Effects of Restitution in the Application of Crush Coefficients

Transcription

1 Eects o Restitution in the pplication o Crush Coeicients Rayon R. McHenry an rian G. McHenry McHenry Consultants, Inc. Cary, NC STRCT Eects o restitution on aage interpretations are copoune by the act that restitution acts to reuce the aount o resiual eoration, or a given axiu ynaic crush, while also acting to increase the total ipact spee change. This paper presents a revise analytical proceure to inclue restitution eects or the CRSH progra an reineents to the restitution oeling within the SMC progra. The conversion o vehicle ipact test results into inputs or the two revise progras is also inclue. The eects o the reineents to the aage analysis proceures on reconstruction results are illustrate by irect coparisons with corresponing results prouce by the original SMC an CRSH progras an with easure ata ro ull scale vehicle ipact tests. INTRODUCTION During a otor vehicle collision, the axiu ynaic eoration generally excees the resiual eoration. Subsequent to the peak ynaic eoration, the collision partners begin a restitution phase as the eore structures restore kinetic energy, or spring back. The restitution orce level an uration eterine the ipulse that acts on the collision partners uring the restitution phase. When an accient vehicle is exaine, the resiual, or peranent, eoration is observe an/or easure. The original or o aage analysis in CRSH oes not inclue provisions or the eects o restitution. The original SMC collision routine inclues a sipliie restitution oel which is cubersoe to apply, can be sensitive to tie increent size, an tens to over-preict the resiual aage. The resulting eects on the accuracy o aage-base reconstructe values o V, or the case o irect, central barrier collisions, ranges ro approxiately 0 to 30% unerestiates, epening on properties o the speciic vehicle an the extent o resiual crush. For the case o oblique, non-central collisions, a siilar range o eects is anticipate on the basis o inirect easures o corresponing restitution values [, ]. t the present tie, crush coeicients or vehicle collision analysis are preoinantly base on ipact spees an aage easureents ro rigi, ixe barrier crash tests. The resiual aage is correlate with the ipact spee by eans o itte linear relationships. In general, there is no consieration given to the eects o restitution in applications o the itte crush coeicients. However, the ignore eects o restitution on the total ipact spee-change, corresponing to a given aount o resiual crush, are copoune by the act that restitution acts to reuce the aount o resiual eoration, or a given axiu ynaic crush, while also acting to increase the total ipact spee change. Thus, substantially ierent vehicles can share nearly equal slopes an intercepts in CRSH-type plots o the approach perio spee-change as a unction o resiual crush. This can occur even though the actual exposure severity or a given resiual crush ay be signiicantly ierent. The eects o restitution on aage interpretations becae an iportant topic o interest in relation to recent eorts by McHenry Consultants, Inc. aie at (a) reucing the sensitivity o restitution control in the original SMC coputer progra [3] an (b) achieving signiicant iproveents in the general accuracy level o aage interpretations. The relate oiications o the SMC an CRSH coputer progras have retaine the existing ors o the itte crush coeicients. However, suppleentary inoration regaring the restitution behavior o iniviual vehicles serves as the basis or reineents in the aage analysis aspects o the cite coputer progras. NLYTICL PPROCH The analytical evelopents presente in this paper are base on liite test ata that are available on the restitution behavior o autoobiles in irect central collisions against rigi barriers. It is assue herein that an analytical oel o the unit-with structural properties, in ters o the loa-election characteristics uring loaing an unloaing, that aequately correlates with the results o irect central Nubers in brackets [ ] inicate reerences at en o paper

