HIGHWAY RESEARCH BOARD Bulletin 104
Vehicle Climbing Lanes
National Research Co HIGHWAY RESEARCH BOARD Officers and Members of the Executive Committee 1955
OFFICERS
G. DONALD KENNEDY, Chairman K. B. WOODS, Vice Chairman
FRED BUBGGRAF, Director ELMER M. WARD, Assistant Director
Executive Committee
C. D. CuRTiss, Commissioner^ Bureau of Public Roads
A. E. JOHNSON, Executive Secretary, American Association of State Highway Officials
LOUIS JORDAN, Executive Secretary, Division of Engineering and Industrial Research, National Research Council
R. H. BALDOCK, State Highway Engineer, Oregon State Highway Commission
PYKE JOHNSON, Consultant, Automotive Safety Foundation
G. DONALD KENNEDY, President, Portland Cement Association
O. L. KiPP, Assistant Commissioner and Chief Engineer, Minnesota Department of Highways
BURTON W. MARSH, Director, Safety and Traffic Engineering Department, Ameri• can Automobile Association
C. H. ScHOLER, Head, Applied Mechanics Department, Kansas State College
REX M. WHITTON, Chief Engineer, Missouri State Highway Department
K. B. WOODS, Director, Joint Highway Research Project, Purdue University
Editorial Staff
FRED BURGGRAF ELMER M. WARD WALTER J. MILLER 2101 Constitution Avenue Washington 25, D. C.
The opinions and conclusions expressed in this publication are those of the authors and not necessarily those of the Highway Resoarch Board. HIGHWAY RESEARCH BOARD BuUetin 104
Vehicle Ctimbing Lanes
PRESENTED AT THE Thirty-Fourth Annual Meeting January 11-14, 1955
1955 Washington, D. C. Department of Design T. E. Shelburne, Chairman Director of Research, Virginia Department of Highways, University of Virginia
COMMITTEE ON GEOMETRIC fflGHWAY DESIGN
D. W. Loutzenheiser, Chairman Acting Chief, Urban Highway Branch, Bureau of Public Roads
R. H. Baldock, State Highway Engineer, Oregon State Highway Commission Warren James Cremean, Urban Projects Engineer, Ohio Department of Highways Ralph L, Fisher, Engineer of Design, New Jersey State Highway Department Fred W. Hurd, Yale Bureau of Highway Traffic, Strathcona Hall Emmett H. Karrer, Professor of Highway Engineering, Ohio State University Elmer R. Knight, Assistant Chief Highway Engineer, Illinois Division of Highways Harry C. Knudsen, Office, Chief of Engineers, Department of the Army O. K. Nermann, Chief, Traffic Operations Section, Highway Transport Research Branch, Bureau of Public Roads William S. Pollard, Jr., Assistant Professor of Civil Engineering, University of Illinois K. A. Stonex, General Motors Proving Ground, Milford Michigan Edward T. Telford, District Engineer, California Division of Highways, Los Angeles C. A. Weber, Assistant Chief Engineer, Michigan State Highway Depart• ment
IV Contents
SIMPLIFIED CLIMBING-LANE DESIGN THEORY AND ROAD-TEST RESULTS
T. S. Huff and F. H. Scrivner 1
MOTOR-VEHICLE PERFORMANCE ON ASCENDING GRADES
Robert E. Dunn 12
TRUCK CONGESTION ON UPHILL GRADES
William E. Willey 21 Simplified Climbing-Lane Design Theory and Road-Test Results T. S. HUFF, Engineer of Road Design, and F. H. SCRIVNER, Supervising Research Engineer, Texas Highway Department A simplified theory of the motion of heavy vehicles on grades is presented. A set of speed-distance curves computed from the theory, based on values of maximum sustained speeds observed in Arizona, is given as the current basis for design of climbing lanes in Texas. Speed-distance curves representing the observed performance of a test vehicle on 11 grades are compared with the corresponding curves developed from the theory. Fair agreement was found, and it was concluded that the simplified theory is accurate enough for use in the design of climbing lanes.
• CONSIDER a vehicle (Figure 1) of gross that although the net driving force must weight, W, travelling at a variable vel• satisfy Equation 1 involving the acceleration ocity, V, on a grade inclined at an angle, and the grade angle, it may also be ex• e, with the horizontal, the value of e pressed independently as some function of being taken as positive if the vehicle is as• velocity only, since each of its components cending and negative if it is descending. If is a function of velocity only. g represents the acceleration of gravity For example, if the truck operates at a and t the time, then, neglecting that part known maximum sustained velocity on any of the driving force required to impart grade, the numerical value of P/W corres• angular acceleration to rotating parts, we ponding to that velocity may be immediately may write the force equation, calculated from Equation 1, which in this case reduces to P/W = sin 9, and that Wdv P - W sin e, where P, magnitude of P/W will always exist at that g Ht velocity, at least approximately, regard• a variable, may be termed the net driving less of the value of the acceleration. In force acting on the vehicle. The above Figure 2 we have plotted values of P/W equation may be rewritten in the form computed in this way against correspond• ing values of the velocity, v, from basic P 1 dv sin e data supplied mainly by Willey (1.) in 1950, W=gc[f ^ (1) and applying to an average heavy vehicle The net driving force is the total traction operating on mountain grades in Arizona. exerted by the driving wheels against the The points plotted in Figure 2 are con• road surface, less wind resistance and road nected by straight lines to form a con• surface resistance. Again neglecting in- tinuous graph of P/W versus v. Each ertial resistance to angular acceleration, straight line segment extending from, say, it follows that if the truck is always operated Vn to v^ may be represented by an at the highest possible speed and always equation bf^the form. within the range of engine speed recom• P /W = av + b mended by the manufacturer, then the total (2) driving force must be expressible, at least where varies within the interval, Vjj approximately, as a single-valued function to n + 1> and a and b are constant of the velocity only. Air resistance in within the same interval. still air is usually considered to be a func• From Equations 1 and 2 we may form a tion of the velocity only, and we shall as• third equation, not containing P/W ex• sume that no wind exists. We shall also plicitly, which becomes the general motion assume that the type and roughness of the equation for the vehicle, as follows: pavement do not change and, therefore, that the road surface resistance may be dv - gav + g (sin 6 b) = 0 (3) taken as constant, or at most as a function of velocity only. We therefore conclude where v is restricted to the velocity in- terval, to v^+j, and a and b are interval to v^+i- Thus, during the constant in the same interval. time t, the velocity changes from VQ to V, the vehicle travels a distance x, and the ratio, net driving force to gross weight, changes m value from (avQ + b) to (av + b). (The logarithm is taken to the base, e).
Pa net driving forci {|b>) grosi Mfight (Ibt) In using Equations 4 for calculating the vihielB It OBCtntfing distance traveled or time consumed by a vehicle while it changes velocity over an Mass X Acctlaralion > Forct, interval greater than that for which a and "fSt-p- b are constant, it is necessary to compute WMrB w = vtlocilr {lt/s»),and the increments of distance and time cor• t ' limm (Mc) responding to each subinterval of the type, (Tha additionol driving force raquirtd lo oeeelarota rotating pans II noglocttd ) Vn to v'n_ ' 'n to ^n+l. and Vn+i, to v, and to add these increments in order to Figure 1. obtain total distance and total time.
