DETERMINATION OF PRECRASH PARAMETERS FROM SKID

40Transportation Research Record 893Table 3. Corrected stopping distances.VehicleLoadingSurfaceTiresChevetteLL WVDABias plyChevetteLTDLLWLLWTranstar- GVWFontaineTar andgravelchipVDAVDABias plyRadialBias 01020304060ASTMSkidNo.at 40mph81.l60.8Slide FrictionCoeffici ent at40 mph forNominal Load0.8480.71481.l0.77381. l0.566SE AsPercentageof AvgCorrectedStoppingDistanceAvg CorrectedStopping Distance (ft)Long CorrectedStopping Distance (ft)Short CorrectedStop ping Distance (ft 0.090.340.942.471.540.240.480.605.020.l45.280.2207 .55.622.546.986 .6213.44.717.743 319.345.679.1167 1.7Not run18.845.077 .8165.010.230.468.9116.lNot 11.102.080.580.78Note: Five test runs were made at each nominal speed.aTen runs were made for this case.locate the end of each skid mark because this isdistinct and occurs where the test vehicle's whee.lsstopped. The start of the mark is harder to locate.The location of the s·tart of the skid marks dependson the measurer's judgment. Therefore, to keep t.heresults as consistent as possible, the same measurerwas used throughout this study.After the skid mark ends had been located, thelength of each· of the skid marks was measured with atape measure, and the results were recorded.If theskid marks were cunell, Lhe path of the skid wa1 followed as closely as possible to determine thetrue length of the mark.During the moderate braking tests, the effect ofchanges in brake pedal force applie'd and road surface composition on the skid marks produced during astop were studied.All test runs were made bystopping the subcompact passenger car from a singleinitial speed of 30 mph on several different pavements. All of these tests were run with the lightlyloaded vehicle and radial tires.The skid trailer tests used an ASTM skid trailerwith l\STM tires to measure the skid numbers of eacho f the test surfaces used du-c ing this study.Peakand slide friction coefficients were also measuredfor each of the passenger car tires. used on a1-l ofthe test surfaces for which each particular tire wastested.Details of the skid trailer testing aregiven etsewhere ll.Repeatability of Skid Mai:k Data--Two methods were used to check the consistency ofthe severe braking test data.FiLst, the variability of the vehicle and the pavement was studiedby looking at the distance the test vehicle took tostop for each test condition. Then, the consistencywith which the measurer was able to mark the ends ofthe skid marks was analyzed.Before the stoppingdistances of test stops that were made from the samenominal prebraking speed but from slightly differingactual prebraking speeds could be compared, it wasnecessary to correct the stopping distances to account for the differing speeds. Corrected stoppingdistances were calculated for each run by means ofEquation 1:CSD SD · V /V'i(l)whereCSDsov11VNcorrected stopping distance,actual stopping d1stance,actual prebraking speed, andnominal prebraking speed.This formula was taken from the Society of Automotive Enqineers recommended practice J-299 , stoppingdis ta nee test procedure.A ter they had been corrected, stopping distances for the same nominalspeed could be compared directly.Equation 1 was used to develop a table to summarize the corrected stopping distances of all of themore than 500 test stops that were made.Thisallowed comparison of the corrected stopping distances for varying loadings, pavements, and tires .Table 3 is a typica.l portion of this table. The lasttwo columns of Table 3 give the amount of variability that was present in the testing.The nextto la.st column contains the standard erroL in thecorrected stopping distance (equal to the standarddeviation divided by the square root of the numberof trials) , and the last column contains the standard error as a percen ge of the average coi::rectedstopping distance. To obtain some idea as to whatthe numbers in the last column mean for the fivetrials that were run for each test case, a standarderror percentage of 1.14 percent means that 95percent of the test values will be within 5 percentof the average value.Analysis of the corrected stopping distancesshowed that the severe braking stops were repeatable . The average standard error as a percentage ofthe average corrected stopping distance was 1. 75percent. This indicates that 95 percent of all ofthe test stops had corrected. stopping distances thatweLe w"thin 10 percent of the average value .Significantly gceater variability in stoppinqperformance was observable for two sets of testcon.d itions. For stops made from a nominal prebraking speed of 10 mph, the average standard errorpercentage was 3 . 14 percent.However, the maximumstandard error for any of the 10-mph cases was 0. 29