2 collision tests, will also prouce a reasonable approxiation o restitution behavior in oblique, non-central collisions. Direct easures o restitution in oblique, non-central collisions o autoobiles are not known to be reaily available. However, analytical proceures have been evelope (e.g., rach [], Ishikawa []) to extract approxiations o the eective coeicient o restitution ro such test ata. These approaches ay provie a eans o extening the current investigation to inclue coparisons with oblique, non-central collisions. The assue or o crush behavior, incluing restitution, is epicte in Figure. The objective o the analytical evelopents has been to establish relationships aong the variables epicte in Figure an the existing CRSH coeicients an [4] that will aintain the linear relationship epicte in Figure. On the basis o results o the analysis, it is conclue that the linear relationship epicte in Figure can be aintaine without changes in an, over wie ranges o properties o the or epicte in Figure. Thus, the relationship o Figure oes not uniquely eine a cobination o crush an restitution properties. Restitution consists o two separate aspects: () a partial iensional recovery an () a partial restoration o kinetic energy. The speciic cobination o the two restitution aspects is eterine by three easures o restitution behavior ro test ata that serve as the basis or our itte constants (,, ρ, Γ, see ppenices). The crush resistance uring increasing loas,, is eterine by CRSH coeicients an an by the extent o iensional recovery. The unit-with crush resistance uring unloaing,, is eterine by an the extent o restoration o kinetic energy. The nature an extent o eects on aage interpretations are outline in the ollowing paragraphs: In Figures an 3, ull-rontal crush properties are epicte or two substantially ierent equal-with hypothetical vehicles which share ientical crush coeicients (i.e., an in the CRSH orat). Yet, at 0 inches o resiual crush, the total ipact spee-changes o the two vehicles ier by approxiately 3% (i.e., approxiately 7.3 MPH) as shown in Figure 4 an 5. Figure : Force v. Crush Figure : pproach-perio Spee-Change vs. Resiual Crush, Syetrical Central Ipacts Figure ssue For o Crush ehavior

3 Figure Full-Frontal Crush Properties Figure 3 Full-Frontal Crush Properties Figure 4 Ipact Spee Change v. Crush, Category 3 Frontal, High Restitution Figure 5 Ipact Spee-Change v. Crush, Category 3 Frontal, Low Restitution

4 The vehicle properties epicte in Figures an 3 are base on theoretical requireents to achieve a linear relationship between V c (i.e., the ipact spee-change uring the approach perio) an the resiual crush. To the extent that such a linear relationship constitutes a reasonable approxiation o actual behavior, the unerlying crush resistance an restitution einitions o Figures an 3 are supporte. It shoul be note that the low-restitution vehicle o Figure 3 is approxiately 3% stier than the highrestitution vehicle o Figure. Yet the crash behavior o each vehicle is eine by ientical values o the current crush coeicients: per reerence [5]: per reerence [6]: = 37 L/IN = 56 L/IN b 0 = 6.74 MPH b =.9 MPH/IN In view o the signiicantly ierent values or the total V at given values o resiual crush as eonstrate in Figures 4 an 5, it is obvious that the current crush coeicients ust be suppleente with restitution inoration. It shoul be note that an absence o restitution throughout the entire range o eoration woul prouce zero values or the itte coeicients an b 0. COMPRISON OF RESTITUTION IN ORIGINL ND REVISED SMC t the tie o evelopent o the original SMC coputer progra, (97, Reerence [3] ) ephasis was on eonstration o the easibility o the overall concept. The selecte analytical approach to restitution at that tie (presently retaine in both original SMC an EDSMC) inclue the use o extensive sipliying assuptions aie at reucing the requireents or associate coputer eory an logic. In particular, ientical loa-election rates were applie or loaing an unloaing o the iniviual raial vectors, that eine the collision interace, an the unloaing was ipleente at orce levels close to the peak values [7]. s a part o the selecte siulation approach, the unloae lengths o the iniviual vectors were ajuste at each tie increent uring increases in loaing. The associate coing thereby avoie any nees or logic to etect the en o loaing at the iniviual raial vectors an or aitional eory to store relate inoration. The selecte original approach perits reasonable control o restitution over a liite operating range about a given value o eoration or which restitution inoration is available. However, the high loa level uring restitution akes the siulation excessively sensitive to tie-increent size. It is also cubersoe to apply an it tens to over-preict the resiual aage. Since the early 990 s the extent o liitations on logic an eory, that are ipose by reaily available coputers, are substantially reuce. lso, the available ata on restitution behavior have been increase. Thereore, the collision routine o SMC has been oiie to achieve iproveents in reconstruction accuracy. Results representative o the changes in restitution an in the ratio o resiual to axiu ynaic crush, each as a unction o the axiu ynaic crush an the resiual crush, are epicte in Figures 6 an 6, respectively The ratio, /, clearly ust vary ro zero, at zero resiual crush, to.000 at that value o resiual crush where there is no urther restitution. Figure 6 shows that original SMC (EDSMC) oes not vary the ratio o / as a unction o in a realistic anner. It is obvious ro Figures 6 an 6 that the ratio o ( / ) ro the original SMC progra (or the equivalent ratio (C R /C T ) in [8] ) shoul not be use as a basis or eterining the appropriate V value or the SMC progra corresponing to the itte CRSH coeicients an. I a easure value o ( / ) or a given axiu ynaic crush value, ( ) is available ro a crash test, equation (8) in ppenix can serve to eine the appropriate v or given values o an. Ipleentation o a revise aage analysis proceure, that inclues restitution eects, was outline or the CRSH coputer progra in [9]. corresponing revision, which was recently incorporate in the SMC coputer progra, has been applie to generate the responses presente on the ollowing pages. Detaile analytical relationships are presente in the ppenices.

