Prediction of Skid Resistance as a Function of Speed From Pavement Texture Measurements

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1 7 Prediction of Skid Resistnce s Function of Speed From Pvement Texture Mesurements M. C. Leu nd J. J. Henry, Pennsylvni Stte University A model tht cn be used to describe the vrition of skid resistnce ith vehicle speed is presented. The model contins to constnts: One is mesure of lo speed skid resistnce, nd the other ccounts for the decrese in skid resistnce s vehicle speed increses. It is dem onstrted tht the constnts cn be predicted from mesurements of pvement microtexture nd mcrotexture. A significnt feture of the model is tht it clerly seprtes the effects of the to texture types. It cn lso be used to determine skid resistnce-speed chrcteristics from single speed mesurement nd mcrotexture mesurement. It is current prctice in the United Sttes to evlute the skid resistnce of highys by tking nnul mesurements of the locked-heel skid number of the primry rod system (1. These mesurements re usully performed t one speed only-typiclly 64 km/h (4 mph-but sometimes t the "previling trffic speed." Such mesurements only prtilly chrcterie pvement sfety in tht they do not indicte the degree to hich skid resistnce chnges ith speed. The mesurement of the reltion beteen skid resistnce nd speed requires testing t to speeds or more, hich ould require three times the effort of conducting n nnul survey. The skid resistnce of pvement is determined by its surfce texture. Kuer nd Meyer (2 hve reported the combined effects of microtexture nd mcrotexture. Microtexture, the fine-scle surfce texture of the pvement ggregte, determines skid resistnce t lo vehicle speeds. Mcrotexture, on the scle of the grdtion of the ggregte, influences et-pvement skid resistnce by determining the rte t hich ter cn escpe from the tire footprint nd therefore the rte t hich skid resistnce decreses s speed increses. Thus, it should be possible to predict the skid resistnce-speed curve from suitble prmeters for mcrotexture nd microtexture. An lterntive method for determining the reltion beteen skid resistnce nd speed for pvement ould be to perform mesurement t ny convenient vehicle speed nd combine the result ith mcrotexture mesurement to predict skid resistnce t other speeds. The objective of this reserch s to develop model for chrcteriing the skid resistnce-speed behvior of pvements nd to relte this model to mesures of pvement texture. Considertions re limited to mesurements of skid resistnce mde ccording to the E test method of the Americn Society for Testing nd Mterils (ASTM (1. The effects of coercil tires, ter-film thickness, nd other test conditions re not considered here. Sesonl effects nd vritions in skid resistnce cused by rin re lso excluded from considertion becuse ll dt ere obtined t the sme time. MODEL FOR THE RELATION BETWEEN SKID NUMBER AND SPEED Three forms of the reltion beteen skid number (SN nd speed (V re considered; eventully, one is selected on the bsis of ho ell it fits the experimentl dt nd reltes to the texture prmeters. A second-order reltion is most frequently used to fit SN dt (: SN = +, Y + 2 Y 2 In this model, represents lo-speed skid resistnce nd ould therefore be expected to be relted to some mesure of microtexture. The skid number-speed grdient (SNG for this model is SNG = - [d(sn/dv] =-(, V (2 nd the percentge SNG (PSNG is PSNG :=(SNG/SN x 1= [-( VIOO/ + 1 Y+ 2 Y 2 ] (3 The results of other investigtions (4, 5 hve shon tht PSNG is function of mcrotexture lone. The model in Eqution 1 contrdicts this observtion becuse Eqution 3 contins prmeter (o tht must be highly dependent on microtexture. Another deficiency of this model is tht it often results in curve shpes tht re cone ve donrd (negtive second derivtive or curves tht indicte n increse of SN ith speed t high vehicle speeds. Mjchercyk (6 hs plotted skid number versus speed dt on log:-log pper nd obtined liner fit, implying the folloing model: SN= b yb I (4 The grdient nd percentge grdient for the model re s follos: PSNG = (-bi/v 1 Mjchercyk found correltion beteen b1 nd mcrotexture tht is consistent ith erlier findings tht PSNG t given speed is function of mcrotexture lone. The deficiency of this model lies in its los peed skid number behvior. The curve is so steep t lo speeds tht it predicts consistently high skid numbers t lo speeds. Thebo prmeter, therefore, cnnot be correlted ith microtexture. The model tht s developed in the course of this reserch is SN= c exp (c 1 V here co is the ero speed intercept nd the grdient nd the percentge grdient re SNG = -c c 1 exp(c 1 Y nd PSNG = -1 c 1 (I (5 (6 (7 (8 (9

