A HANDBOOK FOR THE ROLLING RESISTANCE OF PNEUMIATIC TIRES S K. 4ark and R. N. Dodge INDUSTRIAL DEVELOPMENT DIVISION INSTITUTE OF SCIENCE AND TECHNOLOGY THE UNIVERSITY OF MICHIGAN ANN ARBOR 1979

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PREFACE This handbook is a reprint of a document prepared for the U.S. Department of Transportation, Transportation Systems Center, Cambridge, Massachusetts. Its purpose is to describe the mechanics of tire rolling loss sufficiently so that those interested in understanding fuel consumption in vehicles may make comparative assessments of potential tires for given vehicle weights, tire inflation pressures, and tire construction features. Since tire construction'details are subject to change, it should be understood that the data given here are probably more valuable in indicating trends than in giving exact numerical values for the rolling resistance of current production tires. The authors would like to acknowledge the financial support of the United States Department of Transportation for the funds which made this work possible. We would also like to thank Mr. Stephen Bobo, Technical Monitor, for originating this concept and for many suggestions regarding the handbook's format and content. The data quoted in this report were obtained by the B. F. Goodrich Research Laboratory and thanks are due to Dr. Marion Pottinger and Mr. David Strelow for their very careful and accurate measurement procedures. ii

TABLE OF CONTENTS PAGE LIST OF TABLES.......... iv LIST OF FIGURES..................... v NOMENCLATURE...............vii KEY TO TIRE CONSTRUCTION NOTATION. v......viii I. INTRODUCTION..l........... 1 II. FUNDAMENTALS OF ROLLING LOSS.......... 2 III. EFFECT OF OPERATING VARIABLES.......... 6 IV. MEASUREMENT METHODS AND DATA REDUCTION IN ROLLING LOSS MEASUREMENTS....... 47 Stress Effects.............. 47 Measurement Geometry......... a 48 Combined Effects. 49 V. DESCRIPTION OF TEST METHODS............ 59 VI. BIBLIOGRAPHY Y.........61 APPENDIX - MEASUREMENT METHODS AND DATA REDUCTION IN ROLLING LOSS MEASUREMENTS. 62 iii

LIST OF TABLES Table Page I. Tire Identification and Test Data....... 28 II. Test Data for 7.00-15 LT Tire.......... 35 III. Test Data for 8.00R 16.5 LT Tire....... 35 IV. Test Data for 8.75R 16.5 LT Tire....36 V. Test Data for 9.50-16.5 LT Tire.36 VI. Coefficient of Rolling Resistance for Light Truck Tires at Typical Loads and Pressures.... 36 VII. Equilibrium Rolling Resistance for Tires of Various Sizes Under the Same Load.46 VIII. Measured vs. Calculated Values of Equilibrium Rolling Resistance Using Equation (10).57 IX. Measured and Predicted Equilibrium Rolling Resistance Using Equation (10)....... 58 iv

LIST OF FIGURES Figure Page 1 A Typical Stress-Strain Curve Illustrating Loss................ 5 2 Influence of Temperature on the Loss Characteristics of a Typical Rubber Compound... 5 3 Typical Rolling Resistance vs. Time Variation.................. 8 4 Rolling Resistance vs. Vertical Load for G78-14 Bias Tire.... 0 0.. 9 5 Rolling Resistance vs. Vertical Load for H78-15 Bias Tire........... 10 6 Rolling Resistance vs. Vertical Load for GR78-14 Radial Tire........... 11 7 Rolling Resistance vs. Vertical Load for HR78-15 Radial Tire.......... 12 8 Coefficient of Rolling Resistance vs. Vertical Load for G78-14 Bias Tire.. v..... 14 9 Coefficient of Rolling Resistance vs. Vertical Load for H78-15 Bias Tire...... 15 10 Coefficient of Rolling Resistance vs. Vertical Load for GR78-14 Radial Tire...... 16 11 Coefficient of Rolling Resistance vs. Vertical Load for HR78-15 Radial Tire....... 17 12 Rolling Resistance and Coefficient of Rolling Resistance vs. Reciprocal of Inflation Pressure for G78-14 Bias Tire..... 20 13 Rolling Resistance and Coefficient of Rolliing Resistance vs. Reciprocal of Inflation Pressure for H78-15 Bias Tire.. 21 14 Rolling Resistance and Coefficient of Rolling Resistance vs. Reciprocal of Inflation Pressure for GR78-14 Radial Tire....... 22 v

Figure Page 15 Rolling Resistance and Coefficient of Rolling Resistance vs. Reciprocal of Inflation Pressure for HR78-15 Radial Tire.. 23 16 Rolling Resistance vs. Speed for a Group of Modern Passenger Car Tires......... 25 17 Rolling Resistance vs. Tire Load Rating for a Typical Selection of Passenger Car Tires.. 27 18 Coefficient of Rolling Resistance vs. Tire Load Rating for a Selection of Passenger Car Tires........32 19 Ratio of Equilibrium Rolling Resistance to Initial Rolling Resistance for a Selection of Passenger Car Tires........... 34 20 Rolling Resistance vs. Cooling Time for: (a) BR78-13 Radial Tire; (b) LR78-15 Radial Tire; (c) GR78-15 Radial Tire; (d) G78-15 Bias Tire; (e) A78-13 Bias Tire..... 38 21 Equilibrium Rolling Resistance Values for New, Worn, and Retreaded Tires of the Same Type.. 44 22 Carpet Plot of Rolling Resistance as a Function of Load and Pressure.53 23 Five-Point Carpet Plot........ 53 24 Graphical Representation of the Slope Needed to Determine the Constant for Tire Predictions............ 56 A-1 Free Body Diagram of a Rolling Tire on a Fla-t Surface Under Applied Force.63 A-2 Free Body Diagram of a Rolling Tire on a Flat Surface Under Applied Torque..... 65 A-3 Free Body Diagram of a Powered Tire Dirving a Vehicle.... 65 A-4 Resultant Forces on the Tire While Rolling Qn a Test Drum.. 65 A-5 Geometry of Tire and Test Drum...... 75 A-6 Typical Tire Cross-Sectional Geometry.... 75 vi

NOMENCLATURE General CpCT - constants F - tire rolling resistance on highway, lb r F - tire rolling resistance as measured by axle force xM transducer, lb F - tire rolling resistance when running on a cylindrical XR drum of radius R, lb F - tire load, lb z KL K - constants p - tire inflation pressure, psi, initial cold value R - drum radius r - tire radius rL - tire loaded radius (axle height) r - tire rolling radius r T - temperature t - time Tire Construction B - bias tire N - nylon BB - bias belted tire P - polyester R - radial tire R - rayon F - fiberglas S - steel H - high performance vi 1

KEY TO TIRE CONSTRUCTION NOTATION Example Bias Tires (B): 4 N No. of plies Material Bias Belted Tires (BB): 4N + 2N / 4N Belt Sidewall / Tread Radial Tires (R): 2P + 2S + iN / 2P / Belt Sidewall Tread

I. INTRODUCTI ON Interest in fuel conservation and the national goal of more energy efficient passenger car vehicles has generated considerable interest in the phenomenon of the rolling resistance of pneumatic tires. It is generally recognized that the pneumatic tire represents one of the major loss mechanisms for the engine output of a vehicle, the other mechanisms being considered to be aerodynamic loss, transmission and drive train inefficiency, and the power needed for acceleration of the vehicle. The quantitative influence of tire rolling resistance on fuel consumption. depends heavily on the vehicle and on the specific driving cycle. The most pertinent data, at least for passenger car tires, seem to be those of Ref. [1],* which shows that in the range of present commercial tire characteristics, and for most driving cycles, a 10 percent change in tire rolling resistance yields a 2 percent change in fuel economy. This is a ratio of 5:1 in sensitivity. However, this improvement factor decreases as tire loss becomes less. When more fuel efficient tires have been developed and are in use, their contribution to the overall fuel consumption of the vehicle will be small enough that a much larger percentage change in tire rolling resistance will be required in order to achieve the same percentage change in fuel consumption. _-1-_

- 2 - Recent trip length studies[3 4], show that the average trip length in the United States is less than 5 miles, and that over 40 percent of the vehicle miles traveled by passenger cars is for trips less than 5 miles. Even further, due to the temperature sensitivity of pneumatic tires, their rolling loss tends to be substantially higher in the winter months than in the summer months, and this factor, coupled with short trip lengths, means that a great deal of the passenger car vehicle travel in the United States is carried out under conditions when the tires account for a substantial part of the vehicle rolling resistance. Clearly, the role of the tire is a vital one in this problem, and probably is the single most important component outside of the engine which can be modified or improved to aid in the goal of reduced fuel consumption. II. FUNDAMENTALS OF ROLLING LOSS It is useful to think of the tires on the drive wheels of an automobile or truck as power transmission devices, since they transmit power from the engine to the roadway in order to propel the vehicle. This is accomplished with an efficiency which may vary from nearly 100 percent to zero, although under normal conditions of good traction and steadystate running, the efficiency of the pneumatic tires is quite high, being of the same order of magnitude as that of

- 3 - other power transmission components in the vehicle, say 0.98 to 0.99. The unpowered or free rolling wheels on a vehicle may be thought of as a special case of powered wheels, but now with zero torque applied from external sources. The rolling loss of a tire is made up of three parts: (a) Friction or scrubbing between tire and roadway; (b) Windage loss of the tire; and (c) Hysteretic losses of the tire materials due to cyclic stressing. These have their origin in typical stress-strain curves such as shown in Figure 1, where the shaded area under the curve is the energy lost in one stress cycle. In normal operation the tire loss is essentially all hysteretic, the ground friction and windage being negligible. The hysteretic loss properties of almost all rubber compounds are quite temperature sensitive, being much larger at low temperatures than at high temperatures. This is illustrated in Figure 2. This means that tires have a much higher rolling loss when first starting from ambient temperature conditions than after warming up to equilibrium running temperatures. Further, the higher temperatures in the tire cause the air in the tire to increase in pressure, leading to reduced tire deflation and even further reductions in rolling loss. Because of these two effects acting together, tires show a significant reduction in rolling loss as they warm up. For passenger car tires this reduction is of the

- 4 - order of 1/3 of the initial rolling loss, and occurs over a 20-30 minute period. On the passenger car vehicle every tire performs at least one function other than carrying its assigned share of the load. This may be either driving, in the case of the rear wheels, or steering in the case of the front wheels. Both of these effects obviously influence loss in the tire itself, and greatly complicate quantitative evaluation of one tire design against another. For that reason the present review will be restricted to free rolling tires in straightline motion without steer or applied torque. This will give at least a base-line condition from which the performance of one tire may be judged against another in a relatively simple set of operating circumstances. Even within the framework of the restrictions just stated, the rolling loss experienced by a pneumatic tire still is a function of the tire initial inflation pressure and temperature state, both of which depend not only on the length of time of running but also upon the detailed running history and ambient temperature, as well as the other operating parameters that normally control tire rolling resistance such as vehicle speed and weight. Thus the unambiguous description of the rolling loss of a pneumatic tire requires the complete specification of its operating characteristics. These will be discussed in subsequent sections.

