STATISTICAL BACKGROUND FOR THE PLANNING OF EXTENSIONS TO EXISTING UNDERGROUND RAILWAY NETWORKS

by

F. J. LLOYD

(A paper discussed at a joint meeting of the Royal Statistical Society, General Applications Section and the Students' Society on 18 November 1966)

BOTH the Royal Statistical Society and the Institute of Actuaries are interested in the collection and analysis of data and the use of the results for forecasting possible future trends. This paper deals with future traffic estimates of the number of passengers likely to use new underground railway facilities and the likely effect on the existing underground railway networks and other methods of transport, both public and private. It does not deal with the future planning of main line railway suburban services; nor does it deal with the civil engin- eering and operational problems of construction, although, of course, the capital cost of construction for a new tube and the capital cost of rolling stock have to be taken into account in considering the financial prospect of any new schemes. Underground railways involve a large capital cost and once they are built they are difficult and expensive to alter. Even a relatively simple additional station on an existing underground line is likely to cost at least £1 million in capital costs. But the capacity of an under- ground to move very large numbers of people in cities is unrivalled. With modern station layout and advanced automatic signalling devices it is possible to plan to run on a single track up to 40 trains of eight coaches each in any one hour. Such a service would have the capacity to carry up to 30,000 or more passengers in one hour pro- vided the potential passengers presented themselves evenly. In practice, however, passengers do not so regulate their travel require- ments and one feature of peak hour operation in is the very heavy surges of passengers both on to and off the Underground at certain stations. While planning is related to passengers per hour, it is essential not to overlook the higher loadings in the critical quarter of

115 116 F. J. LLOYD an hour at the top of the peak. However, an underground railway has a great overload capacity, so that it can deal with short-time surges of traffic even if the loadings of individual trains or cars should be unevenly distributed. At the other end of the scale, the bus has a low capital cost, is extremely flexible as regards routeing and stopping, but has a much lower carrying capacity. For example, if it were possible to reserve a special lane for buses with stops every quarter-mile and no over- taking, the planned capacity of that lane would be no higher than about 100 buses per hour which, with a full load of 80 persons per bus, would amount to 8,000 passengers per hour. If laybys were introduced for stops and buses permitted to overtake each other and the stops widened to a mile apart the planned potential capacity might be increased to 150 buses per hour and 12,000 passengers per hour, per lane. Without reserved lanes the capacity would be less. For comparison a lane used only by private cars could accommodate 1,000 to 1,500 cars per hour. Car commuters to London average 1½ persons per car including the driver, so that private cars moving into or out of London in the peaks move about 2,000 people only per lane. From time to time various other technical methods for public transport in urban areas are proposed. There are difficulties in constructing overhead monorails or suspended railways in fully built- up cities because of the destruction of property and amenities. Difficulties of interchanging from one form of transport to another are magnified in an established city with existing surface and under- ground transport. For new cities or for transport over difficult terrain there may well be applications. At the present time a feasibil- ity study is being undertaken in Manchester of a possible monorail link between the city centre and an outlying suburb. There are other ideas, apart from monorails, but they are not discussed in this paper. In practice to obtain high rates of passenger movement within a city requires expert planning and operation under rigid control within a space used solely for that purpose. These conditions can be achieved by an underground railway; they are very difficult to achieve on the roads. In cities with recently developed underground railway systems, and in the early days of underground construction in London, the railways have played an important part in attracting new traffic and opening up the development of virgin land. For example, Stockholm is a city surrounded by lakes and inlets of the sea and there was no PLANNING UNDERGROUND RAILWAY EXTENSIONS 117 available land near to the city centre for housing development. By building an underground railway under various water barriers, it became possible to link newly built suburbs to the city centre. Similarly in London, the early extensions of the from Golders Green to Hendon Central and in 1923-24 in the north, and from Clapham Common to Morden in 1926 in the south, had a major impact on suburban developments. The capital to finance these two London projects was raised by a redeemable debenture guaranteed by H.M. Government under the powers of the Trades Facilities Act 1921-22. The interest payments on this capital were borne by the Common Fund of the Underground group of companies which included the London General Omnibus Company. The importance of the financial contribution of the bus company was underlined by Mr Frank Pick, vice-chairman of the London Passenger Transport Board, who once said, 'It requires certainly two, and possibly three, road miles to support one rail service mile'. He was referring to the conditions of the 1930s and for various reasons the same is not true today. One reason why underground railways are so expensive to finance is that the heavy capital investment is used near to capacity to carry the intensely peaked commuter traffic only twice a day, only five days a week. The split of the density of such underground passenger traffic in London by hours of the day is given in Table 1, taken from the London Traffic Survey, Vol. 1, Table 6-9.

