 1.225 (1-2.26 A 10-5)4.225 where A - altitude (meters) CD - aerodynamic drag coefficient of vehicle (dimensionless). AR - projected frontal area of vehicle (m2).

Of the elements making up VDRIVE, only HPDRIVE was estimated, the remaining elements being specified prior to estimation. To aid users default values for CD, AR, LOAD, TARE are given in Table A4.1 below. HPDRIVE as estimated is also given there.

(b) VBRAKE

VBRAKE - 0 if CR - RF/1000 > 0

- -736 HPBRAKE / 1000 GVW g(CR+GR), otherwise where: HPBRAKE - maximum used braking power (metric h.p.).

Of the elements making up VBRAKE, HPBRAKE is the only one estimated from the data, the remaining elements being specified prior to estimation. Estimates of HPBRAKE are given in Table A4.1.

VCURVE - (RC(FRATIO + 0.01 Sp)g)1/2

where RC - 180,000(r max (18/lI,C))

C - horizontal curvature in degrees per km

II - 3.14159

SP - superelevation C%)

g - 9.81 (m/s 2 )

FRATIO - maximum "perceived" friction ratio (dimensionless).

- max (0.02, FRATIO0 - (FRATiO1)(LOAD)).

The parameters FRATIOO and FRATIO1 are estimated from the data and estimates are given In Table A4.1. Details of the vehicle used In the Brazil study can be found In Table A4.2. For cases in which superelevatIon is not known Watanatada et al. (1987) give the following formula relating superelevatlon to curvature:

SP - .012C (paved roads)

- .017C (unpaved roads). 108 VEHICLE SPEEDS

Users are warned that this formula Is derived from data on Brazilian roads and may not apply generally. Alternative assumptions can lead to large changes in predicted curvature effects.

(d) VROUGH

VROUGH - ARVMAX/(.0882 Ql) where: ARVMAX - "maximum allowable" average rectified velocity of suspension motion of the standard Opala-Maysmeter vehicle.

QI - surface roughness (Ql* units).

The parameter ARVMAX Is estimated and reported in Table A4.1.

(e) VDESIR

VDESIR is an estimated parameter, reported In Table A4.1. For roads narrower than 5m, VDESIR should be replaced by [VDESIR - Bw W']/3.6 where W' Is 5.0 minus actual road width and Bw Is given In Table A4.1.

Some parameters entering VDRIVE, VCURVE, and so forth, like AR (proJected frontal area) and CD (aerodynamic drag coefficient) were not measured during roadside speed observation and were assigned to vehicle classes using Information on typical Brazilian vehicles. Other parameters not obtained during roadside speed observation (HPDRIVE, HPBRAKE, FRATIO, ARVMAX, and VDESIR) were estimated using the speed data.

A relationship between expected attained speed (denoted V In the main text) and the expected values of the constraining velocities whose formulae are given above Is obtained by assuming that the constraining velocities have Independent Welbull distributions with common shape parameter denoted P. This leads to a model In which speeds attained by vehicles have Welbull distributions with location parameters given as functions of VDRIVE, VBRAKE, etc., expressions for which are given above. A Weibull regression model had been developed earlier in the Brazillan study (Chesher 1982) to analyze pavement deterioration data. There, In the analysis of time to pavement failure, data were censored and parameters were estimated by maximum likelihood. The vehicle speed data were not censored so parameters could be estimated at lower cost, using non-linear least squares (Chesher 1982). It turns out that this was a good choice, because prior to estimation the logarithms of vehicle speed data were averaged by vehicle class and road section. Since averaging alters the distribution of the data (inducing normality), maximum likelihood estimates, had they been calculated assuming data distributed according to a Welbull distribution, would have been Inconsistent, the effect on estimates of the shape parameter P being particularly severe. However, the regression function for log speeds Is unaffected by averaging so non-linear least squares applied to the log speed data can produce consistent estimates. VEHICLE SPEEDS 109

Estimates of HPDRIVE, HPBRAKE, etc., are given in Table A4.1 together with estimates of the Welbull shape parameter (,O)and of the across section residual variance of log vehicle speeds (a2). To compute predicted speed (in meters per second) for a homogeneous road section one calculates:

exp (a2 /2) V-

I(VDRIVE)1l/P+(VBRAKE)1/P+(VCURVE)1 '+(VROUGH) '/P + (VDESIR) l0iP

The term exp (U2/2) Is Introduced to correct for bias Induced by exponentiating predictions of log (speed) (see Chapter 3), the non-linear least squares estimation being performed using average log (speed) as dependent variables.

The model described above was estimated using data obtained on relatively short homogeneous sections of highway for vehicles believed to be travelling at speeds close to constraining velocities. In applications in which speeds are predicted on long routes the speed model should Ideally be used to predict speeds over homogeneous sections, account being taken of section lengths and of the possibility that vehicles do not attain steady state speeds. In practice this requires a detailed description of configurations of bends, gradients, and surface condition which may not be available to the highway planner at the time at which an investment appraisal Is performed.

In situations in which detailed Information on highway characteristics Is not available Watanatada et al. (1987) recommend regarding a long route with variable highway characteristics along Its length as composed of two subroutes, one rising, one failling,each with highway conditions constant along its length. On both of these subroutes curvature, roughness and superelevation are constant and equal to their distance weighted averages over the original non-homogeneous route. On the rising subroute gradient is set equal to + RF/1000 (RF - rise + fall, m/km) and on the failing subroute to - RF/1000 where RF is the distance weighted average of rise + fall for the non-homogeneous route. Thus, a route which is flat and straight for half its length and hilly and winding for the remainder Is to be regarded as two routes, each with half the length of the original, one rising, one falling, each with constant gradient, roughness and superelevation, each following a curve throughout Its length given by the distance weighted average of curvature of the route of interest. Taking the harmonic mean of the two speed predictions that result (VU and VD) and multiplying by 3.6 to convert to kilometers per hour the predlcted route speed:

V - 3.6/(0.5(V- 1 + V-1)) u D

Is obtained. 110 VEHICLE SPEEDS

A4.3.2 Brazil: equations estimated from user survey data

The Brazilian study reports two equations obtained using user survey data (GEIPOT 1981). Notation is as follows:

V - vehicle speed (km/hr)

Ql - surface roughness (Qi Index)

RF - average rise + fall (m/km)

0 ADC - average degrees of curvature ( /km)

T - 0 if one round trip per day

- 1 If two round trips per day

D - one way route distance (km).

Passenger cars

V - 66.19 - .270RF - .192QI + 7.26T + .068D (-2.01) (-7.83) (3.41) (6.20)

R2 _ .65, S - 7.19, 91 routes, 4 companies.

Buses

V - 64.07 - .1457QI - .0616ADC + .0182D (-7.07) (-3.79) (5.12)

R2 - .66, S - 6.19, 52 routes, 12 companies.

Approximate Means and Ranges of Explanatory Variables

Cars Buses Variable Min Max Mean Min Max Mean

Ql (Ql Index) 21 191 55 24 197 74 RF(mIkm) 15 44 31 ADC(°/km) 7 189 41 T(0-1 trip dummy) 0 1 .67 D (km) 17 482 193 44 705 228

Source: GEIPOT (1981). VEHICLE SPEEDS 111

Table A4.2: SpecIfication of Vehicles for Brazilian Speed and Fuel Model

Engine Approx.j 1Approx. rated Maximum tare gross Weight No of SAE 3 weight weight Classini- No of Heavy Fuel I rated power No. of Representative 2 Vehicle type (tonms) (tonnes) cation1 tires Axles Type IMetric hp cylinders Vehicle

Brazil4.

Passenger car 1.0 1.2 L 4 0 G 49 4 VW 1300

(small) ______. 4

Pasenger car 1.2 1.5 L 4 0 148 6 Opala (medium) _ _ _ I

Passenger cars 1.7 1.9 L |4 G 201 8 Dodge Dart (large)

Utilities 1.3 2.1 L 4 0 G 61 4 VW Kombi

____ _ ~-T ---- ~-1---~-i------t---t __--- - LargeBuses 8.1 11.5 H 6 2 D 149 6 Merc.Benz 0362 _ . _...... ,_-_------.-- --- . t -' Light trucks 3.1 6.1 H 6 2 aG 171 8 Ford-40O (gasoline) I _.'__1.__[._.

Light truclss 3.3 6.1 H 6 2 D 103 4 Ford-4000 (diesel) -

Medium Trucks 5.4 15.0 H 1 6 2 D i 149 6 Merc.Benz 11135.

Heavy Trucks 6.6 18.5 . H 10 3 D 149 6 Merc.Benz 11136.

Articulated 14.7 40.0 H 18 5 D 289 6 Scania 110t39 Trucks, I

Notes:

1. 1 = light vehicle [rated gross weight under 3.5 (metric) tonnes; H heavy vehicle (rated gross weight of 3.5 tonnes or more)]. 2. The number of heavy axles equals the number of axles of the vehicle if it is a heavy vehicle andzero otherwise. 3. S = gasoline engine; D = diesel engine. 4. Tare weights of Brazil vehicles include 150 kg weight of two drivers. 5. Excludes third rear axle. 6. Includes third rear axle.

Source: Watanatada et al. (1987). 112 VEHICLE SPEEDS

Remarks

Data on car journey times were collected from four companies engaged In collecting bank correspondence on a regular basis from bank branch offices. Information concerning vehicle speeds on 91 routes was obtained from timetables and, In the few cases where timetables were not adhered to, from actual journey time records compiled In drIvers' log sheets. Unofficial stops were minimal since this type of business requires strict control on the part of the company manager in order to ensure a secure and reliable service. The equatlon for car speeds was estimated by ordinary least squares.

Bus speed data were compiled from tachograph records of 52 vehicles. Forty-one of these observations were used in an exercise, described In the main text and reprinted in Watanatada et al. (1987), to assess the predictive accuracy of the Brazil speed model. Speed was calculated as total round trip time less stops divided by total round trip distance. The equation was estimated by ordinary least squares. For reporting, the 01 coefficients have been adjusted to reflect the changes in calculation of Ql subsequent to the car and bus speed analysis reported In GEIPOT (1981). and the resulting coefficients have been converted so that they apply to roughness measured In mm/km.

A4.4 India

The Indian study reports equations derived from roadside speed data and equations derived from user survey data. We present the equations based on roadside speed data first.

A4.4.1 India: roadside speed equatlons

The notation used In the Indian study is as follows:

V - vehicle speed (km/hr)

RS - rise (m/km)

FL - fall (m/km)

0 CV - average degrees of curvature ( /km)

RG - average surface roughness (mm/km)

W - road width (m).

Cars

V - 60.60 + 1.046W - .192RS - .184FL - .0078CV - .0036RG (2.28) (-6.67) (-6.21) (-4.20) (-7.00)

76 averages obtained from 2,920 vehicle speeds. VEHICLE SPEEDS 113

Buses

V - 54.97 + .609W - .301RS - .228FL - .0077CV - .0022RG (1.35) (-10.27) (-7.03) (-3.81) (-6.67)

76 averages obtained from 2,527 vehicle speeds.

Trucks

V - 47.32 + 1.056W - .269RS - .265FL - .0099CV - .0019RG (2.15) (-8.27) (-8.25) (-3.70) (-4.43)

76 averages obtained from 3,769 vehicle speeds.

Approximate Ranges and Means of Explanatory Variables

Variables Min Max Mean

W(m) 3.7 7.0 5.36 RS(m/km) 0 91.0 11.35 FL(m/km) 0 91.0 11.63 CV(0 /km) 1 1,243 274 RG(mm/km) 2,050 15,250 4,494

Source: CRRI (1982).

Remarks

The Indian study also reports a speed equation for 2 wheeled vehicles - scooters and motorbikes - which Is as follows:

V - 47.19 + 0.941W - 0.12ORS - 0.067FL - 0.0048CV - .0021RG (2.33) (-4.68) (-2.62) (-2.86) (-7.41)

76 averages obtained from 2,236 vehicle speeds.

Vehicle speeds were observed at 76 test sections. As In the Kenyan and Caribbean studies roads with non-zero gradients generate two test sections, one for each directlon. Speed measurements were made using observers wlth stopwatches who recorded registration plates. On the straighter sections a radar speedometer, hidden from drivers' view, was used. Care was taken to measure free flow speeds and data obtained while slow moving traffic were hinderlng other vehicles were discarded. Individual speed data and site average speeds were subjected to analysis. The results reported above are obtained by applying weighted least squares to site averages, weightIng observations by (SD/n)- 1 where SD Is the 114 VEHICLE SPEEDS estimated standard derivation of speeds at sites and n is the number of observations taken at a site. This has the effect of giving more weight to speed averages at sites where more observations are available and where speeds are less variable. Unfortunately the R2 statistics reported In CRRI (1982) are obtained from the weighted regression and do not give a good indication of the power of the equations in explalning speed variations. Ordinary least squares estimation with individual vehicle speed data gave R2 statistics varying from 0.18 (two-wheelers) to 0.59 (buses). The Interpretation to be given to reported estimates of disturbance standard deviations (S) In CRRI (1982) Is unclear given the use of weighted least squares. Values of S and R2 obtained In ordinary least squares applied to site averages and to individual vehicle data are shown below.

OLS (Average OLS (Individual Vehicle Class Vehicle Speeds) Vehicle Speeds) R2 S R2 S

Cars .75 5.12 .48 11.5 Buses .81 5.16 .59 9.4 Trucks .73 5.49 .18 17.8 2-wheelers .65 4.26 .28 9.4

Source: CRRI (1982).

R2 statistics for the weighted least squares estimates will be somewhat below those given above, but the resulting estimates are more efficient. The majority of test sections are paved, and only 6 have roughness exceeding 6,000 mm/km.

A4.4.2 India: user survey speed equations

Equatlons reported In CRRI (1982) were re-estimated by generalized least squares allowing for company specific errors and reported In Chesher (1983). As reported by CRRI, speed equations Included the ratio of roughness to width as an explanatory variable, roughness and width being excluded as main effects. In each of the equations reported below one of roughness and width are excluded where muiticollinearity Is so severe as to cause extreme Imprecision In estimates when both variables are Included. Symbols are as In the previous subsection.

Cars

V - 58.66 - .0023RG - .399RF (-2.67) (-3.61)

Su - 2.63 Sw - 2.64.

54 vehicles, 10 companies. VEHICLE SPEEDS 115

Buses

V - 30.56 - .00064RG - .315RF + 2.29W (-3.61) (-12.62) (8.70)

Su - 1.00 Sw - 4.11.

639 vehicles, 20 companies.

Trucks

V - 31.36 - .307RF - 1.48W (-5.11) (2.39)

Su - 5.16 Sw - 3.00

232 vehicles, 30 companies

Approximate Mean and Ranges of Explanatory Variables

Cars Buses Trucks

Variables Min Max Mean Mln Max Mean Mln Max Mean

RG(mm/km) 3,416 6,955 4,987 2,925 12,072 5,953 2,960 15,550 5,331 RF(m/km) 3 36 10 1 50 15 1 58 13 W(m) 4.7 7.0 6.2 3.7 7.2 5.2 3.8 7.0 6.0

Source: Chesher (1983).

Remarks

Speed data were obtained from timetables and operators' schedules and It Is noteworthy that there is substantial across company variation In speeds (large Su) which, In the case of trucks, is substantially greater than the within company speed variation. Multicoilinearity is too severe to allow precise estimates of the separate effects of rise + fall, width, curvature, and roughness to be estimated and the equations reported above should be regarded as providing Indications of the magnitudes of speed responses In transport operations under normal Indian traffic conditions. I I CHAPTER5 Fuel and Lubricant Costs

Fuel costs are an important component of vehicle operating costs. For some vehicle classes, in some countries, they make up more than 50 percent of costs per unit output. It is a relatively simple matter to measure fuel consumption accurately and fuel costs are an obvious candidate for study using experimentation. In each of the four country studies substantlal proportions of the study budgets were devoted to collecting fuel consumption data, most of the data being obtained from experiments performed using specially purchased fleets of test vehicles. Additionally, fuel and lubricant consumption data were collected from vehicles participatIng In road user surveys.

The models developed from the fuel experiment data write fuel consumption as a function of vehicle speed, vehicle characteristics and highway characteristics - gradient, and In some models roughness, but not curvature, except to the extent that curvature affects speed. In the model used in the Brazilian study, fuel consumption Is expressed as a function of used vehicle power which Is, In turn, predicted as a function of vehicle speed and highway and vehicle characterlstics. The models are described In Section 5.1.

Since fuel consumption experiments are conducted under rather artificial conditions, some care needs to be taken In using their results to predict fuel consumption under normal operating conditions. The vehicles used In fuel experiments were new vehicles representative of the types of vehicles found In the study areas, but maintained to high standards. Further, they were driven so as to produce high quality data under controlled conditions, in a way rather different from that found in commercial operations. All the equations reported later that derived from fuel experiment data are based on records of fuel consumption at constant speeds under free flow conditions over short road sections, along which highway conditions varled negligibly. In commercial operations, one can expect to find fuel costs rather higher than those predicted by the studies' experiment based fuel equations and all the studies report adjustment factors to raise predictions to the sorts of levels likely to be encountered In practIce. The Kenyan and Caribbean studies report relatively small adjustments but these are apparently Intended to allow only for the Increases In fuel costs that arise because of speed changes, whose effect Is not modelled In the studies' experiment based fuel equations. The adjustments recommended by the Brazilian and Indian studies are larger and were obtained by comparing experIment based fuel predictions with fuel consumptions obtained from user survey vehicles.

Estimates of relationships between fuel consumption and vehicle speed and highway characteristics are presented and compared In Sections

117 118 FUEL AND LUBRICANT COSTS

5.2 and 5.3. An appendix provides tables showing predictions of fuel consumption and associated speed predictions for combinations of highway roughness, vertical and horizontal geometry. Section 5.4 provides some perspective on the results. Finally, Section 5.5 deals with consumption of lubricants. In the next section the models applied to the fuel consumption data are described.

5.1 FUEL CONSUMPTIONMODELS

Three distinct approaches were taken to modelling fuel consumption in the four studies. The models applied to fuel experiment data in the Indian, Kenyan, and Caribbean studies relate fuel consumption directly to vehicle speed and highway characteristics, exploiting functional forms avaliable In the late 1960s (see particularly Everall, 1968). They do not take explicit account of vehicle characteristics, estimating separate models for each vehicle type used In the experiments. The Brazil study model fitted to experimental data Is more ambitious and was constructed with the intention of allowing users to modify the model so that It could be used to predict fuel consumption for vehicle types not observed during the fuel experiments. Additionally, In the Indian and Brazilian studies, simple linear models were fitted to user survey fuel consumption data, relating fuel consumption directly to highways' and, In some cases, vehicles' characteristics. These user survey data relate to fuel costs Incurred over many hundreds of thousands of kilometers of travel and are particularly Interesting because they are informative about the fuel costs actually experienced by firms In the course of their business operations. Slnce fuel experiments are, by their nature, rigidly controlled, there Is no scope for observing behavioural and, In particular, economic responses In the data they produce.

All the models fitted to experimental data predict fuel consumption as a function of vehicle speed. In the subsequent sections in which results are reported and predictions presented, the speed models described In the previous chapter are used to obtain the required speed predictions. Thus disagreements amongst the studies concerning predicted fuel consumption will reflect differences not only In the fuel-speed models, but also in the speed-highway characteristics models. We can also expect to see differences In predictions due to dlfferen_e In vehicle types used In the four studies.

There Is considerable evidence suggesting that at constant speed, on other than steep grades, the relationship between fuel consumption (per unit distance) and vehicle speed is U-shaped, relatively high fuel consumption occurring when speeds are relatively high or relatively low. Claffey (1960) presents graphs In which this effect Is evident. See also Sawhill and Firey (1960). As estimated, the fuel consumption models reported below, have this U-shaped form. In the Indian, Caribbean, and Kenyan studies an equation of the form:

(1) F - a + b/V + cV 2 FUEL AND LUBRICANTCOSTS 119

Is used, in which F is fuel consumptionper unit distance and V is vehicle speed. This equation, originally used by Everall (1968) describes a U- shaped curve (assumingb,c positive), fuel consumptionbeing at a minimum when vehicle speed Is equal to (b/2c)1 /3. In practice the coefficient "a" Is written as a function of highway characteristicslike rise, fall, and surface roughness, and of vehicle characteristicslike gross vehicle weight and power to weight ratio. In the Kenyan and Indian study models the coefficient "a" is linear in rise (m/km) and fall (m/km, expressed as a positive rate of fall). In the Caribbean study "a" is linear in the product of gross vehicle weight and rise, and quadratic In fall, fuel consumption falling as fall increases and then rising as it increases further. In the Kenyan, Indian, and Caribbean studies' models the effect of changing highway characteristics is to shift vertically the U-shaped fuel-speed relationship.

There is some evidence to suggest that as gradient increasesthe U-shaped fuel-speed relationship is shifted vertically and to the left, so that fuel minimising speed reduces as gradient increases- see for example the graphs in Claffey (1960). In analysis of the Kenyan study data subsequent to Hide et al. (1975), the equation:

2 (2) F = exp(a + tV + 7V ) was fitted (Chesher 1977), the coefficients, a, O, and being written as distinct linear functionsof rise and fall, a depending additionallyon variables describing road surface conditlon. This equation describes a U- shaped fuel-speed relationship (7 > 0), gradient fixed, fuel minimising speed being given by (-P/27). Since this ratio is a function of gradient, fuel minimising speed alters with gradient, and the Kenyan data indicates that it decreaseswith gradient on uphill sections. The equation gives fuel consumption as a non-linear function of gradient for which there Is also some support, both In the Kenyan data, and in the literatureon fuel consumptionmodelling. Results obtained from the Kenyan study data using equation (2) are given in Appendix A.

The Brazilian model too predicts fuel consumption (volume per unit distance) as a U-shaped function of vehicle speed under certain highway conditions, with fuel minimising vehicle speed varying as highway characteristics alter. The Brazilian study model assumes that fuel consumption per unit time period Is a polynomial (convex) function of used vehicle power and vehicle speed, the form of the relationshipbeing determinedby reference to the fuel experiment data. These data give Informationon vehicle speed, but not on used vehicle power so that the latter has to be estimated. This Is done using Newton's force balance equation for bodies not subject to acceleration(reflecting the constant speeds adopted In the fuel experiments)which relates used vehicle power to vehicle speed, and vehicle and highway characteristicswhich are recorded In the fuel experiment data. When the model is used to predict, vehicle speed Is typically not known and It is predictedusing the model described In the last chapter. As for the speed model, on heterogeneousroutes with non-zero gradients, the model Is applied once for uphill travel and once for downhill travel. Fuel consumption per unit distance Is predicted by the distance weighted arithmeticmean of the two predictions that result. 120 FUEL AND LUBRICANT COSTS

Most of the development of the Brazil study model Is In terms of fuel consumption per unit time period (UFC, ml/sec) which is written as a function of vehicle horsepower delivered at the driving wheels (HP) and engine speed (RPM). Horsepower delivered at the driving wheels Is written as the product of vehicle speed (V) and drive force (DF), the latter being related to vehicle and highway characteristics for constant speed travel by:

(3) DF - mg GR + mg CR + p CD AR V2/2.

Here, m Is vehicle mass, g Is the gravitational constant (9.81m/sec2), GR Is road gradient - positive or negative, as appropriate, CR is the coefficient of rolling resistance (a vehicle class specific function of road roughness), p Is the mass density of air, and CD and AR are respectively an aerodynamic drag coefficient and the vehicle's projected frontal area. In equation (3), which Is Newton's force balance equation for bodies not subject to acceleration, the three right hand side terms refer to, from left to right, gravitatlonal, roiling and air resistance.

In order to estimate the model values for vehicle weights, projected frontal areas and aerodynamic drag coefficients were obtained by measuring the vehicles purchased to take part In fuel consumption experiments. In practice, in highway appraisal these vehicle characteristics may not be known In which case It may be possible to use default values provided by Watanatada et al. (1987) and reproduced in Appendix A. These were obtained from study of the quite wide range of vehicles used In the Brazil study fuel experiments but they should be used with caution, and whenever possible values obtained in the environment In which the appraisal Is being performed should be employed. Only the Brazil study model allows this flexibility though Its predictive ability for vehicle designs not studied durlng the Brazil study fuel experiments has not been extensively studied and the possibility that model coefficients may vary across vehicle types has to be borne In mind. Empirically derived equations provided In Watanatada et al. (1987) enabling the coefficient of rolilng resistance to be predicted as a function of road roughness are also reported In Appendix A, one for cars and light goods vehicles, one for buses, medium and heavy trucks.

During estimation of the Brazilian fuel consumption model, engine speed (RPM) was estimated using the equation:

(4) RPM - 60 (V) (DRT) (GRT) / (TC) where RPM - engine speed In revolutions per minute V - vehicle speed (m/sec) DRT - differential speed ratlo GRT - gear speed ratio TC - tire circumference (m). FUEL AND LUBRICANT COSTS 121

In practice information on DRT, GRT, and TC Is unlikely to be available and GRT depends on drivers choice of gears. In applications Watanatada et al. (1987) recommended setting RPM to a value (CRPM In Appendix A) varying across vehicle classes, but not varying with vehicle speed or highway characteristics. Thus in using the model to predict fuel consumption there is an Implicit assumption that engine speed is constant with respect to changes In either vehicle speed or highway characteristics.

The Brazilian speed model, when estimated, produces an equation not dissimilar to that specified by Everall (1968) and used in the other three studies, fuel consumption being given (other variables fixed) by the sum of a term proportional to the inverse of speed and a polynomial In vehicle speed. It is interesting to note also that In the Brazilian speed model gradient appears multiplied by gross vehicle weight, which Is the form specified by Morosiuk (1983) in his analysis of the Caribbean study data. The quadratic effect for gradient (speed fixed) Is similar to the non-linear effect reported In Chesher (1977) for the Kenyan study data.

In the next three sections we employ the "aggregate" Brazil study fuel prediction model which, like the "aggregate" speed model, is intended for use on heterogeneous highways whose characteristics are recorded as distance weighted averages of the varying characteristics along the highway's length. As for the speed model, there are other versions of the fuel consumption model for use when more detailed information Is available and details can be found In Watanatada et al. (1987).

All the models described In this section were estimated using data obtalned from vehicles travelling at constant speeds on relatively short sections of road along which highway characteristics do not vary. To predict fuel consumption over long routes along which highway characteristics vary, one can apply the models using average measures of hlghway characteristics and predictions of average vehicle speed. But then care Is required because the non-linearity of the fuel consumption equations implies that fuel consumption on a uniform route will not be equal to fuel consumption on a non-uniform route with average highway characteristics equal to the characteristics of the uniform route.

In practice some correction to fuel consumption predictions Is required In order to allow for features of real-lIfe commercial operation. All the studies report adjustment factors, reproduced here in Table 5.1. In the next sections, In which fuel predictions are given in graphs and tables, these adjustment factors are applied.

Further details concerning the Brazil study model are presented in Appendix A, where all the studies' equations are given In the forms In which they were originally derived. In the next three sections the results are given for each vehicle class In turn. First, we consider the results for cars and light goods vehicles.

5.2 FUEL CONSUMPTION EQUATIONS AND PREDICTIONS: CARS AND LIGHT GOODS VEHICLES

The cars and light goods vehicles used In the fuel consumption experiments differed quite substantially. Table 5.2 shows brief details of their specification. 122 FUEL AND LUBRICANT COSTS

Table 5.1: AdJustment Factors to Convert Fuel Consumption Derived from Constant Speed ExperImental Data to Fuel Consumption as Experienced in Commercial Operation

Country VehicleClass MultiplyFuel Consumptionby

india(1 ) Cars 1.64 Buses 1.28 Trucks 1.31

Brazil(1) Cars and Light Goods 1.16 Busesand Trucks 1.15

Caribbeanand Cars and Light Goods 1.08 Kenya(2 ) Trucksand Buses 1.13

Note: These adjustments are used In producing graphs and tables of predictions reported later. (1) Obtained by comparing fuel model predictions with user survey fuel consumption data. (2) Obtalned from experiments into effects of speed change cycles on fuel consumption. Source: Hide et al. (1973), Morosluk and Abaynayaka (1982), GEIPOT (1981), CRRI (1982).

Fuel consumption is Improved with the fitting of radial tires, especially where these are steel belted. The Kenyan and Caribbean experimental vehicles were equipped with radial tires although whether these were steel belted is not reported. The Brazilian and Indlan vehicles were fitted with conventional bias ply tires although the Indlan study does report also the results of fuel consumption experiments carried out using cars and auto rickshaws equipped with non-steel belted radial tires. Tire choice can be expected to exert a significant influence on fuel consumption and this complicates inter-study comparisons.

Fuel consumption equations as reported In the four studies are given In Appendix A and summarized In Table 5.3. The relatively complex Brazilian study equation does not appear In this table. All but one of the equations In Table 5.3 are obtained from experimental data.

Comparing the car equations from the Indian, Caribbean, and Kenyan studies, there Is, for all but two of the equations, quite close agreement concerning the effect of gradient on fuel consumption, vehicle speed fixed. The Indian study equation for the Premier Padmini records relatively small gradient effects as does the Indlan study equation derived from survey data but note that the vertical geometry coefficient In the latter equation relates to rise + fall whereas In the equation derived from the fuel experiments there are separate coefficlents for rise and fall.

Flgure 5.1 shows the relationships between fuel consumption and vehicle speed for smooth, flat roads. There are marked differences in the Table 5.2: Fuel ExperimentVehicle Fleets: Cars and Light Goods Vehicles

Country Vehicle Fuel Number Engine Engine Power Tire Fire Vehicle Vehicle Make rype Cylinders Capacity (kw) Size ype Weight (cc) (kg)

Kenya Car G 4 1598 53 at 50OOrpm 165 x 13 R 892 Ford Cortina Station Wagon

Caribbean Car G 4 1593 48 at 4r50rpm 165 x 13 R 1115 Ford Cortina Station Wagon1 .

Brazil Small Car G 4 32 at 4600rpm C 1200 Volkswagon 1300 Medium Car* Q 6 96 at 4000rpm C 1500 (.M. Chevrolet Opala Large Car G 8 131 at 4400rpm C 1900 Chrysler Dodge Dart

India Small Car a 4 1089 35 at 480Orpm 5.20 x 14 C 1215 Premier Padmini Medium Car* a 4 1489 31 at 4200rpm 5.90 x 15 C 1528 Ambassador

Kenya Light Goods a 6 2625 64 at 4500rpm 150 x 16 R 1105 Landrover Vehicle w Caribbean Light Goods G 4 1996 52 at 4500rpm 185 x 14 R 2600 Ford Iransit Vehicle I.I

Brazil Utility* G 4 40 at 4600rpm C 2100 Volkswagen Kombi Light Goods G 8 111 at 4400rpm C 6100 Ford F400 Vehicle2 . Light Goods D 4 67 at 3000rpm C 6100 Ford F4000 Vehicle2 .

India Light Goods 0 4 2350 28 at 2300rpm 6.00 x 16 C 1200 Mahindra Jeep Vehicle

Notes: 1. This vehicle was fitted with an economy carburetter and was a later version of the Kenyan model. 2. These vehicles had dual tires on the rear axles. 3. *Indicates model selected for inter-study comparisons in graphs and tables. 4. R indicates radial tires fitted, C indicates conventional biasply tires fitted. Table 5.3: Fuel Consumption (1000 km): Cars and Light Goods Vehicles

' i i ' ~~~~~~~~~~~~~~~~~~~~~Coefficients Vehicle Country Type of Road i Vehide a._nap |Class |t Study Surface ^ Make Fuel Intercept L. (V_ki_/h) Rise Fall Other Variables (1) Optimal I1/V V2 (r/km) (m/km) Speed(2). i | i _ i | | ._ {~~~~~~~~~~~~~~~~~~~~~~~~~~klanhr) Cars India Experimental Mostly paved Ambassador Petrol 10.3 1676 .0133 1.39 -1.03 +0006R 40 i Cars 0 India Experimental Mostly paved Padmini Petrol 49.88 319 .0035 0.94 -0.68 +.0019R 36 Cars India Survey(3) Mostly paved AAmbassador Petrol -138.0 6213 i .0501 0.37 +.0034R 40 2 Cars |Caribbeany Experimental Paved Ford Cortina Petrol 24.3 969 .0076 1.33 -. 063 +00286FL 40 , Cars ' Kenya ' Experimental IPaved Ford Cortina Petrol 53.4 499 .0059 1.59 -0.85 35 j Cars Kenya Experimental Unpaved Ford Cortina Petrol 46.9 614 .0079 1.72 -1.07 +0.82L + 0.00113R 34 Light Goods I India Experimental I Mostly paved Mahindra Jeep Diesell 30.8 2258 i .0242 1.28 -0.56 +.0012R 36 2 Light Goods Caribbeani Experimental IPaved ;Ford Transit Petrol 72.2 949 .0048 2.34 -1.18 *.0067FL 46 v i i . , i t i ~~~~~~~~~~~~~~~~+1.12(GVW- 2.11)Rt4 Light Goods Kenya Experimental Paved Landrover Petrol 74.7 1151 .0131 1 2.91 -1.28 35 Light Goods Kenya Experimental Unpaved Landrover Petrol 72.8 844 .0137 2.83 -1,31 +1.761 + .0011R 31 31___ ~~~~~s_ .. 1._ __ _ _ . Notes: Equations for vehicle speed are linear in explanatory variables with coefficients as given above.

(1) R = surface roughness (B9: mm/km) FL = fall(/kin) L = depth of loose material (mm) GVW = gross vehicle weight (tonnes) RS = rise (m/km).

(2) "Optimal speed" is speed at which predicted fuel consumption is minimized.

(3) Coefficient recorded in "rise" column is coefficient on rise plus tall (m/kin) (Survey only). FUEL AND LUBRICANT COSTS 125 curves. The Indian Ambassador vehicle has a particularly U-shaped curve with a fuel consumption minimising speed around 40 km/hr, rather higher than that for the Indian Premler Padmini which has a relatively shallow U- shape for Its fuel consumption-speed curve. The difference between the two Ford Cortinas used in Kenya and the Caribbean is noticeable. The Caribbean vehicle was fitted with an "economy" carburettor which gives lower fuel consumption at all but the slowest speeds.

For the light goods vehicles and utilitles the gradient effects are somewhat larger than those found for cars, the exception being the Indian study Mahindra Jeep. Note that this is a diesel fuelled vehicle unlike the Kenyan Land Rover and the Caribbean Ford Transit van. The larger gradient effects found for these vehicles may In part reflect their higher fuel consumption.

The light goods vehicles and utilities have fuel consumption-speed relationships that differ quite substantially. Figure 5.2 shows the relationships for smooth, flat routes. The diesel fuelled Indian Mahindra Jeep, like the Indian Ambassador car, has a relatively U-shaped fuel

Figure 5.1: Car Fuel-Speed Equations

0 0 - N

It 0 _ in 0

+3 0L E

4 11_ ~~~~~~~~~~~~~~~~~~~nC.,t3fl

- indJ t)

0 20 40 60 80 100 120

vshiclQ spead km/hr roughness-2000 mm/km. risa-fall-0 m/km 126 FUEL AND LUBRICANT COSTS consumption-speed curve. The Ford Transit van studied In the Caribbean has a particularly flat fuel consumption-speed curve.

Graphs of car fuel consumption predictions are shown in Figures 5.3 and 5.4. A striking feature of these graphs Is the relatively high fuel consumption predicted for the Brazilian medium car, a 6-cylinder Chevrolet Opala. Figure 5.3 shows the effect of gradient on fuel consumption. The studies predict only moderate effects. The Brazilian model shows almost no gradient effect for gradients less than 6 percent and the Kenyan model's predictions are rather similar. The Caribbean model predicts the largest effects. Figure 5.4 shows the effect of curvature on fuel consumption. Note that curvature does not appear in any of the constant speed fuel models obtained from experimental data so the effects that are shown in Figure 5.4 are the result of speed adjustments. For all but the Brazilian equation the curvature effects are very small but the large Brazilian curvature effect is something of a puzzle since speed falls markedly as curvature increases which might lead us to expect the sort of

Figure 5.2: Fuel-Speed Equations: Light Goods Vehicles

0 m E o0 oN N L L

aL -

jJ 4.) _. - 4- 0 20 4

0 20 40 60__12

vehicle spead km/hr roughnQss=2000 mm/km. ris cfa1 1=0 m/km FUEL AND LUBRICANT COSTS 127

Figure 5.3: Fuel Consumption (F) versus Rise + Fall (RF): Cars

275

B 250

200

175

150' …------

I SD ~~~------_-C ------

125_

75 _ __-

0 ...... - ...... RF 0 1 0 20 s0 40 50 60 70 80 90

Eou tions 3 = Brazil. G. M. Opala Sedan I = India, Anbasador Sedan K = Kenya, Ford Cortina Stationwagon C = Caribbean, Ford Cortina Stationwagon.

UnJ§&: F Fuel Consumpton (t/1O3km) RF = Rise plus Fall (m/km) C = Curvature (0/kmn) R = Roughness, Bl (mm/km). IRI (m/km)

Variables not Plotted: C = Curvature = 50C/Ikrn R = Roughnes = 5500 31 (mm/km), 6.8 IRI (m/km) L = Looseness (Kenya only) = 1 mm ALT = Atitude (Brazil only) 0 GVW = Gross Vehicle Weight (Brazil only) = 1.4 tonnes

For other Brazilian speed model variables not plotted, see default values in the Appendix to Chapter 4. 128 FUEL AND LUBRICANT COSTS

Figure 5.4: Fuel Consumption (F) versus Curvature (C): Cars

30C _ -

250_

225 __-

200-

175-

150

125

100 K -- I

75-

25-

o SOCs *0 00 600 0 100

Fuel Consumption (F) versus Roughness (R): Cars

B (unpaved) ,,

272 - B (paved)

220 --

200

175-

------100

1225

75-

252

2X~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~,2 000

I. 5.1 7.- I. 12I 10R,IRI 2.8 5.1 7.4 9.5 12.0 14.0 FUEL AND LUBRICANT COSTS 129 small reduction In fuel consumption with Increasing curvature evident In the Indian and Caribbean study equations predictions. The predicted roughness effects are shown In Flgure 5.5. The Brazilian model predicts a substantial Influence for roughness, unlike the other three models.

Figures 5.5 to 5.6 show graphs of predictions for the utilities and light goods vehicies. Gradient effects are much larger for these vehicles than for cars, once speed Is allowed to vary In accordance with the speed models. As with cars, the Brazilian model predlcts higher fuel consumptions than either the Kenyan or the Caribbean models. The Brazilian fuel equation Is derived from data on gasoline fuelled Volkswagen Kombis which may show higher fuel consumption. However, a part of the reason for the high fuel consumptions predicted by the Brazilian model may be the speed maximising assumption built into the Brazilian speed model. As for cars the roughness effects predicted by the Brazilian model are a good deal larger than those predlcted by the other models. Appendix C contains tables of predicted car and utility fuel consumption and associated speed predictions.

5.3 FUEL CONSUMPTION EQUATIONS AND PREDICTIONS: BUSES AND TRUCKS

Details of the buses and trucks used In fuel experiments In the four studies are set out In Table 5.4. The technical specificationsof the medium trucks used In the fuel experiments In the four country studies were quite similar. All were two axle vehicles,of conventionaldesign, and used non-turbochargeddiesel engines of around flve llters (80 - 96 kw) to carry payloads between 4.5 and 7.6 tonnes. The test trucks In the Brazilian study Included two rigid, three axied heavy trucks (one with a small hydraulic crane to load test vehicles with concrete blocks) and a large articulated vehicle comprising a two-axle tractor and three-axle semi-trailer.

In the Brazilian study a bus was Included In the experimentalfuel fleet because many firms used monocoque or Integrallyconstructed buses on paved routes In Brazil and it was thought that the fuel consumptlonof these vehicles might differ from that of conventionalfront engine chassis buses. Large buses in Kenya and India were of the latter type which is essentially a modificationof a medium truck design. The Kenyan and Indian study teams believed that fuel consumptlondata from the medium truck would form an adequate basis from which to predict bus fuel consumption.

Fuel consumptionequatlons as reported In the four studies are given in Appendix A and summarized in Table 5.5. The relatively complex Brazilian model Is omitted from Table 5.5 but details are given In Appendix A. All but two of the equations In Table 5.5 are obtained from experimentaldata.

Figure 5.7 shows the relationship between fuel consumptionand vehicle speed on smooth, flat roads for the Caribbean, Kenyan, and Indian vehicles. The Indian Tata, Caribbean Ford, and the Kenyan Bedford vehicles have rather similar fuel-speed curves, at least for speeds in excess of 40 km/hr though the locationof fuel consumptionminimlsing speed varies quite substantially (see Table 5.5). The Indian Ashok Leyland vehicle shows much 130 FUEL AND LUBRICANTCOSTS

Figure 5.5: Fuel Consumption (F) versus Rise + Fall (RF): Light Goods Vehicles and UtilIties

F 275 B

250 - - - -,

225,

200 K

1 50 -, --

125 .---

175

25-

0- ,,,,,,,,, ,-, ., RF

0 20 3 - 40 50 so 70 so so

EQuations B = i3razil VW Kombi K = Kenya Landrover Jeep C = Caribbean :Ford Transit

Units: f = Fuel Consumption (1/103kun) RF = Rise plus Fail Wmkni) C = Curvature t°Sikm) R = Roughn ss Bl (mm/km). IRI (niftm)

Varibblz noA Plo3t 0 = Curvature = SOO/ktm R = Roughness = 5500 i31 (mnm/km) 6.8 IRI tm/ki-e) L = Looseness (Kenya only) = mm ALT = Attitude (Brazil oniY) = GVW = Gross Vehicb WeIght: i3razil only = 2. 1 tonnes Caribbe n only = 2.6 tonnes

For other Brazilian speed model variables not plotted, see default values in the Appendix to Chapter 4. FUEL AND LUBRICANT COSTS 131

Figure 5.6: Fuel Consumption (F) versus Curvature (C): Light Goods Vehicles and Utilities

F 225, -

200,

175

ISO-

125-

100

7S-

0 z200 400 500 800 1000 1200

Fuel Consumption (F) versus Roughness (R): Light Goods Vehicles and Utilitles

-'25 ~~~~~~~~~~~~~~~~~B(ur;pavet) 225~~~~~~~~~~~,

,, _ - B (p-ved)

zoo0 - _- -

175

150

125

100

0 2000 4000 5000 8000 10000 12000

2,8 7.4 9.5 12.0 14 80 i I R, IRI 2.8 S.1 7.4 9.5 12.0 14.0 Table 5.4: Fuel Experiment Vehicle Fleets: Buses and Trucks

Gross Country Vehicle Engine Engine Power Number Tire Tire Tare Vehicle Vehicle Make Capacity (kw) axles Size Type Weight Weight (cc) (kg) (kg)

Kenya Truck 5420 80 at 2BOOrpm 2 825 x 20 R 3345 8420 Bedford J4LC5

Caribbean Truck 6000 84 at 2600rpm 2 825 x 20 R 4030 8420 Ford DIOIO w India Medium Truck 4788 83 at 2800rpm 2 900 x 20 C 6120 12180 Tata 1210 SE/42 01) Heavy Truck 11100 134 at 2200rpm 2 1100 x 20 C 8125 16260 Ashok Leyland Beaver

Brazil Medium Truck 5675 96 at 28OOrpm 2 900 x 20 C 5400 13000 Mercedes Benz L-1113 Heavy Truck 5675 96 at 2BOOrpm 3 1000 x 20 C 6600 18500 Mercedes Benz L-1113 with 3rd axle. Articulated Truck 188 at 220Orpm 5 1100 x 22 C 14700 40000 Scanla 110/39 Bus 5675 96 at 2800rpm 2 900 x 20 C 8100 11500 Mercedes Benz 0362

Notes: 1. AJl non-steering axles were fitted with dual tires. 2. All engines were six cylinder diesels. FUEL AND LUBRICANT COSTS 133 higher fuel consumption than the other vehicles and a distinctively U- shaped fuel speed curve. Note though that this is the most powerful of the four vehicles. With a power to weight ratio of 10 kw/tonne, the common setting used for all vehicles in Figure 5.7, the vehicle Is grossing 13.5 tonnes while the other vehicles are grossing only around 8 tonnes.

For the Kenyan and Caribbean vehicles fuel consumption is predicted to Increase by around 47 Q /103 km wlth every 10 m/km Increase In rise, and to drop by around 23 Q /103 km with every 10 m/km increase In fall, speed held fixed. Gradient effects are qulte similar for the Indlan Ashok Leyland vehicle but smaller for the Indian Tata truck. Fuel consumption minimising speed Is between 30 km/hr and 38 km/hr except for the Indian Tata for which it is higher at 46 km/hr.

As for cars, the Indian survey truck fuel equations show rather smaller gradient effects and rather higher levels of fuel consumption than do the Indian experimental data based equations. The problem of comparing user survey and experiment based fuel equations is considered In Appendix A5.4.2. Predicted fuel consumption obtained using the speed models given In the previous chapter and adjusted using the figures given In Table 5.1 are graphed In Figures 5.8 - 5.13. The treatment of variables not varying over tables and graphs is as described in the previous section.

Figures 5.8 and 5.9 show predicted fuel consumption for buses, all obtained from the Brazilian study model - only this study examined bus fuel consumption in fuel experiments. Roughness effects are relatively weak but the effect of gradient Is substantial. Curvature effects are small, In contrast to those found for cars. As before assumptions concerning superelevation are Important.

Figures 5.10 - 5.11 show predicted fuel consumptions for medlum trucks with gross vehicle weight between 8 tonnes and 16 tonnes obtained using the Brazilian, Kenyan, Caribbean, and Indian models. The Brazilian model predictions relate to the Mercedes Benz 1113 diesel fuelled vehicle. As noted In the previous sections the Brazilian fuel consumption predictions are substantially higher than those obtained In the other three studies - those studies being In broad agreement concerning the level of fuel consurption. The Brazilian and Caribbean models predlct much larger gradient effects than do the Indlan and Kenyan models. All the models ascribe only small Influences to curvature and roughness.

Figures 5.12 - 5.13 show predictions for heavy trucks (GVW - 20 tonnes) and for articulated trucks (GVW - 40 tonnes) obtained using the Brazilian study fuel and speed models. Here the curvature effects are very small given our assumptions concerning superelevation. However, the gradient effects are very substantial, despite the considerable speed reduction that Increasing gradient causes. The general level of fuel consumption predictions for the articulated vehicle Is high. Appendix C contains tables of predicted bus and truck fuel consumption and associated speed predictions. 134 FUEL AND LUBRICANT COSTS

Figure 5.7: Truck Fuel-Speed Equations

C ~______, .______

O~~~~ .....-... - - - - -. -i - - - CrbenWr 0 JndAsn~~~~~Cwb~Fn oD_ _,k~ ___ ,,i L.

L a 0 4J 0

-0

-4J

-40

C.,

-4~~ 0 06 0 0 2

rogn s2000 40m/kmrie80l- mlm w100 kw 2nn Table 5.5: Fuel Consumption (k/10 3 km): Medium Trucks and Buses

Coetfic.ents______Vehidle Country Type of Road Vehicle on speed Clas Study Surface Make Fuel Intercept (V. km/h) Rise Fadl Oher Variables(1) .Optimaj 1/V V2 (m/kn) (m/km) Spod"e(2) .____ .______.____ (tkm/hr) Rus India Surveyi3 ) Mostly paved Tata 69% Disel -12 36 3940 .0681 0.79 *.0028R + .0081K 32

I ______._ LeylarndLeln 31%3% _ __ _ .__ .______. ______

Truck India Experimental Mostly paved Tata Diesel W. 07 3906 .0207 3.33 -1.78 +.0012R - 6.24PW 46 Truck India Experimental Mostly paved Ashok Leyland Diesel 266.50 2517 .036z 4.27 -2.74 +,OOS6R- 6.2ZPW 33 Truck India Survey(2) Mostly Paved Tata 60% Diesel 71.70 5670 .0787 1.43 -3.9fW - 9.2OPW 33 Ashok D_ -- _ Leylandso 33%I_ _ __- ______

Truck f___ ribbea Experimental Paved Ford D1010 Dieell 29.24 2219 .0203 6.83 -2.60 -.85(GVW - 7.0)RS 38 2 (.0 -- ~~~~~~~ -I ------______~~~~~~~~~~~~~~~-- .013F1 . _ _ _ CA Truck Kenya Experimental Paved Bedford J4LCS Diesel1 105.4 903 .0143 4.36 -1.83 -3,22PW 32 Truck Kenya EVprimenta Unpaved Bedford J4LCS 1Z20 796 .0150 4.18 -2.22 -3.51PW + 1.97L 30 _I-_i___~ ____ Notes: Fuel consumptionis a linear function of the explanatory variables with coefficients as given above.

(1) R = surface roughness, Bl (mm/km) FL = tall (m/krn) L = depth of loose material (mm) GVW = gross vehicle weight (tonnes) RS = rise (m/km) PW power to gross vehicle weight ratio (kw/tonne) K vehicle age at survey midpoint (103 km)

(2) "Optimal speed" is speed at which predicted'fuet consumption is minimized

(3) Coeffcient recorded in "rise" oolumn Is oeffhcienton rise plus fall (rn/km) (Survey only). 136 FUEL AND LUBRICANT COSTS

Figure 5.8: Fuel Consumption (F) versus Rise + Fall (RF): Buses

F 800q B

550

500

450

400,

3001

250

200-

150-

100-

.I_ so

O- ...... ,.,.j,.,.,. RF 0 10 20 30 40 50 60 70 80 90

Euaigons: B = Brazil, MercedesBenz 0362

3 UnitSa F 5 Fuel Consumption(1U10 km) RF = Ris,plus Fall (m/km) C = Curvature (Ofkm) R = Roughnes. BI (mm/km). IRI (m/km)

Varkble not Plotted: C = Curvature = 500/km R = Roughness= 5500 81 (mm/km). 6.8 IRI tm/km) ALT = Attitude(Brazil only)= 0 GVW = Gross VehicleWeight = 11 tonnes

For other Brazilian speed model variables not plotted, see default values In the Appendix to Chapter 4. 137 FUEL AND LUBRICANT COSTS

Flgure 5.9: Fuel Consumption (F) versus Curvature (C): Buses

3004 _ .B ------

275

250

22!

200

175

150

125

100

600 1000 1200 0 200 400 ao

Fuel Consumption (F) versus Roughness (R): Buses

B (unpaved) 330

B (paved) 300 B (paved)

270 B (unpaved)

240

210

150

120

10000 12000 0 2000 4000 GOOD z000

.- I I I R, IRI 2.8I 5.1. 14.0 28 5.1 7.4 9.5 12.0 138 FUEL AND LUBRICANT COSTS

Flgure 5.10: Fuel Consumption (F) versus Rlse + Fall (RF): Medlum Trucks

F sno

800

700,

600 C

500 ,, -s/

400- - I

------

100-

00 130 4 so so 70 en 90

Eauations: B = Brazil, Mercedes-Benz Li1113 C = Caribbean, Ford DIOIO I =India. Tata 1210 SEt42 K =Kenya, Bedford J4LC5

Unifts F =Fuel Consumption (A/10)3km) RF = Rise plus Fall (m/km) C = Curvature (°{km) R = Roughness, ENl(mm/km), IRI (mfkm)

ziables not Plotted: C = Curvature = SOO/km R = Roughness= 5500 Si (mm/kmn), 6.8 IRI (m/km) L = Looseness (Kenya only) =1 mm ALT = Altitude (Brazil only) = Gvw = GrossVehicle Weight (Brazil only) = 14 tonnes PW = Power to Weight ratio: Kenya = 10 bhp/tonne India = 10 kw/tonne

For other Brazilian speed model varlables not plotted, see default values In the Appendix to Chapter 4. FUEL AND LUBRICANT COSTS 139

Figure 5.11: Fuel Consumptlon (F) versus Curvature (C): Medium Trucks

F 450…

…------B

400

350

300 - - ___-- __--- ____- ____-- __---__ ------_- - _- -__- - C

250 ------

200 K

15D

100

o 200 400 600 600 1000 1200

Fuel Consumption (F) versus Roughness (R): Medium Trucks

B (unpaved)

450 555 a - 450-~~~~~~~~~_ -a- ~B~paved)

400- _ -55--

350

300------__-_ -_ -___-__--- -___ ------

250 ------, ------_K

200

1so

100

.B*- ,,1,r--,-l,1,R,,.,,,,,,,,,., BI a 2000 4000 60cc BO00 10000 12000

2_8I 5.1 -- r l 1- I 2.8 5.1. ?.4 9.5 12.0 14.0 140 FUEL AND LUBRICANT COSTS

Figure 5.12: Fuel Consumption (F) versus Rise + Fall (RF): Heavy and Articulated Trucks

F B (Artic),

1900-

/~~~~/ 1400

1200 //

0 - , B (heavy)

4000

200

400R

0 10 20 30 40 50 e0 70 ao go

Eguations: B = Brazil: Heavy= MercedesBenzL1113 with 3 xles Articulated= Scanla 110/39 2 axle tractor with tri-aie trailer

Units: F = Fuel Consumption (I/103kn) RF = Riseplus Fall (mrkm) C = Curvature (/km) R = Roughnoss, Bl (mm/km), IRI (m/km)

Variablsnot Plott d: C = Curvature 5=0°/krn R = Roughness= 5500 BI (mm/krn), 6.8 IRI (m/km) ALT = Altitude = 0 GVW = GrossVehice Weight = 20 tonnes Heavy, 40 tonnes Articulated

For other Brazilian speed model variables not plotted, see default values In the Appendix to Chapter 4. 141 FUEL AND LUBRICANT COSTS

Figure 5.13: Fuel Consumption (F) versus Curvature (C): Heavy and Articulated Trucks

B (Artuc)

700-

B (heavy)

200-

400-

300-

2100

100

200 400 800 Sao 1000 1200

Fuel Consumption(F) versusRoughness (R): Heavy and ArticulatedTrucks

B (ArtiC - ~=paved) ~ ~ ~ ~ ~ ~ ~~-

B (Arttic--upaved)

B (heavy - -npaved)

goo B (heavy- paved)

400-

0...... BSi 0 2000 40010 8000~ 8000 100300 12000 I ~ ~~ ~ ~ ~ ~ ~~ ~IR, IRI 2.8 5.'1 7.4 9.5 12.0 14.0 142 FUEL AND LUBRICANT COSTS

5.4 FUEL CONSUMPTION: CONCLUDING REMARKS

The fuel consumption predictions developed from the studies' experiment based data show some substantial differences both in levels of fuel consumption and in the influences of highway conditions. In part these must be due to the differences In vehicle specification outlined earlier and revealed in the fuel-speed relationships graphed In Figures 5.1, 5.2, and 5.7. Users of the equations should take care to ensure that the equations they use are appropriate for the vehicles In the environment that they face. The Brazilian fuel consumption model allows adjustment of certain vehicle characteristics to facilitate transfer to new environments. However, many important features of vehicle and engine design cannot be adjusted by users so even this model should be employed with caution.

The experiment based fuel equations reported In this chapter are intended for use with the vehicle speed models given in Chapter 4, and most of the comparisons of predictions of fuel consumption given here have used the fuel predictions which emerge after predicting speed using those models. The vehicle speed models contain the influences of relative prices and generally of country specific factors and In part the evident differences In the studies' predictions must be due to variations In these factors.