Transportation Research Record 89341ft.Since the fifth wheel measures stopping distance with approximately this accuracy, this levelof error is not significant. Testing on the tar andgravel chip pavement was also less consistent andrepeatable.The average standard error percentage,for stops from all test speeds, was 3.10 percent onthe ta.r: and gravel chip pavement versus the 1.42percent obtained for the other pavements. Correctedstopping distances were less consistent on the tarand gravel chip pavement due to variations in thecomposition and slickness of the surface.Duringthe testing we noticed that the vehicle took longerto stop when a higher proportion of tar was presentin the road.Next, the consistency with which the measurer wasable to measure the length of the skid marks produced during testing was checked.To determine thelength of the skid marks on one side of the vehicle,the measurer must mark three points: the viewed fromabove (VFA) point, the viewed from ground level(VFGL) point, and the start of front marks (SFM)point. Determination of the precise location of thethree points marked by the measurer was a difficultand somewhat subjective process because the skidmarks tended to fade into the pavement.Althoughthe same person was used as measurer throughout thisprogram, there was clearly some run-to-run variability in the locations of the points chosen.To determine the amount of va.r:iability inherentin the measurement process, the length of severalsets of skid marks was measured every day for several days.By measuring the skid marks on a dailybasis, enough time passed between each remeasurementso that the measurer could not remember the locationof the marks from the previous day and had to relocate them.Data collected by measuring the lengthof eight skid marks produced during three stops onseven consecutive days was analyzed.Skid marks decay with time.For the lightlytraveled test surfaces that were used, this decay isvery slow.To prevent this decay from biasing theanalysis, linear regress i on was performed for eachof the skid marks analyzed by using, as the modform ,s c Dn(2)where S is the skid mark length, n is the number ofthe measurement, and c and D are determined by regression . Only skid marks for which the 90 percentconfidence interval on D included zero were thenretained for analysis since these marks showed nosignificant decay with time.The standard error, the standard error as apercentage of the average skid mark length, and the95 percent confidence limits were calculated foreach of the eight skid marks.The mark with thegreatest variability had a 95 percent confidencelimit of 11.1 percent of its average length.Onthe average , the skid marks had a tight 95 percentconfidence limit of 3.8 percent of the averageleng t h.This i ndicates that the skid mark measurement process was repeatable.Va lidity of the Skid Mark Length Ve.rsus PrebrakingSpeed FormulaA detailed a nalysi s of the skid mark length datacollected during the severe braking ·testing wasconducted to either confirm the valid ity or elseimprove the e xist i ng prebrak i ng speed versus skidmark length formulas.This was done by using thesevere braking test data for performing regressionanalyses that determined values of coefficients inthree model equations.The model equations have astheir specific form,(3)(4)(5)wheresvA1 , A2 , A3, B3, C2, and c 3cskid mark length,prebraking speed, andunknown coefficients,which were determinedby regression.Model l (Equation 3) has the same form as the standard skid mark length versus prebraking speed formulas. Model 2 (Equation 4) has the same form as thestandard formulas would have if they were modifiedby assuming a constant distance between the start ofbraking and the onset of skid mark production. Model3 (Equation 5) has the same form as the standardformulas would have if they were modified to accountfor a ramp brake application plus the traveling of aconstant distance prior to the onset of skid markproduction.Separate regression analyses were performed foreach of the 22 different combinations of vehicletype, tire