2 8 As in Eqution 1, lo- speed skid resistnce is indicted by the ero speed intercept of the curve fitting the dt. It ould therefore be nticipted tht Co ould be strongly correlted ith prmeters of microtexture. The c i prmeter is proportionl to the PSNG nd should therefore be relted to mcrotexture prmeters. It is interesting to note tht the P8NG for this model is constnt tht is independent of speed. In fct, the model in Eqution 7 s suggested s result of the observtion tht the PSNG of ctul dt did not vry significntly ith speed. The model cn be derived from the folloing definition of PSNG: Figure 1. Test of three models for reltion beteen skid number nd vehicle speed. ----SN v+ 2 v SN bovb1 -- SN c ec,v PSNG =(-1/SN [d(sn/dv (1 hich cn be rerrnged to obtin [d(sn/sn] = (-PSNG/ 1 dv (11 Integrting from ero to ny speed nd ssuming the PSNG is independent of speed, In (SNv/SN v=o = -(PSNG/l V (12 hich yields the Pennsylvni Stte University (PSU model for skid resistnce-speed behvior: SN= SN exr [-(PSNG/ l VJ (11 here SNo = ero speed intercept (relted to microtexture nd PSNG = percentge skid number-speed grdient (relted to mcrotexture. A significnt dvntge of this model is tht it seprtes the effects of mcrotexture nd microtexture. Figure 1 shos the results of lest squres fit of the three models to three sets of skid resistnce-speed dt. Although the three models fit the dt eqully ell, only the PSU model (Eqution 13 consistently provides the expected shpe nd lo-speed behvior. Further evidence of the superior bility of this model to fit skid resistnce-speed dt my be found in the tretment of dt for six pvements here the vehicle speed rnged from 16 to 8 km/h (1 to 5 mph (7. The speed grdient from Eqution 13 is SNG = SN (PSNG/ 1 exp[-(psng/i OOV] (14 If it is ssumed tht SNo is function of microtexture nd PSNG is function of mcrotexture, then SNG is function of both mcrotexture nd microtexture. For to surfces ith the sme mcrotexture, the one ith better microtexture ill hve steeper grdient. Findings in erlier reserch pper to be consistent ith the PSU model. Sbey (8 nd Glly nd Ros P. (both found higher correltion beteen mcrotexture nd PSNG thn beteen mcrotexture nd SNG. Schule (1, using model surfces, concluded t ht s urfces ithhigh micr otexture produce high skid numbers t lo speeds nd steeper SNG thn do surfces ith lo microtexture. Mhone (11, in reserch on ctul pvements, found tht surfces tht originlly hd steep grdient ould hve n intermedite grdient fter polishing (ering y of the microtexture. DATA BASE The skid resistnce dt used in this study ere obtined by the West Virgini Deprtment of Highys on km / h IOO IO VEHICLE SPEED, miles/ h 2 test sections in West Virgini in July The tests ere conducted in ccordnce ith ASTM E t speeds of 48, 64, 8, nd 96 km/ h (3, 4, 5, nd 6 mph. Telve tests ere mde t ech speed, nd the verge vlues ere used in the study. A lest squres fit of the dt to the PSU model (4 s performed to provide vlues of SNo nd PSNGfor ech pvement. At the time the skid resistnce mesurements ere mde, to core smples ere tken from ech section nd snd-ptch mesurements (8 ere performed by personnel of the West Virgini Deprtment of Highys. Dui ing the sme eek, PSU personnel recorded mc - rotexture nd microtexture profiles. PSU personnel subsequently nlyed the profile dt to obtin root men squre vlues for the heights of the mcrotexture nd microtexture profiles (RMSH..A nd RMSHMr respectively (7 nd obtined British portble numbers from the core smples. PAVEMENT MACROTEXTURE AND PSNG To test the hypothesis tht mcrotexture prmeters cn be used to predict PSNG, to prmeters ere considered: root men squre height (RMSH..A from profile nlysis nd snd-ptch men texture depth (MD. A high degree of correltion s found beteen these to prmeters (Figure 2. Therefore, either of the to cn be selected ith similr results. Figure 3 shos the correltion of PSNG ith MD. The reltion PSNG = 4. l(mdt.4 7 (15 is seen to fit the dt ell. Similr results ere obtined hen RMSH.,A nd other profile-derived prmeters ere used (!