The fuel consumption levels predicted by the studies vary quite substantially - those for the medium and large Brazilian cars and the Brazilian tractor-semi-traller combination being particularly high. As one would expect, gradient has the major impact on fuel consumption and the studies' predictions of the Influence of gradient are fairly close to one another. There Is some disagreement concerning the effects of roughness and curvature. So far as curvature Is concerned, the effect comes largely from the speed equations. The Brazilian model predicts relatively large effects, fuel consumption Increasing with curvature. The Kenyan model predicts an effect In the opposite direction, but this may be unreliable since It is obtained from data covering only a narrow range of curvature. In the Brazilian model, roughness effects are built In to both the fuel and the speed equations and the predicted roughness effects are large relative to those reported by the other studies.

The Indian and Brazilian studies report large correction factors to be applied to raise predicted fuel consumptions to the sort of levels observed under commercial operating conditions. The Kenyan and Caribbean studies give much smaller corrections but It seems that these are designed to allow for speed changes alone and not for quality of maintenance, overloading, and so forth. Users will need to examine the levels of fuel costs In the environments they face to ensure that the equations they use give predictions of appropriate magnitudes.

5.5 LUBRICANT COSTS

Vehicle lubricant costs which include costs associated with the consumption of engine oils, other oils and grease, are a minor element of transport costs and only In the Indian study was substantial effort devoted to collecting detailed vehicle lubricant data. Lubricant costs are generally small and rather difficult to analyze. They typically constitute FUEL AND LUBRICANT COSTS 143

less than 3 percent of total vehicle operating costs and there are large variations across companies in the pattern of lubricant consumption. Engine oil, the most important of the three lubricant categories, Is consumed during regular oll changes and, between oil changes, when oil burned or blown away during operation Is replenished. Oil change Intervals are specified by vehicle manufacturers and In developing countries tend to be around 5,000 km. Most owners instruct their drivers to check engine oll levels each day and replenish as necessary and it Is difficult to get good estimates of amounts of oil used in this way. Transmission oils are checked much less frequently, principally because the drive systems are difficult to reach and little oil is generally lost between service Intervals unless components are damaged. Frequently, the quantities of olls added at servicing are small and the effort required to collect these data Is excessively large given their small contribution to total vehicle operating costs. In this section we discuss only the results concerning engine oil consumption.

In the Kenyan study, records of a large bus company were examined and, based on over seven million vehicle kilometers of operation, It was calculated that oil consumption due to oil changes amounted to 1.96 /103 km while oil consumption due to replenishment between oil changes amounted to 2.34 Z/103 km. A company running large engined trucks recorded 2.4 Z/103 km due to oil changes and 1.55 /103 km due to replenishment between oil changes, the former figure reflecting the larger sump capacity of the 11.5 liter engined vehicles. The Kenyan study reported an average figure for total oil consumed of 4 9/103 km for both bus and truck operations on paved roads. Garages and vehicle owners supplied the average total oil consumption on paved roads for cars and light goods vehicles reported In Appendix B. Additional evidence from vehicle operators suggested that oil consumption doubled on unpaved roads so average oli consumption on gravel and earth roads was obtained by doubling the paved road consumption figures. Data collected In the Caribbean study were felt to be sufficiently close to the Kenyan paved averages to permit the same figures to be recommended in that study.

The equations for engine oil consumption as reported In the Brazilian study are unsatisfactory because they contain, as an explanatory variable, the number of oil changes per thousand km which Is Itself, to some extent, dependent on highway conditlons. The data for buses and trucks were therefore reanalysed (Chesher 1983) and the resulting equatlons are reported In Appendix B. The data on car oil consumption were unavailable at the time of this reanalysis and the car oil consumption equation, as given in the Brazilian study report, is reported In Appendix B, the number of oil changes being set to one change per 5,000 km. The Indian study reported separate equatlons for engine oil, other oils, and grease.

Predictions of engine oil consumption (Q /103 km) at different levels of road roughness are given In Table 5.6. It is evident that Indian cars have high levels of consumption, especially on rough roads. The design of Indian car engines would lead one to expect high oil consumption and the average vehicle age In the survey is close to 100,000 km. However, the effect of roughness seems unreasonably large, with car oil consumption predicted to exceed that of a medium truck on rough routes. Both Brazilian 144 FUEL AND LUBRICANT COSTS

Table 5.6: Engine Oil (Q/103km) Consumptionat Various Levels of Roughness In the Four Studies

Study Roughness Vehicle 8l IRI Kenya Caribbean Brazil India (mm/kmn)(rnkm)

2000 2.8 Car 1.2 1.2 1.5 1.8 Light Goods 1.8 1.8 Bus 4.0 4.0 3.6 3.6 Truck 4.0 4.0 4.1 3.4

4000 5.1 Car 1.2 1.2 1.8 2.6 Light Goods 1.8 1.8 Bus 4.0 4.0 3.7 3.8 Truck 4.0 4.0 4.5 3.5

6000 7.4 Car 2.4 2.1 3.0 Light Goods 3.6 Bus 8.0 3.8 4.0 Truck 8.0 4.9 3.6

8000 9.5 Car 2.4 2.3 3.4 Light Goods 3.6 Bus 8.0 4.0 4.2 Truck 8.0 5.3 3.7

10000 12.0 Car 2.4 2.6 3.9 Light Goods 3.6 Bas 8.0 4.1 4.4 Truck 8.0 5.8 3.8

Notes Variables not plotted set to:

LK,K = Vehkle Age = 300000/km Brazil Bus, 345000/km India Bus. C = Curvature = 1070/kvn (India car) RF = Rise pius Fall = 15m/km India Bus, 13 m/km India Truck. Surfaoe type: 2000 Bl(mm/krn), 2.8 IRI(m/km), 4000 Bl(mm/rkm), 5.1 IRI(m/km), paved, remainder unpaved. FUEL AND LUBRICANT COSTS 145

Table 5.7: Percentage Increase In Engine Oil Consumptlon Moving from Paved to Unpaved Road

Study Vehicle Kenya Brazil India

cars 100 53 89

Buses 100 11 17

Trucks 100 29 9

Notes: Paved= 1000 B8(mm/km), 1.5 IRI(m/km) Unpaved= 8000 Bl(mm/km), 9.5 IRl(m/km)

and Indian buses show small roughness effects and the figures suggest similar levels of oil consumption for these vehicles. Roughness Is predicted to hav_; a very small effect on Indian truck oil consumption and Indian trucks are predicted to consume less than Indian buses at all roughness levels. The average truck age Is less (223,000 km) than buses (345,000 km) Inn the Indian survey but, even so, this result Is surprising. Table 5.7 summarizes the effect of moving from paved to unpaved roads, 2,000 to 8,000 mm/km.

The effects of the explanatory variables were generally found to be weakly determined In the Indian study equations for other oils and grease. Accordingly, average values for the consumption of engine oil, other oils and grease were reported for cars, buses, and trucks. It was found that increasing engine oil costs by 43 percent yielded a reasonable estimate of total lubrication costs. However, experience in Brazil suggests that this figure Is rather high for general use and for the purposes of predlcting total operating costs In the other studles a figure of 25 percent has been used. 146 FUEL AND LUBRICANTCOSTS

APPENDIXA. FUEL CONSUMPTIONEQUATIONS AS REPORTEDBY THE FOURSTUDIES

A5.1 Kenya

Hide et al. (1975) report separate equations for paved and unpaved road surfaces. They use the following notation:

F - fuel consumption ( 103 km) V - vehicle speed (km/hr) RS - rise (m/km) FL - fall (m/km) L - depth of loose material (mm) R - surface roughness (mm/km) PW - power to gross vehicle weight ratio (bhp/tonne) GVW - gross vehicle weight (tonnes)

Means and ranges for explanatory variables have been reported In the appendix to Chapter 4. The fuel consumption equations are as follows. Figures In parentheses are "t-statistics" (ratios of coefficients to standard errors).

Cars, paved roads

2 F - 65.36 + 499/V + .0058V + 1.594RS - .854FL (3.7) (19.0) (53.3) (-30.6)

R2 _ .91, S - 13.94, 776 observations

Cars, unpaved roads

2 F - 46.90 + 614/V + .00788V + 1.724RS - 1.066FL + .822L + .00113R (2.9) (14.2) (23.0) (-14.7) (2.9) (3.7)

R2 _ .87, S - 15.02, 387 observations.

Land Rover, paved roads

2 F - 74.70 + 1151/V + .0131V + 2.906RS - 1.277FL (4.7) (16.7) (56.8) (-29.7)

R2 - .92, S - 19.92, 619 observations.

Land Rover, unpaved roads

2 F - 72.78 + 844/V + .0137V + 2.828RS - 1.306FL + 1.757L + .0011OR (3.1) (14.5) (38.67) (-20.0) (5.3) (3.5)

R2 _ .91, S - 18.77, 488 observations. FUEL AND LUBRICANTCOSTS 147

Medium truck, paved roads

2 F - 105.43 + 903/V + .0143V + 4.362RS - 1.834FL - 2.395PW (13.4) (19.8) (58.5) (-28.7) (-15.9)

R2 _ .87, S - 37.63, 1,215 observations.

Medium truck, unpaved roads

2 F - 121.99 + 796/V + .0150V + 4.176RS - 2.216FL - 2.619PW + 1.969L (9.3) (14.9) (38.9) (-23.2) (-13.0) (3.3)

+ .00145R (3.2)

R2 _ .86, S - 35.20, 836 data points.

Remarks

The three test vehicles were run a minimum of three times over 95 test sectlons (each one kilometer long, 49 paved, 46 unpaved) at a series of constant speeds. Runs were made at 10 km/hr and at 10 km/hr Increments up to the maximum attainable speed of the vehicle. The car and Land Rover were run In one load state and the medium truck was run empty, half loaded and full. Observations used In analysis are averages of replicate runs. The reported estimates of the variance of the disturbance term Indicate non-negligible dispersion In fuel consumption, even under strictly controlled experimental conditions. For Instance, for cars on paved roads, S Is reported as 13.94 which suggests that prior to averaging the standard deviation of fuel consumption over a 1 km long section, speed and gradient held fixed Is around 10 /103 km Implying a 95 percent confidence Interval nearly 40 /103 km wide on fuel consumption In single runs over 1 km long sections. Despite this variability, R2 statistics are high because of the much larger variation In fuel consumption once speed and gradient vary, variation which Is attrlbutable to speed and gradient variation.

Hide et al. (1975) derive a relationship between fuel consumption and gross vehicle weight (GVW, tonnes) using user survey fuel consumption data and add this to the medium truck fuel consumption equations gIven above to allow predictlons to be made for heavy goods vehicles and buses. To Incorporate this adjustment add (-154 + 69.2 (GVW)1 / 2 ) to the medium truck fuel consumption equations. To convert fuel consumption predictions given using the equations reported above to predictions of fuel consumption under normal operating conditions Hlde et al. (1975) recommend multiplying car and Land Rover predictions by 1.08 and multiplying bus and truck predictions by 1.13. In the main text the equations are reported after converting coefficients on the power to weight ratio so that they apply to power to weight ratio In kilowatts per tonne. 148 FUEL AND LUBRICANT COSTS

Chesher (1977) reports estimates of a fuel consumption equatlon of the form:

2 F - exp((ao + a 1RS + a2FL) + (0P + f1RS + p2 FL)V + (70 + 71RS + 72 FL)V ) which allows gradient to have a non-linear effect on fuel consumption and which allows the fuel-speed relationship to be shifted quite flexibly as gradient alters. The estimates obtained by applying ordinary least squares with the dependent variables written as loge(F) are given In Table A5.1. For unpaved roads aO is written as moo + aQ1L + aO2R. Separate equations are estimated for the three load conditions of the medium truck. For the car the dependent variable is F not loge(F).

In the Highway Design and Maintenance Model (HDM ill), these equations appear in a modified form, a gross vehicle weight effect for trucks being Introduced by interpolating the results obtained for the truck In Its three load states.

A5.2 Caribbean

Morosiuk and Abaynayaka (1982) report equations for fuel consumptlon as given below. Notation is as in the previous section.

Passenger cars

F - 24.305 + 969/V + 0.00758V2 + 1.334RS - .0630FL + 0.00286FL2 (15.7) (12.1) (98.7) (-14.4) (7.6)

R2 _ 0.95, 1,161 observations, S not reported.

Light goods vehicles

F - 72.207 + 949/V + 0.00483V2 - 1.183FL + .00573FL2 + 1.118GVW.RS (15.1) (6.5) (-25.2) (13.9) (158.3)

R2 _ 0.96, 2,169 observations, S not reported.

Medium trucks

F - 29.240 + 2219/V + 0.02031V2 - 2.60FL + 0.0132FL2 + 0.8478 GVW.RS (15.7) (11.4) (-25.8) (15.0) (155.1)

R2 _ 0.96, 2,296 observations, S not reported. Table A5.1: Fuel Consumption Equations Incorporating Speed-Gradient Interactions

0 Surface [_"'nen _o aoi I all 02 1 al 2 Yo Yi T 2 d No. No. of

2 2 2 2 Vehicle Type Viable (Intercept) (L) (R) (RS) (FL) (V) (RS. V) (FL. V) CV ) (RS.V ) (FL V ) R S Ober- Sections vationa

Car Paved F 64.48 1.67 .107 -. 133 .00477 -. 0208 .00729 -. 0O0S52 .0000782 .92 13.61 696 43

Car Unpaved F 68.61 420 .890 2.15 -. 380 -. 202 -. 0112 -. 0157 .00930 .0000350 .0000403 .88 14.88 358 25

Landrover Paved b9gF 4.6Sg .0131 .0123 -. 000437 000147 -. 000813 .0000904 -. 00000231 .00000692 94 .119 551 44

Landrover Unpaved iogeF 4.s0 . 00935 .0103 .0154 .00567 .00128 .000100 -. 000601 .0076 -. 00000199.000049 .92 .113 484 38

Empty Paved bg 1 F 4.032 .0203 -.00745 .0129 .0030138 -.00102 .0000186 -.00000189 .000001 .92 .277 528 44 Truck I_I_I_I_I_I

Empty Unpaved iorF 4.489 .0148 .0252 .0199 -. 0313 -. 0-337 -. 00W722 -. 0000799 .000114 .00000050 .00000328 .92 .190 404 38 Truck

'0 Full Paved logF 5.772 W197 -. 0216 -.05S2 .00155 -.0W151 .000638 -. 0000155 .0000165 .90 .415 272 22

Truck I_I_I_I_I_I _I_I_I_I_I_

F Unpaved IoF 5 .32 .2 .018 .0087 -. 0339 -. 0257 .87 -. 10 .000342 -. 0000107 .0000214 .96 .236 141 12

Notes: Dependent variable (column 3) Is a linear function of explanatory varable with coafficnts as ahown abov. F = fuel consumption (C/103 kim) L = depth of loose surfae mnaterial (mm) R = surfaceroughnes (mmfkm) RS = ris (mCkin) FL = fll (m/kin) V = vehiclespeed (km/hr)

Source: Chesher (1977). 150 FUEL AND LUBRICANT COSTS

Approximate ranges and means of explanatory variables, except GVW.RS for which they are not reported, are given In Appendix A4.2

Remarks

The car was operated In one load condition representing two passengers and Instrumentation, the light goods vehicle was run empty and full (1.5, 2.6 tonnes GVW respectively) and the medium truck was operated empty, half loaded and full (4, 7, and 10 tonnes GVW respectively). The test vehicles were run, In each load condition, at constant speeds ranging from 16 km/hr to the maximum speed attainable by the vehicles on each of 82 test sections and the average speed and fuel consumption on each run was recorded. Six runs were repeated at each speed and the mean of the four most consistent runs was used in the analysis.

Morosluk and Abaynayaka (1982) adopt the Kenyan study correction factors (see A5.1.1) to adjust fuel consumption predictions to give predictions of fuel consumption under normal operating conditlons.

A5.3 Brazil

Fuel consumption equations are obtained from experimental data and from user survey data. First we report the experiment results.

A5.3.1 Fuel consumptlon experiments

The fuel consumption model estimated using the fuel experiment data Is described In the main text. Fuel consumption is written as a function of vehicle speed (V) which has to be predicted before the fuel consumption model can be used. Separate equations apply for uphill and downhill road sections. The model as given here applies to routes for which vertical geometry Is described by average rise + fall. The route Is regarded as consisting of two sections, one with rise equal to rise + fall, and fall equal to zero, the other with rise equal to zero and fall equal to rise + fall. Given predicted uphill and downhill speeds (Vu, Vd), uphill and downhill horsepower delivered to the vehicle's wheels are predicted using:

Uphill sections

HPU - [(1000CR + RF) GVW.g.Vu + AIR Vu]/7 36 .

Downhill sections

7 3 6 HPd - [(1000CR - RF) GVW.g.Vd + AIR V3d]/ where: CR - coefficient of rolling resistance (dimensionless) - .0218 + .0000467QI for cars and utilitles - .0139 + .0000198/QI for buses and trucks FUEL AND LUBRICANT COSTS 151

01 - surface roughness (Ql Index) (1QI - 55 mm/km)Bi

RF - rise + fall (m/km)

GVW - gross vehicle weight (tonnes)

g - gravitational constant (9.81 m/sec2 )

Vd,Vu = downhill, uphill speeds (m/sec)

AIR - 0.5 p CD AR where p - mass density of air (kg/m3) - 1.225 (1-2.26 10-5A] A - altitude (m) CD - aerodynamic drag coefficient (dimensionless) AR - projected frontal area of vehicle (m2).

Predictions of fuel consumption per unit time period are made separately for uphill and downhill sections using the following equations.

2 2 UFCi - aO + a1 CRPM + a2 CRPM + a3 HPi + a4 HPI CRPM + a5 HP1

HPI 2 0

2 2 UFCj - aO + a1 CRPM + a2 CRPM + a6 max (NHO, HPj) + a7 max (NHO, HPi)

HPI < 0

with I - u (uphill) and d (downhill).

Here ao, ... , a7 and NHO are estimated coefficients reported In Table A5.2 and UFCU and UFCd are per tIme period fuel consumptlons (ml/sec) on respectively uphill and downhill segments. CRPM Is the "nominal" average engine speed (rpm) assumed constant within a vehicle class, invariant with respect to changes in vehicle speed and highway conditlons. The values of CRPM determined for Brazilian test fleet vehicles are given In Table A5.2. Watanatada et al. (1987) recommend the use of these values In applications In which the maximum rated engine speeds of vehicles are similar to those found In Brazil. Should they differ, they recommend use of a value for CRPM equal to 75 percent of the maximum rated RPM of the vehicle for which predictions are desired.

Fuel consumptlon In liters per 1,000 kilometers Is given by:

(UFCUUFCd F -500a + u Vd where a - 1.16 for cars and light goods vehicles - 1.15 for buses and trucks 152 FUEL AND LUBRICANT COSTS

is an adjustment to convert to fuel consumption under normal operating conditions.

The data used to estimate the fuel consumption model were obtained from eleven test vehicles constructed to ten distinct specifications, two of the vehicles being Identical Volkswagen Kombis. Details of the vehicles are given In Table 5.2 In the main text.

Vehicles were run at constant speed In constant gear in different load conditions over 24 road sections each 1 km long, with constant gradients varying from -14 to +14 percent. Sectlons varled from smooth (1,100 mm/km) to rough (16,000 mm/km), some paved, some unpaved. Vehicles travelled at 10 km/hr and at 10 km/hr Increments until maximum speed was attained. At each speed runs were made In all feasible gears, and, for each combination of speed, gear, load, section, direction, a minimum of three (normally six) runs were made. Data used for analysis are averages of repeat observations.

The variables HP and RPM were derived for each observation and the coefficients a0 .... a7 were estimated by ordinary least squares. The threshold horsepowers NHO, below which fuel consumption Is constant for changes In speed and highway conditions were determined by examining scatter diagrams. For any given vehicle class a number of the coefficients ao .... a7 are specified to be zero, because the coefficients were Judged to be statistically Insignificantly different from zero during estimation. The Chevrolet Opala (medium car) Is the only vehicle with a non-zero 2 coeffIclent "a2 " on CRPM and the Dodge Dart (large car) and Volkswagen Kombi (utility) are the only vehicles with non-zero coefficlent "a4 " on HPu CRPM. The coefficients recommended by Watanatada et al. (1987) for the Volkswagen Kombi are obtained from analysis of data generated by one of the two vehicles of this class that were used In the experiments.

To estimate the model RPM was estimated using Information on gear chosen and gear ratios. Users of the model are unlikely to have such Information and Watanatada et al. (1987) recommend assuming constant RPM under all speed-gradient conditions. The recommended values, CRPM, are reported In Table A5.2. These values were obtained by comparing fuel consumption predictions obtained using a variety of values of CRPM with observed fuel consumption on a number of sections and choosing the CRPM value giving the closest agreement. The Chevrolet Opala (medium car) and Dodge Dart (large car) were not employed In the experiments to collect the data needed to perform this procedure. The Ford-400 (light truck, gasoline) was employed, but suffered Instrumentation faults. CRPM was assigned without reference to fuel consumption data for these vehicles. Reported values of CRPM are between 64 and 87 percent of RPM at rated maximum horsepower.

A5.3.2 Fuel consumption - user survey

During the Brazilian study road user survey fuel consumption data were obtained from transport company records. Vehicle speed data were not available for user survey vehicles so the reported equations relate fuel consumption directly to highway characteristics. The equatlons given below are re-estimates reported by Chesher (1982) of equatlons originally given FUEL AND LUBRICANT COSTS 153

Table A5.2: Estimatesof Coefficients In Fuel Consumption Model

I S Light Truck | Medium/ Articu- Vehicle Small Medium Large Utility | Large - Heavy lated Type Car car Car Bus Gas ,Diesel Truck Truck

Vehicle VW130C Chevrolet Dodge VWKombi Mercedes Ford iFord Mercedes Scania Make Opala Dart Benz 400 14000 Benz 1113 110/39

CRPM 3500 3000-t 3300 3300 2300 3300 2600 1800 1700 (rprr)

a0 -8201 23463 -23705 6014 -8 4-7271803 -22955 -30559

a1 33.4 40.6 100.8 37.6 63.5 127.1j 71.6 95.0 156.1

a2 0 0,01214 0° 0 0° 0 0 0

a3 5630 7775 j 2784 3846 4323 5867 5129 3758 4002

a4 0 0 0.938 !1.398 0 0 0 0 _____._------1-- t------t------a`5 0 0 13.91 O 8.64 43.70,; 0 19.12 4.41

'4 4460 6552 1 4590 3604 2479 i 384312653 2394 4435

a7 0 0 0 0 11.50 0 0 13.76 26.06 _-_ ------t--T--- -t -.4- ______NHO -10 -12 | -15 i-12 -50 -50 -30 -85 -85

No. of , Obser- 1224 1 398 I 421 1043 784 1142 .1020 798 810 vations | , __ _

Source: Watanatada et al. (1987). 154 FUEL AND LUBRICANTCOSTS in GEIPOT (1981) calculated using revised estimates of surface roughness and estimated generalized least squares allowing for random company specific errors. The notation is as follows.

F - fuel consumption ( /103km) Ql - average surface roughness (Quarter car Index) RF - average rise + fall (m/km) C - average degrees of curvature (0/km).

The equations are given below. Figures In parenthesesare ratios of coefficientsto their standard errors.

Cars

loge(F) - 4.423 + .00082 Ql + .00136C (1.9) (5.6)

Su - .072 Sw - .101, 243 vehicles, 6 companies.

Light goods vehicles

loge(F)- 4.790 + .00168 Ql + .00104C + .00666RF (2.4) (1.76) (1.7)

Su - .148 Sw - .091, 33 vehicles, 6 companies.

Buses

loge(F)- 5.618 + .000765Ql + .00036C (5.2) (2.0)

Su - .050 Sw - .076, 462 vehicles, 21 companies.

ApproxlmateMeans and Ranges of ExplanatoryVariables

Vehicle Class Cars Light Goods Buses Variable Min Max Mean Min Max Mean Min Max Mean

QI(QI Index) 27 144 54 25 140 76 23 240 87 C(°/km) 9 276 57 12 58 25 6 258 40 RF(m/km) 12 46 17

Source: Chesher (1982). FUEL AND LUBRICANT COSTS 155

Remarks

There is a good deal of dispersion in user survey fuel consumption data refiecting differences in vehicle specifications and condition, loads, speed of travel, type of business, driver behaviour, and so forth. Note that for any vehicle the user survey fuel consumption data is probably a rather accurate Indication of that vehicles fuel consumption because it relates to many tens of thousands of kilometers of travel. The equations reported above explain only about 10-30 percent of the variation across vehicles In fuel consumption.

The cars In the user survey data set are Volkswagen 1.3 liter rear engined sedans, the most popular Brazilian small car during the survey period. The light goods vehicles In the user survey data set are Volkswagen Kombis with rather small (less than 2 liters) rear mounted gasollne engines. The user survey data set contalns a varlety of buses.

A5.4 India

Fuel consumption equations are obtained from experiments and from user survey data. First we report the experimental results. Notatlon Is as follows:

F - fuel consumption ( /103 km) V - vehicle speed (km/hr) RS - rlse (r/km) FL - fall (m/km) R - surface roughness (mm/km) PW - power to gross vehicle weight ratlo (kw/tonne).

A5.4.1 Fuel consumptlon experiments

Ambassador car

F - 10.31 + 1676/V + 0.0133V 2 + 0.0006R + 1.388RS - 1.032FL (28.2) (21.5) (1.0) (26.2) (-19.7)

R2 _ 0.88, S - 12.73, 343 observations.

Premier Padmini

2 F - 49.84 + 319/V + 0.0035V + 0.0019R + 0.942RS - 0.677FL (5.3) (8.8) (3.0) (36.3) (-25.9)

R2 0.97, S - 4.22, 105 observations.

Mahindra Jeep (diesel)

F - 30.83 + 2258/V + .0242V 2 + 0.0012R + 1.278RS - .564FL (60.36) (48.40) (6.00) (46.8) (-20.70)

R2 _ .97, S - 5.502, 209 observations. 156 FUEL AND LUBRICANT COSTS

Medium truck (Tata)

F - 85.07 + 3905/V + 0.0206V2 + 0.0012R + 3.328RS - 1.777FL - 6.240PW (46.7) (9.4) (0.8) (26.7) (-14.3) (-12.8)

R2 . 0.93, S - 28.64, 352 observations.

Medium truck (Ashok Leyland)

2 F - 266.52 + 2517/V + 0.0362V + 0.0066R + 4.265RS - 2.737FL - 6.260PW (25.2) (13.0) (4.6) (20.0) (-12.8) (-10.5)

2 R . 0.79, S - 41.78, 410 observations.

Approximate Ranges of Explanatory Variables (Means Not Reported)

Variable Vehicle Min Max

RS(m/km) All 0 50

FL(m/km) All 0 50

R(mm/km) Mahindra Jeep 2,130 10,110 Ashok Leyland 4,190 9,334 Others 4,190 8,280

PW(kw/tonne) Tata 4.41 13.65 Ashok Leyland 5.92 16.53

V(km/hour) Ambassador 14 83 Padminl 20 81 Mahindra Jeep 14 74 Tata 10 72 Ashok Leyland 10 58

Source: CRRI (1982).

Remarks

The five test vehicles were each run a minimum of three times at a series of constant speeds over road sections most of which were 1 km long. The number of road sections used In the experiments Is not reported nor are the speeds at which vehicles travelled, though ranges are given above. Observations in the regression analyses reported above are averages of repeat runs. Cars and jeeps carried a driver and two passengers, or an equivalent load. The trucks were run empty and with loads of 5 tonnes and FUEL AND LUBRICANT COSTS 157

10 tonnes. Additionally the Tata 1210 was run wlth a load of 12.5 tonnes and the Ashok Leyland Beaver with a load of 15 tonnes. The majority of buses In use In India at the time of the study closely resembled the Tata 1210 truck, using the same chassis and engine, so fuel experiments were not performed using a bus. It was felt that the data produced by the Tata truck would give an adequate Indication of bus fuel consumption.

In CRRI (1982) fuel consumption while Idling Is reported and the results are given here In Table A5.3. Results of experiments to compare fuel consumption with radial and crossply (blas) tires are also reported, Indicating fuel consumption about 6-7 percent lower on cars with radial tires. For the Ambassador car this reduction Is less marked once speeds are far from the fuel minimising optimum speeds. Fuel consumption equations are also reported for 3-wheeler BaJaJ and Lambretta autorickshaws and for 2-wheeler Vespa scooters. These results are not given here.

Table A5.3: Fuel Consumption While Idling

Fuel Consumption Vehicle Type (cc per min)

Ambassador car 13.0 Premier Padmini car 10.5 Mahindra diesel Jeep 12.3 Tata 121OSE truck 15.3 Ashok Leyland Beaver Truck 35.4

Source: CRRI (1982).

Comparing fuel consumption predictions using the models given above and fuel consumption data obtained during the road user survey, correction factors are derived to convert fuel predictions to predictions of fuel consumption under normal operating conditions. These are reported In the main text In Table 5.1.

A5.4.2 Fuel consumption - user survey

Fuel consumption equations were estimated using data obtained from vehicles participating In the road user survey. In the indtan study Information on vehicle speeds (V) was obtained for all user survey vehicles and the fitted equations take the same form as those reported above, 1/V and V2 being used as explanatory variables. Following CRRI (1982) we report the user survey fuel equations with the dependent variable F* measured In liters per 100 kilometers (not per 1,000 kilometers). The notation Is as In the previous sectlon except: 158 FUEL AND LUBRICANT COSTS

F* - fuel consumption ( /102 km) C - average degrees of curvature (0 /km) LK - vehicle age at survey midpoint (103 km) W - pavement width (m).

Ambassador cars

F* - -13.81 + 621/V + 0.00501V2 + 0.000342R + 0.03669RF (2.6) (3.1) (1.7) (1.2)

R2 - 0.17, S - 1.15, 54 observations.

Buses

F* - -1.236 + 394/V + 0.00581V2 + 0.00028R + 0.00081LK + 0.0788RF + (7.2) (9.4) (3.5) (2.0) (3.0)

+ 0.00213C (1.6)

Sw - 4.21, Su - 4.31, 639 vehIcles.

Trucks

* - 7.170 + 567/V + 0.00787V2 - 0.3889W - 0.9202PW + 0.1432RF (6.2) (9.7) (-1.8) (-5.7) (4.7)

_-2 0.53, S - 2.83, 232 vehicles.

Approximate Ranges and Means of Explanatory Varlables

Variable Vehicle Min Max Mean

V(km/hr) Cars 34 55 43.72 R (mm/km) 3,416 6,955 4,987 RF (m/km) 3 36 10

V(km/hr) Buses 20 55 34 R (mm/km) 2,925 12,072 5,953 LK (Age, 103 km) 22 988 345 RF (m/km) 1 503 15 C (degrees/km) 5 1,021 149

V(km/hr) Trucks 17 55 36 W (m) 4 7 6 PW (kw/tonne) 3 11 7 RF (m/km) 1 58 13

Source: CRRI (1982). FUEL AND LUBRICANT COSTS 159

Remarks

The car and truck equations are as reported in CRRI (1982) and were estimated by ordinary least squares. The bus equation is that reported in Chesher (1983) and was estimated by generalized least squares allowing for random company specific errors. Upon re-estimating the bus equation a curvature effect was found that was not reported In CRRI (1982). In the main text these equations are reported after converting fuel consumption to liters per 1,000 kilometers.

Speed data available for user survey vehicles are average speeds over many tens of thousands of kilometers, during which speeds obviously vary about the reported averages. Similarly fuel consumption Is average fuel consumptlon over the survey period. Generally If fuel consumptlon Is related to speed by:

(1) F - a + b/V +cV 2 , at constant speed, V, then with speed at a series of constant speeds, the relationship between average fuel consumption, F and average speed, V, will not be glven by (1) with F and V replaced by respectively F and V. At first sight then user survey and fuel experiment equations that both use the form (1) are In conflict. However, under particular assumptions there Is no conflict. Suppose that over the kilometers travelled during a user survey, vehicle speeds are approximately log normally distributed, log,(speed) having a normal distribution with mean # and variance a2. Averaged over user survey routes, fuel consumption, F, is given by

(2) F - a + b E(1/V) + c E(V2).

Now, If V Is log normal as assumed above then E(V) - exp (p + 02/2) - V and 1/V and V2 are also log normal. Further, E(1/V) - exp (-p + a2/2) and E(V2 ) - exp (2p + 2a2 ), so that:

E(1/V) - exp (a2) (1/V) and

E(V2 ) _ exp ( 2)V2 .

Thus with V log normal, the relationship between average fuel consumption and average speed is: 160 FUEL AND LUBRICANT COSTS

(3) - a be C (V)2 which Is the same as the functional form relating F and V. However the coefficients "b' and "c" become bea2 Ž b and ceo2 2 c and with equality holding when and only when 02 _ 0 and speed does not vary.

Table A5.4: Comparison of User Survey and Fuel Experiment Coefficients

Experiment Survey Coefficient on Coefficient on

Vehicle Class 1/V V2 1/V (V)2 be/ce bs/cs

(be) (Ce) (bs) (C S )

Ambassador car 1,676 .0133 6,213 .0501 126,015 123,952

Tata truck 3,905 .0207 188,647 5,670 .0787 72,045 Leyland truck 2,517 .0362 69,530

This simple model suggests that coefficients on (1/V) and (V)2 found using user survey data should be larger than those found on 1/V and V 2 In experimental data. However the ratios of the coefficients on (1/v) and (V)2 should be approximately equal to the ratlo of the coefficients on (1/V) and V2. It Is of course this ratio that determines fuel consumption minimising speed.

In practice we would not expect the log normally distributed speed assumption to hold exactly but the comparisons reported above In Table A5.4 do lend some support to the conjectures made above. Indeed In the only case In which a direct comparlson can be made, for the experiment and survey Ambassador cars, the agreement between b/c from the experiment and b/c from the survey Is remarkable. Note also that In all cases the survey coefficients are larger than those found using experimental data. It is at least possible that a partial explanation for the relatively large correction factors applied In the Indian study to convert experimental fuel predictions to the sorts of values observed In the user survey is the variability In the speeds at which user survey vehicles travel. FUEL AND LUBRICANT COSTS 161

APPENDIX B. ENGINE OIL CONSUMPTION EQUATIONS AS REPORTED BY THE FOUR STUDIES

B5.1 Kenya and Caribbean

No engine oil equations were reported In either the Kenyan study (Hide et al. 1975) or the Caribbean study (Hide 1982) but averages were given for the main vehicle and road types found In both user surveys. The averages, In units of liters of engine oil per thousand km, are as follows:

Kenya

Vehicle Type Paved Unpaved

Cars 1.2 2.4 Llght Goods Vehicles 1.8 3.6 Trucks 4.0 8.0 Buses 4.0 8.0

Source: Hide et al. (1975).

Caribbean

Vehicle Type Paved

Cars 1.2 Light Goods Vehicles 1.8 Trucks 4.0

Source: Hide (1982).

B5.2 Brazil

The bus and truck equations reported In the Brazilian study (GEIPOT 1981) were considered unsatisfactory and new estimates were reported In Chesher (1983). The car equatlon was not re-analyzed and is given as reported In the Brazilian study report. The notation for all equations Is as follows:

Oil - Engine oil, liters per 103 km Ql - Quarter Car Index, Roughness (1QI - 55B1, mm/km) 3 K - Vehicle age, at survey midpoint, 10 km.

The equations for bus, truck, and car engine oil consumption are: 162 FUEL AND LUBRICANT COSTS

Bus

loge(Oll) - .475 + .000945QI + .1341og(K) (3.13) (1.64) (7.27)

Su - .441, Sw - .251, 419 vehicles, 18 companies

Truck

loge(Oll) - 1.342 + .00225QI (1.57)

Su - .572, SW - .181, 185 vehicles, 19 companies

Car

Oil - 1.271 + .00713QI (11.46)

R2 _ .88, S - .25, 27 company means, 264 observations.

The variable XOIL, frequency of oil changes per 103 km, that appears In the car oil equation In GEIPOT (1981) has been set equal to the survey data set average of 0.2 to obtaln the equation given above. No ranges or means for exaplanatory variables were reported.

B5.3 India

A number of engine oil equations were reported In CRRI (1982). Those given below Include measures of roughness and geometry. The notation for the equations as reported Is:

RF - Rise + fall (m/km) RG - Roughness (mm/km) LK - Vehicle age, at survey midpoint, 103km CV - Curvature ( 0 /km) EOL - Engine oil (Z/103 km).

The equations for car, truck, and bus engine oil consumption are:

Car

EOL - 1.598 + .00189CV + .000206 RG (2.88) (2.15) (1.81)

R2 - .20, S - .924, 54 observations.

Truck

EOL - 2.48 + .06ORF + .000057RG (4.77) (2.00)

R2 - .24, S - 1.584, 232 observations. FUEL AND LUBRICANT COSTS 163

The variable width (W) that appears in the truck oil equation in CRRI (1982) has been set to 7m to produce this equation.

Bus

EOL - 2.61 + .00178LK + .013RF + .000096RG (6.87) (1.25) (5.38)

R2 - .48, S - 1.284, 640 observations.

The varlables width (W) and number of major overhauls (OHF) that appear In the bus oil equations In CRRI (1982) have been set to W - 7m and OHF - .64 (average for the data set) to produce this equation.

Ranges and Mean Values for the Explanatory Varlables

Vehicle Varlable Min Max Mean

Car CV(°/km) 9 690 107 RG(mm/km) 3,416 6,955 4,987

Bus LK(103 /km) 22 988 345 RF(m/km) 1 50 15 RG(mm/km) 2,925 12,072 5,954

Truck RF(m/km) 1 58 13 RG(mm/km) 2,960 15,500 5,331

Source: CRRI (1982). I FUEL AND LUBRICANT COSTS 165

APPENDIX C. TABLES OF SPEED AND FUEL CONSUMPTION PREDICTIONS

This appendix provides speed and fuel consumption predlctions for each of the studies and most of the vehicle types studied. The predictions come from the analyses of fuel experiment and roadside speed data. The tables show predictions for combinations of highway roughness, vertical and horizontal geometry. Notes to the tables provide values to which other variables appearing In the studies' equations are set in the case of the Brazil study, default values common across tables are given In the appendix to Chapter 4. 166 FUEL AND LUBRICANT COSTS

Table C5.1a: Cars: Kenya, Ford Cortina Station Wagon Speed (km/hr)

Aveae Aversg erag Doereesq d Curvature(/akm) Rie Surface plus Roughness 100 300 SQ0 700 Fan Cm/Im) (mm/Ion) (m/Ian Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 4,000 5.1 89.2 65.3 67.0 41.7 44.8 18.1 22.6 * 10 6,000 7.4 63.5 39.9 16.3 * 8,lW0 9.5 61.7 38.1 * lOOO 12.0 59.9 36.3* 58.2 _ 34.6 - _ - 2,000 2.8 4,000 5.1 84.6 62.4 62.3 38.8 39.9 15.0 17.1 * 30 6,00 7.4 60.6 37.0 * * 8000 9.5 58.9 35.2 *t 10,000 12.0 57.1 33.4 55.3 31.6 *_* 2,000 2.8 _f_t 4,000 5.1 79.6 59.5 57.2 35.8 34.4 * 6,000 7.4 57.7 34.0 6.000 9.5 55.9 32.2 * * 10.000 12.0 54.1 30.4 *t 20,000 12.08232. - 52.3 - 28.S *- 2.000 2.8 74.4 56.5 51.6 32.6 28.0 * 4.000 5.154737 70 6,000 7.4 54.7 30.7 8.000. 9.5 52.9 28.91t 10,00012 0 51.1 27.1 *f* 10.00012.0 49.3 25.3 * *

A = Atud = 0 M = Moisture content = 2.6% RD = Rut Depth = 18.9 mm. *Indlcatesa predIced sped below 15 k/nh. FUEL AND LUBRICANT COSTS 167

Table C5.1b: Cars: Kenya, Ford Cortina Station Wagon Fuel Consumption (t/103 km)

Average Average Average Degrees of Ourvature(0Ikm) Rise Surface plus Roughness -100 300 500 700 FaN el IRI (mlkm) (mm/kmi) (m/klm) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 105 S9 4,000 5.1 159 10 6,000 7.4 169 8 000 9.5 107 94 10,000 12.0 108 97

2,000 2.8 109 95 4,000 5.1 109 97 30 6,000 7.4 110 99 8,000 9.5 ltl 101 10,000 12.0 113 104

2.000 2.8 113 101 4,000 5.1 114 104 50 6.000 7.4 115 106 8,000 9.5 117 109 10,000 12.0 118 112

2,000 2.8 118 109 4,000 5.1 120 112 70 6,000 7.4 121 114 8,000 9.5 122 118 10,000 12.0 123 121

Notes: L = depth of loose material = 1 mm. 168 FUEL AND LUBRICANT COSTS

Table C5.2a: Cars: Caribbean, Ford Cortina Station Wagon Speed (km/hr)

Average Average Average Degrees of CurvatureC0/km) Rise Surface plus Roughness 100 300 500 7C0 F&N Bi IRI (mntm) (mmlkm) (mlkn) Unpaved Unpaved Unpaved Unpaved 62.7 57.9 53.1 48.3 2,000 2.8 61. 0 56.2 51.4 46.6

10 6,000 7.4 59.3 54.5 49.7 44.9 8.000 9.5 57.5 52.7 47.9 43.1 10,000 12.0 55.8 51.0 46.2 41.4

2,000 2.8 61.3 56.5 51.7 46.9 4,000 5.1 59.5 54.7 49.9 45.1 30 6,000 7.4 57.8 53.0 48.2 43.4 8,000 9.5 56.1 51.3 46.5 41.7 10,000 12.0 54.3 49.5 44.7 39.9

2.000 2.8 59.8 55.0 50.2 45.4 4.0C0 5.1 58.1 53.3 48.5 43.7 50 6.000 7.4 56.4 51.6 46.8 42.0 8.000 9.5 54.6 49.8 45.0 40.2 10,000 12.0 52.9 48.1 43.3 38.5

2,000 2.8 58.4 53.6 48.8 44.0 4,000 5.1 56.6 51.8 47.0 42.2 70 6.000 7.4 U49 50.1 45.3 40.5 8,000 9.5 53.2 48.4 43.6 38.8 10.000 12.0 51.4 46.6 41.8 37.0 FUEL AND LUBRICANT COSTS 169

Table C5.2b: Cars: Carlbbean, Ford Cortina Station Wagon Fuel Consumption (/10 3km)

Average Average Average Degrees of Curvature(°/km) Rise Surface plus Roughness 100 300 500 700 FaN El IRI (m/km) (mm/km) (m/lun) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 797 371 4,000 5.1 78 75 72 70 10 6,000 7.4 77 74 72 70 8,000 9.5 75 73 71 70 10,000 12.0 74 n 70 70

2,000 2.8 87 84 81 79 4,000 5.1 86 83 80 79 30 6,000 7.4 85 82 80 79 8,000 9.5 83 81 79 78 10.000 12.0 83 80 79 78

2,000 2.8 S 93 91 89 4,000 5.1 95 92 90 89 So 6,000 7.4 94 91 89 88 8,000 9.5 93 90 89 88 10,000 12.0 92 90 89 88

2,00 2.8 106 104 101 100 4,000 5.1 51011 10 70 6,000 7.4 104 0 101 100 8,000 9.5 103 102 100 100 10,000 12.o 0 0 0 0 ______102 101 100 100 170 FUEL AND LUBRICANT COSTS

Table C5.3a: Cars: Brazil, Chevrolet Opala Sedan Speed (km/hr)

0 Average Average Averag DOgrees ot Curvature( lkrn) Rise Surface _ plus Roughness 100 300 500 700

(m/kn) (mm/km) (Mr/ Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 88.6 73.1 74.3 59.2 64.5 52.4 58.1 48.6 4,!00 5. 1 85.3 71.7 72.8 58.7 63.7 52.1 57.7 48.4 10 6,000 7.4 76.9 67.6 68.4 59.9 61.2 51.1 56.0 47.7 8,000 9.5 66.0 60.8 61.3 53.6 56.6 49.0 52.9 46.1 10oo00 12.0 55.9 53.3 53.6 49.0 50.9 45.8 48.5 43.6

2,000 2.8 88.1 72.9 74.1 59.1 64.4 52.4 58.1 48.6 4,000 5.1 84.9 71.5 72.6 58.6 63.6 52.1 57.6 48.4 30 6.000 7.4 76.7 67.4 68.3 56.9 61. 1 51.0 56.0 47.6 8,000 9.5 65.8 60.7 61.2 53.5 56.6 48.9 52.8 46.1 10,000 12.0 55.8 53.3 53.5 48.9 50.9 45.7 48.5 43.6

2,000 2.8 85.7 71.9 73.0 58.8 63.8 52.2 57.7 48.4 4,000 5.1 83.1 70.7 71.8 58.3 63.1 51.9 57.3 48.2 50 6.000 7.4 75.7 68.9 -67.7 56.6 60.8 50.9 55.7 47,5 8,000 9.5 65.4 60.4 60.9 53.3 56,4 48.8 52.7 46.0 10,000 12.0 55.6 53.1 53.4 48.8 50.7 45.7 48.4 43.6

2,000 2.8 77.5 67.9 57.1 61.4 51.4 51.2 56.1 47.7 4,000 5.1 76.3 67.2 68.0 56.8 61.0 51.0 55.9 47.6 70 6,000 7.4 71.4 64.3 65.0 55.4 59.1 50.1 54.6 47.0 8,000. 9.5 63.3 58.9 59.4 52.5 55.3 48.2 51.9 45.5 10.000 12.0 54.7 52.4 52.6 48.3 50.1 45.3 47.9 43.2

Notes: ALT = Altitude 0 VW Gras Vehicle Weight (W + LD) z 1.4 tonne FUEL AND LUBRICANT COSTS 171

Table C5.3b: Cars: Brazil, Chevrolet Opala Sedan Fuel Consumption (Q/103 km)

Average Average Aveage De>greesof Curvature(0f/in) Rie Surface plus Roughness 100 300 S00 700 Fall (mrn/k) (mm/kmn) (m/km Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 207 217 216 240 229 259 243 272 4,000 5.1 211 222 220 244 234 263 247 276 10 6,000 7.4 219 230 229 251 241 269 254 282 8.000 9.5 235 245 244 264 255 280 266 292 10,000 12.0 260 267 267 283 275 296 284 306

2.000 2.8 207 217 216 240 230 259 243 273 4,000 5.1 211 222 221 244 234 263 247 276 30 6,000 7.4 219 230 229 252 242 269 254 282 8,000 9.5 236 245 244 264 255 280 266 292 10.000 12.0 260 268 267 283 276 296 284 306

2.000 2.8 208 220 218 243 232 262 246 276 4,000 5.1 212 224 222 247 236 265 249 279 50 6.000 7.4 220 232 -231 254 244 272 256 285 8.000 9.5 237 247 246 266 257 282 268 294 10,000 12.0 262 269 269 285 277 298 286 308

2.000 2.8 217 228 227 250 240 268 253 281 4.000 5.1 220 232 230 254 243 271 256. 284 70 6.000 7.4 228 239 238 260 250 277 262 290 8,000. 9.5 244 253 252 271 263 28? 273 299 10.000 12.0 267 274 274 289 282 302 291 313

ALT = Altitude = 0 GVW = Gross Vehicle Weight = 1.4 tonnes 172 FUEL AND LUBRICANT COSTS

Table C5.4a: Cars: India, Ambassador Sedan Speed (km/hr)

Average Average Average Degrees of Curvature(0/km) Rise Surface plus Roughness 100 30 500 700 FaH 81 IRI (m/km) (mm/kn) (rn/km) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 58.1 56.5 54.9 53.4 4.000 5.1 50.9 49.3 47.7 46.2 tO 6,000 7.4 43.7 42.1 40.5 39.0 8.000 9.5 36.5 34.9 33.3 31.8 10,000 12.0 29.3 27.7 26.1 24.6

2,000 2.8 54.3 52.7 51.2 49.6 4,000 5.1 47.1 45.5 44.0 42.4 30 6,000 7.4 39.9 38.3 36.8 35.2 8,0 9. 32.7 31.1 29.6 28.0 10.000 12.0 25.5 23.9 22.4 20.8

2,000 2.8 50.5 49.0 47.4 45.9 S0 64000 7. 4 43.3 41.8 40.2 38.7 8,000 95S 36.1 34.6 33.0 31.5 10,000 12.0 28.9 27.4 25.8 24.3 21 ' 20.2 1laf 17.t 2,000 2.8 4,000 5.1 46.8 45.2 43.7 42.1 70 6,000 7.4 39.6 38.0 36.5 34.9 8,000 9.5 32.4 30.8 29.3 27.7 10,000 12.0 25.2 23.6 22.1 20.5

*R n .. 1fiL...4 ___* *

Notes:

W =Width = 7 m. *Indicates a predicted speed below 15 km/h. FUEL AND LUBRICANT COSTS 173

Table C5.4b: Cars: India, Ambassador Sedan Fuel Consumption (Q/103 km)

Average Average AverageiDegrees of Curvature(0°/m) Rise Surface . _ plus Roughness 100 300 500 700 Fanl Bl IRI (mlkm) (mmflka) (mlkre) Unpaved Unpaved Unpaved Unpaved 143 140 138 135 4,000 S.1 134 133 131 130 10 6,000 7.4 130 130 129 129 8,000 9.5 132 133 134 136 10,000 12.0 142 146 150 155

2,000 2.8 143 140 139 137 4,000 5.1 136 135 134 134 30 6,000 7.4 135 135 136 137 8,000 9.5 141 143 146 149 10,000 12.0 158 163 169 17

2,000 2.8 144 142 141 139 4,000 5.1 140 139 139 139 50 6,000 7.4 142 143 144 146 8,000 9.5 153 156 1S0 166 10,000 12.0 178 186 197 209

2,000 2.8 146 145 144 143 47000 5.1 145 145 146 147 70 6,000 7,4 151 153 156 159 8,0 9. 168 174 180 189 10,000 12.0 207 221 237 258 174 FUEL AND LUBRICANT COSTS

Table C5.5a: Light Goods Vehicles: Kenya, British Leyland Land Rover Speed (km/hr)

lmerag Aerwe AvberageDegrees of Curvature(0Ikrn)

plusNml Roughmne 100 300 SW070 _ __

Fanl- _ _ _ (mike) (rnm/kn) (m/h) Pavd Unpaved Pad U d Paved Unpavd Paved Unpaved

2,000 2.8 77.1 63.2 62.3 43.7 47.5 24.3 32.7 * 4,0W 5.1 61.3 41.8 22.4* 10 6,000 7.4 59.4 39.9 20.5 8,000 9.5 57.5 38.0 18.6 * 10.000 12.0 55.6 36.1 16.7 *

2.000 2.8 72.1 59.2 57.2 39.7 42.2 19.9 27.0 * 4.000 5.1 57.3 37.7 17.9 30 6,000 7.4 56.4 35.8 15.9 8.000 9.5 53.4 33.9 * 10,000 12.0 51.5 32.0 _

2,00 2.8 66.6 54.9 51.4 35.1 36.0 * 19.8 O 4,000 5.1 53.0 33.2 * * so 6.000 7.4 51.1 31.2 * * 8.000 9.5 49.1 29.2 * * 10.000 12.0 _ 47.2 _ 27.2

2,000 2.8 60.5 50.3 44.9 30.0 28.6 * a a 4.000 5.1 48.4 27.9 * * 70 6,000 7.4 46.4 25.9 * a 8.000 9.5 44.4 23.8 * a 10.000 12.0 42.5 21.6 a

A = AlUtude = 0 M = Moisturecontent = 2.6% RD = Rut Depth = 18.9 mm. *Indicates a predicted sped below 15 kmn/h. FUEL AND LUBRICANT COSTS 175

Table C5.5b: Light Goods Vehicles: Kenya, British Leyland Land Rover Fuel Consumption (g/103km)

Average Average Average Degrees of Curvature.(/km) Rise Surface plus Roughness 100 300 500 700 Fall Bi liii Cm/kmn) (mm/kim) Cm/km) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 165 140 4.000 5.1 164 141 10 6.000 7.4 163 142 8,000 9.5 163 144 10,000 12.0 163 145 _

2,000 2.8 175 1-5 4.000 S.1 175 156 30 6,000 7.4 175 1S7 8,000 9.5 175 189 10.0W0 12.0 175 161

2. O0 2.8 187 170 4,000 5.1 187 172 50 6,000 7.4 187 174 8. 000 9.5 187 177 10,0W0 12.0 188 1 7

2,000 2.8 200 Ise 4,000 5.1 200 188 70 6,000 7.4 200 191 8.00 9. 200 194 10.000 12.0 201 198

Notes: L = depth of loose material = 1 mm. 176 FUEL AND LUBRICANT COSTS

Table C5.6a: Light Goods Vehicles: Caribbean, Ford Transit Van Speed (km/hr)

Average Average Average Degrees of Curvature(/knm) Rim Surface plus Roughness 100 300 500 7C0 FaN of 1[R (mkni) (mmlkmn) (m/kn) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 58.3 53.9 49.5 45.1 4,000 5.1 57.0 52.6 48.2 43.8 10 6,000 7.4 55.7 51.3 46.9 42.5 8,000 9.5 54.4 50.0 45.6 41.2 10,000 12.0 53.0 48.6 44.2 39.8

2,000 2.8 56.8 52.4 48.0 43.6 4,000 5.1 55.5 51.1 46.7 42.3 30 6,000 7.4 54.2 49.8 45.4 41.0 8,000 9.5 52.8 48.4 44.0 39.6 10,000 12.0 51.5 47.1 42.7 38.3

2,000 2.8 55.3 50.9 46.5 42.1 45000 5.1 54.0 49.6 45.2 40.8 50 6,000 7.4 52.6 48.2 43.8 39.4

10,000 12 0 51.3 46.9 42.5 38.1 OW 12.0.0.0 S0, 45.6 41.2 36.8 2,000 2.8 4,000 5.1 53.8 49.4 45.0 40.6 70 6,000 7.4 52.4 48.0 43.6 39.2 8,000 9.5 51.1 46.7 42.3 37.9 10,000 12.0 49.8 45.4 41.0 36.6

Notes:

All speeds recorded on paved road sections. FUEL AND LUBRICANT COSTS 177

Table C5.6b: Light Goods Vehicles: Caribbean, Ford Transit Van Fuel Consumption (Q/103 km)

Average Average Average Degrees of Curvature ( 0 km) Rise Surface plus Roughness -100 300 500 700 FaH BDl IR (m/kmi) (mmfkm) (m/kin) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 123 122 121 121 4,000 5.1 123 122 121 121 10 6,000 7.4 122 121 121 121 8,0W 9.5 122 121 121 121 I 10,000 12.0 122 121 121 122

2,000 2.8 144 143 142 142 4,000 5.1 143 142 142 142 30 6,000 7.4 143 142 142 143 8,0W 9.5 143 142 142 143 10,000 12.0 142 142 142 143

2,000 2.8 167 166 166 166 4,000 S.t 165 166 166 166 50 6, 000 7.4 166 166 166 166 8,000 9.5 1 166 166 167 10,000 12.0 166 166 166 167

2.000 2.8 193 192 192 192 4,000 5.1 _ l 70 6.000 7.4 192 192 192 193 8.000 9g5 192 192 192 193 10,000 12.0 192 192 192 193

