COMPARISON OF SEVERAL METHODS FOR REAL PEDESTRIAN ACCIDENTRECONSTRUCTION

Jean-Philippe DepriesterCriminal Research Institute of the French National Gendarmerie(Institut de recherche criminelle de la gendarmerie nationale - IRCGN)FranceChristophe PerrinThierry SerreSophie ChalandonFrench National Institute for Transport and Safety Research (INRETS)FrancePaper Number 05 - 0333

ABSTRACT

The aim of this paper is to evaluate and compareseveral methods allowing the reconstruction of realaccidents involving pedestrians. These differentmethods have various levels of complications andare commonly used in primary or secondary safetyresearch. They can be classified into three cate-gories corresponding to their levels of complica-tions. The first class concerns ”simple” method-ologies based on an analytical or semi-analyticalapproach (”hand-calculi”) such as Searle’s model,Fall and Slide model, equations proposed by Rauet al., Simms et al., etc. The second one is morecomplicated and considers for example the pedes-trian as a single segment as described by Wood. Fi-nally, the last class contains the most complicatedapproaches and is based on three-dimensional multi-body models. Concerning this third class, this workhas been based on the PC-CrashR© and MadymoR©softwares. We have tested all of these methods forone of the most usual real car-to-pedestrian acci-dent configurations: frontal collision with pedestrianwrap trajectory. Data issuing from two real caseshave been used. They have been provided by an in-depth multidisciplinary accident investigation (psy-chology, technical, medical). Reconstructions arethus based on driver and witness statements, on ac-curate information relating to material evidence (e.g.skid marks, car damage, pedestrian injuries, throwdistance) and parameters fitted to vehicle and pedes-trian (e.g. vehicle shape, pedestrian anthropometry,etc). Results have been compared in terms of qual-ity of the reconstruction balanced by the limitationof the different methods. Evaluated elements are inparticular the speed of the vehicle, the final positionof the pedestrian, his kinematics, the impact pointson the car and injuries (when the method allowed it).

In parallel, methodologies have also been comparedqualitatively by establishing the necessary means toapply them. In this way, the potentiality of the meth-ods, their requirements (necessary input data, intooperation bringing time, computer time) have beenevaluated and reported in a general matrix. It al-lows us to summarize advantages and disadvantagesof the different methods.

INTRODUCTION

Several sorts of methods are commonly used to re-construct a real car-to-pedestrian accident. All ofthem are based on a ”model” which is the abstractsimplified representation of the reality. These mod-els are uncompleted and temporary results of thebuilding up of knowledge, which we have from areality. In agreement with this status, the models canbe more or less complicated according to modellingassumptions. Level of complication is so depen-dant on the mathematical hypothetic-deductive sys-tem, the input and output data definition, coherenceof the concepts taking into account the modelling,etc.We took an interest in comparing some different dy-namic hypothetic-deductive models (more precisely,some models of Newtonian Mechanics) used to rep-resent a real car-to-pedestrian collision in the mostusual configuration, i.e. a vehicle frontal impact witha pedestrian wrap trajectory. These models are basedon the Galilean-Cartesian paradigm which does nottake into account the complexity but the complica-tion. It was therefore interesting to observe if theycan propose a collision reconstruction (impact andpost-impact phases) fitted to the reality, even if theysplit up this complex event (a priori irreducible) intosimple problems which have to be treated one byone. It was relevant to determine in what propor-

Depriester 1

tion the increase in complication of a model, as usedin a secondary safety research way, can improve thefindings of the forensic and the in-depth investiga-tion fields.Chosen models have been classified into three cate-gories as regards their complication level:

- a first category concerning simple methodolo-gies based on an analytical or semi-analyticalapproaches (hand calculi): Searle’s model [13],Fall and slide model [4], equations proposedby Rau et al. [11], Toor and Araszewski [17],Simms et al. [15],

- a second one illustrated by the Wood’s SingleSegment Method [18] in which the pedestrianis considered as a single two-dimensional solid(a segment),

- a third one containing the most complicatedapproaches based on three-dimensional multi-body models of the pedestrian (used with PC-CrashR© [9, 10] or MadymoR© softwares).