5 Figure 6 Plotte gainst Maxiu Dynaic Crush Figure 6 Plotte gainst Resiual Crush Figure 6 Siulate Restitution ehavior in Original an Revise SMC Routines

6 RESULTS Daage-ase Reconstructions o Delta-V (D V) In the ollowing coparisons o () reconstruction results obtaine with the original CRSH (EDCRSH) progra an the revise CRSH progra an also () reconstruction results obtaine with the original SMC (EDSMC) progra an the revise SMC progra, the ierences in aage-base V values are prouce entirely by the inclusion o realistic restitution properties in a ully eine hypothetical vehicle. Neglect o restitution eects constitutes an analytical error since it involves the total oission o a signiicant aspect o the collision, particularly at ipact spee changes below 30 ph. In the application o any reconstruction technique to physical evience there are any potential sources o error which ust be properly taken into account. The presente coparisons isolate the changes in reconstruction results that are prouce by eects o restitution. It shoul be note that eaningul irect coparisons o theoretical results with test ata require that the accuracy an the repeatability o the test ata be establishe. lso, such coparisons yiel the total error ro the cobine sources. coparison o results obtaine with the original CRSH progra an the revise CRSH progra or a eine hypothetical vehicle is presente in Figure 7. The igure illustrates the act that an application o the original CRSH aage analysis proceure can prouce V errors (i.e., unerestiates) in the range o 0-30%. coparison o results obtaine with the NHTS SMC (EDSMC) progra an the revise SMC progra or the sae hypothetical vehicle is presente in Figure 8. The igure illustrates the act that an application o the NHTS SMC (EDSMC) progra or aage analysis purposes can also prouce V errors (i.e., unerestiates) in the range o 0-30%. The original or o restitution control in the SMC progra acts to return part o the absorbe energy but it oes so with a less-than-actual iensional recovery (Figure 9, Figure 0 ). s a result, a purely aage-base eterination o V by eans o the original SMC progra tens to unerestiate the true value o V ue to the act that the resiual aage or a given V is overestiate. The cite error source in aage interpretations in original SMC has le to soe isguie ajustents in the crush stiness (e.g., [0]) to achieve a atch o preicte aage extent. coparison o the results obtaine by the various versions o SMC an CRSH are cobine on Figure. It shoul be note that the results or the revise versions o SMC an CRSH are ientical. The retention o an excessive aount o preicte resiual aage by original SMC akes the V errors at low spees soewhat greater than those o original CRSH. Figure 7 Coparison Resiual Delection Delta-V CRSH3 (EDCRSH) v. Revise CRSH

7 Figure 8 Resiual Delection v. DeltaV or Original SMC (EDSMC) v. Revise SMC Figure 9 Siulate Force Delection Characteristics or the original SMC (EDSMC) progra an the Revise SMC progra