Gross vehicle weight (GVW) =2.6a tonnes 178 FUEL AND LUBRICANT COSTS

Table C5.7a: Light Goods Vehicles: Brazil, Volkswagen Kombi Speed (km/hr)

Average Average Averager egres of Curvature(t/1mn) Rise Surface plus Roughness 100 300 S00 700 Fail (m/kmn) (mm/km) (m/kin Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2.000 2.8 75.2 65.0 64.7 54.8 57.4 49.5 52.5 46.4 4.000 5.1 72.1 63.3 63.0 54.0 56.4 48.9 51.8 45.9 10 6.000 7.4 65.7 59.4 59.2 51.9 53.9 47.5 50.0 44.9 8,000 9.5 57.6 53.7 53.6 48.5 49.9 45.1 47.1 42.9 100,D 12.0 49.7 47.6 47.5 44.2 45.2 41.9 43.3 40.2

2,000 2.8 72.5 63.3 63.0 53.9 56.3 48.9 51.8 45.9 4.000 5.1 69.6 61.7 61.4 53.1 55.3 48.3 S1.1 45.5 30 6,000 7.4 63.8 58.1 57.8 51.1 52.9 46.9 49.3 44.4 8.000 9.5 56.3 52.7 52.6 47.8 49.2 44.6 46.5 42.5 10.000 12.0 49.0 46.9 46.8 43.7 44.7 41.5 42.8 39.9

2,00 2.8 66.6 59.6 59.3 51.8 53.8 47.4 50.0 44.8 4,000 5.1 64.5 58.3 58.1 51.1 53.0 46.9 49.3 44.4 50 6,000 7.4 60.0 55.3 55.1 49.3 50.9 45.7 47.8 43.4 8,000 9.5 53.8 50.7 50.6 46.4 47.6 43.5 45.2 41.6 10,000 12.0 47.4 45.6 49.5 42.7 43.6 40.6 41.9 39.2

2.000 2.8 57.4 53.3 53.2 48.0 49.5 44.7 46.6 42.6 4.000 5.1 56.4 52.6 52.4 47.5 48.9 44.3 -46.2 42.3 70 6.000 7.4 53.8 50.6 50.5 46.2 47.5 43.3 45.0 41.5 8.000. 9.5 49.6 47.3 47.2 44.0 44.9 41.6 43.0 40.0 10,000 12.0 44.8 43.3 43.2 40.9 41.6 39.2 40.2 37.9

Notes: ALT = Altitude= 0 GMW - Gaore Vetde Weight (W + UD) 2.1 tonnes FUEL AND LUBRICANTCOSTS 179

Table C5.7b: Light Goods Vehicles: Brazil, Volkswagen Kombi Fuel Consumption (Q/10 3km)

Average Averge Average Degres ot Curvature(I°km) Rise Suface plus Roughness 100 300 S00 70 Fall (mr/krn) (mm/kIn) (mlrnk Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 182 181 182 187 185 194 190 199 4.000 5.1 186 187 187 193 191 199 196 204 10 6,000 7.4 191 193 193 200 19S 206 202 211 8.000 9.5 199 202 203 209 207 215 211 220 10.000 12.0 212 215 215 221 220 227 224 231

2,000 2.8 182 182 183 188 186 195 191 200 4.000 5.1 187 188 188 194 192 200 196 205 30 6,000 7.4 192 194 194 201 199 207 203 212 8,o00 9.5 200 204 204 210 208 216 213 221 10.000 12.0 213 216 217 223 221 228 225 232

.2.000 2.8 191 195 196 206 202 212 208 218 4.O00 5.1 19S 200 200 209 206 217 212 222 50 6.000 7.4 202 207 -207 215 213 222 218 228 8.000 9.5 212 216 216 224 222 231 227 235 10,000 12.0 225 229 229 236 234 241 238 246

2.000 2.8 220 224 225 232 230 238 234 242 4.000 5.1 223 228 228 235 233 241 238 246 70 6,000 7.4 228 233 233 240 238 246 242 250 8,000. 9.5 237 240 241 247 245 252 249 256 10,0DO 12.0 247 250 251 256 254 262 258 266

ALT = Attitude 0 GVW = Gross Vehicle Weight = 2.1 tonnes 180 FUEL AND LUBRICANT COSTS

Table C5.8a: Buses: Brazil, Mercedes Benz 0362 Speed (km/hr)

Avwera Averae Averae Degrees of CurvatureClAwn) Al. Suurfce puw Roughness 100 300 50 70

Fa R ______. _ (mrln) (mm/kmr) (m/Alc Paved Unpaved Paved |Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 72.1 59.3 64.4 51.4 57.9 46.9 53.3 44.4 4,000 5.1 69.2 58.3 62.6 50.7 56.8 46.5 52.6 44.0 10 6,000 7.4 62.5 55.0 58.1 48.9 53.9 45.3 50.4 43.1 8W000 9.5 53.8 49.7 51.5 45.6 49.0 42.9 46.7 41.1 10.000 12.0 45.9 43.7 44.7 41.3 43.3 39.5 42.0 38.3

2,000 2.8 62.4 53.8 57.2 47.9 52.7 44.5 49.4 42.4 4.000 5.1 60.3 52.9 56.8 47.3 51.8 44.1 48.7 42.0 30 6,000 7.4 55.6 50.4 52.6 45.8 49.6 43.0 47.0 41.2 8.000 9.5 49.4 46.3 47.7 43.2 45.8 40.9 44.0 39.5 10.000 12.0 43.3 41.6 42.4 39.6 41.3 38.1 40.2 37.0

2,000 2.8 50.6 45.8 47.8 42.2 45.2 39.9 43.1 38.5 4,000 5.1 49.5 45.2 47.0 41.2 44.6 39.6 42.7 38.2 S0 6,000 7.4 46.8 43.6 45.0 40.7 43.1 38.8 41.5 37.5 8.000 9.5 43.0 41.0 41.9 38.9 40.6 37.3 39.5 36.3 10W000 12.0 38.9 37.7 38.3 36.3 37.5 35.2 36.7 34.4

2,000 2.8 40.2 38.1 39.0 36.1 37.8 34.8 36.7 33.9 4.000 5.1 39.7 37.8 38.6 35.9 37.4 34.6 36.4 33.7 70 6.000 7.4 38.5 36.9 37.6 35.2 36.6 34.0 35.7 33.2 8.000. 9.5 36.5 35.4 35.9 34.1 35.2 33.1 34.4 32.4 10,000 12.0 34.1 33.3 33.7 32.4 33.2 31.6 32.7 31.1

t~~~~M.~_

ALT = Altitude = 0 VW 2 Gross Vehile Weight (W + LD) 11 tonneq FUEL AND LUBRICANT COSTS 181

Table C5.8b: Buses: Brazil, Mercedes Benz 0362 Fuel Consumption (Z/103 km)

Average Aver Average Degreesof CurvatureCI/bn) Rise Surface plus Roughness 100 300 500 70 Fai (mlkm) (mm/lkn) (ml/kn Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 268 250 255 247 249 248 247 249 4,000 5.1 269 255 260 253 254 254 253 255 10 6,000 7.4 266 260 262 259 259 260 259 262 8.000 9.5 265 265 265 266 265 268 266 270 10o000 12.0 272 274 273 276 274 279 275 281

2,000 2.8 284 281 281 283 281 286 283 288 4.000 S.1 287 286 286 288 286 291 287 293 30 6.000 7.4 290 291 291 294 292 297 293 298 8.000 9.5 296 298 297 301 299 304 300 306 10.000 12.0 306 308 307 310 308 313 310 315

2,000 2.8 362 383 363 364 363 365 364 365 4.000 5.1 366 367 366 368 367 368 367 369 so 6.000 7.4 370 371 370 372 371 372 371 373 8,000 9.5 374 375 375 376 375 37 376 377 10,000 12.0 379 380 380 381 380 382 380 384

2.000 2.8 464 465 465 466 465 467 466 468 4.000 5.1 468 469 469 470 489 471 470 471 70 6.000 7.4 472 473 473 474 473 475 474 475 8.o00. 9.5 477 478 477 478 478 479 478 479 10,000 12.0 482 482 482 483 483 484 483 484

Nf:

ALT = Altitude = 0 GVW = Gross Vehicle Weight = 11 tonnes 182 FUEL AND LUBRICANT COSTS

Table C5.9a: Medlum Trucks: Kenya, Bedford J4LC5 Speed (km/hr)

A%ereg Amsrge Avwrag Degreesof cur'vatureaCllae)

-u Rougi_e. 100 300 m0 roo Pmft ______(mukr) (mm/Ikn) (mAImnPaved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2.000 2.8 59. 54 1 48.1 41.9 36.5 29.6 22.6 17.3 4,000 5.1 62.9 40.7 28.4 16.1 10 6,W0 7.4 51.7 39.5 27.2 * 6.000 9.5 50.5 38.3 26.0 1_.00 12.0 49.3 37.1 24.8 0

2,O0 2.8 53.7 49.0 41.6 36.5 29.6 23.8 16.8 * 4,W0 5.1 47.8 35.3 22.5 * 30 6,000 7.4 46.6 34.1 21.2 8,C00 9.5 45.4 32.8 19.9 * 10.000 12.0 44.1 31.6 16.6

2.000 2.6 46.3 43.0 33.6 29.8 19.9 15.6 4,000 5.1 41.7 28.5 50 6,000 7.4 40.4 27.1 * * 8,600 9.5 39.2 25.8 * * 10,0W0 12.0 37.9 24.4

2,000 2.6 37.0 35.6 22.6 21.1 4.000 5.1 34.3 19.5 * 70 6,000 7.4 32.9 16.0 * 8,000. 9.5 31.5 16.3 * 10.w0 12.0 30.1 a *

A = Altitude In paved equation = 0 U = Msture content = 2.6% RD = Rut Depth = 18.9 mm. *Indicates a predicted spod below 15 km/h. FUEL AND LUBRICANT COSTS 183

Table C5.9b: Medium Trucks: Kenya, Bedford J4LC5 Fuel Consumption (Q/10 3km)

Average Average Average Degrees of CurvatureC0/krn) Rise Surface plus Roughness 100 300 500 700 Fas 81 IRI tmlkm) (mm/km) tr/kin) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 191 176 4,000 5.1 193 178 10 6.000 7.4 194 181 8,000 9.5 196 183 10,000 12.0 198 186

2.000 2.8 208 196 4,000 5.1 210 199 30 6,000 7.4 212 202 8,000 9.5 214 205 10.000 12.0 216 208

2.000 2.8 227 220 4,000 5.1 229 224 50 6,000 7.4 232 227 8,000 9.5 234 231 10,000 12.0 236 235

2000 2.8 249 2 4.000 5.1 248 258 70 6,000 7.4 2.4258 8,00 9.5 2527 10.000 12.0 2r1 281

Notes: L = Depth of Loose Material = 1mm. PW = Power to Weight Ratio = 10 bhp/tonne. 184 FUEL AND LUBRICANT COSTS

Table C5.10a: Medium Trucks: Caribbean, Ford DlOD10 Speed (km/hr)

Average Average Average Degree. of CurvatureCO/lkm) Rime Surface plus Roughness 1C 300 500 700 FaS B R (m/lkM) (mm/km) (m/ln) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 51.5 48.1 44.7 41.3 4,0o00 5.1 49.3 45.9 42.5 39.1 10 6.000 7.4 47.1 43.7, 40.3 36.9 8,000 9.5 44.9 41.5 38.1 34.7 10.000 12.0 42.7 39.3 35.9 32.5

2.000 2.8 48.0 44.6 41.2 37.8 4,000 5.1 45.8 42.4 39.0 35.6 30 6,00 7.4 43.6 40.2 36.8 33.4 8,000 9.5 41.4 38.0 34.6 31.2 10.000 12.0 39.2 35.8 32.4 29.0

2.000 2.8 44.5 41.1 37.6 34.2 4,000 5.1 42.3 38.8 35.4 32.0 50 6,000 7.4 40.0 36.6 33.2 29.8 8.000 9.5 37.8 34.4 31.0 27.6 .0,000 12.0 35.6 32.2 28.8 25.4

2,000 2.8 .0 . 40.9 37.4 34.0 30.6 70 6,000 7.4 38.6 35.2 31.8 28.3 8,0QO 7.4 36.4 33.0 29.6 26.1 10.000 12.0 34.2 30.8 27.3 23.9 10,WO_ 12.0 32.0 28.5 25.1 21.6

NoteS:

PW = Power to weight ratio 9.3 Bhp/tonne. FUEL AND LUBRICANT COSTS 185

Table C5.1Ob: Medlum Trucks: Caribbean, Ford DlOD10 Fuel Consumption (Q/103km)

Average Average Average Degrees of Curvature(I/luml Rlse Surface plus Roughness 100 300 500 700 Fall _1 IR (mn/im) (mm/Ian) Cm/kin) Unpaved Unpaved Unpaved Unpaved 2.000 2.8 196 191 188 186 4,000 S.1 193 189 187 185 10 6.000 7.4 190 187 186 185 8.000 9.5 188 186 185 186 10.000 12.0 187 185 186 188

2.000 2.8 302 299 297 296 4,000 5.1 300 297 296 297 30 6.000 7.4 298 297 296 298 8.000 9.5 297 296 297 300 10,000 12.0 296 297 299 303

2.000 2.8 416 414 413 414 4,000 5.1 414 413 414 416 50 6.000 7.4 413 413 415 419 I8.000 9.5 413 414 417 422 10.000 12.0 413 416 420 428

2,000 2.8 4.000 5.1 537 540 70 6~,g000 S. 1 536 537 539 544 70 6.000 7.4 56S 4 4 8,000 9.5 536 538 542 549 10,000 12.0 S10 546 555 539 543 551 564

Notes: GVW Gross Vehicle Weight = 14 tonnes. 186 FUEL AND LUBRICANT COSTS

Table C5.11a: Medium Trucks: Brazil, Mercedes Benz L1113 Speed (km/hr)

Average Aversae Average Degrees of Curvaturs( 0 /kmn) Rise Surface plus Roughness 100 300 500 700 Fail (mlkm) (mm/kmn) (m/Ikml Paved Unpaved Paved Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 64.4 56.0 57.9 48.4 52.8 44.6 49.1 42.4 4.000 S.1 60.3 53.7 55.2 47.2 51.0 43.7 47.8 41.6 10 6,000 7.4 53.0 48.9 49.9 44.2 47.0 41.5 44.7 39.8 8,000 9.5 45.1 42.9 43.4 40.0 41.8 38.2 40.3 37.0 10.000 12.0 38.2 37.1 37.4 35.5 36.5 34.3 35.6 33.5

2,000 2.8 53.6 48.4 49.5 43.3 46.3 40.7 43.8 39.0 4,000 5.1 50.9 46.7 47.7 42.3 44.9 40.0 42.8 38.4 30 6,000 7.4 46.1 43.4 44.1 40.2 42.1 38.2 40.5 37.0 8,000 9.5 40.7 39.1 39.5 37.0 38.3 35.6 37.2 34.7 10,000 12.0 35.6 34.7 34.9 33.4 34.2 32.5 33.6 31.9

2.000 2.8 42.9 39.9 40.6 36.9 38.7 35.2 37.2 34.2 4,000 5.1 41.4 38.9 39.5 36.2 37.8 34.7 36.5 33.7 50 6,000 7.4 38.5 36.8 -37.2 34.8 36.0 33.5 35.0 32.7 8.000 9.5 35.0 34.1 34.3 32.7 33.5 31.7 32.8 31.1 10,000 12.0 31.7 31.1 31.2 30.2 30.7 29.5 30.3 29.1

2,000 2.8 34.6 33.0 33.4 31.2 32.3 30.2 31.4 29.5 4,000 5.1 33.8 32.4 32.7 30.8 31.7 29.8 30.9 29.2 70 6,000 7.4 32.1 31.1 31.4 29.9 30.6 29.0 30.0 28.5 8,000 9.5 30.0 29.4 29.5 28.5 29.0 27.8 28.6 27.4 10,000 12.0 27.8 27.4 27.5 26.7 27.1 26.3 26.8 26.0

Notes: ALT = Attude = 0 QVW = Gross Vehkcl Weight (W + LD) = 14 tennes FUEL AND LUBRICANT COSTS 187

Table C5.11b: Medium Trucks: Brazil, Mercedes Benz L1113 Fuel Consumption (t/lO3km)

Average Aversge Average Degrees of Curvature(/kmn) Rise Surface plus Roughness 100 300 500 700 Fall - (m/kin) (mm/km) (m/km) Paved Unpaved Paved | Unpaved Paved Unpaved Paved Unpaved

2.000 2.8 345 333 335 332 331 335 332 338 4.000 5.1 347 341 341 341 340 344 341 347 10 6,000 7.4 348 349 348 352 349 356 351 359 8.000 9.5 359 362 361 367 363 371 366 374 10.000 12.0 379 382 381 387 384 391 386 394

2.000 2.8 402 405 404 410 407 415 410 418 4.000 5.1 409 412 411 418 414 423 417 426 30 6.000 7.4 419 423 422 428 425 432 428 435 8.000 9.5 434 437 436 442 438 445 441 448 10.000 12.0 452 455 454 459 456 462 458 465

2,000 2.8 537 540 540 544 542 546 543 548 4,000 5.1 544 547 546 550 548 553 550 555 50 6,000 7.4 552 554 -554 558 556 561 558 563 8,000 9.5 563 565 564 568 566 571 568 573 10.000 12.0 577 578 578 581 579 584 581 585

2,000 2.8 683 696 695 700 698 702 699 704 4.000 5.1 700 703 702 706 704 708 706 710 70 6,000 7.4 708 710 710 713 712 715 713 716 8.000 9.5 718 720 719 722 720 723 722 724 10.000 12.0 729 730 729 730 730 731 730 732

Notes:

ALT = Altitude = 0 GVW = Gross Vehicle Weight = 14 tonnes 188 FUEL AND LUBRICANTCOSTS

Table C5.12a: Medium Trucks: India, Tata 1210 SE/42 Speed (km/hr)

Average Average Average Degrees of Curvature(/kml) Rise Surface . plus Roughness 100 300 so0 7G0 FaH Bl IRI (m/kmi) (mm/km) (m/kin) Unpaved Unpaved Unpaved Unpaved 2,000 2.8 47.3 45.3 43.3 41.3 4,000 S.1 43.5 41.5 39.5 37.5 10 6.000 7.4 39.7 37.7 35.7 33.7 8.000 9.5 35.9 33.9 31.8 29.9 10.000 12.0 32.1 30.1 28.1 26.1

2.000 2.8 41.9 39.9 38.0 36.0 4,000 5.1 38.1 36.1 34.2 32.3 30 6,000 7.4 34.3 32.3 30.4 28.4 8,00 9.5 30.5 28.5 26.6 24.6 10,000 12.0 26.7 24.7 22.8 20.8

2.00o 2.8 36.6 34.6 32.6 30.6 4.000 5.1 32.8 30.8 28.8 26.8 50 6,000 7.4 29.0 27.0 25.0 23.0 8.000 9.5 25.2 z3.2 21.2 19.2 10,000 12.0 252 2. 2.2 12 ______21,4 19.4 17.4 15.4 2,000 2.8 4,000 5.1 31.2 29.3 27.3 25.3 70 6.000 7.4 27.4 25.5 23.5 21.5 8,o00 9.5 23.6 21.7 19.7 17.7 10,000 12.0 19.8 17.9 15.9 * ______16.0 * * *

Notes:

W = Width = 7 m. *Indicates a predicted speed below 15 km/h. FUEL AND LUBRICANT COSTS 189

Table C5.12b: Medium Trucks: India, Tata 1210 SE/42 Fuel Consumption (Q/103 km)

Average Average Average Degrees of Curvature(°/km) Rise Surface plus Roughness 100 300 500 700 Fan Bl IRI (rn/kin) (mm/knn) (mr/kn) Unpaved Unpaved Unpaved Unpaved

2,000 2.8 212 212 212 213 4,000 5 1 215 216 218 221 10 6.Ow 7.4 221 224 227 232 8.000 9.5 230 235 240 248 10,000 12.0 243 250 259 270

2,000 2.8 233 235 237 241 4,000 5.1 240 243 248 254 30 6,000 7.4 251 256 263 272 8.000 9.5 266 274 285 297 10,000 12.0 287 299 315 334

2.000 2.8 260 264 269 276 4,000 5.1 272 279 287 297 50 6,000 7.4 289 299 311 326 8.000 9.5 313 328 346 369 10,000 12.0 348 370 398 434

2,000 2.8 294 302 312 324 4,000 5.1 314 326 340 358 70 6,000 7.4 342 359 381 408 8,000 9.5 382 409 443 487 10,000 12.0 443 486 544__

Notes: PW = Power to weight ratio 10 kw/tonne. 190 FUEL AND LUBRICANT COSTS

Table C5.13a: Articulated Trucks: Brazil, Scania 110/39 Two Axle Tractor with TrI-Axle Semi-Trailer Speed (km/hr)

Average Average Averge Degrees of Curvature( 0/kn) Rise Surface _ plus Roughness 100 300 SW 700 Fall _ (mr/km) (mm/kin) (m/krn Paved Unpaved Paved |Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 C2.4 45.3 53.7 40.8 48.2 38.7 44.7 37.6 4,000 5. 1 56.2 43.9 50.7 39.9 46.3 38.1 43.4 37.1 t0 6,000 7.4 45.7 40.0 43.6 37.3 41.4 36.0 39.6 35.2 8.000 9.5 36.5 34.4 35.8 33.0 35.0 32.3 34.2 31.8 10,000 12.0 29.9 29.0 29.6 28.5 29.3 28.1 29.0 27.9

2,000 2.8 45.5 37.6 41.6 35.2 39.0 34.0 37.3 33.4 4.000 5.1 42.5 36.7 40.0 34.6 37.9 33.5 36.4 32.9 30 6.000 7.4 37.4 34.5 36.4 32.9 35.2 32.1 34.3 31.6 8.000 9.5 32.3 31.0 30.1 31.3 29.6 30.8 30.8 29.3 10,000 12.0 27.8 27.2 27.6 26.8 27.4 26.5 27.1 26.3

2.000 2.8 34.3 30.3 32.4 29.0 31.1 28.3 30.1 28.0 4.000 5.1 32.9 29.8 31.6 28.6 30.4 28.0 29.6 27.6 50 6.000 7.4 30.1 28.5 -29.5 27.6 28.9 27.1 28.3 26.8 8.000 9.5 27.2 26.4 26.9 25.9 26.6 25.6 26.3 25.4 10,000 12.0 24.4 24.0 24.3 23.8 24.2 23.6 24.0 23.5

2,000 2.8 26.6 24.8 25.9 24.1 25.2 23.7 24.7 23.5 4,000 5.1 26.0 24.5 25.5 23.8 25.0 23.5 24.4 23.3 70 6.000 7.4 24.7 23.7 24.4 23.2 24.0 22.9 23.7 22.8 8,000. 9.5 23.0 22.5 22.8 22.1 22.6 21.9 22.4 21.8 10,000 12.0 21.2 21,0 21.1 20.7 21.0 20.6 20.9 20.6

Notes: ALT = Altitude = 0 GVW= a.ro Vehkb Weight (W + LD) = 40 tonnes. FUEL AND LUBRICANT COSTS 191

Table C5.13b: Articulated Trucks: Brazil, Scania 110/39 Two Axle Tractor with TrI-Axle Semi-Trailer Fuel Consumption (Q/10 3 km)

Average Averge Average Degrees of Curvature(°ktn) Rise Surface plus Roughness 100 300 500 700 Fanl (mlakm) (mm/lkn) (m/kMt Paved Unpaved Paved |Unpaved Paved Unpaved Paved Unpaved

2,000 2.8 628 640 628 652 635 659 641 664 4.000 5.1 650 665 653 676 659 683 666 687 10 6,000 7.4 682 697 687 707 693 713 698 717 8,000 9.5 732 742 735 750 739 754 743 757 10.000 12.0 792 799 794 804 797 807 800 809

2,000 2.8 835 841 838 841 840 841 841 842 4,000 5.1 849 853 851 853 853 855 853 856 30 6,000 7.4 865 866 865 869 866 871 867 872 8.000 9.5 884 889 886 892 887 894 8SS 895 10,000 12.0 918 922 919 925 921 926 922 928

2,000 2.8 1197 1203 1200 1205 1202 1206 1203 1207 4,000 5.1 1212 1216 1214 1218 1215 1219 1217 1220 50 6,000 7.4 1229 1232 1229 1233 1231 1234 1231 1234 8,000 9.5 1246 1248 1247 1249 1247 1250 1248 1250 10,000 12.0 1265 1266 1265 1267 1266 1267 1266 1267

2.000 2.8 1564 1568 1565 1570 1567 1571 1568 1571 4.000 5.1 1578 1581 1579 1583 1581 1584 1582 1585 70 6,000 7.4 1594 1596 1595 1598 1595 1598 1596 1599 8,000. 9.5 1611 1612 1612 1613 1612 1614 1613 1614 10,000 12.0 1629 1630 1629 1630 1630 1631 1630 1631

Notes:

ALT = Attitude = 0 GVW = Gross Vehicle Weight = 40 tonnes I I I I CHAPTER 6 Tire Costs

Tire costs are an Important element of vehicle operating costs, particularly in developing countries, and they are sensitive to highway conditions. In consequence, in the four user surveys considerable effort was devoted to obtaining tire cost data. The difficulties encountered when collecting these data and the methods adopted in the four studies are the subject of Section 6.1. The statistical methods used to analyze the data are considered in Section 6.2 while in Sections 6.3 and 6.4 the results obtained concerning car tires and bus and truck tires are presented. The final Section 6.5 summarizes this chapter and presents brief comparisons with other sources. The remainder of this section Is devoted to a number of general Issues that arise when tire costs are considered.

Like fuel and oil, tires are consumed continuously as vehicles travel. Each kilometer travelled results in material being removed from the tire and, if for no other reason, tires will eventually wear out from this type of abrasive wear. In addition, like the vehicle itself, tires are stressed and strained as they travel so that, as time passes, the tire's carcass Is also weakened. When the rubber tread of the tire Is worn through, or nearly so, It may be optimal to recap the tire provided that Its carcass is still in serviceable condition and we would naturally expect this practice to be more prevalent when tires are expensive and carcasses robustly built as are the tires found on large trucks. Evidence from the Brazilian study suggests that numbers of recaps performed per tire is around two times higher for heavy trucks using 1100 x 22 tires than for lighter trucks using 900 x 20 tires. Whether or not recapping occurs at any point in a tire's life depends upon the cost of recapping and on the expected lifetime of the tire subsequent to recapping. As the tire ages and the carcass weakens recapping ceases to be optimal and the tire Is scrapped.

The Incidence of tire failure and the rate of tread loss are much greater In developing countries than In the majority of developed nations. This is partly because of the prevalence of relatively low quality tires. Mainly though it Is because travel on poor quality roads, often unpaved, causes Increased carcass stress and ablative tread wear and accelerates normal tread loss. Increased Incidence of overloading causes greater carcass flexing and increases the risk of premature failure particularly for tires placed on drive axles. And where ambient temperatures are high, tires overheat and are more likely to blowout or strip thelr tread. Vehicle owners operating on unpaved routes cannot generally use steel braced radial tires because of risk of side wall damage and owners operating vehicles on paved routes are in many countries unable to purchase such tires due to import restrictions and the absence of such tires In the product range of Indigenous manufacturers. Steel braced radial tires were

193 194 TIRE COSTS not available In Brazil or India during the periods In which user surveys were performed, despite the sizes of the tire markets in these countries.

Truck and bus owners in Industrialized nations can expect tire lives In excess of 100,000 kilometers but in developing countries it Is common to find only half this figure being achieved on paved routes and one third or less on unpaved routes. Consequently, many vehicle owners in developing countries make strenuous efforts to prolong tIre life. Recapping or retreading is one way In which tire life can be prolonged, and this is a common practice in developing countrles encountered In all the user surveys. Often a tire will pass through several "lives," belng successively recapped, and the number of recaps performable and the kilometerages obtained with each recap will depend upon many factors Including vehicle load and speed, highway characteristics and driver behaviour. The first "life" of the tire from new to first recap Is typically the longest In terms of kilometers travelled, successive recaps yielding declining kilometerage. Some indication of tire lives in kilometers as a tire passes through successive retreads Is given in Table 6.1 which Is based on Information obtained from one large Indian organisation.

Tread wear may not vary significantly between new and properly recapped tires on certain vehicle axles. Ker and Soloman (1976) measured tread loss on a sample of line haul and dump truck operations In New South Wales, Australia, and found littie difference between new and recap tire tread wear rates on all trailing axles or on tandem drive axles where the total suspension load did not exceed 14 tonnes, 1.7 tonnes per tire. The lower kilometerage for recap "lives" observed In the Indian study may reflect Increasing Incidence of carcass fallure on successive recaps and Increased recap tread loss due to ablative wear or lifting as a result of accelerative forces on driven axles. On occasions, particularly in bus operations where safety considerations are especially Important, owners will sell tires before first recapping or second recapping. More commonly though tires are retained until scrapping. In large organisations tires may be recapped "in house" but otherwlse recapping will be performed by specialist tire workshops.

There are considerable across company differences in tire costs. These arise because of differences in types of tires used, and because of differences In the Incidence of recapping which reflects differences in types of business and variations In the marginal cost of recapping.

Daniels (1974) draws attention to wide ranges of estimates of tire lives obtained from vehicle operators In service, and the results obtained In the Indian and Brazilian surveys suggest that these differences are real and substantial. Accordingly, In the analysis of these surveys' data sets particular attention was paid to company policy influences and to obtaining estimates of the effects of highway characteristics on tire costs that are not unduly Influenced by across company variation In tire costs attributable to company policy differences.

The equations presented below in Sections 6.3 and 6.4 are very simple, relating tire costs or some straightforward transformation of this TIRE COSTS 195

Table 6.1: Average Kilometers Run by New and Recapped Tires

State In Tire Life Average Kilometers Run Number of Tires Sampled

New-Retread 1 1/ 32,916 26,256

Recap 1 - Recap 2 1/ 21,515 17,533

Recap 2 - Recap 3 1/ 20,853 6,962

Recap 3 - Recap 4 '/ 18,191 1,896

Recap 4 - Recap 5 1/ 10,364 146

Source: RUCS Technical Paper 63, CRRI indla. Note: Sample based on tire pool of one large state organisatlon. 1/ Or Scrapping. variable to linear functions of highway characteristics, specifically road roughness, average route rise + fall and average degrees of curvature. The equations pick up most of the features of the data sets.

None of the surveys reported here use detailed theoretical models for tire costs as the basis for their analysis. There are models available for the relationship between tread wear and road roughness and geometry (see e.g., Bergman and Crum (1973), Sullivan (1977) and Zanlewskl et al. (1981) but, as noted above, tread wear Is only one aspect of tire life, carcass deterioration being as, If not more, important In developing countries since It limits owners' ability to recap. In addition these models do not consider complete tire failure caused by blowouts or ablative tire wear. And models constructed on purely Dhysical principles tend to overstate tread wear unless they are used very carefully, for vehicle owners will adopt tire policies to reduce tire costs In precisely those situations In which tire life Is predicted to be especially short.

Watanatada et al. (1987) report attempts to analyze the Brazilian user survey data using a model that exploits the Idea from Delia Moretta and Sullivan (1976), that tire wear Is a function of tangential energy, proportional to slip energy. Tangential energy is the ratio of squared tangential force per tire to gross vehicle weight per tire, and In Its calculation, forces operating in the circumferential and lateral directions of the tire play equally Important roles. A purely empirical carcass life model has also been incorporated. The models available at the time of writing are not entirely satisfactory, partlcularly so far as the modelling of the effect of curvature is concerned. The difficulties In estimation of a micro-level model built upon fundamental physical principles using user survey data are of course enormous. Detailed Information on road vertical and horizontal alignment, abrasive properties of the road surface, vehicle loads and load distribution, tire Inflation, tire constructlon and rubber properties, and assoclated tire wear are required, and user survey data do 196 TIRE COSTS not contain this Information. Sufficiently detailed Information might be obtained from controlled experiments, but it would be difficult to design experiments which captured the Important effects that are due to driver behaviour and that arise from vehicle owners desires to avoid excessive tire costs.

Here we report the results of analysis that acknowledge the Informatlon content of the available user survey data. These take the form of relationships between the tire costs actually experienced by vehicle owners and the broad, aggregate measures of highway quality that were obtained In the road user surveys. In the next two sections we describe the collection and analysis of tire cost data.

6.1 TIRE COST DATA

The quality of tire cost records varies considerably from company to company. Small organisations rarely adopt formal tire record systems and collecting data from such organisations Is difficult. In large organisations tire control systems are more common and in the Brazilian survey these were exploited as data sources where possible. In large organisations It Is common to find vehicle owners operating a tire pool system in which tires switch from vehicle to vehicle, the system being controlled using documentation that tracks the performance of each tire In the pool.

Tire pools were so prevalent in the companies surveyed in the Brazilian study that the Brazilian tire cost data were collected on an individual tire basis, each tire's history from new to sale or scrapping being recorded. Total kliometerage travelled on each vehicle was obtained together with total kilometerage between each recapping. The Kenyan, Caribbean, and Indian studies collected tire cost data quite differently, focussing on Individual vehicles rather than Individual tires, essentially counting the number of tires used by survey vehicles during the survey period and relating this to the kilometerage travelled by the vehicles. Both approaches present their own special difficulties.

The technique used in the Brazilian study requires quite sophisticated record keeping and the Brazilian research team devoted much effort to designing documentation tailored to Individual companies' operations. For each surveyed tire, every change of vehicle from the tire's first use to sale or scrapping was recorded and highway characteristics experienced by the tire were built up as kilometer weighted averages of highway characteristics experienced by the vehicles on which the tire was placed. For each tire total kilometers travelled from new to scrapping (TK) was recorded together with total number of recaps performed

(NR). The total cost per tire Is PN PTN *] where PN Is the price of a new tire and PR Is the cost of recapping a tire. The dependent variable for the statistical analysis of the Brazilian data Is TC - TK/(1 + NR/6.6) to be Interpreted as kilometers per equivalent new tire, the ratio of the cost of recapping to the price of a new tire being approximately 1/6.6. Tire costs per kilometer are given by PN/TC and tire costs per kilometer per vehicle are given by PN.NT/TC where NT Is number of tires per vehicle. TIRE COSTS 197

In the Kenyan and Caribbean studies, the number and type of tires used by vehicles during the survey period were recorded. Since rather few tire scrappings were observed during the survey period, particularly in the Caribbean study where utilisation was relatively low, data collection was extended to cover replacement of at least as many tires as vehicles had wheels so that, say, for cars the lives of four or more tires would be used to produce the dependent variable for analysis while for trucks six or more tires would used. Tires fitted as used tires were not Included In the data In the Kenyan and Caribbean studies. Using Information on numbers of recaps, the number of equivalent new tires consumed was calculated on a price weighted basis for each vehicle. The dependent variable in the statistical analysis Is the number of equivalent new tires consumed per kilometer per vehicle.

The Kenyan car tire data were derived from Information on 63 vehicles, the bus and truck tire data from 183 vehicles. Both data sets were averaged so that In the statistical analysis only 6 car and 10 bus and truck average tire consumptions are used. The Caribbean study's tire data were derived from Information on 21 cars and light goods vehicles and 19 trucks. Here there was no averaging prior to analysis.

In the Indian survey a detailed study was made of tire costs. Some of the results not available In CRRI (1982) can be found in Kadayail et al. (1981), Lakshmikanthan et al. (1980), and Kadayall et al. (1982). The research began with an investigation Into the differences In tire lives for tires of different brands and for tires made from different materials (rayon or nylon) using data from a single large state owned organisatlon. No significant differences were found and henceforth all tires were treated similarly.

In the Indian study tire consumption was recorded by vehicle as In the Kenyan and Caribbean studies. In order to avoid the difficulties that arise when tire pool systems are In operation, the Indian survey team encouraged vehicle owners to maintain tires on survey vehicles from new to scrapping. This Is not normal practice and It was soon discovered that new and used tires were being substituted for tires that were damaged or required attention. Eventually It was decided to record tire consumption over the period In terms of numbers of new tires fitted (AN), numbers of used tires fitted (AU) and numbers of recapped tires fitted (AR). Using two years data on a large number of tires owned by a large state organisation, the Indian team derived conversion factors relating life (in kilometers) of used and recapped tires to life of new tires. Specifically they report that used tires have life approximately equal to 0.425 times the life of a new tire, the corresponding figure for recapped tires being 0.5. A vehicle receiving AN new tires, AU used tires and AR recapped tires during the survey period was recorded as having tire consumption equal to ET - AN + 0.425 AU + O.SAR "equivalent new tires," and, with the vehicle travelling K kilometers during the survey period, the dependent variable in the statistical analysis, "tire life" Is defined as TL - NT.K/ET where NT Is the number of wheels on the vehicle.

The interpretation of the variable TL presents a number of difficultles. The first arises with the method of counting the number of tires fitted, which may present problems because of double counting. Unless all used tires are bought In as used, some new tires must be removed 198 TIRE COSTS from survey vehicles before they have run their full lives. Then some new tires given a weight of 1.0 In the calculation of ET, "equivalentnew tires," should be given a lower weight. In discussions with L. R. Kadayall, the Director of the Indian Road User Survey, we were Informed that rather few used tires were fitted to survey vehicles so perhaps this double counting can be Ignored.

The major problem with the Indian study dependent variable TL is that It does not bear directly on tire costs and it Is not at all obvious how tire costs can be obtained from the variable TL which might be Interpretedas life of an equivalent new tire. Notice that ET is not the equivalent new tire definition used in the other studies since it is a kilometer weighted rather than a price weighted count of tires consumed. A correct treatment of used and recapped tires on a price welghted basis requires calculation of AN - AS S+ + AR P where AS i the number of new tires removed prior to first recap, PS Is the value per tire of such tires and PU is the price per tire of used tires. Ignoringused tires for now, we see that If PR/PN - 0.5 then the variable TL, constructed in the Indian study, can be interpreted as kilometers per equivalent new tire on a price weighted basis. In fact PR/PN Is likely to be somewhat less than this so that direct use of TL is likely to lead to over statement of tire costs. To allow for this Kadayall et al. (1982) give a correction factor obtained using data from all survey vehicles which reduces tire costs predicted using TL by around 30 percent. These problems with the Indian study's definitlon of the dependent variable in the tire analysis suggest that the Indian study equations may be somewhat unreliable in determining the level of tire costs. However, It Is likely that differentials In tire costs due to differences In highway characteristics are picked up reasonably accurately by these equations.

6.2 ESTIMATION OF TIRE COST EQUATIONS

Except In the case of the Brazilian study, the dependent varlable In the tire cost analyses is an average of tire lives, an average taken per vehicle (or group of vehicles In the Kenyan study) over tires used by the vehicle during the user survey period. In the Brazille study the dependent variable Is essentially kilometers travelled per .ire, each observation relating to a single tire. One result of this Is that reported goodness of fit statistics vary very considerably from study to study, there being of necessity more residual variation In Individualtire lives than In average tire lives.

Table 6.2 shows the effect that averaging has on R2 statistics, in the simple case in which, In each group over which averaging occurs, explanatory variables take Identicalvalues. Table 6.2 gives values of R2 catculated from data which are averages of n observationsfor alternative choices of R2 (1) and n. An R2 statisticof 0.81 obtained using data which are averages of 10 tire lives is equivalent,under the conditions assumed, to an R2 statistic of only 0.3 obtained using Individualtire data. This effect Is lessened If tires grouped together do not travel over Identical highways. However, in practIce the sorts of effects evident In Table 6.2 will be found since tires grouped together for analysis In the Kenyan, TIRE COSTS 199

Table 6.2: Values of Goodness of Fit Statistics (R2 (n)) Obtained Using Averages of Groups of n Observations from Raw Data In Which Value of R2 is R2(1)

R2 (1) 0.1 0.3 0.5 0.7 0.9 n

5 .36 .68 .83 .92 .98 10 .53 .81 .91 .96 .99 25 .74 .91 .96 .98 1 100 .92 .98 .99 1 1

Caribbean, and Indian studies do generally travel similar highways, If only because they are grouped together because they operate on particular vehicles, and user survey vehicles are normally chosen precisely because they tend to maintain operations over fixed unchanging routes during the survey period.

The explanatory variabies In the tire analyses are vehicle and highway characteristics, the latter being averages of highway characteristics experienced by vehicles (tires In the Brazilian survey) over the survey period. This averaging of highway characteristics experienced on a day-to-day basis generally tends to dampen any non linearitles present In equations relating tire wear to highway characteristics so that we observe close to linear, well behaved relationships between tire consumption and highway characteristics In user survey data sets. In practice, for all but the smallest scale highway improvements, routes contain a spread of highway characteristics so that the sorts of relationships observed in road user surveys may not be too far removed from those found In practical applIcations.

As noted at the beginning of this chapter, we can expect quite considerable across company differences In tire lives due to the effects of company policy differences and due to across company variation In type of business. In the Indian and Brazilian studies this has lead to the use of estimatlon procedures that allow for the presence of company specific disturbances In the equations relating tire consumption to highway and vehicle characteristics. In the Brazilian study there was evidence that these company effects were correlated with highway characteristics so that ordinary or generalized least squares procedures appiled to the data might lead to biased estimators of the effects of the explanatory variables. This was In part due to the rather small number of companies contrlbuting data to the Brazilian user survey tIre data set. In the Indian study a larger number of companies are represented In the tire data set and they are better disposed over highway types. In the analysis of the Indlan study tire data It was reasonable to regard company effects as Independent of highway characteristics and therefore possible to use the generalized least squares estimation procedure in the context of the error components model set out in Chapter 2. In the Brazilian study, estimates were 200 TIRE COSTS obtained by allowing each company to generate a separate Intercept In the fitted equations utilising the fixed effect model outlined In Chapter 2. The Kenyan and Caribbean analyses did not allow for across company differences In tire consumption.

In order to predict tire costs using the Brazilian and Indian studies' results, It Is necessary to divide the price of a new tire by a prediction of kilometers per equivalent new tire. If our predictions of kilometers per equivalent new tire are unbiased then the corresponding tire cost predictions will be biased downwards because of the convexity of the tire cost function. Calculations with the Indian data suggest that the required correction Is of the order of 5 percent, that Is that predicted tire costs should be multiplied by about 1.05 In order to approximately remove the blas Induced by Inverting an unbiased estimate of kilometers per equivalent new tire. For the Brazilian data the required correction Is of the order of 20 percent, a larger correction because of the greater dispersion In the Brazilian data In which data were not averaged prior to analysis. In reporting the predictions of Indian and Brazilian tire costs these correctlons have been applied but It must be recognised that they are approximate.

8.3 TIRE CONSUMPTION: CARS AND LIGHT GOODS VEHICLES

Results reported In the Brazilian and Indian surveys relate to crossply tires. Most of the tires used during the Kenyan study were Imported radial tires though soon after the end of the survey the Kenyan government banned Importation of tires as local manufacturers became established. In the Caribbean study both radial and crossply tires were observed, many vehicles operating with radials and crossplys mixed. In all four surveys sample sizes are relatively small compared to those relating to bus and truck tires and, as noted In Section 6.2, the number of data points available varies considerably from one study to another in part because of averaging of data prior to analysis.

In the Indian and Brazilian surveys the dependent variable for the purpose of estimation Is kilometers per equivalent new tire, data being recorded per tire In the Brazilian study and per vehicle In the Indian study. The discussion of the Indian data In Section 6.1 Is relevant here. In the Kenyan and Caribbean surveys, the dependent variable for the purposes of estimation was equlvalent new tires per kilometer per vehicle, data being recorded per vehicle In the Caribbean survey and by groups of vehicles in the Kenyan survey. In this and the subsequent section the dependent varlable for reporting Is T, equivalent new tires (calculated on a price weighted basis) per 103 kilometers per vehicle from which tire costs per 103 km per vehicle are obtained by multiplying T by the cost of a new tire. The factor of .727 (see the appendix to this chapter) recommended In CRRI (1982) has been used to correct the Indian equation to a tire cost expression. Because of the different functional forms used In analysis of the survey data the studies' equations predict rather differently, the Kenyan and Caribbean studies giving tire costs Increasing linearly with highway characteristics, the Indian and Brazilian equations predicting greater and greater Increases In costs as rougher and rougher routes are encountered. TIRE COSTS 201

Equations are reported In Table 6.3 and graphed In Figure 6.1. Predicted tire consumptions are given In Tables 6.4 and 6.5. Equations as originally reported, together with available summary statistics are given in the following appendix. The Brazilian results relate to car tires. A sample of around 60 utilities tires gives the relationship: T - 1/(17.4 - .0012R). For all but the Indian study the equations reported In the main text are Identical to those originally reported In the studies once allowance Is made for changes In units of measurement. In the Indian study (CRRI 1982) two equations are reported, one relating tire consumptlon to surface roughness, the other relating tire consumption to pavement width. It Is not possible to obtain from the Indian data reliable estimates of the effects of roughness and pavement width on car tire consumption when both variables are included in the tire consumption equation. The pavement width effects are not well understood and since we might expect surface roughness effects to dominate, the surface roughness equation Is reported here, after re-estimation by generalized least squares to allow for company specific disturbances In the regression equation. In all four studies tire consumption Is written as a function of surface roughness alone. The data sets relating to car tire consumption are too small and cover Insufficiently wide ranges of vertical and horizontal geometry to enable reliable estimates of the effects of gradlent and curvature to be estimated.

Inspecting Figure 6.1 we see that the Kenyan and Caribbean study equations differ from those obtained In India and Brazil, predicting higher tire consumption at most levels of roughness and greater increases In tire consumption with Increases In roughness over the observed ranges of roughness. The Caribbean equations predlctions are higher than those given by the Brazilian and Indian equations by a factor of two or more depending on the roughness level examined and are around 50 percent higher than the Kenyan equations' predictions. Hide (1982) suggests that the differences between the Kenyan and Caribbean studies' results might be attributable to differences In tire types: the Kenyan vehicles ran on high quality Michelin radial tires while the Caribbean vehicles used mixtures of radial and crossply tires. The differences may also be due to the presence of severely potholed paved roads In the Caribbean, with the differences In profile Irregularity not being well discerned by the bump Integrator Instrument used for measurement of roughness.

Table 6.3: Tire Consumption Equations: Cars

Study Equation

India T - 1/(19.66 - .00193R} Brazil T - 1/(13.16 - .00129R) Carlbbean T - -. 060 + .000076R Kenya T - -. 083 + .000058R 202 TIRE COSTS

Flgure 6.1: Tire Consumption (T) versus Surface Roughness (R): Cars

0.7 T

0.6.

,C /

0.5

0.4

0.3

0.2

0.1 ....

| , , , , , , , ~~~~~~~~~~~~~~R,BI 2000 4000 6000 2.8 51 7.4 R, IRI

Equations: B : Brazil C Carlbbean I : India K : Kenya Units: T : Equivalent new tires per 103km per vehicle. R : Surface Roughness, Bi (mm/km), IRI(m/km).

Table 6.4: Tire Consumption Predictions: Cars

Study Road Roughns _ EN IRI Brazil India Caribbean Kenya (mm/lun) (rnkm)

2,000 2.8 .095 .063 _ - 2,5U0 3.4 .101 .067 _ .062 3,000 4.0 .108 .072 - .091 3,500 4.6 .115 .078 .206 .120 4,000 5.1 .125 .064 .244 .149 4,500 5.7 .136 .091 .282 .178 5,000 6.3 .149 .100 .320 .207 5,500 6.8 - .111 .358 .236 6.000 7.4 - .124 .396 .265 6,500 7.9 - .141 .434 .294 7,000 8.5 - .164 .472 .323 1 7,500 9.0 _ - .510 - 8,000 9.5 - .S48 ______i TIRE COSTS 203

Table 6.5: Tire Consumption Predictions: Cars

Ratiosof EquivalentNew Tiresper tO3 km perVehicle on Road with Given Roughnessto EquivalentNew Tires per tO3km per Vehicle on Roadswith Roughness Equal to 3,500 mm/km.

Study RFoadRoughness SI IRI Brazil India Caribbean Kenya I (mm/kmn) (m/km)

2,000 2.8 .82 .81 _ - 2,500 3.4 .88 .86 _ .52 3,000 4.0 .94 .93 - .76 3,500 4.6 1.00 1.00 1.00 1.00 4,000 5.1 1.08 1.08 1.18 1.24 4,500 5.7 1.18 1.18 1.37 1.48 5,000 6.3 1.29 1.28 1.55 1.73 5,500 6.8 - 1.43 1.74 1.97 6,000 7.4 - 1.59 1.92 2.21 6,500 7.9 - 1.81 2.11 2.45 7,000 8.5 - 2.11 2.29 2.69 7,500 9.0 - - 2.48 _ 8,000 9.5 - _ 2.66

The levels of the Brazilian and Indian car tire consumption equations differ somewhat but their predictions concerning the effects of changing roughness are quite similar as can be seen by inspecting Table 6.5. For example both the Brazilian and the Indian equations predict an 18 percent Increase In equivalent new tires per 103km per vehicle (T) on Increasing surface roughness from 3,500 to 4,500mm/km, while the Kenyan equations predicts a 37 percent Increase and the Caribbean equation a 48 percent Increase. Both the indian and Brazilian equations are non-linear In surface roughness though over the ranges of roughness observed (given approxlmately by the extent of the plotted lines In Figure 6.1) the non- linearity is not marked. On very rough routes the Brazilian and Indian equations predict high tire consumptions so that extrapolation should be undertaken with care. In the case of the Brazilian survey predicted tire consumption Is unbounded once roughness exceeds 10,180mm/km, the corresponding figure for the Indian survey being 10,170mm/km. Of course these are extremely high figures for average roughness experienced by a car over an extended period and In practice one is likely to find few commercial car operations on routes this rough.

On routes of moderate roughness (3,500mm/km) the Brazilian and Indian equations predict tire consumptlon of respectively .115 and.078 equivalent new tires per 103 km per vehicle. With no recapping this Is 204 TIRE COSTS equivalent to Individual tire lives around 35,000km and 51,000km respectively. On routes with roughness equal to 5,000mm/km the corresponding tire life figures are 27,000km for Brazil and 40,000km for India. The large differences In vehicle speeds between Brazil and India could account for much of the differences In tire wear.

6.4 TIRE COSTS: BUSES AND TRUCKS

The data available on bus and truck tire consumption are more extensive than those for car tires and the results obtained are correspondingly more precise and Informative. In both the Brazilian and Indian surveys It Is possible to find some reasonably well determined effects for highway geometry as well as surface roughness. As In the car tire analysis the Kenyan and Caribbean studies write equivalent new tires per km as a linear functloh of roughness. For buses and trucks a multiplicative factor In vehlcle weight Is Included. In the Indian and Brazilian studies kilometers per equivalent new tire Is written as a linear function of roughness.

As In the previous section the Brazilian and Indlan results relate to crossply tires whereas the Kenyan study data mostly relate to radial tires. In the Caribbean study mixtures of radial and crossply tires were observed. The Kenyan and Caribbean studies report bus and truck tire equations on a per vehicle basis, and the Indian and Brazillianstudies report equations on a per tire basis. Thus, for reporting purposes the Indian and Brazilian equations Include a term NT, number of tires per vehicle. In the previous section concerning car tires NT - 4 was passed through Into the coefficients.

The equations are given in Table 6.6 and graphed In Figures 6.2 - 6.5. Predictions are given In Tables 6.7 and 6.8. As before, only the Indlan equation requires comment, the other equations given In Table 6.6 being Identical to those originally reported by the studies once allowance Is made for changes In units of measurement. In CRRI (1982) separate equations are reported for bus and truck tire consumption. The bus tire equation has been re-estimated by generalized least squares allowing for company specific disturbances In the regression equation. Geometry effects not found In the CRRI (1982) analysis have been obtained. On re-estimating the truck tire equation poor results were obtained, In part because truck tire data exhibits little within company variation In highway geometry. Roughness effects were found to be very similar for buses and trucks so the bus tire equatlon has been used to predict truck tire consumption, the Intercept being adjusted to reflect the slight overall differences In truck tire consumptlon. Further details are given In the appendix.

In the Brazilian survey analysis, bus and truck tIre data were merged, separate Intercepts being estimated for each of the three tire sizes: 900 x 20, 1,000 x 20 and 1,100 x 22, covered In the data set. Estimation Is by ordinary least squares fitting distinct Intercepts for each company, thus removing company policy and type of business effects. Slnce no company provided data on more than one tire size and no company provided data on both buses and trucks, the merging of the tire data on TIRE COSTS 205 buses and trucks is less objectionable than would otherwise be the case. In the Kenyan survey bus and truck tire data were merged for analysis, gross vehicle weight being Included as an explanatory variable. Gross vehicle weight plays a role In distingulshing buses and trucks and also In distinguishing vehicles with different numbers of tires since In the Kenyan (and Caribbean) analysis tire consumption per vehicle per distance travelled Is the dependent variable.

Figure 6.2 graphs bus tire consumption agalnst surface roughness. The extent of the plotted lines Indicates the approximate range of roughness observed in the studies. Only three equations are drawn In Figure 6.2 since the Carlbbean study does not report a separate equation for bus tire consumption. The predictions for bus tire consumptlon are In good agreement, the Indlan, Brazillan and Kenyan equations predlcting respectively 0.15, 0.16, and 0.14 equivalent new tires per 1,000 km per vehicle on roads with roughness equal to 3,000 mm/km. The Kenyan equatlon predicts more rapidly Increasing tire consumption with Increases In surface roughness than do the other studies but this equation Is estimated using data over a relatively narrow range of roughness. Table 6.9 gives percentage Increases In tire consumption on Increasing roughness from a base roughness of 4,000 mm/km and the Indian and Brazilian equations are In reasonable agreement.

The predictions for truck tire consumption are plotted against surface roughness In Figure 6.3. The Brazilian study generates two equations, one for a medium truck (e.g., a Mercedes Benz LK 1513/42) fitted wlth six 1,000 x 20 tires, the other for a heavier truck (e.g., a Scania T112H 6 x 2/42 operating as a solo 3-axle rigid truck) fitted with ten 1,100 x 22 tires. The Indian data refers to trucks with an average weight of around 13 tonnes and the Kenyan and Caribbean predictions are obtained using a gross vehicle weight of 12 tonnes. The Kenyan and Caribbean predictlons are generally higher than those given by the Indian equations but quite similar In level to those given by the Brazilian equations. On roads with roughness equal to 5,000 mm/km, equivalent new tires per 103 km per vehicle are predicted to be .143 using the Indian equation, .169 using the Brazil equation for medium trucks (.130 for heavy trucks), .172 using the Caribbean equation and .167 using the Kenyan equation (see Table 6.7).

The effects of Increasing road roughness are rather larger In the Kenyan and Caribbean equations than In the Brazilian and Indian truck tire equations. For example, Increasing roughness from 4,000 mm/km to 7,000 mm/km Is predicted to lead to 11, 10, 31, and 27 percent Increases In tire consumption using respectively the Indian, Brazilian (medium truck), Caribbean, and Kenyan equations (see Table 6.8). Tlre consumption predictions obtained using the Indian study equations are somewhat lower than those derived from the other studies results. As noted eariler, there are some doubts concerning the accuracy with which the general level of tire consumption Is predicted using the Indian study equations because of the use during analysis of a kilometer rather than a price weighted count of tires used by vehicles. In the Indian study there Is evidence to suggest slightly higher tire consumption measured In equivalent new tires per 103 km per vehicle, for buses than for trucks. This phenomenon which Is reflected In the fitted equations may In part be due to a lower number of 206 TIRE COSTS

Table 6.6: Tire Consumption Equations: Buses and Trucks

Study Vehicle Class Equation

Brazil Buses/Trucks T = NT/(47.2S900 + 49.2S1000 + 78.171100.