Data issuing from two real and well-documented (byan in-depth multidisciplinary investigation) caseshave been used to test these different models. Theobjective consists in evaluating their potentiality andtheir requirements in terms of input, output, timeconsumption, etc.Beyond this comparison, this study provided the op-portunity for fruitful, scientific and methodologicalexchanges between connected ways which work to-wards improving the road safety policy with preven-tion or repression (from a forensic point of view) fi-nalities:

- in-depth multidisciplinary investigation field[5]: it is mainly orientated towards primarysafety and belongs to the research field with aclinical thought process. Based on the com-plexity paradigm, it studies the dysfunctionsof the Human-Vehicle-Environmentsystem andalso interactions between its components, fromseveral points of view: psychology, automotivemechanics, theoretical mechanics, road infras-tructure, medicine,

- biomechanics applied to the vehicle passivesafety research: it tries to understand, by ex-perimental (for example with Post Mortem Hu-man Subject - PMHS - tests) and theoretical ap-proaches, the relations between vehicle designand human injury mechanism (e.g. to establishthe influence of front bumper design on pedes-trian lower leg injuries),

- forensic kinematic road accident reconstructionwork: its aim is to provide the judicial court ev-idence relating to the crash sequence, the col-lision configuration, the impact configurationsand the respective behaviour and velocity of ve-hicles involved for each sequence.

IN-DEPTH ACCIDENT INVESTIGATION

With regard to real data, two cases of car-to-pedestrian collision with wrap pedestrian post-impact trajectory were selected. They issue fromthe in-depth investigation database of a researchunit (department of Accident Mechanism) belong-ing to the French National Institute for Transport andSafety Research (INRETS), which has been carryingout multidisciplinary studies on road accident sincethe beginning of the 80’s [6]. In these two cases the”point” of impact and the rest position of the pedes-trian were known on the accident scene.

In the first one, some skid marks are related to thefront track of the accident-involved vehicle. Thesetyre marks, the collision configuration, the final con-figuration and the ”point” of impact classified thiscase as a typical pedestrian wrap trajectory as wasdefined by Ravani et al [12]. Moreover, the tyremarks allow to determine the vehicle impact velocityby an alternative way expressing the kinetic energyloss as a function of the length of the marks and amean given deceleration.

In the second one, no material evidence was re-lated to the vehicle behaviour (deceleration begin-ning unknown) even if this vehicle is not equippedwith an Antilock Braking System (ABS) system.This case corresponds to a pedestrian wrap trajectoryregarding the vehicle-pedestrian contact sub-phase,but it is not typical (cf. relative rest position of ve-hicle and pedestrian). It represents a configurationin which (without a vehicle Event Data Recorder orreference crash tests) the modelling of the pedestrianimpact and post-impact trajectory seems to be theonly solution to determine the vehicle impact veloc-ity.

• case No 1:A January day, at 9 a.m., the weather is dry andsunny. A Citroen XantiaR© vehicle was drivingalong a boulevard in urban areas. In the mid-dle of its lane, the vehicle crashed into the rightside of an old man on a pedestrian crossing. Itbraked in emergency before impact. The pedes-trian died on the spot (see figure 1).

• case No 2:A June day, about 8 a.m., the weather is dryand sunny. A Renault TwingoR© vehicle was

Depriester 2

Human Vehicle EnvironmentDriver: Citroen Xantia emergency braking skid mark length: 14 m

declared driving speed: about 60 km/h mass: 1322 kg

Pedestrian: identified pedestrian impact areas: pedestrian throw distance: 16 mman, 85 years old, height 1.65 m, mass 75 kg low bonnetdeceased, open fracture of the right shoulder high bonnet

right ribs fractures windscreenfractures of the two femurs

face woundsCar approaching speed about 60 km/h, car impact speed about 55 km/h

Figure 1. Case No 1 (some in-depth investigation data).

driving through a village. It crashed into the leftside of an old woman on a pedestrian crossing.She died as the result of her injuries the nextday. The vehicle driver was a priori dazzled bythe sunlight. He did not see the pedestrian anddidn’t begin to brake before impact (see figure2).

