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SAE TECHNICALPAPER SERIES 1999-01-0099

Crush Energy and Structural Characterization

Kevin J. Welsh and Donald E. StrubleStruble-Welsh Engineering, Inc

Reprinted From: Accident Reconstruction: Technology and Animation IX(SP-1407)

International Congress and ExpositionDetroit, Michigan

March 1-4, 1999


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1999-01-0099

Crush Energy and Structural Characterization

Kevin J. Welsh and Donald E. StrubleStruble-Welsh Engineering, Inc

Copyright 1999 Society of Automotive Engineers, Inc.

ABSTRACT

A key aspect of accident reconstruction is the calculationof how much kinetic energy is dissipated as crush. By farthe most widely used methods are derivatives of Camp-bell's work, in which a linear relationship between resid-ual crush and closing speed is shown to imply anunderlying linearity between force and crush. Consant-

stiffness model is the term used for such a representa-tion of structural behavior.

Difficulties arise, however, when significant non-uniformi-ties are present in the crush pattern (as in narrow-objectand/or side impacts, for example). The term "residualcrush" becomes more ambiguous. Do we mean maxi-mum crush, area-weighted average crush, or some othermeasure of residual deformation? And is it sufficient torepresent the non-uniform crush pattern by a singleparameter?

Such considerations led to a re-development of the fun-damental structural models, with an eye to determining

whether the classical constant-stiffness model is themost appropriate. For narrow-object side impacts, a con-stant-force model was developed. For wide-objectimpacts, constant-stiffness and constant-force modelswere developed, along with a three-parameter model.

These models were applied to published side impact andnarrow-object data. The constant-force model emergedas the preferred formulation for narrow-object sideimpacts, and was at least on a par with the constant-stiff-ness model for wide-object side impacts. For frontalimpacts, wide-object test data could not predict narrow-object behavior with acceptable results.

INTRODUCTION

The calculation of crush energy for reasonably uniformcrush shapes, as detailed by Campbell [Campbell 1972],[Campbell 1974] is well understood. For non-uniformcrush, as seen in narrow-object impacts and most sideimpacts, the calculation of crush energy is not as straight-forward. One example of this problem is demonstrated inthe work by Willke and Monk [Willke 1987] in which side

impact tests were run in order to derive stiffness valuesWhen the derived stiffness values were applied to thetest vehicle crush profiles, the test speeds were notreproduced. For stiffness values derived from only twotests, this should be possible.

A different problem exists in the basic behavior of sidestructures themselves. Static crush tests of whole-caside structures conducted at Minicars in the mid 70's, as

well as analysis (conducted by the authors) of data fromnarrow-object side impact tests, suggest that a constantforce model is worthy of consideration for side structures

To attack these problems, it was decided to take a freshlook at the analysis of side impact crashes, and to derivea constant-force model and a three-parameter mode(using force saturation) for side structures. These newtools were then applied to available crash test data toexamine their relative accuracy in predicting crash tescrush energy.

NARROW-OBJECT SIDE IMPACTS

Side impacts with narrow fixed objects do not occur oftenrelative to other types of crashes, but when they do hap-pen they pose special risks to vehicle occupants, particu-larly if the occupants happen to be seated at the locationof the pole impact. Dramatic amounts of crush and intru-sion may be created at speeds that, in a different crashmode, may be deemed by lay persons to be non-threat-ening. Even if structural deformation were somehow tobe avoided, an occupant's head could still be exposed toa direct contact, through the window opening, with anunyielding object.

Such accidents also pose special problems to the accident reconstructionist. One would like to turn to narrowobject side impact tests for engineering results uponwhich to build a reconstruction. However, there are pre-cious few such tests to be found in the literature. Thetests that do exist utilize inconsistent crush measuremenprotocols that have little or no documentation, and someof them present difficulties in calculating an energy bal-ance, due to lack of data regarding post-impact motionsof the vehicle.


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One way of dealing with this situation is to perform a nar-row-object crash test in which the test vehicle structurewill be exercised in a fashion similar to the way it was inthe accident vehicle. Often, one does not have this lux-ury. Even if one can perform a crash test, it is necessaryto make some pre-test calculations so that usable datacan be obtained.

It is thus useful to examine the available test data, how-ever sparse, and derive some insights that may be useful

to the reconstructionist.