MAXIMUM SUSTAINED SPEEDS NUMERICAL VALUES USED IN PLJOTTING GRAPH FOR USE IN Psrcent Sine = v EQUATIONS (91 ,( Max 6rad« P/w (fWllc) le II9I5 Ellimottd - 0096049 11919 T 06983 - 0067991 12926 6 05990 10 27 - 0093993 094811 5 04994 19 20 - 0022699 0796S0 4 03997 17 60 - 00r5594 067419 5 02999 24 00 -0010267 094631 02000 J3 73 - 00090909 037039 00000 73 33
NOTE TU .olun of 0 oiul D opply batnan Iht nlociliti indicated Far tROmplt, b. 079690 in tha valeeity ronga liam 13 20 la 1760 ft / neluiKa
• William E Willa>;uiailll Trach Spaada: ROADS a STREETS,JAN 1990,P92
vdt /sec)
Figure 2. Graph of Equation 2. We now denote the position of the vehicle TEXAS DESIGN METHOD at any instant by its coordinate, x, meas• ured in the direction of motion from a sta• Figure 3 shows speed-distance curves tionary point on the grade behind the truck. computed from Equations 4, the value of We also stipulate that x = t = 0 when v = the constants, a and b, having been taken V(j, and that the grade angle, 6, is con• from Figure 2. By interpolating between stant. Then the solution of Equation 3 may these curves, one may determine the ap• be written in the following form suitable proximate speed, in the range from 0 to for the construction of speed-distance and 47 miles per hour, of Willey's (j.) aver• time-distance curves: age heavy vehicle at any point on any series of successive grades ranging between X = (sin e - b) t minus 7 percent and plus 7 percent pro• (4) vided the speed at one point on the series of grades is known. The upper limit of wherein t = 1_ log/av + b - sin e 47 mph. was selected because that figure ag \avo + b sin e J was the average speed of trucks on ap• proximately level grades in Texas. and both v and v, pre restricted to the EXAMPLE OF USE OF CURVES WARRANTS FOR CLIMBING LANES iDashed Imai on graph indicot* itapt taken in CLASS B HIGHWAYS Providt climbing lont ond parking shouldtr finding propdr location for climbing lont ihawn CLASS C HIGHWAYS — OlSirable treotmsnt lama os for CLASS 8 HIGHWAYS i&=2sa; on ikoten I Minimum treotmcnl convarl shoulder to climbing lone _30M PH ond SPEED-DISTANCE CURVES CLASS D HIGHWAYS Moki studies to determine feosibility of converting occeleroting -Traniitions. stioulder too climbing lone.tohing into oecount ESTIMATED FOR (I) construction costs and, (21 volume of heavy trucks CLIMBING LANE A TYPICAL HEAVY TRUCK CLASS E HIGHWAYS — Climbing lonee not considered necessary
decelirating dvetltroting DECELERATION ACRFl FRATinM on grades indicoted 0 n 9 rades indicated h 32 -5% 1 % K M' f • 1 —t— V U ft / li / / ? f J / r i f ^ k W 'A '1% Vill
• \ 3% • 1 1 / 1 1 • 1 '/ • i • • 3 4 5 6 3 4 S S DISTANCE (Thoutandt of f«et) DISTANCE (Thousands of fsal)
Figure 3. In using the chart for design purposes, DATA PERTAINING TO TEST VEHICLE AND vertical curves are generally ignored and CONDITIONS OF OPERATION speeds are usually taken from Figure 3 on 1. Vehicle identification; International R-195 Tractor. 2. Vehicle overall maximum dimensions: (a) height, 7, 75 the assumption that the vehicle travels in a feet; (b) width, 7. 75 feet. straight line from one point of grade inter• 3. Total gross weight: 57,180 lb. 4. Manufacturer's maximum gross vehicle weight rating: section to the next. Vertical curves can 50, 000 lb. be broken up into straight-line segments, 5. Gear ratios: (a) transmission, 6. 98, 3. 57, 1. 89, 1. 00, 0. 825 (overdrive); (b) aux. trans., none; (c) axle, of course, if the additional accuracy is 6.5, 8.86; (d) total gear reductions, 61. 84, 45. 37, considered worthwhile. 31. 63, 23. 21, 16. 75, 12. 28, 8. 86, 6. 50, 7. 31, and 5. 36. 6. Tire size: 10. 00 by 20. 7. Net engine power at sea level: 146 hp. at 2, 600 rpm. * ROAD TEST OF A HEAVY VEHICLE 8. Altitude: 950 feet. 9. Road service type and condition: bituminous, good. In December 1953 a road test was con• •Brake horsepower, 162 at 2, 800 rpm. ducted by the Planning Survey of the Texas Highway Department (2) on a section of The curves of Figure 3 have been used ranch-to-market Road"93 in Travis and in the design of climbing lanes in Texas Burnet counties west of Austin in an effort since 1952. An example of the design to provide data from which the theory being procedure is given in the figure. Briefly, used in design of climbing lanes could be it consists in finding the point on an as• checked or corrected, if necessary. The cending grade where the speed drops to vehicle used was an International Harvester 30 mph. , and the next subsequent point R-195, two-axle truck tractor (146 net where the speed has increased to 30 mph. horsepower at sea level) and a 33-foot, and the truck is accelerating. These two Hobbs tandem-axle, flat-bed trailer, both points form the limits of the tangent sec• loaned to the department free of charge by tion of the climbing lane. Reversed curves, the respective manufacturers. Table 1 525 feet in length, are added to each end of gives essential data pertaining to the trac• the tangent. Thus the design vehicle is tor. The trailer was loaded with steel removed from the general traffic stream piling, the gross weight of tractor and at a speed somewhat greater than 30 mph. , trailer being 57, 180 lb. (see Figure 4). and likewise is returned at a speed ex• In running the tests, pneumatic tubes, or ceeding 30 mph. detectors, which actuated electric switches
Figure 4. Vehicle used in road test. Tractor is over a pneumatic detector. when run over, were first stretched trans• (Figure 6) recorded the time each of the verse to the highway at 100-foot intervals four axles passed over the pneumatic tubes on a selected grade. Two instruments, an during the test. Esterline-Angus 20-pen graphic recorder Eleven grades ranging from 700 to 1,500 with about "^lo-second accuracy (Figure 5) feet in length, and from 0. 16 percent to and an oscillograph and camera with tuning- 7. 62 percent in inclination, were used in fork timer accurate to about yiooo second the test. In all test runs, the driver, an employee of the department, attempted to maintain the highest-possible speed while remaining within the range of engine speed recom• mended by the manufacturer and marked on the speedometer. The test procedure was as follows:
Up-Grade Acceleration Runs
The driver approached the grade at the bottom at a very-low speed (1 or 2 mph,). When within 3 or 4 feet of the first detector, he accelerated as rapidly as possible and continued to accelerate until he had passed over the last detector at the top of the grade. If he had not reached maximum sustained speed at that time, he returned to the bottom of the grade and repeated the run, except that he approached the first detector at approximately the speed and in the gear he had previously passed the last detector. This procedure was followed Figrure 5. Recorder measured time required until maximum sustained speed was at• for truck to travel distance between de• tained. tectors.
Figure 6. Oscillograph and camera in portable darkroc recorded time each axle passed over a detector. Up-Grade Deceleration Runs types described above. (Figure 7). Both recording instruments performed well, but The driver attempted to approach the it was impractical to operate the oscillo• grade at the bottom at a speed equal to or graph continuously during most test runs greater than 47 mph. and attempted to because the fast-moving recording paper reach the top at the highest-possible vel• would be exhausted before the truck had ocity. K, after passing the last detector, finished the run. his speed was still greater than maximum sustained speed, he returned to the bottom of the grade and repeated the run, except ANALYSIS OF ROAD-TEST RESULTS that he approached the first detector at Approximate values of velocities for approximately the speed and in the gear he use in plotting speed-distance curves rep• had previously passed the last detector. resenting the test runs were computed as The process was continued until the vel• follows from the basic data: (1) From 20- ocity on the grade was reduced to maximum pen recorder data, the velocity at the in• sustained speed. stant when the front axle of the vehicle was midway between two successive detectors Down-Grade Acceleration Runs was taken equal to the distance between detectors (100 feet) divided by the corre• At the top of the grade the driver ap• sponding time interval. (2) From oscillo• proached the first detector at 1 or 2 mph., graph data, the velocity when the mid-point then accelerated as rapidly as possible. between the second and third axles was
UP-GRADE UP-GRADE DOWN-GRADE Decalararion Runt Accalaration Rum Acceleration Rune Groda 610% Grade 0 16% Grade -0 77%
Run 4
Run 9 Run 3
Run 6 Run 2 Run 5
Run 4 ^^^^
Run Z a 20
Run 3
DISTANCE (IPOO')
Figure 7. A few of the 118 speed-distance curves developed from the several runs made on each grade. Runs are numbered in chrono• logical order.
If, on passing the last detector, he had not over a detector was taken equal to the dis• attained a speed of 47 mph., he returned tance between those axles (18. 62 feet) di• to the top of the grade, making his ap• vided by the corresponding time interval. proach on the second down-grade run at Accelerations for use m Equation 1 the speed and in the gear he had previously were computed from oscillograph data only, passed the last detector, and again ac• since such computations require more- celerated as rapidly as possible. The accurate data than velocity determinations. process was repeated until he attained a At low velocities, approximately simultan• speed of at least 47 mph. on the grade. eous values of acceleration and velocity All told, there were 118 test runs of the were computed from the time intervals between the passage of three successive points represent periods during which the axles over one detector. In order to con• truck was apparently traveling at maxi• vert the time data to accelerations, use mum sustained speed, that is, when the was made of finite difference forms of the acceleration was equal to zero. Ignoring derivatives, dVdt^ and dx/dt. At higher areas of the graph where the scatterii^ of velocities, time intervals between the pas• points was too wide to indicate any con• sage of one axle over three successive sistency in the data, an average line was detectors were used in the difference drawn through the remaining points. This equations. line was taken to represent the graphical
Moi wilainad oelocity computed b, SAE method, veriut P/W = tin 8
Max susfoined velocity obMrved during rood leet, vflriue P/W • tin 8
Velocity vertut P/W computed from occelerolion obterved during rood tett (See equotion 3) Gropb of P/W uied in computing tpeed-dittonce oiryet
Figure 8. Graph of P/W versus v from 1953 road-test data (solid line) and from SAE "Truck Ability Prediction Procedure" (dashed line). The approximate acceleration and the form of P/W expressed as a function of grade angle being known for a given instant, velocity only. these values were substituted in Equation 1 On the same graph values of sin 6 were for dv/dt and fl, respectively, and the nu• plotted against the corresponding maximum merical value of P/W was computed for sustained speeds computed by a method that instant. Each computed value of P/W proposed by the Society of Automotive Eng• was then plotted against the corresponding ineers (3). These values, plotted as points velocity in Figure 8, where the solid points enclosed in triangles, are based entirely represent instants when the acceleration on the factors pertaining to the truck and was different from zero, and the circled test environment given in Table 1.