3 9 Although the snd-ptch method is reltively simple, it hs to disdvntges s method for mesuring mc - rotexture: ( It is someht lcking in precision, nd (b it requires closing the pvement to trffic. Noncontcting methods tht cn be used t trffic speeds re under development (5 nd should be considered s substitutes for snd-ptch or profiling techniques. PAVEMENT MICROTEXTURE AND SNo To microtexture prmeters, root men squre height (RMSHM 1 from'profiles nd British portble number (BPN from core smples, re vilble to test the hypothesis tht SNo cn be predicted from microtexture Figure 2. Men texture depth versus root men squre mcrotexture height 'lo.5 Q6 7 Regression Eqution MD= 1.6 RMSHMA Correltion Coefficient R=Q dt. The vlues of RMS 1 depend on the definition of the sie rnge of microtexture. Vlues for RMS 1 ere computed s function of the lrgest velength considered. The cutoff velengths rnged from.5 to 2.54 (.2 to.1 in. A correltion beteen the resulting vlues of RMS 1 nd SNo s then ttempted for ech cutoff velength. The highest correltions, ith correltion coefficients of.69 nd.87 for to dt sets, ere obtined for the cutoff velength of.5 (.2 in (7. Microtexture is therefore defined here s consisting of sperities hose idth is less thn.5. The correltion beteen the RMSHM 1 of sperities less thn.5 (.2 in ide nd the BPN from the core smples is shon in Figure 4. The fct tht only to core smples ere obtined t ech test section could ccount for some of the sctter. In Figure 5, SNo is plotted versus BPN for 2 test sites. A lest squres regression nlysis yields the folloing: SN = BPN (16 ith correltion coefficient of. 75. Other dt obtined t six sites in Pennsylvni, for hich BPN mesurements ere tken t five rther thn to loctions t ech site, re given by Leu (7. For these dt, the regression eqution s - SN = BPN (17 J ec 5 IO ROOT MEAN SQUARE TEXTUlE HEIGHT, RMSHMA (I' 3 il<:h Figure 3. Percentge skid number-speed grdient versus men texture depth L25.. e 1.8..!! f f;l 2 en 1.2 -,5 "' ID ::i; => 1. 8,5.6 Regression Eqution PSNG 4.1 (MD- 47 Correltion Coefficient R.96 O+-...,_--'2-.-_o.3-.-«>o_.&:1+--""oso..._-"o.1.c..,...ec= o MEAN TEXTURE DEPTH, 1 i1ches 4 ith correltion coefficient of.95. PREDICTION OF SNs FROM TEXTURE PARAMETERS By combining Equtions 13, 15, nd 16, reltion cn be obtined for SN, MD, BPN, nd V: SN= ( BPNexp[-.41 V(MDt 47 ] (18 Vlues of SN4 nd SNo, clculted from the texture dt by using Eqution 18, re compred ith the me- Figure 4. British portble number versus root men squre microtexture height :: ID 75 ct: ID "' ::i; ii! Regression Eqution BPN34.3+B4.9RMSl1y 1 Correltion Coefficient R _o_.ooi...,._oo3-_51-.-m_m ROOT MEAN SQUARE TEXTURE HEIGHT, RMSHMI (1-3 inch

4 1 Figure 5. Zero speed intercept skid number versus British portble number. Regress ion Eqution SN ( BPNJ 1 Correltion Coefficient R : ID :I; ::> Cl i2 6 (/ Ii: 5 t- ;;:; 4 N 3 Fi9ute 7. Skid number t 96 km/h (6 mph s mesured end predicted from skid number t 64 km/h (4 mph nd men texture depth. 6 5 : 4 ::> Cl 3 Cl 2 s: MEASURED SKID NUMBER Y X so BRITISH PORTABLE NUMBER sured skid numbers shon in Figure 6. Although the method provides good prediction of skid resistnce, better results could be expected if more extensive BPN dt ere vilble. The combintion of n SN mesurement nd mcrotexture mesurement cn lso be used to predict SNs t other speeds. For exmple, SN4 [64 km/ h (4 mph] nd MD could be used by combining Equtions 13 nd 15 to yield SN= SN 4 exp[-.41 (V - 4(MDt A1] (19 Figure 7 shos excellent greement beteen mesured SNo [96 km/ h (6 mph] nd the predictions from Eqution 19. Noncontcting methods for mesuring mcrotexture t trffic speeds ould provide more convenient technique for use in n eqution of the form of Eqution 19; such methods re no being developed (. Figure 6. Mesured skid number versus predicted skid number for British portble number nd men texture depth. 