SOME STRUCTURAL INSIGHTS FROM STATICCRUSH TESTS We start by examining static crushtests of vehicle side structures, in which the force gener-ated by the structure is plotted against its crush. Onemight think of looking at certification test data from theformer version of FMVSS 214. This standard entailed astatic crush test in which a rigid cylindrical indenter waspushed into a door. However, such data are generally notin the public domain, and in any case the test is usuallyterminated as soon as the required force levels are gen-erated. Consequently, the crush may be much less than

what one might encounter in injury-producing narrowobject impacts. We should also point out that theindenter, unlike most trees and poles, does not extenddown to ground level, or even to a level at which therocker panel would be engaged [FMVSS 214]. So wemust look elsewhere for data.

Early in the Minicars RSV program, some preliminarycrush tests were performed on Ford Pintos [DiNapoli1977]. Two different rigid indenters were used: either a14-inch pole, or a concrete-filled 1974 Pinto front end.Four different tests were conducted:

1. Pinto corner into 1971 Pinto side at 300 degrees2. Pinto front into 1974 Pinto side at 90 degrees

3. Pinto corner into 1974 Pinto side at 300 degrees

4. Pole into 1974 Pinto side at 90 degrees.

The corner tests were such that the corner just missedthe A-pillar. In the 90-degree test with the rigidized Pintofront, the A-pillar was engaged. The pole indenter waslocated at the driver H-point.

The difference between wide and narrow indenters iseasily seen in Figure 1. In Test 2, not only were the forcesdistributed over a wider area, but direct engagement ofthe A- and B-pillars was obtained. We see that a corner

engagement (Test 3) initially produces a softer responsethan a pole (Test 4), but after 10 inches or so theresponses are similar. Since the 1971 Pinto did not havea door beam, whereas the 1974 vehicle did, we see fromTests 1 and 3 that the effect of the door beam is to stiffenthe door early, just as one would expect. Beyond 14 or 15inches, however, the responses are again similar.

Aside from these observations, the significant fact is thatin each test, the structure displayed constant-forcebehavior to a surprising extent. One could say that themost noteworthy difference between the wide- and nar-row-object tests was in the plateau force level. In narrow-object tests, the plateau level was remarkably indepen-dent of the shape of the indenter, and whether a doorbeam was present.

Figure 1. Preliminary Lateral Crush Test Results

Further tests were conducted using a rigidized RSV noseas an indenter. To evaluate the effect of struck car sizeand body style (two or four doors), four 1976-model production vehicles were selected: a two door-Chevettetwo- and four-door Datsun B-210s, and a two-dooChevelle Malibu Classic. For each vehicle, two tests wereperformed: one at 90 degrees with four inches of overlapbetween the indenter bumper and the A-pillar, and one a300 degrees with the indenter corner just missing the A-pillar.

Results of the corner tests are shown in Figure 2. At firstglance, it appears that we do not see constant-force plateaus, except for the two-door Datsun B-210. However, itis worth noting that the tests were stopped at about 13inches of crush. In that range the constant-force behavioin the narrow-object tests of Figure 1 would not show upeither.

At low values of crush, the force levels of the ChevelleMalibu are seen to be very low compared to those of thesmaller (unibody) vehicles. It is not difficult to imagine thelength of the Malibu door being a factor here. Howeverthe force levels start to climb rapidly beyond five inchesor so, most likely due to the involvement of the Malibu'sframe at that point.

Figure 3 shows the results with the indenter at 90degrees and engaging the A-pillar. Once again we seeessentially constant-force plateaus, with a substantial dif-ference between the large and small cars. Virtually no difference is seen between the two-door and the four-doorvehicles, however.


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Figure 2. Static Crush Test Results300 Degree Impact ModeNo A-Post Engagement

Figure 3. Static Crush Test Results90 Degree Impact Mode Engaging A-Post

To study the effect of missing the A-pillar in a 90-degreewide-object impact, an additional 90-degree Chevettetest was run, without such engagement. Figure 4 showsa surprising similarity in the results, suggesting that theA-pillar provides lateral resistance to crush, even if it isnot engaged directly. This is probably due to a strongload path through the door hinges, and to the fact that theintruding door tends to engage the cowl structure. Whenthe A-pillar/hinge complex is just missed by the impactingbumper, it is loaded more in shear than in torsion, and itseems to carry such loads well.

