pole collisions

7/27/2019 pole collisions

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1999 - 01 - 010

Vehicle Crash Severity Assessmen

in Lateral Pole Impact

Michael S. Var

Stein E. HusheKEVA Engineerin

Copyright 0 1999 Society of Automotive Engineers, Inc.

ABSTRACT

This paper surveys some current technologies inreconstructing lateral narrow object impacts. This isaccomplished through a multi-step process. First,

staged crash test data is reviewed and presented inorder to understand the observable vehicle structuraldeformation trends. A commonly used crush energy

reconstruction algorithm (CRASH) is then applied to thetest data and an analysis is made of the application ofthis tool to this impact mode. The use of defaultstructural parameters as used in CRASH 3 is also

discussed. A linear and angular momentum analysis isdeveloped in order to demonstrate closed form vehicle

dynamics prediction methodologies for non-centrallateral impacts. The momentum methods presented arecompared to a commonly used impact simulation tool.

Finally, change in velocity (AV) and the use and analysis

ofAV for lateral pole impact reconstruction is discussed.

INTRODUCTION

Pole impacts, especially lateral, comprise one of themost aggressive impact environments for automobile

structures. Due to the close proximity of occupants tothe side structure, these pole impacts represent a moresevere crash exposure than comparable impacts toother structures. By their nature, these impacts

concentrate the deformation energy in a narrow portionof the vehic le structure. Subsequently, vehicledeformation patterns differ from what is often seen in

vehicle to vehicle side impacts. Because of the uniquenature of these narrow object impacts, the reconstructionof lateral pole impacts requires a careful analysis of bothvehicle structural behavior and the resulting vehiclemotion dynamics. The vehicle structural behavior isdependant on many factors which include the deformedarea of the vehicle, the structural properties of thevehicle, and the width of the impacting object. Theresulting vehicle dynamics are a function of the amount

In this paper, the algorithm for crush energy determination as used inCRASH 3 and other commercially available software will be referred toas the CRASH algorithm. 175

of deformation, the location of that deformation on thvehicle and the orientation of the impact impulse. Thesfactors must be accounted for when performing reconstruction or analysis of these narrow object laterimpacts.

Frontal pole impacts have been well addressed numerous, previous, technical papers. However, laterpole impacts involve vehicle response that is ncommonly seen in frontal collisions. Rotationcomponents often become significant, vehicle structurproperties differ from frontals, and crash severi

assessment becomes more dependent on location withthe vehicle. Though not addressed here, hard spo

(e.g., wheel areas) on the sides of vehicles can alssignificantly influence the resulting deformation pattern

and vehicle dynamics.

CRUSH ENERGY DETERMINATION

The structural response of an impacted vehicle ma

depend on many factors. These factors includconstruction type (unibody, frame on body), materi

(steel, aluminum, plastics such as SMC, etc.), anassembly methods. Additionally, impact parametealso affect the vehicle response, in some instances to greater degree than vehicle structural properties. Thimpact parameters include impacting geometry (shapewidth, etc.), principal impulse direction, and impalocation on the vehicle. In the case of a lateral narrowobject impact, the impact parameters are extreme

important to the determination of a vehicles response timpact and require careful scrutiny.

Vehicle crash testing exists as the most reliable metho

to evaluate impact response. This crash testing hahistorically consisted of distributed impacts by flat rigbarriers. These flat barrier impacts load the vehicle in distributed fashion over a large surface area. Thallows many different structural components of thvehicle to resist the intruding barrier and therefore thresulting crush is a function of many different vehiclcomponents. Pole impacts, however, load the vehicle


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Table 1. Repeat Barrier Moving Pole Impact Tests.

an extremely concentrated fashion. These narrow objectimpacts concentrate the direct load over a width equal tothe pole diameter, which can be extremely small.Therefore, a given amount of absorbed energy for alateral pole impact will result in increased maximumdeformation depth when compared to a flat barrier.

The majority of crash test data available to the accidentreconstruction engineer consists of flat barrier testing.This is due to compliance testing sponsored by the U.S.Department of Transportation for the Federal Motor

Vehicle Safety Standards (FMVSS), none of which, until

recently, have included narrow object impacts.Government mandated lateral crash testing hasconsisted of FMVSS 301 which is a 20 mph lateralimpact by a moving flat barrier and FMVSS 214 which isa 33 mph lateral impact by a crabbed moving barrier

equipped with a deformable honeycomb face. WhileFMVSS 214 is not a flat rigid barrier, it is a distributed

impact that approximates the impact geometry of thefrontal structures of another passenger car. Neither ofthese impacts serve to simulate a lateral pole impactwith its associated narrow load concentration. Recently,the NHTSA has included a 20 mph lateral impact into arigid pole as a part of the head protection standard. It is

hoped, that as these tests become more widespread,that the lateral pole impact database of tests willcontinue to grow.

When researching lateral pole impacts, several data

sources become available. More recently, tests hbeen conducted for the development of the CRAalgorithm reformulation by NHTSA. These moving ptests are summarized in Table 1. The Federal Highw

Administration (FHWA) which has been concerned wthe design of roadside devices such as lumina

supports, roadway sign posts, and guardrails, hconducted extensive crash testing of vehicles wnarrow objects. As the scope of this paper does encompass yielding and non-rigid barriers, only the rpole impacts are reviewed. If desired, however, yield

and breakaway devices have also been extensiv

tested and provide useful vehicle response informatThese tests conducted by the Federal Highw

Administration at the Federal Outdoor Impact Laborat(FOIL) [Hinch,19871 facility are available through National Crash Analysis Center (NCAC) at GeoWashington University and most are summarized in NHTSA Vehicle Crash Test Database (VCTDB) [AS19851.The FHWA - FOIL database of tests contains basetests to evaluate the impact response into rigid polesorder to pursue design activities into breakaway poand luminaire supports. Applicable FOIL tests are lis

in Table 2. Also in Table 2 are single impact pole tefrom the VCTDB. When examining Table 2, there three listed parameters that merit further discussmaximum crush, path travel distance and impumoment arm. The maximum crush is listed as a sin

Table 2. Car to Riaid Pole Imoacts.