8 Figure 0 cceleration v. Tie or Original SMC (EDSMC) an Revise SMC Figure Resiual Delection v. D V or CRSH & SMC progra

9 Coparison o the Matheatical Moel o Crush ehavior with Test Data The lack o exact repeatability o ull scale crash test results introuces scatter in coparisons o the etaile results o ultiple tests. Measureents relate to restitution behavior have been oun to inclue an unusually large aount o scatter, particularly at low values o ipact speechanges. The eective coeicient o restitution can inclue signiicant eects o orces that are external to the two-boy collision syste. For exaple, in an SE barrier crash, aage running gear (e.g., jae or ipee ront wheels) can prouce signiicant rag orces that act to reuce the reboun velocity, particularly at low levels o returne energy. lso, energy absorbers on bupers can act to elay the return o a portion o the absorbe energy. The atheatical oel eine herein aresses the responses o the vehicle structure only. The agnitue o the eects o external orces on iniviual ull-scale tests has not been easure. In the absence o special tests that easure the isolate responses o the structure only (e.g., tests run on casters), it is necessary to ocus attention on correlation with the higher returne-energy en o the available easure responses. While soe coprehensive test ata ro iniviual tests are available, test series over a range o ipact spees with coprehensive reporting are still relatively rare. In Figure, coprehensive test ata ro a series o our tests o 79 through 8 For LTDs [] are copare with the itte atheatical oel. In Figure 3, test ata or six 8-85 For Escorts [] which i not inclue reporting o the ratio o resiual to axiu crush, are copare with the itte atheatical oel. In Figure 4, test ata ro a series o ive tests on VW Rabbits [3] which i not inclue reporting o the coeicient o restitution are copare with the itte atheatical oel. Note that the easureents o ierent aspects o restitution behavior in crash tests that are presente in Figures, 3 an 4 inclue scatter prouce at least in part by the previously cite eects. Figure Coparison o Matheatical Moel with For LTD Tests []

10 Figure 3 Coparison o Matheatical Moel with For Escort Tests [] Figure 4 Coparison o Matheatical Moel with VW Rabbit Tests [3]

11 Collisions between Vehicles with Dierent Restitution Properties In Figure 5 the results o a 30 MPH hea-on irror iage collision, siulate with the revise SMC progra, are isplaye. Note that in the siulate collision o Figure 5, the restitution properties o the collision partners are ientical. Figure 6 epicts the siulate results with the revise SMC progra o a hea-on 7 MPH collision between a high restitution an a low restitution vehicle. Note that the eective restitution is an intereiate value. In the SMC ipleentation, orce equilibriu is aintaine between the interacting structures o the collision partners at all points within the contact zone throughout the unloaing process. y this eans, the two vehicles continue to interact uring the unloaing process until they each reach their resiual values o crush at all contact points. Figure 5 Exaple Response characteristics o revise SMC collision routine, 30 MPH Hea-On Mirror Iage Vehicles

12 In the CRSH ipleentation [9], the restore energy or each o the collision partners is separately calculate by eans o integrations across the aage interace. The resulting values are ae together an then cobine with the total absorbe energy or application in the calculation o V an V. In each or o ipleentation, the eective overall coeicient o restitution in a given collision inclues eects o the with an location on each vehicle o the contact area, the etaile aage proiles, an the iniviual unit-with crush properties o the collision partners. This cobination o eects is believe to constitute a realistic analytical representation o the actual physical syste uring the unloaing process. Figure 6 Exaple Response characteristics o revise SMC collision routine, 7 MPH Hea-On, High an Low Restitution Vehicles.