Figure 4. Effect of A-Post Engagement90 Degree Impact Mode into Chevette

MORE INSIGHTS FROM FHWA POLE RESEARCH Four tests were conducted by the Federal HighwayAdministration (Fhwa), in which vehicles were launcheddirectly sideways into a rigid, instrumented pole [Har-grave 1989]. These tests involved three small cars(Honda Civic - SI#1, Volkswagen Rabbit - SI#2, DodgeColt - SI#3) and a large car (Dodge St. Regis - SI#8)Department of Transportation (DOT) numbers for thesetests were 907 through 909, and 911. Figure 5, takenfrom [Hargrave 1989], shows the vehicle force-deflectioncurves. Again, a ramping is seen until 10 to 12 inches ofcrush, followed by a force plateau. It is noteworthy howsimilar the plateaus are, including the Dodge St. Regiswhich weighed more than 2.5 times as much as the smalcars. (The St. Regis crushed less, not because it wasstiffer, but because it was crashed at 10 mph instead o25 mph for the small cars.)

The FHwA conducted other tests into breakaway polesIn all but one of these tests, there are sufficient dataregarding post-impact motions of the car and the pole toperform an energy balance. However, that remaining testDOT 857, does provide insights regarding head contacthazards. Head contact on the pole produced a HeadInjury Criterion (HIC) of over 2800, even though the polewas very light weight and on a breakaway base, and thevehicle velocity change (V) was "only" 13.3 mph. (Highspeed film shows the reason: the dummy's head con-tacted the pole directly through the window openingbefore the pole achieved detectable motion. Thus headcontact occurred at or above the closing speed of 29.2mph, not at the V. The pole's reduced mass and slipbase mount did not come into play as far as occupantinjury was concerned.)


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Figure 5. Side Impact Force Deflection Characteristicsfor Four Vehicles

INSIGHTS FROM NHTSA RIGID POLE TESTS TheNational Highway Traffic Safety Administration (NHTSA)has conducted rigid pole side impact tests of both base-line and structurally modified vehicles. In DOT 755, a

1981 Volkswagen Rabbit was towed at a yaw angle of 45degrees into a fixed, rigid pole, the diameter of which wasnot reported. The 20 mph impact occurred on the driver'sside (315 degrees), with initial contact at 34.5 inchesahead of wheelbase center. Thus the pole was lined upto partially engage the A-pillar [DOT 755].

In this test, the driver dummy head passed through thewindow opening and contacted the pole, producing a HICof 977. Force-deflection curves are not presented, but theforce-time curve shown in Figure 6 again indicates aforce plateau.

In DOT 749, conducted a week later, another 1981 Volk-swagen Rabbit was crashed under similar conditions,except that the initial contact point was adjusted to 26.5inches forward of wheelbase center. It appears that suchan alignment placed the edge of the pole on a line withthe door cut line, just missing the A-pillar [DOT 749].

Again, the driver dummy head passed through the win-dow opening and contacted the pole. This time the HICwas over 2900, and the dummy's right leg was severedabove the knee. Figure 7 indicates a force plateau.

After another month or so, NHTSA conducted another315 degree pole impact; the impact point was moved still

farther aft, to nine inches forward of wheelbase center.The test vehicle was a modified Volkswagen Rabbit withalterations to both structure and interior padding. The testspeed was increased to 25 mph [DOT 768].

This time the dummy's head just grazed the pole, and theHIC was 152. The peak force was raised to about 46,000pounds, as seen in Figure 8, despite the pole being fur-ther away from the A-pillar and cowl structures. However,the big factor in reducing the HIC was keeping the headtrajectory away from the pole.

Figure 6. 45 Degree Crabbed Volkswagen Rabbit intoFixed PoleTotal of Four Pole Channels

Figure 7. 45 Degree Crabbed Volkswagen Rabbit intoFixed PoleTotal of Four Pole Forces

Figure 8. 45 Degree Crabbed Volkswagen Rabbit intoFixed PoleTotal of Four Pole Forces


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Table 1. Pole Tests

BUILDING A STRUCTURAL MODEL FOR POLEIMPACTS Available pole impact test data were assem-bled in order to determine what sort of structural modelwould best relate crash severity to post-crash measure-ments. These tests are listed in Table 1. Despite obviousvariations in car size, pole diameter, mass, and rigidity,and vehicle angle and impact point, nine of the ten testswere analyzed as a group. Only Test 3, DOT 857, wasexcluded due to lack of information on the struck polemotion.