-5LUd IA STRAIN FIGURE 1. A TYPICAL STRESS STRAIN CURVE ILLUSTRATING LOSS 10o% STRAIN 0.14- PHR _ o GUM 0.12.. o 15 0.0519 o 20 0.0693 0.;10 \. A> 35 0.1122 0.10 \A CARBON BLACK 0.06 u..PHR,'<~~ It15N220 0.04 O%%35 N990 -oO20 N990 GUM 0.02 0 20 40 60 80 100 120 * TEMPERATURE (0C) FIGURE 2. INFLUENCE OF TEMPERATURE ON TRE LOSS CHARACTERISTICS OF A TYPICAL RUBBER COMPOUNDD

- 6 - III. EFFECT OF OPERATING VARIABLES Since all rubber compounds exhibit temperature sensitive loss characteristics, rolling resistance of a pneumatic tire depends on its operating temperature, which in turn is controlled by its inflation pressure, load, and the length of time which the tire has run. Usually the tire starts from a cold state when the vehicle begins a trip, and warms up due to internal hysteretic loss as the trip progresses. During the warm-up process the rolling resistance of the tire decreases, and eventually the tire reaches some nearequilibrium temperature provided that the vehicle is operated in a steady-state condition, such as at constant speed on the highway. Under conditions of start and stop driving, such as in an urban environment, the tire is constantly changing temperature, but due to its poor thermal conductivity it does so with a relatively small set of perturbations about some average warm or hot state. The detailed description of such a temperature state is a function of the exact driving cycle and cannot be described specifically. It has been customary in the study of tire rolling resistance to evaluate this type of effect at some convenient constant speed in order to provide a base-line measurement against which one tire could be compared with another. This is probably as satisfactory a solution as can be obtained at this time for the effect of running time or trip length.

A typical plot of tire rolling resistance versus running time is shown in Figure 3 for Goodyear GR78-14 radial tire. This is typical of the kind of rolling resistance response to time which a pneumatic tire exhibits. There has been considerable interest in the influence of load and running time on the rolling resistance of pneumatic tires, and Figures 4-7 present data on this subject for four common sizes of passenger car tires, these being G78-14 and H78-15 bias tires, and GR78-14 and HR78-15 radial tires. In this case the tire rolling resistance is plotted as a function of load carried, for the case where the cold inflation pressure is set prior to the beginning of the test. The rolling resistance is plotted at various values of time ranging from the initial or the starting value up to the equilibrium value. It may be seen from these figures that there is a nearly linear relationship between the tire rolling resistance and the load for the equilibrium case, as illustrated in Figures 4-7. In all four of these sets of data the linear relationship between load and rolling resistance is very close, and further, to a very close approximation the rolling resistance vanishes at zero load, with a straight line drawn through the data points nearly intersecting the origin of rolling resistance and load. This is illustrated in Figures 4-7 by means of a dashed line extending from the data points to the zero load condition.

Speed 50 mph Tire 618 Goodyear Load 1104 l1b. GR78-14 MKMA HCE 354 20 Cold Inflation Pressure 24psi ai I -j t6!'r6 z 0 4 8 12 16 20 24 28 32 MINUTES FIGURE 5. TYPICAL ROLLING RESISTANCE VS. TIME VARIATION..I ~ ~ ~ ~ ~ MIUE _1~~~IUE3 PCLRLIN SSMEV.TEVRTO 0

60~ — Speed 50 mph Cold Inf lotion 24 psi Tire 601 Goodyear Ambient Temp. 230C G78-14 BIAS S/N CKL9E2A 443 50 t=O 40 z cn 30 ~ w t=5min..j-j 20 0 200 400 600 860 1000 1200 1400 1600 1800 LOAD - LBS. FIGURE 4. ROLLING RESISTANCE VS. VERTICAL LOAD FOR G78-14 BIAS TIRE

..............I I I I. I I I I I' 60| Speed 50mph. I Tire 641- Firestone Cold Inflation 24 psi H78-15 Bias S/N WKVX VEE 145 Avg. Amb. Temp. = 290C 50 (I)uj~~~~~~~~~~~~~ t=O (lo 0 -J 40 ]20 (10 0 0 200 400 600 800 1000 1200 1400 1600 1800 LOAD - LBS. FIGURE 5. ROLLING RESISTANCE VS. VERTICAL LOAD FOR H78-15 BIAS TIRE

241 Speed 50mph _ Tire 618 -Goodyear Cold Inflation 24 psi f GR78-14 S/N MKMA HCE 354 t=O Avg. Amb Temp. ~ 25~C t=s min. () Zj t J16 _t 4 F zl l ll.,, I 0 200 400 600 800 100 0; 200.400 600 800 1000 1200 1400 1600 1800 LOAD - LBS. FIGURE 6. ROLLING RESISTANCE VS. VERTICAL LOAD FOR GR78-14 RADIAL TIRE

I..............I " "'I' i....::t=O' Speed 50 mph Tire 637- Uniroyal Cold Inflation 24 psi HR78-15 S/N APVY EZ 025 24 Avg. Amb. Temp. = 27.60C t=5min. ~20,,:,, /~~~,,11 ~~~~t:lSmin. vj I I 1 I I I (' ~ j~t= tOmin m t te w b.I 0 16 Z t0'/) LJ 12 z__ o8 / 0 200 400 660 800 1000 1200 1400 1600 1800 2000 LOAD - LBS. FIGURE 7. ROLLING RESISTANCE VS. VERTICAL LOAD FOR HR78-15 RADIAL TIRE

- 13 - These data further show that such a linear relationship is not true at the starting point, zero time. However, the tires tend to warm up rather quickly, with rolling resistance values at 5 and 10 minutes being very close to the equilibrium value, much closer than to the starting value. This means that analytical modeling of the pneumatic tire as a function of time for short trip lengths probably is most important in the first 15 minutes of the trip. This is an important segment of the many short trips which occur so frequently. The linear nature of the equilibrium rolling resistance as a function of load is apparently fortuitous, but is well known and has led to the common and very useful concept of the coefficient of rolling resistance, which is defined as the rolling resistance divided by the load carried. Using the data of Figures 4-7, the coefficient of rolling resistance may be replotted as a function of load and time and is shown in Figures 8-11 for the same four tires. The coefficient of rolling resistance is a convenient concept since it allows one to compare various tires for use on the same vehicle. The load carried by a tire will be the same on a given vehicle in a given tire position, so a comparison of the rolling resistance coefficients will show which tire is the most efficient for a given application. On the other hand, tests of tire rolling resistance are usually carried out at the tire rated load or at some relatively large fraction of it, such as 80 percent of tire rated

I iI I....l.0300 - Speed 50 mph f Tire 601-Goodyear I.. _. N Cold Inflation 24 psi G78-14 Bias S/N CKL9E2A 443 It =0t= Avg. Amb. Temp. 230C w.0250' _ 0 I) u).0200 L..j.0150 ( 0 te t3: lc., 0..0100............... w b.. w.0050 0 0 0 J 200 400 600 800 1000 1200 1400 1600 1800 LOAD - LBS. FIGURE 8. COEFFICIENT OF ROLLING RESISTANCE VS. VERTICAL LOAD FOR G78-14 BIAS TIRE

'!I I I llII II I I I I _____ I ___________ I__________ ________I__.0300 Speed 50mph Tire 641 -Firestone Cold Inflation 24 psi H78-15 Bias S/N WKVX VEE 145 Avg. Amb. Temp. 290C w.0250 z' z t=O.j -J.0CC7 0. ttl ~ ~ ~ I t OL 0 ~~~~~~~~~~~~~0 z.0100___ w (D J LI -.0050 _ _ 0 200 400 600 800 1000 1200 1400 1600 1800 VERTICAL LOAD -LBS. FIGURE 9. COEFFICIENT OF ROLLING RESISTANCE VS. VERTICAL LOAD FOR H7y8-15 BIAS TIRE

.....I......... I I.... 1 0300 Speed 50mph 1_ Tire 618 - Goodyeor _____ Cold Inflation 24 psi GR78-14 S/N MKMA HCE 354 i _ | Avg. Amb. Temp.= 25~C o.0350 U) C.v~~,~ z.0 50 0 I, LL 0 t=Smin. 03 t=10min. z.0100 t t o.0050 () o 200 400 600 800 1000 1200 1400 1600 1800 VERTICAL LOAD- LBS. FIGURE 10. COEFFICIENT OF ROLLING RESISTANCE VS. VERTICAL LOAD FOR GR78-14 RADIAL TIRE

.0300~- Speed 50 mph Tire 637-Uniroyal Cold Inflation 24 psi HR78-15 S/N APVY EZ 025 Avg. Amb. Temp. 280C w.0250 o cn (I) uV0200 w ar:I o.0150 LiL t: 5mm. ~~.0100 _____ __ _____ ~~~~~~~~~~~~~t=10min..0100 z t=t UL w.0050 C)~~~~~~~~~~~~~~~~~~~~~~~1 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 VERTICAL LOAD -LBS. FIGURE 11. COEFFICIENT OF ROLLING RESISTANCE VS. VERTICAL LOAD FOR HR78-15 RADIAL TIRE

- 18 - load. Direct presentation of the rolling resistance under these conditions is dependent on the load carried by the tire, which, of course, varies for different tire sizes. Hence, the concept of the coefficient is a generalizing and extremely useful one for both the presentation and interpretation of data. Figures 8-11 show that for the two bias and two radial tires described there, the coefficient of rolling resistance increases with increasing load for the cold, or initial, state. For the equilibrium state the coefficients of rolling resistance are, on the average, essentially independent of load. Examination of data taken at fixed tire load and variable initial inflation pressure shows that the tire rolling resistance decreases as the inflation pressure is increased. This is caused primarily by the reduced deflection of the tire when running under a higher inflation pressure as compared with lower. The effect with pressure is not a linear one, since as inflation pressure is decreased the tire rolling resistance increases markedly. However, it has been shown in the past, and the present data collected for this handbook substantiate this conclusion, that the rolling resistance is nearly linear with the reciprocal of initial inflation pressure under conditions of capped air, steadystate running, and constant load. The four tires discussed in Figures 4-11 were tested under a variety of initial inflation pressures and the resulting rolling resistance

- 19values are plotted as a function of the reciprocal of inflation pressure in Figures 12-15, again for various times so that the influence of running time may be illustrated. From these data it is seen that the simplest and most consistent relationship is a linear one with the reciprocal of pressure for equilibrium running conditions. All four tires exhibit this, and this phenomenon has also been reported elsewhere.[1] It should be noted that the curves do not intersect the zero rolling resistance point as the reciprocal of pressure approaches zero, which implies that at very large inflation pressures some rolling loss would still remain in the tire. Figures 8-11 and 12-15 now suggest that the relationship between equilibrium rolling resistance, load on the tire, and initial inflation pressure may be expressed in the form of Eq. (1). Fre Fz (Cp/p + cT) (1) where Fr = tire rolling resistance at equilibrium conditions Fz = load on tire p = initial inflation pressure p, cT = constants A more thorough exposition of this concept will be made in Section IV of this handbook.