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parameter. As is evident, vehicles having experienced a

collision with a rigid pole have a crush profile that variesover the width of direct and induced damage.Historically, maximum crush has been examined in poleimpact vehicle crashes because it is representative of

the total deceleration distance experienced by thevehicle. Also, for much of the pole impact crash testdata available in the public domain, maximum crush isthe only readily available crush parameter. Therefore, itis useful to attempt to develop relationships between

maximum crush to absorbed energy. Approach andabsorbed energy are both listed as available in Table 2.

Approach energy is the vehicles kinetic energy at themoment of impact. The absorbed energy is the

difference between the vehicle pre-impact and postimpact kinetic energy. For centered impacts, with nopost impact travel, the approach energy approximatesthe absorbed energy (assumes zero restitution). Forhigher speed lateral pole impacts, photographic dataindicates low restitution values are often observed.

There are some additional tests that were done as a partofNHTSAs research into experimental safety vehicles.These 1981 VW Rabbit tests [Bell, 19841 were done withbaseline production vehicles and then modified structure

vehicles in order to document the response changesassociated with modified vehicle structure. Only

production vehicle tests are used in the present analysis.

These are also listed in Table 2.

There is an additional data analysis issue that must beaddressed regarding Table 2. When tests are done in

an oblique fashion, the actual pole deformation travel isnot a distance measured perpendicularly from thevehicle side. Rather, the pole travels a greater distance

while crushing vehicle structure and the actual travel

distance during crush must be accounted for during theimpact phase. Therefore, for the oblique collisions, theactual pole travel distance through vehicle structure isused, rather than the perpendicular crush which isgenerally used when reporting crash test data.

The third parameter of interest is the impulse moment

arm. Mechanics demonstrates that the absorbed energyin an offset impact can be shown to be:

AbsorbedEnergy = i.Mass. V,f (kk+h) (1In Equation (l), k = radius of gyration and h = impulsemoment arm. Therefore, when the impulse moment armis known, the actual absorbed energy can be

determined. This analysis is performed for each test inwhich the impulse moment arm could be determined.Examination of Table 2 will indicate that the impulsemoment arm is unknown for three of the FOIL tests. Thereader is advised that these tests must be applied withcare because the actual absorbed energy may be lowerthan the approach energy listed.

As is evident when examining this data, there is a limitedset of available test data on lateral pole impacts. Thetest data in the public domain is only for limited vehicles ,77

and but for the repeat barrier Golf and Escort, this dis primarily concentrated at a narrow test ranTherefore, any conclusions drawn from this data mustcarefully considered when attempting to apply this dto other vehicles.

Figure 1 is a plot of absorbed energy versus maximresidual crush for the test data listed in Tables 1 andFigure 2, Figure 3, and Figure 4 are absorbed eneversus maximum crush plots for the small cars, lar

cars, and trucks /SUVs respectively. For Figurescrush width is not accounted for. While encompassseveral different vehicles of varying manufacturers, data shows a relatively consistent trend. By plottabsorbed energy, the data accounts for varying weights and impact severity.

Examination of Figure 1 indicates increasing absorbenergy with increasing depth of crush. However, duethe large variability in vehicle type, the data is not wbounded and trends are not readily defined.

When the smaller vehicles are considered, Figure 2,

data indicates a clearly second order relationsbetween absorbed energy and crush. As this is to expected for a linear, isotropic material, Figure

demonstrates the linear, plastic spring may serve asadequate model for these vehicles. Observation of

graph indicates a data point that is outside the boundsthe other data. This data point is found at 34039 ft-lb35 inches crush and is representative of the obliq

Rabbit test conducted at 20.1 mph [Bell, 19841. Wcomparing this test to the other two Rabbit tes

differences in structural stiffness are apparent. Thisdue to the different impact configurations present amoall three tests. The 19.95 mph test had an initial con

point further forward which resulted in structuengagement with the front wheel arch and a-pillar arThe 20.1 mph test however, engaged further rearwand missed this stiffer structure. Examination of the 2mph test results indicates that stiffer structures loca

toward the aft end of the door and rear portion of vehicle are encountered. Therefore, although the savehicle is tested in all three impacts, different structengagement results in different stiffness,

Examination of Figure 3, the large cars also demonstra second order relationship between absorbed eneand residual crush. However, extrapolation of the d

should be considered carefully due to the lack of lowseverity data. In fact, tests with deformation less thaninches are not available in this data set.

Figure 4, the trucks and SUV data once agdemonstrates an approximate second order relationsThe minimal amount of data, however, precludes determination of definite stiffness trends. Two full pickup trucks are shown in Figure 4. While the absorb

energy is approximately equal between the Ford Chevrolet, the maximum reported crush is approxima6 % inches less for the Chevrolet. Review of the data reports indicates that the Chevrolet impac


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Table 3. Crush Profiles and Stiffness Data.

the axis of deformation. A is once again assumed to bezero. The B value is calculated using Equation (11).

B = gL . cos I9 (11)Method 5: Method 5 is similar to Method 2 except that

the average crush depth and width are both corrected bythe cosine of the PDOF measured from normal for theoblique crash tests. This follows from the assumption ofan isotropic material for the vehicle which dictates that

the actual crush resistance should be determined alongthe axis of deformation. A is once again assumed to bezero. The B value is calculated using Equation (12).

30Ec;+24 +24 +2c:-I-24 fc;+c,cz+CIC) +qc4+C&5 +C&

cos2 6 i/L.COSB

Equation (12). B Stiffness Calculation.

CRASH ENERGY CALCULATIONS

Case 1: Case 1 uses the default A and B values as

programmed into the CRASH 3 program. These valuesare based on placing the test vehicles into categoriesbased on wheelbase or structural groupings. The actualcrush profile from the test is then input along with thePDOF. This is a common application of the CRASH

methodology in reconstruction programs.

The energy calculated in this approach varies randomlyfrom under predicting by approximately 93% to overpredicting by approximately 75%. This wide range inerror in predicting crush energy for staged crash testsindicate that the use of default structural properties is notappropriate for a reconstruction of a particular lateral

pole impact. This observation is consistent with w

has been observed for other crash types.