Metrics considered for vehicle damage (dependent vari-able) included (weighted) average crush, maximum

crush, and area under the crush profile. Metrics of crashseverity (independent variable) included vehicle weightand initial speed, momentum, and kinetic energy. Alsoconsidered was system loss of kinetic energy (i.e., crushenergy).

Of all the relationships considered, easily the best fit tothe data was a model in which crush energy and maxi-mum crush were linearly related.

The implication of this finding is that the underlying struc-tural behavior reflects a constant-force crush characteris-tic. To see that this is so, consider the idealized force-deflection characteristic of Figure 9. Here the structure

resists crush by generating a force per unit width thatrises rapidly (in a linear fashion) to some peak value Fs.Cs is the deflection (saturation crush) at which thatoccurs. As crush increases beyond Cs the force per unitwidth remains constant at Fs.

(Note that the basic formulation is similar to a constant-stiffness model with force saturation, except that in thiscase the crush characteristic goes through the origin. Inaddition, a constant-force model emphasizes the plateauforce per unit width Fs by subjecting it, rather than the ini-tial slope, to statistical analysis procedures.)

The crush energy CE associated with a crush of C is sim-ply the area under the crush characteristic of Figure 9We have

(1

The factor of 12 reflects crush C and width L being mea-sured in inches, and crush energy in foot-pounds. If wewere to plot 12CE/L as the ordinate, as a function of theabscissa C, we would have a linear relationship betweencrush energy CE and the crush C, as noted in the studyof pole crash test data. Thus the pole test data do indeed

suggest a constant force model. Moreover, if we were toplot the data with ordinate and abscissa as describedthe slope of such a line fitted to the data would be Fs. Theintercept of the line is the term -FsCs, from which thesaturation crush value Cs could be determined.

Figure 9. Constant Force Model


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IMPLICATIONS OF THE POLE TEST DATA Figure 10is a plot of the nine pole impacts. The regression line isbased on Tests 1, 2, 5, 7, 8, and 9 (the circles), but notTests 4, 6, and 10 (the triangles). Test 4 involved a struc-turally stiffened vehicle, as mentioned previously. It is notsurprising that it lies above the line (i.e., requires moreenergy to produce a certain amount of crush). Test 10involved the only large car in the group, a 4490-poundDodge St. Regis. Its softer behavior is not surprising.Only one other data point, Test 6, is significantly off theregression line. The reasons are unknown.

The six tests on the regression line involve both rigid andbreakaway poles. They involve three different vehicledesigns: Honda Civics, a Dodge Colt, and VolkswagenRabbits. The Rabbit model years included 1976, 1979,and 1981. Angles of impact ranged from 270 to 315degrees, and impact points varied from the A-pillar to dif-ferent locations along the door. In view of thesedifferences, it is surprising how well the data are fitted bya single model, and a constant-force model at that, untilone considers the underlying structural behavior dis-

cussed previously.

Figure 10.

It is noteworthy that the maximum crush produces a bet-ter fit than does average crush. From a theoretical pointof view, one would expect the average crush to work bet-ter. However, the average crush is a function of the wholecrush profile -- most notably the crush width. It is there-fore a more complex measurement to make, and is moresubject to uncertainties regarding how to define the crushwidth and how to include the effects of bowing. (Weshould note that the nine tests were conducted by two dif-ferent Government agencies, each of which used at leasttwo different measurement protocols.) It is probably thisreduced dependence on measurement techniques whichallows the maximum crush to produce a better statisticalfit to the test data.

It would appear that small car structures behave similarlywhen struck in the side by poles, be they rigid or break-away. Therefore, disparate test data can be combined toproduce a good model of the structural behavior. How-

ever, larger cars and those which have been structurallystiffened should be treated separately.