Speed 50 mph Tire 601 Goodyear Load 1104 lbs. G78-14 Bias CKL9 E2A 443 50 05 Avg. Amb. Temp.= 250C 1.0453 45.0408 vj40 ~ =.0362 m~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Q H 35.0317 " z 30.0272'L H ~~~~~~~~~~~Z ( 25 1t5min..0226 w t=00min. ~20 t~te.0181 1 z LL Tj 15 1 I II~LI I I 1 1.0136 H 0 -O zvo 10 C14~~~~~~~~~~ wool~ ~ ~ ~ ~ ~ ~ ~ ~ tLa 5.0045 La 100 50 33.3 25 20 16.7 14.3 P, psi 0.010 220.030.040.050.060.070 1/p I in2 P Ib FIGURE 12. ROLLING RESISTANCE AND COEFFICIENT OF ROLLING RESISTANCE VS. RECIPROCAL OF INFLATION PRESSURE FOR G78-14 BIAS TIRE

Speed 50 mph Tire 641- Firestone Load 1208 lbs. H78-15 Bias S/N WKVX VEE 14550.0414 Avg. Amb.Temp.= 270C m 45 I.0373* i 40.C10.0331 z m t=O.1 i 55 i.0290 ( H Z F25 t=5min..0207 i 5 B t = 10 min. 20 t' =te 0166 z o ]j15.0124 - 0 W.. 10....0083 3 LL 5.0041 t 100 50 33.3 25 20 16.7 14.3Ppsi 8 0.010.020.030.040.050.060.070 1i/p 1 in2 P lb FIGURE 13. ROLLING RESISTANCE AND COEFFICIENT OF ROLLING RESISTANCE VS. RECIPROCAL OF INFLATION PRESSURE FOR H78-15 BIAS TIRE

z I I~~~~~~~~~~~~~~~~~~~~~~ Speed 50 mph Tire 618 Goodyear Load 1104 lbs. GR 78-14 S/N MKMA HCE 354 22 Avg.Amb.Temp.= 240C 20t0..0181 Lu! 18.0163 LU I~~~~~~~~~~~~~~~~~~~~~I 0 3 16. t;5min..0145 H'J~~~~~~~~~~~~~~~~~~~~~~~~U t= 10 min. vn 14.0127 U ~i t: e L Z I 1 2.0091j W I 0! QI:'j / 0 ~8 00001,.0072'x z 0.0054 0 W W) 4...................0036 Y LL LL 2.0018 W 0 190 59 333 25 20 16.7 14.3 P O0.010.020.030.040.050.060.070 1/P 1 in2 P lb FIGURE 14. ROLLING RESISTANCE AND COEFFICIENT OF ROLLING RESISThNCE VS. RECIPROCAL OF INFLATION PRESSURE FOR GR78-14 RADIAL TIRE

24C Speed 50 mph Tire 637 Uniroyal __ t=O Lood 1208 l bs. HR 78-15 22.0182 Avg. Amb. Temp.= 280C S/N APVY EL025 20.0166 L. cf'8 t 5min..0149 uj __ _= z min. 916 _0132 Z 14 t10min.0116 W.W U) _ _ _ _0_ _9 A) bJ z LW t310.0083 -J z 0 uJ J8 -".0066 U0 uJ z _J o 0 6 ~~~~~~~~~~~~~~~.0050 z 4.0033 U LL 2.00170 -'J ~ ~ ~ ~~~~~~~~0 0100 50 3.3 25 2 16.-7 14.3 P, psi.010.020.030.040.050.060.070 1/P 2 ~ ~ ~ ~ I in2 P lb FIGURE 15. ROLLING RESISTANCE AND COEFFICIENT OF ROLLING RESISTANCE VS. RECIPROCAL OF INFLATION PRESSURE FOR HR78-15 RADIAL TIRE

- 24 - Examination of the same figures also shows that no comparably simple relationship exists for the relation between load and pressure and initial or cold tire rolling resistance. The resistance is not linear with load nor with the reciprocal of pressure, and no generalized relation such as that of Eq. (1) has yet been proposed. The question of speed effect on rolling resistance has been one of considerable uncertainty in the earlier published literature. Some measurements have been reported showing rather marked effects of speed on rolling resistance, while other measurements show very little effect. A recent series of measurements on a single set of tires carried out by a number of the major American tire manufacturers showed that the rolling resistance of the sample tires was nearly independent of speed within the speed ranges normally encountered on the American highways today. [4] Figure 16 shows the mean value of rolling resistance for five different common American passenger car tires at three different speeds as measured over nine different laboratories ranging from a 64-inch diameter cylindrical drum to a flat surface. These measurements were carried out at 30, 50, and 70 mph, and show that the rolling resistance is nearly constant with speed up to 50 mph, while at 70 mph the general tendency is for a small increase. It is surmised that the effects-here are combinations of higher temperature and greater pressure buildup associated with higher running speeds, while at the sametime greater dynamic effects are also associated with

- 2522 __ 20. — - L78-15 Bias 18 16 - LR78-15 i4 J 58 12.- 1...,A78-3 Bias 6 ROLLING RESISTANCE___ Men Vlues from 10 Labortories Belt W BR 78-13:2 MA0 10 20 30 40 50 60 70tories 2SPEED, MPH FIGURE 16. ROLLING RESISTANCE VS. SPEED FOR A GROUP OF MODERN PASSENGER CAR TIRES

- 26 - these higher speeds. The two influences are counteracting, and probably tend to cause the relatively uniform response with speed as illustrated in Figure 16. The question of size and construction is an important one in assessing the rolling resistance of a tire. For purposes of this study a wide variety of passenger car tires were tested for their rolling resistance characteristics. These tests involved some 65 different tires encompassing most of the common construction and manufacturers. The results of these tests are expressed as the absolute value of rolling resistance at 80 percent of the rated load of each of the tires, and are plotted in Figure 17 as a function of the tire load rating, with the increasing load ratings being plotted to the right of the figure. (Individual test results are given in Table I.) On this curve each measured rolling resistance is plotted as a single point showing the rolling resistance value obtained at equilibrium conditions and at a speed of 50 mph using 24 psi initial inflation pressure and capped air conditions. The rolling resistance values are generally seen to increase as the tires become bigger in size, but of course the load carried by them also increases. From the data plotted it is seen that radial tires are more efficient than similarly sized bias and bias-belted tires. It is also seen that where more than one tire of a given construction was tested, considerable spread can be observed in the data. This implies that there are differences between the rolling resistance of the

80% TRA Load Tire Mfgr & Cold Inflation Pressure 24 psi o 3"Tire ~* 13"Radial Serial Number Capped Air At14"Tire A 4"Radial given in 50 mph Speed o15"Tire *15"Radial Table I Fuel Efficient Tires 18 ~~~~~~~I I I I I I I II~~~~~ I w16 - _ * f0 I I I T Q I cfU') _ I II C) IL I I I Ia I ~~~~~ I ____ I_ -- _ j 121, OL~~~~~~~~~ 10,J 8I I I i I I I I I ~~~~~~~~ + IIl m: I -I___' zA CI I I I' I I I I "J - ~ el I I I, I.j~~~- 2-j.= 8'........... -! ____::-,1I 78 707878 7817078f70 78' 706050 78 70 78 7084 7817 FIGURE 17. ROLLING RESISTANCE VS. TIRE LOAD RATING FOR A TYPICAL SELECTION OF PASSENGER CAR TIRES