- .0012R - .352RF - .0107C).

India Buses/Trucks T = NT/(50.79rR + 56.82BU - .0057K

- .0015R - .314RF - .0130C + 1.368W).

Caribbean Trucks T = GVW (.0076 + .00000135R}.

Kenya Buses/Trucks T = GVW (.0083 + .00000112R).

T = Equivalent new tires per 103km per vehicle. Nr = Number of tires per vehicle R = Road roughness (mm/km) RF = Average rise plus fall (m/kmn) C = Average degrees of curvature (0/km) W = Average Pavement width (m) K = Vehicle age at survey midpoint (103km) GYW = Gross vehicle weight (t) TR = 1 if vehicle is a truck, 0 otherwise BU = 1 if vehicle is a bus, 0 otherwise SaW = 1 if tires are 900 x 20, 0 otherwise Siooo 1 if tires are 1000 x 20. 0 otherwise S1100 1 if tires are 1100 x 22, 0 otherwise- TIRE COSTS 207

Figure 6.2: Tire Consumptlon (T) versus Surface Roughness (R): Buses

0. 2 5 T

0..20

'A,

0. 1,

_~ ~ ~ ~~~~~~~~~~~~~~~~R, .

0.05

2000 4000 6d00 8600 loobo 12 00R,3 R, IRI 2.8 5.1 7.4 9.5 12.0 14.0

Eqauations: B : Brazil I India K: Kenya

Units: T : Equivalent new tires per 103km per vehicle. R Surface Roughness, BI(mm/km), IRI(m/km)

Variables not Plotted: NT (Number of tires) = 6 5iooo(= 1 it tire is 1000 x 20) = 1 RF (Rise plus fall, m/km) = 20 C (Average degrees of curvature 0/krn) 90 W (Pavement width, m) = 5.5 K (Vehicle age, 103/krm) 350 208 TIRE COSTS

Figure 6.3: Tire Consumption (T) versus Surface Roughness (R): Trucks

T 0.25 .4

0.20 -

- BM

0.15 < BH- .-

0.10

0.05

,R,B I 2000 4000 6000 8000 10000 12000 14000 R, IRI 2.8 5.1 7.4 9.5 12.0 14.0 16.0

Equations: C Caribbean OM Brazil (medium, 1000 x 20, 6 tires per vehicle) BHt Brazil (heavy, 1100 x 22, 10 tires per vehicle) I India K Kenya

Units: T Equivalentnew tires per 103km per vehicle. R Surtace Roughness, Bl(mm/knm) IRI(m/km)

Variabbz n!ot Plotted NT (Number of tires per vehicle) = 6 (except BH- see above) 1000 8110 (mseeabove) RF (Rise plus fal, m/km) = 20 C (Average degrees of curvature 0 lkm) = 90 W (Pavement width, m) 5.5 K (Vehile age, 1O3Ikn) = 350 GVW Gross vehicle weight 0t)= 12 (Kenya and Caribbeanonly). TIRE COSTS 209

Figure 6.4: Tire Consumption (T) versus Average Rise + Fall (RF): Buses and Trucks

T B 0. 25

0_20 7

o.isl~~~0.15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~ -

0.101

0.05

RF .___T___I___,______10 20 30 40 50 60

Eouations: B Brazil, Busimedium truck 13 :India, bus 'T : India, truck

Units: T : Equivalent new tires per 103kn per vehicle. R Surfae Roughness, Bl(mmlkm), IRI(lmkm)

Variablesnot Plotted: NT : Number of tires per vehicle = 6 S1oo0: = 1 (tire size = 100 x 20) R Surface roughness = 5000 BI(mm/km), 6.3 IRl(m/km) C Average degrees of curvature (0/km) = 100 W : Pavementwidth, tm) = 5.5 K Vehicle age, (103/km) 350 210 TIRE COSTS

Figure 6.5: Tire Consumptlon (T) versus Average Degrees of Curvature (C)

T 0.25 'B

T--B 0.20-

0.15

0.05 -

1000 C 100 200 300 400 500 600 700 800 900

Ehukthm: B Brzil, Bus/medium truck l'B : India, bus IT : India, truck

3 Unft: T Equivalent new tires per 10 km per vehicle. R: Surface Roughness (mm/kn)

V Iabie not Potted: NT Number of tires per vehice = 6 Sa,=o: = 1 (tire size = 100 x 20) R Surace roughnoss = 5000 BI(mm/ktu), 6.3 IRICm/km) RF: Average rise plus fal (m/km) = 210 W Pavementwidth, (m) = 5.5 K Vehibe ae. (103/km) = 350- TIRE COSTS 211

Table 6.7: Tire ConsumptionPredictions: Buses and Trucks Equlvalent New Tires per 103km per Vehicle

t T~~~~~~~~ni Brazil | Caribbean Konya

| Road I Rou|Truck Bus(?) Med Truck/ Heavy Artiulated Truck Bus/Mod Rough,km Trck I Truck . 81Rmone=) TrucTck Triuler(5) CTruckb). (IRI(m/km) ) I

2,000 (2.8) .129 .142 .154 .148 .265 .124 .126 3,000 (4.0| .133 .147 ,158 .150 .270 .140 .140 4,000 (5.1) .132 .153 .164 .152 .275 .156 .153 5,000 (6.3) .139 .160 .169 .156 .280 .172 .167 6,000 (7.4) .149 .166 .175 .158 .284 .188 .180

7, 0O (8.5) .154 .173 .181 .161 - .205 .194 8,000 (9.5) .161 .181 I .188 .164 _ .221 .207

9,000 (10.6) .168 .190 .196 - - - -

10,000 (11.6) .15 .200 .203 - - - _

11,000 (12.6) .183 .210 .211 - - - _

12,000 (13.7) .192 .222 .220 - - - 13,000 (14.7) .202 .234 - - - - _ 14,000 (15.7) .213 .250 _ _ _ _ 15,000 (16.7) .225 .267 - _ _ _ _

Notes: (1) NT = 6; K = 230; RF = 20; C = 90; W =5.5 (2) NT = 6; K = 350; RF = 20; C = 90; W = 5.5 (3) NT = 6; S S1loo; RF 20; C 90

(4) NT = 10; S S1010 ; RF 20; C 90

(5) NT = 18; S 11 0( ; RF 20; C S0 (6) GVW = 12. 212 TIRE COSTS

Table 6.8:

Tire ConsumptionPredictions: Buses and Trucks Ratios of Equivalent New Tires per 10 km per Vehicle (T) on Roads wlth Given Roughness to Equivalent New Tires per 103km per Vehicle on Roads with Roughness Equal to 4,000 mm/km

India Brazil Caribbean Kenya

Roadi__t 2 Roughness Truck(,) U a| ) Med Truck/ Heavy Articulated Truck () Bus/Med 5 8l(mnmIkm) Bus (3) Truck 4) Truck & TraiI.r( )| Truck(6). [IRI(m/kmn))

2,000 (2.86 93 .92 93 .97 .97 .79 .82

3,000 (4.0) g96 96 .96 .96 .96 .90 .92 4,000 (5.1) 1.00 1.00 1.00 1.00 1.00 1.00 1.00

5,0Q0 (6.3) 1.03 1.04 1.03 1. 02 1.02 1.10 1.09 6,000 (7.4) 1.08 I 1.08 1.07 1.04 1.03 1.21 1.18 7.000 (6.5) 1.11 1.13 1.10 1.06 - 1.31 1.27

8,000 (9.5) 1.16 I 1.18 1.15 1.08 - 1.42 1.35

9,000 (10.6) 1.21 1.24 1.19 _ - - -

10,000 (116) 1.27 1.30 1.23 - _- _

11,000 (12.6) 1.32 1.37 1.28 - _- _

12,000 (13.7) 1.39 1.45 1.34 - _- _

13,000 (14.7) 1.45 1.53 - - I _ _ _

14,000 (16.7) 1.54 1.63 _ _ | _ _ |

15.000 (16.7) 1.62 1.74 _ _ | _

Notes: (1) NT = 6; K = 230; RF = 20; C = 90; W = 5.5

(2 ) NT = 6; K = 350; RF = 20; 0 = 90; W = 5.5

(3) NT = 6; S = Slo8o; RF 20; C = 90

(4) NT = 10; S = Slloo; RF 20; C = 90

(5) NT = 18; S = Slioo; RF 20; C = 90

(6) GYW = 12. TIRE COSTS 213

Table 6.9:

Tire Consumption Predictions: Buses and Trucks Ratios of Equivalent New Tires per 10km per Vehicle on Roads with Given Rise + Fall to Equlvalent New Tires per 103 km per Vehicle on Roads with Rise + Fall 20m/km

India Brazil Rise Plus Fall (m/km) Bus(1l Truck(l) Bus/Med(1 ) Heavy(2). Truck Truck 20 1.00 1.00 1.00 1.00 30 1.09 1.08 1.12 1.06 40 1.20 1.18 1.25 1.12 50 1.34 1.30 1.43 1.20 60 1.50 1.44 1.67 1.218 70 1.72 1.62 2.00 1.38

Notes: Surfaceroughness = 5,000 BI(mm/km), 6.3 IRI(m/km) Averagedegrees of curvature= 1000/km. Pavementwidth = 5.5m. Vehicleage = 350,000 km (India)

(1) 6 tires per vehicle (1000 x 20 for Brazil) (2) 10 tires per vehicle, 1100 x 22

recaps being performed per tire for tires used on buses for reasons of safety.

Increasingly there Is a need in cost benefit analyses to predict vehicle operating costs for heavy articulated vehicles grossing 30 to 40 tonnes. Only the Brazilian study gives Information on tire costs for this type of vehicle which typically operates wlth large 1,100 x 22 tires. Table 6.7 gives predicted tire consumptions for articulated vehicles grossing around 40 tonnes fitted with 18 tires.

Both the Indian and Brazilian surveys report effects for highway geometry. Analysis of the Indian survey's bus data produced reasonably well determined effects for rise + fall, average degrees of curvature and pavement width. From the Brazilian study's data a quite well determined effect for rise + fall was obtained and the curvature effect was small, and statistically Insignificant. Figures 6.4 and 6.5 graph tire consumption for buses and trucks against rise + fall (m/km) and average degrees of curvature (0 /km) and It Is clear that the predicted effects from the two studies are quite similar. Increased average rise + fall leads to increased tire consumption - predictions are given In Table 6.10. Increasing average rise + fall from 20m/km to 50m/km Is predicted to Increase tire consumption by from 30 to 43 percent for the medium weight vehicles and by a lesser amount for the larger Brazilian heavy truck. Once 214 TIRE COSTS average rise + fall becomes large successive increases In rise + fall brlng large Increases In tire consumption.

The curvature effects can be appreciated by examining Figure 6.5 and Table 6.11, the latter containing predictions. Even Increasing average degrees of curvature from 1000 /km to 1,0000 /km leads to only 40-50 percent increases in tire consumption. The evidence from the Brazilian study is scanty to say the least, since there only a very limited range of curvature was observed. However the evidence from the Indian study for buses Is more convincing since these vehicles were observed operating on routes with average degrees of curvature exceeding 1,0000/km and in practice these vehicles do not have massively greater tire consumption. The small magnitude of the estimated curvature effects may be in part due to driver behaviour, the curvature experienced by the vehicle being smalier than that measured In the survey as a result of drivers taking lines through corners which tend to straighten bends out. In addition there are probably subtle speed effects.

The Indian study equation contains a pavement width effect. Reducing pavement width from 5.5m to 4.5m Is predicted to Increase tire consumption by around 4 percent for buses and trucks using the settings for other variables used in Tables 6.10 and 6.11 (in particular rise + fall = 0 20m/km, average degrees of curvature - 100 /km). These effects are small and their origin Is unclear. Roughness measuring Instruments In India tended to leave the highway on narrow routes when encountering slow moving

Table 6.10: Tire Consumption Predictions: Buses and Trucks Ratios of Equivalent New Tires per 104km per Vehicle on Roads with Given Curvature to Equlvalent New Tires per 103 km per Vehicle on Roads with Curvature 1000 /km

India Brazil Average Degrees of Curvature BuJ(t) Truck' 1 ) us/Med ( 1) Heavy(2), 0/kin Truck Truck

100 1.00 1.00 1.00 1.00 200 1.04 1.03 1.04 1.02 300 1.08 1.07 1.07 1.03 400 1.12 1.11 1.10 1.05 500 1.17 1.15 1.14 1.08 600 1.22 1.19 1.18 1.09 700 1.27 1.24 1.23 1.11 800 1.33 1.30 1.27 1.13 900 1.40 1.35 1.32 1.15 1000 1.47 1.41 1.38 1.18

Notes: Surface roughness = 5,000 BI(mm/km), 6.3 IRl(mfkm) Rise plus fall = ZOm/ikm Pavement width = 5.5m. Vehicle age = 360,000 km

(1) 6 tires per vehicle (1000 x 20 for Brazil) (2) 10 tires per vehicle, 1100 x 22 TIRE COSTS 215 Table 6.11: Ratios of Tire Costs on Gravel Roads (6,000mm/km) to Tire Costs on Bitumen Roads (3,000mm/km)

Vehicle Class Study Ratio, Gravel/Bitumen

Cars India 1.71 Brazil 1.71 Carlbbean 2.34 Kenya 2.91

Buses India 1.13 Bus/Medium Truck Brazil 1.11 Bus/Truck Kenya 1.29 Trucks Caribbean 1.34 Heavy Trucks Brazil 1.06

or approaching traffic so that the roughness measurements on narrow routes contain a contribution due to shoulder roughness. The width effects reported here may be due to Increased acceleration and deceleration due to more frequent speed changes on the relatively congested narrow Indian routes.

6.5 CONCLUDINGREMARKS

As noted in Sectlon 6.1 tire data are difficult to collect because, at least in large organisatlons, tires are moved from vehicle to vehicle. Further tire life varies greatly from tire to tire even under Identical operating conditions. Tire life also varies considerably according to load carried, position on the vehicle, speed of operation, driver behaviour and depends on company policy regarding standards of maintenance of tires and vehicles and regarding frequency and standard of recap. Even with the relatively large samples obtained In India and Brazil It Is difficult to extract information on the relatlonship between tire consumption and highway characteristics. The equations reported in Sections 6.3 and 6.4 are not estimated with great accuracy. However there Is some agreement between the studies, particularly the larger studies carried out In Indla and Brazil. And the information these studies provide is relevant to planning decisions because It tells us about tire costs In real life operating conditions - the conditions under which the benefits of highway Improvement schemes will be reaped.

The effect of road roughness comes through In all the studies. For car tires, the effect of increasing roughness from 3,500 to 5,000 mm/km Is to increase tire consumption by about 30 percent (55-70 percent If the Kenyan and Caribbean results are used). For trucks and buses (but not 216 TIRE COSTS heavy trucks) the effects are far smaller - around 6 percent (and less still for heavy trucks) - again the Kenyan and Caribbean equations predict larger effects.

Using the large bus and truck tIre data sets obtained In India and Brazil It Is possible to find effects for rise + fall and average degrees of curvature and these two studies are In broad agreement concerning magnitudes of these effects. Increasingaverage rise + fall from 20m/km to 60m/km results In an Increase In tire consumption of around 50 percent (less for heavy trucks). Increasing average degrees of curvature from 1000 /km to 1,0000/km increasestire consumptionby around 45 percent (again less for heavy trucks).

There Is only limited Information available from other sources on the effects of highway characteristics on tire costs under actual commercial operating conditions. De Weille (1966) cites Doyen (1960) and Moyer and Tesdall (1945), giving tire costs 100 percent higher on gravel than on paved roads. Comparing 6,000 mm/km routes with 3,000 mm/km routes we obtain from the four studies the percentage Increases In costs shown In Table 6.11. Doyen's figures agree only with the Kenyan and Caribbean results for cars. Generally the studies predict smaller differentials though for car tire wear the differentialspredicted In the Brazilian and Indian studies approach those given by Doyen. For buses and trucks the differentialsare much smaller. Moyer and Tesdall's results are based on tire technologyof the 1940s and Doyen's work reports an International literaturereview carried out In the 1950s, so differences are to be expected.

It Is not easy to compare the results of the four studies reported In Sectlons 6.3 and 6.4 with those from other studies. First, there are few studies reporting tire costs as they relate to highway characteristics under normal operating conditions. Studies have been made on tire costs for off-highway operations, for example logging (Sullivan 1977) and open cast haul dump operations but the vehicles are so specialized that their costs are not usefully compared with the results reported In this chapter. Second, studies that have measured tire wear and reported estimates of tire costs have sometimes omitted to adJust for the benefits of recapping. Bonney and Stevens (1967), for example, found that the distance run on new tires and recaps was frequently similar on Identical routes (see the earlier discussion of Ker and Soloman (1976)) and priced recaps at the same price as a new tire. Finally, the data from other sources which have been processed to give a good Indication of tire costs In commercial operation are frequently assoclatedwlth broad classes of road and so car only be used to compare levels of tire consumption or cost predicted from the reported user cost studies.

Tire technologyand manufacture continues to change fundamentally and rapidly and It is clear that future research Into tIre costs for road vehicles Is required to measure the benefits of new polyester tire materials, different recapping techniques, the manufacture In developing countriesof new tire types like steel braced radlals and super singles, as well as the possible use of variable central tire Inflationequipment on large articulatedvehicles (Kyle 1983). TIRE COSTS 217

APPENDIX. TIRE EQUATIONS AS REPORTED IN THE FOUR STUDIES

This appendix contains the tire cost and tire life equations as reported by the four studies, together with comments concerning the statistical aspects of the equations.

A6.1 Kenya

The dependent variable In the Kenyan equatlons Is TCV, number of equlvalent new tires consumed per kilometer. Equations are reported for cars and light goods vehicles and for medium and heavy goods vehicles and buses.

Cars and light goods vehicles

TCV - (-83 + .058R).10-6 .

R2 - 0.98, 6 data points, averages from total of 63 vehicles.

Approximate Ranges and Means of Explanatory Variables

Variable Mln Max Mean

R(mm/km) 2,440 7,000 3,810

Source: Hide et al. (1975).

TCV - Number of equivalent new tires consumed per km per vehicle.

R - Road roughness (mm/km).

Medium and heavy goods vehicles and buses

TCV - (83 + .0112R).10-7 L

R2 - 0.94, 10 data points, averages from total of 183 vehicles.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 2,440 7,500* 3,110

Source: Hide et al. (1975).

* 4 vehicles exceeding 4,100. 218 TIRE COSTS

L - Total vehicle weight (tonnes) TCV,R - as above.

Remarks

The fit of the reported equations to the data Is very close. Only 2 percent of the variability In reported tire consumption remains to be attributed to across company policy differences,highway geometry, driver behaviour differences and so forth. Of course the data are averages relating not to tires' Individualhistories but to vehicles' consumptionof tires over a one-year survey perlod during which, utilisation was around 77,000 km for cars, 119,000 km for buses and 47,000 km for trucks. In addition data used in the analysis are averages of tires consumed per vehicle taken over groups containingfrom 6 to 25 vehicles for cars (1 to 76 vehicles for buses and trucks). Both averaging processes will tend to IncreaseR 2 statistics. Neverthelessthe reported values are very high.

The results for medium and heavy goods vehicles and buses are somewhat Influencedby three data points relating to 4 of the 183 vehicles In this data set, operating on routes with roughness averaging 5,125 mm/km, 7,000 mm/km and 7,500 mm/km. If these three data points are removed R2 drops to 0.78. No allowance is made for variations across vehicles In numbers of tires per vehicle but a multiplicativevehicle welght effect Is Incorporated.

In the main text the dependent variable for reporting tire cost equations Is T - equivalent new tires per thousand kilometers per vehicle defined as: T - 103.TCV.

A6.2 Caribbean

As In the Kenyan study the dependent variable Is number of equivalentnew tires consumed per kilometer per vehicle.

Cars and light goods vehicles

TCV - (-.0601 + .0000764R).10-3.

R2 - 0.81

21 vehicles (111 equivalent new tires).

Approximate Ranges and Means of ExplanatoryVarlables

Variable Min Max Mean

R(mm/km) 3,500 8,000 5,333

Source: Hide (1982). TIRE COSTS 219

TCV - Number of equivalent new tires consumed per km per vehicle.

R - Road roughness (mm/km).

Trucks

TC - (.0706 + .0000135R).G.10-4 .

R2 _ 0.91

19 vehicles.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 3,500 7,500 5,711

G(tonnes) 4.5 11 7

Source: Hlde (1982).

Remarks

As wlth the Kenyan study the equations fit the data very closely. Here Individual vehicle data are used so that In the Caribbean study the high R2 statistics relate directly to across vehicle varlation in tire consumption over a one-year period.

In the main text the dependent variable for reporting tire cost equations Is T - equivalent new tires per thousand kllometers per vehicle defined as T - 103.TCV.

A6.3 Brazil

The equations reported In GEIPOT (1981) were re-estimated (Chesher 1982) Incorporating recalculated roughness statistics, with the results shown below. The dependent varlable In the Brazil analysis Is 104 kilometers per equlvalent new tire, TC, defined as total kilometerage per tire In 104 kilometers divided by 1 + RC/6.6 where RC Is number of recaps per tire and 6.6 Is the ratlo of new tire price to recapping price. The unit of observatlon for analysis In the Brazilian study Is a tire, not a vehicle or group of vehicles which form observatlonal units for analysis In the other studles.

Cars

TC - 6.315 - .0341QI (-3.89) 220 TIRE COSTS

SW - 2.126

R2 , .03

Number of tires - 245

Number of companies - 1.

Approximate Ranges and Means of Explanatory Variables

Varlable Min Max Mean

Q1(QI*) 34 87 48

Source: GEIPOT (1981).

TC - 104 kilometers per equivalent new tire.

Qi - Road roughness (01*, Quarter car Index).

Buses and trucks

TC - 5.67S900 + 5.91S1,000 + 9.38S1,100.

(16.30) (10.14) (24.31)

- .0O768Qi - .0422RF - .00128C (-3.58) (-3.81) (-.59)

Sw - 1.820

2 R - .87 (includes effect of company Indicators)

Number of tires - S900 : 2,516

S1 000 517

S1,100: 502

TOTAL : 3,535

Number of companies - 18. TIRE COSTS 221

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

Q0(Ql*) 23 240 84

RF(m/km) 10 49 29

C(°/km) 8 294 65

Source: GEIPOT (1981).

RF : Rise + fall (m/km) C : Average degrees of curvature (0 /km). Sgoo : 1 If tire size Is 900 x 20, 0 otherwlse. S1 000 : 1 If tire size Is 1,000 x 20, 0 otherwise. S1 100 : 1 If tire size is 1,100 x 22, 0 otherwise.

Remarks

The basic analysis file contained over 20,000 tire changes and produced an analysis file of 245 car, 63 light goods vehicle, and 3,535 bus and truck tire lives. The car tires are all crossply 500 x 15, coming from one company operating over a ilmited range of roughness. All but two of the 245 car tires were used on user survey vehicles for at least 90 percent of their lives and very few were recapped. Hlghway geometry variation Is very llmited in the car tire data set and no geometry effects can be found.

The bus and truck tire data come from 18 companies, 94 percent of the data coming from Just 11 companies. Recapping Is common with bus and particularly with truck tires, up to 9 recaps per tire being recorded. There Is considerable dispersion In number of recaps per tire. The average number of recaps per tire In the bus and truck tire data set was 1.4. Road roughness and geometry variation Is more extensive In this data set though average degrees of curvature does not exceed 3000 /km for any tire. Seventy-five percent of the tires in this data set were used on user survey vehicles for at least 90 percent of their lives.

The bus and truck tire equation is estimated Including a binary Indlcator variable for each company so that only within company variation In tire lives and route characteristics Is exploited In estimating the coefficients on highway characteristics. The reported coefficients are therefore Insensitive to across company differences In tire policy, type of business and so forth. The reported Intercepts are obtalned by taking weighted averages of estimated company specific intercepts after grouping 222 TIRE COSTS

companles by tire size, with weights equal to number of tires per company in the data set. No company provided data on more than one tire size and no company provided data on both truck and bus tires. There Is considerable tire to tire variation In tire lives in this data set and variations in highway characteristics explain rather little of the variation in Individual tire lives.

However, the data set is so large that moderately accurate estimates of the effects of highway characterlstics on average tire lives can be obtained. The effect of vertical geometry Is quite well determined but the effect for horizontal geometry is Inaccurately estimated. The horizontal geometry coefficient Is retained because It gives realistic predictions and agrees well with the coefficient found In the Indlan study.

The dependent variable In the tire equations reported In the main text is T - equivalent new tires per thousand kilometers per vehicle

defined as T - T where TC Is 104 km per equivalent new tire and 10.TC NT Is number of tires per vehicle. Roughness coefficients have been converted so that they apply to roughness measured In mm/km using the conversion 1QI* - 55 mm/km.

A small sample of light goods vehicles tires gIves the relationship

TC - 6.97 - .0265QI which after change of units and assuming four tires per vehicle becomes:

T - 1/(17.4 - .0012R).

As noted In Sectlon 6.2 of the main text, predicted tire consumptions have been Increased by 20 percent to correct approximately for biases Introduced upon Inverting predictions of kilometers per equivalent new tire.

A6.4 India

The Indian tire analysis file contains tire lives from 54 cars, 640 buses, and 232 trucks.

The tire life equations reported In CRRI (1982) were re-estimated by Chesher (1982). The car tire equation reported by CRRI (1982) has as explanatory variable the ratio of road roughness to pavement width, RC/W. There is rather little evidence to support the use of this specific Interaction term, excluding main effects for roughness and width and the ratio Is apparently used to attempt to overcome multicollinearity In the data set. The equation as re-estimated omits pavement width and yields a roughness coefficient that broadly agrees with that found In the Brazilian study.

The bus tire equation was re-estimated by generalized least squares allowing for company and vehicle specific random disturbances and TIRE COSTS 223 on doing this moderately well determined coefficients are obtained for roughness, rise + fall, curvature and pavement width.

The truck tire data set Is particularly difficult to analyze. Exploiting just within company variation we obtain roughness and pavement width coefficients very close to those obtained for buses. Because within company varlatlon In highway geometry Is very llmited In this data set the coefficients on rise + fall and curvature obtained in this way are very poorly determined. The equatlons reported by CRRI (1982) are obtalned by applying ordinary least squares to the raw vehicle data Including company ownership indicators (government/private) and are Inconclusive concerning the effect of highway geometry. The similarity of the roughness and width coefficients obtained using within company variatlon In tire lives and highway characteristics and the similarity of the deslgn of Indian buses and trucks leads us to use the estimated bus tire life equation for trucks as well, adjusting the Intercept term to allow for differences In tire lives for buses and trucks. This adjustment Is explained below.

The dependent variable In the Indian survey tlre analyses Is TL, kilometers per equivalent new tire, equivalent new tires belng defined using a kilometer weighting. Because of the manner In which tire life data were complied In the Indian survey it Is necessary to multiply the reported equatlons through by 0.727 to allow for the effect of recapping and the use of used tires. This Is explained further In the text In Sectlon 6.1.

Car tires

TC - 60,024 - 5.858R (-5.61) SW - 5,323

Su - 2,827

Number of vehicles - 54

Number of companies - 10

TL - Tire life (km per equivalent new tire)

R - Road roughness (mm/km).

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 3,416 6,955 4,987

Source: CRRI (1982). 224 TIRE COSTS

Remarks

The equation Is estimated by generalized least squares allowing for random company and vehicle specific disturbances. The equation explains about 50 percent of the vehicle to vehicle variation in average tire lives. Vehicles were observed for from 9 months to 28 months, on average for 24 months, so that, given the utiilsatlon figures reported, each data point relates to average tire life for a group of around ten tires.

Buses tires

TC - 36,101 - 1.126R - 241RF - 10.54C + 1,044W - 4.34 K (-4.20) (-3.55) (-2.81) (2.56) (-3.77)

Su - 3,346

SW - 5,886

Number of vehicles - 639

Number of companies - 20

TL - Tire life (km per equlvalent new tire)

R - Road roughness (mm/km)

RF - Rise + fall (m/km)

C - Average degrees of curvature (0 /km)

W - Pavement width (m)

3 K - Vehicle age at survey midpoint (10 km).

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 2,925 12,072 5,953 RF(m/km) 1 50 15 C(°/km) 5 1,021 149 W(m) 3.7 7.2 5.2 K(103 km) 22 988 345

Source: CRRI (1982). TIRE COSTS 225

Remarks

This Is the equation re-estimated by Chesher (1983) by generalized least squares allowing for random company and vehicle specific disturbances. A single trailer bus (the only vehicle of this type) with a distinctive pattern of costs was deleted from the data set reducing the number of vehicles to 639. Geometry and roughness effects are qulte well determined and there is a small but statistically significant effect for vehicle age. The fitted equation explains about 50 percent of the vehicle to vehicle variatlon In average tire life, vehicles consuming on average around 40 tires during the survey period. The magnitude of Su suggests considerable across company variation In tire lives.

Truck tires

In Chesher (1983) the following equation Is estimated by applying ordinary least squares to the truck data set, Including company specific Indicator variables.

TL - 31,339 + 109.9RF - 1.150R + 1,096W + 12,784 AX6 (.71) (-1.43) (.77) (14.07) Sw - 5,178

Number of vehicles - 232

Number of companies - 30.

TL - Tire life (km per equivalent new tire)

R - Road roughness (mm/km)

RF - Average rise + fall (m/km)

C - Average degrees of curvature (0 /km)

W - Pavement width (m)

AX6 - 1 If vehicle has axle code 6 (truck-trailer combination fitted with 12 tires per vehicle).

Approximate Ranges and Means of Explanatory Variables

Variable Mln Max Mean

R(mm/km) 2,960 15,500 5,331 RF(m/km) 1 58 13.4 C(°/km) 8 1,215 137 W(m) 3.8 7.0 6.0

Source: CRRI (1982). 226 TIRE COSTS

Remariks

Coefficients in this equation are poorly determined but the roughness and pavement width coefficients are close to those obtained for buses. No sensible geometry effects can be found explolting only wlthin company variation. The similarity in design of Indian trucks and buses and the similarity of the roughness and width coefficlents reported above suggests that the bus equation may be applicable to trucks with minor adjustments to allow for different average tire lives for buses and trucks. The equation reported In the main text for trucks Is the bus equation given eariler, with the Intercept modified so that at mean values of explanatory varlables In the truck data set the equation predicts the mean tire life observed In the truck data set.

In the main text the dependent variable for reporting tire equations Is T - equivalent new tires per 1,000 km per vehicle defined as NT.1,000/TL. As noted In Section 6.1 tire costs estimated In the Indian study are multiplied through by 0.727 to allow for the effects of recapping and use of used tires. As noted in Section 6.2 of the main text, predicted tire consumption has been increased by 5 percent to convert approximately for blas Introduced by Inverting predictions of tire tile. CHAPTER 7 Maintenance Costs

This chapter, which concludes Part II, contains results concerning vehicle maintenance costs, parts and labor, and their relationship to highway and vehicle characteristics. Maintenance costs are crucially Important In the calculation of benefits to highway Improvements. They are a large component of total vehicle operating costs, they are sensitive to highway conditions, particularly surface condition, and their progression as vehicles age Is Influential In determining vehicle replacement expenditures, and thus depreciation and Interest costs. Firms' choices of maintenance strategies have Implications for the analysis, Interpretation and transferability of the studies' results and the remainder of this sectlon is concerned with these Issues. Sections 7.1 and 7.2 give brief details of the methods used to collect maintenance cost data and the statistical procedures applied to them. The rest of the chapter describes and comments on the relationships reported by the studies.

Maintenance costs depend upon the characteristics of the routes over which vehicles travel, on the way In which vehicles are used and on the characteristics of the vehicles. Vehicle owners can Influence maintenance costs by controlling ioads, speeds, and drivers' behavior. They can Influence the progression of maintenance costs as vehicles age by Investing In "preventative maintenance" and we can expect the extent of preventative maintenance to vary across countries due to differences in relative prices of maintenance labor, parts, and new vehicles. When components are replaced vehicle owners can choose the nature and quality of the repair that Is performed. Thus owners can choose to replace with components that are new, bought-in reconditioned or reconditioned In-house. Relative prices Influence this decision and the decision to Invest In a major vehicle overhaul or partlal reconstruction.

Firms differ In thelr access to maintenance facilItles and In the damage that the service they provide Inflicts upon vehicles. So we can expect to see across company as well as across country differences In maintenance policies and expenditures. These need to be addressed when considering the statistical analysis of user cost survey data and when comparing the results obtained from the four vehicle operating cost studies. One Issue that arises then Is the relationship between maintenance expenditures and vehicle prices.

In the Kenyan and Caribbean studles the dependent variable In the statistical analysis of maintenance parts costs Is, apart from a factor involving vehicle age, the ratio of maintenance parts costs per kilometer to vehicle price. In the statistical analysis of the Brazilian and Indlan user survey data, parts cost In monetary units per unit distance, or some non-lInear transformation of this was used as the dependent variable. In

227 228 MAINTENANCE COSTS

presenting the results of the four studies later In the Chapter we report as the dependent variable: P/VP where P Is parts consumption In monetary units per 1,000 kilometers and VP is new vehicle price In 105 monetary units, modifying coefficients where necessary, as explained in Appendix A. This standardization of the dependent variable Is carried out in order to simplify notation and to ease to some extent the problems of comparing the results of the four studies. However, this is to a large extent a cosmetic operation since there Is little reason to expect there to be a static relationship between vehicle prices and maintenance parts costs transferable across environments even under common highway conditions. The ratio P/VP gives the illusion of being a measure of malntenance parts consumption that is free of monetary units, and equations for P/VP at first sight express some fundamental physical relationship between parts consumption and highway and vehicle characteristics. However, the removal of monetary units by dividing parts costs by vehicle prices does not remove the Influence of prices on the parts consumption relationship. The Influence of relative prices on maintenance policy has already been noted. One of the prices foremost In the vehicle owner's mind will be the price of a new vehicle.

In Chapter 2 we noted that, for cost minimising firms, new vehicle prices and malntenance costs were related through the condition governing the optimal scrapping of vehicles, and that the flow of maintenance costs depends upon highway conditions and vehicle utilizatlon, the latter being within firms' control. The situation Is pictured In Figure 7.1, in which vehicle age In years Is measured horizontally and costs per time period are measured on the vertical axis. The progression of maintenance and other running costs Is shown by the line m(t), which excludes costs associated with vehicle purchase and replacement. Deterioration In highway conditions and Increases In utilization both cause m(t) to swing upwards. Cost minimlsing firms scrap vehicles at a date s, such that the present value of the shaded area In Figure 7.1 Is equal to new vehicle price.

Equal proportionate changes In the prices of all Inputs to the production of transportation leave the ratio of maintenance costs to new vehicle prices unchanged because of the homogeneity of fIrms' cost functions. So use of P/VP is warranted when we wlsh to allow for variations In the general level of prices across countries and across types of business. However, the situation we face when we examime the studies' results Is one In which relative prices vary across countries. Thus, in India, mechanics' labor Is cheap relative to new vehicles compared with the other countries studled and we can expect this to lead to relatively labor Intensive maintenance practices in India, to relatively low ratios of parts costs to new vehicle prices and to relatively long-lived vehicles. Table 7.1 shows approximate averages for P/VP for the four studies. As expected, the ratios are uniformly low In the Indian data. There is considerable variation In P/VP across vehicle classes, buses giving rise to the lowest ratios and cars to the highest.

Within any vehicle class we can expect P/VP to be Influenced by fIrms' choice of vehicle specificatlon. Consider a transport company making a vehicle purchase decision, faced with two alternative vehicle MAINTENANCE COSTS 229

Figure 7.1: RelationshIpbetween Vehicle Price and MaintenanceCosts $/yearI

M (t)

S vehicle age (years)

Table 7.1: ApproxImateAverages of Ratio of MaintenanceParts Costs (monetaryunits per 1,000 km, P), to Price of EqulvalentNew Vehicles (105 monetary units, VP), FinancialCosts, Obtained In the Four User Surveys

VehibeCla Skudy PNVP

Cars idian 10

Cars Urezi 200

COr and light goods Cwibbean 500

Car and light good, Km" 2SO

Light goods kraza 350

_Su kdia 60

use Brazil 70

suss Kea sO

Medium trucks 1ndI 100

Medium trucks Brzzd 160

Medium truck Cwibben 270

Medium and hay truck Kenya 200

Heavytrucks bezl 200 230 MAINTENANCE COSTS specifications, one cheap to purchase and lightly engineered, the other more expensive to purchase but more robust. The less robust vehicle can be expected to generate higher maintenance costs but It may be the optimal purchase for the transport company depending on the Interest rate and demand conditions faced by It. The less robust vehicle yields a high value of P/VP since P Is high while VP is low. So, when alternative vehicle specifications are available, division of parts cost by new vehicle price can actually Induce variation In the dependent variable. And then there Is a danger that variation In P/VP due to owner's choice of vehicle specificatlon may be attributed spuriously to varlations In route characteristics.

Owners' ability to choose appropriate vehicle specificatlons is likely to have some effect on the extent to which user survey data can reveal the sensitivity of maintenance costs to highway conditions. On poor quality routes more expensive vehicles may be suitable purchases if their malntenance costs are lower than those of cheaper, less robust vehicles. Total costs per unit output are higher on the poorer quality route because of the higher cost of purchasing robust vehicles. However, where alternative vehicle specifications are available, analysis of data covering a wide range of highway conditions Is likely to understate the effect of highway quality on maintenance costs that applies to any single vehicle type. If maintenance costs Increased with, say, roughness as In Figure 7.2, so that owners switch vehicle type at roughness Rs, then, In analysing user survey data, we will obtain estimates of the lower envelope of the maintenance cost-roughness curves.

In practice It has not been possible to distinguish between vehicle specifications within broad vehicle categories since there are Insufficient data for such a detailed analysis. This probably has a substantial effect on the survey equations for buses obtained In Brazil where bus companies tended to operate chassis-based buses on rougher routes, using unitary (Cmonocoque") designs on smoother routes.

7.1 COLLECTION OF MAINTENANCE COST DATA

The collection of malntenance cost data presents special problems due to the discreteness of maintenance expenditures and o the wide variation In cost recording practices employed by transport firms. Maintenance expenditures occur at Isolated points In time and reflect the uses to which vehicles have been put over extended periods of their history. Consequently, user surveys attempt to select vehicles which have travelled for relatively long periods on one or a few routes and survey teams attempt to record maintenance expenditures regularly over a substantial period of time.

In all the studies parts costs were recorded In current monetary units. The Kenyan and Caribbean studies collected data during a twelve- month period of a vehicle's history, recording prices for parts at the time of fitting rather than using prices at which parts were purchased. Price Inflation was low in Kenya and the Caribbean at the time of the studies so It was not necessary to make adjustments for price changes during the MAINTENANCE COSTS 231

Figure 7.2: Rate of Flow of Malntenance Costs as a Function of Roughness: Two Vehicle Specifications

S/kilometer

Vehicle A Vehicle B

Roughness Smooth R Rough s

survey perlod. The situation was very different In Brazil where, by the end of the survey, prices were Increasing at over 100 percent per year. There, the survey team recorded parts prices at the time of fitting to vehicles and, prior to aggregating parts costs, deflated prices to January 1976 using a price Index for spare parts specially developed for this purpose. Similar procedures were adopted In the Indian study In which vehicles were observed for periods In excess of two years.

In the Indian study, parts costs and descriptions of maintenance activities were recorded, the latter because maintenance labor hours were to be obtained for most survey vehicles by using Information on "standard" labor hours required to perform maintenance tasks. The study team found It extremely difficult to record details of all spare parts and only those Items costing more than Rs5O (US$10) were recorded In detail, spare parts costing less than this being held In aggregate form.

It is Important to note that, In all the studies, accident costs were removed from maintenance expenditures. Large expenses, like replacement engines, were Included In the Brazilian and Indian studies' maintenance cost data. In Kenya and the Caribbean where relatively short twelve-month vehicle histories were examined, these expenditures were adJusted prior to being added to other maintenance cost data. 232 MAINTENANCE COSTS

Only a few companies In developing countries record maintenance labor data on a vehicle specific basis. Resources were limited In the Kenyan and the Caribbean studies and the survey teams were unable to collect Information other than that contained In company records. In the Kenyan survey company average labor costs were collected from seven companles operating In total 204 vehicles. The Caribbean study collected labor data only from companies who had maintenance performed by commercial garages and reported an average ratio of labor costs to parts costs was estimated.

In the Brazilian study two approaches to modelling maintenance labor costs were attempted. First, total workshop hours were related to the vehicle fleet route characteristics for fleets within which vehicles operated over relatively similar route types. The results are reported In Wyatt et al. (1979). Second, survey vehicle cost histories were examined to Identify vehicles that possessed long, concurrent parts and labor cost streams. Typically companies recording labor data had not done so throughout the survey perlod and the maintenance parts streams were always longer than maintenance labor cost streams. Vehicles with at least twelve months concurrent parts and labor data were used to develop the labor equations reported below.

The Indian survey had an ambitious program for the collection and transformation of parts cost data Into labor cost data. With major private operators and government enterprises, where It was possible to Identify service schedules and consumption of spares and major overhauls on a vehicle basis, the following procedure was used. Spare parts costs were grouped Into five classes, namely, periodic maintenance, small parts replacement, larger parts replacement, major assemblies installation, and reconditioning of major assemblies. Standard labor hours tables were developed using manufacturers' recommendations and data obtained from some of the blgger workshops. Labor cost assoclated with periodic maintenance was obtained from workshop records. Labor hours associated with reconditioning and rebuilding major assemblies were derived from manufacturers' data and workshop experience. Where this procedure could not be applied because parts costs were only available at the company level, total labor hours recorded at the workshop was related to total consumption of spare parts over the same period. The labor hours produced by these two procedures were converted to labor cost using an hourly mechanic's wage of 2.25 1978 Rupees (25 cents 1978 U.S. dollars).

7.2 STATISTICAL ANALYSIS OF MAINTENANCE COST DATA

An Important feature of maintenance, cost data Is that maintenance practices tend to be company specific. First because companies develop their own style of working, second because companies often have a distinctive geographical and local economic environment, and third because companies tend to specialize (particularly In truck transportation) in type of business performed and In user surveys the need to find vehicles operating on homogeneous routes results In truck companies that specialize In a single type of business being over represented. The result Is that vehicles compared within companies tend to be more similar to each other In respect of maintenance costs than are vehicles compared across companles. MAINTENANCE COSTS 233

The experience of the Brazilian study was that after controlling for highway and vehicle characteristics the variance of costs within companies, across Individual vehicles was of a similar order of magnitude to the variance of average company costs across companies. Variances of costs across companies In bus operations tend to be rather smaller, since bus operators are engaged In similar businesses. Because there are company specific variations In maintenance costs, care needs to be taken if equatlons are estimated by ordinary least squares, since the disturbance term In the cost equation Is likely to have an error components structure. As noted in Chapter 2, this leads to at best Inefficient estimation and biased standard errors and possibly to biased estimates If high and low cost companies are not disposed at random over highway types.

The results reported for the Indian and Brazilian studies were almost all obtained either using generalized least squares, regarding company influences as randomly sampled from a distribution of company Influences, or by applying ordinary least squares after Introducing company specific indicator variables so that cost equations are regarded as having a common slope across companies but a separate intercept for each company. Where there was evidence of correlation between company effects and highway characteristics or other explanatory variables, the latter, within company estimator was used.

The Kenyan study results were obtained using averages of costs and highway characteristics across groups of vehicles. These groupings do not always correspond to a company grouping so that one company can generate more than one average. Our understanding Is that vehicles grouped together were similar In all respects as far as values of explanatory variables were concerned. The Caribbean study results were all obtained by applying ordinary least squares to raw vehicle data.

7.3 MAINTENANCE PARTS COSTS: ESTIMATED EQUATIONS

The Kenyan and Caribbean studies present equations for the ratio of parts expenditure per 1,000 kilometers to the price of an equivalent new vehicle, this ratlo being divided by vehicle age (square root of age for buses). To report these equations we have multiplied through by the age effect so that It appears on the right hand side of the parts equations, and changed units of measurement leaving the left hand side variable as P/VP where P is parts expenditure In monetary units per 1,000 km of travel and VP Is vehicle price measured in 105 monetary units. The Brazilian and Indian studies present equations for the natural logarithm of parts expenditure except for the Brazilian truck equation which uses parts expenditure as It stands. In reporting the Indian and Brazilian study equations we have exponentiated the fitted relatlonships and, where necessary, redenominated parts expenditure In monetary units per 1,000 kilometers. We have then divided through the right hand sides of the equations by the representative vehicle prices (in 105 monetary units) shown In Table 7.2, rewriting the left hand side of the equations as P/VP. Thus all four studies' equations are reported with P/VP as the dependent variable. To retrieve parts cost In monetary units per 1,000 km as analysed In the Indian and Brazilian studies the equations reported here 234 MAINTENANCE COSTS

Table 7.2: New Vehicle Prices (Financial) Used In Defining Ratios of Parts Costs to New Vehicle Price

Study -Currency Dato for Vehicle Class Price

, _ I _ prices _ _ __

India_ t) Rupees 1978 Cars 64800 Buses 234000 Trucks 180700

ar.zil(2) Cruzeiroi Jan.1976 Crrs 31856 Light Goods Vehcle 43S70 , 8w0~~~~~~~Bss 316S70 l ~~~~~~~~~Trucks:2-axle 138621 3-,xle 170961 Tipping 146616 Semitrailers: Trtor 317781 Trailer 119923

Kenya(3) I Kenyon 1973 Cars 16900 shillings Buses 132000 Trucks: 2-axle 40000 Heavy unit 120000

3 Caribbeant 1977 Cers 21000 dollars Trucks 48M00

(1) Includes % tax. (2) Includes 1S% tax, (3) Data expreased as ratio of parts coststo vehicle price prior to analysis.

should be multiplied up by the appropriate representative vehicle prices from Table 7.2. We stress again that these equations require calibrating prior to use, that as vehicle prices alter parts costs cannot generally be expected to adjust proportionately and that In other environments the ratio of P to VP is likely to differ from the levels observed In the four studies.

Vehicle age is measured In thousands of kilometers of travel since first registration. In the Brazilian and Indian studies vehicle age was measured at the survey midpoint but In the Kenyan and Caribbean studies at the survey endpoint. In an attempt to present comparable equations the Kenyan and Caribbean equatlons have been amended by calculating for each vehicle class, average survey period utilization and replacing the reported age In the Kenyan and Caribbean equations by survey midpoint age (K) plus one half of this average utilization.

7.3.1 Maintenance Parts Costs: Cars and Light Goods Vehicles

in the Kenyan and Caribbean studies these vehicle classes were analysed together but In the Brazilian study cars and light goods vehicles were subjected to separate analysis. The Indian study reports results obtained from a very small sample of jeeps. These results are unreliable and Indian study results given be,low relate to cars alone. In all four studies cars and light goods vehicles were In commerclal operation, largely on rural roads. MAINTENANCE COSTS 235

The equations are presented in common units and in a common notation in Table 7.3. In all the equations the explanatory variables are road roughness (R) In mm/km, and vehicle age (K) In thousands of kilometers, the only exception being the Indian study equation in which vehicle age does not appear. This equation should be taken to refer to vehicles of average age in the Indian Road User Survey - around 100,000 km.

The relationships recorded In Table 7.3 are graphed in Figure 7.3 against road roughness for fixed vehicle age and In Figure 7.4 against vehicle age for fixed roughness. The relationships differ in a number of Important respects. Firstly, the Kenyan and Caribbean equations are llnear In road roughness whereas the Brazilian and Indian equations give parts consumption as an exponential function of roughness. Secondly, the Kenyan and Carlbbean equations write parts consumption increasing proportionately with vehicle age whereas In the Brazilian equation parts consumption Increases with approximately the third root of vehicle age. In all four studies the data sets on cars and light goods vehicles were rather small and the range of roughness over which vehicles were observed was relatively restricted (except for Brazilian light goods vehicles which were observed on extremely rough routes). In Kenya and the Caribbean only restricted ranges of vehicle ages were observed.

A feature of the Kenyan and Caribbean results Is their very good fit to the data and In consequence the apparently high degree of precision in the estimation of roughness coefficients in these studies. However, in the case of the Kenyan study equations, this Is part spurious, being attrlbutable to the effects of averaging over groups of vehicles, and the comments made above (Section 6.2) In respect of the statistical methodology for tire analysis apply here also. In the Brazilian and Indian studies, parts consumption was found to vary greatly from vehicle to vehicle and only moderate precision In the estimation of coefficients was achieved.

Considerlng first the effect on parts consumption of changing road roughness, the exponential form used In the Brazilian and Indlan studies predicts relatively small changes In parts consumption on Increasing roughness on smooth roads by, say, 1,000 mm/km, but on rough roads a similar magnitude change in roughness Is predicted to lead to large changes In parts consumption. In India it appears that parts costs increase less fast as roughness Increases but It is necessary to note here that the cars observed In India, are generally of rather sturdier construction, albeit of older design, than the cars found In commercial operation in Brazil, and that vehicle speeds In India are generally low.

The form of equation used In the Kenyan and Caribbean studies requires equal magnitude Increases In parts consumption on Increasing road roughness by, say, 1,000 mm/km, regardless of Initial roughness. Thus on smooth roads they tend to predict larger, and on rough roads, smaller changes than do the Brazillan and Indian study equations. Some care Is needed In applying these equations to smooth roads because they can predict quite large reductions in costs on Improving a road from, say, 3,000 mm/km to 2,000 mm/km, reductions that can lead to large predicted benefits to highway improvement If the Initially quite smooth road Is heavily trafficked. 236 MAINTENANCE COSTS

Table 7.3: Maintenance Parts Cost Equations: Cars and Light Goods Vehicles

Study VehicleClass Equation India Cars P = exp(4.172 + .000169R),

Brazil Cars P = exp(3.306 + .000249R)K 308,

Brazil Light Goods P = exp(4.378 + .000OS4R)K-306, VP

Caribbean Cars and Light Goods P = (-5.50 + .00262R)(K+8)

Kenya Cars and Light Goods P = (-2.03 + .0018R)(K+38)

Notes: See Appendix7.1 for equationsas reported, summarystatistics etc.

P = Maintenanc parts cost (monetaryunits per 1O3 kin)

VP = New vehicle price (10s monetaryunits)

R = Road roughness,81 (mm/kim)

K = Vehicleage at surveymidpoint (103 km).

Turning now to the magnitude of the roughness effect, we can see from Table 7.4 and Table 7.5, the latter giving predicted percentage changes in parts costs after a roughness change of 1,000 mm/km, that the four studies differ somewhat In their predictions. The Kenyan and Caribbean studies predict a 35 percent Increase In parts consumption on Increasing roughness from 4,000 mm/km to 5,000 mm/km the corresponding figure for India and Brazil belng 18 and 28 percent, these figures applying to a 1,000 mm/km change In roughness from any base. Brazilian light goods vehicles are less affected by roughness, parts costs per 1,000 km increasing by only 10 percent with each 1,000 mm/km Increase In roughness. This Is to be expected given these vehicles' sturdler construction. The figure for Brazilian cars may be something of an over estimate for normal operating conditions because most of the cars In the Brazilian road user survey were Involved in unusually high speed delivery operations. At higher levels of roughness the roughness effect estimated In the Caribbean study Is larger than that found In the Kenyan study. Hide (1982) suggests that this difference arises because the Caribbean data are mostly obtained from paved road operations, In contrast to the Kenyan data, so that the roughness coefficients differ In part because of differences In surface type and assoclated differences In the effects of roughness on vehicles' deterioration. MAINTENANCE COSTS 237

Figure 7.3: MaintenanceParts (P/VP) versus Roughness (R): Cars, Light Goods Vehicles and Utilities

P/VP

1600 *

1400 . K/

1200 /

1000 /

800 / BC -

600 /

400 _ - - / / -

400 _ -- ,, -I

200 ......

I R, BI 2000 4000 6000 8000 10000 12000

I I I III I u , t R, IRI 2.8 5.1 7.4 9.5 12.0 14.0

Equations: BC = Brazil Cars BU = Brazil Utilities C = Caribbean : Cars and Light Goods I = India : Cars K = Kenya Cars and Light Goods

Units: P = Parts consumption (monetary units/103km). VP = Vehicle price (105 monetary units) R = Road roughness Bi (mm/km), IRI (in/krn) K = Vehicle Age (103 km)

Varables not Plotted: K = Vehicle age = 100,000km (not India). 238 MAINTENANCE COSTS

Figure 7.4: Malntenance Parts (P/VP) versus Vehicle Age (K): Cars, Light Goods Vehicles and Utilities

P/VP _@BU

900 - -- -- B

K, _ 700 * I ,/ I ,'

600 I//

500 'I, ~~~BC 400 - -

300 '

200

100

K 100 200 300 400 500 600 700 800 900 1000

Equations: BC = Brazil Cars BU = Brazil Utilities C = Caribbean : Cars and Light Goods I= India Cars K = Kenya : Cars and Light Goods

3 Units: P = Parts consumption (monetary units/10 km). VP = Vehicle price (10s monetary units) R = Road roughness BI (mm/km), IRI (m/km) K = Vehicle Age (103 km)

Variables not Plotted: R = Road roughness = 4,000mm/km. MAINTENANCE COSTS 239

Now consider the vehicle age effects. In the Brazilian study the rate of Increase in parts consumption with vehicle age Is predicted to decline as age Increases, see Figure 7.4. Separate relationshipswere estimated for cars and light goods vehicles but, as it happens, the predicted age coefficientseffects are identicalto 3 significant figures, each doubling of vehicle age being associatedwith a 24 percent increase in parts cost per 1,000 km. In the Kenyan and Caribbean studies' results the effect of vehicle age Is very much more marked. It Is unclear whether the exponent of 1.0 on vehicle age was estimatedor assumed In producing the Kenyan and Caribbean equations. Redefining age to be survey midpoint age (which It is as reported here but not as estimated in the studies) and re- estimating these equations gives disappointing results (for instance,for the Kenyan data R2 drops from 0.92 to 0.44 though Interestinglythe roughness coefficlent Is virtually unchanged). It seems that the estimated age effects from the Kenyan and Caribbean studies are somewhat fragile. The Brazil study age effects are In line with those obtained for other vehicle classes In Brazil and in India and seem more reasonable,for If parts consumption really does double with every doubling of a vehicle's age then optimal vehicle lifetimeswill be very short.

The age effects estimated in the Kenyan and Caribbean studies are very large. In Chapter 8, In Part liI, we examine the Implicationsthat the studies' maintenanceequations have for vehicle scrapping decisions in order to obtain information concerning depreciation and Interest costs. When malntenance costs become large, owners will optimally scrap vehicles and replace them with new vehicles which incur low maintenance costs. For Indian and Brazilian vehicles, predicted vehicle lives are rather long, probably because maintenance costs are understated by the studies' equations due to neglect of accident costs, omission of small maintenance expendituresand for other reasons discussed in detail In Chapter 8. For Kenyan vehicles (except buses) and for Caribbean vehicles, predicted vehicle lives, in kilometers,are very short indeed,because of the steep rise In costs with vehicles' kilometer ages that these studies' equations predict.