1 The reltion beteen SN nd V for vrious mcrotextures nd microtextures is shon grphiclly in Figure 8. In designing pvements for good skid resistnce t lo speeds, it is importnt to provide high BPN levels; for dequte skid resistnce t high speeds, it is necessry to hve high MD vlues. CONCLUSIONS AND RECOMMENDATIONS Skid resistnce t ny speed cn be predicted from one microtexture nd one mcrotexture prmeter by using the Pennsylvni stte University model for skid resistnce-speed behvior. An dvntge of this model is tht it clerly distinguishes the roles of mcrotexture nd microtexture. Another ppliction of this model permits the prediction of skid resistnce t ny speed Figure 8. Reltion beteen skid number nd vehicle speed for vrious conditions of pvement texture. --MD=.76 (3x 1-3 in MD=.51 (2 x 1-3 in ----MD=,25 (1 x 13 in - -Mo=.13 (5 x 1-3 in eo 7 CJ (64km/hl4mph o (96 km/h 6 mph : o MEASURED SKID NUMBER 1 O:t---c.::2 --:-:::-4"-::-:::- ;6 :.:.,,,o::_:km/h so 6 VEHICLE SPEED, miles I h

5 from mesured skid number t one speed nd mcrotexture mesurement. Although British portble number nd snd-ptch texture depth re dequte mesures of microtexture nd mcrotexture, they do require the interruption of trffic. It is unlikely tht microtexture cn be mesured t high vehicle speeds. Progress is being mde hoever, in the development of noncontcting, high-'speed methods for mesuring mcrotexture. The development of these methods should be encourged so tht simultneous mcrotexture mesurement nd skid numbr mesurement cn be obtined tht ill mke it possible to determine the skid resistnce-speed chrcteristics of pvement from single test. ACKNOWLEDGMENTS Ti or s sponsored by the Federl Highy Ad1strtion (FHWA. We ish to express our grtitude to R. R. Hegmon of FHWA nd E. Hoerter of Ensco Corportion for their ssistnce in obtining the experimentl dt used in this ork. The suggestions nd dvice of W. E. Meyer contributed significntly to the reserch. The contents of this pper do not necessrily reflect the opinions of the sponsoring gency. REFERENCES 1. Rod, Pving, Bituminous Mterils; Skid Resistnce. Annul Book of ASTM Stndrds, pt. 15, H. W. Kuer nd W. E. Meyer. Tenttive Skid Resistnce Requirements for Min Rurl Highys. NCHRP, Rept. 37, W. E. Meyer nd others. Locked Wheel Pvement Skid Tester Correltion nd Clibrtion Techniques. NCHRP, Rept. 151, J. J. Henry nd R. R. Hegmon. Pvement Texture Mesurement nd Evlution. ASTM, Phildelphi, Specil Technicl Publ. 583, R. E. Veres nd others. Use of Tire Noise s Mesure of Pvement Mcrotexture. ASTM, Phildelphi, Specil Technicl Publ. 583, R. Mjchercyk. Influence de l Rugosite Geometrique d 'un Revetement sur l 'Evcution de l'eu l'interfce Pneu-Route et sur le Derpge des Vehicules. Annles de l'institut Technique du Btiment et des Trvux Publics, No. 318, 1974, pp M. C. Leu. The Reltionship Beteen Skidding Resistnce nd Pvement Texture. Pennsylvni Stte Univ., Automotive Reserch Progrm Rept. S78, B. E. Sbey. Rod Surfce Texture nd Chnge in Skidding Resistnce With Speed. British Rod Reserch Lbortory, RRL Rept. 2, B. M. Glly nd J. G. Rose. Mcro-Texture Friction, Cross Slope nd Wheel Trck Depression Mesurements on 41 Typicl Texs Highy Pvements. Texs Trnsporttion Institute, Texs A&M Univ., Reserch Rept , K. H. Schule. Typen der Oberflchenfeingestlt und Ihre Wirkung uf den Reibungsiderstnd bei Nsse. Interntionles Colloqttium Uber St1'ssengriffigkeit und Verkehrssicherheit bei Nsse m 5. und 6.6., Berlin, Beitrg 15, D. C. Mhone. Skid Number nd Speed Grdients on Highy Surfces. TRB, Trnsporttion Reserch Record 62, 1976, pp Discussion Willim P. Chmberlin, Ne York Stte Deprtment of Trnsporttion One of the mthemticl models proposed by Leu nd Henry llos prediction of skid number t one vehicle speed from combintion of skid number t nother vehicle speed nd mcrotexture mesurement. Eqution 