TABLE I.-TIRE IDENTIFICATION AND TEST DATA Initial Equilibrium Initial Equilibrium Initial Equilibrium Tire Tire Inflation Inflation Cavity Cavity Rolling Rolling Construction lrhnufacturer Serial Number Load, Number Description o n Pressure, Pressure, Temperature, Temperature, Resistance, R psi psi C C lb lb 1 078-14 B 4P Goodyear CKL9 E2A 443 828 24 27.8 21 48 16.91 11.32 2 G78-114 B 4P 3oodyear'CKL9 E2A 1443 1104 24 29.0 19 58 25.36 1.5.70 078-11 B P Goodyear CKL9 E2A 443 1380 24 51.0 22 69 34.72 19.93 4 G78-14 B LP Goodyear CKL9 E2A 443 1656 24.0 21 84 45.90 23.70 5 078-14 B 4? Goodyear CKL9 E2A 443 1104 16 21.4 23 76 39.25 19.62 6 oiG8-14 B 14 Goodyear CKL9 E2A 443 1104 20 25.3 23 69 28.38 17.52 7 G78-14 B 14 Goodyear CKi9 E2A 443 1104 28 32.5 25 59 21.74 14.49 8 G78-14 B 4P Goodyear CLK9 E2A 443 1104 32 37.0 25 56 19.71 12.98 9 78-15 B I4P Firestone WKVX VEE 145 906 24 27.3 28 48 17.40 11.55 10 178-15 B 4P Tirestone WKVX VEE 145 1208 24 28.5 26 57 24.59 16.19 11 H78-15 B 4P Firestone WKVX VEE 145 1510 24 30.0 27 66 32.69 21.29 12 H78-15 B 4P Firestone WKVX VEE 145 1812 24 32.0 28 79 42.29 25.19 13 H7 8-15 B 4P Firestone WKVX VEE 145 1208 16 22.2 25 69 38<39 19.79 14 178-15 B 4? Firestone WKVX VEE 145 1208 20 24.6 24 63 30.90 17.99 15 178-15 B 4P Firestone WKVX VEE 145 1208 28 31.8 26 53 23.39 15.30 00 16 178-15 B 4? Firestone WKVX VEE 145 1208 32 35.8 25 50 19.49 14.10 17 GR78-14 B 2P+2S/2P Goodyear- KMA HCE 354 828 24 26.4 25 41 12.72. 8.79 18 0278-14 R 2P+2S/2P Goodyear NKMM HCE 354 1104 24 27.0 24 44 16.06 11.51 19 G278-14 2 2P+2S/2P Goodyear MKMA HCE 354 1380 24 28.5 21 50 20.90 14.24 20 0278-14 R czP+2S/2P Goodyear MKMP HCE 354 1656 24 29.0 22 57 22.42 16.35 21 GR78-14 R 2P+2S/2P Goodyear MKMA HCE 354 1104 16 19.8 19 56 19.39 13.78 22 GR78-14 R 2P+2S/2P Goodyear MKMA HCE 354 1104 20 23.0 21 49 17.57 12.42 23 GR78-14 R 2P+2S/2P Goodyear MKMA HCE 354 1104 28 30.8 22 45 13.94 10.45 24 GR78-14 R 2P+2S/2P Goodyear MKMA HCE 354 1104 32 35.0 23 44 12.72 9.84 25 1HR78-15 R 4P+2S/2UJl Uniroyal AP`VY EL 025 906 24 27.6 25 44 12.04 8.72 26 1128-15 R 4P+2S/2N Uniroyal APVY EL 025 1208 24 29.0 24 51 16.70 11.73 27 BR78-15 2 4P+2S/2N Uniroyal APVY EL 025 1510 24 30.3 25 60 22.57 14.74 28 HR78-15 2 4P42S/2N1 Uniroyal APVY EL 025 1812 24 31.5 29 67 27.08 18.05 29 11278-15 R 4P+2S/2N Uniroyal APM EL 025 1208 16 20.0 26 63 24.39 15.04 30 11278-15 R 4Pt2S/2N Uniroyal APVY EL 025 1208 20 24.9 27 57 18.96 12.78 31 1178-15 R 4P+2S/2N Uniroyal APVY EL 025 1208 28 32.9 27 50 14.29 10.84 32 1178-8-15 2 4P+2S/2N Uniroyal APVY EL 025 1208 32 36.5 25 48 13.24 10.23

TABLE I. -CONTINJIED Initial Equilibrium Initial Equilibrium Initial Equilibrium Vertical Tire Tire Inflation Inflation Cavity Cavity Rolling' Rolling Construction Manufacturer Serial Number Load, Number Description Pressure, Pressure, Temperature, Temperature, Resistance, Resistance, lb psi psi "C OC lb lb 3h 0-! R -- - - 1104Rl 24 28.6 23- 52 15.55 10.98 7 360-i= _ 4N General VTVF W6M 493 1104 24 26. 5 25 57 17.75 15.80 3R B. F. Goodrich BEUF LE2 416 1104 24 26.8 23 50 16.33 11.65 37 S79-15 R 4P Lee JCNY LAF 344 1104 24 27.5 27 57 21.7r 15.20 38 aR70-1i 7 R 2P+2S/2P Goodyear MJU5 CXL 454 11O 24 26.5 24 44 14.64 11. 16 44 A78-1, B 4P Goodyear MJF5 E2A 034 720 24 27.7 25 52 15.70 9.86 l5 E70-14 B 4P Lee JCLB LAF 145 952 24 - 27 55 18.29 12.18 46 H7-1- B 4P Lee JCU6 LAF 334 1208 24 27.6 23 56 25.55 15.55 47 A78-13 B 4P Dunlop DAFS C47 104 720 24 - 25 61 17.70 10.78 49 F78-14 B 4P 9 Dunlop DBL7 C47 234 1024 24 27.5 26 54 19. 55 12.73 50 G78-14 B 4P Dunlop DBL9 C47 204 1104 24 27.7 25 56 20.56 13.30 51 078-15 B 4P Dunlop DBVV C47 194 1105 24 28.6 23 93 19.89 13.26 52 PU8-1 =, B 4P Dunlop DBVX C47 462 1208 24 28.2 21 93 22.52 15.O1 53 A70-13 BB 2P+2F/2P Goodyear M,7F4 Y4A 244 720 24 - 27 48 12.82 9.80 ~O 54 E70-14 BB 2P+2F/2P Goodyear MDLB Y4A 343 952 24 27.5 23 52 17.40 oO 55 G70-15 BB 2P+2F/2P Goodyear MJU4 YYA 163 1105 24 28.8 23 48 18.74 12.40 56 A78-13 BB 2P+2F/2P Goodyear MBF5 F5A 393 720 24 28.3 24 58 1 6.ol 9.85 57 C78-14 BB 2P+2F/2P Goodyear MNL1 DDA 134 840 24 28.0 26 53 17.70 11.44 58 D78-14 BB 2P+2F/2P Goodyear MJL3 DDA 244 896 24 27.0 23 51 17.52 11.73 99 E78-14 BB 2P+2F/2P Dunlop DBL5 C42 20o 952 24 28.0 24 51 17.93 11.85 60 PU8-1h BB 2P+2F/2P Goodyear MBMB DDW 154 1208 24 28.8 20 54 22.28 14.75 61 F78-15 BB 2P+2F/2P Goodyear CDWF KSDF 1024 24 27.8 21 50 21.15 62 G78-15 BE 2P+2F/2P Goodyear MMV4 DDA 134 1104 24 28.8 21 53 22.59 1 ~.61 63 H78-15 BB 2P+2F/2P Goodyear MKUX DDH 124 1208 24 28.2 23 53 22.37 15.O 1 64 J78-15 BB 2P+2F/2P Goodyear MKV1 DDH 114 1264 24 26.2 19 58 23.38 16.63 65 L78-1= BB 2P+2F/2P Goodyear MEU3 FKH 244 1340 24 29.0 19 56 25.72 16. 30 66 L84-1- BB 2P+2F/2P Goodyear MEWA DHH 234 1340 24 28.3 25 54 25. 96 16.41 67 Gw78-15 BB 2P+2S/2P Goodyear MKVV E9H 443 llO4 24 28.0 23 57 22.30 14.77 68 L78-1l BB 2P+2S/2P rxsodyear MKY3 E9H 493 1340 24 27.0 23 57 27.51 16.74 69 155 SR-17 R 2P+2S/2P Goodyear NBE5 AC2 373 648 24 26.0 25 44 11.81 8.39 70 165 SR-13 R 2P+2S/2P Goodyear NBE9 AC2 493 688 24 27.0 23 47 14.51 9.62 72 165 SR-14 R 1P+2S/2P Goodyear NEJ1 NN2 373 768 24 27.0 23 43 13.20 9.37

TABLE I. -CONCLUDED Initial Equilibrium Initial Equilibrium Initial Eqibru,ire Tire Vetcl inflatioii Inflation Cavity Cavity RollingRoln Number Description onstruction Manufacturer Serial Nubr oi Pressure, Pressure, Temperature., Temperature, Resistance, Reitn, Description ~ ~ ~ ~ ~ ~~~~lb psi psi OC 6Clbb 73 155 SR-115 R 2P+2S/2P Goodyear N)OP7 AC2 07k, 692 24 28.0 25 44 11.64 85 74 165- SR 15- R 2P+2S/2P Goodyear NCTB AC2 3-93 768 24 26.3 2 41.097 75 A7-13_7 R P4PS2P Goya MJOJ JKT 174 720 24 26.5 25 48 13.91 92 76 EF77o-14 R 2P+24R+lS/2P Goodyear MJLC JKT 08 4 9952 24 26.8 22 49 16.93108 7T FR7C-l4 B - - - ~~~~~ ~~~~~~~ ~ ~~~1024 24 28.2 25 5119.90120 78 iR710-15 R 6R415S/2R Daytona MY5HNl 513~ 1104 24 28.0 25624.00138 79:-UZ7 0 -l B 2P+2S+IAN/2P Goodyear MKLI7 FwH 3z14 1208 24 27.0 19 44 18.0 12.3 80 JRO-5 6R+1.S/'2P Daytona 1iY13 Htg l 154, 1261L 24 27.0 20 5421.74143 81 TLr7O0- 1 B 6R+1S/2R Day-tona HYDlN 2 134 24 27.8 2360 28.64161 82 GRTO-15 B 2P+25/2P Firestone - ~~~~~ ~~~~1i0h 24 27.0 23 58 22.94137 83 AiR78-132 R 2P+2S/2P Cooper UPKK NDN 404 720 24 28.0o94 2.386 81. -H78-1h R 2P+-2S/2P Goodyear MKMC AYH 23z4 10 42. 54 8226 85- ER78-14 B 2P+2S/2P Cooper UTL6 HDT 115 952 24 28.5 24 57 16.76112 86 G~R78-14 B 2P+2S/2P Cooper UTMA HDV` 115' 1104 24 27.52451781.2 87 HR78-14 R 2P+2S/2P Cooper UTYIW HlDW 115 1208 24 27.8 25 57 18.71128 88 GR78-115 B 2P+2S/2P Cooper UTVW F8N 115 1104 24 28.0 25 53 16.441.70 89 HR78-l5 R 2P —2S/2P Cooper uTvT F6P 15-4 1208 24 28.0o 23 54 17.29128 90 JR78-15 B 2P+2S+112/2P Goodyear MEtI2 FNE 084 1264 24 26.8 23 47 17.08119.91 LR78-l15 B 2P+2S/2P Cooper UTVY HDT 234 1340 2-4 28.3.22 57 20.65139 92 GR78-15 R 6R/2R Firestone VEVW XVD 234 1104 24 27.8 25 61 21.42150 93 LR78-195 B 6R/2B Firestone VEVY XVD 254 1208 24 27.5 25 62 22. 551.6 94 LR78-15- BR B. F. Goodrich BEv4 P71225- 1340 24 27.2 24 52 21.24151 95 rGR7 8- 1 B 2P+2S/2P B. F. Goodrich BEVW DR 150-4 1104 24 27.3 23 50 15.26102 96 G-W78-l15 BR 1104 24 2'7. 0 25 50 16. 301.6 97 16 i-3R 2R+2S/2R Michelin I(G4 5392 N/h4 688 24 26.8 26 46 12.05 74 98 15R-3R 2+/R Mchln- 688 24 25.5 26 43 10.43 72 99 A78-13 BB - ~~~~~~Goodyear -720 24 - 24 5 63 09 101 P78-IL4 B 4P Dunlop DBL7 C47 234 840 42. 5481.695 102 G78-14 B 4P Dunlop DBL9 C47 204 780 24 26.5 26 46 12.40 83 103 E78-11L BB 2P+2F/2P Dunlop DBL5 C42 204 840 24 27.5 24 51 14.59103 104;i{8-14 BB 2P+2F/2P Goodyear MBMB DDW 154 840 24 26.5 26 44 13. 55.96 105- LR78-l5 R 2P-4 —2S/2P B. F. Goodrich - 114 24 26.8 24 48 16.60 1.9 106 GR78-15 B 2P+2S/2P B. F.Goodrich* BEVW DR 1504 1104 24 - 25 57 22. 33135 10f7 165- HR-13 R 2R+2S/2R Michelin* IGM 51392 N/h4 688 24 -24 49 13.69 89 108 p215 / 65 390 - Goodyear. TX 8503-13 1065 26 —— 106 109 P185 /8oB 13 - Uniroyal AJ-22-3118 1041 26 —- 102 110 P195/75R 14 - Firestone R 73.9 1120 26 —— 136 *Retreaded.