13 CONCLUSIONS ND RECOMMENDTIONS. Daage analyses which ake use o either the original SMC or CRSH progras prouce lower-than-actual values or the ipact spee-change, with the axiu errors occurring at low spees where restitution is greatest. The original CRSH (EDCRSH) oes not, o course, inclue restitution. The siplistic or o siulation o restitution in the original SMC (EDSMC), which restores a portion o the crush energy as neee in a tie-history solution or, oes so in a anner that retains an excessive aount o preicte resiual aage. s a result, the error in a purely aage-base V is soewhat greater or SMC than CRSH at low spees an soewhat less at high spees.. The evelope ipleentations or both SMC an CRSH o a revise aage-base proceure that inclues restitution have been shown to be capable o proucing signiicant iproveents in the accuracy o reconstruction results. They also can serve to insure copatibility o the inputs that eine crush properties or the SMC an the CRSH ors o analysis. 3. The revise aage analysis proceures or CRSH an SMC provie a unique capability or entering separate einitions o the restitution properties o collision partners. 4. The liite coparisons o the atheatical oel o crush behavior with test ata that have been possible to ate inicate a reasonable egree o correlation. The general or o the atheatical oel is ictate by the assuption o a linear relationship between the Delta-V preceing restitution (i.e., to the point o a coon velocity) an the resiual crush. It shoul be note that the speciic analytical approach that is eine in ppenices an is not inherently liite to the case o a linear orce-election characteristic. Moiication o the oele crush behavior to inclue a saturating orce coul be reaily accoplishe i corresponing test ata were to becoe available. 5. The reporte research results are consiere to constitute an iportant eonstration o a eans o achieving signiicant iproveents in reconstruction accuracy. The restitution aspects o test ata neee to ully utilize the escribe reineents are soeties inclue in test reports. They shoul be ae to be a routine part o crash test reports. REFERENCES. rach, R.M., Ipact nalysis o Two-Vehicle Collisions, SE Paper No Ishikawa, H., Ipact Center an Restitution Coeicients or ccient Reconstruction, SE Paper No McHenry, R. R., Coputer Progra or Reconstruction o Highway ccients,, SE Paper No , Seventeenth Stapp Car Crash Conerence, Oklahoa City, Oklahoa, Noveber -3, McHenry, R. R.,, User s Manual or the CRSH Coputer Progra, Calspan Report No. ZQ-5708-V-3, Contract No. DOT-HS-5-04, January Monk, M. W., Guenther, D.., Upate o CRSH Coputer Moel Daage Tables, Volue, Vehicle Research an Test Center, National Highway Traic Saety inistration, East Liberty, Ohio, Report No. DOT-HS , March Capbell,.L., Energy asis or Collision Severity, SE Paper No , 3r International Conerence on Occupant Protection, Troy, Michigan, July 0-, McHenry, R.R., Jones, I.S. an Lynch, J.P., Matheatical Reconstruction o Highway ccients, Calspan Report No. ZQ-534-V-, Contract No. DOT-HS , Deceber Nystro, G.., ost, G., an Werner, S.M., Stiness Paraeters or Vehicle Collision nalysis, SE Paper No. 909, February McHenry, R.R., McHenry,.G., Revise Daage nalysis Proceure or the CRSH Coputer Progra, SE Paper No , Thirtieth Stapp Car Crash Conerence Proceeings, San Diego, Caliornia, October 7-9, Day, T.D., Hargens, R.L.,"Further Valiation o EDSMC Using the RICSC Stage Collisions", SE Paper Raglan, C., Frontal Ipact Protection Progra - Frontal Structures: nalysis o Frontal Crash Test Data, NHTS, Oice o Vehicle Research, Sept erkho, J.F., Varat, M.S., et al, n Investigation into Vehicle Frontal Ipact Stiness, EV an Repeate Testing or Reconstruction, SE Paper No Navin, F., MacNabb, M. an Miyasaki, G., Elastic Properties o Selecte Vehicles, SE Paper No CONTCT INFORMTION Questions or coents on the paper are welcoe an can be aresse to the authors: e-ail: chenry@interpath.co Postal Service Mail: 03 ray Court, Suite 00 WWW: Cary, NC 75 US PPENDIX : Fitting o Crush Properties to Crash Test Data Deinition o Sybols:

14 CRSH3 Crush Coeicients, Re. [5]: = Intercept, Lb./Inch = Slope, Lb./In Capbell Coeicients, Re. [6]: b o = b = E a = E r = Figure : F = F = = = Intercept, Miles per hour Slope, Miles per hour/inch bsorbe energy, inch-lb. Restore energy, inch-lb. Crush resistance orce, Lb. Virtual crush resistance orce, Lb. Crush resistance per unit with or increasing loas, lb./in Crush resistance per unit with or ecreasing loas, lb./in v = SMC crush resistance, Lb./in Re. [3] L = M = V c = V o = V = V c = V = = = = Γ = ε = ρ = Contact with, inches Mass, lb.-sec /in Coon velocity o contact regions at en o approach perio o collision, inches/sec Initial velocity, inches/sec. Final (separation) velocity, inches/sec Ipact spee-change uring the approach perio o the collision, inches/sec Total ipact spee-change, inches/sec. Crush, inches. Resiual crush, inches. Maxiu ynaic crush, inches Restitution constant. Coeicient o restitution Restitution constant. To the extent that the approach-perio ipact spee change, V c, can be reasonably approxiate as a linear unction o the resiual crush,, the corresponing relationship between the coeicient o restitution, ε, an the axiu ynaic crush,, ust be eine in the or: ε Γ = + ρ { i ε >.00, ε =.00 } where ρ an Γ are itte constants. While the itte an coeicients o CRSH are retaine to eine V c as a linear unction o, those coeicients are suppleente by easures ro crash tests o the restitution behavior. The cobine crash test inoration is applie in the or o a total o our itte constants:,, ρ, Γ The itting proceure consists o ollowing: Fro easure ata in crash tests, a test conition is selecte at which the restitution behavior is to be atche. For that selecte conition the axiu ynaic crush, ( ), the ratio o resiual crush to axiu ynaic crush, ( / ), an the corresponing coeicient o restitution, (ε), are eterine to suppleent an. The our itte constants are then calculate: Γ = ρ = ( ε) = ( ε) Γ ( ) = = () () (3) (4) ρ L IN (5) L IN (6) The lack o exact repeatability o crash test results akes it clearly necessary to rely on ultiple crash tests or a einition o crash behavior an to eal with the scatter o the results by eans o statistical proceures. Measureents relate to restitution behavior have been oun to inclue an unusually large aount o scatter, particularly at low levels o returne energy (or exaple, see coparisons with test ata elsewhere in this paper).

15 In view o the preceing, it is highly esirable to use regression analysis on ultiple ata points, to insure that the selecte test conition is representative o the overall easureents o behavior. In the case o ultiple ata points, linear regression is irst use to eine the coeicients o equation (8) o ppenix, an, thereby, an. Next, the coeicient o in equation (9) o ppenix is establishe by eans o a it to the reporte values o an with an intercept at -/. value or ( ) is selecte an the corresponing values o ( ) an ( / ) are calculate ro the itte equation (9). The easure value o (ε), corresponing to ( ), is establishe an entere. s ore easureents o restitution behavior becoe available, it ay becoe possible to establish patterns in the itte constants or ierent vehicle types. The physical signiicance o the itte constants ay be seen in Figures an. In Figure, it shoul be note that the peak values o orces, F an F' are not ientical. The plot o F' against election ust be recognize to constitute a virtual orce election, since the orce an the election o not exist at the sae tie. It can be shown analytically that the ratio o the peak orces in Figure is eine by the ollowing: ( ) F F ' PE VLUES = (7) Further analytical relationships inclue the ollowing: = ρ = ε = = + + INCHES (9) (0) () + ρ () The relationship o the our itte constants to an ay be urther eine: The unit-with crush stiness or increasing loas can also be establishe ro the ollowing relationship, which is inepenent o the extent o restore energy an, thereby, o the restitution coeicient: = ρ L / IN (3) = + ( ) L IN (8) = Γ L / IN (4) Saple applications o equation (8) are presente in Fig. 3.