Table 1 Weekday journeys inside the survey area by residents of the survey area by periods of arrival Percentage of Journeys by Underground by Period of Arrival Terminating in Terminating in Survey Area Central Area Early morning off peak 7.6 7.9 Morning peak (2 hours) 301 49.7 Midday off peak (7 hours) 191 20.7 Evening peak (2 hours) 31.6 160 Evening off peak 11 6 5.7 Total (24 hours) 1000 1000 The survey area covers 941 square miles with its boundary 15-20 miles from Charing Cross and includes most of the underground system; the central area covers about ten square miles. 118 F. J. LLOYD It is seen that very broadly during one-sixth of the hours of operation over a week two-thirds of the passengers are carried mainly in one direction only. Before condemning these figures as unproductive, remember that the life of London depends on its underground services. Apart from providing direct commuter facilities for dormitory areas, the has the function of distributing commuters from main line stations to their offices or other work places in the central area. As a result of future changes in population and employment patterns, it is expected that the number of outer suburban commuters, mainly using the suburban railways, will increase and additional underground facilities will be required to distribute these passengers in the central area. A further reason for creating new underground railway facilities in central London is the need to relieve overcrowding on existing underground lines. Not only can the points of congestion be eased and the passengers given reasonable travelling conditions, but other parts of the existing underground network can be brought into more pro- ductive use. For example, the when in operation will ease the present intense loadings between Victoria and Charing Cross on the District Line in the morning and evening peaks. A further very necessary relief will be given on the immediately north of Kings Cross. In both examples it has been estimated that the easement will amount to 20 to 25% of the present crush loading conditions. Yet another reason is the need to provide relief to traffic-con- gested streets. The 20th century has seen the fantastic growth in private transport brought about by the motor car. It is clear from North American experience that one of the problems of the present is to learn how to live in cities with the private car. Recent American experience shows a realization that the private car alone cannot move everyone into and out of cities, and there has been a resurgence of 'rapid transit' (or underground railways in London terms). Great cities clearly need an underground railway network with 'park-and- ride' facilities which will tempt the motorist to leave his car at his local station or at a convenient station nearer the centre, and to continue his journey by underground railway. In considering underground railway planning in London it must be remembered that while the origins of the underground system might be regarded as a series of historical accidents rather than the PLANNING UNDERGROUND RAILWAY EXTENSIONS 119 result of an overall plan, it would be truer to say that there were plans but there were too many and they were not co-ordinated. But follow- ing the formation of the Underground group of companies and later the London Passenger Transport Board there have been several comprehensive plans to rationalise and expand the system. The 1935-40 Programme brought, among other things, various extensions of the in-town underground system outward into the suburbs. This 1935-40 Programme was financed by a loan raised from the public by a finance corporation and the Treasury guaranteed the principal and interest. The London Passenger Transport Board borrowed from this finance corporation and met the appropriate interest charges. In 1949 the London Plan working party report was made to the Ministry of Transport. This published report considered urban railway planning from first principles and made several proposals for new cross-London facilities. No special arrangements for financing this programme were made by Governments. The one major result of the 1949 plan is the building of the Victoria Line, due to open the first section in 1968. This planning has been developed further and the latest proposals, which were summarized in London Transport's annual report for 1965, are: (i) extension of the Aldwych Branch to Waterloo; (ii) extension of the Victoria Line to Brixton via Vauxhall and Stockwell; (iii) a new tube, the Fleet Line, across central London taking over the Stanmore branch of the north of Baker Street and running via Bond Street, Green Park, Trafalgar Square/ Strand, Aldwych, Ludgate Circus, Cannon Street/Monument, Fenchurch Street and Surrey Docks to New Cross, New Cross Gate and Lewisham; (iv) extension of the Piccadilly Line from Hounslow West to the centre of London Airport at Heathrow. Appendix A sets out some of the background information about the underground services of London Transport. These new extensions to existing underground facilities have been planned to fulfil some or all of the functions mentioned above. The traffic expected to use a new railway link will consist of: (i) existing passengers transferred from existing underground lines; (ii) existing passengers transferred from suburban railways; (iii) existing passengers transferred from buses; 120 F. J. LLOYD (iv) existing motorists transferred from private cars; (v) new passengers generated by the new facility; (vi) new passengers generated on existing lines as a result of the new facility.