- 31same size tires from different manufacturers, as well as differences between rolling resistance of the same size tires from the same manufacturer. The exact quantitative value of such spread is a matter for further investigation. Most of the major American tire manufacturers now have development programs for so-called "fuel efficient" tires, that is, tires with markedly reduced rolling resistance but with acceptable levels of performance in other areas. Three of these tires were also tested for this program of measurement, and the resulting rolling resistance values are also plotted in Figures 17 and 18 using a special symbol for the data point. While these tires are designed to operate normally at either 26 or 35 psi inflation pressure, we have adjusted the tire rolling resistance to a value of 24 psi in order to make the data consistent with the other measurements given in those figures. When this is done it is clear that these tires do not exhibit much improvement over existing commercial radial tires. Their advantage seems to be that they can be operated at higher pressures, such as 26 or 35 psi, in which case they are more fuel efficient than existing lower-pressure radial tires. These same data may be presented in a somewhat different fashion by plotting the coefficient of rolling resistance of the tires discussed in Figure 17, again as a function of tire load rating. This is shown in Figure 18. From this it may be seen that for a given vehicle the most efficient tires in terms of rolling resistance are the larger sizes,

80%TRA Load 013"Tire *13"Radial Tire Mfgr: Cold Inflation Press. 24 psi a t4"Tire A 14" Radial GY-Goodyear L- Lee Capped Air o15"Tire 15" Radial GE-General C-Cooper o 50 mph Speed * Fuel Efficient Tires OF-Goodrich D-Dunlop o at 24 psi U-Uniroyal M- Michelin F-Firestone I 88 i I I I ~16G - I G y %D; GYI (114 GY GY I F oGYVGY LG I o GY A A L Gy GV L qbY 0GY oGY1 GY* A D GYMi'D.'fG Y m BF~~~~ D D*DD O CGYI C GY ADI OGY AGY, % FF DIGYA F ___ ~BF 08 ~~~~~~~~~~~~~ ~ ~~~~~~~~~~I —I ~ — 1 G I __ __I_ U I I 1 i i (X: 8 I I I I LL I I~~~~~~~~~___ i II I I I I- II I z~ I _ _ _ _ _ ___ LU 4-t —— zN I Iii I _ 1 I I I I I 8 I _L 0 - 80 % TRA LOAD LIMIT AT 24 PSI 0 720 840 896 952 i 024 1104 1208 1264 1344 7 78 70. 087 8 70 160 150 78 70 78 170-84 78 170 ASPECT RATIO A IC D EI F G H L LOAD RATING FIGURE 18. COEFFICIENT OF ROLLING RESISTANCE VS. TIRE LOAD RATING FOR A SELECTION OF PASSENGER CAR TIRES

- 33 - since their coefficients of rolling resistance are slightly less than those of the smaller sizes. Again the radial tires are definitely more efficient than bias and bias-belted tires and are to be preferred where available. The role of aspect ratio is not clear in Figure 18. On the whole there may be some tendency for low aspect ratio tires to exhibit slightly reduced rolling resistance coefficients as compared with higher aspect ratio tires. This would be expected from physical considerations. The effect is small in these data and the benefits, if they exist, are not very striking. In view of the rapidly increasing numbers of light trucks and vans in the American vehicle fleet, the rolling resistance characteristics of light truck tires are an important factor in vehicle fuel simulation. For that reason a group of four common sizes of light truck tires was chosen, and rolling resistance measurements were carried out on them. Since they are considerably larger and operate at higher pressures and loads than passenger car tires, the results of these measurements are presented in Tables II through VI. The reduction in rolling resistance as the tire warms up can be expressed as the ratio of rolling resistance at equilibrium to that at the cold, or initial, state. These data are given in Figure 19 for the same group of tires described in Figures 17 and 18. There seems to be very little trend reflected in these data. There may be some small

80% TRA Load Cold Inflation Pressure 24 psi ol3"Tire 13"Radial Capped Air 14"Tire A 14"Radial 50 mph Speed C 15"Tire 15"Radial Ld) I I I' " Z, I < U.80 ZILI I I I I I I I I I -~~~~~ 1 -4 -4 —-.,I I I I I II _ _ __ cr ~ I I I I *I w I I, I 5, —T I —I W~~~~~ A' ___ 0L Q.6.- -....... _ i KJ__ _I __ _::~ I I I II IZ 0 0,Or__ 1 I IA el I i I 0-~~~~~~~~~~~~~~~~~ ~~Z*5Q I -— "r —— t- r~~~~~~~~, t9 6.70 Io Lii~~~~~~ I __ _ I.' Zr I0 - I - i - I I- - - - ~ ~ i i I I iI I I a) ~ ~ ~ a & ~~~I II ~~~In I _ _ _ __ _ 78~O7887 708010100I... Z.5 - - -'' i..... [, c -I-,,A -. - I I C3 I It I i I d~ 78 70 78 78 -78 70 178170 78 70 160 150 78 170 78 70 84 78 70 ASPECT RATIO A CD E FI G H I L LOAD RANGE FIGURE 19. RATIO OF EQUILIBRIUM ROLLING RESISTANCE TO INITIAL ROLLING RESISTANCE FOR A SELECTION OF PASSENGER CAR TIRES

35TABLE II.-TEST DATA FOR 7.00-15 LT TIRE Dia. = 29.6 in. Tire Inflation Rolling Resistance Load, Pressure lb (cold), psi t = t0 min tte 1220 25 28.64 22.38 20.88 1220 35 23.27 17. 30 16.41 1220 45 19.54 14.92 14.17 960 35 16.26 12.38 11.63 1480 35 27.45 20.88 18.95 TABLE III.-TEST DATA FOR 8.00R 16.5 LT TIRE Dia. = 28.34 in. Tire Inflation eLoad Pressure Rolling Resistance Load, Pressure lb (cold), psi t = O t=O min t te 1610 45 24.62 16.97 15. 01 1610 55 22.06 15.77 14.41 1610 65 19.82 15.01 13.51 1380 55 17.71 13.51 12.61 1840 55 24.62 17.43 15.92

- 36 - TABLE IV.- TEST DATA FOR 8.75R 16.5 LT TIRE Dia. = 29.46 in. Tire Inflation Rolling Resistance Load, Pressure lb (cold), psi t 0 O t=10 min t.te 1850 45 27.19 18.52 16.73 1850 55 25.39 17.68 15.53 1850 65 18.82 16.43 15.53 1590 55 20.00 15.28 14.93 2110 55 27.47 19.70 17.61 TABLE V.-TEST DATA FOR 9.50-16.5 LT TIRE Dia. = 30.56 in. Tire. Inflation Rolling Resistance Load, Pressure lb (cold), psi t = O t 10 min t te 2190 40 40.07 28.80 24. 04 2190 50 32.95 25.53 22.12 2190 60 29.09 22.12 20.19 1880 50 26.72 20.78 18. 41 2500 50 38.00 28.50 24.34 TABLE VI.-COEFFICIENT OF ROLLING RESISTANCE FOR LIGHT TRUCK TIRES AT TYPICAL LOADS AND PRESSURES (A) (B) Equilibrium Coefficient Tire Size Inflaton at Rolling of Rolling Tire Size Pressure Load at' PressureMaximum Resistance at Resistance, (cold), psi Pressure Conditions A,B lb/.000 lb 7.00-15 LT 35 1220 16.41 13.45 8.00R 16.5 55 1610 14.41 8.95 8.75R 16.5 55 1850 15.53 8.39 9.50-16.5 LT 50 2190 22. 12 10.10

- 37 - differences between bias and radial tires since bias constructions seem to exhibit a slightly lower ratio of equilibrium drag to initail drag, but other than that, size, aspect ratio, and load range seem to matter very little. The tires used in the tests plotted in Figures 17 and 18 were manufactured by a variety of different American manufacturers in 1973-1975, and their detailed description is given in Table I of this report. From Figure 3 it was observed earlier that the equilibrium running state of the tire appears to be reached somewhere after 10 to 20 minutes running, and at 30 minutes of operation at a reasonable speed such as 50 mph, most passenger car tires are almost at their equilibrium temperature state and hence at the steady-state value of their rolling resistance. Approximate methods for calculating such warm-up [5] times have been presented in the past. Generally such warm-up times are of value for studying the fuel consumption characteristics of vehicles in short urban trips, but there is some interest also in the length of time necessary for the tire to be stationary in order for it to cool down to its ambient state and again regain its high value of initial rolling loss. A short study done on this for the present report shows that tire rolling resistance as a function of cooling time may be plotted approximately in Figure 20; where the cooling time is measured from the tire rolling resistance equilibrium value, as indicated at time t=0 on Figure 20. From these data it was concluded that the time

- 38 - Speed 50 mph Tire 200 Goodyear Load 780 lbs. BR78-13 Cold Inflotion Pressure 24 psi MMFW FNA 413 18 m,16 I,_ _. I4 Cold 2 2 c( 110 o 6 COOLING TIME, MINS. FIGURE 20. ROLLING RESISTANCE VS. COOLING TIME

- 39,Speed 50 mph Tire 041 Goodyear Load 1340 lb. LR78-15 MJV4 FNE 044 22 Cold Inflotion Pressure 24 psi Cold 3 18 o 16 812 2(3 10 20 30'40 50 60 710 0...FIE 20. CONIED z 4 0 10 20 30 40 50 60 70 COOLING TIME, M-INS. FIGURE 20. CONTINUED

- 40 - Speed 50 mph Tire 640 Uniroyal Load 1104 Ibs. GR78-15 Cold Inflation Pressure 24 psi APVW DR 015 18 Cold 05 16,14 z cnc z2 0 8............ 6 0 10 20 30 40 50 60 70 0 10 20 3COOLING 40 50 60 70 COOLING TIME, MINS. FIGURE 20. CONTINUED.

