International Journal of CrashworthinessVol. 13, No. 5, October 2008, 469–478

A study of the pedestrian impact kinematics using finite element dummy models: the corridorsand dimensional analysis scaling of upper-body trajectories

Costin D. Untaroiua∗, Jaeho Shina , Johan Ivarssona , Jeff R. Crandalla , Damien Subita , Yukou Takahashib,Akihiko Akiyamab, and Yuuji Kikuchib

aCenter for Applied Biomechanics, University of Virginia, Charlottesville, Virginia, USA; bHonda R&D Shimotakanezawa,Tochigi, Japan

(Received 10 September 2007; final version received 9 March 2008)

Pedestrian–vehicle impact experiments using cadavers have shown that factors such as vehicle shape and pedestrian an-thropometry can influence pedestrian kinematics and injury mechanisms. Although a parametric study examining thesefactors could elucidate the complex relationships that govern pedestrian kinematics, it would be impractical with cadavertests because of the relative expense involved in performing numerous experiments on subjects with varying anthropometry.On the other hand, finite element modelling represents a more feasible approach because numerous experiments can beconducted for a fraction of the expense. The current study examined the relationship between pedestrian anthropometryand front shape of a mid-size sedan using a PAM-CRASH model of the 50th-percentile male (50th M) Polar-II pedestriandummy extensively validated against experimental data. To evaluate the influence of pedestrian anthropometry on responsekinematics, scaled dummy models were developed on the basis of the weight and height of the 5th-percentile female (5thF), 50th-percentile female (50th F) and 95th-percentile male (95th M). Simulations of the 5th F, 50th F, 50th M, and 95th MPolar-II finite element models struck at 40 km/h by a mid-size sedan were used to generate trajectories of the head, upperthorax, mid-thorax and pelvis. In an effort to assess the validity of scaling techniques when interpreting trajectory data fromvehicle–pedestrian crashes, the trajectories of the 5th F, 50th F and 95th M model were scaled to the 50th M and comparedwith those generated by the 50th M model. The results demonstrated non-linear behaviour of dummy kinematics that couldnot be accounted for with traditional dimensional analysis scaling techniques.

Keywords: impact; finite element method; pedestrian dummy; pedestrian kinematics; scaling

1. Introduction

The pedestrian is one of the most vulnerable road users,and they comprise about 65% of the 1.17 million annualtraffic-related fatalities in the world [28]. The probability ofa pedestrian being injured or killed is much higher than thatof a vehicle occupant. In 2005, 8.7% of vehicle–pedestrianimpacts in the United States were fatal, whereas thecorresponding fatality rate for occupants in crashes was1.3% only [15].

Protection of pedestrians in car-to-pedestrian collisionshas recently generated increased attention with regulationsimplemented or proposed in Europe [5], Korea [29] andJapan. Although subsystem experiments are currently beingused as the basis of evaluations for these regulations, car-to-pedestrian dummy impact tests or car-to-human/dummyimpact simulations provide complimentary data that betterdescribe the complete vehicle–pedestrian interaction.

An advanced pedestrian dummy, called Polar-II, hasbeen developed and continuously improved by Honda R&D,GESAC, and the Japan Automobile Research Institute[1,2,4,16,23]. Although the dummy incorporates advanced

∗Corresponding author. Email: costin@virginia.edu

instrumentation in the head, neck, chest, pelvis and lowerlimbs [1], the primary purpose of the Polar-II dummy wasreproducing pedestrian kinematics in a collision with a ve-hicle. Kerrigan and colleagues [9,10] performed vehicleimpact tests on the Polar-II and post-mortem human sur-rogates (PMHS) in identical conditions and showed thatthe Polar-II dummy generally replicates the complex kine-matics of the PMHS. However, the Polar-II dummy has thegeneral characteristics of the 50th-percentile male (50th M)and can therefore not predict kinematics for all statures ofpedestrians.

A finite element (FE) model of the Polar-II dummy hasbeen developed, validated in component tests [21] and ver-ified at the full-scale level against kinematic data [21,22]recorded during the vehicle–dummy impact experimentsperformed by Kerrigan et al. (2005a). The Polar-II FEmodel was developed using Hypermesh (Altair Engineer-ing, Troy, MI, USA) and Generis (ESI) as pre-processors,and PAM-CRASH/PAM-SAFE FE solver (version 2001,ESI Group, Paris, France) was used for impact simula-tions. The model contains 27,880 elements that represent

ISSN: 1358-8265Copyright C© 2008 Taylor & FrancisDOI: 10.1080/13588260802055387http://www.informaworld.com

470 C.D. Untaroiu et al.

Figure 1. The population distribution of standing height [6].

the head, neck, thorax, abdomen, pelvis, upper arms, fore-arms, hands, thighs, knees, legs and feet and has a totalmass and height close to that of the 50th M.