Under the first three headings there would be savings to be taken into account. In estimating the traffic under these headings, a distinction has to be made between the position to be expected soon after open- ing the new line and the position after a number of years, when the impact of expected long-term trends would be felt. Statistically, the problem is to decide what data can be collected, how reliable are the data, and how can they be interpreted? Traffic estimates are required for two distinct purposes: first, in terms of two-way traffic per annum so as to assess the general traffic importance of a proposed new line and to permit the preparation of revenue estimates, based on estimated passenger mileage per annum; and secondly, in terms of one-way peak hour (or top-of-the-peak quarter-of-an-hour) traffic so as to obtain design data for the capacity requirements not only of the train services but also of the station facilities. In an underground system, passengers are in the care of the management from the moment they enter a station, on their journey by stairs, lift or escalator down to the platform, on the train, and then up to street level at their exit station. Safety in move- ment is vital and the handling of large numbers of people under peak hour conditions in restricted passages underground is a skilled job. The planning of station facilities and the flow of passengers is based on observation and calculation. For example, in 1956 a London Transport operational research team studied the flow of passengers in subways, including the effect of constrictions such as stairs and corners. Actual observations were made; the boys at a well-known public school co-operated; practices abroad were studied. The result of the investigations set standards which are incorporated in new underground facilities. Traffic forecasts of passenger movement are therefore required not only on the trains but in and out of each station, and at interchange stations of the movement of passengers changing from train to train inside the station. For example, at Holborn, one of London Trans- port's busiest peak hour stations, the possible additional traffic expected as a result of the Aldwych extension to Waterloo called for detailed study of all passenger flows within the station to determine PLANNING UNDERGROUND RAILWAY EXTENSIONS 121 what changes to the layout would be required. Appendix B gives three tables showing the peak hour flow patterns in matrix form for 1965, for 1981 with the Victoria Line, and for 1981 with the Victoria Line and the Aldwych extension to Waterloo. Among the data required for an assessment of the 'immediate' (i.e. short-term) effect of a new link in an existing underground rail- way network, the most important are those indicating the volume and distribution pattern of existing underground traffic. In London Transport the information obtainable from an analysis of tickets sold at stations is of rather limited value as ordinary tickets sold at a given station are valid to any other station within the range of the fare concerned, and season tickets are not always used to the farthest station to which the ticket is available. Traffic volumes at given points can of course be visually counted or estimated. Among the data available from such direct observation in London are regular annual counts of persons leaving the under- ground stations in the central area each quarter of an hour during the morning peak period and entering these stations each quarter of an hour during the evening peak period. Such peak period counts are also carried out in the opposite direction (inwards in the morning and outwards in the evening) at certain underground stations which, because they serve a main line terminal, may have a heavier peak traffic in that direction. Among the directly observed data available are also the train loading observations, obtained by a team of loading observers who are able, from experience, to note down a reasonable estimate of the number of passengers in a train leaving or arriving at a station. Such loading observations, repeatedly taken at certain key stations during the validity period of each timetable, provide a reasonably good picture of the volume and fluctuations of traffic on a given section (usually a key section) of line. Of particular interest are the bottleneck sections of the lines at the top of the peak. However, none of these directly observed data can provide information about the individual journeys of the people observed, namely their origin and destination pattern. More useful data can be obtained from the so-called 'point-to- point' test which is carried out in London once a year in a week in February. For this test, the ordinary tickets are collected at each destination station and, as each ticket bears the name of the station of origin, it becomes possible to build up an 'origin and destination' pat- tern for holders of ordinary tickets. Less frequently, this point-to-point 122 F. J. LLOYD test is supplemented by a so-called 'route test' where the ordinary tickets are additionally clipped in interchange passages so that the route taken by the passengers can later be identified from the collected ticket. At the same time, an origin-and-destination analysis of the season tickets valid during the test week is carried out. By superimposing the results of this analysis upon those of the analysis of ordinary tickets, it is possible to obtain a reasonable pattern of the total of the individual journeys between any two stations on the underground, that is a complete origin-and-destination pattern of the traffic. To illustrate the marked difference between the data described in the last three paragraphs, Table 2 sets out the relevant figures for seven central area stations: Table 2 Annual number of passengers at certain London Transport stations Originating Station Bookings and Ending Platform Traffic Users million million million Charing Cross 5.9 (12) 19.6 (9) 480 (1) Liverpool Street 10.5 (4) 45.1 (1) 47.2 (2) Kings Cross 11-5 (3) 31.2 (6) 440 (4) Oxford Circus 9.5 (6) 31-9 (5) 44.7 (3) Piccadilly Circus 12.5 (1) 33.9 (3) 43.6 (5) Waterloo 100 (5) 32.8 (4) 34.7 (7) Victoria 121 (2) 341 (2) 34.1 (9)