MODELS

Simple Models

With regard to the first above-mentioned model cat-egory, some models with a simple mathematical for-malism (even if they are the results of a great amountof research) are considered. They can be classi-fied as analytical or semi-analytical methods. Mostof the analytical ones derive from fundamental me-chanics equations and correspond to a modelling of apedestrian post-impact trajectory part: airborne and

ground-pedestrian sub-phases (see figures 3 and 4).They are based on a 2D kinematics applied to thepedestrian centre of gravity. Two usual and well-known models have been chosen: ”fall and Slide”[4] and Searle’s ”fall, bouncing, sliding” model [13]which tries to take into account pedestrian bounceson ground (see figure 4). Their respective mathe-matical expression (equations 1 and 2) proposes arelation between pedestrian projection speedVp(tp),projection angleθ, a partial throw distanceD2 +D3,vertical distanceH2 between projection momenttp

and first contact on ground momenttg, gravitationalaccelerationg, and pedestrian friction coefficient ongroundµp.

D2 +D3 = Vp(tp)

√

2H2

g+

V2p (tp)

2 µp g(1)

Vp(tv) =

√

2µpg[(D2 +D3)−µpH2]

cos(θ)+µpsin(θ)(2)

Depriester 3

Human Vehicle EnvironmentDriver: Renault Twingo no emergency braking skid marks

declared driving speed: about 45 - 50 km/h mass: 885 kg rest position: 34 m from point of impact

Pedestrian: identified pedestrian impact areas: pedestrian throw distance: 19 mwoman, 69 years old, height 1.60 m, mass 60 kg bonnet

deceased, cranial trauma with loss of consciousness (> 24 h) windscreenhaematoma corpus callosum, sub-arachnoid haemorrhage

comminuted fracture of C2 vertebra, spleen fractureright forearm open fracture, right hip dislocation

right and left ischio-pubic fracture, right patella fractureright tibia and fibula open fracture

Car approaching speed about 45 - 50 km/h, car impact speed about 40 - 45 km/h

Figure 2. Case No 2 (some in-depth investigation data).

The Searle’s model allows us to provide a range ofpredicted pedestrian projection speeds for a givenpartial throw distance with a mathematical lowerbound (equation 3) and an arbitrary upper bound(equation 4).

min{Vp(tv)} =

√

2µpg[(D2 +D3)−µpH2]√

1+µ2p

(3)

max{Vp(tv)} =√

2µpg[(D2 +D3)−µpH2] (4)

These models are suited for typical wrap trajectories,considering the total throw distanceDt ≈ D2 + D3

and the vehicle impact speedV0 equal to:

V0 =1

PEVp(tp) (5)

wherePE is defined as an impact factor [4] or a pro-jection efficiency [17]. The use of this factor is ratherempirical.Semi-analytical models can be, on one hand, basedon experimental (with dummies and PMHS tests) re-sults or real well-documented collision data. Con-sidered as empirical, they use regression curves be-tween vehicle impact speed and total throw dis-tance without modelling projection processes. Onthe other hand, they can derive from a statistical ap-proach which is based on a variability study (col-lision parameters and circumstance factors) and onan analytical study of the three trajectory phases.These statistical models correspond to a mathemat-ical function with a simple formalism, but are re-sult of a great modelling way effort. Both empirical

Depriester 4

distance

time

D1 D2 D3

Dt

t−i

t+itp t−g

t+gtr

vehicle - pedestrian airborne ground-pedestrian sub-phase

post-impact phase

first impactwith the vehicle beginning

of airbonesub-phase

first contactwith the ground Rest

position

Figure 3. Schematic diagram of impact and post-impact phases corresponding to a wrap trajectory: phases,sub-phases, events, time and distance.

time

X

Z

⊗Y

−→Vp(tp)

θ

H2

1stb

ounc

e

2nd

boun

ce

nth

rebo

nd

rest

D2

D3,1 D3,2 D3,3 D3,n D3,n+1

D3

tp t−b,1

t+b,1

=

t−g

= t+gt−b,2

t+b,2

t−b,3

t+b,3

t−b,n

t+b,n

tr

airborne ground-pedestrian

bouncing sliding

(sub-phase)

Figure 4. Schema corresponding to the pedestrian centre of gravity trajectory in Searle’s model entitled”fall, bouncing and sliding” [13].