So far as the Caribbean vehicles are concerned, this may be due to confusion of the effects of calendar and kilometer ageing. The vehicles studied In the Caribbean achieved very low annual utilization,around 10,000-25,000kilometers per year. All the vehicles (cars and trucks) in the CarIbbean study that had travelled over 100,000 kilometers were 5 or more years old and It Is possible that these older vehicles Incurred substantialmaintenance costs because of calendar related age effects, due, for example, to corrosion. Age in kilometers and age in years are quite closely correlated In the Caribbean study's data sets, so that on regressing parts costs on either kilometer or calendar age significant, positive coefficientsare obtalned. This suggests that It would be unwise to extrapolate the Caribbean study's maintenance equations to high vehicle kilometer ages. In Chapters 8 and 9, where total operating cost calculationsare performed, the Caribbean study's maintenanceequations are only employed to predict costs in a low utilizatlonenvironment, In which high kilometer ages do not arise. 240 MAINTENANCE COSTS

Table 7.4: Maintenance Parts Cost Predictions: Cars and Light Goods, against Roughness and Vehicle Age by Study. Entries In Table Are Values of P/VP

RUC STUDY

Road Roughness Vehide Kenya Caribbean India Brazil Brazil B IRI Age Cars Light Goods (mmfksm)(m/km) (000 kmn)

50 138 - - 149 321 2000 2.8 100 217 - 91 185 397 1S0 296 - - 210 450 200 374 - 229 491

50 297 137 _ 192 352 3000 4.0 100 465 255 108 238 436 150 633 373 _ 270 494 200 802 491 _ 295 540

50 455 289 - 246 387 4000 5.1 100 713 538 127 305 479 150 971 787 - 346 543 200 (1230) 1036 - 378 593

50 613 441 - 316 426 5000 6.3 100 962 821 151 391 527 150 (1311) 1201 - 569 597 200 _ 1581 - 484 652

50 772 593 - 405 467 6000 7.4 100 (1210) 1104 179 502 578 150 (1648) 1615 - 569 655 200 - - - 621 716

50 930 745 - 520 513 7000 8.5 100 (1459) 1387 212 644 635 150 (1988) (2029) - 730 719 200 - - _ 797 786

50 - 897 - 667 564 6000 9.5 100 - 1670 251 826 698 150 - (2443) - S36 791 200 - - 1(1023) 864

Nots: "( )" indicates number out of range of study observations. "- " indicates not available. MAINTENANCE COSTS 241

Table 7.5: Percentage Increases In Maintenance Parts Costs per 1,000 km on Changing (a) Road Roughness, (b) Vehicle Age

% Increase in Parts Cost per 1000 kim.

(a) (b) Study HighwayType Increasing Roughness Doubling by 1000mm/km Vehicle Age

Kenya, Cars and Smooth 73% Light Goods (2500mm/kmi)

Average 35% (4000mm/kmi)

Caribbean, Cars Smooth 250% and Light Goods (2500mm/km)

Average 35% (4000mm/kmi)

Brazil, Cars ALL 28% 24%

Brazil, Light Goods ALL 10% 24%

India, Cars ALL 18%

Notes: (1) Calculatedassuming base age = 50,000km. 242 MAINTENANCE COSTS

This sort of explanation of large kilometer age effects does not seem to apply to the Kenyan study results, for in Kenya vehicle utilization was not particularly low. The Brazil study age effects reported above are not particularly large and are in line with those obtained for other vehicle classes In India and in Brazil.

7.3.2 Maintenance Parts Costs: Buses

The equations for bus maintenance parts consumption as reported in the studies are given in Appendix A. Results are available only for the Indian, Brazilian, and Kenyan studies. The equations are reported in Table 7.6 and graphed against roughness for fixed vehicle age In Figure 7.5 and against vehicle age for fixed roughness in Figure 7.6. Predictions are given In Tables 7.7 and 7.8.

In all the three studies which report results for buses, wide ranges of vehicle ages were observed. In both Kenya and Brazil, data on maintenance costs were obtained from buses over one million kilometers old. So, for this vehicle class It is possible to obtain precise estimates of the effect of vehicle age on maintenance costs and in this respect the three studies agree. As with the Brazil car data, the rate of Increase of parts costs with vehicle age Is found to decrease as vehicles age. Many owners make major maintenance expenditures when buses are between 350,000 and 500,000 km old, thereafter incurring a reduced flow of maintenance expenditures. This discontinuity In maintenance expenditures associated with the rebuilding of engines and/or vehicles tends to be smoothed over in user survey data since different vehicles receive this treatment at different ages. Examining Table 7.7, which gives percentage Increases in parts cost per kilometer attendant on doubling vehicle age, we see that the three studies are in broad agreement concerning the lifetime progression of maintenance costs, every doubling of vehicle age being associated with an Increase In parts consumption of between 30 and 40 percent. The Kenyan and Brazilian age coefficients are virtually identical but the Indian age coefficient is lower than the Brazilian age coefficient and the difference Is, statistically, highly significant.

The Indian and Brazilian studies are in broad agreement concerning the Influence of road roughness, predicting an effect smaller than that found for either cars or trucks. The Brazilian and Indian roughness coefficients differ by an amount that is statistically Insignificant. The Kenyan study predicts large effects for roughness. It Is difficult to reconcile this substantial difference. The Brazilian and Indian studies predict an Increase of only around 6 percent In parts cost per 1,000 km with every 1,000mm/km increase in road roughness, while the Kenyan study predicts increases in parts costs of the order of 30 percent for a 1,000mm/km increase on rough routes and as high as 70 percent for the same roughness increase on smooth routes. The range of roughness observed in Kenya (2,440mm/km - 4,430mm/km for the bus parts data set) Is very substantially narrower than that observed in India (3,000mm/km - 12,000mm/km) or In Brazil (1,300mm/km - 11,500mm/km) and extrapolating the Kenyan relationship to roads rougher than 7,500mm/km Is not recommended. MAINTENANCE COSTS 243

Figure 7.5: Maintenance Parts (P/VP) versus Roughness (R): Buses

P/VP

160

140 K

120

100

80 , - ,,.

60/_,-'

. R,BI 2000 4000 6000 8000 10000 12000

i I I i I I R, IRI 2.8 5.1 7.4 9.5 12.0 14.0

Equations: B = Brazil I = India K = Kenya

Units: P Parts Cost (monetary units per 103km) VP New Vehicle price (10s monetary units) R: Road roughness BI (mm/km), IRI (m/km) K: Vehicle age (103km)

Variables not plotted: K: Vehicle age = 350,000km. C: Average degrees of curvature = 1500/krn RF Rise plus fall = 20rn/km W: Pavementwidth = 5.5m. 244 MAINTENANCE COSTS

Table 7.6: Maintenance Parts Cost Equations: Buses

Sudy Equation

India P = exp{1.252 + .OO52S6R + .000282C + .00675RF + 2.OOIW)K,358.

Brazil P = exp[1.607 + .O000647R)K-483.

Kenya P = 4-2.12 + .0019R)(K460)0 .5.

P = Parts cost (monetary units per 1O3km). VP = New vehicle price (1lo monetary units) R = Road roughness Ul (mmfkm) K = Vehicle age at survey midpoint (103km) C = Average degrees of curvature (°/km) RF = Rise plus fall (m/km) W = Pavement width (m)

It Is doubtful whether vehicle owners could recoup from their customers the high maintenance costs predicted by the Kenya equation on roads rougher than this.

In the Indian study some Influences for highway geometry and pavement width can be detected and these appear In the equations given In Table 7.6. Introducing measures of both vertical and horizontal geometry results In large standard errors for estimated coefficients because of high correlation between rise + fall and average degrees of curvature In the India data. Collectively the geometry measures explain a small but significant proportion of the variation in parts costs though this Is not evident from examination of reported standard errors. Other coefficients are altered little as geometry measures are included.

Increases In gradient or curvature and decreases In pavement width are each associated with Increases in parts costs. Every lOm/km increase In rise + fall Is predicted to Increase parts costs by 7 percent and every 1000 /km increase In average degrees of curvature Is predicted to Increase parts costs by 3 percent. Thus even moving from one extreme of the Indian survey data to another and Increasing average degrees of curvature from 00 /km to 1,0000 /km Is predicted to Increase parts consumption by only 33 percent. However, moving from flat straight highways (say, rise + fall - lOm/km, average degrees of curvature - 500 /km) to steep curving highways (rise + fall - 70m/km, average degrees of curvature - 1,0000 /km) results In a predicted Increase In parts costs of 96 percent which Is substantial. Reducing pavement width from 7m to 5m Is predicted to Increase parts costs per km by 12 percent, a further reduction to 4m resulting In a further 11 percent Increase In parts costs. MAINTENANCECOSTS 245

Table 7.7: Maintenance Parts Costs (P/VP): Buses

RUC STUDY

1 Road Roughness Vehicle india( ) f Brazil Kenya Bl IRI Age (mm/km) (mlkim) (000 km)

100 37 56 45 400 60 109 77 3000 4.0 700 73 143 99 1000 83 170 117

100 41 64 93 400 67 125 158 5000 6.3 700 82 163 203 1000 93 194 (240)

100 45 73 141 400 74 142 (240) 7000 8.5 700 91 116 (308) 1000 103 221 (364)

100 50 83 l19 400 82 161 (321) 9000 10.6 700 101 211 - 1000 114 251 -

1010 56 94 - 400 92 184 - 11000 12.6 700 112 241 - 1000 127 286 -

(1) Assuming: Rise plus all = 2Cm/km Average degrees of curvature = 1500 /km Pavement width = 5.5rm. For each increase (decrease) of lOmikm rise plus tall multiply by 1,07 (0.935). For each 0 increase (decrease) of 100 k/kn average degrees of curvature multiply by 1.029 (0.972). Indicates out of range of study obssrvations.

Table 7.8: Percentage Increases In Parts Consumption: Buses

Study Highway Increaing Doubling Increasing Increing Decreaing Type Roughness Vehicle Rise plus Average Pavement by I Age Fall by Curvature Width 1o0minm/km_ lOm/km by 1000 Sm - 4m

India . ALL 5% 28% I 7% 3% 11%

Brzil ALL 7% 40% _- _

1 Kenya' ) Smooth 72% 37% (2000mm/kin)

Average 42% 37% _ _ (35ODmm/km)

Rough 26% 37% _ _- (5000mm/km) _ .

Notes: (1) Assuming initial age 400,000nm. 246 MAINTENANCECOSTS

Figure 7.6: MaintenanceParts Cost (P/VP) versus Vehicle Age (K): Buses

P/VP B

180K

160-

140

120-

100

60 -I

40 /'

K 200 400 600 800 1000 1200

Eaustimm: B = Brzil I = Indla K = Kenya

Unitx: P: PawtsCost (monetary units per 103km) VP: New Vehce price (10s monetary unts) R: Road roughnes S (mm/km). IRI (m/km) K : Vehice age (103km)

Varible not ottd: R Road roughnes = 4000 D (mm/km). 8.1 (m/km) K Vehcle ag = 350,000km. C: Average deg of curvature = 1C0°/km RF: Ris plus all = 20m/km W: Pavement width = 5.5m. MAINTENANCE COSTS 247

7.3.3 Maintenance Parts Costs: Trucks

All four vehicle operating cost studies report equations with which to predict truck maintenance parts costs but In many respects these equatlons are less satisfactory than those obtained for buses. Two major problems arise when analysing truck maintenance data. First, truck maintenance costs are Inherently more variable than bus maintenance costs, largely because trucks, unlike buses, are engaged in diverse types of business. Maintenance expenditures alter substantlally as we move from trucks engaged In, say, gasoline transportation to trucks engaged In, say, haulage of aggregates. Since type of business varies more across companies than across Individual vehicles wlthin companies, this suggests that fruitful results might be obtained from examining the relationships between within company variations In routes and within company variations in maintenance expenditures.

Unfortunately, rather little useful information emerges from such an analysis because most surveyed truck operators were located in relatively compact geographical areas. So when we come to examine within company varlations in route characteristics we find that this variation Is often too small to produce accurate estimates of the effects of highway characteristics on maintenance parts costs. We are forced then to work with the rather variable cost data available at the company level. Unfortunately, we then run the risk of associating cost differentlais that occur largely at the company level with variation In highway characteristics at the company level when In fact the cost differentials at this level may be due to type of business. Slnce user cost surveys typically examine only a rather small number of companies there Is the danger that companies may be curiously disposed over highways of different types, leading to a "correlation" between type of business and highway characteristics.

In order to obtain usable equations with which to predict truck maintenance parts costs we have had to modify to some extent equations as reported in two of the studies. The equations as reported In the studies are given In Appendix A where we present the reasoning that leads to the equations reported here in Table 7.9.

The first point to note Is that the studies differ in their treatment of the effect of vehicle specification. The Indian study equation Includes gross vehicle weight as an explanatory variable and applies In principle to vehicles In the weight range 8 tons - 28 tons though most of the vehicles providing data were within the 10 - 16 tons range. The Indlan study uses the logarithm of parts consumption as the dependent variable and coefficients on highway characteristics like roughness can be Interpreted In terms of percentage changes In parts costs attendant on given changes In highway characteristics. Typical net and gross vehicle weights observed In the studies are given in Table 7.12. In the Brazilian study equation, as originally estimated, trucks of different types (2-axle, 3-axle, tipping (all 2-axle) and semi-trailer tractors) were allowed to generate different Intercepts In the linear parts cost, 248 MAINTENANCE COSTS

Table 7.9: Maintenance Parts Cost Equatlons: Trucks

Stdy Truck Equation Type

Inda ALL P = exp(0.48 + .000143R + 3.4*3GW .0531 GVW)K340.

Brazil 2-avxe P = (1.931 + .00864R)K-371.

3 1 Brazil Tipping P = (4.490 + .00S36R)K 7 . VP

Brazil 3-axle P = (11.168 + .00717R)K.37 1 .

Brzil Semi-trailer P = (13.562 + .00386RK,371. Tractors VP

2 Caribbean ALL P = (-. 54 + .00316R - I I I0021R ) (K6)

Kenya ALL P = (0.48 + .00037R)(K.23)

Notes : See Appendix 7.1 tor equations as reported, summery statistics etc. P = Maintenance parts cost (monetary units per 103 kn) VP = New vehicle price (105 monetary units) R = Road roughnes, 81 (mm/akm) K = Vehicle age at survey mid point (103 km) W = Pavement width (m) GVW = Gross vehice weight (t)

roughness equation. After division through by vehicle prices which vary over truck types the equations' slopes and Intercepts become specific to truck type. The Kenyan and Caribbean studies address the problem of merging different sized vehicles Into a single truck data set for analysis by using the ratio of parts costs to vehicle prices as the dependent varlable.

In the Brazilian survey equations the maintenance parts costs for semi trailers relate to the tractor unit only. Trailer maintenance parts costs were estimated at around one-third of tractor parts costs, though it should be noted that the data available relate to only 34 tractor-trailer combinations. The difficulty here Is that trailers rarely remain associated with a since vehicle so that It Is difficult to obtain rellable Information on characteristics of routes travelled by trailers. The other studies did not cover semi trailers though the Kenya study does contaln some truck-trailer combinations. Most of the Caribbean surveys' trucks were relatively light. MAINTENANCE COSTS 249

Of the equations reported In Table 7.9 only that obtained in the Indian study Is non-linear. An exponential equation was estimated and reported in the Brazilian study but It was found to extrapolate badly and was abandoned In favor of the linear form reported here. All the studies report a multiplicative age effect, those obtained in Brazil and India being similar and predicting a 25-30 percent Increase In parts costs per km with every doubling of vehicle age. The Kenyan and Caribbean equations Incorporate a linear age effect which In practice cannot be extrapolated far without predicting unrealistically high parts consumption. All the Caribbean study's truck data comes from vehicles with very low annual utilization. In part, the large kilometer age effects predicted by the Caribbean truck maintenance cost equation may be due to confusion of the effects of calendar related and kilometer related ageing.

The equations In Table 7.9 are graphed against road roughness for fixed vehicle age In Flgure 7.7 and against vehicle age for fixed roughness In Figure 7.8. Predictions are given In Tables 7.10 and 7.11. Inspecting Figure 7.9 and recalling that the extent of a graphed line In these diagrams Is a rough Indication of the range of the explanatory variable In the study data set producing the line, we see that in the Kenyan and Caribbean surveys trucks were young relative to those covered In the other studies, vehicles In these surveys being generally less than 300,000 km old at the survey midpoint. For more Information on ranges see Appendix A.

All the equations include road roughness as an explanatory variable. The coefficients on roughness differ somewhat, In part because of the different orders of magnitude of the dependent variable P/VP across countries. Average P/VP Is, for trucks In India around half the value found for trucks In Brazil for example. Comparing percentage increases in parts costs per 1,000 kilometers attendant on increasing road roughness by 1,000 mm/km (see Table 7.11) we do find rather similar results from all the studles with the exception of the Caribbean study. Using the Kenyan, Indlan, and Brazilian equations we find that parts costs Increase by from 15 to 21 percent on increasing roughness by 1,000 mm/km on a moderately good route with roughness around 4,500 mm/km. The Caribbean study predicts an 86 percent Increase In the same situation. It Is Interesting to note that these Increases are larger than those found for buses (at least in the Indian and Brazilian studies). Loaded trucks generally have higher centres of gravity than buses resulting In rolling and pitching which may lead to faster component failure. And, of course, overloading Is far more common In truck than In bus transportatlon and overloaded vehicles may be more sensitive to roughness changes.

The roughness coefficients obtained In the studies are each only determined to within + 35-40 percent (calculating approximate 95 percent confidence Intervals) so that the sorts of differences found In Table 7.11 are, with the exception of the Caribbean study, consistent with common roughness Influence, costs increasing by around 15-20 percent with 1,000 mm/km Increases In roughness on average routes. As for the car vehicle class the roughness effects for trucks are found to be large In the Table 7.10: Maintenance Parts Costs (P/VP): Trucks

1 RUC SrUDY INDIAM ) BRAZIL CARIBBEAN KENYA ROAD VEHICLE T ROUGHNESS AGE I Semi Trailer 2 ) 2 B IRI (000kn) TRUCK TYPE GVW=12t( VW=is6t( ) 2-axle 3-axle Tipping Tractors i ALL ALL

(mmlkm) (m/km) ___ - 100 43 53 157 180 j 63 139 111 196 3000 4.0 400 68 85 263 302 1 273 I 232 426 636 700 83 102 323 371 336 286 - - 1000 93 115 - - 326 _ _

100 57 70 255 260 256 181 425 287 5000 6.3 400 91 113 426 434 427 303 1628 (932) 700 110 136 524 534 526 373 - _ 1000 124 154 - - - 426 - _

100 76 93 337 339 348 224 561 378 7000 8.5 400 121 150 563 567 582 375 (2147) (1299) l 700 146 181 693 697 716 461 - _ _ 1000 165 204 - - -526

O:) 100 101 124 - _ _ _ - _ 9000 10.6 400 161 199 ______700 195 241 _ _ _ _- _ _ 1000 220 272 _ _- _ ----

100 134 166 _ I _ - ! - _ _ 11000 12.6 400 215 265 _ _ _- _ 71700 260 321 _ ___ [ _ __ | 1000 293 j362 _ | ______

Notes: Numbers in parentheses are out of range for their studies.

(1) Assuming pavement width = 5.5m. For 4m pavement width multiply by 1.27, for 7m pavement width multiply by 0.87 (2) Assuming same vehile specification operated at different loads. MAINTEHANCE COSTS 251

Table 7.11: Percentage Increase In Parts Consumption: Trucks

Increasing Doubling Study Vehicle Type Highway Type Roughness Vehicle by 0OOOmm/km Age

India ALL TRUCKS ALL 15% 26%

Brazil 2-axle Smooth (3000mm/km) 31% Average (4500mm/kmi) 21% Rough (6000mm/km) 16%

3-axle Smooth (3000mm/km) 22% Average (4500mm/kmi) 17% 29%A Rough (6000mm/kmi) 13%

Tipping Smooth (3000mm/kmi) 28% Average (4500mm/km) 20% Rough (6000mm/km) 15%

Semi Trailer Smooth (3000mm/km) 15% Tractors Average (4500mm/kmi) 15% Rough (6000mm/kmi) 12%

Caribbean ALL Smooth (3000mm/km) 181% Average (4500mm/kmi) 86% 94%(1) Rough (6000mm/kmi) 61%

Kenya ALL Smooth (3000mm/km) 23% Average (4500mm/km) 17% 81%(1) Rough (Sooomm/km) 14%

(1) Assuming initial age = 100,000km. 252 MAINTENANCE COSTS

Figure 7.7: Malntenance Parts (P/VP) versus Roughness (R): Trucks

P/VP ,c

900 - /Bo 800 -/

700 /

/ /K

600 / 1'/ 500,

400 - )f AXo

300

- s

200 3 - - - 100BT - - _____.. =_- 16

BT ------B 2

10 w R, BI 2000 4000 6000 8000 10000 iI I I I I I I I R, IRI 2.8 5.1 7.4 9.5 12.0

EBato2 :Brazil, 2-axle. 83 : Brazil, 3-axle BT :Brazil, tipping BS :Brazil, Semi trailer tractor C Caribbean 16 : India, 16 tonne gross vehicle weight l12 : India, 12 tonne gross vehicle weight K : Kenya

Units P Parts cost (monetary units per 103km) VP: New vehicle price (los monetary units) R : Road roughness 81 (mm/Dim), IRI (m/km) K : Vehicle age (103 kim)