- 41 -... I II Speed 50 mph Tire 366 Load 1104 lbs. G78-15 Bias 24 Cold Inflation Pressure 24 psi Cold 22 - mm - co 20 I18 Cl) U - J 0 1 -4 0.j~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 2 1 (d) 5 0 0 10 20 30 40 50 60 70 COOLING TIME, MINS. FIGURE 20. CONTINUED

- 42 - Speed 50 mph Tire 127 Goodyear Load 720 Ibs. A78-13 Bias Cold Inflotion Pressure 24 psi MKY3 E9H 493 Cold w 0 10 20 30 40 50 60 70 w14 FIE 20. CONCLUDED 0,

- 43 - to regain the cool state is substantially longer than the warm-up time, which is consistent with the approximate heat transfer coefficients that would be appropriate for the moving and stationary states of the tire. Such information is also of value in the study of short urban driving cycles. Considerable interest has been shown in the role of tire wear in modifying the rolling resistance of a new tire, since essentially all of the measurements which have been made on tire rolling resistance have been done on new tires. For the purposes of this study, two pairs of tires with very specific characteristics were collected from used automobiles. Each of these pairs was made up of one tire which was nearly at its fully worn condition, and a second tire that had been kept as a spare and was essentially unworn. These tires were tested for rolling resistance under identical conditions of inflation, load, and time, and their results reported for purposes of this report. Subsequent to this test program, each of the worn tires of the pair was retreaded by a commercial retreader and the tire again measured for its rolling resistance value. The results of these measurements are shown in Figure 21, where it is seen that in both cases the retreaded tire shows higher rolling loss than either the new tire or its worn counterpart. Caution should be used in interpreting this as a general result due to the small amount of data on this subject. Caution should also be used in using this result as indicative of the amount of rolling loss that can be assigned

15 10 crz ~io (I) w 05 0 4) (1) z~~~~~~ cr~~~~~~~~~~~~~~~~~c do~~~~~~~- V a) 0 0)O a, Q 0 ~ ~ ~ ~ 00 GR 78 -15 165HR 13 LOAD 11 04 LBS LOAD 685 LBS PRESSURE 24 PSI COLD PRESSURE 24 PSI COLD CAPPED1AIR CAPPED A8 L FIGURE 21. EQUILIBRIUM ROILING RESISTANCE VALUES FOR NEW, WORN, AND RETREADED TIRES OF THE SAME TYPE

- 45 - to the tread of a tire. At first glance it might appear that the influence of the tread is reasonably small in determining the overall rolling loss of the tire. However, it should be recognized that a worn tire exhibits a somewhat different pattern in its carcass than does a new tire. This probably means that one cannot use the relationship between a fully worn or buffed tire and a new tire as indicative of the contribution of the tread alone, since the increased deformation of the carcass tends to mask the tread effect. This point needs further study and experiment. Finally, the problem of tire selection for a given vehicle requires further elaboration. If rolling resistance is the only, or more important criterion, the data of Figures 17 and 18 show that the best strategy is to select an oversize tire and operate it in an underloaded condition. This is confirmed by test data obtained specifically for this report, where several tires of different load ratings were run at identical loads, most of them underloaded. The equilibrium values of the rolling resistance are given in Table VII as illustrative of this phenomenon.

TABLE VII.-EQUILIBRIUM ROLLING RESISTANCE FOR TIRES OF VARIOUS SIZES UNDER THE SAME LOAD TIRE MFGR LOAD RATED EQUILIBRIUM ROLLING LOAD RES I STANCE, lbs Goodyear C78-14 1 8401 1050 11.44 2P+ 2F 12P E78-14 Dunlop 84011190 10.03 F78-14 Dunlop 84011280 9.55 4P Goodyear H78-14 Goodyea2 840/1510 9.63 2P+ 2F /2P Goodrich GR78-15 2P+2SP 1104/1380 12.49 Goodrich LR78-15 2P+2SP 1104/1680 11 97 2P + 2S / 2 P'

- 47 - IV. MEASUREMENT METHODS AND DATA REDUCTION IN ROLLING LOSS MEASUREMENTS Most rolling resistance measurements are made on indoor cylindrical roadwheels for a variety of reasons. The most important of these reasons is the need for very accurate, reproducible measuring systems independent of weather effects, and the need to warm the tire up thoroughly prior to measuring its equilibrium rolling resistance, starting from a common temperature state. All this is most easily done indoors, and by far the most common indoor equipment is the cylindrical roadwheel. It is necessary to clearly define the relationships between quantities measured on cylindrical roadwheels and those measured on the road, since in the final analysis it is the rolling resistance on the road that influences vehicle fuel economy.'The details of the derivations of the various relationships are given in the Appendix. Most of these have appeared in previous reports.[6] The results of the analyses in the Appendix may be summarized into separate effects, one due to tire stress and one due to measurement methods. STRESS EFFECTS For the same tire load and inflation pressure the rolling resistance of a tire on a curved drum of radius R is greater than on a flat surface due to increased stress

- 48 - levels in the tire. The relationship between these is F = Fr (1 + r/R)1/2 (2) where F = rolling resistance on a drum of radius R XR F = rolling resistance on the highway r r = outside radius of the tire R = drum radius MEASUREMENT GEOMETRY (A) The rolling resistance on a curved drum, as measured by an axle force transducer, is less than the rolling resistance F due to the interaction of normal forces with meaR sured rolling loss. This is caused by elastic deformation of the tire. The relationship between the two is FXM FxR (1 + rL/R) 1 where F = rolling resistance obtained-from axle force meaXM surements, taken on a drum of radius R rL = loaded radius (axle height) of the tire above L + drum surface F = actual rolling resistance of the tire on the X R curved drum

- 49 - (B) The rolling resistance on a curved drum, when measured by either drum shaft torque, coast down, or motor electrical power converted to torque, is given by Eq. (4) Fx T/R (4) where Tw is the drum axle or drag torque and R is the drum radius. F is again the actual rolling resistance of the R tire on the curved drum. (C) When a tire is powered to drive a freely rolling drum and the axle force on either the drum or tire is used as a measure of rolling loss, then the rolling resistance of the tire on the curved drum is given by FX FX (R+rL/rr) (5) xR xM where r = tire rolling radius COMBINED EFFECTS If one wishes to conduct a test on a curved drum maintaining equal tire deflection on the drum as on the road, then only the corrections for measurement geometry, i.e., Eqs. (3)-(5) need be made. If one wishes to conduct a test on a curved drum using the same tire loads as used on the road, then both correction

- 50 - for stress effects (Eq. (2)) and for measurement geometry must be made. For example, in the case where axle force transducer measurements are used, and the load is held the same between the tire on the drum and the tire on the road, then both corrections given by Eqs. (2) and (3) must be used simultaneously in order to reduce the data to that on the flat surface. This gives Eq. (6). F =FR 1 + j (l ++) (6) Load and inflation pressure are the most important variables defining tire rolling resistance. One may observe from Figures 4-7 and 8-11 that there exists close linearity of the rolling resistance with load on tire and with the reciprocal of inflation pressure. These relations lead to one method of measuring the rolling resistance at a selected number of points and using this information to predict the rolling resistance of the same tire at other load and pressure values. This consists of expressing the tire rolling resistance in the form of Eq. (7). Fr =Fr + KL(Fz - F) + Kp (l/p - l/pO) (7) wheO O where

- 51 - F = tire rolling resistance at load F, pressure po r z' o o Fr = tire rolling resistance at load Fz pressure P KL = slope of the load dependence of Fr Kp = slope of the reciprocal pressure dependence of Fr, where 1/p is used to define the slope. The slope of the load dependence of rolling resistance KL is obtained by determining the rolling resistance over a range of loads spanning the appropriate load for the tire in question, and passing the best straight line through these. This is usually done using a single pressure, say p0, although it may be done at a variety of pressures. Similarly, Kp, the slope of the pressure dependence of rolling resistance, is carried out by varying 1/p over a range of values appropriate for the tire, again either holding the load constant or at a variety of loads. This allows a carpet plot of the rolling resistance of the tire to be constructed, and when the lines of the carpet plot are parallel, then Eq. (7) becomes adequate for prediction purposes. This is illustrated in Figure 22, where a carpet plot is shown for three different pressures and three different loads. Such a carpet plot cannot be represented by Eq. (7), since the slopes of the load dependence and the pressure dependence are different at the different points. It is necessary to use it in its entirety in order to obtain accurate values of the rolling resistance at points other than those measured.