It is believed that pedestrian kinematics is highly influ-enced by vehicle geometry and pedestrian anthropometry[13]. Although the dependence of pedestrian kinematics onvehicle geometry has been previously shown [9,10], therehave been few studies presenting the influence of the adultpedestrian anthropometry [22]. Thus, vehicle–pedestriansimulations were performed with a mid-size sedan vehiclemodel and a family of dummies corresponding to peaksand extremes of the adult population (Figures 1 and 2),and the trajectories of several upper-body locations werecalculated. In addition, a traditional dimensional analysisscaling technique has been applied to normalise PMHSupper-body trajectories of scaled dummies relative to thosecorresponding to the 50th M.

2. Methods

2.1. Pedestrian anthropometric data

The development of pedestrian dummies requires the an-thropometric data of subjects in standing posture. Most

Figure 2. The population distribution of weight [6].

anthropometric data have been gathered for subjects in atypical semi-reclined seating posture for design of occu-pant dummies [19,20]. A few studies (e.g. [6,14]) alsoconsidered anthropometric characteristics of the standingposture. The anthropometric survey (ANSUR) of US Armypersonnel conducted during the 2-year period from 1987to 1988 [6] includes over 132 anthropometric measure-ments collected for 9000 subjects in standing and sittingpostures. This database showed symmetric distributionsof height and mass around average values, those con-sidered corresponding to the 50th percentile of anthro-pometric subjects (Figures 1 and 2). To study the influ-ence of anthropometry on pedestrian kinematics in lat-eral car-to-pedestrian impacts, four dummy models werecreated:

� A 50th M and a 50th F which represent the adult popu-lation peaks.

� A 5th F and a 95th M that represent extreme subjects ofthe adult population.

The Polar-II FE model [21] was used to represent the50th M because it closely approximated the anthropomet-ric characteristics (Figures 1 and 2). The other three modelswere derived by scaling this model according to the method-ology presented in the next section.

2.2. Scaling of the Polar-II FE model

2.2.1. Scaling of dummy geometry

A preliminary study of the ANSUR anthropometric data re-vealed non-proportional variations in all anatomical direc-tions of body measurements for all anthropometric subjectsunder study (5th F, 50th F, 50th M and 95th M), which makesscaling a challenging task. For the purpose of the currentstudy, we selected mass and height as the most important an-thropometric characteristics to match with the correspond-ing data of ANSUR subjects. Therefore, the scaling of eachmodel was performed in two steps:

� Scaling in vertical direction (z axis) – to match the stature(height)

λz,subject = Hsubject

HPolar - II(1)

� Scaling in the transverse plane (x − y plane) – to matchthe total mass

λx,subject = λy,subject =√

msubject

mPolar - II λz,subject(2)

To verify the scaled dummy models obtained accord-ing to this methodology – 5th percentile female (5F-S),50th percentile female (50F-S), and 95th percentile male

International Journal of Crashworthiness 471

Figure 3. Anthropometric dimensions used to compare scaleddummy models with corresponding ANSUR data [6].

(95M-S) models – several specific anthropometric dimen-sions of the scaled models and the Polar-II model werecompared with the corresponding data of the ANSUR sub-jects. These specific dimensions in all anatomical directions(Figure 3) are as follows: (1) cervical height, (2) iliocristaleheight, (3) vertical thumb tip reach down, (4) knee height,(5) menton-top of head, (6) head breadth, (7) bideltoidbreadth, (8) waist breadth, (9) chest depth, and (10) buttockdepth.

2.2.2. Scaling of inertial properties

The components of the Polar-II model can be classified aseither deformable or rigid parts. Using the mass densities ofeach component, which was assumed constant between thePolar-II FE model and scaled dummy models, the inertialproperties (mass and the components of the inertia tensor)of the deformable parts were calculated from their meshes.The inertial properties of rigid bodies, which usually havesimplified meshes, were defined in the input file of themodel on the basis of measurement data. As a consequence,an algorithm for obtaining the mass and components of theinertia tensor relative to new centres of gravity of scaledrigid models was developed (see Appendix 1) and appliedfor all scaled dummy models. The same factors used toscale the dummy geometry were also used to scale inertiaproperties of rigid parts.