Variables not Plotted

K: Vehicle age = 180,000km W Pavementwidth = S.5m. MAINTENANCE COSTS 253

Figure 7.8: Maintenance Parts (P/VP) versus Vehicle Age (K): Trucks

P/VP K

500 /

400

300 / - - - _B_---

200 -

~~~~~'f ,/c-~~~~~~~~~~~------16

I.----.. ~ ~ ....------1 4--- ~ ~ ~ ------

100 2 00 300 400 500 6 00 700 800 90'0 10,00

EAuations B2 Brazil, 2-axle. 83 Brazil. 3-axle BT Brazil, tipping BS Brazil, Semi trailer tractor C Caribbean '16 India, 16 tonne gross vehicle weight '12 India, 12 tonne gross vehicle weight K Kenya

Units P Parts cost (monetary units per 103km) VP New vehice price (105 monetary units) R Road roughness Bi (mm/km). IRI (m/km) K Vehicle age (103km)

Variables not Plotted R Road roughnes = 4000mm/km W Pavementwidth = 5.5m. 254 MAINTENANCE COSTS

Figure 7.9: Maintenance Labor Hours (L) versus Maintenance Parts (P/VP) Cars: India

20-

15. India

Uoita: L Labor hours (hours pw 10Wxkm) P Prts coat (montry unit per lo0km) 10 - VP Now vahldb pric (105 monawry undt) R Road roughness U (mmtkm)

P/VP 100 260 30b 450 5 O'

Table 7.12: TypicalGross and Net VehicleWeights In BrazilianStudy by TruckType

VehIce 1TaWeWeight Grows Repmsnftativs Category Ctonrnee VehicleWeight Maks/MO"s

1. 2-AYJO 4.75 ~~~13-15Mercedes Benz L1313IL1513 Flat

2. flppr 5.5so 13-15 MercedeseBenz LK1313/LK1513 Dump

3. 3-Axsa L.13513(2)ereds5n

1.20136 x 2 Flst

4. Sei-trller 14.70(3) 40 Sas113

Notes:

1.This categorYCan Prtat2WhtGWi 4fombtmrayrust t. n 6 x 2 form. 2. The tWO50Sale "I fghM fd0 hr YO4ddt hng rr o6x2 tVe racomafieded 3W ~ti ofkiisnxei185tn . 3. o1m1rllingTrectcf75tn"Sdtre4ASfttalr72tnm MAINTENANCE COSTS 255

Caribbean. As noted In Section 7.3.1, Hide (1982) ascribes this to the Influence of surface type.

The Indian study equation gives information on the effect of pavement width and gross vehicle weight, parts costs increasing by around 5 percent for every 1 tonne Increase in gross vehicle weight and by around 27 percent on reducing pavement width from 5.5m to 4m.

7.4 MAINTENANCE LABOR COSTS: ESTIMATED EQUATIONS

In this section we present estimates of equations relating maintenance labor quantity per unit distance to parts consumption per unit distance and vehicle and highway characteristics. Equations as originally reported and amendments introduced to achieve a common reporting style are documented in Appendix B.

The Kenyan study reports equations for the composite variable LH/(PC/VP) where LH is labor hours per kilometer, PC is parts cost per kilometer and VP Is new vehicle price. To produce the equations reported here, PC/VP Is multiplied through Into the right hand side, and the resulting dependent variable, denoted L, Is expressed In labor hours per 1,000 kilometers. The Brazilian study reports equations for labor cost in Cruzeiros per 1,000 kilometers at January 1976 prices. Here a figure of 13 Cruzeiros per hour has been applied to convert labor costs to labor hours. Representative vehicle prices (Table 7.2) have been used to express the Brazilian study equations in terms of L and P/VP which was the dependent variable used In reporting parts consumption In the previous section.

The Indlan study data were re-analysed (Chesher 1983) using the original labor hours data and the resulting equations are reported In this section, using as dependent variable: L expressed In labor hour per 1,000 kilometers. As with the Brazilian study, representative vehicle prices have been appiled so that In this section the ratio of parts cost to vehicle price, P/VP, rather than parts cost Is an explanatory variable. The Caribbean study reports in terms of labor costs and wage rates are not provided. With the exception of the Caribbean study, all results presented In this section use L, labor hours per 1,000 kilometers as the dependent variable and P/VP, the ratio of parts cost to vehicle price, as an explanatory variable.

The Indian and Brazilian equations relate labor hours to a power function of parts costs, the equations taking the form L - a(P/VP)P. Uniformly p is found to be less than 1 varying from 0.47 (Indian buses) to 0.65 (Indian trucks), the Brazilian study numbers lying within this range. Increases In parts costs are predlcted to lead to Increases in labor hours but at a decreasing rate. This may reflect the relatively capital Intensive nature of major repairs and the substitutability of maintenance "labor" for maintenance "capital" though It may also reflect the presence of fixed labor inputs. The coefficient a Is found, for some vehicle classes, to be affected by road roughness. In the Indian and Brazlilan studies where roughness effects were found, Increases In roughness lead to 256 MAINTENANCECOSTS

Increases in labor hours, holding parts costs fixed, suggesting that maintenance activities for vehicles on relatively rough routes are relatively labor intensive. In the Kenyan study roughness effects are reported but these operate In the opposite direction, relatlvely less labor at given parts cost being applied on relatively rough routes.

The results are presented here by vehicle class. We note now that the Caribbean study reports a single relationship, obtained from a small sample of garage work, which gives labor cost equal to 0.45 times parts cost. Turning to the other three studies we consider first the maintenance labor relationships for cars and light goods vehicles.

The equations for car maintenance labor costs are given in Table 7.13 and graphed In Figures 7.9 and 7.10. The Kenyan equation, which relates to cars and light goods vehicles, Is fairly close to the equation for Brazilian cars. The striking feature In these graphs Is the extent to which Indian study labor hours exceed those for the other studies and this Is a feature of the results for all vehicle classes. In Table 7.14 gives approximate averages of labor hours per 1,000 km by vehicle class for the Indian, Brazilian, and Kenyan maintenance labor data sets. The Kenyan and Brazilian labor hours are apparently of similar orders of magnitude, for example, from 3 to 5 hours per 1,000 km being applied to buses or medium trucks. The Indian labor hours data are around three times greater.

To some extent this must reflect differences In wage rates. The ratio of the cost of 2,000 hours (around one year) of mechanics' time to new vehicle price Is about 0.024 In India and about 0.19 In Brazil, around eight times higher, so we cannot be surprised to find labor hours per 1,000 km differing between the two countries by factors of the order of three. However, the differences In labor costs per 1,000 km are less startling. What are factors of three or so In terms of labor hours are factors of less than two In terms of labor costs relative to vehicle prices.

Doubling parts consumption Is predicted to Increase labor hours per 1,000 km by 50 percent using Indian study results, by 46 percent using Brazilian study results (for cars and light goods vehicles) and by 100 percent using Kenyan study results. As noted eariler roughness effects go In different directions In the Brazilian and Kenyan equations, a 1,000 mm/km Increase In roughness being predicted In the Brazilian study to lead to a 10 percent Increase In labor hours per 1,000 km, parts costs being held constant. Of course In practice roughness Increases lead to parts cost Increases so that there are two Influences for roughness to be considered.

Equations for maintenance labor hours for buses are given In Table 7.15 and graphed In Figures 7.11 and 7.12. As for cars, the Indian predlcted labor hours are considerably higher than those predicted using the Kenyan or Brazilian study equations. However, the Brazilian and Indian equations are In agreement concerning the effect of doubling parts costs (predicted to Increase labor hours by 39 percent using the Indian study equation and by 43 percent using the Brazilian study equation). As before MAINTENANCE COSTS 257

Table 7.13: Malntenance Labor Equations: Cars and Light Goods Vehicles

Study Class Equation

India Cars L = 1.347(P1VP)-"4.

Brzil Cars L = 0.142 (PIVP) 547 .

Brazil Light goods L = 0.166 exp(.624TG + .0000923R})(PVP) 5 1.

Kenya Cars L = (.00851 - .00000078R}(P/VP}.

L = Labor hours (hours per 1O3knm) P = Parts cost (monetary units per 103krn). VP = New vehicle price (io5 monetary units) R = Road roughness Bi (mm/km) = 1 if vehicle is gasoline fueled = if vehicle is diesel fueled

Table 7.14: Average Maintenance Labor Hours per 1,000km

Study

Vehicle Class India Brazil Kenya(a).

Cars 27 4

Light goods _ 12 0.7(b)

Buses 28 9 2.1

Medium trucks 32 10 5.0

Heavy trucks _ 32 _

(a) Approximate figures obtained using available information.

(b) Cars and light goods vehicles. 258 MAINTENANCE COSTS

Figure 7.10: Maintenance Labor Hours (L) versus Maintenance Parts Cost (P/VP)-Cars. Light Goods, Utilities: Brazil, Kenya

18 B

16 .

14.

12 -

8 .

6 / /~~~~~~~~~~~~~~~~~~~ B / ~~~~~~~~~~~~~~~~~K

100 200 300 400 500 600 700 800 900

Equations: BU = Brazil, utilities BC = Brazil, cars K = Kenya, cars and light goods

Unit: L : Labor hours (hours per 1000km) P Parts cost (monetary units per 1000km) VP Now vehicle price (105 monetary units) R : Road roughness Bl (mm/km)

Variabes not Plotted: R = Road roughness = 4000 BI mm/km (not Brazil cars) TG = Type of fuel indicator = 1 (gasoline. Brazil utilities only). the Kenyan equation Is linear In parts costs. The Indian and Brazilian study equations both predict Increasing labor hours, parts costs held constant, with Increasing road roughness, a 1,000 mm/km Increase In road roughness being predicted to lead to a 10 percent Increase In labor hours using the Brazilian study equation and a 4 percent Increase In labor hours using the Indian study equation, before the effect of roughness on parts cost Is considered. MAINTENANCE COSTS 259

Table 7.15: Maintenance Labor Equations: Buses

Study Equation India L = 2.625 exp{.175G + .0000426RI(P/VP) 47 3.

Brazil L = 0.763 exp(.OOOlOR}(P/VP* 51t7.

Kenya L = (.0264 - 00000078R)(PVP}).

L = Labor hours (hours per 103km) P = Parts cost (monetary units per 103km). VP = New vehicle price (105 monetary units) R = Road roughness 81 (mm/km) G = 1 it vehicle is government owned = a if vehicle is privately owned.

Flgure 7.11: MaintenanceLabor Hours (L) versus Maintenance Parts Cost (P/VP), Buses: India

60 -. 10

40 I

35 --.--

~25. ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ S

20 ~~~~ 7 ~~~ggjatgm I1lo n=dls,roughness = 10,000 mmlkmn. 17 = India, roughne = 7,000 mm/km. 14 = Indi, roughness= 4,000 wml/h. 15 * X uL Labor hours (hou pw 1,000 1km) 10 P Pos :oat (montwy unAb per 10km) 10 VP:Nwvk pic (105 oom unf) R road roughne BU (mm/li)

5 Vlblew not Pltted: a Ownershipnodlooror 0 (prloa)

P/VP 20 40 60 80 100 120 140 160 180 200 260 MAINTENANCE COSTS

Figure 7.12: Maintenance Labor Hours (L) versus Maintenance Parts Cost (P/VP), Buses: Kenya, Brazil

40 10 _ 10

35 ,

z~ ~ ~ ~~~ ~ ~~~~~~~~< - -/ -3 -~~~~~~~~~-

25 ~~ ~~~-

2520- ,,,' -/ -

/ -i t W

r / ~~~~~~~~~~~~~10- B /l, rogns "10.0 = m ihr.=10 ,

5 -lhm, B 4 S o o8/ = 4, 0 .

S.L t ULdw Lm:L (oune 1pw,D ion) 10P : P = SbU ero = 7.000tO..,lM)u K VP: Nowvh_ p_b (106 Aow unft) R : rad roughnes Bl tw_{bl)

. , ., P/-P 50 100 150 200 250 300

Equatoons for maintenance labor hours for trucks are given in Table 7.16 and graphed in Figures 7.13 and 7.14. As for the other vehicle classes, Indlan labor hours are higher than those observed In Brazil and Kenya but comparing the Brazilian and Indian results, the effect of, say, doubling parts cost is not too dissimilar, a 57 percent Increase In labor hours per 1,000 km being predicted using the Indian equation, 43 percent using the Brazilian study equation. No roughness effects were found using the Brazilian study data and only small effects in the Indian study. Again the small effect found there Is In the opposite direction to that found In the Kenyan study though the Kenyan data Is extremely limited in the information that It provides on roughness Influences (see Appendix B).

7.5 THE EFFECT OF HIGHWAY GEOMETRY ON MAINTENANCE COSTS

One notable feature of the results presented In Sections 7.3 and 7.4 Is the rather limited Influence that highway geometry Is predicted to have on vehicle maintenance costs. Only the Indian road user survey reports effects for geometry - they are not very well determined, and it is difficult to distinguish the effects of vertical and horizontal geometry. One's first feeling Is that geometry "should" affect maintenance costs expressed per unit distance but the results of four Independent road user surveys suggest that the Influence of geometry Is negligible. Is this because of some deficiency In these studies, or Is It In fact true that MAINTENANCECOSTS 261

Figure 7.13: MaintenanceLabor Hours (L) versus MalntenanceParts Cost (P/VP). Trucks: India

110

80. 7

70 ..- 4

60.-e-- et~

S . _ P/VP 50 400 150 200 250 300 350 400

Eouaions: Ilo0 = India roughnon = 10, 000 81 nm/kmn. I17 = India roughness= 7,000 Bl mm/kmn. 14^ = India roughness= 4.000 Bl rmm/km.

Units: L :Lobor hours (hoursper 1 000 kmn) P :Ports cost (monetry units per 10'km) VP S Now hkt prbe (10s monetaryunits) R :road roughnessBl (mm/km)

V30,abb not Plotbd: S O : Ownerhip indeWor= (private) TTNK : Trucktype indFator = (non-tanker) 262 MAINTENANCE COSTS

Figure 7.14: Maintenance Labor Hours (L) versus Maintenance Parts Cost (P/VP), Trucks: Kenya, Brazil L 50

45 -B ST

40 -

35 -

30.

25 .

/ B 3AX 20 / __

15. T

10. / -

P/VP 100 200 300 400 500 600 700

Equations: K Kenya BST = Brazil, semi trailer tractors. B3jUt = Brazil, 3-axle vehicles. B2Axe = Brazil, 2-axle vehicles. STnp = Brazil, tipping vehicles (2-axle)

LL Labor hours (hours per 1,000 kIm) P Parts cost (monetary units per 103km) VP New vehkle price (10 S monetary units) R road roughness Bi (mm/km)

Vriables not Plotted: R : Roughness= 4,000 13mm/km (Kenya only) MAINTENANCE COSTS 263

Table 7.16: MaintenanceLabor Equations: Trucks

Study Equation

IndiS L 1.296 exp(.240G + .000025OR+ .191TTNK)(P/VP 654.

anzu L = (.61T2AX + .76T3A + .466Tp + 1.6WST5)(P-VP)- 5 I9 .

Kenya (.=0298 - .00O007SR)(P^VP).

L = Laborhours (hours per 103km) P = Pat cost (monetaryunits per 10ksn). VP = New vehile prie (105 monetaryunis) R = Roadroughne, Bl (mm/km) G = 1 it vehile is governmertowned = O if vehicle is privatelyowned.

TTNK =1 itvehicle Is a tanker. 0 otherwie T2AX = 1 if vehicle is a 2-axle truclk,0 otherwise

T3AX = 1 if vehice Is a 3-axle truck. 0 otherwIe rT-p = 1 it vehicle Is tipping truck, 0 otherwise Tsrr = 1 it vehicle Is semi trailer tractor, 0 otherwise

highway geometry's influence on maintenance costs can be neglected? We examine these Issues In this section.

Before we proceed It Is most important to note that geometry does have significant effects on fuel consumption and, of course, on vehicle speeds. Highways built to poor geometric standards are travelled slowly - particularly In other than free flow conditlons. So utilization is lower on such highways and Interest and other fixed costs accruing per year are spread over fewer kilometers thus ralsing costs per unit output. So to Justify Improving highways' geometric standards It Is not necessary to assume that poor highway geometry leads to substantially higher maintenance costs.

All other things being equal we can surely expect deterioration In highway geometry to lead to Increases In maintenance costs If vehicle owners choose to repair all damage done to their vehicles rather than accept accelerated depreciation. But other things are not equal. In particular owners will operate their vehicles at slower speeds on hilly or sinuous routes than they would on flat straight routes and speed reductions associated with deterioration of geometry may dampen the effect of geometry on per kilometer maintenance costs.

Owners' decisions regarding loads carried are likely to dampen the effect of geometry on maintenance costs. At least In truck transportation, owners can choose the loads that their vehicles carry and In many developing countries we find vehicles carrying loads above those 264 MAINTENANCE COSTS recommended by vehicle manufacturers. On hilly routes and on sinuous routes where ability to accelerate might otherwise seriously be Impaired owners may choose to reduce the extent of overloading, thereby reducing their per trip revenues but gaining from the Increase in speed thus obtained (and so In utilization and in revenues per time period) and gaining from reductions In maintenance costs.

User surveys typically obtain substantial variation In highway geometry only by examining vehicles operating In different geographical regions, some hilly, others flat. To the extent that owners ply routes with homogeneous geometry (i.e., all flat or all hilly) they can choose vehicle specifications suited to the routes that they travel so that geometry effects pass largely through vehicle price. Thus in hilly regions we may find vehicles with larger capacity engines, perhaps turbocharged, and we might expect these vehicles to show different, perhaps lower, maintenance costs than less powerful vehicles whose engines and transmissions would be over worked operating at speeds that the more powerful vehicles can attain on such routes. In analysing user survey data one might attempt to distinguish different vehicle specifications but in practice the data sets obtained are too small and too variable to allow this. So what Is estimated is a geometry effect after allowance for vehicle owners' efforts to dampen geometry effects via appropriate choice of vehicle.

Choice of speed, load and vehicle can all serve to dampen geometry effects on maintenance costs and then driver behavior must be considered. Sinuous routes can be driven so that curves are straightened out - hilly routes can be driven to some extent in a "roller-coaster" fashion so that downgrades are used to Increase velocity for coming up grades. And drivers who keep costs down in this fashion are likely to be rewarded. So It Is at least possible that the effects of geometry on maintenance costs (though not necessarily on other costs) are rather small. If they are small then can they be detected In user survey data?

In Table 7.17 approximate means and ranges for rise + fall and average degrees of curvature obtained In the four user surveys are given. The data In user surveys relate to vehicle operations (costs and highway characteristics) over a period of at least a year, sometimes as long as 2.5 years. Detailed geometry measures are averaged to produce route average geometry and then averaged again to produce average geometry experienced by each vehicle. So the geometry measures associated with each user survey vehicle are very crude Indicators of the conditions actually faced by the vehicles. Though vehicles may experience extremes of geometry at times, their average experience tends to be rather uniform and this Is reflected In the ranges recorded In Table 7.17. Thus In one of the larger surveys, In Brazil, no vehicle experienced average survey period gradients greater than 5 percent and most vehicles experienced far more benign conditions. The Indian survey contains a few vehicles experiencing average gradients approaching 6 percent and In the Kenyan and Caribbean surveys vehicles were observed on routes with average gradient as high as 7 percent but there were relatively few vehicles In these surveys and given the sort of variation to be expected across vehicles in maintenance cost data, a considerable mass of Information on routes with extreme geometry would be MAINTENANCE COSTS 265

Table 7.17: Approximate Means and Ranges of Geometry Measures In User Cost Surveys

RIb Plus Fall Average Degrees Study Class No of of Curvature Vohice (mrn/m) (0/kn)

Min U. Max Min Mean Max

India Care 54 3 10 36 9 107 690 Bus 640 1 15 50 5 150 1021 Trucks 232 1 13 58 8 137 1215

8razil( 1 ) Cars 93 12 28 39 11 46 202 Light goods 65 12 25 46 6 40 328 Buses 449 10 24 39 6 41 189 Truck. 200 10 32 49 7 63 294

Kenya(2) Buse 101 17 33 69 9 12 15 Trucks 66 15 16 39 8 31 45

Caubben Care and Light Goods 32 26 44 60 180 376 600 Trucks 28 23 46 70 160 421 700

(1) Parts consumption data set, ranges are narrower in labor cost data set. (2) Parts consumption data set.

required to determine geometry effects, particularly If these are In fact rather small. And If data were obtained on vehicles operating exclusively on steep routes, so that average gradient exceeded, say, 10 percent, then we would expect these vehicles' owners to take steps to avoid excessively high maintenance costs, or thelr customers might be unprepared to pay for the service they provide.

The situation with respect to curvature Is similar. The Caribbean survey produces some data on vehicles operating over sinuous routes but with only around 30 vehicles In each vehicle class no Information on curvature effects can be obtalned. The Indian survey does produce data on routes with high curvature and limited Information on geometry effects. However, the effects found are small. It Is Important when considering the Indian survey to recognize the effect of congestion and slow moving animal traffic which may limit the magnitude of curvature effects on these sinuous routes which are often narrow.

Even If extremes of geometry can be found, disentangling the effects of gradient and curvature Is exceptionally difficult, because steep gradients and extreme curvature tend to be associated with each other, particularly In user survey data. User survey data often comes from 266 MAINTENANCE COSTS distinct geographical regions, some hilly some flat. Certainly in the hilly regions we expect to find curved routes as highway designers try to avoid excessive gradients. The perceived trade off between gradient and curvature, particularly with regard to vehicle speed and safety, results In moderate gradients and substantial curvature In hilly regions while In flat regions there are, of course, negligible gradients and generally neglilgble to only moderate curvature. This pattern Is apparent In Table 9.18 in which correlations amongst rlse + fall, and curvature range from 0.85 to 0.93 and the situation is little better In the Caribbean study. At first sight the Brazilian data set fares better In this respect but recall that ranges, partIcularly for curvature, In this data set Is very limited. User survey data exhibits strong multicollinearity, by the nature of survey designs and of the realities of highway planning. The result Is that, while on occasions statistically significant coefficients can be obtained for one of the geometry measures with the other omitted, when both are Included one Is unable to attribute the cost variation unambiguously to rise + fall and curvature so that their separate contributions are at best Inaccurately estimated. This problem Is clearly present In the India bus maintenance parts data set (see Section 7.4) and was found by the authors In extensive analysis of the Brazilian study data. On occasions weak and poorly determined geometry effects were found In the Brazil maintenance data but no effects sufficiently strong and reliable to recommend for use.

The evidence of the road user surveys In India, Brazil, Kenya, and the Caribbean Is that the effects of geometry on maintenance costs per kilometer are virtually undetectable. Where they are found In the India bus maintenance parts data set, they appear to be rather small, lOm/km Increases In rise + fall being associated with 7 percent increases In maintenance parts costs per kilometer, 1000 /km Increases In curvature being associated with 3 percent increases In maintenance parts costs per kilometer. The effects on total maintenance costs obtained by feeding these effects additionally through the labor hours equations are even smaller.

7.6 CONCLUDING REMARKS

The four studies provide separate relationships for maintenance parts costs and maintenance labor costs, the equations for maintenance labor cost using parts costs as an "explanatory variable." For some vehicle classes and studies the maintenance labor equations Involve road roughness as a separate explanatory variable so that to assess the full effect of roughness on labor costs and on total maintenance costs It Is necessary to consider both the direct effects estimated In the labor hours or cost equations and those effects that pass through from the parts costs equations.

When parts costs are eliminated from the labor costs equations, the effects of roughness on labor hours are fairly close once allowance is made for the different orders of magnitude of the labor hours data across the studies. Table 7.19 shows predicted percentage increases In labor hours per kilometer attendant on increasing road roughness by 1,000 mm/km. The Kenyan study predicts somewhat larger Increases than either the MAINTENANCECOSTS 267 Table 7.18: SimpleCorrelations between Highway Characteristics In User Cost Surveys

Study Vehicle NO Of Correlations Class ~Vehicles RF xC RF xR Cx R

India Cars 54 .93 .48 .37 Buses 640 .85 .33 .24 Trucks 232 .92 .69 .76

ramziI(1 ) Care 93 .03 -. 74 .02 Light goods 65 .52 -. 24 .34 Buses 449 .03 .04 .10 Trucks 200 .74 -. 03 .59

Kenya(2 ) Buses 101 .74 .72 .33 Trucks 66 -. 26 .52 -. 63

Caribbean Cars and Light Goods 32 .58 .63 .30 Trucks 28 .91 .59 .52

(1) Parts consumptiondata set. (2) Unweighted.

Table 7.19: PercentageIncrease In LaborHours per kmnon IncreasingRoad Roughnessby 1,000rmm/km

Study VehiceJClass Pecentage Incroeas in LaborHours per km

Brazil Qua 15% Light goods 15% Buses 14% Trucks(1) 2-axle 13% 3-axle 10% Tipping 12% Semi Trailers 7%

India Cars 10% Buses 7% Trucks 13%

Kenya(1) cars 23% Buses 37% Trucks 16%

(I) Assuming initial roughness 3.500 mm/kmn 268 MAINTENANCECOSTS

Brazilian or Indian studies. This Is, of course, because of the large magnitude of the roughness effects on parts consumption In the Kenyan study, here feeding through Into the labor hours equation. The Indian and Brazilian study equations predict labor hours per km increasingby from 7 to 15 percent as roughness Increases by 1,000 mm/km on moderately good quality routes - omitting the expensive Brazilian semi trailers and the Indian buses, the latter particularlyInsensitive to roughness- this range narrows to 10 - 15 percent. The Kenyan figures range from 18 to 37 percent.

For the Brazilian and Indian studies In which new vehicle prices are available It Is possible to express labor costs as a fraction of new vehicle price after converting from labor hours using the wage rates of 2.25 Rupees per hour and 13 Cruzeiros per hour for India and Brazil respectively. Then we can add the resulting equations to those for parts cost expressed as a fraction of new vehicle price to obtain equations for malntenance costs (parts plus labor) as a fraction of new vehicle price.

The Indian study predictionsfor maintenance costs fall well below those found In Brazil but there Is broad agreement between the two studies concerning the effects of both road roughness and vehicle age on maintenance costs. Table 7.20 gives predicted percentage Increases In

Table 7.20: Percentage Increase In Maintenance per km on (a) IncreasingRoad Roughness by 1,000 mm/km (b) Doubilng Vehicle Age

Percentage increase in M/VP(1).

(a) (b) Study Vehile Class Increaing Roughness Doubling from 3500mm/km Vehice to 4500 mm/km Age

Brazil Cars (2) 24 20 Light goods vehicies(2 ) 13 18 Buses(3) 9 33 Trucks '4 ': 2-axle 23 25 3-axle 17 25 Tipping 21 25 Semi Trailers 12 24

India Cars(2) 16 3 5 8uses' )" ' 5 24 Trucks '4) (6) 14 23

(1) M/VP = Maintenance cost (monetary units per 103km)/vehicle price (1lo monetary units). (2) Initial age 100,000 km (3) Initial age 350,000 km (4) Initial age 180.000 km (5) C = 1500/km, RF = 20rn/km, W = 5.5m. (6) C = 1500 /km, RF = 20m/km, W = 5.5m. GVW = 12t. MAINTENANCE COSTS 269 maintenance costs attendant on increasing road roughness from 3,500 mm/km to 4,500 mm/km and on doubling vehicle age from base ages appropriate to the vehicle classes (100,000 km for cars and light goods vehicles, 350,000 km for buses, 180,000 km for trucks). Buses are least sensitive to roughness and most sensitive to age once total maintenance costs are considered but the age effects are very similar across vehicle classes now. Different base ages have been chosen for this comparison - for each class they correspond to an initlal age located around one third of the way through the life of an average vehicle. Apart from the Brazilian buses which show a relatively large 33 percent increase In malntenance costs on doubling vehicle age, the remaining classes show increases in maintenance costs of from 18 to 25 percent.

The roughness effects are fairly similar too. As before buses and semi trailers show relatively small roughness effects an cars and 2-axle trucks relatively large effects, the figures obtained for the two studies and various vehicle classes suggesting an Increase in maintenance costs per km of around 15 percent when road roughness Increases by 1,000 mm/km.

The Brazilian and Indian studies present similar pictures of maintenance costs and their dependence upon vehicle and highway conditions. Geometry has a barely detectable effect on maintenance costs, the major influence being highway roughness. The Kenyan and Caribbean studies support this conclusion. The Influence of vehicle age is substantial and involves an Increase in maintenance costs of around 25 percent with every doubling of vehicle age. The Kenyan and Caribbean studies provide conflicting evidence on this magnitude but we are Inclined to discount their results In this area because of the special conditions prevailing in the Caribbean and because of the relatively narrow ranges of ages and small numbers of vehicles observed.

The progression of costs with age Is Influential in determining owners' scrapping policy and thus the rate of flow of vehicle replacement costs. These are the subject of the next chapter. 270 MAINTENANCE COSTS

APPENDIX A. MAINTENANCE PARTS EQUATIONS AS REPORTED BY THE FOUR STUDIES

A7.1 Kenya

The equations reported by Hide et al. (1975) are as follows:

Cars and light goods vehicles

PC 1 C (-2.03 + .0018R).1011 VP.K

R2 - 0.92, 8 data points, averages from total of 62 vehicles.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 3,200 6,400 3,166 K(103 km) 22 152 81

Source: Hide'et al. (1985).

Buses

PC - - (-0.67 + .0006R).10 VP.K 1/2

R2 - 0.92, 13 data points, averages from total of 101 vehicles.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 2,440 4,430 3,230 K(10 3 km) 85 1,092 477

Source: Hide et al. (1985). MAINTENANCE COSTS 271

Medium and heavy goods vehicles

PC (0.48 + .00037R).10 11 VP.K

R2 - 0.92, 16 data points, averages from total of 66 vehicles.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 2,400 7,500 2,949 K(103 km) 48 374 135

Source: Hide et al. (1975).

PC - Parts cost per km (Kenyan shillings/km) VP - Price of equivalent new vehicle (Kenyan shilling) K - Age of vehicle at survey end point (km)

R - Surface roughness (mm/km).

Remarks

The data used In the analysis are a small number of averages of data (raw vehicle data not reported) from groups of vehicles, presumably operating under similar conditions and of similar ages. The equatlons fit the data remarkably well given the sort of variatlon that we might expect to find In maintenance expenditure data, variation found In the Indian and Brazilian studies. Of course averages are necessarily less variable than are the Individual vehicle data used to calculate the averages so that the reported R2 statistics are higher than those that would have been obtained had the raw vehicle data been analysed directly (see Chapter 6). Further, the R2 statistics refer to the amount of variation in PC/VP.K (or K1 /2 for buses) that is explainable In terms of roughness variation. The R2 statistics would have been different had PC/VP or PC been used as the dependent variable. Hide et al. (1975) report no standard errors with which to assess the accuracy with which the roughness coefficlents are estimated.

In reporting these equatlons In the main text we Introduce an adJustment so that vehicle age In the equations reported In the main text Is age at the survey midpoint as In the Indian and Brazilian studies. Using data reported In Hlde et al. (1975) we calculate average survey period utillsation In thousands of kilometers per year (U), (see Table 272 MAINTENANCECOSTS

A9.1), and define survey midpoint age as survey endpoint age minus U/2. Thus In the main text the equations above appear with K replaced by K + U/2, K now being interpreted as survey midpoint age.

Table A7.1: Average Survey Period Utilisation

Vehicle Class Utillsatlon (1,000 km/year)

Cars and Light Goods 77 Buses 119 Trucks 47

Source: Hide et al. (1975).

A7.2 Caribbean

The equations reported by Hide (1982) are as follows:

Cars and light goods vehicles

PC P (-5.501 + .00262R).10 VP.K

R2 _ 0.91 32 vehicles.

R observed In the range: 3,500 < R < 8,000, average R - 4,969 mm/km.

Trucks

PC 111 - (-6.538 + .00316R - .00000021R2)10 VP.K

R2 - 0.95 28 vehicles.

R observed in range: 3,000 < R < 7,500, average R - 5,681 mm/km

PC - Parts cost per kilometer Barbados dollars, E. Caribbean

VP - Cost of an equivalent new vehicle dollars as appropriate

K - Age of vehicle In kilometers at survey end point

R - Surface roughness (mm/km). MAINTENANCE COSTS 273

Remarks

Here the data refer to individual vehicles observed for a one- year period. The fit of the equations to the data Is remarkably good. So far as we are aware no averaging has occurred so that the R2 statistics reported here suggest an even closer relationship between PC/VP.K and roughness than do the Kenyan results. Less than 10 percent of the between vehicle variability in PC/VP.K remains to be explained by factors other than road roughness. Given the inherent randomness of maintenance cost data there can be at most small effects for highway geometry and no reliable effects can be found in these data. No standard errors are reported but we must conclude that the coefficients are very well determined. The quadratic truck equation predicts decreases In PC/VP.K with Increases in roughness for roughness exceeding 7,523 mm/km. The highest value for R observed In the data set is 7,500 mm/km. As with the Kenyan results the age effects have been modified so that in the main text vehicle age refers to the survey midpoint. The utilisatlon data reported In Hide (1982) were used for this purpose, average utilisation being calculated as In Table A7.2.

Table A7.2: Average Survey Period Utillsation

Vehicle Class Utilisatlon (1,000 km/year)

Cars 16 Trucks 12

Source: Hide (1982).

A7.3 Brazil

The equations reported In GEIPOT (1981) were re-estimated by Chesher (1982) after modification of the method for calculating average survey period road roughness (see Paterson and Chesher 1982). The effect was to Increase the magnitude of roughness coefficients by from 3 to 21 percent, this Increase reflecting the contraction In the roughness scale caused by the adoption of the new method for calculating roughness statistics. The re-estimated equations are reported here. In these equations costs are expressed in January 1976 Cruzeiros. GEIPOT (1981) reports In December 1981 Cruzeiros. In the main text the equations are reported using the variable R to measure roughness In mm/km, obtained from the equations reported here In QI* units using the conversion equation 1QI - 55 mm/km (see Chapter 2). Equations In exponential form here are reported In the text after exponentiation, the Intercept term being adjusted In order to correct for bias In estimating mean parts costs that arises when exponentlating unbiased estimates of mean In(parts costs). The correction, obtained by assuming that the regression equations error 274 MAINTENANCE COSTS terms are approximateiy normally distributed, Involves adding to the reported Intercepts exp(Co2 /2) where 02 Is an estimate of the variance of the regression equation error term. Where error components models are fitted 02 Is taken to be the sum of the estimates of the across (s2) and within (s2) company variances (see Chapter 3). Throughout "In" Indicates natural logarithm and:

PC - Parts cost per 1,000 km (January 1976 $Cr per 1,000 km) 01 - Surface roughness (Ql*) 3 K - Vehicle age at survey midpoint (10 km). Figures in parentheses below coefficients are ratios of coefficients to (asymptotic) standard errors.

Cars

ln(PC) - 1.890 + .013701 + .3081n(K) (4.35) (3.44)

SU - .582 Sw - .452

93 vehicles, 6 companies.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

Ql(Ql*) 40 140 3,650 K(103km) 27 330 114

Source: Chesher (1982)..

Remarks

The equation is estimated by generalized least squares allowing for random company and vehicle specific errors. The results are similar to those obtained exploiting only within company variation and the roughness coefficient alters little on excluding vehicle age. R2 statistics are not available. The equation explains around 20 percent of the vehicle to vehicle variatlon In parts costs and the coefficients are quite well determined.

Utilities

In(PC) - 3.318 + .0051701 + .308In(K) (2.24) (4.14) MAINTENANCECOSTS 275

SU - .556 Sw - .392

65 vehicles, 7 companies.

ApproximateRanges and Means of ExplanatoryVariables

Variable Min Max Mean

QIl(QI*) 24 204 76 K(103km) 12 980 156

Source: Chesher (1982).

Remarks

In fact, the 65 vehicles used In this estimation come from 13 companies,7 of which are single vehicle businesses that are grouped in to a single "company"for the purpose of estimation. Individualvehicle data is used throughout. The equation Is estimated by generalized least squares allowing for random company and vehicle specific errors and differs little from that obtained by exploiting only within company variation. R2 statistics are not available. The equation explains around 20 percent of the variatlon in parts costs and the coefficientsare quite well determined.

Buses

In(PC)- 2.564 - .965 U248 + .00357QI + .4831n(K) (-2.05) (3.98) (16.03)

su - .452 Sw - .434

449 vehicles, 22 companies.

Approximate Ranges and Means of ExplanatoryVariables

Variable Min Max Mean

QI(QI*) 23 212 87 K(103km) 20 1,100 284

Source: Chesher (1982). 276 MAINTENANCE COSTS

Remarks

The dummy variable U248 Isolates company no 248 which had a distinctive maintenance policy so that in estimation only within company variatlon In this company is exploited. In reporting in the main text U248 is set equal to zero. The equation is estimated by generalized least squares allowing for random company and vehicle specific errors. R2 statistics are not available but the equation explains around 50 percent of the vehicle to vehicle variation In parts costs. The coefficients are well determined.

Truck

Exponential relationships fitted to these data give unrealistic predictions on extrapolation and a linear equation is preferred (see GEIPOT 1981). In GEIPOT (1981) and Chesher (1982) a plecewise linear equation was fitted, Insensitive to marginal roughness changes for Ql < 40Q1*. To obtain results more easily compared with those obtained in other studies this has been re-estimated in straightforward linear form as below:

PC - 137.360 - 90.017TIP + 172.634ST - 118.114AX2 + 4.848QI (-1.05) (2.04) (-1.11) (4.69)

Su - 1 3 5 SW - 182

200 vehicles, 19 companies.

Approximate Ranges and Means of Explanatory Varlables

Variable Min Max Mean

QI(Qi*)(ST-0) 24 129 58 QI(Ql*)(ST-1) 26 100 56

Source: Chesher (1982).

TIP - 1 If vehicle Is tipper, - 0 otherwlse ST - 1 If vehicle Is semi-trailer tractor, - 0 otherwise AX2 - 1 If vehicle Is 2-axled vehicle, - otherwise.

This Is the basis for the equation reported In the text. However, the equatlon reported above does not contain vehicle age. In order to report an age effect for comparison with the results of other studies we use the age effect estimated In the log linear relationship (Chesher 1982):

In(PC) - 2.989 - .2398TIP + .3634ST - .0785AX2 + .0164QI + .371In(K) (-1.36) (2.24) (-.37) (7.73) (6.70) MAINTENANCE COSTS 277

SU - .292 sw - .349

200 vehicles, 19 companies.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

Ql(CQI*) as above K(103 km) 33 898 204

Source:

In the main text we report the linear equatlon above, multiplied 371 through by (0437 where 204 Is mean age In the data set in 103 km.

A7.4 India

In the Indian study and In this Appendix parts costs are reported In Palse/km. In the main text we have converted to Rupees per 1,000 km and report after divislon through by representative vehicle prices in 105 Rupees. As In the Brazilian study we have reported in the main text log- linear equations after exponentiatlon and after adjustment for bias Introduced on exponentiation. In the Indian study equations were estimated by ordinary least squares or by ordinary least squares after Introducing company specific dummy variables. Where appropriate the equations have been re-estimated using generalized least squares allowing for company and vehicle specific random errors. In addition, equations have been re-estimated In an attempt to discover effects for highway geometry and In order to obtain estimates that are not Influenced by certain variables that are either endogenous or difficult to measure in practical applications.

Throughout figures In parentheses below coefficients are ratios of coefficients to (asymptotic) standard errors. Both s2 and sW are unbiased estimates of variances of respectively company and vehicle specific random errors.

Cars

The Indian study (CRRI 1982) reports two equations, one including surface roughness, the other width. The equation using surface roughness Is re-estimated In exponential form by generalized least squares giving:

In(SP) - 1.264 + .000169R (1.45) 278 MAINTENANCE COSTS

su ' .399 Sw - .429

54 vehicles, 10 companies.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 3,416 6,955 4,987

Source: CRRI (1982).

SP - Parts cost (Palse per 100 km) R - Surface roughness (mm/km).

Remarks

The roughness coefficient Is rather poorly determined and no effect for vehicle age Is detectable. Average age at survey midpolnt for these vehicles was 98,600 km.

Buses

Equations reported in the Indian study (CRRI 1982) Include as an explanatory variable number of major overhauls during the survey period. This variable depends on surface quality, length of survey period and utilisation during the survey period, Is endogenous and In practical applications Is not easily measured. Chesher (1983) re-estimates omitting this variable and Including measures of highway geometry with the following results. A single articulated traller bus was deleted from the data set prior to estimatlon.

ln(SP) - -.309 + .0000526R + .000282C + .00675RF + 1.999/W + .3581n(K) (2.61) (1.03) (1.38) (2.46) (13.88)

su - .167 Sw - .436

639 vehicles, 20 companies.

Approximate Ranges and Means of Explanatory Variables

Variable Min Max Mean

R(mm/km) 2,925 12,072 5,953 C(°/km) 5 1,021 149 RF(m/km) 1 50 15 W(m) 3.7 7.2 5.2 K(10 3km) 22 988 345

Source: Chesher (1983). MAINTENANCE COSTS 279

Remarks

The equation is estimated by generalized least squares allowing for company and vehicle specific random errors. The equation accounts for about 50 percent of the between vehicle variation In parts costs. The coefficients on highway geometry are poorly determined but of reasonable orders of magnitude. Using curvature without rlse + fall gives a curvature coefficient of .000586 with a standard error of .00016. Using rise + fall without curvature gives a rise + fall coefficient of .0108 with a standard error of .0029. Other coefficlents are virtually unchanged on deleting either curvature or rise + fall. Introducing both curvature and rise + fall, as above, leads to an Increase In standard errors because of correlation between these two varlables In the data set (r - .85). However, the resulting coefficlents are smaller In magnitude than those obtained when only one of the geometry variables is included and should prove acceptable for use In conditions similar to those observed In the Indian study. The alternatives would seem to be to delete geometry from the equatlons entirely or to proceed omitting one of the geometry measures, confident in the knowledge that the remaining coefficient Is too large. The approach adopted here, Including both geometry measures seems preferable.

Trucks

There Is considerable across company and limited wlthin company variability In highway characteristics. Estimating equations allowing for company effects does not produce satisfactory results (see CRRI 1982, Chesher 1983). The equation reported In CRRI (1982) Includes number of overhauls In the survey period as an explanatory variable which is unsatisfactory. This equatlon as estimated by CRRI (1982) Is:

ln(SP) - -.8979PA - 1.3325PH + .0402GA - .5587GH + .0001431R (5.35)

+ 3.483/W + .0531GVW + .23321n(K) + .27620HF (2.30) (4.22) (5.46) (4.50)

R2 - 0.64

232 vehicles, 30 companles.

SP - Spare parts cost (Palse per 100 km)

PA - 1 If company is private, average maintenance level, - 0 otherwise.

PH - 1 If company is private, high maintenance level, - 0 otherwise.

GA - 1 If company is government owned, average malntenance level, - 0 otherwise.

GH - 1 If company Is government owned, high maintenance level, - 0 otherwise. 280 MAINTENANCE COSTS

R - Surface roughness (mm/km)

W - Pavement width (m)

GVW - Gross vehicle weight (tons)

K - Vehicle age at survey midpoint (103 km)

OHF - Number of overhauls In survey period.

Use of OHF as an explanatory variable seriously affects the vehicle age coefficient. Estimating by generalized least squares deleting OHF using a variety of specifications gives age coefficients around 0.340 with standard errors of the order of 0.05 and results In only small changes In the surface roughness coefficient. The equation reported In the text utillses this age coefficient, deleting OHF and adjusting the Intercept to eliminate the variables PA, PH, GA, GH, as recommended by L. R. Kadayall (Indian Road User Survey Director) so that, at sample mean values of the explanatory variables the equation reported In the main text gives the same predicted parts cost as the CRRI equation does when used with Kadayall's recommended Intercept (-0.877). The resulting Intercept Is -1.340 so that the basis for the equation reported In the text is:

ln(SP) - -1.340 + .000143R + 3.483/W + .0531GVW + .340 In(K).

After exponentlating, correcting for bias thus Introduced and change of units we obtain the equation reported In the text. MAINTENANCE COSTS 281

APPENDIX B. MAINTENANCE LABOR EQUATIONS AS REPORTED BY THE FOUR STUDIES

B7.1 Kenya

The equations reported by Hide et al. (1975) are as follows:

Cars

PC/VP 851 - 0.078R

Data: 3 averages relating to 28 vehicles. Buses

LH 2640 - 0.078R

Data: 3 averages relating to 100 vehicles. Trucks

LCHVP - 2975 - 0.078R

Data: 1 average relating to 58 vehicles.

Approximate Ranges and Means of Explanatory Variables (All Classes)

Variable Min Max Mean

R(mm/km) 2,700 4,500 3,052

Source: Hide et al. (1975).

LH : Maintenance labor hours (hours/km) PC : Parts Cost (Kenyan shillings per km) VP : Price of equlvalent new vehicle (Kenyan shillings).

Remarks

Separate relationships were fitted (by ordinary least squares) to the three bus averages and the three car averages (in a sense two averages for cars, since only two distinct roughness levels were observed for this vehicle class). The reported coefficient on roughness of -.078 is the arithmetic mean of the two coefficients thus obtained. Roughness variation In this data Is very limited. No standard errors or other summary statistics are available and In any event their Interpretation would be difficult given the composite dependent variable and the averaging carried out on the data prior to analysis. 282 MAINTENANCE COSTS

B7.2 Caribbean

Hide (1983) gives a relationship obtained from a small sample of garage work:

Labor cost - parts cost x 0.45.

B7.3 Brazil

The Brazilian study reports (GEIPOT 1981) equatlons for labor cost in Cruzeiros per unit distance travelled. Where roughness effects are reported the equations were re-estimated (Chesher 1982) to allow for modifications in the method for calculating average survey roughness (see Appendix A). The resulting equations are:

Cars ln(LC) - 1.24 + .547 ln(PC) (4.24)

R2 _ .29, S W - .500

48 vehicles, 4 companies.

Utilities In(LC) - 1.23 + .624TF + .551 ln(PC) + .00508QI (4.03) (4.79) (2.98)

2 .70, sw - .222

33 vehicles, 8 companies.

Buses ln(LC) - 1.70 + .517 ln(PC) + .00548QI (8.42) (2.31)

R2 _ .51 Sw - .240

81 vehicles, 5 companies.

Trucks ln(LC) - 1.91 (2-axle) 2.02 (3-axle) 1.67 (TSpping)-n(PC) + .519 2.47 (Semi-traplers) (1.84)

R2 _ .50, sw - .264

150 vehicles, 13 companies. MAINTENANCE COSTS 283

Approximate Ranges and Means of Explanatory Variables

Variable Class Min Max Mean

PC($Cr/103 km) Cars 25 713 89 Utilities 41 608 191 Buses 34 742 112 Trucks (medium) 53 1,366 235 Trucks (semi trailers) 156 1,556 578

QI(QI*) Cars 37 144 77 Utilities 27 184 88 Buses 27 126 45 Trucks (medium) 24 106 60 Trucks (semi trailers) 26 100 54

Source: Chesher (1982).

TF - 1 If vehicle is fuelled with gasoline - 0 If vehicle Is fuelled with diesel.

Remarks

These equations are fitted estimating separate Intercepts for each company. The R2 statistics relate to the proportion of within company variation In log labor costs that Is attributable to within company variation In the explanatory variables. sW is an unbiased estimate of the variance of the vehicle specific (within company) error term. Reported Intercepts are weighted averages of company Intercepts with weights equal to number of vehicles per company. Truck Intercepts are obtained by estimating truck type Intercepts using within company variation and averaging over companies.

In reporting, labor cost Is converted to labor hours at an average unit labor cost of 13 Cruzeiros per hour and coefficients are adjusted so that the explanatory variable Is the ratio of parts costs ($ per 1,000 km) to new vehicle price in 105 Cruzeiros using the representative vehicle prices given In Table 7.2.

B.4 India

The Indian study reports labor cost relationships giving labor cost as proportional to maintenance parts costs thus:

Cars: LC - 0.550SP R2 _ .65 54 vehicles, 10 companies.

Buses: LC - 0.403SP R2 . .51 640 vehicles, 20 companies.

Trucks: LC - 0.369SP R2 _ .84 232 vehicles, 30 companies. 284 MAINTENANCE COSTS

LC - Labor cost (Paise per km) SP - Parts cost (Palse per km).

The labor cost data Is obtained by costing labor hours (the data collected in the study) at 2.25 Rupees per hour, average labor cost per hour In 1978 prIces. These equations are presumably estimated by ordinary least squares. It Is not clear whether R2 statistics have been adjusted to allow for the constrained zero Intercept. Plots of the data given In CRRI (1982) Indicate that errors In these equations are heteroscedastic.

Chesher (1983) re-estimated labor cost equatlons following the methods used In the Brazilian study, relating ln(LC) to ln(SP) and applying generalized least squares allowing for random company and vehicle specific random errors with the results given below. In this analysis the dependent variable Is in(LH) where LH Is labor hours per 1,000 km.

Cars In(LH) - 1.896 + .584 In(SP) (11.41)

s2 _ .048, SW - .024.

Buses: ln(LH) - 1.652 + .473 ln(SP) + .0000426R + .175G (27.17) (5.72) (1.74)

.044, SW - .049.

Trucks: ln(LH) - 1.378 + .654 In(SP) + .0000250R + .240G + .191TNK (27.56) (2.52) (3.58) (2.80)

u- .014, 52 _ .027

LH - Labor hours (hours per 1,000 km) SP - Parts cost (Palse per km) R - Surface roughness (mm/km) G - 0 If company privately owned - 1 If company government owned TNK - 1 If vehicle Is tanker - 0 otherwise.

Approximate Ranges and Means of Explanatory Variables

Variable Mln Max Mean

Cars SP 3 33 9.7 R 3,416 6,955 4,987

Buses SP 2 43 13.9 R 2,925 12,072 5,953

Trucks SP 2 74 17.2 R 2,960 15,500 5,331

Source: Chesher (1983). MAINTENANCE COSTS 285

Remarks

in Chesher (1983) a single trailer bus was deleted from the data set so that data on 639 vehicles are used In estimating the bus equation given above. R2 statistics are not available but the equations above fit at least as well as those given earlier, reported In CRRI (1982). In reporting In the main text, units of measurement have been changed so that parts cost (P) Is recorded in Rupees per 1,000 km and using the representative vehicle prices given In Table A7.2 the equations have been rewritten so that LH is related to P/VP where VP Is vehicle price in 105 Rupees. I

I PART III Total Vehicle Operating Costs

Here the user cost equations reported In Part 11 are brought together to produce estimates of vehicle operating costs expressed per vehicle, per unit distance, for alternativehighway conditions and vehicle classes. The estimates are presented In Chapter 9, In which details of their calculatlon are set out and Issues concerning their use and transferabilityto new environmentsare discussed.

In calculatingtotal vehicle operating costs It Is necessary to Include the depreclation and Interest costs associated with vehicle purchase and replacementexpenditures. The studies provide only a little direct Information on these costs. In Chapter 8, we examine this Informationand consider how the studies' results can be used, together with the economic theory of the transport firm set out In Part 1, In order to arrive at estimates of the costs associated with vehicle purchase replacement.

287 I~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CHAPTER 8 The Calculation of Transport Costs

The equations presented In Part 11 allow fuel, lubricant, tire and maintenance costs to be calculated on a per unit distance basis as functions of highway conditions and vehicle characteristics. Depending on the application users have in mind, some adjustment will usually be required to express these costs on the per unit output basis that is relevant for cost benefit analysis of highway investments, perhaps by adjusting for loads carried. In this chapter and In the succeeding chapter, in which illustrative calculations of costs of provision of transport services are presented, such adjustments are not made and we work throughout with costs expressed per vehicle per unit distance.

In Chapter 9 tables showing costs of provision of transport services are presented for a variety of highway conditions and vehicle classes. The calculations are based on the results set out in Part 11. The costs presented in Chapter 9 include crew costs but costs associated with the provision of managerial services are excluded because the studles provide little e <2'nce concerning the magnitudes of these costs. For the same reason costs associated with ownership and maintenance of office and garage accommodation and of tools and workshop equipment are excluded.

Costs associated with vehicle ownership and replacement are included. They are important and cannot be neglected if we wish to estimate transport costs per unit output and gain some idea of the prices that fIrms' customers will pay for transport services and of the price changes consequent on changes in highway conditions. Unfortunately, the four studies provide little direct evidence on these costs. In this chapter we examine ways of remedying this deficiency and consider how the information provided by the studies can best be used.

Fleets of vehicles are major Investments for transport firms, and the funds devoted to fleet purchase and replacement could in principle be used for alternative purposes - In alternative business enterprises to earn profits, or lent out to earn interest. The foregone returns on the capital Invested In transport enterprises - Interest costs - are real costs borne by transport firms which must be counted when the cost of provision of transport services Is calculated. Consideration must also be given to the costs which arise because capital invested in a fleet of vehicles is used up as transport services are produced. Flrms maintain their vehicles, reinvesting in their fleet, replacing to some extent the capital that is dissipated as transport services are produced but, for sound economic reasons, firms rarely make good all the damage done to their vehicles In the course of producing transport services. The required maintenance costs would usually be excessive. in calculating the cost of provision of

289 290 CALCULATION OF TRANSPORT COSTS transport services, depreciation costs, that is the costs associated with the decline In value of firms' fleets of vehicles must be counted.

If we had relationships enabling vehicles' values to be predicted as functions of their age and of the characteristics of the highways over which they have travelled, then calculation of interest and depreciation costs and their sensitivity to highway conditions would be straightforward. But none of the studies report such relationships. All the studies report vehicle value-vehicle age (in years) relationships, mostly obtained from nationwide surveys of used vehicle prices, and these are set out in Appendix A and discussed in the next section.

These relationships do not involve highway characteristics, but they form the basis for those depreciation and interest cost calculations that the studies report. These calculations involve specifying a vehicle age and then using the value-age relationship to predict vehicle value. Interest costs per time period are computed as a constant fraction of the predicted vehicle value, and depreciation costs per time period are obtained by calculating the change in value as the vehicle ages. Finally, these per time period costs are placed on a per unit distance basis by dividing through by per time period utilisation obtained with the aid of the vehicle speed equations presented in Part il. We shall refer to this method of calculating depreciation and interest costs as the VA (value-age) method. In applying this method, variations in loads carried due to changes In highway conditions are not allowed for, though they could be if Information on the likely magnitude of responses were available. The calculations reported by the studies and given later do not take into account possible responses in hours driven to changes In highway conditions because we have no Information on the magnitude of such responses which will usually be critically dependent on local conditions.

This approach, based on the studies' vehicles value-vehicle age relationships, suffers from three defects. First, vehicles' values predicted by the studies' equations are not related to the quality of the routes over which vehicles have travelled. Second they are not related to the number of kilometers that vehicles have travelled, only to their calendar age. On low quality routes, vehicles will typically have travelled relatively few kilometers at any calendar age, but each kilometer travelled will have caused more damage. The effect on vehicles' values depends, of course, on how much maintenance has been performed and it is here that the third problem with the use of the studies' vehicle value-age relationships arises. Using these relationships, one fails to recognize the link between the running costs that a vehicle incurs and the vehicle's value. That there is a link Is clear, for, other things being equal, vehicles which will present their owners with relatively high running costs will have relatively low values.

This Idea can be made more precise by recalling the economic theory of the transport fIrm set out in Chapter 2 In Part 1. Recall that we assumed cost minimising firms, purchasing new vehicles at a price VP, facing running costs (fuel, tire, oil, maintenance costs, and so forth) flowing at the rate m(t) per year for a t year old vehicle, and scrapping vehicles when they are s years old. The condition governing optimal scrapping requires that vehicle life, s, satisfies: CALCULATION OF TRANSPORT COSTS 291

S -rt (1) o m(s) - m(t))e dt - VP.

Further, the flow of running costs at the scrapping date, m(s), is equal to the sum of the flows of depreciation costs, D(t), Interest costs, I(t), and running costs, m(t), at any vehicle age, that is:

(2) m(s) - D(t) + i(t) + m(t).

This latter condition implies that depreciation and interest costs are zero at the date of scrapping, and that total operating costs are invariant with respect to vehicle age, increases in running costs (m(t)) being offset by decreases In depreciation and interest costs (D(t) + I(t)).

These two results are important for the following reasons. The second result (2), Implies that, if we know vehicle lives, s, then by calculating terminal running costs, m(s), we obtain an age invariant prediction of total vehicle operating costs. In order to use equation (2) to calculate total operating cots, vehicle lives must be specified. But how is this to be done? The studies do provide limited information concerning vehicle lives but no information on how they vary with highway conditions.

The first result, equation (1), provides a way of predicting vehicle lives because, given the discount rate, r, new vehicle prices, VP, and the studies' Information concerning the flow of running costs and its increase with vehicle age, m(t), equation (1) can be solved for vehicle life, s. Then terminal running costs can be evaluated and a prediction of total vehicle operating costs can be obtained. ThIs method of producing estImates Is referred to later as the OL (optimal life) method.

8.1 RELATIONSHIPS BETWEENVEHICLE VALUE AND VEHICLE AGE

All the studies report equations relating vehicles' vaiues, V(t), to calendar age, t, and new vehicle price, VP. In the Kenyan study the vehicle value data obtained were either resale valuations by professional assessors or actual resale prices. In the Caribbean study vehicle values are given for some of the vehicles appearing In the user survey. These data were supplemented by Information obtained from operators outside the user survey and from vehicle dealers In order to produce the Caribbean study's vehicle value-age relationship. In both the Indian and Brazilian studies, surveys of vehicles traded on the second-hand market provided data with which to estimate vehicle value-age relationships. The Brazilian commercial car equation was obtained using data from user survey companies on prices obtained for their vehicles in second-hand markets. The studies' vehicle value age equations reflect local conditlons at the time that data were collected. In applications thelr relevance should be considered carefully. 292 CALCULATION OF TRANSPORT COSTS

Only In the case of the Indian study do the reported equations predict vehicle value equal to new vehicle price at vehicle age equal to zero. In the rest of the studies the smooth curves or lines that apply over the majority of the age range do not capture the Initial one or two years decline In vehicles' values. The Kenyan and Caribbean studies' equations for cars and light goods vehicles apply for vehicles two or more years old, separate figures being given for the value of one year old vehicles. The remaining Kenyan and Caribbean study equations and the Brazilian study equations apply for vehicles one or more years old. In most cases the relationships indicate a sharper fall in vehicle value over the first one or two years of life than data on older vehicles would lead one to expect. This is possibly due in part to effects associated with the expiration of, or non-transferability of, manufacturers guarantees, and, maybe, to some kind of "market for lemons" effect (see Akerloff 1970). Purchasers can only judge new vehicles of a given specification as Identical. But, since young used vehicles may not be offered for sale unless their owners foresee high future maintenance costs, purchasers may take the offer for sale of a young vehicle as an Indication of.below average quality, thus depressing second-hand market prices for young vehicles. The Indian study equations do not predict faster rates of depreciation for younger vehicles but It appears that the data have been adjusted to remove any differential effects.

In the Brazilian study, except for commercial cars, and in the Indian study vehicle value is an exponential function of calendar age, Implying that per time period depreciation is a constant fraction of current vehicle value for vehicles of all ages. The Brazilian commercial car equation and the car and light goods vehicle equations for the Kenyan and Caribbean studies give vehicle value divided by new vehicle price as linear In vehicle age, Implying that per time period depreciation costs are a constant fraction of new vehicle price. The Brazilian commercial car equation shows a fast decline in vehicle value as vehicles' age which reflects the experience of the user survey companies that provided the data used to estimate the equatlon. These companies used cars In high utillsation operations, described In Section 8.2. The Caribbean and Kenyan studies' equations for buses and trucks express vehicle value divided by new vehicle price as a power function of vehicle age. In these studies except where llnear age functions are used, the equations give vehicle value as a strictly convex function of vehicle age Implying that depreciation costs per time period fall as vehicles age. The vehicle value-age equations reported in Table 8.1 are graphed In Figures 8.1 to 8.5.

Table 8.2 shows the per annum rate of flow of depreciation costs on the tth anniversary of the vehicle's first registration as D(t), equal to minus the derivative wlth respect to calendar age of vehicle value V(t). In all cases depreciation costs per annum are either constant or fall as vehicles age. Depreciation costs per time period are predicted to be a larger fraction of current vehicle value by the Brazilian study equations than by the Indian study equations and the Indian study results Indicate that the vehicles depreciate more slowly there than in Brazil. There Is very llttle Information available on vehicle lives but what Information there Is suggests that cars and jeeps at least are more long lived In India than In Brazil. CRRI (1982) reports 3.9 percent of Indian cars and jeeps CALCULATION OF TRANSPORT COSTS 293

Table 8.1: VehIcle Value V(t) as a Function of Vehicle Age (t) and New Vehicle Price (VP)

Country Vehicle Cass Equation Restrictions

INDIA Cats V(t) = exp(-.081t)VP

Buses and Trucks V(t) = exp(-. 147t)VP

BRAZIL Cwrs (commercial) Vt) = (.859- .143t)VP 1 C t1 5 V(t) = .14VP t >VS

Cas (private) V(t) = 1.07 exp(-.173t)VP 1 C t 4 12 V(t) = .13VP t > 12

Light Goods Vehicles V(t) = .75 exp(-.124t)VP 1 C t ( 15 V(t) = .11VP t ) 15

Buses V(t) = .95 exp(-. 169t)VP 1 S t ( 12 V(t) = .12VP t . 12

Medium Trucks V(t) = .83 exp(-.175t)VP 1 < t C 12 V(t) = .1OVP t ) 12

Heavy Trucks Vtt) = .84 exp(-.160t)VP 1 At C 12 V(t) = .12VP t z t2

CARIBBEAN Cws and Light V(t) = .78VP t = 1 GoodsVehices V(t) = (.795 - .078t)VP 2 C t ( 9

3 Trucks V(t) = (1.553- 6GM1tl1)VP 1 C t 4 12

KENYA Cars and Light V(t) = .7sVP t_ 1 Goods Vehices V(t) = t.793 - .077)VP 2 C t ( 9

Busesand Medium V(t) = (1.317 - .625t113 )VP 1 4 t 4 8 and HeavyTrucks 294 CALCULATION OF TRANSPORT COSTS

Figure 8.1: Vehicle Value at Ago t Years (V(t)) Divided by Now Vehicle Price (VP) versus Vehicle Age: India

V(t) VP 1.0

0.8

I :,,

ST. _d m Tn,ds

0.6

0.4

0.2

t 2 4 6 8 10 12 14 16 18 20vhicle age (years)

Figure8.2: VehicleVaiue at Age t Years V(t)) Dividedby New VehiciePrice (VP) versusVehicle Age Brazil: Cars and Light Goods Vehicies

V (t VP

0. 1

" =~~~~~~~~~~~~~~~~~~~~~oPrhUscas 0.6 0.6 co~~~~~~~~~~~~~~~~~~~~~~~c....orwo.CW

0.4

2 4 6 8 l0 12 14 16 18 20 vehicle age (years) CALCULATION OF TRANSPORT COSTS 295

Figure 8.3: Vehicle Value at Age t Years (V(t)) Divided by New Vehicle Price (VP) versus Vehicle Age

Brazil: Buses and Trucks

V (t) VP

1.0 t

HT MsbT =

0.6 T IT '.y NT = T-o

0.4

0.2

0.44 14 16 18 20 vehicle ag (year) Figure8.4: VehicleValue at Age t Years (Vt) Dividedby New VehiclePrice (VP) versusVehicle Age Caribbean

0(t) VP

0.8,

0.6~ ' LG C-r Wo Ught Good. V.hW1.

0.4

0.22

CLG

2 4 6 8 10 12 14 vehicle age (years) 296 CALCULATIONOF TRANSPORT COSTS

Table 8.2: Per Annum Rate of Flow of DepreciationCosts on tth Anniversaryof Vehicle Registration

0ounv VMio Cloaw Equatn R onso

INDIA Cer D(t) = .081 V(t)

Buss ad Trucks D(t) = .147 V(t)

BRAZIL Cam (oomm.rclI) D(t) = .143>P 1 V(t) 1 4 t C 5 6.0 - t Crs (Prlpvt) D(t) =.1I3V(t) 1 C t C 12

Light GoodsVehk*l D(t) - .124V(t) 1 4 t C 15

Eub D(t) = .16SV(t) 1 4 t 4 12

Medium rudo D(t) = .175V(t) 1 t C 12

HeswrrwTud D(t) =.1IV(t) 1 4 t C 12

CAIDIEA Cos and Light D(t) = .078VP= I 1V(t) 2 C t C 9 GoodsVehic. 10.2-t

Trucs D(t) = .221t 1VP V(t) 1 C t C 12 t(7.0t -13)

KENYA Cars and Light D(t) = .0" = 1 V(t) 2 C t 4 9 GoodsVehIces 10.3-t

Bus"nd V rcns D(t) = .2a8t 2/3VP = -1 3 t) 1 t 4 t (G.33t -1/13) CALCULATION OF TRANSPORT COSTS 297

Figure 8.5: Vehicle Value at Age t Years (V(t)) Divided by New Vehicle Price (VP) versus Vehicle Age

V(t Kenya VP

La 1

0.8

0.61 ^ O I~~~~~~~~~d

0.4

0.2

2 4 6 8 10 vehicle age (years)

as over 25 years old and 3.3 percent of Indlan buses and trucks over 12 years old. While the latter figure is not out of line with Brazilian experience the former Is. Graphs presented in the Kenyan study report (Hide et al. 1975) suggest vehicle lives of around twelve years In Kenya at the time of the study.

The per annum rate of flow of Interest costs on the tth anniversary of first registration Is given by l(t) - rVMt) where r is a per annum discount rate. In Illustrative calcuiations reported In the Brazilian study (GEIPOT 1981) an annual discount rate of 0.12 Is used which results in ratios of per annum depreciation costs to per annum interest costs varying from 1.03 to 1.46 as shown in Table 8.3. In Illustrative calculations reported In the Indian study (CRRI 1982) an annual discount rate of 0.15 Is used giving ratios of per annum depreciation costs to per annum Interest costs of 0.98 for buses and trucks and 0.54 for cars.

To convert per annum depreciation and Interest costs to the per unit output basis required for assessing the benefits to highway Improvements, It Is necessary to divide the predicted per annum costs by output per vehicle per year. Prediction of output per vehicle per time period Is therefore of great importance and It Is to this topic that we turn In the next section. 298 CALCULATION OF TRANSPORT COSTS

Table 8.3: Ratios of Per Annum Rates of Flow of Depreclation Costs (D(t)) to Interest Costs (I(t)): Brazil

Vehicle Class D(t)/i(t)

Private Cars 1.44 Light Goods Vehicle 1.03 Buses 1.41 Medium Trucks 1.46 Heavy Trucks 1.33

Note: Annual discount rate = 0.12.

8.2 VEHICLE UTILISATION

There are two distinct aspects to vehicle utilisation as defined here. On the one hand we have to consider kilometers travelled, or trips made, per vehicle per time period and on the other we must consider loads carried or passengers carried per vehicle per trip or per kilometer. in the studies performed in India, Brazil, the Caribbean, and Kenya considerable emphasis has been placed on kilometers travelled - Indeed in the Indian and Brazilian studies "utlilsation" Is taken to mean kilometers travelled per time period and the Issue of loads carried receives little attention. The four country studies provide little information on loads carried and no information on the responsiveness of loads carried to changes in highway conditions.

With vehicle specification fixed firms can adjust loads carried to only a limited extent but, where it Is economic to do so they may choose to overload vehicles and perhaps, faced with steep, sinuous routes, firms may deliberately carry loads less than the maximum recommended by manufacturers. A dimension to the "load carried" choice not considered at all In the four country studies Is choice of vehicle capacity. When a highway is improved we may find larger capacity vehicles being operated. In part the more extensive use of large capacity vehicles on good quality routes may be a result of market conditions. High quality routes tend to be high volume routes on which firms can be assured of operating large vehicles to capacity. But It Is likely that highway conditions affect the vehicle capacity choice directly.

In the Brazilian study semi-trailer combinations were rarely found operating on unpaved routes or on routes built to low geometric standards. The available evidence indicates that for such vehicles operating costs rise sharply once highway conditions drop below a fairly high standard. In CALCULATION OF TRANSPORT COSTS 299 one notable Instance In the Brazilian study a company was found operating semi-trailers on unpaved routes, in a eucalyptus logging operation, but this was on a road network constructed and maintained by the company who ensured that road conditions were good. In assessing highway Improvement projects the possibility that larger capacity vehicles will be operated once a route is Improved must be considered. These vehicles cost more to purchase and generally Incur higher depreciation, interest, and maintenance costs per time period. But on good quality routes and where the vehicles can be operated near to capacity, costs per unit output are likely to be lower than for lower capacity vehicles.

So far we have considered vehicle loads and capacities but as important in determining output per vehicle per year is the prediction of annual kilometerage. Both the Indian and the Brazilian studies provide equations relating annual kilometerage per vehicle to highway characteristics obtained using user survey data. Neither the Kenyan nor the Caribbean studies provide information on annual kilometerage derived from user surveys. Unfortunately annual kilometerage equations obtained from user survey data are not at all easy to interpret because kliometers travelled per year per vehicle varies greatly from company to company and Is heavily dependent on the type of business in which the company is Involved. Route length plays an important role too. Obviously vehicles employed on short haul deliveries will spend considerable time loading and unloading compared with vehicles Involved in long distance haulage on Inter-urban routes.

Inevitably, highway planners will have to pay close attention to local conditions when predicting utilisation. The annual kilometerage equations reported In the Brazilian study (GEIPOT 1981) and In the Indian study (CRRI 1982) reflect the particular practices and types of business of the relatively small number of companies that appear in the surveys. They are unlikely to be useful outside the environments in which they were obtained and they are not reported here. However, to give some Idea of the annual kilometerage achleved by survey vehicles and the variation across countries and vehicle classes, we present in Table 8.4 average annual kilometerages by vehicle class as recorded In the four studies.

The high annual kilometerage of the commercial cars in the Brazilian user survey is not representative of general commercial car operations in Brazil. All of the cars in the Brazilian survey were Involved In bank courier work In which speed of delivery was highly valued by customers and by the nature of the bank courier business, courier cars have high utilisatlon - they depreciate fast, as would be expected. The low annual kilometerage of the Caribbean vehicles Is distinctive, but typical of commercial operations on the small islands where there are considerable seasonal fluctuations in the amount of freight transported.

In practice output per vehicle per year does have to be predicted and the effect on utilisatlon of highway characteristics Is of considerable Interest. Some progress towards predicting utilisation can be made by explolting the vehicle speed equations given in Chapter 4 In Part 1i, though care should be taken to ensure that speed equations are calibrated 300 CALCULATIONOF TRANSPORT COSTS for the environment In which they are to be used. Annual kilometerage Is the product of average vehicle speed In kilometers per hour (V) and hours driven per year (H). The equations In Chapter 4 predict vehicle speed as a function of highway characteristicsand, given hours of operation per year-, annual kiiometeragefollows. In predicting hours of operation per year local conditions are highly relevant because customs and local working practices vary from country to country. As before, type of business is an Importantconsideration as well. The Brazilian and Indian studies present average annual hours driven by vehicle class and we give these figures In Table 8.5. These figures reflect the type of business and working practices of the companies surveyed In the two studies. They may not be good indicatorsof general Brazilian or Indian experience and they are unlikely to apply In different environments.

Table 8.4: Average Annual Kilometerageof Survey Vehicles (Kilometersper Year)

User Survey Vehicle Class India Brazil The Caribbean Kenya

Private cars - 20,000

Commercial Cars 37,000 93,000 f16,000 24,000

Light Goods - 89,000 1 94,000 Buses 93,000 94,000 - 113,000

Medium and Heavy Trucks 55,000 101,000 13,000 48,000

Table 8.5: Average Annual Hours Driven (Hours per Year)

Vehicle Class Brazil India

Cars 1,560 800 Light Goods Vehicles 1,800 - Buses 2,400 1,380

Medium Trucks 2,040 1,300 Heavy Trucks 1,800. CALCULATION OF TRANSPORT COSTS 301

Given predictions of annual hours driven (H), vehicle speed (V) and load carried per vehicle (L) utilisatlon can be obtained as:

U - V.H.L. and for any predicted output of transport services, Q, the number of vehicles operated by companies can be predicted as N - Q/U. However, It must be borne in mind that annual hours of operation as well as loads carrled can vary with highway conditions so that not all the response comes through vehicle speed changes. Variation in loads carried was discussed earlier in this section.

Thomas (1983) provides a useful discussion of the effects of highway Improvements on the utilisation of commercial vehicles. He finds, in the context of a particular project in West Malaysia, that utilisatlon Is, for certain of the vehicles surveyed, rather Insensitive to changes in highway conditions that permit higher speeds, because of restrictions on numbers of Journeys per day and on working hours. In most highway Improvement proJects one can find examples of firms for which time savings resulting from highway improvement are not easily utillsed - perhaps because time savings are insufficient to allow vehicles to make, say, two trips per day when before they made just one. It Is clearly Important to consider local conditions before proceeding to assume that all time savings due to Increased speed of travel can be used to Increase utillsatlon. However, In many large scale Improvements we find firms In the situation described above approximately "balanced" by firms for whom small time savings allow major Increases In utilisation because just a small Increase In speed allows, say, two trips per day where two trips per day were only barely Infeasible prior to the Improvement.

The four studies provide no Information concerning the way in which hours of operation vary with highway conditions so, In calculating depreciation, Interest, and crew costs, we proceed here and In Chapter 9 by specifying hours driven per year as constant across highway types and develop utilisation as the product of hours driven and speed as predicted using the equations of Chapter 4.

8.3 DEPRECIATION, INTEREST, AND MAINTENANCE COSTS

In this section, the two methods of calculating depreciation and Interest costs, described In the beginning of this chapter are examined In some detail. The VA method (value-age) Involves specification of vehicle life in years and calculation of per annum depreciation and Interest costs, using the studies' vehicle value-age relationships. Assuming a value for hours driven per year, annual utilisation Is derived using the studies' vehicle speed equations, and the predictions of per annum depreciation and Interest costs are divided by utilisatlon so that they are expressed per unit distance. The depreciation and, where available, Interest cost calculations reported by the studies were obtained using methods similar to this. 302 CALCULATION OF TRANSPORT COSTS

Though the studies predict large effects on maintenance costs only for road roughness, the summed maintenance depreclation and Interest costs given In Table 8.6 are sensitive to variations In highway geometry. This Is because the costs given In Table 8.6 are expressed per unit distance and are calculated assuming hours driven are Insensitive to highway conditions. Thus they reflect the sensitivity of vehicle speed to geometry.

Table 8.6 shows predictions of the sum of maintenance depreclation and Interest costs for Brazilian and Indlan buses and Caribbean cars, obtained using the VA method, exploiting the studies' vehicle value-vehicle age (in years) relationships. Maintenance costs have been added to permit direct comparlson with predictions obtained using the OL method, reported shortly. The prices used to derive the predictions given here and later In this Chapter are reported in Table 8.7. They are discussed In Chapter 9, where more detailed cost tables are given. For the moment, we note that all prices are in local currency at or close to the studies' dates. The Caribbean study's equations cannot be extrapolated to roughness as low as 2,000 mm/km, so, for the Caribbean car, maintenance costs are predicted at 4,000, 6,000, and 10,000 mm/km.

Predictions are given for vehicles aged 2, 5, and 10 years. Hours driven have been specified at 2,500 hours per year for Brazilian and Indian buses and at 350 hours per year for Caribbean cars. The reason for using a much lower value for the Caribbean vehicle will be explained shortly. These values, together with the studies' speed equations, Imply the total number of kilometers run at ages 2, 5, and 10 years given In the columns headed "K" In Table 8.6. Vehicles operating over lower quality routes are predicted to attain lower total kilometer age at any calendar age because speeds are reduced as we move to lower quality highways. Increases in hours driven could offset this but any need for Increased time off the road for maintenance activities would work in the opposite direction.

As examination of Table 8.6 reveals, application of the VA method can result In some curious effects. For the Brazilian and Caribbean vehicles, the sum of maintenance, depreciation, and interest costs (and thus of total operating costs, since no other cost components are predicted to be affected by vehicle age) are predicted generally to Increase with vehicle calendar age. For Indian vehicles they are predicted to decrease with vehicle calendar age.

In the context of the model used In Part I and given our definition of vehicle value, this suggests some mis-matching of the studies' maintenance cost equations and their vehicle value-calendar age equations. The effect may be due to the exclusion from the latter of kilometer age and to highway condition effects.

So far as maintenance costs are concerned there are two effects operating in Table 8.6 pulling In opposite directions. Lower quality routes are associated with lower speeds, thus with lower utillsation and lower kilometer ages at any calendar age, and this brings maintenance costs down. But lower quality routes are associated with higher maintenance costs via roughness and geometry effects. It Is possible for either effect to dominate. Table 8.6: Sum of Malntenance (Parts and Labor) - Depreciation and Interest Cost (P + L + D + I) and

Kilometer Age (K, 1000 km) by Vehicle Age Obtained Using Studies' Vehicle Value - Calendar

Age Equations (VA Method)

Rise Roughness_ BRAZILIAN BUSES_ INDIAN BUSES CARIBBEAN CARS Curvature plus BI: mm/km Age: 2 years Age 5 years Age: 10 years Age: 2 years Age: 5 years Age: 10 years Age ; 2 years Age; 5 years Age: 10 years 0/km Fall (IRI m/kms m/km P+L+D+I K P+L+D+I K P+L+D+I K P+L+D+1 K P+L+D+I K P+L+D+} K P+L+D+I K P+L+D+I X P+L+D+l K

2000(1) 783 361 852 901 955 1802 433 257 396 643 354 1285 227 44 300 110 421 219 {2.81

10 6000. 1010 274 1078 684 1187 1368 506 151 471 533 420 1065 311 42 476 104 751 208 (7.41

10000 1308 218 1393 545 1528 1090 623 169 575 423 504 845 463 39 802 98 1367 195 (12.0) 100 . 2000 1) 870 253 849 633 870 1265 525 204 488 510 434 1020 231 42 298 105 410 209 {2.81

50 6000 1079 218 1076 544 1121 1088 653 160 600 399 523 798 312 39 467 99 724 197 0 (7.4)

W 10000 1358 189 1389 471 1474 943 862 116 773 289 653 578 459 37 778 93 1308 185 (12.01

2000(1) 846 273 846 682 886 1365 452 242 424 604 382 1208 243 37 296 93 384 186 (2.81

10 6000 1140 188 1088 470 1087 940 546 198 509 494 454 988 320 35 448 87 663 174 (7.4)

10000 1392 174 1392 435 1447 870 682 154 627 384 549 768 455 32 724 81 1173 162

500 ______.__ ___ 2000(1) 925 219 863 546 845 1093 568 189 529 471 470 943 250 35 297 88 374 176 (2.81

50 6000 1189 171 1103 426 1069 853 719 144 658 360 571 720 325 33 442 82 637 164 (7.4)

10000 1432 161 1398 401 1423 803 980 100 871 250 726 500 456 30 703 78 1116 152 {12.0o)

NOTES:

(1) Roughness set to 4000 =cc/km in place of 2000 mm/km to evaluate parts costs for Caribbean cars. (2) Hours driven: 2500 hours/year, Brazil, India, 350 hours per year, Caribbean. 3 3 (3) P+L+D+I is the sum of parts, labor, depreciation and interest costs in : Brazil, 1976 Cruzeiros/10 kms, India, 1978 Rupees/1 km; Caribbean 1978 3 Eastern Caribbean dollars/10 km. For details of prices see Table 8.8 and chapter 9. (4) Interest rate: 12% per year. 304 CALCULATION OF TRANSPORT COSTS

Table 8.7: Vehicle Prices (1) and Mechanics Wage Rates(2)

Item Amount India Brazil Caribbean(3) 1978 Rupees 1976 Cruzeiros 1978 EC

Car 1 vehicle 64800 43000 21000 Bus . 234000 I 316970 _ Medium truck . 180700 138621 48000 Articulatedtruck and trailer . 437704

Labour services Mechanic 1 hour 2.25 13 _

(1) Prices inclusiveof taxes

(2) For further details see Table 9.1. Chapter 9.

(3) Caribbean study labor costs obtained by prorating parts costs.

The studies' vehicle value-calendar age equations which determine per annum depreciation and interest costs underlying Table 8.6 do not allow for the Influence of vehicles' kilometer age nor for the Influence of highway conditions. It is likely that, applied to two vehicles travelling similar routes, they understate the rate of depreciation of the higher utilised vehicle and that, applied to two vehicles with similar utilisation, they understate the rate of depreciation of the vehicle on a lower quality route. So far as Table 8.6 Is concerned, these effects pull against each other because the vehicles operating on lower quality routes are predicted to have lower utilisation. It Is difficult to determine under what circumstances the studies' vehicle value-calendar age equations lead to under and over prediction of depreciation and Interest costs, particularly when It Is realized that vehicle owners' maintenance policy is highly relevant since increased maintenance expenditures on vehicles travelling on low quality routes may substantially offset the decline In value that would arise were damage done to vehicles to be left unattended.

We suggest that the VA method should be used with caution and advise those who wish to employ this sort of procedure to calculate depreciation and Interest costs to take care to check that the vehicle value relationships are consistent with the running costs equations that they use. In applying the VA method In Chapter 9 we specify both calendar and kilometer ages, avoiding some of the problems evident above, but it should be noted that different choices of calendar and kilometer. ages would result In slightly different cost predictions. CALCULATION OF TRANSPORT COSTS 305

In the absence of reliable information concerning vehicles' values and their relationship to calendar and kilometer age and to highway conditions, depreciation and Interest costs can be calculated using the OL method. This exploits the Information contained In the equations relating running costs to vehicle age and so is consistent with them. Further, it produces total vehicle operating cost predictions that are consistent with the model used In Part I and with our definition of vehicle value, predictions that are invariant with respect to changes In vehicle age.

The OL method (optimal life) Involves specification of hours driven per year and derivation of a vehicle age Invariant annual utillsatlon, as In the VA method. The vehicle scrapping condition, equation (1) In this chapter is then used to derive running costs per unit distance at the termination of vehicles' lives. Equation (2) tells us that these terminal running costs, Incurred when vehicles have negligible value, and are hence Incurring negligible depreciation and Interest costs, are equal to the total operating costs (i.e., running and depreciation and Interest costs) of vehicles of all ages. Details of this calculation are set out In Appendix B. In fact, only maintenance costs are found to be substantially affected by vehicle age so that other costs are not relevant In determining vehicle lives. Thus, In using the OL method here, only maintenance costs are considered and the procedure yields a vehicle age Invariant prediction of the sum of maintenance, depreciation and Interest costs to which fuel, lubricant, and other costs must be added to arrive at total vehicle operating costs.

Strong simplifying assumptions are used to obtain depreciation and Interest costs In this way, but without them little progress can be made. In all applied economic analysis simplification Is necessary If sallent magnitudes are to be predicted. Of course, the results one obtains from simple models must be appraised carefully.