type, pavement type, and loading thatwere tested.Regressions were performed for theskid marks left by each of the vehicle's individualwheels as well as for the average length from combinations of wheels.The numbers that follow werefound by using the four-wheel average s id marklength. Similar results were obtained, however, forthe regressions that were performed by usinq each ofthe individual wheel ' s skid marks.Tables 4 and 5 give the results of the regressions by using the fou r -wheel average skid marklength for each of the three models.For the IHTranstar-Fontaine rig,for which the four-wheelaverage length was not used because this rig hadmore than four wheels, the regressions performedwith the left front whee l and with the left leadingtractor tandem data are g i ven.Table 4 contains the coefficient of determination(R 2 ) that was calculated for each model for thevarious test conditions.The lowest value of thecoefficient of determination that was obtained forany of the models for any set of test conditions was0,9784.For more than two-thirds of the casesshown, R2 was above 0. 9950 and 85 percent of thecases had it above 0.9900. These are extremely highvalues for the coefficient of determinat i on andindicate that all three models could closely fit theexperimental data.However,because R 2 was solarge for all of the test cases, it was inadequateto determine which model was most accurate. This isbecause a model with more terms in it, such as model3, normally accounts for more of the variation inthe data.It may, however, be less useful foraccident reconstruction than is a model wit,h fewerterms in it such as model l. To see how much moreaccurate the models that contained more terms actually were, the mean square error was studied.The mean square error, which is the second measure of goodness of fit given in Table 4, is anestimate of the deviation of the regression curvefrom the actual data.It was analyzed by taking theaverage of the mean square errors for each model forall of the test cases given in Table 4. Also lookedat was the influence of vehicle type, tire type,vehicle loading, and pavement composition on modelaccuracy.This was done by computing the averagemean square error for selected subsets of the testconditions.The average values of the mean square error that

42Transportation Research Record 893were fou nd for all o f t he test cases were 2 8.01 formodel 1, 2 0.0 8 f or mode l 2, and 17.50 for mode l 3.This ind icates t h at model 3 was the moat a ccurate,fol l o wed by mo dels 2 a nd l , respecti vely .Howeve r ,t he imp rove me n t i n accur a cy between mod els was no tgreat.The mean squu:::e error is the normali z ed s umof the squa r es of the residuals. The square root oft h e a verage va lues g i ven s ho ws that mode l l h as aroot mean square deviation betweenthe model ' spredicted s k id mark len g th a nd t he actual skid mar kle ngth o f slig h tly o ver 5 .25 ft versus sligh t l yunder 4 . 25 ft f o r model 3 .Glvea n average skidmark leng th o f a pprox imate ly 50 f t, this i mp r ovementof about l ft i n accur acy is n o t s ig n ifi cant .A look at the i nd i v i dua l tes t cases s hows largecase-to - ca s e v ariatio ns i n the mean square err o r f orthe di f fering models .Fo r s ome test c onditionsmodel 3 is significantly more acc u rate than model 1,w.ith improvemen ts i nt h e de v iatio n b e t wee nt hepredicted and act ua l sk id mar k le ng th s o f up t o 5 . 25ft o ccurri ng .Th ere does not , however, seem to beany way of predicting in advance when this improvement will occur.Table 4. Goodness of regression WLLWLLWGVWVDAVDASkid padSkid padTar and gravel chipTar and gravel chipVDABias plyRadialBias plyRadialBias WLLWGVWVDAVDASkid padSkid padTar and gravel chipTar and gravel chipVDABias plyRadialBias plyRadialBias plyRadialRadialF-250LLWHalfGVWVDAVDAVDABias plyBias plyBias plyF-7000LLWGVWVDAVDABias plyBias sBiasBias3Results for left fro nt 99530.99840.9988Model 3Model 2Model 31.0069 73.822.2332.2296.8818.508.656.043. 2.725.314.84bRcsults for left leading tractor tandem wheeLTable 5. Coefficients determined by WLLWLLWLLWLLWLLWGVWVDAVDASkid padSkid padTar and gravei chipTar and gravel chipVOABias plyRadialBias plyRadialBias WLLWGVWVOAVOASkid padSkid padTar and gravel chipTar and gravel chipVDABias plyRadialBias plyRadialBias plyRadialRadialF-250LLWHalfGVWVDAVDAVOABias plyBias plyBias plyF-7000LLWGVWVDAVDABias plyBias sBiasBias3Results for left front wheel.1ily"plybply"plybModel1,A1Model 4200.05730.07730.06210.04690.07070.0613b Results for left leading tractor tandem wheel.Model 3-2.237-1.500-2.333-2.232- !0.068-7.4910.121-3 .4740.1170.925- 0.1941.320-1.641-2.952-14.151- 0.016-5.830-4.125-2.683- 5.2140.058- 06890.0603-0.199-0.121-0.040-0.121-1 . .508- 2.316-9.584-1.896-8.815-6.086- 8.27823 598