Figure 9. Figure 10. 8
(The reason for the wide scattering of points on Figure 8 is not known, but it might have been due in part to unavoidable variations in wind direction, wind velocity and driver behavior. Some of the scatter• ing might also have resulted from the in• herent inaccuracies encountered in the sub-
t s 0i9T«HCE IIPOO)
Figure 13. parent tracing cloth, was placed over a j„i corresponding test curve plotted to the same scale, and the velocity lines (hori• zontal lines) on the two graphs were i : ; ; matched. The computed curve was then »•"•••"«»• moved horizontally, keeping the velocity Figure 11. lines matched, until it appeared to pass stitution of difference equations for differ- through the midpoint of the test curve, ential equations. And some scattering could be expected because of variations in the force required to change the angular ve• locity of rotating parts while the truck accelerated at varying rates). I Next, from the graph of average values | of P/W versus velocity (Figure 8), and by • use of Equations 4, a set of three speed- distance curves (up-grade deceleration, up-grade acceleration, and down-grade acceleration) was plotted for each of the eleven test grades. D)ITI.tt 1,0001
Figure 14. Then the test curve was traced on the cloth with the computed curve. If the curve so transferred coincided with the computed curve, then it could be concluded that, within the range of velocities covered by the test curve, the computed curve repre-
—iWi-
OISTANCE lipOOl
Figure 12. Finally, the 118 speed-distance curves (Figure 7) previously plotted directly from the observed data, (referred to hereafter as "test curves") were compared with the corresponding speed-distance curves com• puted by use of the graph of average values of P/W (referred to hereafter as "computed curves") in the following mannen The computed curve, drawn on trans- Figure 15 9
ing force acting at any sustained velocity was, on the average, greater than the net driving force acting at the same velocity when the vehicle was accelerating or de• celerating. This apparent anomoly in vehicular performance might be explained by the fact that the driver, while rapidly accelerating or decelerating, had little time for searching out the best gear, whereas his sustained speed on any grade occurred only after he had had ample time to find the proper gear for that grade. In this connection it was also noted that the maximum sustained speeds computed for the test vehicle by the method recommended by SAE (see points enclosed in traingles in Figure 8) agreed rather well with the
Diitonct djOOO') observed values (the circled points in Fig• ure 8) except in the velocity range of about Figure 16. 14 ft. per sec. to 30 ft. per sec. (9. 5 mph. to 20. 5 mph.). In this range the values sented the test data well. On the other computed by the SAE method were some• hand, the contrary was true if the test what greater than the observed values. curve departed substantially from the com• In spite of the exceptions noted above, puted curve. Figures 9 through 17 show the speed-distance curves computed from these comparisons. the graph of average values of the ratio, net driving force to gross weight (Figure COMPARISON OF TEST RESULTS WITH 8), appeared to represent the average per• THEORY formance of the test vehicle fairly well. Therefore, Figure 18, which was made up Although fair agreement frequently -ex• isted between the shapes of the speed- by use of Figure 8 and Equations 4, for in• distance curves plotted directly from the tegral values of grade percentages, may data, (the solid lines of Figures 9 through be taken as a general summary of the av• 17) and the curves computed from the graph erage performance of the test vehicle. If of average values of P/W (the dashed lines detailed comparisons of Figure 18 are of Figures 9 through 17), two major ex• made with Figure 3, it will be seen that ceptions are noteworthy: the test vehicle was generally slower than 1. On many runs, the test curves in• the design truck in current use in Texas. dicated some irregularity in the motion of the vehicle, apparently caused in part by gear shifting. This irregularity was es• pecially noticeable on some of the up• grade deceleration runs at velocities ap• proaching maximum sustained speed, when the vehicle frequently first slowed to 2 or 3 mph. below maximum sustained speed and then accelerated. 2. The observed maximum sustained speed was frequently from 1 to 3 mph. greater than the speed shown on the com• puted curves. The reason for this dis• crepancy may be found by reference to Figure 17. Figure 8, where it can be seen that most CONCLUSIONS of the circled points (which represent net driving force to gross weight at maximum 1. Inspection of the test curves of Fig• speed) lie above the line representing the ures 9 through 17 indicate that, even under average of all points. Thus, the net driv• controlled conditions, the relation between EXAMPLE OF USE OF CURVES
(Ooihad linaa on graph indicofa staps tahan in finding propar location for climbing lono ahown J*=299L. on iketch 1 3aM PH ond SPEED-DISTANCE CURVES a on grades Indicated on grodes indicated 3 4 5 3 * S 6 DISTANCE (Thousonds of f66t) DISTANCE (Thousonds of r66t) Figure 18. 11 the speed and the distance travelled by the full-scale tests. average heavy vehicle handled by a driver of probably better than average skill may ACKNOWLEDGEMENTS not always be consistent. 2. The speed-distance curves com• The following department employees puted on the assumption of a net driving were especially helpful in conducting the force which varies only with velocity agreed road test; Reed Baker, K. G. Crawford, fairly well with the corresponding curves W. R. Welty, Hubert Henry, S. W. Adair, plotted directly from test data, at least in and Gene Voltz. Miss Leah Moncure did those cases where the vehicular perform• the numerical work in connection with the ance was consistent. Therefore it appears reduction of the data and the preparation of that the simplified theory (Equations 4) is the graphs. sufficiently accurate for use in design of For their generous cooperation thanks climbing lanes. are also due Johnny Wright, of Hobbs 3. The Society of Automotive Engineers Trailer Company; H. T. Rosell and J. H. has provided a method for computing max• Gillum, of International Harvester; P. J. imum sustained speeds for any gross Rudolph, of the Petty Geophysical Engi• ' weight to horsepower ratio (3). Values so neering Company; and C. M. Ogle, of the computed, if used in conjunction with the Texas Motor Transportation Association. simplified theory of truck motion present• Fred B. Lautzenhiser, Chairman of the ed herein, should make it possible to pre• SAE Subcommittee on Classification and dict, at least approximately, the behavior Evaluation of Transportation Engineering on grades of vehicles of any gross-weight- Formulas, furnished formulas used in to-horsepower ratio without resorting to computing maximum sustained speeds (3), References 1. "Uphill Truck Speeds", by William by Willey. E. WiUey, Roads and Streets, January 2. "Texas Highways", Texas Highway 1950, p. 52. See also, "Uphill Speeds Department, Austin, Texas, January, of Trucks", Highway Research Board 1954, p. 14. Proceedings, 1949, p. 304; and "Sur• 3. "Truck Ability Prediction Pro• vey of Downhill Speeds of Trucks on cedure", Second Edition. SP-82, Society Mountain Grades", Highway Research of Automotive Engineers, Inc., 29 West Board Proceedings, 1950, p. 322, both 39th Street, New York 18, New York, Motor-Vehicle Performance on Ascending Grades ROBERT E. DUNN, Assistant Traffic Engineer Washington State Highway Commission The purpose of this paper is to present a graphical type of analysis that was developed to provide sufficient information within reasonable time and cost limits for the determination of the proper location of climbing-lane termini. The procedure employs various types of traffic studies to develop a pro• file of the average running speeds of commercial vehicles and unimpeded passenger cars and a measurement of the additional travel-time required by the overtaking and passing maneuvers of delayed traffic. The graphical anal• ysis determines: (1) the length of the impeding zone within which the grade effects a reduction in the normal speed of trucks; (2) the proper positioning of a climbing lane based upon selected acceptable speed differentials between passenger cars and trucks; and (3) the rating of ascending grades through an economic comparison of time-delay and accident costs of motor vehicle opera• tion. The conclusion of this research is that it is an economical and dependable method of obtaining such supplemental information as may be required for the planning, programming and construction of safe and efficient highway facili• ties. # THERE are over 5, 800 miles of state relation to the benefits to be derived, (3) highway on the rural system in the State of adverse topographical features that affect Washington. The heaviest-traveled routes excavation or fill quantities, and others. of the network either cross the Cascade Two principal operational features have Mountain range that divides the State geo• been found in Washington that tend to graphically, or, in many places, traverse lengthen the climbing lane normally re• rolling forested or agricultural terrain. quired. First, Gypo loggers employing ob• Less than 200 miles of the system have solete equipment in forest regions, and been constructed to four lanes. Increasing farmers utilizmg underpowered trucks in volumes of traffic are causing accidents agricultural areas, present performance and congestion on certain critical two-lane problems different from the weight-power facilities due to the capacity-reducing ratios of the big Rigs operating on inter• effects of slow-moving vehicles on ascend• state hauls to and from industrial centers ing grades. Second, state statutes limit the speed oi Sufficient dependable information is commercial vehicles exceeding 10,000 lb. available to determine where climbing in gross weight to a maximum of 40 mph., lanes for slow-moving vehicles are war- while permitting day and night passenger rented on various gradients and lengths of car speeds of 50 mph. and, at some selec• grades. Other published information can ted locations, 60 mph. be used to position the climbing lane on the The extent to which the operational char - grade so that it will meet the operational acteristics of the average running speeds requirements of average reported traffic of passenger cars and trucks was found to characteristics. There are certam physi• deviate from nationally-reported data in cal and operational characteristics, how• the instance of "Swauk Creek Hill" and ever, found to be peculiar to some ascend• vicinity, is shown m Table 1. ing grades, that involve a deviation from The observed speed of passenger cars published criteria for the proper location and trucks operating on level terrain was and design of a climbing-lane facility. 