2.2.3. Scaling of joint properties

Several components of the dummy are connected by definedjoint models, for which the joint stiffness is characterisedby a moment–angle curve. On the basis of the principlesof dimensional analysis [11], the moment of a scaled entitycan be expressed as a function of the length-scale factors

[7,12]:

Mscaled = λxλyλzMPolar - II (3)

As a result, all moment–angle curves of the scaled-dummymodels were scaled using the equation given above.

2.3. Vehicle–pedestrian simulations

Four full-scale pedestrian impact simulations were per-formed using the Polar-II dummy model and scaled-dummymodels. The methodology used to perform these simula-tions was similar to that used in previous verification stud-ies presented by Shin and colleagues [21,22]. The Polar-II dummy model was positioned laterally at the vehiclecentreline in a mid-stance gait with the left lower extrem-ity in the leading position and the right lower extremityclosest to the vehicle (a mid-size sedan). To promote re-peatability and reduce test-to-test variability, the upper ex-tremities were bound at the wrist with the left wrist closerto the abdomen. The front end of the vehicle model in-cluded all exterior structures that could contact the dummyas well as the stiff underlying structures (e.g. engine compo-nents) that could be loaded by the exterior vehicle structuresduring the impact. Contacts between the dummy body re-gions and the vehicle were defined using a penalty-basedsliding interface recommended for crash simulations [17].This interface type with the same scale factor for sliding-interface penalties (0.05) was also applied in both validationsimulations of Polar-II component tests [21] and vehicle–dummy impact tests [22]. In the experiment, approximatelyabout 24 ms prior to initial bumper contact, the dummywas released from an overhead support and settled underthe load of gravity. Thus, in the FE simulations, a planesimulating the ground level was specified and a sliding-interface contact (Type 11 as in [22]) was defined betweenthe dummy feet and the ground. To simulate the reactionloading from the ground, an initial preload was employedthrough feet-ground-sliding interfaces corresponding to thedummy weight. The friction coefficients were defined forpedestrian–ground and pedestrian–vehicle contacts as 0.6and 0.5, respectively, [27] as Shin et al. [22]. The massof the simplified vehicle model was adjusted to the massof the vehicle sled buck by adding the mass differential tothe vehicle’s centre of gravity (CG). A 40 km/h initial ve-locity in the impact direction (towards the pedestrian) wasapplied to the vehicle model at the beginning of the simula-tions. Kinematic trajectories of the head CG, top of thoracicspine (T1), mid-thoracic spine (T8) and pelvis CG (loca-tions of the photo targets used in the full-scale PMHS testsby Kerrigan and colleagues [9,10]) were calculated to al-low for comparison with body-segment trajectories of fourdifferent dummy models (Figure 4). In addition, the wrap-around-distance (WAD) to head contact was calculated in

472 C.D. Untaroiu et al.

Figure 4. Node set of the pedestrian dummy model used in thekinematics analysis.

all simulations. To provide a basis for validation of thepedestrian dummy against the PMHS data, the PMHS kine-matic response was linearly scaled to the 50th M’s responseusing a length-scale factor. Thus, the original PMHS tra-jectories for x(t) and z(t) together with time were scaledusing the height ratio of the PHMS relative to the 50th M[9,10]. To verify the validity of this method, all trajecto-ries of the dummy models (5F-S, 50F-S and 95M-S) werescaled to Polar-II data using the same methodology. Thepercentage error between scaled trajectories and the corre-sponding Polar-II trajectories was calculated according tothe equation given below:.

ε =(zscaled dummy − zPolar−II

)× 100

zPolar−II

∣∣∣∣∣∣xscaled dummy=xPolar−II

(4)

3. Results

3.1. Polar-II scaled dummy models

Three new dummy FE models – 5F-S, 50F-S and 95M-S(Figure 5) – were obtained by scaling the Polar-II modelwith the factors calculated using Equations (1) and (2) andlisted in Table 1. Although the scaling of 5th F and 50thF dummy models involved almost uniform scaling (under1% variation between λz and λx = λy scaling factors), asubstantial variation (3.4%) was observed between scalingfactors in the x − y plane and the z direction of the 95th Mmodel.

The specific body measurements (Figure 3) of eachdummy model exhibit good agreement with the corre-sponding data of the ANSUR subjects. Polar-II dimensionsare similar (±2%) in all directions with the correspondingdimensions of the ANSUR 50th M. Although specificdimensions of the scaled dummy models in the z direction(Figure 6) are close to corresponding values of the ANSURsubjects (±2%), several variations (±6%) in the x − y

plane were recorded (Figure 7). All scaled dummy modelshave the same height and mass as their correspondingANSUR subjects (5th F, 50th F and 95th M).

Figure 5. Polar-II FE model and its scaled models: (a) 5th female(5F-S), (b) 50th female (50F-S) and (c) 95th male (95M-S).