ANALYSIS OF COLLINEAR VEHICLE-TO-VEHICLE IMPACTS

Another valuable source of data comes from running arigid, but movable barrier into the side of a vehicle. Thereare numerous problems associated with the use of mov-

ing barrier impacts for derivation of stiffness values, themost significant being post-impact run-out. In an attemptto deal with this problem, an analysis was undertaken ofuniaxial (collinear) vehicle-to-vehicle impacts in whichrestitution is included. This analysis should apply to bothfixed and moving rigid barrier impacts; to front and rearas well as side impacts as long as yaw rates post-impactare not significant. The analysis resulted in the followingrelationship between energy dissipated (in crush) andclosing velocity:

(2

where CE denotes energy dissipated (ft-lb), W1 and W2are vehicle weights (lb), g is the gravitational constant (fts2), Vcl is closing velocity (ft/s), and is the restitutioncoefficient, for which we used 0.10 in our analysis. Notethat, in general, the energy term on the left side of thisequation pertains to the total energy dissipated by bothvehicles in crush. In the special case of a rigid movingbarrier impact, it is assumed that all of the crush energyis absorbed by the struck vehicle.

This value for energy absorbed can then be equated tothe integration of the crush shape as proposed by Camp-

bell [Campbell 1972].

STRUCTURAL MODEL AND CRUSH MAGNITUDEMETRIC To date, the preferred structural model fovehicle structures has been a constant stiffness modeloriginally proposed by Campbell [Campbell 1972]. Inorder to determine whether a constant force structuramodel is more appropriate for side structures, both a con-stant force and a constant stiffness analysis were devel-oped. The question also arose of whether usingmaximum crush or weighted average crush as the crushmagnitude metric would produce the better results. It wastherefore decided to proceed with four separate develop-

ments: two structural models, each using one of the twocrush magnitude metrics.

CONSTANT STIFFNESS MODEL The most generadevelopment turns out to be that for a constant stiffnessstructural model using the maximum crush to characterize the deformation, which was previously discussed bySmith, et. al. [Smith 1987]. In that development, oneobtains the familiar equation

(3


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where c = c(x) = crush, and x represents crush width. Asusual, A is in pounds per inch, B is in pounds per squareinch, and CE is in foot-pounds. Introducing c(x) = E f(x)(where E is max crush and f(x) is the function which rep-resents the crush shape), and performing the algebra todetermine G, the equation becomes

(4)

where

(5)

and

(6)

For a piecewise-linear crush profile, where the shapefunction is defined as

(7)

the form factor is determined to be

(8)

while the form factor is

(9)Equating the crush energies in Equations (2) and (4)results in the relationship

(10)

where Weff = WvWb/(Wv+Wb), Wv is test vehicle weight inpounds, Wb is barrier weight in pounds, L is the crushwidth in inches, and Vcl is closing velocity in mph. Thisequation then allows the plot of [(/L)/(/L)] E vs. the lefthand side of equation (10) to produce a straight line witha slope of B and an intercept of A/B.

Following this same development, but using weightedaverage crush as the magnitude metric, rather than maxcrush, yields the equation

(11)

Beta in this equation has the same form as the in Equation (9), but with E replaced by , the average crushAgain equating this result with Equation (2) then resultsin the equation

(12

This equation can be used to plot (/L) vs the left sideof equation (12) to obtain a straight line with a slope of Band intercept of A/B.

Note that the form factor does not show up in this equa-tion. This is because by definition, deviations from theaverage crush balance each other and thus integrate tozero when the crush profile is integrated over the crushwidth. By contrast, deviations from the maximum crushdo not integrate to zero, and the form factor remains inthe equation. Also, the stiffness B is multiplied by thesquare of c; the variations do not average out in the inte-gration of c2 but are carried along in the factor.

Further, it can be shown that these two developmentsare, in fact, equivalent. Therefore, only the weighted average crush development will be included in the analysis otest data.

CONSTANT FORCE MODEL Now considering a constant force model using maximum crush as the crushmagnitude metric, we start with the basic assumption thawe have a constant force per unit width

(13

The crush energy density per unit width is then

(14

Introducing c = E f(x), where E is max crush, and integrat-ing gives the expression for crush energy

(15

where CE is in foot pounds, A is in pounds per inch, G isin pounds, and is as defined previously. Thus, a plot o

12CE/L vs (/L)E

will be a straight line with a slope of Aand an intercept of G. Note that with the constant stiff-ness model, the form factor was associated with thestiffness B. Since this formulation does not involve stiff-ness, neither B nor shows up.