19 is n expression of this model in hich the constnts ere derived from tests on 2 bituminous pvements in West Virgini. For the West Virgini pvements, SN4 vried from 26 to 61 nd men sndptch texture depth from.8 to.83 (.3 to.32 in. It hs recently been shon (12 tht Eqution 19 is lso vlid for 31 experimentlly textured bituminous pvements in Texs (_!! for hich the rnge in SN4 is comprble to tht in West Virgini but the rnge in texture depth is much greter [.25 to 3.15 (.1 to.12 in]. The purpose of this discussion is to sho tht Eqution 19 pplies eqully to group of experimentlly textured concrete pvements in Ne York Stte. The Ne York dt ere collected t five different experimentl sites, nd ech s textured by the sme four methods-burlp drg, nturl bristle pving broom, ire brush, nd fluted flot (14,15. Skid resistnce t 64.5 nd 88.5 km/h (4 nd55mph nd snd-ptch texture depths ere mesured ieditely fter construction nd t vrious times over the next 4 yers. SN4 in the Ne York dt vried from 2 to 72 nd snd-ptch texture depth from.2 to 1.65 (.8 to.64 in. The Ne York dt ere first used to develop the reltion beteen MD nd PSNG (Figure 3. Fitting n exponentil curve of theform of Eqution 15 to these dt resulted in the regression shon in Figure 9. Although the sctter of dt points bout this regression is greter thn tht found by Leu nd Henry, the correltion coefficient (.61 is significnt t the.1 level nd more importnt, the constnts in the regression eqution re similr. Becuse of this similrity, Eqution 19 s used ith the uthors' constnts (4.1 nd.47 to estimte vlues of SN55 from mesured vlues of SN4. Comprison of the estimted nd mesured vlues of SN55 is shon in Figure 1 in hich the.95 prediction limits for the regression nd the line of equlity re shon s broken lines. The regression itself is not plotted becuse of its close correspondence ith the line of equlity. The prediction limits correspond to stndrd error of estimte of 2.6 skid numbers vlue only slightly lrger thn the mesurement erro ssocited ith typicl skid tests performed ccording to ASTM E 274 (16. Thus, experience ith bituminous pvements in Texs nd concrete pvements in Ne York, hich represent textures produced by vriety of methods, supports the uthors' contention (bsed on experience in West Virgini tht skid resistnce t one speed cn be estimted ith resonble ccurcy from combintion of skid resistnce mesured t nother speed nd mesurement of pvement mcrotexture. REFERENCES 12. Pvement Texture nd Avilble Skid Resistnce. Office of Reserch, Federl Highy Administrtion, Nov J. F. Nixon nd others. Sprinkle Tretment for Skid Resistnce Surfces. Texs Stte Deprtment of Highys nd Public Trnsporttion, Reserch 11

6 12 Figure 9. Percentge skid number-speed grdient versus men texture depth for experimentl concrete textures in Ne York. 2.5, l.so \ \ Regression Eqution: PSNG 4.53 (MD Curr.,lLluu Cu.,fflcltmL: R.61 "' cu cu p., "' I... cu., "' '".. "'... i:l cu u...,.. cu Jl ::J.s:l.5.ZS.... Note: l.39 in. l km.62 mile.5 l Men Texture Depth, 1-3 in. 6 Figure 1. Prediction of SN 5 5 by use of the Leu nd Henry model. Regression Eqution: MSN 55 Correltion Cefficient: R U"\ U"\ ti "' cu... <Jl Ill " (l :>:: 4 2 / /Line of Equlity o / Predicted SN 55 6

7 13 Rept. 51-IF, Vol. 1, Dec W. P. Chmberlin nd D. E. Amsler. A Pilot Field Study of Concrete Pvement Texturing Methods. HRB, Highy Reserch Record 389, 1972, pp W. P. Chmberlin. Concrete Pvement Texturing Methods-A Revie of Experience in Ne York. Engineering R&D Bureu, Ne York Stte Deprtment of Trnsporttion, Feb R. R. Hegmon. Sesonl Vritions in Pvement Skid Resistnce-Are They Rel? Public Rods, Vol. 42, No. 2, Sept Authors' Closure We ould like to express our pprecition to Chmberlin for mking vilble dditionl dt in support of one spect of our reserch. Chmberlin's regression coefficients of 4.53 nd.497 re in good greement ith ours of 4.1 