3.2. Vehicle–dummy lateral impact simulations

Dummy postures relative to the vehicle at the time of headimpact for the original Polar-II dummy and the scaleddummy models are illustrated in Figure 8. In all cases, thecar–pedestrian dummy head impacts occurred in the wind-shield region, except for the 5th F dummy model for whichthe vehicle–head impact took place in the cowl region. ThePolar-II WAD-to-head contact obtained from the simulation(1959 mm) was within the range of Polar-II experimentaltest data (1947 ±21 mm) suggesting good kinematic pre-dictability of the FE dummy model (Figure 9). A linearvariation of WAD-to-head contact with respect to dummyheight was observed in both simulations using FE dummymodels (R2 = 0.996) and PMHS tests (R2 = 0.899) [10].However, the dummy WAD obtained from simulations andPolar-II test data [9] were lower than that of the correspond-ing value of the PMHS data (Figure 9).

Kinematic trajectories of the head CG, T1, T8 and pelvisCG together with their trajectory corridor (area bordered bythe extreme trajectories) are illustrated in Figures 10–13.All trajectory curves were calculated until head strike ina system fixed with respect to the vehicle’s motion, whichwas called the vehicle coordinate system. The origin of thevehicle coordinate system is defined by the intersection ofthe vertical line (z axis) passing through the initial position

Table 1. The factors used to obtain dummy FE models by scalingthe Polar-II FE model (50th percentile male).

Scale factors

Dummy model λz λx = λy

5th percentile female (5F-S) 0.873 0.87150th percentile female (50F-S) 0.93 0.93895th percentile male (95M-S) 1.069 1.107

International Journal of Crashworthiness 473

Figure 6. Specific dimensions (vertical direction) normalised tocorresponding dimensions of the 50th percentile ANSUR male[6]. Comparison between Polar-II scaled models and ANSURdata.

of the dummy head CG and the horizontal line (x axis) ofthe ground level [9]. A linear variation of upper-body tra-jectories is observed between the time the bumper strikesthe legs and the time the dummy pelvis flesh starts to inter-act with the leading edge of the hood. However, after thatpoint, a strong non-linearity was observed in all pelvis-CGtrajectories. Kerrigan et al. [8] have indicated that this maybe a function of the pelvis sliding over, penetrating into orbouncing off the hood depending on the extent of pelvicinteraction with the leading edge of the vehicle. The largestpelvis bounce was observed in the 5F-S dummy model forwhich some of the upper-body trajectories (pelvis CG, T1and T8) were closer or even slightly higher than the corre-sponding trajectories of a taller dummy model – 50F-S.

Upper-body trajectories of the 5F-S, 50F-S and 95M-Sscaled to the corresponding data of Polar-II are illustratedin Figures 14 and 15. These scaled curves have two portionsdelimited by specific events: (1) after bumper-leg contact,but before pelvis flesh-leading edge contact and (2) afterpelvis flesh-leading edge contact, but before head strike.

Figure 7. Specific dimensions (transversal plane) normalised tocorresponding dimensions of the 50th percentile ANSUR male[6]. Comparison between Polar-II scaled models and ANSURdata.

Figure 8. (a) 5F-S, (b) 50F-S, (c) Polar-II (50th percentile male)and (d) 95M-S dummy models at the pedestrian head-strike time.

Figure 9. Wrap around distance to head contact versus heightcurves. Comparison between Polar-II and dummy results, andPMHS data [10].

474 C.D. Untaroiu et al.

Figure 10. Head centre-of-gravity (CG) trajectory corridor andcomparisons between the Polar-II and scaled dummy models.

Figure 11. T1 trajectory corridor and comparisons between thePolar-II and scaled dummy models.

Figure 12. T8 trajectory corridor and comparisons between thePolar-II and scaled dummy models.

Figure 13. Pelvis CG trajectory corridor and comparisons be-tween the Polar-II and scaled dummy models.

Figure 14. Scaled head CG and T8 trajectory comparisons be-tween the Polar-II and scaled dummy models.

Figure 15. Scaled T1 and pelvis CG trajectory comparisons be-tween the Polar-II and scaled dummy models.

International Journal of Crashworthiness 475

Figure 16. The maximum error (%) of the scaled pedestriantrajectories.