9 mph. and 10 mph. faster, respectively, Physical factors often limit the length than that of the average reported data. that can be provided for a climbing lane. However, the differential between the speed These include such considerations as: (1) of the two vehicle classifications was ex- the location of crossroads, particularly sentially the same for both the observed at or near the crest of the grade, (2) the and reported data. A greater deviation of economics of right-of-way acquisition in observed speeds from reported speeds was 12 13 found in passenger cars than trucks on 5 prior to the construction of the climbing percent grades. This created a 46-per• lane. Inasmuch as the climbing lane was cent higher differential in grade speed be• in the programming stage at the time of tween the two vehicle classifications than the survey, the findings of the study had is provided for by published design crite• no effect upon its design. ria. SCOPE OF OPERATIONAL RESEARCH PURPOSE OF STUDY The study of vehicle performance on The preparation and review of contract the particular ascending grade of Swauk plans for the provision of a climbing lane Creek Hill is one for which a climbing lane on an ascending grade involves three was proposed in 1953 and constructed in principal considerations: First, there is 1954. This is an ascending grade for west• the application of available research data bound tratfic, approximately 0.6 mile in and design criteria to determine the war• length, onus 10 (Primary State Highways), rants for and the requirements of the facil• 12 miles west of the City of Ellensburg. ity. Second, certain physical and economic US 10 is an important and relatively heavy- factors have a tendency to effect a modi• traveled (4,300 vpd.) two-lane highway on fication in the preliminary design. Third, the interstate system in this vicinity. deviations of observed motor-vehicle per• The Swauk Creek grade is on a general formance from average reported opera• east-west alignment that parallels the tional characteristics may require further Yakima River. The study section passes adjustments m the design to compensate for 6. 5 miles through a narrow and wind• for local traffic peculiarities. ing gorge. Railroads runnmg along both The resolving of these factors that in• river banks have prevented highway con• fluence the design of a climbing lane can struction on a water-level grade, and this sometimes be achieved through opinions condition has necessitated several steep based upon engineering judgment and ex• grade rises and sharp horizontal curves perience. In other instances, the divergent over the rolling terrain. The pavement is nature of existing data may necessitate 20 feet in width, with substandard gravel supplemental information before a deci• shoulders and numerous passing-sight- sion can be reached as to the adequacy of distance restrictions. Valleys located at the design. The survey procedure and both ends of the river gorge allow for long graphical analysis process, hereinafter tangents that are conducive to high vehicle discussed, was specifically evolved topro- speeds. The posted absolute speed limits vide a hand-tailored method of determining on this highway at the time of the study the proper position and length of a climbing were 50 mph. for passenger cars and 40 lane on an ascending grade at such locations mph. for trucks. where published design criteria are not ap• Swauk Creek Hill is one of four ascend• plicable. ing grades encountered by traffic traveling in either direction through the gorge. All TABLE 1 four grades were included in the field sur• REPORTED AND OBSERVED FREE VEHICLE SPEEDS (Swauk Creek HiU and Vicinity) vey, but Swauk Creek Hill was the only one involved in a program for climbing-lane Data Grade Average Running Speed (mph) Speed Source Percent Passenger Cars Trucks Differential construction. Due to the mechanics of pre• Reported ^ Level 46 mph 37 mph 9 mph sentation involved in the graphical analysis Observed' Level 55 mph 47 mph 8 mph process, only the operational research Reported ' + 5% 40 mph 27 mph 13 mph findings on Swauk Creek Hill will be de• + 5% 49 mph 30 mph Observed' 19 mph scribed. A comparison of the effect of the ' Table III-17 AASHO Policy on Geometric Design of Rural several factors of time delay and accident Highways 'Swauk Creek Study of Motor Vehicle Performance on costs on this ascending grade, in relation Ascendmg Grades to the other three, will, however, be pre• sented in the scope of this paper. The study of motor vehicle performance on Swauk Creek Hill was an operational re• PROCEDURE OF STUDY search project conducted for the purpose of improving methods of instrumentation, The study of vehicle performance on and to obtain data on the ascending grade ascending grades in the Swauk Creek Hill 14 vicinity employed various traffic engineer• These measurements were procured by ing procedures to measure the following a three-man crew operating in a cruising basic operational characteristics: (1) vol• survey car equipped with a calibrated sur• ume and classification of traffic; (2) aver• vey odometer reading to 0.01 of a mile, age running and spot speeds of passenger and a sweep-second-hand stopwatch. The cars and trucks; and (3) distance an over• odometer and watch were both started from taking vehicle followed an impeding truck. a zero reading as the cruising car followed Figure 1. Swauk Creek Hill before construction of climbing lane. TRAFFIC VOLUME AND VEHICLE a sample vehicle past the initial point of CLASSIFICATION the study section. A time recording to the Three consecutive weekdays in July nearest second was taken from the contin• 1953, having normal seasonal traffic condi• uously-running stopwatch at each 0. 05 or tions, were selected for the field instru• 0.10 distance readings of the odometer. mentations and observations; 24-hour di• The first interval was used for slow-speed rectional traffic volumes were secured operation, and the latter for high-speed by a mechanical hourly recording traffic recordings as a matter of safety and con• counter. The classification of vehicles by venience. The time and distance readings the license registration of passenger cars 24 HKjr AWO volumt < 4300 (II3%ADT) and the axle arrangement of 10 classes of 9 Hour Volumt • 2300 (34% of AW D ) 30th Hour Volumt'600 ( I 5.8% of AOT) trucks were conducted simultaneously with I I I V\ 1 I / \ I Total the operation of spot speed stations to _ /| \ Both Oi utilize available manpower. OPERATING SPEEDS OF PASSENGER CARS AND TRUCKS Instrumentation of vehicle performance ill ..>,^ol|Oul otlOutofL llPantiaj Dual was made between 9 a. m. and 6 p. m., the Cc»uniy|county|smt« j^^g" PichLip] Ti r«a hours of maximum traffic volumes. Opera• ting speeds were calculated in the office 10 Noon 2 analysis from time and distance measure• ments made in the field. Fipure 2. Traffic volume and classificatic 15 for unimpeded passenger cars and for an GRAPHICAL ANALYSIS adequate sample of trucks of various axle The graphical analysis of vehicle per• classifications selected at random from formance on ascending grades is the pri• the traffic stream were secured in this mary objective of the method of procedure manner. reported upon in the scope of this paper. Radar speed meter equipment was used The purpose of the analysis is to provide a to obtain a larger sample of operating graphical determination of: (1) passing- speeds than was possible by the cruising- sight-distance restrictions on the ascend• survey-car method. The spot speeds were ing grade; (2) the length of the impeding taken just below the crest of the grade so zone within which the grade effects a re• as to secure a check on the minimum crawl duction in the normal operating speed of speed of slow-moving vehicles. trucks; (3) proper termmal locations of a climbing lane, based upon selected accept• able speed differentials between passenger DISTANCE OVERTAKING VEHICLES cars and trucks; and (4) time-delay in• FOLLOWED IMPEDING TRUCKS curred by overtaking passenger cars that A measurement of the distance that an are impeded by slow-moving vehicles. overtaking vehicle followed an impeding or slow-moving truck was recorded simultan• eously with the time and distance data PLAN AND PROFILE OF THE GRADE secured on the truck. The cruising car, The plan and profile of the ascending in assuming the operational performance of grade under study (Figure 3) provides the truck at a safe passmg distance behind information of value m supplementing other it, was considered as having an impeding data in the subsequent analyses. Swauk influence similar to the truck. A passing Creek Hill contains a grade rise of 130 maneuver around the cruising car (but not feet in a run of 3,000 feet. There is a necessarily the truck) by an overtaking 400-foot vertical curve on either end of a vehicle would, therefore, have been theo• 5-percent grade. The relationship be• retically the equivalent of the passing of tween the length of grade, as measured in the truck, had the survey car not been in the field by the use of survey odometer its position in the traffic stream. The stations 3.20 to 3.75, and the engineering distance that an overtaking vehicle followed stations of the construction plans, is the truck was secured by first recording conveniently indicated on the plan and pro• the survey odometer readmg at the loca• file. Scale measurements show that there tion where the speed of the overtaking is approximately 50 percent sight-distance vehicle