Case 2: Case 2 also uses the default A andstructural properties. However, unlike Case 1, Tangential Correction Factor (TCF) is applied to calculated energy. As would be expected, the calculaenergy is consistently lower for the oblique crash teand this methodology consistently under-predicts crenergy for all cases. The under-prediction varied fromto almost 100%. While some calculations resultedzero errors, that is not the situation for every vehicTherefore, unless staged collision test data is availato verify the results, this Case 2 method is

recommended for use in the reconstruction ofparticular accident.

Case 3: Case 3 also uses crush coefficients A and

based on default class categories. However, rather thinput the test crush profile, the crush width and averacrush are input instead. The average crush

determined such that the crush area will be correct. TTangential Correction Factor is applied to the calcula

crush energy.

The energy calculated in this approach underestimaenergy from 0 to almost 100%. Except for 2 of oblique tests, Case 3 consistently performed worse th

Case 1.

Case 4: Case 4 is exactly the same as Case 3, excthat no Tangential Correction Factor is applied.

The energy calculated in this approach varies randofrom under predicting by approximately 95% to opredicting by almost 50%. Case 4 and Case 3 reporthe same errors for the non-oblique tests.

Case 5: Case 5 uses calculated structural proper,8, based on the test data. The A value is assumed to


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zero because there is no elastic energy absorptioncomponents (such as bumpers) on vehicle sides.Vehicles experience permanent damage with extremelylow severity lateral impacts. The B value used is

calculated by Method 1.

You will note that in the calculation foris used. This average is determined in

as described earlier.

The energy calculation is performed

B, average crushthe same fashion

by inputting theactual crush profile and then applying the TCF to theresults. As would be expected, because B is calculatedusing the average crush and the energy calculation isperformed on the crush profile, differences must result.The use of the Tangential Correction Factor (TCF),

without accounting for this factor in the B calculationresults in significant errors in the oblique tests. In fact,the range of over-prediction for this methodology is from27 to 67% for the non-oblique tests. Over-predictionerrors for the oblique tests ranged from 148% to 192%.

Case 6: Case 6 is done with a B value calculated in the

same fashion as Case 5 (Method 1). Unlike Case 5,there is no TCF applied when the CRASH energyequation is used to calculate absorbed energy. As inCase 5, since the B value is calculated using the

average crush, and the energy is calculated using theprofile crush, then there must be errors. The errors inthe oblique tests decrease with this methodologyshowing an over prediction from 24% to 46%. The non-oblique tests reported the same errors as Case 5.

Case 7: Case 7 employs the same Method 1 B

calculation as Case 5. That is, B is calculated using the

average crush. The energy, however is also calculausing the average crush. Subsequently, the energycalculated using the same methodology as is assumfor the B calculation. The TCF is then applied. The Twill only affect the results for the oblique tests.

As would be expected , si nce the crush enercalculation is performed using the same assumptionsthe B value calculat ion, the predicted enerdemonstrates zero error for the non-oblique tests. T

merely proves that the assumptions in the model consistent. If you calculate B using the average, in or

to achieve the same results in CRASH, the case must analyzed using the average crush. As would also expected, the TCF doubles the calculated energy for oblique tests because the TCF is neglected in thevalue calculation. Subsequently, the oblique tests sh100% error in predicted crush energy.

Case 8: Case 8 is conducted in a similar fashion

Case 7, except that the TCF is not employed in tenergy calculation. Method 1 is used to calculate

The calculated energy in this case predicts the t

energy accurately for all tests. This is to be expectbecause the CRASH analysis is performed in the exsame fashion as the B value calculation.

Case 9: As is found in the previous cases, when thestiffness coefficient is calculated using the averacrush, and the actual crush profile is input into CRASH method, differences will result. Therefore, Ca9 calculates B by solving the CRASH Energy equatfor B with all other parameters known. Therefore, thisMethod 2 for calculating B. A is once again assumedbe zero. The actual crush profile is then input i

Table 4. Energy Calculations

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Table 5. Percent Errors in Predicted Crush Energy.

CRASH with the B value consistent with that. The TCFis then applied. The TCF will only affect the results forthe oblique tests.

The energy calculated in this approach predicts the

energy accurately for the non-oblique tests. This is ofcourse expected, since the B value calculation and theCRASH calculation are performed using the exact same

basis. For the oblique tests, the TCF causes thecalculated energy to be in error by 100%. This isbecause all of these oblique cases are at 45 degreeswhich is the maximum value of 2 for the TCF. This

result is also expected for the oblique cases, because

the B value is calculated without accounting for the TCF.

Case IO: The same B value as in Case 9 is used. Thatis, Method 2 is employed. However, no Tangential

Correction Factor is applied in the CRASH energycalculation. The test profile is entered into the CRASHenergy calculation.

Since the same assumptions are used for both the Bvalue calculation and the energy calculations, thismethod predicted the test energy accurately, with zero

errors for all tests.

Case 11: Case 11 is the same as for Case 9, except

for some small variations. The same B value is used asdetermined through Method 2. The TCF is applied to theenergy calculation. The only difference is that theaverage crush is used in the CRASH energy calculation.

Since B is determined using the profile crush, and theenergy calculation is performed using the average,errors are to be expected. This case consistently under-predicts the non-oblique tests by 20% to 40% while

consistently over-predicting the oblique tests by 37% to60%.

Case 12: Case 12 is conducted in the same fashion asCase 11. The only difference, is that the TCF is notapplied.

Case 12 results in consistent under-prediction by 19% to

40%. The non-oblique tests showed the same errors aCase 11. The oblique test errors are all less than Cas11 oblique test errors.

Case 13: In many commercially available CRASHversions (e.g. EDCRASH, SLAM, etc.), the TCF cannobe removed from the energy calculation. Therefore, it desired to arrive at a consistent B value calculatiomethod that will result in zero errors for all tests. Case

13 accomplishes this. The A value is set to zero for thesame reasons as previously discussed. The CRASHenergy calculation, including the tangential correctio

factor is solved for each crash test for the B valueTherefore, in the oblique tests, the calculated B assumethat the TCF will be applied later and the B value idecreased to compensate for that. This is previous

described as Method 3 for calculating B.