As expected, in the first part, scaled trajectories matchedvery well with the corresponding trajectories of the Polar-II. However, significant differences between scaled trajecto-ries and corresponding 50th-percentile trajectories appearin the second region, especially close to the time of headstrike. The maximum error between these trajectories cal-culated as the percentage difference between vertical dis-placements at the same horizontal level are illustrated inFigure 16. As can be observed, the scaled trajectories of the5F-S dummy overestimate the corresponding Polar-II tra-jectories for all recorded upper-body segments, with the er-ror decreasing from pelvis to head region. A similar trend isalso observed for scaled trajectories of the other dummy thatis smaller than the Polar-II. However, although the pelvisCG/T8 scaled trajectories overestimate the correspondingPolar-II trajectories, T1/head-CG scaled trajectories under-estimate the corresponding Polar-II trajectories. In case ofthe largest dummy, 95M-S, the maximum error of upper-body scaled trajectories shows an opposite trend. Althoughthe pelvis CG, T8 and T1 underestimate the corresponding50th M trajectories, an overestimation is recorded in scaledtrajectory of the head CG. Overall, the maximum error ofall scaled trajectories varies from −12% (50th F head CG)to 11.6% (5th F pelvis CG).

4. Discussion

Three new FE-pedestrian dummy models were obtainedusing the validated FE model of Polar-II dummy asreference [21,22]. Uniform scaling in the vertical directionand transverse plane was used to obtain FE dummy modelscorresponding to three representative ANSUR subjects.Although several differences between specific dimensionsof scaled models and anthropometric data (maximum7% in transversal plane) were observed, global dummycharacteristics (height and mass), which may have a majorrole in pedestrian kinematics during a vehicle impact, werematched by this scaling technique. In addition, specificvertical dimensions of scaled dummies, which may have asignificant influence on the vehicle–pedestrian interaction

due to joint positions, showed minor differences (under2%) relative to anthropometric data. The scaling methodused in the current study to obtain new dummy models withdifferent anthropometry from a reference model showseasy implementation and relatively good results. Althoughdifferences between all specific dimensions of dummyand anthropometric data may be reduced by using morecomplex scaling techniques (c.f. Kriging method used forscaling a pelvis FE model by Besnault et al. [3]) withspecific scaling factors for each body segments, the effortto connect scaled body parts into the whole-dummy-scaledmodel will increase considerably. Due to lack of test databetween joint properties and anthropometry, joint stiffnessproperties of the new dummy models were obtained by scal-ing Polar-II stiffness curves [11]. Therefore, when this datawill be available in literature, an update of joint stiffnesscurves for all scaled models is recommended. A penalty-based formulation was used to model the contacts betweenthe dummy body parts and the vehicle front structure. Al-though the study on accurate contact compliance of impacttest simulations is still a developing area within the fieldof applied mechanics [18], the contact forces of the slidinginterfaces may depend on the contact formulation used inthe FE simulations. However, in this study, the simulationsof vehicle impacts with scaled dummy models have usedthe same contact definition and parameters as those used inthe previous validation simulations of Polar-II componenttests [21] and full-body impact tests [22]. Thus, the contactdefinition used should not significantly influence the scaleddummy kinematics obtained in this study.

A complex variation of pedestrian upper-body trajec-tories was observed in simulations of vehicle–pedestrianlateral impacts with different-sized dummies and the samevehicle model having a 40 km/h initial velocity. As reportedin the vehicle-PMHS impact tests [8,24], the dummy kine-matics depends significantly on the interaction of the hipand pelvis with the vehicle. Although the pelvis region ofthe dummy was essentially pinned for pelvis contact occur-ring close to the leading edge (i.e. the case of the shortestdummy), sliding was observed for a pelvis contact on thehood (i.e. the case of the tallest dummy) likely due to the lowslope of the hood. Dummy trajectory corridors, defined asthe surface that covers all dummy trajectories, are uniformduring the initial phase of impact but demonstrate differentbehaviour after pelvic interaction with the vehicle and be-fore head strike. Although the pelvis CG corridor narrowsafter the pelvis flesh starts to interact with the vehicle, asignificant extension of the head CG corridor is recordedfor the same period. Trajectory corridors with almost con-stant widths are recorded for T1 and T8 trajectory corridorsbefore head-strike event.

In dummy simulations, as in PMHS tests [9,10], linearrelationships were observed between WAD and pedestrianheight. However, the dummy models predict lower WADsthan the PMHS tests. A potential cause of these kinematic

476 C.D. Untaroiu et al.

differences between dummies and PMHS could be themusculature effects in the neck, spine and chest, whichhave been incorporated in the dummy models [4].