This same development using weighted average crushgives the result

(16)


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where is the average crush. So for the constant forcemodel using weighted average crush, a plot of 12CE/L vs

will give a straight line with a slope of A and an inter-cept of G.

Again, the developments for max crush and weightedaverage crush turn out to be equivalent. This can bequickly verified by multiplying the definition for (Eq. 8)by E , which results in

(17)

The right side of this equation is the area under the crushcurve divided by the crush width, which is the definition ofweighted average crush ( ). So Equation (15) reduces toEquation (16) (as do the crash-plot abscissa definitions)and the two developments are equivalent.

Comparison of Equations (1) and (17) allows the follow-ing physical interpretation: A is the constant force leveland that the saturation crush Cs can be computed once Aand G are known.

RELATING WIDE TO NARROW-OBJECT IMPACTS Inthe previous work by Smith [Smith 1987], the constantstiffness/max crush analysis was used to predict frontalnarrow object crush energy in tests of a 1984 HondaAccord, 1983 Renault Fuego, 1983 Dodge Omni, and aseries of repeated impact tests of a 1975 Olds Delta 88.For comparison, we ran the constant stiffness/weightedaverage crush analysis for the Honda and Omni tests toexamine the effect of the difference in crush magnitudemetric. As expected, the results for both developmentswere almost identical. For the Omni, Smith's predictedcrush energies (with max crush metric) for the two tests

were 32% and 53% of actual, while our developmentusing weighted average crush predicted 33% and 56% ofactual, respectively. For the Honda, Smith's analysis pre-dicted crush energies at 50% and 65% of actual, whileour average crush development predicted 52% and 66%of actual, respectively. As has been noted, the develop-ments for both magnitude metrics are equivalent, and soit is not surprising that the results are so similar. One pos-sible explanation for why they are not identical is that andare not included in the definition of G in the Smith paper,as they are here.

As these results show, the prediction of narrow object

impact crush energy from frontal barrier data is prone togross under-estimation. One obvious problem is thatinduced damage in the form of reduced crush width isactually causing a decrease in the estimate of crushenergy, when in fact this reduction in crush width requiredenergy, and therefore should somehow be included as anincrease in crush energy. Smith recommended multiply-ing the predicted crush energy by a correction factorequal to the undamaged width divided by the damagedwidth. This is certainly a step in the right direction, but asshown in the Smith paper, this does not go far enough tocorrect the under-estimation.

At present, it does not appear that a single structuracharacterization (i.e., a single set of parameters such asA and B, for example) will accurately predict crush energyfor both side and narrow-object impacts. However, in nar-row-object impacts we have developed a single charac-terization for a variety of vehicles, pole configurationsimpact angles and locations. This could be used toreconstruct a particular narrow-object impact, even if thesubject accident involved a different vehicle and impacconditions. Such an approach appears preferable toextrapolating from wide-object crash test data, even ifsuch testing involved the "right" vehicle. If a choice has tobe made, it is better to match the crash mode, comparedto matching the vehicle.

THREE-PARAMETER MODELS As noted earlier, thecrush characteristic for a constant-force model passesthrough the origin, whereas for a constant-stiffnessmodel, it does not. Otherwise, a constant-stiffness modewith force saturation would have a similar appearance toa constant-force model (although it is the initial slope inthe former, and the plateau force in the latter, which are

subjected to statistical analysis procedures).Such thoughts give rise to a three-parameter modelwhich is sort of a combination of the two. The underlyingcrush characteristic for such a model is shown in Figure11, in which the force-deflection curve is described bythree parameters: the force intercept F0, the force saturation level (plateau) Fs, and the saturation crush Cs.

Figure 11.

At first glance, it might appear that three parameterswould enable a perfect fit to the data from a three tesseries. However, the three resulting equations are nonlin-

ear, and such is not the case. The best one can do isobtain a "best fit" solution.

APPLYING THE MODELS TO VEHICLE-TO-VEHICLESIDE IMPACT TEST DATA As with the analysis oimpacts with narrow fixed objects, it is necessary to fullyaccount for post-impact kinetic energies of the collisionpartners, as well as the allocation of crush energybetween them. Unfortunately, the second considerationvirtually eliminates the use of the dynamic FMVSS 214crash tests, because the total crush energy is distributedin some unknown way between the struck vehicle and the


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moving barrier. We must therefore search for tests involv-ing an unyielding impactor.