was influenced by the.cruising car. restrictions for ascending traffic because A second form entry was made at the odo• of the combined effect of two 6-deg. hori• meter station where a passing maneuver zontal curves and the vertical curve at the was completed around the survey vehicle. crest of the grade. SURVEY TIME AND MANPOWER PASSENGER CAR AND TRUCK SPEED REQUIREMENTS DIFFERENTIAL The survey time required to conduct a The difference between the average study of vehicle performance on an ascend• running speeds of unimpeded passenger ing grade depends upon the length of road• cars and various types of trucks (Figure 4) way to be observed and the frequency of provides the data essential for the proper sample arrival for instrumentation. Swauk selection of the length of a climbing lane Creek Hill, with a grade 0.6 mile m length, to fit the local traffic characteristics and a zone of influence of 1.2 miles, and a physical grade conditions. A graphical weekday volume of 4,000 vehicles, re• presentation of the average running speeds quired two days of field observations for for the length of the impeding zone within a crew of three. The office calculations which the grade effects a reduction in the and graphical analysis, exclusive of report normal ijpeed of trucks is of value in preparation, entailed approximately three checking several design criteria. man-days for each man-day spent m field The fundamental principal of climbing work. lanes is to reduce the differential in speed 16 PROPOSED TRUCK LANE PLAN- SWAUK CREEK TRUCK LANE LENGTH Toper OtoiZ Sta 345+00 to 348*00 = 300' Lone 12' Sta 348+00 to 383+50 =3^50' Toper 12 too Sta 383+50 to 386+50 • 300' ELEV. SPOT SPEED STATION 1900 0 00% 7 -0 64K* ^ ^^^^ TRAFFIC COUNT STATION 1800 -o .^^ % t700 d-PROPOSED TRUCK LANE-O it Grade Rite oT 130ft in 3,000 ft Run - PROFILE - 0 > - "o "o • 1600 * 330 340 390 360 370 380 390 400 410 420 ENGINEERING STATIONS Figure 3. Plan and profile. between passenger cars and trucks to a to what constitutes such a speed differential safe minimum. The length of a climbing but, rather, to illustrate the method by lane is, therefore, predicated on an ac• which the termini of a climbing lane can be ceptable safe-speed differential for the located in special situations, once such conditions found at the specific location criteria has been determined by the de• under consideration. It is not the purpose signing engineer. of this paper to enter into a discussion as Table 2 contains various graphical de- TABLE 2 VARIOUS GRAPHICAL DETERMINATIONS OF CLIMBING-LANE LENGTH (Swauk Creek Hill) Climbing Equivalent Speed Selected Graphical Criteria Lane In Grade Differential Length Length Start EHcT Length of Grade mcli. 3ing Vertical Curves 3,000 ft. 1.0 AASHO Design (Truck Speed less than 30 mph) 2,600 ft. 0.9 23 mph 19 mph Proposed Truck Lane excluding Tapers 3,550 ft. 1.2 10 mph 19 mph Permissible Speed Differential of 15 mph* 3,900 ft. 1.3 15 mph 15 mph Normal Speed Differential of 10 mph 5,400 ft. 1.8 10 mph 10 mph Truck Speed less than Legal 40 mph Limit 6,500 ft. 2.2 10 mph 8 mph •H the average speed for trucks at the bottom of the grade were the same as for all vehicles, this differential would be comparable to the permissible speed reduction of 15 mph. in AASHO policy. 17 terminations of climbing lane length, based cars and trucks and would inject them back upon the findings of vehicle performance on into the travel lane at a differential of 19 Swauk Creek Hill. The climbing lane, as mph. originally proposed and constructed, starts The selection of a speed differential of at a point on the grade where there is an ap• 15 mph. would create a climbing-lane proximately normal 10-mph. differential length that is 0.1 mile longer than the pro• between the average speeds of passenger posed design, but the beginning point would cars and trucks and, also, where the latter be moved approximately 550 feet up the is reduced by the effects of the grade to grade. The investigation of other climb• less than 40 mph. The end of the climbing ing-lane design criteria, based upon a lane is at a location beyond the crest of the local legal speed differential of 10 mph. grade where the speed differential is 19 between passenger cars and trucks, or a mph. and at which point the trucks have speed of trucks that falls below the legal accelerated from an avesage minimum limit of 40 mph., produces abnormal equiv• crawl speed of 20 mph. to 30 mph. The alents of 1. 8 to 2. 2 times the length of climbing lane, as constructed, is 1.2 grade. The application of these last two times the length of the grade. standards would probably be unfeasible or Averoge Running Speed^of Unimpeded Pqssenger^ Cars | ^ (PTL) I I I I r BMPH llOMPH SPEED DIFFERENTIAL I \ I i 111 I DIRECTION Of TRAVEL < \ M I I I Average Running Speed of Various T..^Type s o-(f T....i.Trucks. !^ Average Poss Cor Speed at Spo< Speed Station Average Truck Speed at Spot Speed Station (MiUs) 45 44 43 4Z 41 40 39 36 37 36 35 3 4 33 32 31 30 29 28 27 SURVEY ODOMETER STATIONS ELEV | SPOT SPEED STAnON 1900 L i 0 00% ^ -0 62%* ^ -IS MPH L. Is M PH — 10 MPH , 10 MPH SPEED DIFFERENTIAL - 8 MPH DIFFERENTIAL (Average Truck Speed 40 MPH)— 1800 ^ T7 1 ' ' Average Ttn ck S^td 4 0 MPHJ if*w*i 1 1 IP 35% _| hPROPOSED TRUCK LANE—Ol Grode F i>a of 130 feet 1700 < In 30 00 ft Run — PROFILE — > > 8 g • 1600 1 320 330 340 350 360 370 380 390 400 410 ENGINEERING STATIONS Figure 4. Passenger-car and trucks speed differential. The investigation of one AASHO design uneconomical in most cases. Neverthe• criterion that locates the termini at the less, they show the true length of the zone points where the truck speed falls below, at Swauk Creek Hill within which the grade and rises above, 30 mph. provides a effects a reduction in the speed of trucks climbing lane that is 0. 9 times the length and creates an ensuing delay and hazard to of the grade. The application of this stand• passenger-car operation. ard to Swauk Creek Hill, however, would OVERTAKING AND PASSING not remove the slow-movir^vehicles from PERFORMANCE the traffic stream until there was a speed differential of 23 mph. between passenger Passing maneuvers on a two-lane as- 18 DISTANCE DELAYED PASSENGER CARS FOLLOWED IMPEDING TRUCK IMPEDING TRUCKS DELAYED RftSS CARS SELECTED I Z MILE IMPEDING SPEED ZONE AXLES,BODY AV.ZONE TYPEond LOAD SPEED TIMEREQ 43mph ZSmph B2SMI 31 mph 60 Sea 38 mph 3 S«Ct 31 mph 0 39 l4Sac< 19 mph 64SMS Z8 mph 96SKt Z8 mph 100 SMI (Miles) 44 43 42 41 40 39 38 37 36 35 34 33 SURVEY ODOMETER STATIONS ELEV 1 1 "AnniT ONAL TIME REQU RED"IS bos Id u( on _ on A (erog e Possen ger Zar S peed of _ 1900 0 00% * rouah the 1 • tr 49 m ph th 1 2 mli e In• pedi >0 - Spee d Zo ne - uiuuB ni»e ui 130 ft - •n nnn fon t Ru n 1800 -PROFILE— T M II TTT / .-0 35% PROPOSED TRUCK LANE 1 1 1 1 1 1 1 1700 1 Figure 5. Overtaking and passing. cending grade are primarily controlled by graphical preseatation (Figure 5) of the the two factors of sight distance and the data procured on the overtaking and pass- volume of traffic in the opposing lane. The ing performance of vehicles on Swauk TABLE 3 ANNUAL COST OF MOTOR VEHICLE IMPEDIMENT on ASCENDING GRADES IN THE SWAUK CREEK HILL VICINITy (Based upon the Hours of Maximum Traffic -- 9 a. m. to 6 p. m.) Ascending Grade Swauk Cr. -2 3- Item Westbound Westbound Eastbound Eastbound July 1953 AWD (9 am - 6 pm) 1,107 1,107 1,185 1,185 ADT 1953 (9 am - 6 pm) 819 819 878 878 Number of Trucks (Dual-Tired) ' 117 117 125 125 Average Pass. Car Delay/Truck' 50 sees. 65 sees. 51 sees. 32 sees. Vehicle-Hours Delay/Year 592 Veh-Hr 780 Veh-Hr 645 Veh-Hr 405 Veh-Hr A. Time-Delay Cost to Pass. Cars' $592 ??80 $645 $405 Number 1953 Accidents Involving Trucks 16 2 1 B. Annual Accident Cost * $710 $4,260 $1,420 $710 C. TOTAL ANNUAL IMPEDIMENT COST $1,302 $5,040 $2,065 $1,115 ' 14.3% of ADT (9 am - 6 pm) ' Based upon Figure 5 for Swauk Creek Hill and similar tabulations for other grades ' Time Costs are based upon $1.00 per vehicle-hour * Based upon all reported property damage costs 19 Creek Hill is based upon the observed cars and trucks. There are, however, operation of passenger cars and trucks other useful applications that can influence between 9 a.m. and 6 p.m. During this the considerations involved in the proper period, the directional traffic volume ex• use and design of climbing lanes: (1) effect ceeded 100 vehicles per lane per hour. of commercial vehicles in lowering high• The analysis presents: (1) the type of way capacity, (2) effect of slow truck truck observed m each cruising survey speeds upon delayed vehicles, and (3) car run, (2) the location where the over• effect of impeding trucks on traffic acci• taking vehicles were impeded, (3) the dents. distance the delayed cars followed the truck, and (4) the additional passenger EFFECT OF "SWAUK CREEK HILL" car travel time required due to the re• ON HIGHWAY CAPACITY duction in the normal operating speed. The relating of the findings of the sur• The overtaking and passing performance vey analysis with research data contained was recorded for vehicle operation through in the "Highway Capacity Manual," pre• the 1.2-mile length of the impeding zone. pared by the Committee on Highway Capa• Cruising-survey-car Run 1 was the ob• city of the Highway Research Board, serves servation of a six-axle high-horsepower to illustrate the effect that commercial combination gas truck and trailer running vehicles had on the two-lane highway as• empty up the Swauk Creek Hill. The aver• cending Swauk Creek Hill prior to the age speed of this vehicle through the im• construction of the climbing lane. peding zone was43mph. It was overtaken, The manual states that one commercial but not passed, by two passenger cars that vehicle has approximately the same effect followed it through most of the zone for a as 2.5 passenger vehicles on two-lane total of 1.65 vehicle-miles. The overtak• roadways in level terrain. Applying this ing vehicles required 17 additional seconds to the classification of traffic on the level of operating time in following the impeding tangent approaches in the Swauk Creek Hill truck through the zone above that which vicinity, the thirtieth-hour volume of 300 would have been necessary could they vehicles per hour per