16 Figure : Crush Resistance Force Per Unit With, Lb/In Figure : Coeicient o Restitution, e Figure 3: Loaing Stiness vs. Resiual/Max Crush Ratio

17 PPENDIX : Derivation o Equations Fro Figure, the ratio o returne to absorbe energy ay be expresse: E E R = ( ) = (5) Since the coeicient o restitution is equal to the square root o the energy ratio, E R ε = = E (6) Since = constant, Solution o (3), or Γ ε = + ρ Fro (4), (), an (), Γ + = 0 =. = 0, yiels: (4) (5) Solving (6) or, Fro (0) = ε (7) = (6) Substitution o (6) into (5) yiels: In orer or V c at a given value o resiual crush,, to be equal in the CRSH an SMC ors o analysis (see Figure ), the relationship between an ust be eine by the ollowing two equations: (6): Γ = (7) The ratio / is eine on the basis o equation V V c c L L = + (8) M M L = M Fro (8) an (9), = = Fro equation (7), = ε ε = + ε (9) (0) () () (3) = ε ( ) (8) where (ε) an ( / ) are obtaine ro crash test ata or the speciic vehicle or which crush properties are being eine. Fro equation (4), ( ε) ρ = Γ ( ) (9) where (ε) an ( ) are obtaine ro crash test ata or the speciic vehicle or which crush properties are being eine. Fro equations (5), (7) an (4): = ρ (30)

18 PPENDIX 3: Clariications The review process has reveale several points that ay be conusing to soe reaers. The ollowing is aie at clariication o those aspects o the paper:. The existence o signiicant errors relate to restitution that are present in both the original CRSH (EDCRSH) an original SMC (EDSMC) coputer progras ust be acknowlege. It is coon knowlege that the original CRSH (EDCRSH) progra unerestiates the V in barrier crashes by approxiately 0 to 0% at 30 MPH an by a greater aount at lower spees as a result o the act that restitution is copletely ignore. The original SMC (EDSMC) or o siulation o restitution is crue, with rarely change inputs, an it cannot rationally be expecte to prouce reliable an accurate cobinations o iensional recovery an partial return o absorbe energy or all vehicles uner all collision conitions. In act, its uner-preiction o structural recovery prouces a siilar range o unerestiates o V. Thus, the status quo regaring restitution eects in existing coputer progras is very iicult to een on a logical basis.. The ranges o errors (unerestiates) inicate in the paper or aage-base V values ro the original CRSH an SMC progras, that are prouce either by a total neglect o restitution (CRSH) or by unerpreiction o structural recovery (SMC) are intene to provie the reaer with approxiate easures o the practical signiicance o the eects o restitution. 3. On the basis o Figures, 6, an as well as the closely relate SE it shoul be clear that ε is set to.000 whenever the calculate value excees.000. Thereore any concern about an ininite liit or ε is unoune. 4. The oele value o ε, at zero resiual crush, is not necessarily equal to.000. Rather, it is eine by equation (6): E R ε = = E Results o applications o equation (6) to test ata where the liiting value o ε was substantially less than.00 are shown in Figures 3 an 4. In Figure 3, the restitution coeicient or the Escort never excees In calculations relate to Figure 3 perore by one reviewer the value o ε was incorrectly set equal to Energy is absorbe whether or not a structure is elastic. It is the extent o return o the absorbe energy that istinguishes elastic ro inelastic behavior. 6. The ter aage in this paper is use to reer to the generally accepte resiual crush, as oppose to any cosetic isigureent o ragile boy parts. 7. The general or o the, crush coeicients use in the CRSH(EDCRSH) progra iplies an eective elastic eoration range, in ters o ull iensional recovery, equal to /. 8. The lack o exact repeatability o iniviual easureents in crash tests that are perore uner ientical test conitions acts to prouce ranges o easure responses rather than single values. For this reason, rigorous easures o reconstruction accuracy ust be base on the ean experiental easureents or a given set o test conitions. 9. vailable experiental easureents o restitution behavior over ranges o ipact spee (e.g., Figures, 3, an 4) inclue only single easure values at the iniviual test conitions. Clearly, progress towar a rigorous an coplete valiation stuy is ata-liite at the present tie.