The energy calculations are then performed using thcrush profile and the TCF and the resulting errors arobserved. As would be expected, the calculated energexactly matches the test recorded energy for all tests.

Case 14: If the same B values (Method 3) as used inCase 13 are then applied in the CRASH energequation, without the TCF, then the results are aexpected. Here the B value is calculated to account fothe TCF being applied in the energy calculations

However, the TCF is turned off for the energy calculatiowhich results in this case accurately predicting the nonoblique tests (no TCF required) but under-predicting aof the oblique tests by 50%.

Case 15: Case 15 is an exact duplication of Case 13

except that the CRASH energy equation is calculatewith the average crush. That is, the 2 point version othe Crash Energy equation is applied using a E? valuthat is obtained by back-calculating the 6 point version othe CRASH energy equation. The TCF is applied i

Case 15. Therefore, Case 15 demonstrates the situatioof using the crush profile to calculate B, then using th,83 average crush in the CRASH energy calculation. A


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expected, energy is under-predicted by 19% to 40%.Errors observed are the same as for Case 12, which isto be expected.

Case 16: Case 16 duplicates the calculation methodused for Case 15 (B from Method 3), except the TCF isnot applied. As expected, the errors are the same asCase 15 for the non-oblique tests and rise considerablyfor the oblique tests. The energy calculated in this

approach under predicts by 21 to 66%.

Case 17: As seen in the earlier discussion of crush

path, oblique damage is seen as an increase in crushpath which is proportional to the cosine of the angle offnormal. Addit ionally, the crush width decreases inproportion to the cosine of the angle. Therefore, basedon geometry, the cosine of the angle off normal wouldappear to be a better factor to use to account for obliquecrush than the TCF used in CRASH. The validity of thisapproach would depend on the assumption that thevehicle behaves isotropically. The isotropic assumptionrequires the structural resistance to not vary by direction.To apply this factor, a version of CRASH that allows

eliminating or modifying the TCF would have to beused. This may preclude some commercial versions ofthe CRASH methodology. In order to investigate the useof the cosine adjustment, the following analysis isperformed. For oblique crush, the pole travel distancecan be determined for the six crush points by dividing bythe cosine of the angle off of normal. Then, as in

previous cases, the CRASH energy equation is back-calculated and solved for the B value assuming thisincreased crush depth and decreased crush width. This

B value is then used back in the CRASH equation alongwith the actual crash test damage profile. For oblique

crush, the crash test damage profile is also adjusted by

the cosine of the angle when input into the CRASHenergy equation in order to be consistent with the Bvalue calculation method. The A value is kept at zero.

This B value calculation method is described in Method5. As expected, this case resulted in zero errors for allpredicted crush energy values. The advantage of thismethod is that a B value may be calculated from a non-oblique crash test, and with the assumption of an

isotropic material, can be applied to an oblique crash.The oblique crush damage merely has to be adjusted forthe actual deformation distance into the vehicle which is

dependant on the cosine of the angle off normal. Thelarge errors sometimes seen due to the TCF are

corrected with this approach.

Case 18: Case 18 is conducted in the same fashion asCase 17 (B calculation by Method 5) except that theaverage crush is input into the CRASH energy equation.Since the B value is calculated using the profile, and theCRASH energy equation is computed using the averagecrush, Case 18 involved inconsistent basis and resultedin under-prediction of 19% to 40% for crush energy. Asexpected, the errors are the same as for Case 15 andCase 12.

Case 19: In order to verify that a consistent application

of data will result in correct answers, Case 17 is nrecomputed using the average crush. That is, average crush is corrected by the cosine of the angle normal and used to calculate the B stiffness value. Tis described in Method 4. Then a 2 point version of CRASH energy equation is computed with the averacrush again modified by the cosine of the angle normal. As expected, since the average value is usfor both the B calculation method and for the applicatof the CRASH energy equation, the results are identi

and zero errors are observed for all tests.

Case 20: While the Cosine Correction Method appeato accurately predict crush energy, the user has to abeware of some of the simplification errors that cresult. Case 20 uses the average crush to calculate B value (Method 4) and then inputs the actual profile ithe CRASH energy equation. Since the average is usto determine B, and the actual profile is used to calculathe energy using the B determined from the average, inconsistent basis exists. The energy calculated in tapproach over predicts by 24 to 67%. This Cademonstrates the inherent, expected errors through

use of the average crush to calculate stiffnecoefficients and then using the actual crush profile in energy calculations. As expected, the observed errare the same as for Case 6 where a similar approachmade.

COMPARISON BETWEEN FLAT BARRIER APOLE BARRIER

Due to the limited availability of lateral pole impact cra

test data, it is unlikely that a specific test will exist every vehicle encountered in an actual collision analys

However, lateral crash tests with distributed barriers

more common and may be available for a specvehicle. It is of interest to determine how well a latepole impact can be reconstructed using data fromdistributed impact.

In order to evaluate this, an impact by a rigid movbarrier into a 1988 Ford Escort [Markusic, 19951analyzed and used to predict the absorbed energy the 1986 Ford Escort lateral pole impacts [ Marku19911. The crush profile for this distributed impactshown in Figure 7.

3-6Figure 7. Escort RMB Crush Profile

This analysis is performed using several differtechniques. For all techniques, the A value in CRASH methodology is assumed to be zero. The heof crush becomes a confounding variable in tt84 analysis. The moving rigid barrier uses a front pro


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hat approximates a car frontal shape. Therefore, thebarrier slightly over-rides the side sill. Subsequently,here is greater penetration into the door at the h-point

elevation than at sill elevation. A rigid pole impactedvehicle, however, experiences similar crush depth withvarying elevation due to the configuration. For the

ollowing analysis, the h-point height crush and the sillelevation crush are averaged in the rigid moving barrierest to create an effective crush profile to calculate the B

value. This B value is then applied to the three Escort

pole impacts and absorbed energy is predicted. Forexample, Figure 8 is a scale plot of the second Escortpole impact which has a similar absorbed energy as theRMB impact, Figure 7. Note, however, the differences incrush profiles between the distributed impact versus thenarrow object impact.