Transportation Research Record 89343To show the effects of pavement composition andvariability on model accuracy, the average meansquare error was calculated for eaeh test sur.face.The results are given in the first three lines ofTable 6. All of the models most accurately fit theexperimental data for the testing on the skid padithe VDl\. data ran a close second. Much poorer accuracy was obtained on the tar and gravel chip road.Note that this result is consistent with the greatervariability in stopping performance on this surfacethat was pointed out earlier. Even on this surface,despite the relatively large improvements in meansquare error from model l to model 3, the improvement in average root mean square skid mark leng-therror was only about 2 ft, which is not significant.Table 6 also gives the results of average meansquare error calculations, which were made to determine the effect on model accuracy of tire type ,vehicle loading, and vehicle type.The fourth andfifth lines of the table show that higher accuracy,and hence more consistent experimental nata, wasTable 6. Average value of mean square error of selected test conditions.Test ConditionModel 1Model 2Model 3Tar and gravel chip roadSkid padVDABias ply tiresRadial tiresVehicle at LLWVehicle at LLW and on skid pad orVDAVehicle at GVWPassenger car testsPassenger car le-sts on skid pad or VDAPickup !ruck 1es1sAir-braked truck tests90.917.3717.4417 .9 744.7426.646.8673.146.3210.2611 .9 533.6322.006.2556.435.9910.6411.5227.4617.575.6 132.1537.8718.5817.388.6716.2827.7711.289.376.2013 .3521.869.297.475.49Note: Values are lh" uverage of the mean square error for all tests run with the specifiedtest condi11 oo.s.obtained with bias-ply tires than with radial tires.Since vehicles at GVW were only tested on the VDA,it was decided that this result should not be compared with the average mean square error from all ofthe LLW tests because these include the data fromthe highly variable tar: and gravel chip surface.Comparison of the average mean square error from theGVW stops with that from the LLW steps, which weremade on the skid pad or VOA, shows that t he modelsless accurately fit the GVW data. Most of thisincrease in mean square error is attributable to thepeculiar stopping behavior o f the loaded Ford LTD.Comparisons of model accuracy among passengercars, pickup trucks, and the air-braked trucks wasalso mad e by using only the skid pad and VOA data.This revealed that the h ighest accuracy was obtainedfor the air-b·raked vehicles followed by the pickuptr uck, with the passenger cars third.This orderwas something of a surprise because the time delaysthat are inherent in air brakes were expected toresult in less-consistent data.Also, it was ant icipated that, due to these delays, model 3 would beby far the best for the air-braked vehicles. I nstead, only a small improvement, which amounted to0. 5 ft in the average root mean square skid markle ngth error, was obtained.For a ll three models, theoretical ana lysis of theassumed deceleration versus time curves and integration to determine stopping distance shows that thecoefficient of sliding friction (Us) is related tothe coefficient of the ve locity squared term (ll.1,A2, or A3) by the equation(6)U, l/2gA1where g is the acceleration due to gravity.Thecomplete theoreti cal analysis is contained elsewhere(j).From Equation 6, along with the values ofl\.1 1 A2, and AJ in Table 5, va1ues of the slidefriction coefficient have been calculated f or eachof the test conditions.These values are given inTable 7 along with results from two o f the methodsTable 7. Calculated and measured slide friction coefficients.Measured Slide FrictionCoefficientsCalculated Slide Fr

to see if skid marks would be produced; and 3. Skid trailer tests, which measured peak and slide coefficients of friction for many of the tires used in this study, were performed on each of the different pavements used; the skid numbers of these pavements were also American Society for test tires.