The search narrows quickly to rigid moving barrier sideimpacts performed by Willke and Monk [Willke 1987], andby Aloke Prasad [Prasad 1991]. In the Willke work, two-test series were run on a Ford Escort, Mitsubishi Tredia,Chevrolet Citation, and Ford LTD, at 10 and 20 mphdelta-V. A third 25 mph delta-V test was run on the Cita-tion. In the Prasad tests, the repeated impact method (as

described by Warner, et.al. [Warner 1986]) was used torun three- and four-test series on a 1983 Ford Tempo,1984 Honda Prelude, 1985 Nissan Sentra, 1985 ChryslerLeBaron, and 1985 Chevrolet Celebrity.

The proposed constant-force and constant-stiffnessstructure models involve two parameters. Therefore, ifone has only two tests from which to determine theseparameters, the resulting structural characterizationshould fit perfectly. Stated another way, if one is drawinga straight line between two test data points, it should bepossible to make the line go through the points exactly.The model would then "close the loop," meaning that the

model would accurately predict the crush energies in thecrash tests from which the stiffness values were derived.Recall that Willke and Monk reported some difficulties inthis regard.

The two structure models (constant force and constantstiffness) were evaluated in this way against the two-testFord Escort series run by Willke and Monk. The highesterror in predicting the test crush energy was 0.08 percent, which can be assumed to be due to round off.Therefore, both models do indeed close the loop.

Beyond merely closing the loop, the models should accu-rately predict crush energy over a range of crash severi-

ties. To examine goodness of fit in this way requires aseries of at least three tests. The Prasad tests meet thisrequirement. Since they entailed repeated impacts, the

procedures as outlined by Warner [Warner 1986] wereincluded in the analysis.

For each vehicle, two crash plots were generated -- onefor the constant force model, and one for the constantstiffness model. The form factors and were calculated foreach crush profile, and regression techniques were usedto determine the model parameters A and B or A and Gas appropriate. Since two of the vehicles (Prelude andLeBaron) were hit four times, there was a choice in deter

mining the parameters for these vehicles: use all foutests or only three (the first three or the last three). Forthe Prelude and LeBaron, therefore, three sets of param-eters were generated for each of the constant-force andconstant-stiffness models.

A set of parameters for the three-parameter model werealso developed for each test series, and combination otests, as described above. The parameters derived foreach vehicle and series of tests are shown in Table 2.

The three models and derived parameters were thenused to calculate a predicted crush energy for each crashtest. The percent error in each prediction is shown in

Table 3. In this table, "Lo" indicates that the first threetests in a four test series were used in deriving theparameters, "Hi" indicates that the last three tests wereused, and "All" indicates all four tests were used.

RESULTS OF THE VEHICLE-TO-VEHICLE SIDEIMPACT TEST DATA ANALYSIS For the three-parame-ter model, the saturation crush levels ranged between 4.2and 9.8 inches. This parameter tended to increase some-what when the fourth test was included in the calcula-tions.

The force intercept values were surprisingly close to zero

ranging from 0.05 to just over one pound per inch. Astrong similarity to the constant-force model is thus indi-cated, and indeed the results for these two models trackeach other closely.

Table 2. Derived Model Parameters


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Across the board, the models perform better for thehigher energy tests. It is also noteworthy that the con-stant stiffness model over-estimated the energy for everyone of the lowest energy tests but one. This is not so forthe constant force and three-parameter models, whichtended to under-estimate the energy in many of the low-est energy tests. So for low-speed impacts, the constantforce and three-parameter models give the most conser-vative estimate of energy dissipated.

For either four-test series, the inclusion of the fourth testin the calculations caused a dramatic increase in theerror associated with the first test -- particularly if the firsttest was not used in the calculations. The implication isthat if one is attempting to reconstruct a low- or moder-ate-severity impact, one should exclude the higher-sever-ity tests in the calculation of model parameters.

For either four-test series, the exclusion of the fourth testin the calculation of model parameters leads predictablyto the highest error in that fourth test. If all four tests areused, the prediction of crush energy in the fourth test isimproved, but if one bases the model parameters on the

last three tests only, the crush energy predictions areeven better in the fourth tests. The moral to this story isthat the best results are obtained from test data nearestthe subject crash in severity, and that extrapolating tospeeds beyond the crash test data should be avoidedwhenever possible.