Table 8.8 shows for Indian and Brazilian buses and for Caribbean cars the vehicle age Invariant sums of maintenance, depreciation, and Interest costs obtained using the OL method, solving for vehicle lives as described In Appendix B, and evaluating terminal maintenance costs. As above, we have assumed 2,500 hours driven per year for the Indlan and Brazilian buses and 350 hours per year for the Caribbean cars, and used the studies' speed equations to derive vehicle age Invariant utilisation. The costs we obtain fall uniformly between those recorded for the oldest and youngest vehicles In Table 8.6, derived using the VA method, and the magnitudes are reasonable. At first sight, the OL method seems to provide the answer to the problem of calculating depreciation and Interest costs when reliable Information on vehicles' values Is not available, and Its consistency with the running cost equations and with the definition of vehicle value is attractive. However, there Is a problem that requires discussion - the vehicle lives that the studies' maintenance equations Imply are, In the case of the Indian and Brazilian studies, generally too long, and In the case of the Kenyan study, except for buses, too short. We argue below that, so far as the Indian and Brazilian studies' equations are concerned, the consequences for predicting total vehicle operating costs are unlikely to be severe. 306 CALCULATION OF TRANSPORT COSTS

Table 8.8: Sum of Maintenance (Parts and Labor), Depreciation and Interest Costs (P + L + D + I) Obtained Using Studies' Maintenance Cost Equations to Evaluate Terminal Maintenance Costs (OL Method)

1 Curvature Rlse plus Roughness Brazilian Buses Indian Buses Caribbean Cars - 0/km Fall Bl: mm/km P+L+D+l P+L+D+I P+L+D+I m/km!

20001 846 406 1 309 10 6000 1061 486 432 10000 1396 592 612 100 __ 20001 885 497 312 50 6000 1112 609 434 10000 1419 777 615

20001 875 436 319 10 6000 1138 524 442 10000 1434 643 623 500______. 20001 908 537 323 50 6000 1158 665 446 10000 1451 868 627

1. For notes, see Table 8.6

The short predicted vehicle lives obtained using the Kenyan study's maintenance cost equations arise because costs are predicted to Increase steeply and linearly with vehicle age. Each doubling of vehicle age doubles predicted maintenance costs which soon rise to such high levels that fIrms that did not scrap vehicles would be paying in maintenance costs every few thousand kilometers amounts sufficient to purchase new vehicles which would Incur low running costs. For Kenyan buses, the problem Is less severe because for these vehicles maintenance costs are predicted to Increase with the square root of vehicle age.

The Caribbean study also predicts linear age effects and we might expect the same difficulty to arise here. Indeed, it does If we try to predict vehicle lives assuming the Intensity of utilisation found In the other studies. However, the Caribbean study obtained data from vehicles achieving very low utilisation and, as noted In Chapter 7, the strong age effects found by the Caribbean study are likely to be due to confusion of the effects of calendar and kilometer ageing. If the OL method Is applied to the Caribbean study's maintenance equations assuming the sort of utilisation actually achieved by Caribbean vehicles, then predicted vehicle lives are not understated; Indeed, they are, If anything overstated, as happens when the OL method Is applied to the Indian and Brazilian studies' equations. Here, and later In Chapter 9, predictions derived using the Caribbean study's equations are confined to low utillsation operations. CALCULATION OF TRANSPORT COSTS 307

Overstatement of vehicles' lives when the OL method Is applied to the Brazilian, Indian, and Caribbean studies' maintenance equations (the latter assuming low utilisation) almost certainly arises because the studies' equations tend to understate maintenance costs and generally the progression of running costs with age. Further, the analysis of Part 1, set in a stationary environment, does not allow for technical change and consequent vehicle obsolescence and advanced scrapping.

Figure 8.6 shows the effect of understanding running costs and their progression as vehicles age. The curves m'(t) and m(t) show respectively true and estimated rates of flow or running costs as functions of vehicle age, t. The discounted values of the areas ABC and A'B'C are both equal to new vehicle price, by virtue of equation (1) and consequently estimated vehicle lives, s, are longer than actual lives, s'. If running cost streams are relatively flat for older vehicles, then the understatement of total vehicle operating costs (AA') may not be large, particularly with non-negligible discount rates. We return to this later.

There are a number of reasons for believing that the studies' maintenance cost equations understate maintenance costs and their rate of increase as vehicles age. When recording maintenance costs, errors Involving omission of cost Items are more likely than errors Involving spurious attribution of costs to vehicles, and in all the studies major accident repair costs were excluded from maintenance costs. Further, maintenance expenditures in practice arise at discrete points In time and, for older vehicles can be large in magnitude when they do arise. Vehicles near to the ends of their lives are likely to be scrapped early when their owners face large maintenance costs so that the large costs which would bring about scrapping are not observed. This will lead us to understate the costs associated with running vehicles which are near to thelr scrapping dates.

Additionally, there Is a problem of adverse selection. Suppose there are vehicle specific differences in costs In addition to those attributable to highway conditions, vehicle age and so forth. Then, by virtue of equation (1), relatively high cost vehicles will be scrapped relatively early. Under these circumstances, the oldest vehicles observed in user surveys are representative not of average vehicles of their "cohort," but of the lowest cost vehicles of their "cohort" and the fitted relationships between costs and vehicle age will tend to follow a path somewhat below that followed by costs for average vehicles, and to a greater extent, for older vehicles.

There are other reasons to expect solved values for vehicle lives obtained using the OL method to be longer than vehicle lives observed in practice. For example, It Is likely that many cost components show some increase with vehicle age. Engine efficiency declines and suspension and steering systems deteriorate so that, as vehicles age, fuel, lubricant, and tire costs rise. Wlth a few exceptions such effects have not been detected in the cost component by cost component analysis of the studies' data probably because for any single component, except maintenance, the effects are small and difficult to estimate accurately using quite scattered data. In sum though, the effects may be non-negligible, In which case the 308 CALCULATION OF TRANSPORT COSTS

Figure 8.6: Effect on Predicted Lives and Costs of Understating Running Costs

$ /year

A ' E=m (t)

t (years) SI S

Increase in costs with age Is understated If only the Increase in maintenance costs Is considered.

In practice, vehicles are scrapped not just because their running costs become large relative to those Incurred by new vehicles of similar design but also because their running costs become large relative to new vehicles of new design. The long lives that arise using the OL method are not always achieved In practice, In part because vehicle design and technology change, rendering older vehicles obsolescent. This is an Influence not allowed for In our analysis In Part I which forms the basis of the 01 method since that analysis assumes a stationary environment.

Though the vehicle lives predicted when the OL method Is applied to the studies' cost equations are overlong (with the exceptlon of the Kenyan study) the consequences of this for the prediction of maintenance, depreciation, and interest costs may not be too severe. For example, If the problem arises because of under-prediction of maintenance costs mainly for older vehicles, then, unless the discount rate Is small, the effect on total cost predictions may be negligible. Figure 8.7 Illustrates this situation. Here, m(t) and m'(t) are respectively estimated and true rates of flow of running costs Implying estimated and true ages at scrapping of CALCULATION OF TRANSPORT COSTS 309

Figure 8.7: Effects on Predicted Costs of Understating Running Costs for Older Vehicles

$/year

Al A m(t)

C~~~~~~~~~~~~~~~~~~

t (years)

respectively s and s' years. The optimal scrapping condition requires that the discounted values of the areas CA'B and CAB are both equal to new vehicle price and thus that the discounted values of the areas AA'BE' and DEB are equal. When the discount rate Is at all far from zero, then AA', the extent to which total vehicle operating costs are understated need not be large In order to achieve the equality of the discounted values of AA'B'E and DEB since the latter is discounted more than the former.

Clearly the OL method should be used with care, and its predictions of operating costs should be examined to ensure that they are reasonable. As with the VA method, one will need, In practice, to ensure that utilisations used to derive costs are appropriate for the application in mind. The OL method has a number of advantages - It does not require Information, usually hard to obtain, concerning vehicles' values and their relationship to kilometer and calendar age, and highway conditions and using it one guards against the possibility of predicting unreasonably high costs In situations in which running costs are predicted to increase rapidly with vehicle age. It exploits the informatlon contained in new vehicle prices and In estimates of running costs and their progression with age and though, in practice, these may be somewhat understated the consequent downward bias in predictions of operating costs may be small, particularly if it Is malnly for older vehicles that running costs are under-estimated.

In the following chapter we report cost predictions obtained using both the VA method and the OL method. The overall predictions concerning the effects of highway conditions on vehicle operating costs are not wildly different. Our Inclination is to regard those derived using the OL method as more accurate. 310 CALCULATIONOF TRANSPORT COSTS

APPENDIX A. RELATIONSHIPSBETWEEN VEHICLE VALUES AND VEHICLE AGE

In this appendix the relationships between vehicle value and vehicle age In years reported by the user surveys carried out In India, Brazil, the Caribbean, and Kenya are reported In the form in which they were originally presented In the studies' reports. In all cases the vehicle value data are either prices obtained for vehicles on second-hand markets or estimatesof such prices as would be obtained were vehicles offered for sale on second-handmarkets. Throughout vehicle age should be taken to be age In years since first registration.

A8.1 Kenya

Notation

DP - new vehicle price minus vehicle value at given age new vehicle price Y - vehicle age in years.

Cars and light goods vehicles

DP - 0.207 + .077Y 2 < Y < 10

R2 _ .90, relationship apparently obtained from 15 data points.

DP - 0.22 Y - 1

Medium and heavy goods vehicles and buses

DP - -0.317 + 0.625Y1/3

R2 - .96, relationship apparently obtained from 15 data points.

This equation predicts DP - .308 at Y - 0 so presumably Is to be used for Y > 1.

A8.2 Caribbean

Notation: as In A8.1

Cars and light goods vehicles

DP - 0.205 + .078Y 2 < Y

R2 - 0.80, relationship apparently obtained from 34 data points. CALCULATION OF TRANSPORT COSTS 311

DP - 0.220 Y - 1

Trucks

DP - -0.5532 + 0.6615Y1 /3

R2 - 0.82, relationship apparently obtained from 22 data points.

A8.3 Brazil

Notation

VA - value of vehicle aged A years on second-hand market expressed as a proportion of new vehicle price.

Commercial cars

VA - .859 - .143A 1 < A < 5

R2 * .98, 75 observations.

VA - .14 A > 5

Private cars

VA - exp(.063 - .173A)

R2 - .98, 162 observations.

VA - .13 A > 12

Light goods vehicles

VA - exp(-.294 - .124A)

R2 _ .99, number of observations unknown.

VA - .11 A > 15

Buses

VA - exp(-.053 - .169A)

R2 _ .99, 240 observations.

VA - .12 A > 12

Medium trucks

VA - exp(-.185 - .175A) 312 CALCULATION OF TRANSPORT COSTS

R2 . .92, 180 observations.

VA - .10 A > 12

Heavy trucks

VA - exp(-.174 - .160A)

R2 .94, 120 observations.

VA - .12 A > 12

A8.4 India

Notation

DV - (resale price of vehicle after deducting premium due to shortages) new vehicle price

A - age in years.

Cars

DV - 0.9223A

R2 _ .97, 192 observations.

Buses and trucks

DV - 0.8631A

RZ _ .92, 127 observations. CALCULATION OF TRANSPORT COSTS 313

APPENDIX B. OPTIMAL VEHICLE LIVES

In this appendix the method used to obtaln estimates of optimal vehicle lives and thus of depreciation and interest costs is descrlbed. In order to deduce optimal vehicle lives (s, measured in years) we solve the equation:

(A8.2.1) m(s) - m(t))e rt dt - VP

where r Is the per time period continuous discount rate, VP Is new vehicle price and m(t) is the per year rate of flow of running costs for a t year old vehicle. Some manipulation of the studies' results Is required before equations corresponding to (A8.2.1) can be obtained.

First note that running costs that do not vary with vehicle age can be neglected when solving for s. Thus, If m(t) - mO + m1 (t) then optimal vehicle life satisfies (A8.2.1) with m(t) replaced by m1 (t). The four studies find that only maintenance costs are substantially affected by vehicle age and they report maintenance costs expressed per 103 kilometers for vehicles 103K kilometers old as functions which we denote here by n1 (K). These functions vary across vehicle classes and across studies and depend on highway characteristics but these dependencies are not made explicit here.

3 Let m1 (t) be the per year analogue of the per 10 kilometer rate 3 of flow of costs, n1 (K) and let utilization (10 km/year) be denoted by u. We make the crucial assumption that utilization does not vary wlth vehicle age. If It does, then (A8.2.1) Is no longer the optimal scrapping condition. With this assumption m1 (t) - un1 (ut), since K - ut, and in terms of the cost functions reported by the studies the optimal scrapping conditlon Is:

r -rt (A8.2.2) (un1(us) - un1 (ut))e dt - VP.

Let K. - us denote optimal vehicle life In 103 kilometers. Then (A8.2.2) can be rewritten as:

rK -rk/u (A8.2.3) J (n1 (Ks) - n1 (K))e dK - VP. 0

Given knowledge of n1 (.) provided by the studies, values for r, u, and VP, (A8.2.3), can be solved for optimal lives measured In 103 kilometers, K., and for optimal lives measured In years, Ks/u. Then, 314 CALCULATIONOF TRANSPORT COSTS n1(Ks) gives the vehicle age Invariant sum of per 103 kilometer maintenance,depreciation and Interestcosts.

All the maintenance (parts and labor) equations reported by the studies can be expressed in the form:

(A8.2.4) n1 (K) - a + a1 K 2 -

For example, In the Kenyan study, maintenance parts costs per 103km for cars are:

P - VP(-2.03+ .0018R)(K+ 38) and maintenance labor costs per 103km are:

w(.00851 - .00000078R)(P/VP) where w Is the hourly mechanics wage rate, R Is road roughness (mm/km) and VP is new vehicle price. Rearranginggives:

ao - 38(-2.03 + .0018R)(VP+ w(.00851 - .00000078R))

a1 - a0/38

P1 - 1, a2 - P2 - 0-

Those studies which report labor costs as a non-linear function of parts costs (Brazil, India) generate functionswith P2 ¢ 0, a2 ¢ °-

Substitutingfor n1(K) in equation (A8.2.3) gives:

2 fKs(a1KsP + a2KsP _ 1KPi - a2KP2)erK/udK - VP

as the equation determining Ks. Changing variable to q - rK/u, and defining:

qs - rKs/u 315 CALCULATION OF TRANSPORT COSTS

X, - a 1 (u/r) 1 p2 X2 - a2(u/r) 2

function, r(a,b) - Jx e dx, the Incomplete Gamma 0 we have: P1 P2 -qs - AL(qC) (A8.2.5) (X1qs + X2qs )(1 - e )

- rVP/u + xlr(pi+ 1,qs) + X2r(p2 + 1,qs)

- AR(qs)

vehicle life which must be solved for qs and thus for Ks - uqs/r. Optimal In years Is qs/r.

Figure A8.2.1: Determination of Optimal Vehicle Life

,~~~~~~~~~~~~ (q

AL~~~~A(qs)

-Aus rVp U

0 optimal q.

Z _ _ _ (a1+ 1) + 2 (a2+ 1) CALCULATION OF TRANSPORT COSTS 316

The studies all report a1 , a2 > 0, max (a1, a2 ) > 0, which ensures similar conditions apply to X1 and X2* and they report pil P2 2 0. Under these conditions (A8.2.5) admits a unique positive solution for q5.

The solution to (A8.2.5) Is depicted In Figure A8.2.1 with a single positive solution for qs - rKs/u - rs. The equation Is easily solved using Newton's method.

Optimal lives, maintenance, depreciation, and interest costs obtained using this method are given In Section 8.3. CHAPTER 9 The Costs of Transport Services

In this chapter estimates of vehicle operating costs under alternative highway conditions are presented and compared. The estimates are discussed In Section 9.1 and details of their calculation and cost tables are given In Appendix A. The concluding Section 9.2 Is concerned with the use and transferability of the studies' results.

It must be stressed that the calculations reported here are only illustrative. They are obtained using a number of simplifying assumptions that may well not be appropriate in particular applications. Users will need to perform their own calculations, perhaps along the lines described In Section 9.1, using prices relevant to the economic environment in which they are working and taking Into account the local conditlons that they face. The calculations presented below are Intended to give some feel for the ways In which highway conditions affect the cost of provision of transportation and they allow us to see whether the results obtained in the four user cost studles are In broad agreement.

In fact there is a good deal of agreement among the four studies on the broad effects of highway conditions on the costs of provision of transport services. However, the precise magnitudes Involved are predicted somewhat differently by the four studies. In part this Is a result of differences in the models used and It is also due to sampling variations. In each of the country studies samples of vehicles were used and limited numbers of experiments were performed. For all cost components the reported equations are statistical estimates of cost equations and they are necessarily, to some extent, inaccurate. Some of the differences In the cost predictions reported here may be due to differences In the economic and physical environments encountered In the four studies. We examine this issue In Section 9.2. It is a matter of some Importance, for users of the equations will typically face economic and physlcal conditions that differ from those found In the four studies, and they will wish to consider the extent to which the results reported here are relevant to their application.

9.1 COSTS OF PROVISION OF TRANSPORT SERVICES

The tables in the Appendix to this chapter give predictions by user cost study and vehicle class of costs per thousand kilometers associated with fuel, lubricants, tires, maintenance parts, maintenance labor, depreciation, interest, and crew. Because Information on accident costs is not available for most of the studies these are not Included. The experience of the Brazilian study suggests that, to allow for vehicle repair costs arising as a result of accidents, maintenance expenditures

317 318 COSTS OF TRANSPORT SERVICES may need to be Increased by as much as 18 percent. We do not Include any costs associated with capital equipment except those associated with ownership of the vehicle fleet, because the necessary information is not provided by the studies. Interest and depreciation costs associated with ownership of office and garage accommodation and of tools and other maintenance equipment are not included in the Illustrative calculations, even though In the long run these may be variable costs. Thus the maintenance labor wage rates used to predict maintenance labor costs are Intended to reflect wages paid to mechanics, not labor charges made by commercial garages to customers, which may reflect rents on property, equipment, and so forth. Time savings are not included in these Illustrative calculations except In so far as they are assumed to allow Increased utilization of vehicles and crew and consequently lower depreciation, Interest and crew costs per thousand kilometers. Time savings In hours per thousand kilometers are easily calculated by dividing the vehicle speeds recorded In the tables In the following appendix, Into 1,000.

Costs are calculated using prices In local currencles as they were, In so far as we can Judge, at the dates at which the studies were carrled out. Thus results obtained using respectively the Indian, Brazillan, Caribbean, and Kenyan equatlons are presented In respectively 1978 Rupees, 1976 Cruzeiros, 1978 Eastern Caribbean Dollars, and 1973 Kenyan Shillings. Where the necessary Information Is available some calculations have been performed using prices net of Indirect taxes of primary incidence (notably gasoline, vehicle purchase, and tire sales taxes) as well as using prices pald by transport firms.

It would be possible to convert all costs to a common currency at a single date, but errors Introduced by Inaccuracies In price deflators, and exchange rate anomalies make comparisons of cost levels misleading. Since we are prlmarily Interested in the cost differentials associated with alternative highway configurations which are, of course, unchanged under such conversions, the costs have been left In local currencies at study dates.

The prices used to calculate vehicle operating costs are recorded In Table 9.1, gross and net of Indirect taxes where the necessary Information Is available. Exchange rates against the U.S. Dollar at the times that the studies were performed are also shown In this table. Relative prices vary substantially across the studies. Table 9.2 shows for each country the cost of a new bus, a new truck and of a 1,000 x 20 tire In terms of liters of diesel fuel In prices gross and net of taxes, and the price of a new car and a car tire in terms of liters of gasoline. Of course some of the variation Is due to differences In vehicle specification but It seems clear comparing the price relatives that vehicles were expensive relative to fuel In Brazil and cheap relative to fuel In India at the times at which the studies were conducted.

Depreciation and Interest costs are, where possible, calculated once using the studies vehicle value-calendar age equations (the VA method) and once using the studies' maintenance cost equations to solve for terminal maintenance costs and thus the age invariant sum of Table 9.1: Prices and Exchange Rates

INDIA BRAZIL CARIB8EAN KENYAK

Itexi Amnount Price Prke Not Prim Prke Not Price Pr" Not |Prim Prim Not (Rupees) of Tax (Cruzeiros) of Tax (E.Caribbean 4) of Tax (Shilings) of TAx

Fuel: gasoline I liter 3.47 1.94 3.24 1.60 0.55 _ 1.1 Fuel: dbeel 1 liter 1.73 1.36 1.54 1.20 0.47 - I - 0.9 Engine oil 1 liter 6.S4 3.43 7.76 3.88 2.64 _ _4.68 Other aU tI llr 11.42 5.7t _7 7 P Grous 1kIg. 10.Z9 5.15 __ + __

Tire: car jIUre 4100(5.90x15) 216 160)(165x3) 139 80(165x13) _ 1t60(165x13) Uuty |1tire I _ _ 278(750I13) 242 - _ _ 16)(t65x13) bus Itire 1964 9001X20) 1007 1942 (1000x20) 16Y9(1) ___ 1250 (100;0M) medium truck 1 tire 2245(1000x20) 1212 1942(100lW 20) 1689 475(825x20) _ _ SS0(l0x20) heavyartic buck I tire 2430(110tx20) 1312 2054(110x22) 1766 - _ 11400(1100t 22)

Vehicle: cur |I whkle 64800 39880 4300=QZ) 37W6I(2) 21000 _ _ 181 utJlity Ivewhkb - - 43670 37646 - _ _ 3GOO0 W bs 11Vehiclb 234000 140400 316970 273250 _ _ _ 117O0 mad buck 1 vehicle 180700 108420 138621 119501 48000 _ _ 560w0 heavy buck |1 vehicle - - 170961 147380 142000 artc truck 11 vehicle 317En 2739 225000(3) artc trailer 1 vehicle - 1

Lsbor: mechanic 1 hour 2.25 2.05 13 7.8 - _ _ 6 cr: car 1 hour 3.50 3.18 15 I 9.0 2.8 _ I _ 4.5 crew: utity 1 hour - - 15 S9.0 - _ 4.5 crew: bus 1 hour 3.50 3.18 5 9.0 - 8.0 crew: aed buck, hour 3.50 3.18 15 9.0 2.8 _ _ 8.0 crew: heavy 1 hour 3.50 3.18 15 9.0 9.5

Date for prces July: 1978 j 17//76 1978 1973 Currency: Rupees Cruzeros I Eaten Caribbean Dollars Shillings Exchange rate at study date: t 4 = 8. 6 Rupes 1 4 = 8. 13 Cruzeiros 1 a= 2.74EC 1 4 = 7.14 Shillings

(1) Price of 900 x 20 tire, Brazil, 1471 Cruzeiros groas of tax, 1279 Cruzeiros net of tax. (2) GM Chvroblt Opal,price of VW 1300 is ICr 31856 Inc. taxes. $Cr 27462. exc. taxes. (3) Price of 3-axle heavy truck and 3-axle draw-bar trailer.

Source: See appendix to this chapter. Table 9.2: ApproxImate Price Relatives

INDIA T BRAZIL CARIBBEAN KE__A

Prices Presi Pric Prices Pries PricPri Pri Price Relative Inc. xc. inc. exc. i Inc. exc. inc. exc. Taxs Taxs Tat" TMe j TOMe Taes TMes Tows

Price of New Bu 135000 000 00 20O000 228000 | - - _ 130000 Price of 1 liter diesl 1

Price of now mod. trucx 104000 790 102- Price of 1 liter dies

lit r tire 1300 9Ct 1300 14000Ot( - 1400

Price of now car 19000 2000C 100W(2) 1700I (2) 38Wt - - 16000 Price of 1 liter gasoline

3 W Prke. a tire( ) 115 110 50 f5 145 _ 146 Nt Price of 1 iter guoline

(1) 825 x 20 tire (2) VW 1300. price relatives for G.M, Chevrolet Opal& are inc. taxs: 13000. exo. taxes:23000. (3) 166 x 13 except: India. 5.90 x 15. COSTS OF TRANSPORT SERVICES 321 maintenance, depreciation and Interest costs (the OL method), as described In Section 8.3 and Appendix B of Chapter 8.

A real discount rate of 12 percent is used In calculating Interest and depreciation costs. It Is likely that rates facing firms differed across the studies and this may explain some of the observed differences In maintenance costs and vehicle replacement decisions. We have no information to help us choose study specific discount rates and proceed using a single value, noting that In applications the discount rate, like all the prices used here, will require adjustments. It would be Interesting to consider the effect on costs of varying the discount rate and the prices used In the Illustrative calculations, but anything approaching a complete Investigation of price effects would very substantially increase the volume of results to be presented.

The calculations require values for vehicle utilization (103 km/year) and these have been obtained using two assumptions. Our Intention Is to use assumptions whose import Is clear and which are easily adjusted. As noted above the calculations presented In this chapter are purely Illustrative and cannot be applied without modification In assessing benefits to highway Investments. The first assumption we make Is that hours driven per year are fixed, Invariant under changes In highway conditions. In calculations with the Brazilian, Indian, and Kenyan equations we specify 1,500 hours driven per year for cars and medium trucks and 2,500 hours driven per year for buses and heavy trucks. The problems that arise In predlcting costs using the Caribbean study's equations for vehicles with utilization typical of that found In the other studies have been noted In Chapters 7 and 8. In calculations with the Caribbean study's equations we assume only 350 hours driven per year corresponding to the low utilisation recorded for the vehicles surveyed In the Caribbean study.

Assuming that hours driven per year are fixed Is likely to result in cost predictions that are to some extent more sensitive to highway conditions than will be found In practice. Firms faced with a deterioration In highway conditions are likely to adjust hours driven to minimise cost Increases and firms faced with highway Improvements are likely to make adlustments to maximise the cost reductions that can be achieved. None of the studies provide generally applicable results concerning these sorts of adjustments, so we proceed assuming hours driven are fixed.

To compute kilometers travelled per year the fixed hours driven are multiplied by vehicle speeds (recorded In the sequences of Tables which follow) predicted using the relevant equations In Chapter 4 In Part If (i.e., Kenyan study equations for Kenyan study cost tables, etc.) Thus our second assumption, discussed earlier In Section 8.2 of Chapter 8, Is that time savings attendant on highway Improvements, due to increased vehicle speed, are exploited to Increase utilisation.

Two further points should be noted. The first Is that the vehicle speeds used here are obtained from observation of free flow speeds and, In the case of the Brazilian speed model, from data on vehicles 322 COSTS OF TRANSPORT SERVICES attaining steady state speed. It is likely that the vehicle speeds are, to some extent, over estimates. The second Is that costs are expressed per thousand kilometers. Trucks in particular are commonly overloaded and the extent of overloading may well vary with highway conditions and across countries. Users will want to take account of overloading and calculate costs on a passenger, tonne, or volume kilometer basis, as appropriate, depending on the nature of the transport service provided.

In many applications users will wish to make assumptions other than those employed in producing the cost tables given below. These tables are not intended as reference tables to be applied without modifications In planning exercises. They are presented to give some Indication of the relative magnitudes of effects on costs associated with different highway characteristics, to provide the reader with a feel for the way In which the effects described In the previous chapters add up to produce effects on total costs, and to allow us to compare the results concerning total costs that emerge from the four studies.

The details of the calculation of the cost components are described in the appendix.

The Appendix Tables A9.1 - A9.9 give predlctions of cost components and of total costs on a per 1,000 kilometer basis for cars, buses, medium trucks, and heavy trucks using prices gross of taxes as given In Table 9.1 and equations generated by three of the four studies. These tables are calculated using the VA method to determine depreciation and Interest costs. Kenyan price data are only available net of indirect taxes of primary incidence so Kenyan study predictions are not included in this sequence of table though they are considered later. We have not calculated bus cost predictions using Carlbbean study equations and only the Braziilan study equations are used to generate predictions for heavy trucks. These predictions relate to large articulated vehicles - tractors and trailers.

Consider first the percentage contributions to total costs of Individual cost components. For all but the Carlbbean vehicles fuel costs are a substantial proportion of total operating costs, especially for cars for which fuel costs make up around 50 percent of the total. Tire costs are a much lower proportion of total costs for cars than for the other vehicle types. For trucks and buses they make up 15-20 percent of total costs though again the proportion Is rather iower for the Caribbean vehicles. Note that in producing predlctions for these vehicles utillsatlon has been set to a very low value, commensurate with the Caribbean study's experience, so that depreciation and interest costs are a rather higher proportion of total costs In the Caribbean study cost tables. Estimates of the Importance of depreciation and Interest costs vary somewhat across the studies. These reflect differences In predicted speeds and thus utillsation as well as differences In the studies vehicle value-calendar age equations. Except for the Caribbean cars, maintenance costs are rarely predicted to make up more than 30 percent of total vehicle operating costs per 1,000 kilometers, but this figure depends crucially on the calendar and kilometer ages used to produce these tables. COSTS OF TRANSPORT SERVICES 323

The VA method produces depreciation and Interest costs that, expressed per unit of time, are Invariant to changes In highway conditions. Expressed per unit distance these costs do vary with highway conditions because vehicle speed Is sensitive to roughness, vertical, and horizontal geometry.

Table 9.3 shows costs expressed as a proportion of costs Incurred on a relatively smooth, flat, straight highway. In the discussion of this Table we Isolate for attentlon five specific block rows shown as rows "R," "G," "C," "GC" and "GCR" in Table 9.4 which serves as a "map" of Table 9.3. The top left hand row "B" (for "Base") gives the basis for cost comparisons which has roughness set to 2,000 mm/km (except for the Caribbean, 4,000 mm/km), rise + fall set to 10 m/km and curvature set to 1000 /km.

The block row "R" (for "Roughness") shows cost Increases as very rough routes (10,000 mm/km) are encountered on routes with good geometry. The row above this shows the effect of less extreme roughness. Generally cars are predicted to be particularly affected by roughness Increases, costs rising by from 60 to nearly 100 percent as extreme roughness Is encountered. Bus costs are predicted to be least sensitive to roughness, costs only Increasing by around 40 percent as extreme roughness is encountered.

The block row "C" (for "Curvature") shows the effect of Increasing curvature from 1000 /km to 5000 /km, which represents quite a sinuous route, on flat highways with good paved surfaces. The Brazilian study equations predict a moderate increase in costs, 15-20 percent for cars and trucks, but the other studies suggest increases of only around one-third to one-half of this. The relatively large curvature effects predlcted by the Brazilian study equations come largely through large predlcted speed reductions (around 25 to 30 percent) which, under the assumptions made, lead to increases in depreciatlon, interest, and crew costs per kilometer. Of course the constant hours driven and the appropriateness of the vehicle value age equations are crucial here.

The row "G" (for "Gradient") in Table 9.3 shows the effect of Increasing rise + fall on a smooth, relatively stralght route. All the studies predict very small effects on car costs, largely because car speeds are generally found to be Insensitive to all but severe gradients. The effects on buses and trucks are more marked. The Brazilian and Indian studies reach close agreement on the effect of gradient on bus costs, predicting an increase In costs of around 25 percent as average rise + fall increases from 10 m/km to 50 m/km.

The row "GC" (for "Gradlent" and "Curvature") allows us to obtain some idea of the effects of moving from highways with good geometry In plain areas to typical mountainous terrain. The row "GC" corresponds to a smooth route wlth quite severe vertical and horizontal geometry. Indian car costs are relatively unaffected. The Brazilian and Caribbean studies suggest similar effects, but the low utilisatlon assumed in the calculation of Caribbean cost tables makes comparison difficult. But costs are predicted to be around 35 percent higher on this steep and Table 9.3: Predicted Ratios of Costs Including Taxes on Highways with Given Characteristics to Costs

on Highways with 2,000 mm/km Roughness, 10 m/km Rise + Fall, and 1000 /km Average Degree

of Curvature

_ Syvo CURVATURE : lo0/Ii CURVATURE: SW*1mI Roughnes I EN IR car ans k.dium Truck Atti car an Medium Truck Artie (mm/km) (m/km) . _ Truck Trwck India rmzai C_rlb4 Indi Braznd Inil BrCzil CaIbbean ii K BrZu CariWb,en lTnd Brazil C-abznr-B Czibb_ rall

Rb_ 2.8 1.00 1.00 1.00 1.00 1.00 1.0 1.00 1.00 1.00 1.00 1.21 1.10 1.08 1.0Q 1.06 1.14 1.10 1.15

Rism Pkl 6000 7.4 1.16 1.31 1.33 1.13 1.22 1.19 1.37 1.19 1.38 1.19 1.73 1.45 1.22 1.43 1.26 1.61 1.23 1.62 Fall-

1oo00 12.0 1.e0 1.91 1.89 1.34 1.53 1.45 1.80 1.32 - 1. 71 2.23 2.04 1.46 1.70 1.61 1.98 1.47 -

2000 2. 1.04 1.01 1.06 1.24 1.29 1.2z 1.42 1.21 1.49 1.06 1.22 1.10 1.33 1.40 1.36 1.56 1.38 1.58

ui ~~Rise r'a Pkla 6000 7.4 1.28 1.32 1.40 1.4? 1.48 1.84 1.J1 1.43 1.81 1.34 1.74 1.83 1.62 1.r3 1. 4 2.09 1.S0 1.96

50n/km

10000 12.0 1.93 1.92 1.8 1.66 1.62 2.02 2.24 1.88 - 2.13 2.12 2.11 2.06 2.37 2.45 1.2 _

ODprecation and Interestcost calculated using studies vehicl value - vehie ge equations. COSTS OF TRANSPORT SERVICES 325

Table 9.4: "Map of Table 9.3

su4fm OMVA1UE U CURVATURE 5iPkm

(mmlk,m) CAv a" Mmdiii.Truck Artic Cw a Mmiim Truck Allic

1ndiSMZk rbbmm kx. Smz i kazN C Tafmmbil Mi Brl Cl hWM BaI h dbAil C.a llil

Rl' -lllOR O WR B". OW ROnR ¢ C ".

am Fall OOtlO._ ___

lOmf/Im IO - R 0 W nR.

Al" 2010 OR W "Gi OR W "GCi

Plus

Fall __.___

bami_ lOO R 0 W rGCRn

sinuous route. Articulated trucks' costs (obtained from the Brazilian study) are affected quite severely, as are Brazilian trucks generally. The lower right hand block row "GCR" (for "Gradient," "Curvature," and "Roughness") allows us to compare a rough road with poor geometry and a smooth, relatively flat,and straight route. For virtually all vehicle classes costs are predicted to be at least twice as high per kilometer on the poor quality route.

Table 9.5 summarizes some Illustrative calculations of costs per thousand kilometers using prices net of Indirect taxes of primary Incidence. The equations for car costs obtained In the Kenyan study could not be extrapolated to curvature as severe as 5000/km so the results for Kenyan cars relate to curvature of 1000 /km and 3000 /km. Prices net of tax could not be obtained for the Caribbean at the study date so no Caribbean study predictions appear in this sequence of tables. A direct comparison of the studies' predictions using prices net of tax can be gained by examining Table 9.6 which shows predlctlons of medium truck costs using the Indian, Brazilian, and Kenyan study equations. Fuel costs make up a relatively small proportion of total costs In the Kenyan truck predictions while crew costs are a relatively major contributor.

The effects of highway characteristics on costs are very similar, gross and net of taxes. Consider first row "R" which can be located using the "map" provided by Table 9.4. This row shows the effect of roughness. Large roughness effects are predicted by the Kenyan study car equations. Smaller effects are predicted using the Indian and Brazilian study Table 9.5: Predicted Ratios of Costs Excluding Taxes on Highways wlth Given Characteristics to Costs

on Highways with 2,000 mm/km Roughness, 10 m/km Rise + Fall, and 1000 /km Degrees of Curvature

CURVATURE: Suraose CURVATURE: 1olkm 300I/km CURVATURE 500S/km

Car Bus Medium Truck Crs Medium Truck Bl (mm/km )_ ._ __ __ .______.______(IRI(m/km)) Km" Indi Brazil Kenya Km"na Kenya India Braio KW"

2000 (2.8) 1.00 1.00 1.00 1.00 1.00 1.03 1.27 1.05 1.10 1.26 Rim______RPlus Fall 6W0 (7.4) 1.97 1.51 1.19 1.39 1.40 2.19 1.78 1.27 1.62 1.87

1000 (12.0) 2.78 1.90 1.48 1.85 1.71 3.07 2.20 1.63 2.09 2.25

2000 (2.8) 1.06 1.16 1.25 1.42 1.18 1.14 1.95 1.35 1.54 1.98 Rime _

Fal 600 (7.4) 2.05 1.73 1.53 1.82 1.59 2.39 2.66 1.72 2.05 _ 60m/km ______

0W000 (12.0) 2.88 2.15 2.03 2.30 1.91 3.31 3.26 2.37 2.52 _

Depreciation and interest costs calculat . using the studie" vehicle value-vehicleage equations (se Chapter 8) Table 9.6: Comparison of Cost Ratios for Medium Trucks Including and Excluding Taxes

Surface CURVATURE 100°/bun CURVATURE 500°/kn Roughness INDIA BRAZIL INDIA BRAZIL 81(mm/km ) (IRI(m/km)) Including Excluding Including Excluding Including Exdluding Including Excluding Taxes Taes Taxes Txes Taxes Taxes Taxes Taws

2000 (2.81 1.-1J 1.00 1.00 1.00 1.06 1.05 1.11 1.10

Plus FaN 6000 (7.41 1.19 1.19 1t37 1.39 1.26 1.27 1.61 1.62

10000 (12.0) 1.45 1.48 1.80 1.85 1.61 1.63 1.98 2.09

W 20o0 (2.8) 1.27 1.25 1.42 1.42 1.38 1.35 1.55 1.54 Rise _ _ _ Plus Fall 6000 (7.4) 1.54 1.53 1.81 j 1.82 1.74 1.Z2 2.03 2.05 50mtkm _ _

10000 (12.0) 2.02 2.03 2.24 2.30 2.37 2.37 2.45 2.52

Depreciation and interext costs calculated using the studies' vehicle value-vehicle age equations (see Chapter 8) 328 COSTS OF TRANSPORT SERVICES equations and prices including taxes. Roughness effects on bus costs are also predicted to be relatively high using the Kenyan study equations and prices net of taxes, costs nearly doubling as roughness increases from 2,000 mm/km to 10,000 mm/km. For medium trucks the Brazilian and Kenyan study equations predict rather similar roughness effects, costs Increasing by about 80 percent as extreme roughness is encountered.

The row 'C" shows the effect of increasing average degrees of curvature from 1000 /km to 5000 /km on a smooth flat route. The Kenyan study equations predict large curvature effects for trucks but not for cars. These are due to large predicted curvature effects on truck speeds. Note that the car results refer to a 3000 /km not a 5000 /km route because the Kenyan car equations cannot be extrapolated to extreme curvature. The row "RI indicates the effect of Increasing average rise + fall from 10 m/km to 50 m/km. As in the other studies the gradient effects are predicted to be small for cars using the Kenyan study equations. For trucks the results obtained using the Kenyan study equations are also qulte similar to those obtained with the other equations, costs being predicted to Increase by 18 percent. As in Table 9.3, costs more than double on moving to a rough, steep, and sinuous route, the effects on car costs being particularly severe.

So far we have examined cost predictions calculated using the studies' vehicle value - calendar age equations to produce estimates of depreciation and interest costs. As we noted In Chapter 8, unless these equations are well matched to the equations used to predict other costs, there can be problems In interpreting the predictions that result, which can be sensitive to the specification of vehicle age.

An alternative is to calculate all costs using the studies' running cost equations alone, regarding terminal running costs as equal to a vehicle age Invariant sum of running costs and depreciation and interest costs. Predlctions obtained In this way, using the OL method described In Chapter 8 are given in Appendix Tables A9.10 - A9.18 and summarised in Table 9.7. The same broad conclusions reached earlier concerning the contributions of components to total vehicle operating costs come through here. Fuel costs are a high proportion of total costs for Brazilian cars, for which tire costs are low, and fuel costs make up around 20-30 percent of total costs for Brazilian and Indian buses and trucks. As before the Caribbean predictions are Influenced by the low utilisation assumed in calculating these tables. For these vehicles, maintenance, depreciation, and Interest costs make up around 70 percent of total costs but for Indian and Brazilian vehicles, assumed to be achieving much higher utilisation, they make up less than 50 percent. Depreciation and interest cost per unit distance calculated by the OL method are sensitive to roughness because the method links these costs with maintenance costs which depend on roughness and because of the effect of roughness on vehicle speed. They are sensitive to vertical and horizontal geometry because vehicle speed, and thus utilisation, depend on these highway conditions.

For most vehicle classes the effects of highway conditions are less marked for costs calculated by the OL method, but the differences are rarely substantial. The Brazilian articulated truck predictions are more Table 9.7: Predicted Ratios of Costs InclUding Taxes on Highways with Given Characteristics to Costs on

Highways with 2,000 mm/km Roughness, 10 rn/km Rise + Fall, and 1000 /km Average Degrees of Curvature

Surfaeo CURVATUREIODOIlN CIJRVATURE500fl.rn Roughness~~Car Bus MediumTruck Atccar BsMdu rc ri

el IRI ______Truck ______-_ _ _ _ Truck

Brazil CaribbeanI Ini Brazil India iBrazi Caben Brazil IBrazil Caribbean Indi Brazil Ini BrzlCiben rzl

Rime 200 2. .0 1.00 1.00 1.00 1.00 I1.00 1.00 11.00 1.18s 1.04 1.06 1.06 1.06 1.09 1.04 1.10

Fall~ 60 {1. 33 1.35 1.12 1.18 i .s .7 1.24 1.33 11. 70 1.'40 1.20 1.36 1.30 1.56 1.29 1.50

iooco12.0 1.92 1.83 1.31 1.44 1,~441 1.75 j 1.34 t -[2.219 1.881 1.43 1.57 1.58 1.859 1.40-

L RI" 2000 2.8 1.01 1.04 1.22 i1.241 1.25 1.38 1.16 11.40 1.19s 1.09 .3 1.33 1.35 1.51 1.23 1.47

Fall 600 7.4 1.34 1.39 i1.43 1.451 1.51 1.76 1.40 1.88 1.71 1.44 1.57 1.61 1.70 1.94 1.48 1.60

1000012.0 1.93 ~1.68 1.7 1.9612.14 1.82 2.20 1.94 2.01 1.90 2.28 2.33 1.6.3-

Depreciation and interest coats calculated by solving for optimnalvehicle lives and evaluating terminal running coats (see Chapter 8). 330 COSTSOF TRANSPORTSERVICES affected than most, costs being predicted to be 80 percent higher on the worst case route than on the best case route by the OL method but 96 percent higher by the VA method. For most vehicle classes the differences are smaller than this.

9.2 TRANSFERABILITYAND USE OF COST EQUATIONS

We have now examined the studies' predictions concerning the influencesof highway conditions on costs of provision of transport services. While some similaritiesemerge there are evident differences in the studies' predictionsand in consequence those who need to predict the cost changes arising as a result of highway investmentsneed to choose amongst the equations.

Of course all the results presented earlier are estimates or predictions, the results of statistical analysis of what are not particularly large data sets, containing observations of what are generally rather variable costs. Many Influences on these costs went unmeasured In the studies and the measurements that were taken were far from perfect. Thus there are many dimensions to highway surface condition and geometry, summarised in just three measures In the analysis of the studies' data, and many features of vehicles and of the firms that owned them which one might expect to influence costs do not appear In the studies' equations. It would thereforebe optimistic to expect very close agreement between the studies' results, even if they were generated under broadly similar conditions.

However, It is evident that conditions were not similar In the study regions. Two major influences working to produce dissimilarity In the studies' results should be noted because they are relevant to the choice and use of the equations given earlier. They are vehicle design and the economic environment.

The costs of providing transport services depend upon the prices at which inputs are purchased and on the ways In which Inputs can be efficiently combined to produce transport services, that is on the production function. Changes in highway conditions lead to changes In this production function which maps from efficient combinationsof inputs to output, and it Is these changes that are the focus of, for example, the fuel consumptionexperiments that are reported In Part 11, In Chapter 5. The production function facing transport firms is also affected by vehicle design and technology,fuel and tire quality and similar factors. The production function facing the Indian firms studied by the IndianCentral Road Research Institute differed substantially from that facing the Brazilian firms studied by GEIPOT and their collaborators and we can expect these sorts of differences to be influential In producing differences in the effects of highway conditions on vehicle operating costs. For example, the relatively high powered Brazilian vehicles travelledmuch faster than Indian vehicles and on relativelyuncongested highways, and consequentlyexperienced more substantial speed changes on encounteringpoor quality surfaces. COSTS OF TRANSPORT SERVICES 331

Relative prices of Inputs to production are Important determinants of Input usage and of the response of costs to changes in the production function induced by changes In highway conditions, and price configurations did vary across the environments in which the results reported earlier were obtained, as noted in Chapter 3. To the extent that firms have flexibility In organising efficient production, that is to the extent that there are opportunities for substituting alternative inputs, one for another, different input price configurations will lead to different methods for organising production and, except in special cases, to different relative weights of the many inputs to the production of transport services. In practice firms do have flexibility in organising efficient production. Speeds, loads carried, vehicle capacities, engine specificatlons and hours driven are all adjustable. Maintenance activities can be adjusted and vehicle scrapping delayed or advanced. So In general we can expect to see differences in the contributions to total costs of the various inputs to the production of transport services when we compare costs In environments in which relative prices differ, differences which reflect price differences, but which also reflect choices concerning how to organise production.

When assessing the benefits to a highway investment it is the reduction In total transport costs per unit of output that arises that is of Interest. It is notable that in all the studies reported earlier little attention was paid directly to these total costs, the focus being rather on the component costs that make up the total. In general if changes in highway conditions lead to differential changes In the productivity of inputs to the production of transport services then firms faced wlth changes in highway conditions will reorganise their affairs so as to minimise the impact of highway deterioration and maximise the impact of highway improvement. This reorganisation, involving possibly changes in operating speeds, loads carried, dates for vehicle replacement, choice of vehicle type, and so forth - will be Influenced by the relative prices of Inputs to the production of transport services.

One route to predicting the impact on costs of changing highway conditions Is to measure the influence of highway conditions on the output achieved by efficiently combining inputs, that is, to measure the production function and Its response to changes in highway conditions, and to combine the resulting model of the production "technology" with an economic model of the cost minimising firm, an input to which will be information on the production function and the relative prices for Inputs that firms face. Given such a model we could then with some confidence produce predictions of the effects of highway conditions on costs In alternative physical and economic environments, though we would of course need to inspect the prevailing conditions closely to determine whether the assumptions underlying such a model could be reasonably maintained.

This approach has not been taken in the four studies reported In this book. Only in the case of fuel consumption have results been obtained which bear directly on the technological relationship between highway conditions and the productivity of an Input to the production of transport services. The other data that were collected give information about the effects of highway conditions on firms' uses of various Inputs, 332 COSTS OF TRANSPORT SERVICES other Inputs varying as firms adJust their manner of production so as to minimise costs. In general the effects of highway conditions on a given Inputs' usage will depend upon the prices of inputs, on the nature of the production function and on the effect of changes In highway conditions on all Inputs' productivities. While the results reported here do bear directly on the responses of Interest, they embody the influences of prices and generally the economic and technological environment In the locations and at the times at which they are obtained. To some extent the differences in the studies' predictions concerning the effects of highway conditions on vehicle operating costs are due to differences In relative prices of Inputs to production of transport services, as well as to differences in vehicle technology and design.

Other features of the environment are Important too. We have noted earlier the problems that arise when the Caribbean study's equations, derived from vehicles achieving only low utilisation, because of the sporadic and seasonal nature of demand for transportation, are applied In a high utilisatlon environment. When utilisation Is low cost components like fuel and tire costs are a relatively small proportion of total costs and this affects the sensitivity to highway conditions of total vehicle operating costs. In principle the cost equations and predlctions presented earlier are not freely transferable across space and time. Whether or not they produce good approximations Is a matter for empirical study and for careful checking In applications, and depends upon the extent to which firms can adjust thelr production processes and on the local conditions encountered compared to those prevailing when the four studies were performed.

In practice determining the technological relationships llnking Inputs to the production of transport services, and constructing a realistic model of firms' behaviour Is an enormous task and predictions of costs and the effects of highway conditions on them obtalned via this route are not available. And In practice planners need guidance on the sorts of magnitudes of cost reductions that can arise when highways are Improved. The results presented In this book can provide that guidance, so long as they are used with care. In this regard, the following points deserve mention.

First, it has to be accepted that, as noted earlier, all the results reported are estimates or predictions and are consequently subject to error. The equations cannot be expected to be helpful in ordering alternative Investment projects that yield rather similar cost savings. Second, since the equations all embody the effects of the technological and economic conditions at the times that the studies were performed, great care should be taken In applying them In radlcally different environments. Users would be well advised to check on the magnitudes of the cost differentials that the equations predict. In competitive environments this may be done by comparing prices charged for transportation on alternative routes that differ in terms of highway conditlons. With horizontal long run supply curves these prices provide a direct window on the marginal and average costs of provision of transport services. Third, the levels of costs reported In the studies cannot be taken to be representative of cost levels because the companies surveyed COSTS OF TRANSPORT SERVICES 333

In the studies were not chosen to be representative of vehicle operators generally in the countries in which the studies were performed. Users who require to predict cost levels as well as cost differentials are advised to calibrate the equations to local conditions.

A large number of results have been reported In the previous chapters. In practical applications only one set of equations can be used but how are users to decide which equations to adopt? To answer this we should note first that It makes little sense to mix equations, taking one from this study and one from that. As we have remarked, firms' policies are Influenced by the economic and physical environment In which they operate. Since within each study price relatives and other economic and physical conditions were approximately constant, each study's equations make up a coherent picture which Is lost If equations from different studies are mixed.

This leaves four sets of equatlons from which to choose and at this point the particular application that the user has In mind has to be considered. The argument so far In this section leads to the conclusion that one should use the set of equations obtained In the environment most closely resembling that In which the equations are to be used. That Is, that faced with Indian type conditions - relatively cheap labour, long lived vehicles, and vehicles of relatively old design, one should use the Indian equations, and so forth. While there is a good deal to recommend this argument, consideration does have to be given to the reliability and coverage of the studies' results. Thus It has to be recognised that the Kenyan and Caribbean studies were small in scale relative to those carried out In Brazil and India, particularly their user surveys. The Kenyan study pioneered the way for the three subsequent studies and made a major contribution to the study of road user costs. But the Information It provides Is relatively out of date and the base from which Its results are produced Is relatively small. The large effects for roughness for tire and particularly maintenance costs predicted by the Kenyan study equations should be treated with caution and the very substantlal effect for vehicle age on car and truck maintenance costs Is anomalous and unlikely to be generally applicable. The results obtalned from the Carlbbean are more up to date but the conditions that prevail there, on relatively small Islands with a considerable seasonal element In production and In transportation, are qulte different from those encountered In the majority of countrles where major highway investments are being made. Vehicle utilisatlon was very low on the Caribbean Islands at the time of the study and It Is likely that the study's maintenance cost equations reflect this. It would be unwise to use the Caribbean study's maintenance equations to predict maintenance costs for old vehicles except In applications In which utilisation Is expected to be low.

These arguments suggest that in many applications one will wish to use the Brazilian or the Indian studies' results. It Is without doubt the case that far greater resources have been devoted to the analysis of the Brazilian data, if for no other reason than that data collection was completed considerably earlier in Brazil. While the analysis of the Indian data benefitted from the experience of the Brazillan study, there Is doubtless more to be gained from further analysis of the Indlan study 334 COSTS OF TRANSPORT SERVICES data and the numbers that have been reported here are sure to be refined In the future. However, It Is likely that the Indian study equations reflect the broad features of the Indian data. One would need to have serious misgivings over either the quality of the Indlan study's data or the analysis of the data If one were to wish to use the Brazillan study equations to predict costs in India, or in conditions like those found In India, and there do not seem to be grounds for such misgivings.

So the user faces a choice. In many applications It will be most approprlate to use either the Braziilan or the Indian study's equations. In many respects they are quite similar and, as we have remarked one cannot expect to be able to predict costs to a very high degree of accuracy. The Braziilan equations reflect conditions In a fast developing, relatively rich country In which vehicles were generally of relatively modern design and operated on relatively uncongested roads and In which firms had considerable choice of vehicle specification. The Indian equations reflect conditions In a populous country with a highly developed rail transport system, relatively cheap labor, and a limited range of vehicles of relatively dated design operated on roads that were often congested and which carried heterogeneous traffic.

As we have seen earlier In this chapter, the conclusions from the studies concerning the broad effects of highway conditions on vehicle operating costs are In many respects qulte similar. Used with care their results can substantially Improve the quality of highway Investment decisions. COSTS OF TRANSPORT SERVICES 335

APPENDIX. TABLES OF TOTAL COSTS AND THEIR COMPONENTS

This appendix contains predlctions by user cost study and vehicle class of costs per thousand kilometers associated with fuel, lubricants, tires, maintenance, depreciation, Interest, and crew. The price Information for India was obtalned In personal communications wlth L. R. Kadayall, the Indian Road User Cost Study Director, and with E. Viswanathan, a member of the projects staff. The Brazilian price Information was obtained from staff at Empresa Brasileira de Planejamento de Transportes - GEIPOT. The Caribbean study price data were obtalned from staff at the British Transport and Road Research Laboratory, who recommended using for the Kenyan predictions price data published In Robinson et al. (1975) which describes an application of user cost equations to predicting costs on the Yala-Busia highway on the Kenya- Uganda border in the early 1970s at around the time at which the Kenyan user cost study was performed.

Calculations using the VA method are given In Tables A9.1 - A9.9. Calculations using the OL method are given in Tables A9.10 - A9.18. In all cases prices are Inclusive of taxes.

Cost components are calculated as follows.

Fuel Costs

Fuel consumption in liters per 103km Is predleted using the equations In Chapter 5, exploiting the vehicle speed equations of Chapter 4. The adjustments to normal operating conditions given In Table 5.1, Chapter 5, are applied and costs per 103km are calculated using the fuel prices (gasollne or diesel as approprlate) given In Table 9.1.

Lubricant Costs

Engine oil consumption In liters per 103 km is predicted using the equations In Appendix B of Chapter 5. The prices given In Table 9.1 are applied to obtain engine oil costs per 103km and these are Increased by 43 percent for Indian vehicles and by 25 percent for other vehicles to allow for consumption of transmission oils, grease, and other lubricants.

Tire Costs

Number of equivalent new tires per 103 km per vehicle are predicted using the equations presented In Chapter 6 and priced as In Table 9.1. The formulae used In the studies Incorporate costs associated with recapping.

Maintenance Costs

Ratios of parts costs per 103 km to new vehicle price are predicted using the equations in Chapter 7 and from these predicted labor hours per 103 km are obtained. These are costed at wage rates as given in Table 9.1 to give maintenance labor costs per 103km. Parts costs per 103 km are obtained by multiplying through by new vehicle prices (expressed 336 COSTS OF TRANSPORT SERVICES

In 105 monetary units), as given In Table 9.1. In all cases but one (the Brazilian car) the vehicle prices used for this exercise are those used to express the maintenance parts equations In the form (P/VP) in Chapter 7. Most of the cars observed In the Brazil study road user survey were small cars (e.g., VW 1300s). To provide a better comparison with the medium sized cars found In the other studies we have predicted parts costs using the price of the larger G.M. Chevrolet Opala (see Table 9.1).

Depreciation and Interest Costs

Two methods are used to calculate these costs. In Tables A9.1 - A9.9 they are calculated by using the vehicle value - age in years relationships reported in Chapter 8, and the vehicle prices given in Table 9.1 to derive vehicle values and per annum rates of flow of depreciation costs at a specified point In a vehicle's life. Note that we do not calculate depreciation costs over a one-year period, but rather the rates of flow of costs at the ages given, expressed In per annum terms. Interest costs per year are derived by multiplying vehicle values by 0.12, assuming a real discount rate of 12 percent per annum. Per annum interest and depreciation costs are then put onto a per thousand kilometer basis by dividing by vehicle utilisation, the product of vehicle speed (km/hr) and hours driven (103 hours per year). This Is the VA (value-age) method described In Chapter 8. Note that we specify both age In years and age in kilometers in making these calculations. The values used are reported in notes accompanying the tables.

Tables A9.10 - A9.18 are calculated using the OL (optimal life) method described In Chapter 8. Utilisatlon is specified as described above and the relationship between maintenance costs and vehicle age Is used to solve for vehicle lives. Terminal maintenance costs (per 103 km) then provide an estimate of the sum of maintenance, depreciation, and interest costs per 103 kilometers experienced by vehicles of all ages. A real discount rate of 12 percent per annum Is used here, as above. There Is no requirement to specify either vehicle calendar or kilometer ages In deriving costs using this method.

Crew Costs

Wages paid per year are calculated using wage rates given In Table 9.1 and the hours worked recorded in the tables In Section 9.2. Division through by annual kilometerage (103 km) gives crew costs per 103 km.

The Caribbean study maintenance parts equation for trucks cannot be extrapolated to roughness as low as 2,000 mm/km or as high as 10,000 mm/km. Consequently the maintenance parts predictions for trucks obtained using the Caribbean study equations refer to roughness of 4,000 mm/km, 6,000 mm/km, and 7,500 mm/km, the latter figure being close to the value of roughness at which the Caribbean maintenance parts equation starts to predict decreasing parts costs with increasing roughness. For similar reasons car maintenance costs are predicted using roughness set at 4,000, 6,000, and 10,000 mm/km. For both cars and trucks the other predicted cost components obtained using the Caribbean study equations refer to roughness COSTS OF TRANSPORT SERVICES 337 of 2,000 mm/km, 6,000 mm/km, and 10,000 mm/km. In a few other cases In the tables In this section It has not been possible to extrapolate to high roughness levels for particular cost components and predictions have then been made using a lower roughness level for the cost components that cause difficulty. Where this happens the roughness values used are recorded In notes to the tables.

Abbreviations Used In Tables A9.1 - A9.17

1. V : vehicle speed (km/h) 2. F : fuel costs (monetary units/103km) 3. 0 : lubricant costs (monetary units/103 km) 4. T : tire costs (monetary units/103km) 5. P : maintenance parts costs (monetary units/103km) 6. L : maintenance labor costs (monetary units/103km) 7. D : depreciation costs (monetary units/103 km) 8. I : Interest costs (monetary units/103 km) 9. C : crew costs (monetary units/103 km) 10. TOTAL : Sum of 2 - 9 (monetary units/103 km)

Figures In parentheses thus (23) Indicate that associated cost item makes up 23 percent of total costs per thousand kilometers. Percentages may not add to 100 because of rounding.

Figures In brackets thus : f1.36J indicate that ratio of costs on given route to costs on the base case route Is 1.36. The base case route has average roughness 2,000 mm/km, average rise + fall 10 m/km, average degrees of curvature 1000 /km. Where choices are available 2,000 mm/km routes are taken to be paved, 6,000 mm/km routes and 10,000 mm/km routes are taken to be unpaved. 338 COSTS OF TRANSPORT SERVICES

Cost Tables Caiculated by the VA Method TABLE A9.1 Predicted Vehicle Operating Costs: Cars, India 1978 Rupees per Thousand Kilometers, Including Taxes

Suuace CURVATURE 100I/km CURVATURE: 5D0°w/bn Ro ~~~iigns __rrlXfX_ 1------Bf(mm/km) V F ° P D ITOTAL VTAL {IRI(m/kmn) ) 2 I I

200 58 4 25 42 2 s80 873 479 29 25 59 42 87 71 86 877 Rlxe {2.8) _ (57) ( 3) ( 3) 79 1 7) 5) (10) 1 8) (10) (1.00] Rise ___] pkus 6400 451 30 50 116 63 109 89 107 J 1015 4 448 36 50 116 63 117 96 115 1041 Fail (7.4) (46) ( 3) 1 5) 111) ( 6) (11) I 9) (11) E1.1 . (43) 1 3) ( 5) M11) ( 6) (11) ( 9) (11) [1.19] lOm/kml 1un00() 493 38 97 | 228 93 162 133 159 1403 521 46 97 228 93 182 149 179 1495

(12.0) 29.3 135) C 2) ( 7) (16) ( 7) (12) (10) (11) [1.61] 26.1 (35) ( 3) ( 6) (15) 1 6) (12) (10) (12) E1.71]

2000 500 22 25 59 42 94 77 92 911 489 29 25 59 42 100 82 99 925 Rise (. 6) (55) (2) (3) (6) (5) (10) (8) (10) [1.04] (53) (3) 3) (6) 15) (11) ( 9) (11) [1.06] plus 6w00 361 493 30 50 116 63 132 108 129 1121 S530 36 50 116 63 144 118 141 1168 Fall (7.4) (44) i( 3) ( 4) (10) 1 6) (12) (10) (12) [1.28] (43) ( 3) ( 4) (10) ( 5) (12) (10) (12) [1.34]

(182.0 21.7 618 38 7 ~228 9 1 1 215-6725 1687 8.684 46 97 228S 3 255 209 | (12.0) j 137) il 2) jl 5) (14) |{ 6) (13) (11) 113) [1.93] 6(37) (2) (5) (12) 1 2554)(11) 214) [2 13]

Notes: (1) Tire coats predicted at roughness of 8000 BI mm/km. 9.5 IRI mn/kin (2) Hours drivn: 1500 per year, hours operated: 2000 per yer (3) Vehicle age: 2 years, 100000 km. (4) Pavemont width: 7 m. (5) 1 crew (6) Depreciationand interest costs calculatedusing the VA method TABLE A9.2 PredictedVehicle Operating Costs: Cars (Medium) Brazil 1976 Cruzelros per Thousand Kilometers, IncludIngTaxes

SurfhAe CURVATURE: 10/lmi - {CURVATURE: $lbnm Roughtnes__s __ _ _ _ 81(mm/km) V F O T P L D I C TOTAL V F 0 T P L D I C TOTAL (IRI(m/km)) __ 200 88 670 15 16is 0 32 42 29 226 1110 769 i0o15 16 32 61 4 330 1346 Rue (2.8) (60) ( 1) ( t) t 7) ( 3) ( 4) ( 3) (20) E1.001 (57) C 1) ( 1) ( 6) ( 2) t 5) |( 3) |(25) E1.211

pkus 6000 67.2 747 20 29 1 216 55 55 38 298 148 42.9 96 20 29 216 55 6B8 61 470 1925 Fall (7.4)16 (51) ( 1) ( 2) (15) ( 4) ( 4) ( 3) (20) [1.311 (51) ( 1) ( 2) (11) ( 3) C 5) ( 3) (241 [1.731 lam/km 10ooo 1 ) s89 25 5s 584 95 70 49 376 2125 1053 25 58 564 95 93 65 497 2470

(12.0) .2(41) ( 1) 3) (2T) 4) ( 3) 2) . ( 43)418)311911 ( 1) C 2) (24) ( 4) ( 4) ( 3) (20) [2.23]

2000 674 15 16 s0 32 44 31 1 234 1126 778 15 16 80 32 62 44 333 1380

Rise (2.8 85.7) (60) " ( 1)I 7) ( 3) ( 4) ( 3) (21) (1.011 60 (57) ( 1) 1) 6) ( 2) C 5) ( 3) (24) [1.23] O plws 600D 754 20 29 216 55 56 40 | 301 1471 995 20 29 216 55 87 61 467 1930 Fall (12.0) (51) ( 1) 2) |(15) ( 4) ( 4) ( 3) (20) [1.331 42.8 (52) C 1) ( 2) (11) ( 3) ( 5) ( 3) (24) [1.741 5OM/km~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ---- ____ 50m/km 104am(,) 53 0 874 j 25 58 I 554 95 71 49 377 2133 1402l06 25 5s 584 96 92 65 497 2476 (12.0) (41) (1) (3) 1(27) (4) (3) (2) (18) [1.921 (43) (1) (2)(24) (14) (3) (20) [2.233

Notes: (1) Tire costs predicted st roughnes of 6000 Bl (mm/km). 9.5 IRI m/km). (2) Hours driven: 1500 per year, hours operated: 2000 per yer (3) Vehicle age: 2 years. 100000 km. (4) 1 crew (5) 2000 mm/km roughnes is paved. 600o and 10000 mm/km is unpaved (6) Gross Vehicle Weight: 1.4 tonnes; Attitude: 0. For other Brazilian model variables, see default values in Appendix A.4. (7) Depreciation and interest costs caiculated using the VA method TABLE A9.3 PredictedVehicle Operating Costs: Cars, Caribbean 1978 Eastern Caribbean Dollars per Thousand Kilometers, IncludingTaxes

Surfaceo CURVATURE : 1000 /km CURVATURE :5000'11vn Boumhnekm L1D -T0_AL Roumhnems V F 0 T 0 IO T OA T P I C TOTAL

_RI(mkr) _I

2ls000( 5844 4 32 103 46 75 8 674 451 40 4 32 1103 4692 3 8 7 70 37

Fall (7.4) C9) ( 1) ( 7) (23) (10) (18) (17) (15) (1.33] ( 8) C 1) 77) (21) C 9) (19) (19) (16) (1.45] IOM/km10000 41 4 56 209 94 84 82 12 642 39 4 56 209 94 101 100 87 680 (12.0) (5.6) C 1) ( 9) (33) (15) (13) (13) (11) (1.89] 462 6) C 1) C 8) (30) (14) (15) (14) (13) (2.04]

2.oOo4) 598 53 4 7 50 23178 77 67 358 50.s 4 7 50 23 93 92 so 398

IRise (2.8) - (14) ( 1) ( 2 ) (14) (6) (22) (21) (19) (1.06] (13) ( 1) I(22) 1(13) C 6) (23) (23) (20) 1[11.18)

C~plus 6000 52 41 32 1103 46 1(83 82 71 473 49 4 32 103 46 100 s8 85 517 -~Fall (7.4) 54 1) 1) 7~) 2 (10) (8) (17) (15) (1 40] 468 9 C 1) C 6) (20) C 9) l(19) I(19) (16) (1.53] 50rn/km 110000) 51 4 56 29 94 88 87 76 665 19 4 56 209 94 18 16 92 718 (12.0) 529 ( 8)(1 (14 (13) (13) C1 [1.98] . j7) 1 (8) (29) (13) (5 (1)(13) (2.12]

Notes: (1) Hours driven: 350 per year, hours operated: 500 per year (2) Vehicleage: 2 years, 40000 km. (3) 1 crew (4) Predictionsof maintenanceparts and laborcosts at 4000, 6000 and 10000 mm/km roughness (5) Depeciationand interestcosts calculated using the VA method TABLE A9.4 Predicted Vehicle Operating Costs: Buses, India 1978 Rupees per Thousand Kilometers, IncludingTaxes

Surfce CURVATURE 100D/km | CURVATURE : 5lO/kan Roughnes --- r ------E9(mm/km) V F P L D I |C TOTAL V |F ! T P L D I C TOTAL (IPd(mtklm))

2000 384 38 1 1951 123 42 91 146 136 1155 381 38 215 138 44 97 156 145 1214 Rbse (12.8) (34) ( 3) (16) (11) 1 4) 8) (13) (12) [1.W] 3(32) C 3) 1(17)(11) (4) 1 8) (13) (12) [1.06] plus G6000 392 42 215 152 55 110 177 164 1307 396 42 255 170 58 118 191 177 1407 42.6 39.5 Fall (7.4) (30) ( 3) (16) (12) ( 4) C 8) (14) (13) [1.131 (28) ( 3) (17) (12) ( 4) ( 8) (14) (13) [1.22]

lOin/km 130000 424 46 254 188 72 138 223 207 1552 33.8 30.7I 441 46 294 210 76 152 245 228 ISM (12.0) (28) ( 3) (16) (12) C 5) ( 9) (14) (13) [1.341 (26) 3) 1(17) (13) ( 5) 9) (15) (14) [1.46]

2000 40.8 | 452 43 254 161 48 115 184 172 1429 459 43 294 181 so 124 200 186 1537 (2.8) (32) C 3) (17) (11) j( 3) (8) (13) (12) (1.24] 1(30) (3) (18) (12) (3) |8) (13) (12) [1.33] plus 6800 492 47 293 199 62 147 236| 219 1695 513 47 352 223 66 163 261 243 1868 Fall (7.4) 19 29) 3) (17) (12) 4) 9) 1(14) (13) [1.47 8.8 (28) 3) 18) (12) 4) 9) (14) (13) [1.62]

SOn/kin |10000 23.1 584 51 | 353 |246 82 203 326 303 2148 | 636 51 430 275 86 234 376 350 2438 ( {12.0) 1 (27) I(2Z) 116)i 6(12)( 4) 1(10) (15) (14)1 [1.861 (26) 1(2) (17) 111) ( 4) (10) 111) 114) t2.11]

Notes: (1) Hours driven: 2500 per year, hours operated: 2500 per year (2) Vehicleage: 5 years, 500000 knm. (3) 2 crew (4) Gross vehicle weight: 10 tonnes; Power to weight: 8.4 kw/tonne; Road width: 7m. (5) Depreciation and interest costs calculated using the VA method TABLE A9.5 PredictedVehicle Operating Costs: Buses,BrazilI 1976 Cruzeirosper ThousandKilometers, Including Taxes

0 CUJRVATURE: 500 11kn Surface -- --- CURVATURE :100,/km Roughness ' - - - I. 1 -1-- L Df I C TOTAL BI(mmlkm) V F 0 T P L D I C TOTAL VIF 0 T P (IRI(m/km))

3 0 62 10 12 14 4 11 I2(1) 413 37 260 362 140 123 86 312 7331 37 3 36 40 12 14 12 10 (2.8) 11723154.6 C7) (9) (6) (22) t[1.09] (24) ( 2) (16) (21) (8) ( 7) ( 5) (18)i(1[00] (20) (2)1 (16) (19) (2.8) ~ 4-- - -- .--v-- Rise ______-- 416 40 39 469 23 236 166 598 2513 plus I6000 5. 400 40 302 469 239 163 114 (411 [2138 376 (17) (2) (14) (19) (10) (9) (7) (24) [1.43] Foil (7'.4) (19) ( 2) (14) (22) (11) (68) ( 5) (19) (122] ------_ ]67 47 _ ------607 407 255 179 647 2978 Il0m1km loom 223.6 4 -T(49 67 40 203516 120o 3. 444 43 396 (1) (3 2)(4 ) 6 2)1-0 {12.0) (16) ( 2) (13) (23) (15) ( 8) C 5) (19) (11.53] (15)

(1) 2) 1)6_ (9) (6) (22) [1.40] Rise

579 40 606 469 239 261 163 660 3097 plus 600OD 571 40 490 469 239 204 144 517 2674 Fall (74) ~~~3.534.1 (19) C1) (20) (15) (8) (9) (6) (22) [1.73] Fall (7.4) ~ (21) C1) (18) (I8 I ) (8) (5) (19) (1 53] 50m/km - t ~f 43 792 607 407 276 194 701 3619 I I I 565 43 606 607 407 235 1165 597 3245 599 ____(17)~ 1) j(22) '(17') '(11) 8) 5) (19) [2.06] (12.0) (1"j8) (1) (19) [(19) 10) 7 5 (8 [1.86]

Notes: (1) Hours driven: 2500 per year, hours operated: 2500 per year (2) Vehicle age: 5 years, 500000 km. (3) Tire size: 10.00 x 20 (4) 1. 5 crew (5) Gross vehicle weight: 11 tonnes; Attitude: 0. For other Brazilian mnodelvariables, see default values in Appendix A.4. (6) Depreciation and interest costs c-alculated using the VA method TABLE A9.6 PredictedVehicle OperatingCosts: Medium Trucks) India 1978 Rupees per Thousand Kilometers, IncludingTaxes

Surface CURVATURE 1009/kmn CURVATURE : 5tO°/km

8R(u9mmnk) V FT 1 F 0 T P L D I C TOTAL (IRI(m/km)) i i - _

2000 4Y.3 4161 32 259 78 36 153 238 197 1409 416 32 262 78 36 167 260 216 1487 RiB (2.8) (30) 2) (18) 1( 6) ( 3) (11) (17) (14) [1.00. (26) ( 2) |(18) ( 5) 2) (t1) (16) (15) (1.06] plus 6WO 39 PIUS 6000 ~~39. 7 | 432 34 307 138 I 58 182 284 235 1670 442 34 331 35 31 18138 562.7158 2t2 316 2661 17te Fall (7.4) (26) 22) (18) | 8) ( 4) 16 10Fai 1I0 2 4I 3 4 (11) (17) (14) [1.116 (25) ( 2) (16) ( 8) (3) (11) (18) (15) E1.26 6 41 8 )(1 (16 (1)(.6 iowo 1 470 36 331 1 244 9a3 225 351 291 2041 498 36 401 244 93 257 401 332 2Z26 {12.0) 3 (23) 3) (16) |12) 5) (11) (17) J( (14) (1.45] 26.1 (22) ( 2) (17) (11) ( 4) (11) (18) (16) (1.61] 200 366 499 56 354 78 36 197 306 255 1783 515 56 401 78 36 222 346 286 1940 (2.8) (2)8_ C 3) (19) (4) 2) (11) (18) Rim29.0 (14) (1.27] (27) ( 3) (20) ( 4) ( 2) (12) (18) (15) (1.38] 2. I @ PuRlus 6000 2 550 | 58 401 138 58 249 3S9 3Z2 2165 566 56 495 138 56 2S9 451 373 2450 b Fail (7.4) |(26) C 3) (18) C 6) ( 3) (12) (18) (15) [1.54] (24) ( 2) (19) ( 6) ( 2) (12) (19 ) t1.74] SOm/km 100001 21 4 651 ;, 602 4Sl95 2 939 338 527 436 2644 738 60 612 244 93 41S 648 535 3346 (I12.0) 2 ,(23) 2) (17) ( 9) 3) 1(12) (19) (15) t2.02] 1.4 (22) ( 2) (18) j 7) ( 3) (13) (20) (18) [2.37] ______I i w L Notes: (1) Hours driven: 1500 per year. hours operated: 2000 per year (2) Vehicle age: 3 Yars. 2000D0 km. (3) 2 crew (5) Gross vehicle weight: 13 tonnes; Pavement width: 7m; Power to weight: 6.5 kw/tonne. (6) Depreciation and interest costs calculated using the VA method TABLE A9.7 Predicted Vehicle Operating Costs: Medium Trucks, Brazil 1976 Cruzelros per Thousand Kilometers, Including Taxes

Surface I CURVATURE: 10°/kin CURVATURE 5000/lwn RoughnesuI K~ 8(m/kan) V F 0 T P L D I C TOTAL V |F 0 T P - D r, C 1QTAL {IRI (m/km ) }

I - .. - - - ______2000 644 Sal 40 280 194 104 129 85 466 18S 48.8 10 40 302 194 101 1 1CS 601 207 (2.8) (29) ( 2) (15) (11) ( 6) ( 7) ( 5) (25) ( 41.00] (25) ( 2) (15) (10) ( 5) C 6) ( 5) (30) [1.11] Rise - - __ _ _ _._- plus 600D 48 53757 47 3I2 544 178 171 t11 616 2616 34 5157 47 349 544 178 239 155 t6S 296 Fail ! (7.4) (21) ( 2) (12) (22) ( 7) ( 7) ( 4) (25) (1.37] (20) ( 2) (12) (19) ( 6) ( 8) ( 5) (29) (1.61] lOm/km_ __ 10000 370 5868 56 349 894 230 225 147 811 W00 30 S 6 56 396 694 230 26S 176 971 3618 (12.0) (18) ( 2) (11) (27) ( 7) ( 7) ( 4) (25) [1.80]. (17) t 2) (11) (25) ( 6) ( 7) C 5) (27) [1.98] C' __ I_ .__ _

120s 100 42.9 8US 40 420 194 104 194 127 69U 26 6Y65S35 40 490 194 104 222 145 600 2681 (2.8) (32) t 2) (16) t 7) 1 4) C 7) ( 5) (27) [1.42] (30) ( 1) (17) ( 7) ( 4) ( 8) ( 5) (26) 11.55] Rise I - - - . - ______Plus sa0 36.7 654 47 490 544 178 227 148 817 3305 300 8 47 606 544 178 277 181 1000 3711 Fail (7.4) ( 1(26)1) (15) (17) C 5) ( 7) ( 5) (25) (1.811 (24) ( 1) (16) (15) l 5) ( 7) ( 5) (27) [2.03] 50m/km - _ _ - ______1000 1 891 S6 611 w 23 269 17S gs8 40llS 9t412 S6 | S 894 230 303 ISO 10X14 44eo 1 10000 ~31.0 27.4 6 ~ 64 20 30 18IS 4 (12.0)| . (22) ( 1) (15) (22) ( 6) ( 7) ( 4) (24) 12.24] (20) ( 1) (18) (20) ( 5) ( 7) ( 4) (24) [2.45]

Notes: (1) Hours driven: 1500 per year, hoursoperated: 2000 per year (2) Vehicle age: 3 yer, 200000 km. (3) Number of tis: 6 (4) 2000 mm/km roughness is paved, 6000 and 10000 mm/km roughness is unpaved. (5) Gross vehicle weight: 14 tonnes; Altitude: 0. For other Brazilian model variables, se default values in Appendix A.4. (6) Depreciation and interest costs calculated using the VA method TABLE A9.8 Vehicle Operating Costs: Medium Trucks, Caribbean 1978 Eastern Caribbean Dollars per Thousand Kilometers, IncludingTaxes

0 0 ISurface f __ CURVATURE: 100 /km CURVATURE: 500 /km Roughness V F 0 T P L DII C TOTAL V F 10 T P L D I C TOTAL

(IRI(m/km)) ____

20W 51. 87 13 59 67 30 282 191 78 807 48 84 13 59 67 30 32 2 a 6 Rise (2.8) (11) C2) ( 7) (8) ( 4) (35) (24) (10) (1.00] C 9) ( 1) ( 7) ( 8) ( 3) (37 (25) (10) [1.10] Rlus 6o 4. 85 13 90 119 54 308 208 85 9620. 83 13 so 49 54 30 23 S 9 Fall (7.4) C9) C1) ( 9) (12) C 6) (32) (22) C 9) [1.19] C 8) C 1) ( 9) C 5) C 5) (36)1(25) (10) [1.23]

tOm/km I __ - _ __ __ i0000(3) i43.1 83 13 119 131 59 338 228 93 1064 363 83 13 119 131 59 401 271 110 1187 (12.0) C8) C1) (11) (12) C 6) (32) (21) C 9) (1.32] ( ) CI1) I(10) C11) C 5) (34)] (23) ci) [1.47']

3 CA) _9=00( ) 445 173 13 59 67 30 327 221 so 980 172.71 59 67 301I366 2i1o i9 3 (2.8) (18) I) C6) C 7) C3) (33) (23) ( 9) [1.21] ''(16) j(1) (5) (6) t ) 1(35)]1 (24) (10) [1.36] Rise 12 1 0 19 5 3124 19 19 Plus 6000 172 13 90 119 5436 245 99 1154 1 3 I 1 I 3 43 9 1 Fall (7.4) (15) (1) C8) (10) C5) (31) 1(21) (9) [1.43] (13) C1) C7) 1)4)(34)1(23)(9) [1.60]

1000(3 17 3 119 11 59 406 273 III 11283 22 175 13 119 131 59 49 337 1717 ______j ______0 (13) j(1) !(9) j(lO)j() (32) j(21) (9) [1.59] 9. (12) (1) (8) (9) 4 J(23) (9) [1.82]

Notes: (1) hours driven: 350 per Year. hours operated: 500 per year (2) Vehicle age: 3 years. 45000 km. (3) Maintenance parts and labor coats predicted at 4000, 6000. 7500 mm/km roughness. (4) All roughness settings for paved road. (5) 2 Crew (6) Gross vehicle weight: 12 tonnes; Power to weight 9.3 Bhp/tonne (7) Depreciation and interest costs calculated using the VA method TABLE A9.9 Vehicle Operating Costs: Articulated Trucks, Brazil 1976 Cruzelros per Thousand Kilometers, Including Taxes

0 Surface ! CURVATURE 1009/e CURVATURE: 500 /mbn iRoughness. f _ - Bl(mm/km) V F 0 T P L D i C TOTAL V F 0 T P L D I C TOTAL (IRI(m/km))____-

Rise 2000 .3 8 40 517 746 421 225 175 578 3670 42.8 S35 40 542 746 421 328 255 841 4168 8) ( 6) (20) [1.14] (PI^uIg 12.8)| (2fi) t 1) (14) (20) t12) ( 6) ( 5) (t6) 11.01 ! 4 24) ( 1) (13) (18) (10) (

t5 47 566 1281 56 354 120t1505 47 592 1288 560 523 407 1343 5961 Fallf lomfkm6000 ~ 396 7 561. 6 5 16 50h 26.8 n/km 0--21)( 1) (11) (25) (11) ( 7) ( 5) (l18) [1.38] 1 (20) ( 1) (10) (22) ( 9) ( 9) ( 7) (23) [1.62]

Rise 200 34.3 1844 40 641 746 421 48 ! 11050 5468 29.6 1854 40 690 7 421 4,3.| 369 1216 5aos o Plus (2.8) (34) 1) (12) (14) (8) ( 7) 6) (19) [1.49] (32) t 1) (12) !(13) 7) (8) (6) (21) [1.58] Fall iII omlkan 6 097 28,3 47 715 1288 560 49S 387 1271 6660E 1914 47 764 1288 560 606 473 1558 7210 5 (7.4) 3 ( 1) (11) 19) J 19) [1.81] . (27) ( 1) (11) i(18) |( ( 8)( 7) (22) (1.96

Notes: (1) Hours driven: 2500 per year. hours operated: 2500 per year (2) Vehicle age: 3 years, 200000 km. (3) 1.5 Crew at 24 Cruzeiros per hour. (4) Paved road operation at 2000 B1 mm/km, 2.8 IRI m/km. unpaved road operation at 6000 BI mm/km, 7.4 IRI m/km. (5) Maintenance parts and labor costs are derived by factoring the tractor costs by 1.33. (6) Number of tires: 18; Tire size: 11.00 x 22 (7) Gross vehicle weight: 40 tonnes; Altitude: 0. Other default values for the Brazilian model are given in Appendix A.4. (8)Depreciation and interest costs calculated using the VA method 348 COSTS OF TRANSPORT SERVICES

Cost Tables Calculated by the OL Method

In these tables the column headed P+L+D+I gives the sum of maintenance parts and labour costs and depreciationand Interestcosts. Since these costs are constant as vehicles age, under the assumptions underlying the OL method, no vehicle age Is specified In producing these tables. TABLE A9.10 PredIcteti Vehicle Operating Costs: Cars (Medium), Brazil

0 t Surace CtURVATURE: 100 7gwn CtRVATURE : 500klun Roughness 81 (mmlkm) V F 1 0. P+L+1 | C TOTAL| V 1 F O t I P+LD+l C TOTAL

i IRI(mflwn,) ______4 t______

2000 8 670 15 16 220 226 1147 76 15 16 227 330 1357

I t I; H ~~~~(2.8)- 158) (1) . 11) (19) } 120) ; 1. OtD] f ( 57)14 11) 11) (17) (24) [ 1. 18

i Rreplus r 6000 747 20 29 434 298 |S28 9m 20 29 445 470 1950 !ta|" I 67.2 i I 42.9 1 IOM/km (7.4) (49) (1) (2) (28) (20) (1.338 (61) (t) (1) (23) (24) (1.70]

I ~__ _ __ I 10000 ts36 25 877 376| 2204 i03,_ I_ 25 _ 5 84 . 497 2517 5I 87 53841 2 49 21 C., 53.2 I I I 40.2i 4% (12.0) 1 13. (3¢(3) (40) (17) (1.92] (42)! (1) (2) (35) (20) [2.19]

i 2000 1685.715 16 2201 234 1I159 778 15 16 227 333 law 857 1 ~~~~~~~~~~60.0! I {2.8) |) (58) (1) (19) (20) [1.01] j (57) ' (1) (1) (17) (24) [1.19]

Su; 6a 66.5 754 20 29 435 301! 1539 4. 529 445 467 1966

50m/km (7.4) (49) (1) (2) (28) (20) [1.34] (51) (1) (1) (23) (24) 1 .71]

t. _ _ .t1I l 100W 874 25 58 877 377 1 2211 10160 25 5e 864 497 2524 53.0O| j| i4.2i (12.0) (40)1 (1) (3) j (40) (17) [1.8193 4 (42) (1) (2) (35) | (20)1 [2.20]

Notes wee Table9.4

OreWftlon and interest coatscalculted using the OL methcd TABLE A9.11 PredictedVehicle Operating Costs: Cars (Medlituu),Brazil

I Surtace ~~~~~CURVATURE00/ CUJRVATURE:5W0Ihvn Roughness ~ J F O .++ EN(Mmlkm) I 0 T P+L+DI.1 c TOTAL V F 0 PLD TOTAL

2000 431 41 71 309 64~ 427 40 417 319 75 445 62.7 I53.1 [2.8) (10)1 (1) (2) (72' (15)1 (1.00] (9) i(1) (2) (72) (17) ( 1.04]

Rise plus 6=0 42 4 132 j 432 ST 57 '401 4 I32 442 go 598 fall 59.3 49.7 bin/km {7.4) 7) (1)1 (6) (75) (12)1 (1.35] 7) () () (74) (13) [1.40]

10000 41 4 56~ 612 72 785 39 4 56 623 87 O0M 55.8 146.21

I (12.0) C5) (1) (7) (718) ) [.3 ( 5) I(0) (7) (7) (11) E[1.89]

53 7j 312 671 443 50 4 7 323 s0 464. I ~~~~~59.8 (7)50.2 (2.8) (12) (1)1 (2) (15)1 [1.04] (I11) (1) I(2) (70) (1 7) [1. 09] fall 56.4 Ii46.8 50Cm/km (7.4) (9) (1)1 (73) 1 (12) [ 1.39] (8) (1) (5) (72) (14) [ 1.44]

10000 51 4156: 615 749 4 56 627 92 m2 I()()(12.0) (6) (1)1 (7) (77) (9) [1.89] ls () 7 (76) (11) [ 1.94]

NoWe am Tabe .95

Depciamon and intre.t ODAt calculated using the 01 method TABLE A9.12 Predicted Vehicle Operating Costs: Buses, India

0 Surface LCURVATURE: IODO km CURVATURIE 50,00 1km IRoughnessII St(mm/km) i V F 0 T P+L+D+I, C 'TOTAL V F 0 T C+++ OA IRI(m/km) PLO ~ OA

2000 384 38 196 406 136 1159 381 38 215 436 145 1215 51.448.3I (2.81 (33) (3) (I17) (35) (12) 1(1.00] (31) (3) (18) (36) (12) (1.05]

Riset plus ~~~6000 2 1 I9 486 164 1299 396 42 255 524 177 1384 Fall ~~~42.639 2 2539.5 Fafmlkm (7.4)1 (30) (3) (17)1 (37) (13)1 11.12] (28) (3) (18) (38) (13) (1.20] - 10 ~~~~~~~~46 20 53441 ~~42446 294 643 228 i1652

33.8 3. {12.0) (28)1 (3) (71 (39) I(14) (1.31] (27) (3) (18) (39) (14)1 (1.43]

2000 452 43 1 2154 I497 172 1418 45 3 294 537 186 1519 (2.18) 32) (3) (18) (35) (12) (1.22) (30) (3) ( 18) (35) (12) (1.31] plus 6000 492 I47 293 609 219 i1660 513 47 352 666 243 1820 Fall 31.9' 28.8 (8~(7 50 rn/km (7.4) (30)' (3) (18) (3) (13) (1.43] (28)1 (3) 1) (37) (13) [157

10000 584' 51 353 777 303 2068 8680N 350 2335 (12.01 (28)1 (2) (17) (38) (15) (1. 78]j j(27)'(2) I(81 (37) (15) L2.01)

Notes See Table S. 6 DWeprcatmonand interest costs calculated using the 01 method. TABLE A9.13 Predicted Vehicle Operating Costs: Buses, Brazil

Surface CURVATURE 100°/kmn CURVATURE500°/km Roughness - . , I_ Bi (mm/kmn) V F 0 | T P+L+D+l C TOTAL V F 0 T P+L*D+I C TOTAL IRI{m/kmn)

2000 413 37 280 846 312 1888 381 37 302 875 412 2007 72.1 54.6 (2.8) (22) (2) (15) (45) (17) t1.00] (19) (2) (15) (44) (21) [1.06]

Rise plus 6000 400 40 302 1081 411 2234 416 40 M9 1138 SW 2541 Fadl 54.7 37.6 10 m/km (7.4) (18) (2) (14) (48) (18) [1.18] (16) (2) (14) (45) (24) [1.35]

10000 422 43 349 13S6 516 2726 444 43 396 1434 647 2964 43.6 34.8 (12.0) (15) (2) (13) (51) (19) [1.44] (15) (1) (13) (48) (22) [1.57]

2000 557 37 420 8Q5 444 2343 560 37 490 908 515 2510 50.6 43.7 (2.8) (24) (2) (18) (38) (19) E1.24] (22) (1) (20) (36) (21) [1.33]

Rise plus 6000 571 40 490 1112 517 2730 579 40 Ms 158 660 3043 Fall 43.5 34.1 50 m/km 17.4) (21) (1) (18) (41) (19) [1.45] (19) (1) (20) (38) (22) [1.61] -I~~~6-6 9 _F4 10000 SW 43 1419 597 3250 599 43 792 1451 701 3586 37.7 32.1 (12.01 (18) (1) (19) (44) (18) (1.72] (17) (1) (22) (40) (20) [1.90]

Notes See Table9.7 Dsprcciaion and interest costs calculated uing the 0L method. TABLE A9.14 Predicted Vehicle Operating Costs: MediumnTrucks, India

Surfce CURVATURE: 100°/kmn CURVATURE500S /km Roughness _ - - _ EN (mm/km) V F 0 T P+L+04i C TOTAL V F 0 T P+L+D.I C TOTAL IRI (m/km }

200W 416 32 268 446 S197 1352 416 32 282 472 216 1418 47.3 43.3 (2.8) (31) (2) (19) (33) (15) (1.00] (29) (2) (20) (33) (15) (1.05]

Rise plus 6000 432 34 307 596 235 1604 442 34 331 628 316 1752 Fall 38.7 36.7 10 m/km (7.4) (27) (2) (19) (37) (15) [1.1]9 (25) (2) (19) (36) (18) (1.30]

W 10000 470 36 331 825 291 1953 498 36 401 874 332 2141 cn 32.1 28.1 (12.0) (24) (2) (17) (42) (15) [1.441 (23) (2) (19) (41) (16) [1.68]

20W0o 3 499 56 354 526 255 imO 515 56 401 570 286 1828 36.6 32.6 (2.8) (30) (3) (21) (31) (15) [1.26] (28) (31 (22) (31) (16) (1.36]

Rism plus 6CC0 550 56 401 708 322 2040 so. 56 486 7eo 373 2294 Fall 29.0 25.0 50 m/km (7.4) (27) (3) (20) (35) (16) [1.51] (26) (3) (22) (34) (16) [1.70]

100W0 651 60 495 1006 436 2646 781 s0 612 1141 536 3087

(12.0) _ (25) (2) (19) (36) (16) l1.96] (24) (2) (20) (37) (17) [2.26]

Nse- :S s rTble 9.6 D.peMmm and kied cms cal=ulted umfM the OL mwthod. TABLE A9.15 Predicted Vehicle Operating Costs: Medium Trucks, Brazil

Surface CURVATURE : 100O/kn CURVATURE 500°/km Roughness Ru(mm/km) V F a T P+L*D+l C TOTAL V F 0 1 P+L+DlI C TOTAL IRI(m/km) . _ _

2000 531 40 280 577 466 1894 510 40 30Z 60 601 2065 64.6 49.9 (2.8) (28) t2) (15) (30) (25) t1.00] (25) (2) (15) (29) (29) (1.09]

Rise plus 6000 537 47 302 1087 616 2589 575 47 349 1125 859 2955 Fall 48.7 34.9 10 m/km (7.4) (21) (2) (12) (42) (24) [1.37] (19) (2) (12) (38) (29) [1.56]

(A) 10000 5s8 56 349 1510 811 3314 626 56 196 1533 971 3582 oh 37.0 30.9 (12.0) (18) (2) (11) (46) (24) E1.75] (17) (2) (11) (43) (27) [1.89]

2000 n28 40 420 622 699 2609 836 40 490 645 850 2861 42.9 37.5 (2.8) (32) (2) (16) (24) (27) [1.38] (29) (1) (17) (23) (30) [1.51]

Rise plus 6000 654 47 490 1118 817 3326 878 47 6W6 1149 1000 3680 Fall 36.7 30.0 50 m/km (7.4) (26) (1) (15) (34) (25) [1.76] (24) (1) (16) (31) (27) [1.94]

l10000O 89 56 606 1533 968 4054 912 56 792 1552 1094 4406 31.0 27.4 | (12.0) (22) (1) (15) (38) (24) [2.14] (21) (1) (18) (35) (25) t2.33]

NoW See Table9. 9. DOepeciatn and interest costs calculatedusng the 01. method. TABLEA9.16 Predicted Vohicle Operating Costs: Medium Trucks. Caribbean

0 Surface CURVATURE : 100/krn CURVATURE 500 /km

Roughness - - - _ EU (mmlkmn) V F 0 T P+L*D+I C TOTAL V F 0 T P+L+O+i C TOTAL IRI(rm/kmn) t - ___-

2000 87 13 59 577 78 814 84 13 59 606 as 850 51.6 44.8 (2.8) (11) (1) (7) (71) (t10) 1.00] (10) (2) (7) (71) (10) [1.04]

Rise plus 6000 85 13 90 734 85 1007 83 13 so 764 99 1049 Fall 47.3 40.5 10 mr/km (7.4) () (9) (73) (8) [1.24] (8) (1) (9) (73) (9) [1.29]

10080 _ 83 13 119 779 93 1087 83 13 119 817 110 1142 (112.0) 43.1 36.3 (8) (1) (11) (72) (9) [1.34] (7) (1) (10) (72) (10) [1.40]

2000 173 13 59 606 90 941 172 13 59 648 105 988 44.5 37.7 (2.8) (18) (1) (6) (64) (10) (1.16) (17) (1) (6) (65) (11) [1.23]

Rise plus 6000 172 13 90 765 99 1138 172 13 90 812 119 1206 FaIl 40.3 33.5 50 r/km (7.4) (15) (1) (8) (67) (9) [l.401 (14) (1) (7) (67) (10) t1.48]

10000 172 13 119 819 111 1234 175 13 119 882 137 1326 36.0 29.2 (12.0) (14) (1) (10) (66) (9) [1.52] (13) (1) (9) (67) (10) [1.63]

Notes S"eetable 9.10. DWpraoiaton and interest cost, calulaed usng the 0X method. TABLE A9.17 PrsdictedVehicle operating Costs: ArticulatedTrucks. Brazil

Sajrfece ~~~CURVATURE:IWO/Im CURVATURE500J/W Roughness I Si (mm/kmn) V F IT -- D1V TOA F 0 T P'+L.D44 C TOTAL

IRI(m /Iun)__ _I______