- 52 In cases where the slopes or gradients of rolling resistance with load and pressure do not vary significantly, then Eq. (7) becomes an adequate representation and the data may be presented as shown in Figure 23. In Figure 23, as in Figure 22, the data may be obtained using either capped air or regulated air test conditions. In the capped air condition, the tire is inflated at room or ambient temperature to the specified initial pressure, and then run under the appropriate load until rolling resistance equilibrium is reached. During this process temperature will rise as will inflation pressure. Nevertheless, the plots are made using the initial inflation pressures of the tire. An alternate approach, and one which results in more rapid achievement of equilibrium conditions, involves using regulated air conditions in the test program. Here, an estimate is made of some reasonable air pressure buildup which the tire might have during warmup. This is added to the desired cold inflation pressure and is used as the regulated air value at which rolling resistance is obtained. The air pressure is maintained at this constant value during the warm-up process of the tire, and the tire rolling resistance reaches its equilibrium value quicker than in the capped air experiment. This has the advantage of reducing test time in order to obtain data points. The regulated values of pressure are then used to make plots such as Figures 22 or 23. This is a very efficient process in terms

Fz3 Pi Fz0 F,~~ 1 FIGURE 22. CARPET PLOT OF ROLLING RESISTAANCE AS A FUNCTION OF LOAD AAND PRESSURE Fz0 Fz3, t Fzo,Po Fz zoF FA Zopo FIGURE 23. FIVE mINT CARPET PLOT

- 54 - of test time, since in the case of Figure 22 it requires nine points to obtain an adequate carpet plot over a range of loads and pressures, while in Figure 23 only five points are required. In the case of regulated air, it has been reported that equilibrium times can be reached in approximately 10 to 15 minutes, while in the case of capped air 20 or 30 minutes are needed. An alternate approach to that of Eq. (7) uses a somewhat different view of the dependence of rolling resistance on load and pressure in order to give a predictive framework which is more general. This concept begins with the observation that there is a nearly linear relationship through the origin of the tire equilibrium rolling resistance versus load curve, and an equally linear relationship between the reciprocal of cold inflation pressure and rolling resistance, although here the linear extrapolation does not pass through the origin. This is clearly seen by reference to Figures 4-7 and 8-11. This gives rise to a general form for the dependence of equilibrium rolling resistance on load and pressure, given in Eq. (8). F Fr = (Fz/F ) (Cp' o/P + cT) (8) O O where cp, cT = constants for each tire Fr, F, F, F, p, p defined as in Eq. (7) NtO O Note that a further requirement is that

- 55 - cp + cT 1 (9) Combining Eqs. (8) and (9) leads to Fr = F (F/F )[1 + c (p /p - 1)] (10) r o z p o which is an expression for rolling resistance at any load and pressure as a function of the rolling resistance F at r o some base-line condition of load Fz and pressure po This expression contains only one constant cp, characteristic of the tire, and expressing the sensitivity of that tire's rolling resistance to inflation pressure. Hence the use of the symbol cp denoting a pressure coefficient is appropriate. This means that the entire load-pressure-rolling resistance map of a tire can be determined if one value of the rolling resistance F is known at one load F and one inrO flation pressure po, provided that the constant cp is also known for the tire. This constant may be determined most easily by fixing load F at its base-line value and measurz ing the tire rolling resistance over several pressures, such as shown in Figure 24. As is clear from that figure, only a limited number of tests are necessary to determine the constant cp. A minimum of two would be hecessary, but it would be much more desirable to use at least three points in order to obtain a check on the linearity of the data.

- 56 - r0 CP Zo FIGURE 24. GRAPhICAL REPRESENTATION OF THE SLOPE NEEDED TO DETERMINE THE CONSTANT FOR TIRE PREDICTIONS This has been done for four passenger car tires, and one light truck tire under a test program carried out for this report, and the results are presented in Tables VIII and IX. In each case, three points were used to determine the constant cp for each of the five tires, following which this constant for each tire was used to predict other rolling resistance values at different loads and pressures. These were compared with test data obtained from the same tires. From the predictions of Table VIII and the corresponding measurements it appears that to a close approximation the rolling resistance of the tire can be determined as a function of load and initial pressure using Eq. (10), with the constant cp being determined experimentally by three points. In the case of the passenger car tire data of Table

5- 7 - TABLE VIII.-MEASURED VS. CALCULATED VALUES OF ROLLING RESISTANCE USING EQ. (10) GOODYEAR FIRESTONE GOODYEAR UNIROYAL G78-14 BIAS H78-15 BIAS GR78- i4 RAD HR78 -15 RAD cp.564* cp.468** cp.456* cp =.547** S/N CKL9 E24443 S/N WKVXVEE 145 S/N MKMA HCE354 S/N APVY EZ 025 LOAD PRES. PREDIC. MEAS. PREDIC. MEAS. PREDIC. MEAS. PREDIC. MEAS. 828 20 13.1 0 13.59 9.42 9.54 828 24 11.78 11.32 8.63 8,79 966 18 16.32 16.61t 1.60 1 1.66 t 04 20 17.47 17.52 12.56 12.42 1104 28 14.44 14.49 10.76 10.45 1380 24 19.63 19.93 14.39 i4.24 1380 28 18.04 19.62 13.45 13.02 1656 24 23.55 23.70 17.27 16.35 906 20 13.28 13.80 9.76 9.93 906 24 12.1 4 1 1.55 8.80 8.72 1057 1 8 16.38 16.49 12.14 12. t 9 1208 20.17.71 17.99 13.01 12.78 1208 28 15. t 15.30 10.81 10.84 1208 32 14.30 14.24 10. 13 10.98 151 0 24 20.24 21.29 14.66 t4.74 151 0 28 18.88 19.64 13.52 14.1 4 181 2 24 _ _ _ 24.28 25.19 _ _ a 17.60 18.05 *Determined from Fzo= 1104, p= 16, po=24, p$= 32psi cold **Determined from FL,= 1208, p. 16, p,,24,p_ 32 psi cold

- 58 - TABLE IX MEASURED AND PREDICTED EQUILIBRIUM ROLLING RESISTANCE USING EQ. (10)* 500 lb. 1000 lb. 1500 lb. 2000 lb. 2500 lb. 3000 lb. 20 psi 6.25 13.60 21.10 (6.89) (13.78) (20.68) 35 psi 5.25 10.70 15.90 (5.28) (10.56 (15.84) 50 psi 4.95 9.50 13.90 18.50 22.80 (4.63) (9.27) (13.90) (18.53) (23.17) 65 psi 4.85 8.80 12.90 16.80 20.80 24.80 (4.29) (8.57) (12.86) (17.14) (21.40) (25.70) 80 psi 4.75 8.70 12.40 16.00 19.90 23.80 (4.07) (8.13) (12.20) (16.27) (20.30) (24.40) * 67-inch drum 8.75 R-16.5 Light Truck Tire c = 0.325 Abs. Avg. Error = 0.33 lb (Calculated values are in parentheses just below the measured values.)

- 59 - VIII those points were obtained by capped air tests with the tire inflated from cold inflation conditions. Similar computations were carred out for the rolling resistance of a light truck tire, and the results of these are shown in Table IX. Here the data were obtained from regulated air tests, so the method appears to work well for both techniques. V. DESCRIPTION OF TEST METHODS The data quoted in this handbook have not been taken from the existing literature but instead rely entirely on measurements of the tire rolling resistance carried out especially for this study. The tires in question were furnished by the U.S. Department of Transportation and were thoroughly broken in by virtue of having been used for cornering force measurement studies at Calspan, Inc., Buffalo, N.Y. Rolling resistance measurements were carried out on these tires by the B. F. Goodrich Research Laboratories, Brecksville, Ohio under the direction of Dr. Marion Pottinger and Mr. David Strelow. The test equipment used was a 67inch diameter steel roadwheel with smooth steel surface, and torque was measured with a shaft torque meter whose output was filtered and recorded on a strip chart recorder.

- 60 - Tests were controlled by specifying tire load. Hence, it was necessary to divide all measured rolling resistance forces by the quantity (1 + r/R)1/2 [cf. Eq. (2)] in order to obtain the rolling resistance force which the tire would exhibit on a flat test surface. These reduced values have been used in reporting all the data given in this report. All tests were run under capped air conditions, and all pressures are the cold inflation pressures.

VI. BIBLIOGRAPHY (1) General Motors Corporation Comments on Tire Rolling Resistance to U.S. Environmental Protection Agency, February 23, 1978. (2) Bidwell, J.B., "Conserving Vehicle Energy," General Motors Research Report 2218, October 6, 1976. (3) Motor Vehicle Manufacturers Association, "Facts and Figures, 1976" p. 52. (4) Johnson, T. M., D. L. Formenti, R. F. Gray, and W. C. Peterson, "Measurement of Motor Vehicle Operation Pertinent to Fuel Economy," SAE Paper 750003, February 1975. (5) Dodge, R. N., and S. K. Clark, "Tire Transient Temperatures," The University of Michigan, Report 013662-5-I, U.S. Department of Transportation, January 1977. (6) Clark, S. K., "Rolling Resistance Forces in Pneumatic Tires," The University of Michigan, Report 013658-1-I, U.S. Department of Transportation, Janaury 1976.

APPENDIX MEASUREMENT METHODS AND DATA REDUCTION IN ROLLING LOSS MEASUREMENTS MEASUREMENT GEOMETRY The measurement of rolling resistance can be a difficult process if care is not taken in clearly defining the relationship between the measured quantities and the true rolling resistance of the tire. This is because the direct application of the rolling resistance is to vehicle fuel economy, which occurs on the flat road surface. On-the other hand, most rolling resistance measurements are made on cylindrical drums because of their common availability in the tire industry and because they allow sufficient stable running for the tire to reach its thermal equilibrium state. For this reason, it is necessary to clearly define the relationships between quantities measured on cylindrical roadwheels and those observed on the highway. The following analyses attempt to examine the technically important test configurations in order of increasing complexity. For clarity all computations use force resultants only. CASE 1 —FREELY ROLLING TEST TIRE ON FLAT SUFACE For this case either the tire axle may move or the test surface may move. Figure A-1 shows a free body diagram of the force resultants acting on the tire and wheel. - 62 -

- 63 r FXh N-Fz FIGURE A-1. FREE BODY DIAGRAM OF A ROLLING TIRE ON A FLAT SURFACE There Fr is the tire rolling resistance, while F is the XM horizontal force measured by an axle force transducer. F Fx O; =Fr (A-l) XM r EFz = 0; Fz =N (A-2) Mo= 0; FE1 = Fr r (A-3) e1 = Frre/FZ The measured horizontal force is the tire rolling resistance.

- 64 - The vertical force resultant moves forward by an offset E as given in Eq. (A-3). This is the type of measurement which is carried out on the TIRF machine at Calspan, Inc., Buffalo, N.Y., or alternately is the type of measurement which would be obtained by an instrumented axle force transducer on a vehicle or a trailer. An alternate version of this type of motion is given in Case 2 below. CASE 2 —TEST TIRE UNDER TORQUE AT CONSTANT VELOCITY ON FLAT SURFACE In this case, a torque applied to the tire is used to propel to the right at a constant velocity, where the notation is the same as used in Figure A-1. The appropriate equations of equilibrium are given by ZF 0; Fz = N (A-4) E M- 0; NE2 = T ~2 = T/Fz The torque shown in Figure A-2 is just sufficient to sustain the rolling losses of the tire and to move the tire and wheel at constant velocity to the right.