In general, the constant-stiffness model performed betterfor the Prelude and Sentra, while the constant-force andthree-parameter models were better predictors for theTempo, LeBaron, and Celebrity. There is no wisdomforthcoming on why one model works better than anotherfor a given vehicle. However, as one would predict from

the constant force behavior of side structures in staticcrush and narrow object impact tests, the constant forcemodel is capable of providing good crush energy esti-mates for side structures.

CONCLUSIONS

Side pole test data were analyzed and found to be best fitby a constant-force model using only the maximum crushmeasurement to characterize the residual crush pattern.Maximum crush out-performs other metrics such as aver-age crush, perhaps because they may be more sensitiveto ambiguities in determining crush width, or to any fail-

ure of six-measurement crush profiles to capture themaximum crush.

Despite a diversity of vehicles, poles, and test conditions,a single model was able to adequately predict the crushenergy. The underlying explanation of why such a modelworks so well can be found by examining the force-deflection characteristics of both static and dynamic nar-row-object tests.

Table 3. Comparison of Percent Error in PredictingCrash Test Crush Efficiency

For frontal impacts, models were developed for wide-object tests, and the resulting parameters were thenapplied to narrow-object impacts. The ability to predictthe crush energy in the narrow-object tests was slightlyimproved relative to previous models, but still far short oacceptable. In reconstructing narrow-object impacts, it ismore appropriate to use narrow-object test data (fromother vehicles) to derive a structural model for a givenvehicle than it is to use wide-object testing for that vehicleitself.


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For wide-object side impacts, it was found that a singleparameter was insufficient information with regard to theresidual crush pattern. Additional form factors and arenecessary in some cases for a fully-accurate calculationof crush energy. When such factors are incorporatedproperly, both maximum crush and area-weighted aver-age crush turn out to be equivalent measures of damageseverity.

The fact that both the constant-force and constant-stiff-

ness models "closed the loop" when fitting a model to thetwo-test Ford Escort series indicates that the addition ofform factors is the necessary ingredient, compared toearlier analyses.

For wide-object side impacts, constant-force, constant-stiffness, and three-parameter models were developed.These models were applied to rigid moving barrierimpacts into the sides of vehicles. With the three-parame-ter model, the zero-crush intercept was so close to zeroforce that the three-parameter model behaved very muchlike its constant-force cousin.

On this basis, one would expect better prediction ability

from the constant-force model than from the constant-stiffness model. This turned out to be only slightly true, asboth formulations gave good results as long as the acci-dent vehicle crush is within the range of the three crashtests used to determine the model's parameters. No pat-tern was seen as to why one model would work slightlybetter than the other for a particular vehicle.

Generally, attempts to extend the range of applicability ofeither model by adding the fourth data point are counter-productive. If a data point is added to one end of therange of crush magnitude, the crush energy prediction atthe opposite end of the range is degraded. Similarly, both

models were sensitive to extrapolation, particularly whenusing higher-severity test data to predict low-speed crushenergy. The best results are obtained from test data near-est the subject crash in severity.

If one must extrapolate, the conservative approach wouldbe to use a constant force-model. It tended to under-pre-dict crush energy at the ends of crash severity ranges,whereas the constant-stiffness model tended to over-pre-dict in these circumstances.

If a test at higher crash severity results in structural sepa-ration, recommended procedure has been to use sillcrush averaging, which tends to reduce the crush magni-tude (while at the same time introducing discontinuities inthe crush measurement protocol). An alternate recom-mendation has been to adjust the crush profile to reflectthe deformed shape without separations (i.e., to movethe separated portion of the profile so as to close thegaps). Either procedure tends to result in a lowered esti-mate of crush energy.

The latter procedure requires that the crush be mappedin all its detail. If this is done, all the raw crush informationis preserved and can be used later to make adjustmentsor consider new means of characterizing the crush. Consequently, we recommend mapping whenever crush dataare being collected.

When using a constant-stiffness model, either procedureappears to be a useful counterweight to the model's overprediction tendencies at the high end. For a constant-

force model, however, such adjustments would not berecommended.

ACKNOWLEDGMENTS

The authors would like to thank Esther Welsh and DonaldL. Struble for their help in preparing the figures.

REFERENCES

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energy transfer in car collisions

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