Dimensional-analysis scaling of dummy upper-bodytrajectories to the corresponding responses of the 50thM with respect to dummy height showed importantlimitations. A consistent error pattern in terms of verticaldisplacement for a certain horizontal displacement wasidentified between the scaled dummy trajectories based ondummy size and the location of recorded targets. The scaledtrajectories of smaller dummies tended to overestimate thecorresponding response of the 50th M model in regionsclose to pelvis, and to underestimate (or in the case of the5th F, to overestimate) the regions close to the head. Theopposite pattern was observed for the taller dummy model(95th M). Although the current study is limited to onlyone vehicle type, one vehicle speed and one pedestrianorientation, these observations suggest that the dimensionalanalysis scaling of upper-body trajectories must be usedcautiously with an awareness of the inherent assumptionsand limitations. Ultimately, the results suggest that anadvanced non-linear approach that may use optimisationtechniques [25,26] must be developed to predict the correctkinematics. Alternatively, a complete family of physicaland/or computational dummy models will be requiredto describe the complexity of the pedestrian–vehicleinteraction as a function of their relative geometry.

5. Conclusions

Three FE dummy models of different anthropometry wereobtained by scaling the Polar-II dummy – a pedestriandummy previously validated in pedestrian-impact condi-tions. All dummy models that were intended to representthe anthropometric breadth of the general adult populationhave similar mass and height characteristics as equivalentsubjects obtained from an anthropometric database. In ad-dition to stature and mass, several specific body measure-ments also showed agreement with the corresponding an-thropometric data. The dummy models were used to studythe influence of pedestrian anthropometry on kinematic re-sponses in vehicle–pedestrian impact simulations. Whereasthe WAD-to-head contact demonstrated a linear relation-ship with the dummy height, upper-body trajectories ap-peared to be influenced by the target location and dummysize. Thus dimensional analysis scaling of PMHS trajecto-ries to the corresponding 50th M trajectories has potentiallysignificant limitations in terms of reproducing the correctkinematics.

References[1] A. Akiyama, M. Okamoto, and N. Rangarajan, Develop-

ment and application of the new pedestrian dummy, Pro-ceedings of the 17th International Technical Conference onthe Enhanced Safety of Vehicles (ESV), Amsterdam, TheNetherlands, 2001, Paper 463.

[2] A. Akiyama, S. Yoshida, T. Matsuhashi, S. Moss, M.Salloum, H. Ishikawa, and A. Konosu, Development ofhuman-like pedestrian dummy, Proceedings of JSAE AnnualCongress, Chiyoda-Ku, Tokyo, Japan, 1999, Paper 9934546.

[3] B. Besnault, H. Guillemot, S. Robin, F. Lavaste, and J.Y. LeCoz, A parametric finite element model of the human pelvis,Proceedings of the 42nd Stapp Car Crash Conference, 1998,pp. 33–46.

[4] J. Crandall, K. Wiley, D. Longhitano, and A. Akiyama, De-velopment of performance specifications for a pedestrianresearch dummy, Proceedings of the 19th International Tech-nical Conference on the Enhanced Safety of Vehicles, Wash-ington, DC, 2005, Paper 05-0389.

[5] European Enhanced Vehicle-Safety Committee, Improvedtest methods to evaluate pedestrian protection afforded bypassenger cars, EEVC Working Group 17 Report, 2002.Available at http://www.eevc.org, (December 1998 withSeptember 2002 updates).

[6] C.C. Gordon, T. Churchill, C.E. Clauser, B. Bradtmiller,J.T. McConville, I. Tebbetts, and R.A. Walker, 1988 An-thropometric survey of U.S. army personnel: Methods andsummary statistics, Final Report (NATICK/TR-89/027) U.S.Army Natick Research Development and Engineering Cen-ter, Natick, MA, 1989.

[7] B.J. Ivarsson, J. Crandall, D. Longhitano, and M. Okamoto,Lateral injury criteria for the 6-year-old pedestrian – PartI: Criteria for the head, neck, thorax, abdomen, and pelvis,Proceedings of the SAE Congress, Detroit, MI, 2004, Paper2004-01-0323.

[8] J. Kerrigan, J. Crandall, and B. Deng, Pedestrian kinematicresponse to mid-sized vehicle impact, Int. J. Vehicle Saf. 2(3)(2007), pp. 221–240.

[9] J. Kerrigan, C. Kam, C. Drinkwater, D. Murphy, D. Bose,J. Ivarsson, and J. Crandall, Kinematic comparison of thePolar-II and PMHS in pedestrian impact tests with a sport-utility vehicle, Proceedings of the 2005 International Re-search Council on the Biomechanics of Impact (IRCOBI),Prague, Czech Republic, 2005a.

[10] J. Kerrigan, D. Murphy, C. Drinkwater, C.Y. Kam, D. Bose,and J. Crandall, Kinematic corridors for PMHS testedin full-scale pedestrian impact tests, Proceedings of the19th International Technical Conference on the EnhancedSafety of Vehicles (ESV), Washington, DC, 2005b, Paper05-0394.