Figure 8. Escort Pole.

Case A: First, the B value is determined for the flat

barrier test using the average crush and not correctedor the 27 degree oblique angle experienced in that test.

The B value of 229 lb/in/in is obtained. This is thehistorical method to calculate B for staged collisionesting and has been described as Method 1 previously.

Case B: Method 2 is next employed to calculate B.

Case B involved determination of the B value from thecrash test using the crush profile and solving for the Bvalue, without averaging. This is the proposed B valuedetermination methodology presented earlier thatnvolves back calculating the CRASH Energy equation toarrive at B. Again , the 27 degree oblique nature of the

eference test is neglected. The B value of 194 lb/in/in isdetermined. The crush profile for the pole impacts inhe CRASH algorithm is used.

Case C: Method 3 is next employed to calculate B.

Because the reference flat barrier test is oblique by 27degrees, the B value calculated in Case B is correctedor the oblique nature of the crush by factoring out theenergy due to oblique damage. This is done by

accounting for the TCF as previously described inMethod 3. The B value of 154 lb/in/in is determined.

Case D: Case D involves calculating the B value for theactual deformation path by increasing the crush depth bycosine of 27 degrees and decreasing the width by thesame amount. This is referred to as Method 4. Then,using the corrected crush values, the crush is averagedand a resulting B value of 204 lb/in/in is calculated.

185

Case E: Case E involves solving for the B value fromthe flat barrier test and correcting the crush depth andwidth by the cosine of 27 degrees. Then instead ofaveraging this corrected crush as is done in Case D, theCRASH energy equation is once again solved for the Bvalue. This is described as Method 5. The B valueobtained is 173 lb/in/in.

The errors in this absorbed energy prediction are shown

in Table 6.

Table 6. Errors in Crush Energy Predictionusing Fiat Barrier to Predic/Case A / Case B 1CaseC

C sumMethod

C Avg. C sum I+tar+2Method Method Corrected

EscortPole -21.8% -33.7% -47.4%Test 1

EscortPole 88.6% 59.9% 27.0%Test 2EscortPole 357.5% 287.8% 207.9%Test 3

DISCUSSION OF CRASH RESULTS

Pole impacts.Case D Case E

Cosine CosineMethod MethodC avg C sum

-30.3% 40.9%

68.1% 42.5%

307.6% 245.6%

This presentation has concentrated on analyzing theability of the CRASH methodology, both in original formand modified form, to predict absorbed crush energy.

While some significant errors are seen for some of theassumptions analyzed, note that calculated speed is not

linearly proportional to the absorbed energy. Therefore,

for a single vehicle into pole impact, the error in AV willbe less than the error in absorbed energy. Since theCRASH analysis has demonstrated the possibility of100% errors in absorbed energy calculations, a 41%

error in calculated speed could be expected. Table 7gives the relationship between observed predictionerrors for absorbed energy and resulting errors in

predicted AV.

Table 7. Delta V Error VersusAbsorbed Energy Error.

Energy

Error20% 40% 60% 80% 100% 200%

AV

Error9.5% 18.3% 26.5% 34.2% 41.4% 73.2%

Examination of the CRASH results indicates that theprogram may serve as a useful predictor of crush energyas long as the structural properties of the vehicle areproperly analyzed. If using average crush to determinethe B stiffness value, the use of average crush in theenergy calculation will avoid errors. If using a crushprofile in the energy calculation, then the crush profile

should also be used to determine the B stiffness value.When using a distributed barrier impact to determinestructural parameters to apply to a pole impact,significant errors in predicted energy may result.Therefore, eliminating inconsistencies between the data


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used to calculate the stiffness parameters and theapplication of those parameters in a reconstruction will

avoid undesired simplifications from adversely affecting

the results.

SPIN DYNAMICS

When the principal impulse line of action passes through

the center of gravity, there is no moment developedaround the center of gravity and therefore the vehicle

cannot experience post impact spin. For this case, thevehicle stops at impact with possibly a minor amount ofrebound post impact motion due to the restitutionproperties of the vehicle. However, a perfectly centeredcollision, with no induced collision moment is rare.When the principal impulse does not pass through thecenter of gravity, a moment is developed. This isreferred to as a non-central or offset collision. When thisoccurs, by definition, the vehicle continues moving afterimpact and post impact rotation is developed. A workingknowledge of dynamics indicates that this post impactrotation is dependent on the impact severity, vehicleinertial properties, and location of the principal impulse

line of action.

Lateral, offset pole impacts often result in large momentarms which can introduce large post impact vehiclerotations. This rotational energy must be accounted for

in post impact energy analysis. Because a completeaccident reconstruction attempts to account for all of thevehicle energy when analyzing speed, it is necessary to

develop techniques that can predict spin rate at theinstant of separation. This spin rate can then be used to

calculate the post impact rotational energy which can beused in a conservation of energy analysis to arrive at areconstructed impact speed.

SPIN MODEL-l

Impulse momentum relationships may be used todevelop a first order approximation to the resulting postimpact spin rate for an offset lateral collision. While thesimplifying assumptions present in this analysis do notprecisely follow real world collision behavior, thistechnique is useful to obtain an initial approximation tospin.

Start by writing Newtons second law in time dependent

form.

P = Momentum = 5Fdt = mAV (13)Multiply both sides by the moment arm of the collisionimpulse. This can now be thought of as theconservation of angular momentum and is equal to

mk2ca:

k = radius of gyration about the c.g. and h = impulsemoment arm. The next steps are algebraicmanipulation.

mk2w = mhAVk2cx = hAV

,=$AV ( 1 5 )

As can be seen in Equation (15) the resulting posimpact rotation rate is a function of the collision impulsemoment arm (h) as well as the severity of the collision

(AV). Additionally, the radius of gyration is also presenin this analysis as the only required vehicle inertiaparameter. This simple relationship assumes that thevehicle rotation center is at the vehicle center of gravity

As observed by collision analysts, this is not always thecase. Generally, in a lateral collision, the vehicle rotatesabout the collision interface. Therefore, while this is afirst order approximation to the rotating vehicle analysis

it is simplified as the assumption of rotation center maynot be correct for most collisions.