Bookings — include season tickets on the basis of 600 journeys per annum per ticket. Originating — is the number of passengers passing through and Ending the barriers in the station entrance hall. Traffic Station — includes the passengers interchanging at the Platform station from one line to another in addition to Users the originating and ending traffic. The figures in parentheses indicate the order of magnitude of the station relative to all other underground stations. This origin and destination pattern is the basis for estimating the passenger journeys likely to be diverted to a new link in an under- ground network. For this purpose certain techniques have been developed to assign a varying proportion of the traffic between any two stations A and B to the new route as a function of the 'notional time saving' of the new route compared with the old one. The 'notional times' used for calculating the savings consist of the actual PLANNING UNDERGROUND RAILWAY EXTENSIONS 123 journey time (namely station entering time, average waiting time, train journey time, station leaving time and, where applicable, inter- change time which includes subsequent waiting time) and notional extra times—found empirically—to allow for the physical and psychological effort involved in changing from one train to another; in practice passengers prefer a through journey without interchange to a journey with one or more interchanges provided the time differ- ence is not too large. The assignment formula assumes that if the saving in notional time on a new alternative underground route is zero 45% of passenger traffic will divert from the existing route. In other words there is a presumption of a 5% bias representing the passenger resistance to transfer. The formula for diversion from existing to new route may be expressed: where P = percentage of traffic transferred S = saving in notional journey time in minutes T = existing notional journey time in minutes. When new traffic is assigned between two alternative existing routes there is no bias, so that the formula for diversion from existing to other existing route may be expressed:

It may be that this linear formula can be criticized as somewhat crude, but it appears reasonably adequate within the limits where judgments have to be made. Appendix C sets out some actual and notional journey times for various alternative routes and shows the calculated percentage distribution with the actual distributions found during tests. A formula which has been found to give acceptable results in the case of more than two alternative routes is: where N = number of possible routes T" = average notional journey time for all possible routes S't = saving in notional journey time for route i compared with average notional journey time for all other routes. 124 F. J. LLOYD Several new tube proposals under examination by London Trans- port are across the central area with many possible points of inter- change. The sheer volume of the data and the number of possible routeings render conventional clerical methods inappropriate and the analysis becomes a task for a computer. London Transport is being assisted by the Transport Network Theory Unit at the London School of Economics. This research unit is sponsored by the Ministry of Transport and one of its objectives is to test techniques for processing data available from transport surveys. This T.N.T. study is concerned with traffic flows between the Inner Circle area stations and between these stations and outer suburban stations. The origin and destination pattern provides two- way traffic flows per week between any two inner central stations, and between any of these stations and an outer suburban line. One problem is to convert these weekly two-way flows into peak hour one-way flows. A factor, being the ratio of peak flow to total flow, is required, but it is not available for the origin and destination figures. From the traffic tests a ratio of peak flow to total flow is available for originating and ending traffic at each central area station and from these ratios appropriate other ratios for origin and destination have to be estimated. To some extent the method is by trial and error, for the calculated peak hour flows under existing conditions can be tested against such existing flows. The one-way peak hour diverted flows following the introduction of the Victoria Line and later the Fleet Line are then calculated. This research project has both academic interest to the Unit and practical value to London Transport. Other aids in estimating the short-term effect of a new under- ground link, not only on existing underground traffic but also on suburban railway traffic, include a most useful origin-and-destin- ation survey which the Southern Region of have carried out on their commuter lines, using questionnaires, in 1964. This survey indicates the present volume of commuter traffic from any station on these lines to each of various zones in central London and elsewhere. By using similar assignment techniques, it is again possible to estimate the number of passenger journeys likely to be diverted to the Underground through, for example, interchange with the pro- posed Fleet Line in the Lewisham area. The London Traffic Survey was a very large study jointly spon- sored by the Ministry of Transport and the London County Council PLANNING UNDERGROUND RAILWAY EXTENSIONS 125 and Volumes I and II have been published; phase III has been renamed the London Transportation Study. In all these studies British Rail and London Transport have been associated and are contributing, particularly by their expert knowledge of public transport potential. Phase I of the London Traffic Survey was authorized for 'the collection, analysis and presentation of the basic information of current traffic movements in to enable the best location of design capacity of the main new and improved roads to be decided'. The study was subsequently broadened in scope so as to provide the basis for developing a co-ordinated transportation plan. The scope of Phase II of the Survey was twofold. First, to make a forecast of the extent and nature of future (1971 and 1981) travel demands and secondly, to make a preliminary study of 'what actual patterns of travel would result if these demands were channelled into the routes that could be foreseen'. The emphasis in Phase II was on assigning traffic to road networks, with comparatively little attention to varying the contribution of rail, underground and bus services. Accordingly, the Phase II results are a projection to 1981 which amounts to an intensification of current developments, leaving aside major changes in public transport which could be introduced as a result of fresh policy. These possibilities will be studied in Phase III of the exercise, now in progress, which is known as the London Transportation Study. The London Transportation Study is concerned with the 'realistic assessment of the material and forecasts made in Phases I and IF and the comprehensive planning of transport facilities for which they show the need. The object of the exercise is to find the best solution to London's transport problem. Various combinations of road (including motorway) systems and public transport (rail, under- ground and bus/coach) networks are being developed and tested. Detailed assignments of travel to the alternative systems will then be made, and the economic and social implications of the alternatives will be evaluated. London Transport and British Rail are co-operating in the work with the consultants, Messrs Freeman, Fox, Wilbur Smith and Associates, who are retained by the Greater London Council, to ensure that realistic public transport proposals are in- cluded in the networks being tested, and that due weight is given to the value of public transport in the testing and evaluation processes. In common with the forecasts on which the London Transportation 126 F. J. LLOYD Study was based, any estimates of future traffic on the existing and planned London Transport underground railway network must be based on an assessment of certain long-term trends such as land use, population, employment, etc. In this respect use is made of forecasts prepared by the planning authorities; of population forecasts by the Government Actuary's Department and the Registrar General's Office; and of employment statistics prepared by the Ministry of Labour. Population statistics and forecasts are available for three basic areas: (i) Greater London—being the Greater London Council area with a radius of approximately 14 miles; (ii) Metropolitan Area—having a radius of approximately 40 miles; (iii) South East Region—covering Greater London, Surrey, Hert- fordshire, Hampshire, Oxfordshire, Berkshire, Buckinghamshire, Bedfordshire, Essex, Kent, Sussex, the Isle of Wight and Poole M.B. in Dorset. By differencing the figures information is obtained for the areas between each of these three basic areas. Table 3 shows the annual increase or decrease operating over three periods of time. The forecast figures in this table are taken from the Quarterly Return (2nd Quarter 1966) of the Registrar General. Table 3 Annual increase in population (thousands per annum) Period Greater Rest of Metropolitan Rest of South- London Metropolitan Area S.E. East Area Region Region 1952-62 -22 + 108 + 85 + 41 + 126 1962-65 -18 +94 + 76 + 58 + 134 1965-81 + 4 + 61 + 65 + 61 + 126 The forecast figures in the last line are amended from time to time. The overall picture at present is that the population living in the Greater London Council area is likely to remain static with increases in the outer areas. Many of the daily commuters to the central area are among those moving out, leading to an increase in long-distance commuting. Table 4 shows the annual increase or decrease in central area employment over three periods of time. PLANNING UNDERGROUND RAILWAY EXTENSIONS 127 Table 4 Annual increase in central area employment (thousands per annum) Period Annual Source Increase 1951-61 + 7 Census 1961-64 - 5 Ministry of Labour 1964-81 Forecast +12 London Traffic Survey, Vol. II The planning authorities and London Transport and British Rail have planned on the expectation of a demand for the carriage of roundly 200,000 more commuters to and from central London by 1981. This forecast of employment and other conditions in central London 15 years ahead must be somewhat tentative and very much dependent on the various and changing policies of central Govern- ment, and the consequent reactions of firms and people to these policies. But underground railways take a long time to plan and build and the penalty to be paid for failing to anticipate trends is a heavy one. From all these estimates, it is possible to assess the traffic volumes in terms of two-way annual traffic and two-way annual passenger mileage for each relevant section of an extended underground net- work under present-day conditions and under conditions likely to prevail at a target date in the future, say, in 1981. It is then possible to draw up for the proposed extension a financial balance sheet. The figures in Table 5 are taken from the Report of the Select Committee on London Transport, published in 1965. Thus the line is expected to do more than pay its annual expenses, but will not fully service the interest on the capital investments. A deficit of this sort is to be expected, as it is an almost general experience throughout the world that underground railways can no longer pay their way in a narrow conventional financial sense. How- ever, it is now widely recognized that underground railways are, like roads, essential ingredients of a living metropolis. This view is reflected in the policies adopted in many large cities where a large part or all of the initial capital costs of new underground railways are borne by the community at large (normally the local authorities) but often with subsidies from regional or national government or both and the transport authority is required to operate the line and cover the running costs from the fares revenue. Indeed, there are many cities where the underground, in common with other public 128 F. 3. LLOYD Table 5 Estimates for the Victoria Line