[11] H.L. Langhaar, Dimensional Analysis and Theory of Models,John Wiley & Sons, New York, 1951.

[12] H.J. Mertz, Injury risk assessments based on dummy re-sponses, in Accidental Injury: Biomechanics and Preven-tion, 2nd ed., A.M. Nahum and J.W. Melvin, eds., Springer-Verlag, New York, 2002.

[13] Y. Mizuno, Summary of IHRA pedestrian safety WG activ-ities 2005 – Proposed test methods to evaluate pedestrianprotection affordable by passenger cars, Proceedings of the19th International Technical Conference on the EnhancedSafety of Vehicles (ESV), Washington, DC, 2005, Paper05–138.

[14] NASA Anthropometric Sourcebook, NASA Reference Pub-lication No. 1024, Houston, TX, 1978.

[15] National Highway Traffic Safety Administration (NHTSA)(2007). Available at http://www-nrd.nhtsa.dot.gov/Pubs/TSF2005.pdf

[16] Y. Okamoto, A. Akiyama, M. Okamoto, and Y. Kikuchi, Astudy of the upper leg component tests compared with pedes-trian dummy tests, Proceedings of the 17th InternationalTechnical Conference on the Enhanced Safety of Vehicles(ESV), Amsterdam, The Netherlands, 2001, Paper 380.

International Journal of Crashworthiness 477

[17] PAM System International, PAM-CRASH/PAM-SAFESolver Reference Manual, Version 2004, 2004.

[18] V. Rokach, On the accurate determination of contact com-pliance for impact test modeling, Int. J. Solids Struct. 40(11)(2003), pp. 2715–2729.

[19] L.W. Schneider, D.H. Robbins, M.A. Pflug, and R.G. Snyder,Development of an anthropometrically based design spec-ifications for an advanced adult anthropomorphic dummyfamily, Vol. 1–3, Final Report DOT-HS-806– 715, NationalHighway Traffic Safety Administration U.S. Department ofTransportation, Washington, DC, 1985.

[20] A. Seidl, RAMSIS – A new CAD tool for ergonomic anal-ysis of vehicles developed for the German automotive in-dustry, Automotive Concurrent/Simultaneous EngineeringSAE Special Publications, 1233 (1997), pp. 51–57.

[21] J. Shin, S. Lee, J. Kerrigan, K. Darvish, J. Crandall, A.Akiyama, Y. Takahashi, M. Okamoto, and Y. Kikuchi, De-velopment and validation of a finite element model for thePolar-II upper body, Society of Automotive Engineering,2006, Paper 2006-01-0684.

[22] J. Shin, C. Untaroiu, J. Kerrigan, J. Crandall, D. Subit, Y.Takahashi, A. Akiyama, Y. Kikuchi, and D. Longitano, In-vestigating pedestrian kinematics with the Polar-II finite el-ement model, Society of Automotive Engineering, 2007,Paper 2007-01-0756.

[23] Y. Takahashi, Y. Kikuchi, M. Okamoto, A. Akiyama, J.Ivarsson, D. Bose, D. Subit, J. Shin, and J. Crandall, Biofi-delity evaluation for the knee and leg of the Polar pedes-trian dummy, Proceedings of the 19th International Techni-cal Conference on the Enhanced Safety of Vehicles (ESV),Washington, DC, 2005, Paper 05-0280.

[24] C. Untaroiu, J. Kerrigan, C. Kam, J. Crandall, K. Yamazaki,K. Fukuyama, K. Kamiji, T. Yasuki, and J. Funk, Correlationof strain and loads measured in the long bones with observedkinematics of the lower limb during vehicle-pedestrian im-pacts, Stapp Car Crash J. 51 (2007a), pp. 433–466.

[25] C. Untaroiu, J. Shin, and J. Crandall, A design optimizationapproach of vehicle hood for pedestrian protection. Int. J.Crashworthiness 12(6) (2007b), pp. 581–589.

[26] C. Untaroiu, P. Allaire, and B. Foiles, Balancing of flexiblerotors using convex optimization techniques—generalizedmin-max LMI influence coefficient method, J. Vibration andAcoustics/ASME Trans. 130(2) (2008), pp. 02106–1:5.

[27] D.P. Wood and C.K. Simms, A hybrid model for pedestrianimpact and projection impact, Int. J. Crashworthiness 5(4)(2000), pp. 393–404.

[28] World Bank Group: Road Safety, (2007), Available at http://www.worldbank.org/html/fpd/transport/roads/safety.htm(accessed September 6, 2007).