lane with 15 percent have traveled at the average unimpeded dual-tired trucks, has the equivalent vol• passenger car speed of 49 mph. ume of 368 passenger cars per hour per Cruising-survey-car Run 6 was the ob• lane. servation of a two-axle underpowered farm Table 14 of the "Highway Capacity Man• truck loaded with hay that represented the ual" indicates that one commercial vehicle other extreme of observed operational has the same effect as 10.1 passenger performance. The average speed of this cars on Swauk Creek Hill, where there is vehicle through the 1.2-mile impeding sight distance restriction of 50 percent and zone was 19 mph. It was overtaken and a length of grade of 0.6 mile. The 15 per• passed by four vehicles after each had cent of trucks during the thirtieth-highest followed but a short distance. The total hour, under these conditions, has the vehicle miles of following was 0.55, and effect of 455 passenger cars. This, added the total additional travel time required tc the actual number of passenger cars, amounted to 64 seconds. The average raises the equivalent volume on the grade speed of all trucks through the impeding to that of 710 passenger cars per hour per zone, as observed by the cruising survey lane. In terms of pure passenger-car car, was 30 mph. The minimum crawl equivalents, therefore, the operational speed recorded at the spot speed station, characteristic of traffic on the two lanes of located near the crest of the grade, was Swauk Creek Hill had nearly twice the vol• 10 mph. ume effect as that on the two-lane level tangent section approaching the grade. APPLICATION OF THE ANALYSIS TIME-DELAY AND ACCIDENT COSTS The principal application of the data secured in this type of survey is perhaps The application of the survey data to the that previously described concerning the economics of operation provides a method selection of proper climbing-lane termini, of comparison that is useful in relating the based upon a selected safe differential in effects of vehicle performance on several the average running speeds of passenger ascending grades in the same vicinity hav- 20 Figure 6. Swauk Creek Hill after construction of climbing lane. ing identical traffic characteristics but construction of safe and efficient highway different physical features. The annual facilities. The second objective is to costs of vehicle impediment on the ascend• develop a technique in the application of ing grades in the vicinity is contained in various types of traffic-study methods that Table 3. The comparison of the annual will provide sufficient dependable informa• time-delay costs to passenger cars (Item tion within reasonable time and cost limits. A) reveals that Swauk Creek Hill ranked The procedure evolved and discussed in third in the four ascending grades studied this paper for the study of vehicle per• in the scope of the survey. This same formance on ascending grades has satis• ranking is also maintained in the summary factorily achieved these objectives with of annual accident costs and total impedi• respect to the location and design of ment costs (Items B and C) for the four climbing lanes. ascending grades. The application of the Two general conclusions were derived economics of operation can serve a useful from the complete study of the 6. 5-mile purpose to establish the priority of need length of highway in the vicinity of Swauk when construction funds are limited or a Creek Hill. First, the total section is stage development of an ultimate plan is nearing its practical capacity due to the contemplated. effect of the rolling terrain on sight dist• ance and the operational performance of commercial vehicles. Second, climbing lanes for slow-moving vehicles on all of CONCLUSIONS the four ascending grades are warranted The first objective of operational re• and should be considered as part of a stage search on motor-vehicle performance is development plan for ultimate four-lane to obtain such information as may be nec• construction to increase highway capacity essary for the planning^ programming and and reduce accidents and congestion. Truck Congestion on Uphill Grades WILLIAM E. WILLEY, Engineer, Division of Economics and Statistics, Arizona Highway Department #WnH the end of World War H in 1945 on grades rangingfrom 2 percent to 7 per• and the resumption of near-normal activi• cent. The study disclosed a crawl speed ties in 1946, everyone connected with of 7 mph. on a 6-percent grade, with an highway construction faced many problems. entrance speed of 47 mph. and after travel• The Bureau of Public Roads realized there ing 1, 700 feet up the grade. We said at would be various states working on many that time it would be desirable if we could divergent tangents of the same problem set 25 mph. as the minimum speed of pas• unless a coordinated effort was made to senger vehicles on uphill grades under all channel research activities along well- conditions. It was also pointed out that the organized lines. One of the problems speeds of trucks due to improved motors and confronting the Arizona Highway Depart• higher horsepower would perhaps increase; ment was the matter of building new high• however, it was felt that the minimum ways, as well as remodeling old ones, crawl speed would not be raised much in through very rough mountainous areas. We the near future. In other words, the only were concerned with such things as per• way to speed up the travel of passenger centage of grade, truck speeds, sight cars through the hills was to provide a distance, passing opportunity, roadway means of removing the slow vehicles from width, congestion, and uphill truck lanes. the normal path of travel negotiated by the faster automobiles. The obvious answer In July of 1947, Arizona was visited by was to build uphill truck lanes. Bureau of Public Roads officials from San Francisco and Washington, who explained The matter of economics and general the various types of most-urgent and most- lack of overall highway revenue prompted desired research projects on which ad• further investigation into evaluating the ditional basic data were needed. O. K. congestion caused by these slow-moving Normann, of the Traffic Operations Divi• motor vehicles. By slow-moving vehicles sion of the Washington office of the Bureau we do not mean heavy trucks alone but in• of Public Roads, made several sugges• clude passenger cars pulling house trailers tions as to the type of studies that Arizona as well as older vehicles that become limit• could best participate in. One of these, and ed in power and speed because of over• the one on which we have spent most of our heating. Only trucks of a capacity of lYi effort, had to do with truck operational tons or greater were considered in this speed characteristics on mountainous high• study, however. A heavily loaded vehicle ways. The original suggestion was that we was defined as one loaded to capacity or combine a loadometer survey with a speed nearly to capacity. study on various percentages of grades The results of the first study were pre• under different conditions of traffic, align• sented to the Highway Research Board ment, elevations, etc. at the annual meeting in Washington on During the 2-day conference a total of 15 December 16, 1949. The title of the re• different research projects were discussed. port was, "Survey of Uphill Speeds of Four were finally accepted by the Arizona Trucks on Mountain Grades." It is re• Highway Department as being well within corded in the proceedings of the Twenty- 1 its limited capabilities of personnel and Ninth Annual Meeting. While we were en• finance. It was decided that the department gaged in the study of speed it was felt ad• would check into the uphill speed character• visable to check into the downhill speed of istics of heavy trucks on long, steep moun• heavily loaded trucks as well as the uphill tain grades, then go to the downhill charac• speed characteristics. During 1950 the teristics, and finally study the congestion field investigations were made and the I caused by slow-moving vehicles on uphill analysis was completed soon thereafter. I grades. This presentation represents the In January of 1951 the report was read at final phase of the original program. the annual meeting of the Highway Research In 1948 the project was begun by ob• Board. The title of the second paper was, serving the minimum speeds of heavy trucks "Survey of Downhill Speeds of Trucks on 21 22 fit- Figure 1. Queen Creek Tunnel, showing striping for uphill truck lane. Mountain Grades." The findings of this study that trucks need little special con- phase of the truck project are in the pro- sideration on downgrades and generally ceedings of the Thirtieth Annual Meeting. assume speed characteristics commonly It was ascertained from the downhill associated with passenger vehicles. Ex- Figure 2. Texas Canyon, showing end of truck passing bay. 23 Figure 3. Congestion on Yarnell Hill. cept under congested traffic conditions, it uphill speeds, which are determined by the may be said that downhill truck speeds are hill-climbing ability of the truck. On the largely controlled by the mental attitude of downhill study we could not find any corre- the driver. This is in sharp contrast with lation between speeds, weight, or grade. AKIZ ONA HIGHWAY DEPARTMENT DIVISION OF ECONOMICS AND STATISTICS ACCUMULAILD DAILY DELAY, YARNELL HILL AHHANCED IN ASCENDING ORDER OF — TRAFFIC VOLUMES FOR SURVEY DAYS Figure 4. 24 It is interesting to note, that in connection ance from the minimum crawl speed of 7 with passing lane studies and because of mph. recorded in 1949 to 12. 5 mph. in brake failure on long downgrades, many 1952, on a 6 percent grade.' This im• states are studying, and some are con• provement bears out the original conclu• structing such things as runaway ramps, sion that relief from congestion must be braking barriers, or walls that trucks provided by highway construction rather may be driven against in case of an emer• than larger truck motors. Furthermore, gency. Runaway ramps are generally in 1954 with the construction of passing steep, adverse upgrades adjacent to the bays and because of improved alignment, downhill lane onto which a truck out of truck speed was increased only 1. 