£m Capital costs for land and easements, civil engineering, track, signalling and electrical work, and rolling stock 57.8

Capitalized interest during construction at 6% 5.8 Total cost 63.6

Additional annual revenue £m new traffic 0.9 traffic diverted from road 0.6 traffic diverted from rail 0.9 net commercial advertising and lettings 01 + 2.5 Effect on other L.T. services loss of traffic diverted -0.6 savings 0.7 +01 Additional annual working expenses -1.4

Total effect on L.T. working surplus + 1.2 Additional annual interest charge on capital at 6% 3.8

Annual deficit 2.6 transport, is run at an annual revenue deficit which is borne by the taxpayers. In Stockholm about half the initial capital costs have been borne by the city public works department and about one-quarter of the running expenses are covered by an annual subsidy from the city council. In Toronto the capital costs of new construction are shared according to a formula by which the municipality meets the costs of tunnels, track and stations, while the transit commission meets the costs of signalling, power supply, rolling stock and other direct operating equipment. In New York the city owns the transit system and leases it to the transit authority; the authority pays no rent and neither depreciation nor obsolescence are charged as operating expenses. Consequently all capital costs are borne by the city. In Paris the transport authority is required to meet all expenses of PLANNING UNDERGROUND RAILWAY EXTENSIONS 129 running the system including interest on capital and provision for renewal of assets. However it is indemnified in two respects: (i) if the Government decides fare increases are against the public interest the transport authority is reimbursed the loss of additional fares revenue; (ii) for loss of revenue due to fares concessions—these payments are borne 70% by the state and 30% by the local authority. In 1964 they amounted to about 33 % of total revenue. A new regional express railway network is being built to complement the Metro jointly financed by the state and the local authorities. Differing forms and degrees of state or municipal financial assistance are given to public transport undertakings in other major cities. It is recognized that conventional accounting usually shows deficits on the future operation of underground extensions when capital costs have to be serviced. On the other hand public investment in an underground railway can bring positive benefits to a city. It might be argued that any deficit thrown up by conventional financing should be compared with the present value to the com- munity at large of a new underground railway. In a very simple example, the electrification of certain main line railways out of London has greatly increased the value of houses adjacent to stations on these lines although the owners of these houses have not contri- buted to the cost of the electrification. In recent years research has been directed to assess and quantify the relative merits of different schemes to the whole community. One of the reasons for this research was the need to find a common measuring scale for investments in highway improvements, such as motorways, where a direct revenue is generally not even expected, and on underground railways where, as has been shown, the narrow financial appraisement is unfavourable. Social benefit research, as it is generally known, was conducted by Mr C. D. Foster and Pro- fessor M. E. Beesley in assessing the proposals for the Victoria Line in London. They reported their findings in a paper to the Royal Statistical Society in December 1962 (J.R.S.S. Series A, 126). In these or other similar studies, an attempt is made to work out the money equivalents of savings in time, improvements in the comfort and convenience of travel, reduction in accidents and reduction in traffic congestion, and other benefits, and to bring these items to book. Appendix D is an extract from Foster and Beesley's paper. 130 F. J. LLOYD The social benefit study approach is logical and based on economic theory but considerable care is required to define and segregate the various benefits and then to value them. For example, what rate of interest should be used in the calculations for discounting costs and benefits to present values? Economists suggest a rate of interest to represent on the costs side, the value of the opportunities forgone by not using the capital for other purposes, and on the benefits side, the community's time preference in preferring a benefit today rather than tomorrow. The rate of interest is not supposed to represent an actual market rate of interest either short term or long term. But is this the right basis to use? There is as yet a gap between the practical man who barely believes in this method of assessment and the economist who declares that each and every project should be subject to social benefit study and the decision for action based entirely on the result of the study. The truth is somewhere between, although it must be admitted that the results so far obtained from social benefit studies must still be regarded as somewhat controversial. But the principle of taking account of the overall value to the whole com- munity of an investment in an underground railway must be sound. The need is to improve the techniques of assessment so that valid comparisons can be made of different projects. If a city is to continue to live and prosper, relatively speedy and convenient movement of people is an essential condition. Investments must be made to maintain and improve the ease of movements. The authorities are therefore faced with the problem of deciding on priorities. Such decisions should be based on the soundest possible estimates of future usage. In preparing such estimates, statisticians have an important part to play. I have drawn extensively from research done and being done in this field but any views expressed are my own. I am most grateful for the many constructive suggestions I have received and especially grateful to colleagues in the London Transport Planning Department both past and present. PLANNING UNDERGROUND RAILWAY EXTENSIONS 131