SPIN MODEL-2

Because of the limitations inherent in the previous

analysis of a spinning vehicle, it is useful to extend thedevelopment to assume rotation about the collisioninterface. This is done through plane kinematics. To

begin this analysis, draw the free body diagram, Figure9. Next, the kinematic diagram, Figure 10, is drawn toshow the accelerations and motions. Note that tireforces are neglected in this treatment.

a+-- hV

Figure 9. Free Body Diagram

Pe h = h SFd t = mk*w (14)186


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Ep=;$2 +h22 >.(Ay,>2EPAvp = (y)mi- (29)

We now have an expression that relates the absorbedenergy to the local velocity change at the collisioninterface. Because this analysis is being performed foran impact into a non-yielding barrier, Point P at the

collision interface comes to a stop at the end of thecollision phase. Therefore, as previously identified, the

local AV at Point P is also the vehicles impact speedinto the barrier, assuming zero restitution and assumingnegligible pre-impact rotation. Therefore, Equation (29)

may be re-written as follows:

2EPImpact Velocity =--r>m (30)Because the AV at the center of gravity is also desired,

that relationship is easily determined. This isaccomplished by plugging Equation (29) into Equation

(28) to obtain:

AVg =(Y) 4 2EP-(r>m(31)

Equation 31 relates the center of gravity AV to theabsorbed energy due to vehicle crush. This value may

then be vectorially combined with the separation velocityand the impact speed calculated. Additionally, impactspeed may also be directly calculated from Equation 30;the same answer should result. It is necessary for the

reader to also understand that the above relationshipsdo not account for collision restitution. Since restitutionis generally quite low for higher speed lateral collisions,neglecting restitution is considered valid for thisdiscussion. However, at low collision severity, restitutionmay be significant and neglecting restitution in an

application to an individual collision analysis may causeundesired errors. While one may use the CRASH linearspring algorithm to calculate absorbed energy, othermethodologies may also be used. Therefore,

irrespective of the methodology to calculate theabsorbed energy, these relationships, based on plane

kinematics, may still be applied as long as the analystunderstands the underlying assumptions.

SMAC COMPARISON

In order to evaluate the previously developedtechniques, the following comparison is performed. TheSMAC computer simulation model [McHenry,19711 was 189

originally developed to model the dynamic response ofcolliding vehicles. The SMAC program has beenpreviously validated and is accepted as satisfactory foruse here to compare to the developed closed formsolutions presented in Equations (15) (18), (30) and(31). While this is not a validation exercise, thecomparison to an accepted simulation model doesprovide some meaningful insight into the expectedcorrelation one should expect when using these

equations corn bined with other reconstructiontechniques.

u.0dE*

I _IFigure 12. SMAC Graphical Output

The sample collision developed for analysis is a 2500 lb.vehicle, with a 100 inch wheelbase and a 60%/40% F/Rweight distribution. Radius of gyration (about the c.g.) isassumed to be 50 inches. The vehicle impacts a 12 inchwide barrier, approximating a pole impact, at 35.9 mph,at an offset of 60 inches from the center of gravity. A

SMAC run with these initial conditions results in a center

of gravity AV of 15.4 mph and a separation velocity of20.5 mph. Peak rotation rate is 336 deg/sec.Spin Model 1: Equation (15) is applied to this collision

scenario and a post impact rotation rate of 370 deg/sec

is calculated. This is a difference of 10.1% and is thelargest difference seen in any of the predictedparameters when comparing to the SMAC referencesimulation. Given the simplifications assumed inEquation (15) 10% difference would be consideredacceptable agreement. When the instant center ofrotation is examined in the SMAC simulation, it is foundthat the vehicle is rotating about the collision interface.Even with the different assumed rotation center of

Equation (15) the agreement is satisfactory for somereconstruction uses.

Spin Model 2: Equation 18 is next applied. This results

in a predicted rotation rate of 353 deg/sec. This is adifference of 5.1% from the SMAC reference.CRASH Based Model: The CRASH based model is

next applied. Using the same absorbed energy as givenby SMAC, Equation 30 predicts the impact velocity as36.3 mph, a difference of 1.1%. Equation 31 results in a

calculated center of gravity AV of 14.5 mph, a differenceof 5.8% from the SMAC simulation model reference.

Subtracting the AV from the impact velocity results in a


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predicted separation velocity of 21.8 mph, only a 5.2%difference than predicted by SMAC.

Using the SMAC computer simulation model as areference, the developed closed form equations

demonstrate satisfactory correlation in this example for

many accident reconstruction purposes. The largest

difference in any of the predicted parameters is 10%.The results of the comparison to the SMAC computer

simulation reference are summarized in Table 8. As theclosed form solutions are based on the same physics

upon which the SMAC simulation is based, correlationbetween the techniques would be expected.

Table 8. Comparison of SMAC Output

to Closed Form Equations

RECONSTRUCTION APPLICATIONS

There has been signif icant discussion in the

reconstruction community concerning impact speed

calculations when post impact velocity is known for asingle vehicle collision into a pole. Historically, the

separation velocity is calculated and the AV is vectoriallyadded to arrive at impact velocity. Before continuing, a

review ofAV is required. The AV is the vector change invelocity measured at a specific point on the vehicle.

Generally, for accident reconstruction speed calculationpurposes, the AV at the center of gravity is required.

This center of gravity AV is then added directly to theseparation velocity to arrive at the impact velocity.

When examining the literature, it is found that theprocedure as defined in the CRASH 3 manual, states,Knowing the separation velocities, the impact speed

can be estimated from momentum considerations, or by

simple vector addition of AV + [separation velocity].[CRASH 3, 19821. Unfortunately, there has also beenconfusion by some inexperienced reconstructionists whohave continued to calculate impact velocity by adding

the sum of squares of AV and separation velocity. This

is incorrect. While there is absolutely no physics basisfor this adding squares method, there is a historicalbasis for this error. When examining the kinematicsequations for a different, standard accidentreconstruction problem, some insight is gained into thesource of the error for the pole impact reconstruction.

Consider the following accident reconstruction scenario.