nd.47 respectively, considering the precision of the correlted dt (SN4 nd men depth mesured by the snd-ptch method. Reserch tht ill consider 2 sites in Pennsylvni is plnned for 1979, so e ould elcome similr dt from others. Eqution 19 elimintes the prmeter SNo from our model (Eqution 13. We hve found tht this prmeter is ffected by both microtexture nd short-term vritions in ether. Wether-relted effects re eliminted by conducting ll skid mesurements in one ether re t the sme time. Hoever, it is probbly not possible to compre dt sets tken t different loctions t different times ithout correcting for etherrelted fctors such s rinfll history. The differences beteen Equtions 16 nd 17 cn be ttributed in prt to these effects, nd lrger differences might be expected. Reserch into sesonl nd short-term vritions is under y nd, if it is successful, e my be ble to ccount for microtexture nd ether in generlied model. Publiction of this pper sponsored by Coittee on Surfce Properties- Vehicle Interction. } Determintion of Skid Resistnce-Speed Behvior nd Side Force Coefficients of Pvements V. R. Shh, Dorr-Oliver Compny, Stmford, Connecticut J. J. Henry, Pennsylvni stte University \./ Pvement friction chrcteristics including skid resistnce-speed dependence, side force coefficients, nd brke slip numbers re seen to be derivble from dt obtined in the trnsient slip test. The trnsient slip test is described, nd it is noted tht ny friction tester ith forcemesuring trnsducers cn be used for these mesurements. The brke slip numbers re shon to be independent of the rte of heel lockup, hich leds to the observtion tht brke slip numbers obtined during trnsient slip test re equivlent to locked-heel skid numbers t the sme sliding speed. Side force coefficients cn be computed from trnsient slip dt ith the help of model. The dt nd conclusions pply to the stndrd skid-test tire operting under fixed test conditions nd norml lod, ter film thickness, nd infltion pressure. Highy sfety in the United sttes is currently evluted by using locked-heel skid numbers (1. During the lifetime of pvement ering course, the skid number (SN is mesured t lest once yer t single vehicle speed-usully 65 km/ h (4 mph-lthough sometimes t the "previling trffic speed." Becuse vehicles re operted on highys t vriety of speeds nd only rrely in the locked-heel mode, the rnking of pvement sfety by mens of locked-heel test t single speed cn be questioned. Furthermore, vehicles require dequte lterl forces to mintin directionl stbility in cornering mneuvers. In complete evlution of pvement sfety, it is necessry to mesure the complete frictionl chrcteristics of pvement t vrious speeds, cornering ngles, nd heel stop rtes. It ould clerly be imprcticl to do this for ech pvement in the country on n nnul bsis. Reserch s initited t the Pennsylvni Trnsporttion Institute (PTI, Pennsylvni Stte University, to determine the degree of interreltionship mong slip, side force, nd locked-heel dt (2,3. The objective of this reserch s to determine the-most efficient mens of evluting the frictionl cpbility of pvements. As result of this reserch, methodology s developed for processing dt from single mesurement t one vehicle speed to obtin the speed dependence nd side force frictionl chrcteristics of pvement. EXPERIMENTAL PROCEDURE The Penn Stte Mrk III Rod Friction Tester (4 s used in this study. The tester hs single heel, six-component force-torque mesuring hub, nd hydrulic system tht cn steer the test heel into ngles of up to 12" in reltion to the forrd velocity of the toing vehicle. To rotry vrible differentil trnsformers mesure the ngle of the test triler nd the ngle of the free-triling fifth heel reltive to the truck xis. In this y, the ctul y ngle of the test trilerincluding the correction for ny y it induces in the

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