2 mph. control may be diverted and stopped. to an average of 13.7 mph, or only 50 per- ARIZONA HIGHWAY DEPARTMENT DIVISION OF ECONOMICS AND STATISTICS CONGESTION PROPII.E, YARNELL KILL AVERAGE DAILY UPHILL TRAFFIC FOR 7 WEEK DAYS 337 TRUCKS 16 Z% AVERAGE DAILY DOWNHILL TRAFFIC FOR 7 WEEK DAYS 326 AVERAGE DAILY TOTAL TRAFFIC 663 . (Figures ihown are for the 8-hour •urvey period 9 00 AM to 5 00 PM) (Aimual average VPD • 1801) i" 30 I U U ZO v; 20 10 u 10 PASSING ZONES I - -1 t STATION NO 0 MP 273 Figure 5 By the end of 1951 data were available cent of an overall desirable minimum road relative to uphill speeds and downhill speeds speed. With this thought in mind we moved that definitely indicated the following con• our research to the field of congestion, clusions: (1) upgrades of 4 percent and which was the third and final phase of this for a length of 3, 600 feet—and for a 6- project. We undertook to show that the percent upgrade with a length of 1,700 congestion caused by slow-moving vehicles feet—uphill passing lanes or bays should on certain lengths of various uphill grades, be investigated; (2) on the descent, extra within definite traffic volume groups, when passing lanes are not warranted, in most eliminated, would result in sufficient saving cases, inasmuch as all vehicle speeds are to the motorist to pay for the cost of con• about uniform, except over the crest of the struction of an uphill lane, or of passing hill; and (3) on uphill passing lanes the lane bays as required at certain critical points. should be extended over the crest of the While conducting the uphill survey a hill to a point approximately at which the limited amount of data were noted on the truck speed builds up to the normal pas• work sheets regarding the delay caused to senger car operational speed. other vehicles by slow-moving trucks. The Modern design has improved perform- time and location of a car back of a truck 25 were noted. If passing became possible the capital investment plus maintenance if farther up the hill, this also was noted. a favorable benefit ratio of greater than one Serious study was given these data in 1949, IS obtained. (6) With the addition of uphill and a definite need for more factual infor• lanes will the number of accidents decrease? mation became evident. It was not until As a preliminary step in this study late in 1951 that finances and personnel we were able to have the district engi• became available, so that we could observe neers stripe some uphill lanes on ex• and record what happens when trucks or isting roadways where there was at least a other slow-moving vehicles cause delay on minimum width for three lanes. These uphill grades under actual operational con• sections should not be confused with three- ditions. lane highways but rather as a roadway with It was decided to conduct the congestion two uphill lanes, the inside for fast travel investigation on one of the hills that had and the outside for slow travel with one previously been studied relative to uphill downhill lane. At all of the locations where truck speeds, inasmuch as some pre• this expedient has been tried it has worked liminary data were available and observa• exceptionally well and has materially re• tion stations had been designated for the duced congestion. hill. The length of hill was 4 miles and the Any study of congestion, whether it be grade was a continuous 6 percent. It is on a level highway or on a 6-percent grade, located on US 89 between Wickenburg and IS quite involved. That is, when does con• Prescott, Arizona, and is known locally gestion actually set in? Is it when moving as Yarnell Hill. The highway was of a along on an open highway at the normal rate narrow, two-lane type with a roadway only of speed and someone passes you ? Did the 22 feet wide; a surface width of 20 feet and driver pass because he felt that the car with very-poor alignment. The Arizona ahead was an obstruction and he was being Highway Adjusted Sufficiency Rating totaled delayed or congested ? A dictionary defines 41 points, a very-low score. Average daily the word "congest" as: "to aggregate; ac• traffic was 1,800 vpd. including 290, or cumulate, to affect with over-crowding, to 16. 2 percent, heavy trucks. Sight distance gather; become congested." It might also was substandard and passing opportunity have said aggravate or irritate when con• was almost nonexistent. Slow-moving ve• sidering long queues of passenger cars de• hicles operating over such inadequate high• layed by slow-moving vehicles through ways, present a real challenge to highway mountainous areas. It was our decision to safety as well as a menace to the ever- consider that all vehicles delayed behind any increasing problem of congestion. slow-moving truck were congested, inas• In the early phase of this congestion study much as the truck speed, at its best, was there were a number of items that were only half of the minimum desired passenger- outlined as being pertinent to the problem: car speed of 25 mph. under any condition of (1) Can the need for uphill passing lanes grade or alignment. It might also be said or bays be determined by volume of traffic that perhaps there are two causes of con• when related to percentage of trucks ? (2) gestion, i. e., voluntary and involuntary. On any particular upgrade where should the The voluntary type appears when a driver widening begin and where should it end? intentionally slows down through mountain• (3) Is there a definite point or area on a ous area so that his passengers may view mountain grade where the delay factor is the scenery or, perhaps, because the an important item and for how long does driver is fearful of mountain grades and it continue? (4) Can passing bays 1,000 prefers to go very slowly. The involuntary feet long help relieve congestion? (5) type IS when a driver is forced to proceed Original highway locations in most cases slower than his desired rate of speed, of have been in service some 30 years. Such course. With the problem being discussed roads are probably those where this type this occurs when a vehicle must decelerate of delay is most frequently found and where and follow, one traveling at a lower than relief is most needed. Can this extra lane normal rate oi speed where there is little be economically justified? Will the life of or no opportunity to pass. This lack of the improvement be such that the savings opportunity to pass depends not only on the to the motorist will offset the cost? Basic• traffic in the same lane but also upon the ally, from an engineering economic stand• volucie and type of opposing traffic. point the savings in dollars should exceed For this project a field party consisting 26 of four men was used. One man recorded or vehicle passed the 0-mile point on the and classified all traffic, while the others hill, at which time the stop watch was tabulated congestion data. The grade under started; (3) stop-watch time as each station observation was divided into Xo-mile inter• marker was passed; (4) stop-watch time vals with panels of high visibility cloth used when overtaking vehicles either piled-up as station markers. Since the observation or passed without delay; (5) approximate posts could not be perpendicular to the meeting point with opposing traffic; (6) roadway at all points, a line of sight from stop-watch time of completion of passing the observation point was used to adjust the movement of delayed vehicle; and (7) roadside interval markers. This method miscellaneous data such as test section assured that a vehicle passing behind the location, type of vehicles, date. marker represented a distance of mile During the course of this study two test of roadway traveled. sites were examined. The second location T».r.«t » .J Figure 6. Delay patterr Each truck was considered as a single was at Ashf ork Hill on US 66 in the normern unit, and the foUowingdata were recorded: part of the state. For the purpose of this (1) classified manual traffic count by 15- presentation only the data obtained at Yar- mmute intervals; (2) time at which a truck nell Hill will be discussed because of time I 27 limitations. The terrain at Yarnell Hill showed the number of trucks- (1) causing made it possible to view the entire section no delay through tne entire test section; under consideration from one observation (2) causing no delay at the corresponding station. Because of this favorable situ• station; (3) charged with delaying one car ation, it was possible to make records as it passed the corresponding station: and on as many as four trucks at the same (4^ delaying two cars, three cars, etc. time. The truck traffic was such that The chart also noted the number of cars we were able to observe and survey 95. 4 added to or subtracted from the existing percent of the total truck traffic. All trucks •stack or queue between stations. From did not create congestion, since only 41. 5 this chart the maximum and minimum days percent of the total caused delay to other of traffic congestion were related to num• vehicles. The survey data was accumu• ber of cars being delayed, as well as the lated during approximately eight normal total hours of delay during the day. LEGEND • 42 Trucks cousing no delay . One truck deloying t»o pcieenger cars, etc Wednesday, 3-23'52"' Thursdoy, 3-24'S2 641 Totoi traffic 570 Total traffic 571 Upgrode 259 Upgrade 66 Trucks classified 46 Trucks clossified 66 Surveyed, of which 45 Surveyed, of ahich 49 caused 23 coused 8917 seconds delay 4820 seconds delay *All figures stiown ore 8 hour totals i I •••• S EE S IS : For Yarnell Hill working days. The first step in the office The next step was to compute the delay was to organize the field data in a con• to each vehicle caused by slower-moving venient and usable form. traffic in the same lane. This analysis This was done on a delay chart which involved: (1) time at which the car (or 28 J Figure 7. Illustration to accompany Yarnell Hill afterstudy, before. cars) became a tail to the slower moving passed the truck; (3) time interval the car truck; (2) time when the delayed car finally was back of the truck was computed; (4) Figure 8. Illustration to accompany Yarnell Hill afterstudy, after. 