A vehicle is travelling at some unknown initial velocity,then slams on the brakes and ultimately strikes a wall;

at the end of impact with the wall, the vehicle is stopFigure 13 shows the velocity time graph for

described scenario.

IFigure 13. Velocity Time Graph.

This problem can be examined quite easily with pa

kinematics. The goal is to calculate the initial ve

velocity prior to brake application while knowing theand the braking deceleration level. The analysis follows: dsv=-

dt

dva=-dt

:. vdv = adsVmpnct

I vdv =askid ds5v i n i t i a l si

z& act =vJcitial + 2a,, (s - s,>v in i t i * l = VZnpac* - 2asJ (32)

In Equation (32) the acceleration can be input negative value (braking). Additionally, if one ass

the coefficient of restitution to be zero, then the

velocity (impact into the wall), is also the AV. Whileprecisely correct, this assumption is widely usedhigher velocity collisions, this is often well withinuncertainty present in many reconstruction ana

This is because coefficient of restitution values tedecrease with increasing seventy [Kerkhoff, 1

Assigning these assumptions to Equation (32), resufollows:

a = - a

e = 0.0

190

1-w AV = vimpact


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(33)As can be seen in Equation (33) when assuming a zerorestitution collision, and when there is absolutely no post

impact velocity, then the AV and the pre-impact skiddingphase may be added as a sum of squares for the above

presented scenario. While this numerical value ofAV isinput into Equation (33), it is important to note that thephysics dictates that the actual velocity at the end of theskidding is what is actually being input into the aboveequation. It is only because of the zero restitution

assumption, and zero post impact velocity, that the AValso numerically equals the wall impact velocity and canbe substituted.

The pole impact reconstruction problem that arises fromthe above analysis, is the assumption that, because, for

this specific scenario, the AV is added under a square

root, the AV is an energy parameter. By erroneously

assuming the AV to be an energy parameter, someanalysts have tried to assign it as an energy parameterin other accident scenarios. As is previously discussed,

the AV is a vector and must be treated as such in any

accident reconstruction analysis. Therefore, the AV is

directly added to post impact runout vectorially and notas a sum of squares.

To illustrate potential problems with assuming AV to bean energy parameter, consider now the situation of avehicle impacting a tree in an offset impact andexperiencing post impact runout. Some analysts haveerroneously attempted to apply the previously developedrelationship to this new scenario. This new scenario is

represented by the velocity time curve in Figure 14.

Fig& 14. Velocity Time Graph - Vector Addition ofDelta V and Separation Velocity.

For the scenario demonstrated in Figure 14, the accident

reconstruction use of AV would involve first using thepost impact dynamics to calculate the separationvelocity, then vectorially adding the separation velocity to

the AV. For this situation,,one does not add the AV andrunout velocity as an addrtron of squares.191

Vimj7act =* +Vsep*ra*ion (35)Two primary fallacies exist when the impact velocity i

accepted to be the sum of squares ofAV and separatio

velocity, Equation (34). First, it is assumed that the AVcan be directly converted to absorbed energy withou

having any other knowledge of the impact geometryThis is false and is demonstrated in Equation (31) wher

it is found that the AV is not only a function of thabsorbed energy but also of the impulse moment arm

Therefore, to calculate absorbed energy from AV, thimpulse moment arm must be accounted for. Secondlypost impact rotational energy is assumed to be zero

the AV is combined with the separation velocity as a sumof squares. This is addressed in the followinconservation of energy section .

CONSERVATION OF ENERGY

The addition of the squares of post impact runout anAV has also been justified by some reconstructionists athe method to employ when applying the conservation oenergy to a lateral pole impact collision. The attempt i

made to think of the AV as representative of absorbeenergy. This assumption is based on the fact that thchange in kinetic energy of the vehicle can b

determined from the AV and post impact runout velocityThe fallacy with this approach is evident when examininthe plane kinematics relationships previously developedIf there is post impact runout, then, by definition, thimpact is not a centered collision. Therefore, a momenarm has been developed by the impulse around thcenter of gravity.

35000 1

i50 100 150 200 250 300 350 400 450

Peak Rotation (deglsec)Figure 15. Rotational Energy

Mechanics has been shown to dictate that if there is a

AV and a moment arm, then by definition, there must bpost impact rotation developed. To ignore this posimpact rotation, is to ignore a possibly significancontribution of energy and therefore, any calculatespeed will be incorrect. Additionally, determining th

absorbed energy from the AV requires a careful analysof the impact geometry.


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A conservation of energy analysis is performed byplacing a control volume around the impact phase andsumming all of the energy out to arrive at the energy

coming in to the control volume. Energy to be addedgenerally includes vehicle deformation energy, barrier

deformation energy (if non-rigid barrier or breakawaypole), and post impact vehicle linear and rotationalmotions. The rotational components may contribute asignificant amount to the overall calculation of impactvelocity. Consider a 2500 lb vehicle (a small vehicle)having a 100 inch wheelbase and a 50/50 weightdistribution. Considering the radius of gyration to be

approximately 50 inches, Figure 15, shows the kineticenergy contributed by rotation at varying angular spinrates. Figure 15 assumes the rotation to be about themass center of the vehicle. Since vehicles often have aninstant center of rotation away from the mass center,

these values are conservative (low) for many accidents.As can be seen, at 150 deg/sec, this lightweight vehiclepossesses 5000 ft-lb of energy. That potentionallysignificant energy indicates that whenever there is postimpact rotation, the collision analyst should calculate therotational component in order to determine the rotational

energy contribution to the velocity calculation.Neglecting the rotational energy contribution may often

contribute to significant errors in a reconstruction.

CONCLUSIONS

.

.

.

.

.

.

.

.

.

.

Techniques are presented to predict post impactrotational velocity. These prediction methodologies

are shown to match the reference computersimulation (SMAC) within 10%.

Further work is necessary to investigate thestructural response of other vehicle types to high

speed lateral pole impacts.

Further work is necessary to investigate thestructural response due to hard spots and pole

diameter variations.

The small, unibody vehi cl es o f differentmanufacturers studied behave in a similar fashionwhen subjected to high speed lateral pole impacts.

Default structural parameters as used in CRASH 3are not appropriate for use to reconstruct individuallateral narrow impacts.