APPENDIX A BACKGROUND DATA RELATING TO THE UNDERGROUND SERVICES OF LONDON TRANSPORT For Year 1965 or at end of 1965 Miles Route Mileage Managed by London Transport 215 Run over by London Transport trains Tunnel—Tubes 66 Cut and cover 22 Open 156 Total 244

District 45 Metropolitan 60 Circle 13 Bakerloo 32 Piccadilly 38 Northern 40 Central 51 Rolling Stock Coaches Coaches Motor 2,852 Tube 2,607 Trailer 1,198 Surface 1,443 4,050 4,050 Stations, Depots, etc. Passenger stations Managed 228 Served 273 Depots 20 Workshops 1 Operating Statistics Car miles run Over London Transport lines 203 m. By London Transport trains 217 m. Average scheduled speed 20.1 m.p.h. Traffic Statistics Passenger journeys 657 m. Average distance travelled 4.57 miles Average fare paid 13.0d. Passenger miles 3,002 m. Average load per car 151 Average charge per mile as from 16 Jan. 1966 2.93d. Revenue Statistics Traffic Receipts £35.9 m. Working expenses (excluding interest on capital) £33.9 m. £20 m.

B 132 F. J. LLOYD APPENDIX B HOLBORN 'MODEL' OF TRAFFIC FLOW PATTERN DURING MORNING PEAK 60 MINUTES (08.30-09.30) Present System and Present Traffic (1965) Table Bl To: C(W) C(E) PCS) P(N) Street A1d. Total From: C(W) 60 250 4,140 60 4,510 C(E) 2,250 150 4,730 70 7,200 P(S) 140 1,800 2,250 40 4,230 P(N) 2,800 1,550 3,610 510 8,470 Street 250 170 110 80 0 610 A1d. 50 40 10 10 0 110

Total 3,240 3,560 2,430 490 14,730 680 25,130

Present System+ Victoria Line with Estimated 1981 Traffic Table B2 To: C(W) C(E) P(S) P(N) Street A1d. Total From: C(W) 100 300 4,000 70 4,470 C(E) 2,800 200 6,400 100 9,500 P(S) 150 1,800 2,400 50 4,400 P(N) 1,400 1,700 3,700 530 7,330 Street 300 200 180 120 0 800 A1d. 80 80 20 20 0 200

Total 1,930 3,780 3,100 640 16,500 750 26,700

Present System + Victoria Line and Aldwych Line Extension Table B3 to Waterloo with Estimated 1981 Traffic To: C(W) C(E) P(S) P(N) Street A1d. Total From: C(W) 100 300 3,950 70 4,420 C(E) 2,800 200 6,350 1,040 10,390 P(S) 150 1,800 1,800 50 3,800 P(N) 1,400 1,700 3,700 1,050 7,850 Street 300 200 180 120 50 850 A1d. 80 880 20 890 1,800 3,670

Total 1,930 4,580 3,100 1,510 17,600 2,260 30,980

Notes on abbreviations: C Central Line P Piccadilly Line A1d. Aldwych Extension W, E, S, N Westbound, etc. PLANNING UNDERGROUND RAILWAY EXTENSIONS 133

APPENDIX C COMPARISON OF 'TRAFFIC TEST' AND 'ASSIGNMENT FORMULA' WITH PENALTY FOR INTERCHANGE OF 4 MINUTES PLUS 50% OF WALKING TIME FOR JOURNEYS BY ALTERNATIVE ROUTES BETWEEN SPECIFIC STATIONS Number Journey Time* Percentage distri- of bution between Changes alternative routes according to