- ~~~o 4 Sr 14 78134'95 40 1542 166 841 424

Rim ~~~(2.8) 1(25): 1 1) () (23) 42.844 (1) (19) (1. 10]

FallI 1Orn/km 6000 11075;47 15624 0 271201 47 an 274 1343 5w9 39.61 I I8 I74)(21) (1 01 (I)(311E1 CA) '-* 1 -r~~~~~~~~~~~~~~~~~~~~~171 3 (20 1) 10l(6

2000 1644 40 641 196 150 5537 1 1654 40 1Go 2010 1216 5610 34.3 I29.61 Rimse (2.8) (33) (1) (12) (35) i(19) [ 1 410] (32) (1) (112) (9) (21) [ 1.471

S m/km 1 6000 ilea? 477?15: 18~21 66511 47 76 2m0 m55m75

(7.4) (28)(iiil ) (ta (19) ( 1.69] M31Y(2) () (11) (40) (22) (1El.80] Notes :See Table 9.1II. Deprediation an neetcstcalculated using the OL method. ANNEX

Accidents

For a variety of reasons, a decision was taken early In the design of all four studies - Kenya, the Caribbean, India, and Brazil - to devote only limited attention to the study of accident costs, not least because the focus of these studies was rural low volume highways on which traffic interactions are relatively Infrequent. Accident costs, though large in aggregate - as much as 1 percent of GDP In some developing countries (Jacobs & Sayer 1983) - are a small component of the transport costs incurred by firms, especially those firms that operate on non-urban, low volume routes. The various factors that affect accident rates and severity are difficult to disentangle and It was felt that it would be unwise to spread the resources available to the four studies too thinly especially as large scale research on causes of accidents were already underway, worldwide. However, some small efforts were made in the Indian study and to a lesser degree in Brazil. In this appendix, we review the results that were obtalned together with other evidence concerning road accidents in developing countries.

The effects of highway Improvements on accident rates and on accident severity are complex and not yet fully understood, and there Is much debate over the appropriate methodology for costing accidents and valuing accident risk reduction. Jones-Lee (1976) provides a review. We present results concerning the relationships between accident rates and highway characteristics, drawing on the Indian Road User Cost Study (CRRI 1982), on work reported by the U.K. Transport and Road Research Laboratory (Macbean 1982; Jacobs and Sayer 1983) and on a literature survey carried out by John McLean of the Australian Road Research Board for the World Bank (McLean 1984). The Indian Road User Cost Study report gives estimates of accident costs and these figures and some results from the Brazilian study are reproduced here. Accident costs were not estimated In the studies carried out In Kenya and the Caribbean and accident cost estimates are not reported for these countries. It is not possible to give generally applicable figures with which to cost accidents, and in assessing particular highway Investment projects planners will need to obtain data with which to cost accidents that are relevant to the environment being studled.

There is very little empirical evidence to support relatlonships between accident rates or accident severity and highway characteristics that are relevant to non-urban travel In developing countries. Virtually all the available evidence relates to accident rates and little attention has been paid to accident severity. The results presented below suggest that accident rates may be lower on highways with higher geometric design standards. Care needs to be taken In Interpreting these results for, if vehicle speeds are higher on highways with higher geometric design

357 358 ACCIDENTS

standards, then the fewer accidents that do occur may be more severe and more costly.

Accurate prediction of accident rates requires detalled knowledge of highway conditions and in particular of the configuration of bends, gradients, Junctions, and so forth. The equatlons reported below express accident rates as functions of broad measures of average highway conditions - average rise + fall, average degrees of curvature and similar measures - In line with the vehicle speed equations given earlier Chapter 4. The equatlons give at best a broad Indication of accident rates on highways of different general types and they cannot be expected to give a good Indication of the benefits to Isolated highway Improvements. As will be seen the relationships avaliable give somewhat different predictions of the effects of gradient and curvature on accident rates and If the equations given here are used, they should be used with caution.

We start by considering the Indian study which reports two Investigations Into accident rates, one obtained by comparing variations In accident rates with variations In highway characteristics along the length of a single highway, the other obtained by comparing accident rate variations across routes with across route variation In highway characteristics. In the first Investigation accident rates at 114 one- kilometer long sections of the 157 kilometer long Bombay-Pune highway were obtained, each observation being an average of from one to three years data derived from pollce records. This highway passes through both plain and hilly terrain and for each one kilometer long section average rise + fall, average degrees of curvature and number of Junctions per kilometer were recorded. The route carries around 1.7 milion vehicles per year, about 10 percent of which Is slow moving, animal or man-powered traffic, and of the total traffic around 60 percent Is commercial traffic. The accident data Include all reported accidents Including those In which there was no personal Injury. The equation given below was estimated by ordinary least squares.

(1) AA - -.66 + .093RF + .013C + 2.07J (4.27) (6.42) (5.51)

R2 _ .80 S - 1.83

(ratios of coefficlents to standard errors In parentheses),

where: AA - total reported accidents per km per year.

RF - average rise + fall (m/km)

C - average degrees of curvature (0 /km)

J - no of Junctions (Junctions/km).

The means and ranges of the explanatory variables are shown In Table A.1. ACCIDENTS 359

Table A.1: Means and Ranges of Explanatory Variables: Equation (1)

Variables Mean Min Max

RF(m/km) 11 1 58 C(0 /km) 65 0 710 J(no/km) 2 0 6

Source: CRRI (1982).

Using the average annual traffic figure given above and information concerning the proportion of accidents Involving personal inJury (40 percent on this highway), this equation is converted (see CRRI 1982) to give the following relationship for personal Injury accidents per 106 vehicle kilometers (Ap):

(2) Ap - -.15 + .022RF + .0031C + .48J.

Evaluating (2) at mean values of the explanatory variables gives a predicted rate of 1.25 personal injury accidents per 106 vehicle kilometers. Increasing average rise + fall by 10 m/km from Its average leads to a predicted increase in the accident rate of 18 percent, while increasing average degrees of curvature by 1000 /km from its average, rise + fall held fixed, leads to a predicted increase in the accident rate of 25 percent. In the Indian study analysis traffic volume Is regarded as constant along the length of the highway though the possibility of local variation is noted. It seems likely that local traffic will be higher In the neighbourhood of Junctions - also, Junctions may be more frequent near to villages where there is likely to be relatively more slow moving traffic. Though these observations suggest that the coefficient on numbers of junctions per kilometer should be interpreted carefully, many Investigations In developed countries have indicated the Importance of the effect of this variable on accident rates.

The second investigation reported In CRRI (1982) compares average accident rates for the period 1976-80 on 34 routes varying in length from 9km to 509km, five of which are sections of the Bombay-Pune road considered above. Accident rates were obtained from police records and include accidents not Involving personal injury. For each route average rise + fall, average degrees of curvature, average pavement width, and number of junctions per kilometer were measured. Two sets of analyses are reported, one using accidents per kilometer as dependent variable, the other, accidents per vehicle kilometer. In CRRI (1982) the former are recommended, largely on the grounds that the goodness of fit "R2" statistics are higher when the dependent variable Is expressed as accidents per kilometer. However, it Is not meaningful to compare "R2" statistics 360 ACCIDENTS

from equations in which the dependent variables differ by a nonlinear transformation. Further It seems unreasonable to write the effects of gradient and curvature as independent of traffic volumes as Is done in the linear specification used In CRRI (1982) for the equation for accidents per kilometer. Consequently we report here equations for accidents per 106 vehicle kilometers (AA). None of the reported equations Include measures of both vertical and horizontal geometry, presumably because of multicollinearity in the data set, so we give two equations, one Involving average rise + fall, the other average degrees of curvature.

(3) AA - 1.50 + .00342C + .39J - .26W + 1.27T (4.14) (1.43) (-1.58) (3.34)

R2 _ .49 S - .765

(ratios of coefficients to standard errors in parentheses).

(4) AA - 0.19 + .0638RF + .55J - .12W + 0.96T (4.48) (2.00) (-0.73) (2.65)

R- .52 S - 743

where symbols are as defined as above and additionally:

W - Pavement width (m)

T - Annual traffic (106 vehicles per year).

The means and ranges of the explanatory variables are shown In Table A.2.

Table A.2: Means and Ranges of Explanatory Variables: Equations (3) and (4)

Variable Min Max Mean

RF(m/km) 1 45 17 C(0 /km) 16 727 159 J(no/km) 0 2.7 .73 W(m/km) 4 7 6.0 T(106 vehicles/yr) .14 1.73 .78

Source: CRRI (1982).

To convert to personal Injury accidents per 106 vehicle kilometers (Ap) we multiply through by .48 as recommended In CRRI (1982), obtaining ACCIDENTS 361

(5) Ap - .72 + .00155C + .19J - .13W + .61T

(6) Ap - .09 + .031RF + .26J - .06W + .46T.

Since curvature and rise + fall are positively correlated In this data set (r - 0.85) It Is likely that the coefficients on curvature and rise + fall given above are over estimates though we note that the curvature coefficient is smaller than that reported In equation (2).

Setting explanatory variables at their average values for the data set gives a predicted personal injury accident rate of around 0.81 per 106 vehicle kilometers. Increasing average rise + fall by 10 m/km from its average leads to a predicted Increase In accident rate of 38 percent. Alternatively, Increasing average degrees of curvature by 1000 /km from its average leads to a predicted increase in accident rate of 19 percent. While the rise + fall effect Is similar to that found In the Investigation of the Bombay-Pune road, the curvature effect is smaller.

These Indian study results are somewhat at variance with those reported by Jacobs (1976) and discussed In Jacobs and Sayer (1983). Using data from Kenya and Jamaica, Jacobs obtains the following equations for personal Injury accidents per 106 vehicle kilometers:

for Kenya:

(7) Ap - 1.09 + .031C + .062RF + .62J + .0003R

and for Jamalca:

(8) Ap - 5.77 - .755W + .275J

where symbols are as above and additionally:

R - Surface roughness, Bi (mm/km).

The coefficients In equation (7) are not particularly well determined but even so, the magnitude of the curvature effect relative to those obtalned in the Indian study Is noteworthy. Of course the Kenyan, Jamaican, and Indian environments are quite different and It may be asking too much to expect close agreement, particularly when the descriptive power of the average measures of geometry used In these studies Is recognised.

McLean (1984) surveys empirical results on accident-geometry relationships and presents results in the form of adjustment factors appilcable to roads deviating from some specified norm: The user Is expected to provide accidents rates for the base case road and then apply 362 ACCIDENTS adjustment factors multiplicativelyto obtain accident rates of Interest. Drawing on early German work by Bitzl (1957) reported In Highway Users Federation for Safety and Mobility (1981) McLean provides the adjustment factors given In Tables A.3 and A.4 to be applied to accident rates for flat, straight roads. It appears that all McLean's results refer to reported accidents includingthose not involvingpersonal injury.

Table A.3: Accident Rate AdJustment Factors for Grade

Grade (%) Adjustment Factor: KG

0 - 1.9 1.00 2.0 - 3.9 1.04 4.0 - 5.9 3.27 6.0 - 8.0 3.83

Source: McLean (1984).

Table A.4: Accident Rate AdJustment Factors for Curvature

Curve Radius (m) Adjustment Factor: Kc

> 4,000 1.00 300 - 4,000 1.20 200 - 300 1.33 100 - 200 1.78 < 100 2.13

Source: McLean (1984).

If AB Is the accident rate per vehicle kilometeron a near level, near tangent road, then the predicted accident rate, A, wlth grades or curves as specified Is given by:

(9) A - KC KG AB.

McLean comments that the factors given In Tables 4.29 and 4.30 will tend to underestimate the effects of grades and curves In Isolation. He also notes ACCIDENTS 363 that the tables are based on "limited, and somewhat dated, data," and that "they should be regarded as tentative values only."

Macbean (1982) analyses U.K. data on accidents at rural nonjunctIon sites. He finds no assoclation of accident risk with gradient but a positive correlation with curvature. Curvature effects are found to be small for curves with radius greater than 500 m but curves sharper than this are associated with "fairly abrupt Increases in risk." Macbean does not provide equations relating accident rates to curvature. On the questlon of the effect of road width on accident rates Macbean comments:

"Research results on the relationship between accident risk and road width are confusing. Certainly any effect of width is much smaller than that of curvature: the majority of those studies which have sought a relationship have failed to find one. The remainder are fairly evenly divided between those which find that accident risk decreases with increasing width and those which find the opposite. This study falls into the last group.' (Macbean 1982, p. 15.)

Table A.5, derived from McLean (1984)'s Table I and Figure 2, gives results of five studies In which the effects of travelled way width and shoulder width are considered separately. Users are required to specify an accident rate (accidents per vehicle kilometer), AB, for a road with travelled way width 7.2 m or greater and shoulder width 3m or greater. Predicted accident rates, A, are then given by:

(10) A - KTKSAB-

Table A.5 also shows base accident rates, AB, used In the five studles surveyed by McLean.

Table A.6 gives results from three studies in which total road width (including shoulders) Is used as an explanatory variable and is derived from McLean (1984). The table gives adjustment factors KR to be applied to base accident rates, AB, for roads with width less than 13.2m. Predicted accident rates are given by:

(11) A - KRAB-

Zaniewskl et al. (1981) In a report prepared for the U.S. Federal Highway Administration use data collected from 1975-78 by the Texas State Department of Highways and Public Transportation to examine the relationship between accident rates and the Present Serviceablilty Index (PSI), which Is a measure of highway surface conditlon closely (but Inversely) related to surface roughness. They conduct separate analyses for Inter-reglonal highways (class 1), U.S. and state highways (class 2), and for farm to market and ranch road highways (class 3). Regression analyses of accidents per mile and of accidents per vehicle mile suggest that on class 1 highways, accident numbers and rates Increase as PSI 364 ACCIDENTS

Table A.5: Adjustment Factors for Travelled Way and Shoulder Width

Base Accident Rate Travelled way width Shoulder Width (Accidents/vehicle adjustment: KT Adjustment: KS Study kilometers)_ l AB 6.5 0 1 2

Silyanov (1873) 1.0 1.8 1.6 1.4 1.3 1.1 _ 1.6 1.15 (various)

Jacobs(1976) 1.t 2.0 1.8 1.5 1.3 _ _ _ (Jamaica)(

Lelsch and .9 - 1.5 1.3 1.1 - - 1.05 Neuman (197S) (U.S.)

*~~~~- -_ - - -_ - !Jorgensen (1978) .6-1.3 - - 1.2 1.1 1 1.6 1.4 |1.1 I(U.S.) ______

Zegeer et al 1.1 1.8 1.7 1.4 1.4 1 1.3 1.3 1.05 (1981)(U.S.)

Source: McLean (1986).

Table A.6: Adjustment Factors for Total Roadway Width

RoadwayWidth Adjustment: KR

i Study 6m 8m 1om ; 12m

Leisch and _ 1.4 1.2 1.15 Neuman (1979)

(U.S.) ______

Jorgensen (1978) 1.7 1.4 1.2 1.05 1 (U.S.)

Zgeeretat 1.7 1.4 1.2 1 (1981) (U.S.)

Notes; For base accident rates used in studies (AB) seo Table 4.31.

Source: McLean (1986). ACCIDENTS 365 increase, that is as surface condition Improves. On class 2 and class 3 highways there is some evidence to suggest that accident numbers and rates decrease as PSI Increases. Zaniewskl et al. remark that

"The analyses In this study suggest that there Is a statistically significant relatlonship between PSI and accidents, but that the relationship is small, and the direction of the relationship depends upon which analysis approach one believes" (Zaniewski et al. 1981, p. 87).

They quote Tignor and Lindley (1981) as finding no statistically significant relationship between accident rates and pavement Improvements but some evidence pointing to increases in accident rates as pavements are Improved.

The cost of accidents and the value to be placed on reductions in accident risk vary across time and across countries. The Indian study reports data on accident costs. Their calculations lead to the figures reported in Table A.7.

Table A.7: Accident Costs: Indian Study

Cost per Accident (1978 Rupees)

Fatality 49,804 Serious Injury 29,510 Minor injury 321 Damage to buses 5,467 Damage to trucks 6,111 Damage to cars 1,200

Source: CRRI (1982).

The vehicle damage costs for buses and trucks are obtalned from 112 user survey vehicles Involved In accidents and Include repair costs and costs incurred because vehicles are unable to provide their normal service while being repaired. Car damage costs were collected from insurance companies. Minor injury costs are calculated as medical expenses plus loss of earnings. Serious injury costs are calculated as medical expenses plus legal expenses plus value of loss of output to the community as a result of hospitalization of disability. Fatality costs are calculated as value of loss of output plus a notional value for paln, grief, and suffering of relatives etc. plus medical and legal expenses.

Harrlson (1982) reports an exploratory analysis of accident data obtained from companies cooperating in the Brazilian study road user survey In which he finds no sIgnificant relationship between accident costs and average surface roughness. Information on accident frequency and accident costs Is given in Table A.8. Rows 1 - 3 of this table give details of 366 ACCI DENTS

Table A.8: Accident Costs: Brazil User Survey

Light Med Heavy Cars Goods Buses Trucks Trucks

1. No. of conpanies surveyed 4 2 10 5 3

2. No. of vehicles surveyed 129 16 230 30 12

3. No. of vehicles recording 54 11 182 21 12 accident costs

4. Total km travelled (103km) 10,605 4,584 23,942 2,286 789

5. Total km travelled by vehicles 5,283 2,702 19,118 1,801 789 recording accident costs (103km)

6. Total accident costs 105,000 114,000 1,471,000 40,000 44,000

7. Accidentcosts per unit 19.9 42.2 76.9 22.2 55.8 distance,vehicles recording accidents(1976 Cruzerios/10 3km)

8. Accidentcosts per unit 9.9 24.9 61.4 17.5 55.8 distance,all surveyedvehicles (1976 Cruzerios/103 km)

9. Accident costs per unit 19 13 18 4 6 distances as % age of maintenance costs excludilng accident costs

10. Accident frequency (km/accident) 80,000 142,000 70,000 82,000 29,000

11. Cost per accident 1,600 6,000 5,400 1,800 1,600 (1976Cruzerios)

Source: HarrIson (1982). ACCIDENTS 367 numbers of vehicles and companies sampled. Around half the vehicles sampled had experienced accidents during the survey period; some had experienced more than one. Average accident frequency Is recorded In row 10 and ranges from 1 accident per 29,000 km for heavy trucks to 1 accident per 142,000 km for light goods vehicles. Note that sample sizes are small for light goods vehicles and for medium and heavy trucks and that recorded accidents are all incidents leading to vehicle repair costs but that vehicles so severely damaged as to be written off do not appear in the user survey records. Consequently, the accident frequency and cost figures In Table A.8 should be regarded as underestimates.

Rows 7 and 8 of Table A.8 show accident costs per unit distance and row 9 gives these costs as a percentage of maintenance costs excluding accidents. These costs relate to repair costs only and do not Include costs associated with cargo damage, personal injury, or with the unavailability of vehicles during repair. I I I References

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I I I I I I t NW- The World Bank

The Highway Design and Maintenance Standards Series

To provide road design and maintenance standards appropriate to the physical and economic circumstances of developing countries, the World Bank in 1969 instituted the Highway Design and Maintenance Standards Study, which developed into a major collaborative research project with leading research institutions and highway administrations in Australia, Brazil, France, India, Kenya, Sweden, the United Kingdom, and the United States. The aims of the study comprised the rigorous empirical quantification of cost tradeoffs between road construction, maintenance, and vehicle operating costs; and, as a basis for highway decisionmaking, the development of planning models incorporating total life-cycle cost simulation. Controlled experiments and extensive road user surveys were conducted to provide comprehensive data on highway conditions and vehicle operating costs in radically different economic environments on three continents. The five volumes in the series represent the culmination of the 18-year endeavor, along with a computerized highway sector planning and investment model, currently in its third version (HDM-III). The first three volumes in the series provide theoretical foundations and statistical estimation of the underlying physical and economic relationships. The other two discuss the model and its use and are essential references for applying HDM-III.

Vehicle Operating Costs: Evidence from Developing Countries Andrew Chesher and Robert Harrison

Presents an economic model of firms' management of vehicle fleets, which serves as a framework for the statistical analysis of vehicle operating cost data.

Vehicle Speeds and Operating Costs: Models for Road Planning and Management Thawat Watanatada, Ashok M. Dhareshwar, and Paulo Roberto S. Rezende Lima

Presents the theory and estimation of a comprehensive set of models to predict speeds and operating costs under free flow conditions for a wide range of vehicles on medium- and low-volume roads as functions of road geometry and condition.

Road Deterioration and Maintenance Effects: Models for Planning and Management William D. 0. Paterson

Contains an extensive analysis of the physical processes, causes of deterioration, and performance prediction relationships, as well as the effectiveness of maintenance practices on unpaved and paved roads.

The Highway Design and Maintenance Standards Model Volume 1. Description of the HDM-III Model Volume 2. User's Manual for the HDM-II1 Model Thawat Watanatada, Clell G. Harral, William D. 0. Paterson, Ashok M. Dhareshwar, Anil Bhandari, and Koji Tsunokawa

Volume 1 organizes relationships described in the first three volumes, as well as a road construction submodel, into interacting sets of costs related to construction, maintenance, and road use. Volume 2 provides guidance on the use of this model including input data forms, inference ranges, and default values-and gives numerical examples.

ISBN 0-8018-3588-7 ISBN 0-8018-3668-9 (5-volume set)