Care should be taken when applying conservation ofenergy reconstruction techniques in order tocarefully account for all energy, including that due to

rotation.

AV is a vector and should be used in reconstruction

calculations appropriately.AV is not an energy

parameter.

Care should be taken to correctly account for thedifferences between local (crush zone) and center of

gravity AV.

When applying the CRASH algori thm, thecalculation of absorbed energy should be performedin the same manner as the structural stiffnesscalculation.

When calculating the B structural stiffness parameterwith average crush, and then applying the actual

crush profile in the CRASH energy equation, oprediction of energy occurs.

When calculating the B structural stiffness paramwith the crush profile, and then applying the avercrush in the CRASH energy equation, unprediction of energy occurs.

The tangential correct ion factor shouldconsidered in the structural stiffness calculation.

Failure to consider the TCF in the structural stiffncalculations will result in large errors in calculabsorbed energy for oblique collisions.

CONTACT

Comments or questions are welcome and maydirected to the authors:

KEVA EngineeringTransportation Accident Analysis and Reconstructio

5636 La Cumbre RoadSomis, California 93066www.kevaena.com

REFERENCES

Au tomat ed Sc ie nce s Gr ou p, NHTSA Da ta TReference Guide, Volume I: Vehicle Crash Tests, Oof Vehicle Research, NHTSA, US DOT, 1985.

Bell, L., Car To Pole Side Impact Test of a 45 DeCrabbed Moving 1981 Volkswagen Rabbit Into a FRigid Pole at 20.1 MPH, DOT HS 840706, 1984.

Bell, L., Car To Pole Side Impact Test of a 45 De

Crabbed Moving 1981 Volkswagen Rabbit Into a FRigid Pole at 24.9 MPH, DOT HS 840803, 1984.

Bell, L., Side Impact Aggressiveness Attributes: Ca

Pole Side Impact Test of a 45 Degree Crabbed Mov1981 Volkswagen Rabbit Into a Fixed Rigid Pole19.95 MPH, DOT HS 806853, 1984.

Bell, L., Side impact Aggressiveness Attributes: CaPole Side Impact Test of a 45 Degree Crabbed Mo1977 Volkswagen Rabbit Into a Fixed Rigid Pole at MPH, DOT HS 806856, 1984.

Brown, C.M., Ford Taurus Broadside Collision WiNarrow Fixed Object FOIL Test Number: 958

Contract NumberDTFHGI-94-C-00008, 1996.Brown, C.M., Ford Taurus Broadside Collision WiNarrow Fixed Object FOIL Test Number: 95sContract NumberDTFHGI -94-C-00008, 1996.CRASH 3 Users Guide and Technical ManuPublication No. DOT-HS-805732, National HighTraffic Safety Administration, Dept. of TransportaWashington, DC, February 1981; Revised April 1982

EDCRASH Version 4.6 Users Manual, Enginee, 92 Dynamics Corporation 1993.


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Hargens, R.L., Day, T.D., Vehicle Crush StiffnessCoefficients for Model Years 1970-1984 with DamageProfile Supplement. EDC Library Reference Number

1042.

Hinch, J.A., Stout, D., Thirty MPH Broadside Impact of aMini-Sized Vehicle and A Breakaway Luminaire Support,PB89214571, 1987.

Hinch, J.A., Stout, D., Thirty MPH Broadside Impact of aMini-Sized Vehicle and A Breakaway Luminaire Support,

PB89214589, 1987.


Pole Barrier impact Into a 1987 Volkswagen Golf 3-DHatchback In Support of CRASH III Damage AlgoritReformulation, DOT HS 807 911, 1991.

Markusic, C.A., Final Report of a Non-DeformaCrabbed lmpactor into a 1988 Ford Escort 3-DHatchback in Support of CRASH III Damage AlgoritReformulation, PB96179213, 1995.McHenry, R.R., Development of a Computer Program

Aid the investigation of Highway Accidents, CalsReport No. VJ-2979-V-1, December 1971, HS 800 82

Meriam, J.L., Kraige, L.G., Engineering MechanVolume 2 - Dynamics, John Wiley and Sons., NYork, NY, 1986.

SLAM for Windows, TRANTECH, 1994.


APPENDIX


PB89214613, 1987.

Hinch, J.A., Stout, D., Thirty MPH Broadside impact of aMini-Sized Vehicle and A Breakaway Luminaire Support,FHWA-RD-89-094, 1987.

Hinch, J.A., Manhard, G., Stout, D., Owings, R..,Laboratory Procedures to Determine the BreakawayBehavior of Luminaire Supports in Mini-Sized Vehicle

Collisions, Volume II. Technical Report, PB87204376,1987.

Hinch, J.A., Manhard, G., Stout, D., Owings, R..,Laboratory Procedures to Determine the Breakaway

Behavior of Luminaire Supports in Mini-Sized VehicleCollisions, Volume III. FOIL Operation and Safety Plan,PB87204384,1987.Hinch, J.A., Stout, D., Thirty MPH Broadside Impact of aMini-Sized Vehicle and A Breakaway Luminaire Support,PB89214639, 1988.


PB89214647, 1988.

Kerkhoff, J.F., Husher, S.E., Varat, M.S., Busenga, A.M.,

Hamilton, K., An Investigation into Vehicle FrontalImpact Stiffness, BEV and Repeated Testing forReconstruction, SAE Paper 930899, Warrendale, PA,1993.

Markusic, C.A., Final Report of 270 Degree Moving PoleBarrier Impact Into a 1986 Ford Escort 3-DoorHatchback in Support of CRASH III Damage AlgorithmReformulation, DOT HS 807 776, 1991.

The following are crush profiles or vehicle impact photas available, to graphically demonstrate the associa

deformation patterns.

10 L-,--dIOI__- ,.,- 2-d _OD,.~~4~.1.~(.~~11.. .L.~~~~oo~..

Figure Al _ Ford Escort crush profileat bumper height (DOT HS 807 776,3-4).

Figure A2. Ford Escort crush profileat bumper height (DOT HS 807 776,4-4).

Markusic, C.A., Final Report of a 315 Degree Moving193


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