[29] Y. Youn, S. Kim, C. Oh, M. Shin, and C. Lee, Research andrule-making activities on pedestrian protection in Korea,Proceedings of the 19th International Technical Conferenceon the Enhanced Safety of Vehicles (ESV), Washington, DC,2005, Paper 05–0117.

Appendix 1

Scaling of rigid partsA rigid part is usually defined in an FE model by its mass, m,and the components of the mass moment of inertia tensor, I, withrespect to a local coordinate system with the origin at the rigidbody CG. To find a relationship between the inertial properties ofa rigid body obtained by scaling and its initial inertial properties(in original configuration), the following theorem will be used.

Figure A1. Rigid body in initial and scaled configurations, aparticular case – the axes of local system are parallel to those ofthe global system.

Theorem: Assume a rigid body with the mass m and themass moment of inertia tensor I with respect to a local coordinatesystem oxyz (the direction of the local axes parallel to the globalaxes) and o(x, y, z) – the centre of gravity (Figure A1).

I =

Ixx Ixy Ixz

Iyx Iyy Iyz

Izx Izy Izz

(A.1)

Assume a linear transformation (scaling) with respect to the globalcoordinate system O1x1y1z1 with scale factors λx, λy, λz and aconstant mass density between models. Thus, the mass of thescaled model will be,

M = mλxλyλz (A.2)

and the components of the inertia tensor with respect to the newlocal-coordinate system O(λx · x0, λy · y0, λz · z0) will be

IXX = λxλyλz

(λ2

yJy + λ2zJz

)IYY = λxλyλz

(λ2

xJx + λ2zJz

)(A.3)

IZZ = λxλyλz

(λ2

xJx + λ2yJy

)IXY = λ2

xλ2yλzIxy

IYZ = λxλ2yλ

2zIxz (A.4)

IYZ = λxλ2yλ

2zIxz

where

Jx = (Izz + Iyy − Ixx)/2

Jy = (Izz + Ixx − Iyy)/2 (A.5)

Jz = (Iyy + Ixx − Izz)/2

Proof: Linear scaling (transformation) with respect to theglobal system O1x1y1z1will move each point P of the originalbody (�) which has a coordinate (x, y, z) with respect to thesystem oxyz and coordinate (x1, y1, z1) with respect to the sys-tem O1x1y1z1into the point into P′ of scaled body (�′), whichhas coordinate (X, Y , Z) with respect to the system OXYZ and

478 C.D. Untaroiu et al.

Figure A2. Rigid body in initial and scaled configurations, gen-eral case.

coordinate (X1, Y1, Z1) with respect to the system O1x1y1z1

(Figure A1).

X1 = λxx1 = λxx + λxxo1 = X + XO1

Thus, X = λxxSimilarly, it can be shown that Y = λyy, Z = λZzThus, the scaled diagonal components of inertia tensor will

be

IXX =∫ ′

�

(Y 2 + Z2)ρdV =∫

�

(λ2

yy2 + λ2

zz2)ρλxλyλz

dv = λxλyλz

(λ2

yJy + λ2zJz

)

Similarly, it can be shown that

IYY = λxλyλz

(λ2

xJx + λ2zJz

)IZZ = λxλyλz

(λ2

xJx + λ2yJy

)

The scaled off-diagonal components of inertia tensor will be

IXY =∫ ′

�

YZρdV =∫

�

λxλyxyρλxλyλzdv = λ2xλ

2yλzJxy

Similarly, it can be shown that

IYZ = λxλ2yλ

2zIxz

IYZ = λxλ2yλ

2zIxz

When the axes of the local coordinate system are not parallel tocorresponding axes of the global system (Figure A2), the compo-nents of mass inertia tensor in the new local system of a scaledrigid body OXYZ can be determined by the following procedure:

� Obtain the inertia tensor i ′ with respect to a system ox′y ′z′ withaxes parallel to the global coordinate system O1x1y1z1 fromthe mass inertia tensor i, from the initial coordinate systemoxyz.The inertia tensor i ′ will be

i ′ = Q · i · QT (A.6)

where Q is the transformation matrix (orthogonal matrix)

between oxyz and ox′y ′z′.� Obtain the inertia tensor I ′ of the scaled rigid body with respect

to a system OX′Y ′Z′ (with the axes parallel to the global systemaxes) using (A.3) and (A.4) equations.

� Obtain the inertia tensor I ′ with respect to a system OXYZ withaxes parallel to the initial local coordinate system oxyz.

Thus, the inertia tensor I will be

I = QT · I ′ · Q