29 from this was subtracted the time interval was to correlate the delay in numbers of the car would have traveled that same dis• cars to the actual 6-percent profile grade tance at the posted speed limit of 30 mph; of the highway. These findings are shown the difference being considered the delay as Figure 5. time. The next objective of the congestion All delays to each car, whether singly study was to evaluate the money value of or in a long line, were computed separately. the delays, together with other economic There were some cases where trucks were factors, to see if a full-length uphill truck delayed by other slower-moving trucks. lane could be justified. A cost analysis for In these instances it was figured that the construction and maintenance was made and delayed truck could have made the 12. 5- related to savings to the motorist in a mph. average truck speed rather than the benefit ratio comparison. In this compu• slower speed of the lead truck and the de• tation, passenger-car driver time was lay was computed accordingly. The time listed at $1.10 per hour and overall truck delay is shown by bar graph as Figure 4 operational costs, based on local fleet relating the delay in hours to the total vol• records was $5. 28 per hour. When the ume of traffic by days. truck desire speed was related to delay ARIZONA HIGHWAY DEPARTMENT DIVISION OF ECONOMICS AND STATISTICS COMPARISON OF CONGESTION PROFILES, YARNELL HILL Old congestion profile average of seven 8-hour days New congestion profile average of eight 8-hour days u > u J 3900| •< u PASSING ZONES 3600 I It I STATION NO. 0 t New passing bay MP Z73 Figure 9. The next step was to identify the accu• speed the total truck cost was figured at mulated amount of congestion with the $5. 51 per delay hour. These costs were established stations up the grade. This Intentionally made low so as to be on the was done in graph form and is illustrated conservative side when making the eco• by Figure 6. The chart shows the delay nomic analysis. pattern for the low volume day and the high It was not at all surprising, what with volume day, giving the number of trucks solid rock excavation, that the capital costs that caused no delays; those that delayed far exceeded the benefits that could be ex• one car, two cars, etc. The arithmetic pected. In other words, the benefit ratio mean of the number of cars delayed at each factor was considerably less than one. station is shown for the 8-day survey With the full uphill lane out of the picture period. From this chart, the next step economically, the next best thing was to 30 consider the benefits that could be pro• three passing bays at an estimated 15 per• vided by relatively short passing bays lo• cent of what a full extra uphill lane would cated at strategic points. cost, it was found that we could expect to The congestion profile showing the de• reduce congestion by 70 percent. These lays at various stations clearly indicated figures were obtained by office analysis mm s Station o 3 4 7 numbers mi P S: NEW PASSING BAY LEG i Comparison of maximum observed congestion days: Congestion pattern Wed. March 21, 1952 (prior to construction of passing bay) Con; One truck delaying three passenger cars, four passenger cars, etc. Figure 10. Comparison oi the areas of greatest congestion buildup. and could only be checked after the passing It was a simple matter then to designate bays were constructed and a new study by highway stations the best locations for made of the improved situation. the passing bays. Selling these locations Three bays, each 1, 000 feet long, were to the field engineers was not such an decided upon and were to be located at the easy matter, inasmuch as it was their bottom, middle, and near the top of the choice to construct the bays where it was hill. Because of the bad alignment and easier to dig and not where it was indicated sight distance, these locations represented the greatest relief in congestion could be the areas of greatest congestion. The obtained. Differences were finally resolved length was determined by an analysis of when a further analysis disclosed that the the average number of trucks causing de• passing bays would have a benefit ratio of lay, together with the number of cars that greater than one. Also, by constructing would desire to pass in the wider area pro- 3r vided by the new bays. This length figured ers, it was noted during the course of this out to be 800 feet with a 100-foot transition study that of all passing maneuvers 32. 6 at each end, so the total length became percent were made in clearly marked no- 1, 000 feet. Table 1 lists the theoretical passing zones. It might well be stated that passing distance for various numbers of a 1,000-foot bay properly signed should *mwm- ••{ «••• • •I •••I • ••I • •••IMes ••••I 8 10 11 12 13 4 15 16 ND Congestion eliminated by new passing bay estion pattern Wed. June 9, 1954 [after construction of passing bay) congestion patterns. motor vehicles on a 6-percent grade, com• adequately handle a total daily traffic vol• pared to what was actually observed after ume of 3,000 vehicles, with 20 percent the bays were constructed. trucks. Cars took longer to pass in the new bays The field work for the congestion study than was previously anticipated. This was was supervised by J. W. Dewey, project especially true of the Number 4 car and chief, and H. C. Burnett and A. B. Anthony, those following it. The 1,000-foot bay, project assistants, all of the Arizona High• under ideal conditions on a 6-percent grade, way Department. should allow 14 vehicles to pass a truck Because of budgetary limitations it was moving at the crawl speed. As a practical not feasible to construct all three bays matter, only nine can expect to clear a truck under one contract so they were built one at at any one passing bay on Yarnell Hill. As a time. To date two have been built and the a commentary on sign observance by driv- third is planned for this year. The relief Some HRB Publications Relating to Geometric Design BULLETIN 35: HIGHWAYS WITH A NARROW MEDIAN (1951) 95 p. $1. 50. Contains reports of the following states: California, Connecticut, Illinois, Michigan and New Jersey. Also contains the papers: "The Effect of Various Types of Median Dividers on the Lateral Positioning of Cars," by E. B. Shrope, and "A Discussion of Pre-Cast Concrete Traffic Dividers - Ohio," by Ralph O. Lehman. BULLETIN 72: DIRECTIONAL CHANNELIZATION AND DETERMINATION OF PAVEMENT WIDTHS (1953) 49 p. $. 75. This publication contains two papers. "Directional Channelization Design," by W. R. Bellis describes unique methods for the efficient movement of traffic through high-volume intersections at grade by the use of channel• ization. The paper by L. F. Heuperman, "Determining Widths of Pavements in Channelized Intersections" describes in detail a practical method for desigmng pavements at channelized intersections by checking the design through the use of scaled models of typical motor-vehicle types. BULLETIN 104: VEHICLE CLIMBING LANES (1955) 33 p. $. 60. SPECIAL REPORT 5: CHANNEUZATION: THE DESIGN OF HIGHWAY INTERSECTIONS AT GRADE (1952) 250 p. (size 11" x 17", plastic binding) $6. 00 per copy (Foreign postage $. 50 extra). This publication represents the cooperative efforts of the Highway Research Board's Committee on Channelization and the many state and city engineers who furnished the field data for the 59 examples included in this publication. The examples of channelization show "Before" and "After" diagrams and critical comments or reviews of each example. SPECIAL REPORT 12: RESEARCH NEEDED IN GEOMETRIC HIGHWAY DESIGN (1953) 49 p. $. 75. This publication includes research problem statements outlining areas for large and small unit research on different phases of 26 selected subjects for which data are needed in highway design. HBB: 11-300 HE NATIONAL ACADEMY OF SCIENCES—NATIONAL RESEARCH COUN• CIL is a private, nonprofit organization of scientists, dedicated to the Tfurtherance of science and to its use for the general welfare. The ACADEMY itself was established in 1863 under a congressional charter signed by President Lincoln. Empowered to provide for all activities ap• propriate to academies of science, it was also required by its charter to act as an adviser to the federal government in scientific matters. This provision accounts for the close ties that have always existed between the ACADEMY and the government, although the ACADEMY is not a govern• mental agency. The NATIONAL RESEARCH COUNCIL was established by the ACADEMY in 1916, at the request of President Wilson, to enable scientists generally to associate their efforts with those of the limited membership of the ACADEMY in service to the nation, to society, and to science at home and abroad. Members of the NATIONAL RESEARCH COUNCIL receive their appointments from the president of the ACADEMY. They include representa• tives nominated by the major scientific and technical societies, repre• sentatives of the federal government designated by the President of the United States, and a number of members at large. In addition, several thousand scientists and engineers take part in the activities of the re• search council through membership on its various boards and committees. Receiving funds from both public and private sources, by contribution, grant, or contract, the ACADEMY and its RESEARCH COUNCIL thus work to stimulate research and its applications, to survey the broad possibilities of science, to promote effective utilization of the scientific and technical resources of the country, to serve the government, and to further the general interests of science. The HIGHWAY RESEARCH BOARD was organized November 11, 1920, as an agency of the Division of Engineering and Industrial Research, one of the eight functional divisions of the NATIONAL RESEARCH COUNCIL. The BOARD is a cooperative organization of the highway technologists of America operating under the auspices of the ACADEMY-COUNCIL and with the support of the several highway departments, the Bureau of Public Roads, and many other organizations interested in the development of highway transportation. The purposes of the BOARD are to encourage research and to provide a national clearinghouse and correlation service for research activities and information on highway administration and technology.