Traffic Actual Notional Test Formula (minutes) Turnpike Lane— via Finsbury Park and Northern City Line 1 19 234 90 89 via Kings Cross and Northern Line 1 23½ 28¼ 10 8 via Kings Cross and circlel T .ine 1 23¾ 29 Nil 3 Total 100 100 Turnpike Lane—Liverpool St. via Finsbury Park, Northern City Line and Moorgate 2 23 32½ 13 30 via Kings Cross and Circle Line 1 25½ 30¾ 70 53 via Holborn and Central Line 1 28¾ 33¾ 17 17 Total 100 100 Turnpike Lane—Bank via Finsbury Park, Northern City Line and Moorgate 2 23¾ 324 24 21 via Kings Cross and Northern Line 1 25| 30½ 39 46 via Holborn and Central Line 1 264 31½ 37 33 Total 100 100 Kilburn Park, Maida Vale and Warwick Avenue—Russell Square via Piccadilly Circus 1 24½ 29 97 95 via Oxford Circus and Holborn 2 29 35 H 4 via Baker Street and Kings Cross 2 29¾ 36 1½n 1 Total 100 100 1½ Kilburn Park, Maida Vale and Warwick Avenue—Caledonian Road, and Arsenal via Piccadilly Circus 1 29¼ 33¾ 71 73 via Oxford Circus and Holborn 2 33¾ 39} 1 5 via Baker St. and Kings Cross 2 31 37i 28 22 Total 100 100 134 F. J. LLOYD Notting Hill Gate—Moorgate via Bank and Northern Line 1 25½ 30¾ 3 1 via Circle (direct) 24 24 97 99

Total 100 100

Notting Hill Gate—Kings Cross via Holborn 1 21¾ 26¾ 4 Nil via Circle (direct) 17i 17i 96 100 Total 100 100

Notting Hill Gate—Charing Cross via Oxford Circus 1 18¾ 23¾ 7 13 via Circle (direct) 19i 19i 93 87 Total 100 100

Stockwell—Chancery Lane via Bank 1 21 26½ 46 56 via Tottenham Court Road 1 22 27| 54 44 via Leicester Sq. and Holborn 2 26i 36i Nil Nil Total 100 100

* All journey times exclude the time between street and platform at the begin- ning and end of the journey. 'Actual' time consists of 'waiting' time, 'interchange' time (without any penalty) and time on train. 'Notional' time includes the 'penalties'.

APPENDIX D

Social benefit and loss table—Victoria Line Assumptions: Period: 5½ years' construction plus 50 years' operation Rate of interest: 6% p.a. Trend (see column below): (a) Constant throughout (b) Increase of 1½% p.a. (c) Increase of 5% p.a. for 15 years and 2% p.a. thereafter (d) Fall to zero at the end of 50 years of operation PLANNING UNDERGROUND RAILWAY EXTENSIONS 135 Trend Annual Present Assumed Amount Value £m £m (A) Costs (other than interest charges) Annual working expenses (a) 1-413 1616 Benefits (B) Traffic diverted to V.L. (1) Underground: Time savings (a) •378 4.32 Comfort and con- venience (d) •347 3.96 (2) British Rail: Time savings (b) •205 2.93 (3) Buses: Time savings (a) •575 6.58 (4) Motorists: Time savings (c) .153 3.25 Savings in vehicle oper- ating costs (c) •377 802 (5) Pedestrians: Time savings (b) •020 •28 (B) Sub-total 2055 29.34

(C) Traffic not diverted to V.L. (1) Underground: Cost savings (a) •150 1.72 Comfort and con- venience (d) .457 5.22 (3) Buses: Cost savings (a) •645 7.38 (4) Road users: Time savings (a) 1.883 21.54 Savings in vehicle oper- ating costs (a) •781 893 (C) Sub-total 3.916 44.79

(D) Generated traffic Outer areas: Time savings (b) •096 1.37 Fare savings (b) •063 •90 Other benefits (b) •375 5.36 Central area: Time savings (b) •056 •80 Fare savings (b) •029 •41 Other benefits (b) •203 2.90

(D) Sub-total •822 11.74

(E) Terminal scrap value .29 (F) Total benefits (B+C+D+E) 8616 (G) Net current benefit (F - A) 7000 (H) Value of capital expenditure 38.81 © Net benefit (G-H) 31.19 (J) Social surplus rate of return* 11.3% * Total benefits less costs other than interest charges (G) as a return on the capital invested (H), averaged over the whole period of operation and construction. Note: The complete table in Foster and Beesley's paper included values at other rates of interest.