- 65 - Fz N FIGURE A-2. FREE BODY DIAGRAM OF A ROLLING TIRE ON A FLAT SURFACE UNDER APPLIED TORQUE Vehicle FD FF fD N FIGURE A-3. FREE BODY DIAGRAM OF A POWERED TIRE DRIVING A VEHICLE

- 66 - Figures A-1 and A-2 may be related by consideration of the. work done in one complete revolution of the tire by the force acting to move it. Equating the work done in the two cases gives Fr 2 1T rr =T 2 where rr is the rolling radius, gives rr = r - /3 (A-5) where 6 is the tire deflection. Using Eqs. (A-3) and (A-4) E1 = F r/F 2 = T/F = F r /F z yr z and E1/2 = r,/rr / 1 so that normal force resultant offsets are not the same in the two cases. If additional torque is applied, then the wheel will either accelerate or will be capable of exerting a force on a vehicle in order to propel it forward at constant velocity. This is illustrated in Figure A-3, where the driving force is denoted as FD and is shown acting on the driven tire and in an opposite sense on the vehicle which it

- 67propels. Again the offset of the vertical force resultant is denoted by 3,' and this may be different from that of the freely rolling cases such as shown in Figures A-1 or A-2. CASE 3 -- TIRE OPERATION ON A CYLINDRICAL SURFACE The tire is assumed to conform to the cylindrical drum as shown in Figure A-4. The drum rotates clockwise due to a clockwise torque TR. The wheel is also subjected to a driving torque Tw. The free body diagram of the tire in Figure A-4 shows the forces acting on the tire. These are normal and tangential to the drum surface, being denoted by the normal force N and the tire rolling resistance, FX, now offset by an arc length S4 along the drum surface from the vertical line of centers. Each element of drum surface has acting on it a pressure component normal to the surface and one tangential to it. The component normal to the surface passes through the drum center causing no moment about the center. Hence, the resultant of the normal forces, made up of the sum of the small incremental normal components, cannot cause any moment about the drum center and must be perpendicular to the drum surface. The sum of tangential components forms a resultant tangential force at the drum surface, essentially perpendicular to the normal force resultant, i.e., tangent to the drum. This tangential component is the rolling resistance force of the tire as measured on the drum of radius R.

- 68 - Vi AdAX / N Drum R Drum2 ~\ ~ /~Direction R // Rotation URE RN TTR FIGURE A-4. RESULTANT FORCES ON THE TIRE WHILE ROLLING ON A TEST DRUM

- 69 - A horizontal force F is shown at right angles to the center line between the drum and the tire. This is the force normally measured by an axle force transducer. The equations of equilibrium for the tire itself are written below, and are used to solve for the unknown F in terms of the other variXM ables: Fz = 0; F + Fx sino( + N cos c = 0 (A-6) Assume F << F and o( small. Then XR Z F = N (A-7) z I F = O; -F + FXR coso( - N sinc = 0 Z x XM R or F =F - (F (A-8) XM xR ZMA O; -FZ 4 + F rL - T 0 (A-9) where rL is the axle height above the drum surface. Using Eq. (A-8) and the relation ~4 = Ro( in Eq. (A-9) gives F. ROe = (F -cF) rL -T z ~xR z L w or

70 - = F / F L (A-10) X z R+rL FZ(R+rL) This can be used in Eq. (A-8) to give M XR 1 + + T (R+rL) (A-ll) For an internal drum one uses a negative value for R. Finally, the torque input TR to the dynamometer drum can be obtained from the free body diagram of that drum, and by taking moments about point B of Figure A-4 of the drum, one obtains TR F R.(A-12) One special case of technical interest can now be considered separately, namely, that of the freely rolling tire where Tw = 0. Using Eq. (A-11), one obtains M=F + (A-13) x x R This is the condition which commonly is found when a driven dynamometer drum powers a freely rolling tire mounted in bearings on an axle force transducer. The axle force transducer will record the quantity FX and from this the rolling M resistance force F must be inferred. Using Eq. (A-13) one XR

- 71 - may observe the relation between the tire rolling resistance force, and the axle force transducer measurement. This leads to the conclusion given immediately below. POWERED DRUM, FREE ROLLING TIRE WITH AXLE FORCE TRANSDUCER MEASUREMENT Axle force transducer measurements made on a powered drum misrepresent the rolling resistance of the tire on the curved drum, giving a rolling resistance smaller than the true value on a convex drum and larger then the true value on a concave drum. The reason for this is interaction of the contact pressure force resultant with the rolling resistance measurement. To correct such force measurements, the axle force transducer measurement should be multiplied by the factor (1 + rL/R). Examination of the free body diagram shown in Figure A-4 shows that the torque on the drum is related to the tire rolling resistance force directly through the drum radius as given in Eq. (A-12). This leads to the common measurement system where either a drum axle torque transducer or motor power meter is used to obtain the torque needed to drive the drum at constant velocity. SHAFT TORQUE, MOTOR POWER, AND COAST DOWN MEASUREMENTS OF FREELY ROLLING TIRE ON CYLINDRICAL DRUM It may be seen from Eq. (A-12) that either torque, power input, or coast down measurements on a powered drum, either

- 72 - convex or concave, reflect the true value of the rolling resistance of the tire on a curved surface, although the rolling resistance may be different from that on a flat surface. In this case, it is only necessary to divide the measured torque by the drum radius in order to obtain the effect of the radius of the drum in question. Finally, one may note that it is possible to power the tire and to have a freely rolling drum, in which case Eq. (A-11) may be used to interpret the resulting condition. In the case of the freely rolling drum, in the absence of bearing friction, the force F tangent to the drum surface must R vanish. Thus, Eq. (A-11) is left in the form given by Eq. (A-14): Tw = Fx (R + rL) (A-14) w XM M This may be related to the rolling resistance of the tire in the same way that Figure A-2 relates to Figure A-I, where it may be assumed that the relation between torque necessary to keep the wheel in motion and the force necessary to do the same are given in Eq. (A-15). Tw F rr.(A-15) R From this one may conclude that the effective rolling resistance of the tire is given by Eq. (A-16): R FXM j Rr_ )(A-16)

- 73 - This leads to the general rule for measurement of the rolling resistance using a powered tire and a freely rolling drum as given below. POWERED TIRE AND FREELY ROLLING DRUM, WITH AXLE FORCE MEASUREMENT OR TORQUE MEASUREMENT Where a powered tire is used to drive a freely rolling drum, the relationship between the torque needed to rotate the tire and drum and the rolling resistance of the tire F is given by Eq. (A-15), or if an axle force transducer XR is used either on the powered axle or on the drum, the relationship between the measured axle force F and the rolling xM resistance of the tire FX is given by Eq. (A-16). R TIRE STRESS EFFECTS The previous discussion concerning measurement methods on flat and curved drums considered only the kinematics of determining rolling resistance force on the tire from force or torque measurements made at other convenient locations. No consideration was given in those analyses to the fact that the rolling resistance of the tire at a given load may be different on a curved surface than on a flat surface due to the fact that on a curved surface larger tire deflections are encountered, so that higher cyclic stresses are generated. To a first approximation, it is now thought that to obtain the same rolling resistance force on a curved drum and

7-4 - on a flat surface, the tire deflection'should be the same on both the drum and flat surface. This means that matching rolling resistance conditions in the two cases requires determination of the tire deflection rather than load. The condition of equal deflections may be used to determine an approximate load by a simplified analysis such as given below. Assume that the tire diameter conforms to the rigid roadwheel as shown by the dark lines in Figure A-5. The contact path length L is given by L = 2R sin - = 2r sinQ. (A-17) Assume both I and e to be small angles. Then to a first approximation L 2R = 2re. (A-18) The maximum tire deflection c is given by = r(l - cos ) + R(1 - cos ). (A-19) Note that for an inside roadwheel one uses Eq. (A-19) but now with a negative value for R. Again assuming small angles, Eq. (A-19) may be written 8 = r 2/2 + R/ /2 = L 2/2 (l/r + l/R) (A-20)

- 75 - INSERT FIGURES A-5 and A-6 HERE - One page a/W 7- -, 7'/ Drum. Roadwheel Surface r FIGURE A-6. TYPICAL TIRE CROSS-SECTIONAL GEAOMETRY

- 76or L/2 = 62(1/2r + 1/2R)% (A-21) Consider next the cross section of the tire at its center plane, as shown in Figure A-6. The width b of the contact path is given by b = 2r sine A 2rl w/3. (A-22) where w = tire section width r2 = radius of tire cross section. Also =- rI (1 - cos3 ) - w/2( 2/2 (A-23) Combining (A-22) and (A-23) gives b/2 = (6w)2 (A-24) We now assume, as has been done in the past, [3] that the load carried by the tire is the product of its contact area and inflation pressure po, and further that the contact area is an ellipse of semi-major axis L/2 [Eq. (A-21)] and semi-minor axis b/2 [Eq. (A-24)]. Using Fz for the tire load

- 77 2L b, 1/2 1 1-1/2 F R rpo Lb 2 X pA (W) 1 (A-25) z o 2 2 Ij R} or ( 1/2 = )(A-26) By general consideration of linear elasticity the strain on a body is proportional to the deflection at a point divided by a characteristic length. Equation (A-26) describes the maximum deflection. For the same tire, the deflection on a flat surface would be given by Eq. (A-27). (A-27) If the loads, inflation pressures and geometries are the same, then the ratio of tire deflection on the drum to that on the flat surface is given by Eq. (A-28). r/df = (1 + r/R)f (A-28) It is known from a great deal of test data that to a first approximation the equilibrium rolling resistance of the tire is proportional to the first power of its deflection for the same cold inflation pressure, so that it is anticipated that

- 78 - a ratio of rolling resistance on a drum to that on a flat surface is the same as given by Eq. (A-28). F Fx (1 + r/R) (A-29) R This leads to the conclusion that if deflection is to be used as a criterion for loading of a tire, then to the best of our present understanding the same equilibrium rolling resistance will be obtained on the drum as on a flat surface when equal tire deflections are maintained. On the other hand, if load is used as a criterion for adjusting the tire on the drum, then the ratio of rolling resistance on the drum to rolling resistance on the flat surface is given by Eq. (A-29), where it is seen that the rolling resistance on the drum Fx is greater than the corresponding rolling rexR sistance Fv on the flat surface by the factor (1 + r/R) 2.

THE UNIVERSITY OF MICHIGAN DATE DUE UNIVERSITY OF MICHIGAN I II 111111111 III ll 1iii