Depriester 5

X

Z

YO

x

z

y

⊕V0 h

dh

dh0

2bW

ldC

Figure 5. Schematic representation of vehicle and pedestrian segment at primary impact - illustration ofsome parameters used in Wood’s SSM equations.

X

Z

YO

⊕V(t−p )

⊕

x

z

Gp

ld

CISldCα

X

Z

θ(t−p )

Figure 6. Schematic representation of vehicle and pedestrian segment at secondary impact - illustration ofsome parameters used in Wood’s SSM equations.

Figure 7. General view of the multibody system (Madymo).

Depriester 6

and statistical models enable us to provide a range ofvalue with variable degrees of certainty. Three mod-els have been chosen: two empirical ones (cf. Rauet al. [11], (equation 6), Toor and Araszewski [17],(equation 7)) and a statistical one (cf. Simms et al.[15], (equation 8)):

Dt = 0.0052V20 +0.0783V0 (6)

with Dt in m andV0 calculed in km/h (±5 km/h).

V0 = 8.25D0.61t (7)

with Dt in m andV0 calculed in km/h (±7.7 km forthe 15th and 85th percentile prediction interval).

V0 =mv

mv +mpC [Dt −SO]D (8)

with Dt in m, V0 in m/s, and whereC, D, S0 are re-gression parameters (see [15] to chose a set of re-gression parameters functions of circumstances andcertainty degree in order to determine lower and up-per bounds) andmv (respectivelymp) is vehicle (re-spectively pedestrian) mass.

Advanced Models

To illustrate the second above-mentioned model cat-egory, one model has been chosen: Wood’s Sin-gle Segment Model (SSM) [18]. It is a mixed an-alytical formulation (equation 9) for the total post-impact trajectory. It models the vehicle-pedestriansub-phase considering that the pedestrian could berepresented by a single 2D segment (see figures 5and 6). Then, it models the following sub-phases(airborne and ground-pedestrian) with the Searle’sformula considering the pedestrian could be repre-sented by a weighted point. It makes the assump-tion that there are two vehicle-pedestrian impacts: aprimary impact relating to the pedestrian lower part(see figure 5) and a secondary impact relating to thepedestrian head (see figure 6).

Dt =V2

p (tp)(cos(θ)+µpsin(θ))2

2µpg

−k2 θ(t−p )

h+µp(H2) (9)

with k radius of segment gyration andh vertical dis-tance between pedestrian centre of gravity and up-per contact point on the vehicle front.Vp(tp)cos(θ),Vp(tp)sin(θ), θ(t−p ) andH2 are functions of vehiclemass, pedestrian segment geometry, secondary im-pact location, vehicle braking rate, vehicle impactspeedV0, etc. Segment angle at the beginning of sec-ondary impact,θ(t−p ), is more particularly a functionof the following parameters:

θ(t−p ) = f (θ(t−p ),V0,mv,mp,α,h,dh,bw,g) (10)

with α bonnet angle,dh distance between segmentcentre of gravity and top (head),bw segment half-width (see figures 5 and 6).It is worth noting that this model (with a complicatedformalism) was the theoretical base of some statisti-cal models (with a simpler formalism) (e.g. Wood’sHybrid Model [19]).

Complicated Models

Concerning the third category which referred tocomplicated model, two softwares have been used :the PC-Crash V6.0 one and the Madymo V6.0 one.PC-Crash software is a common commercial toolto reconstruct road accidents [3]. A part of this onehas been developed to take into account vehicle-pedestrian accidents with a specific pedestrianmultibody model and a single body vehicle whosegeometry shape is detailed [10]. This approachhas been validated with dummy crash-tests andwell-documented real cases [9]. The human bodymodel chosen in this paper included 20 bodiesinterconnected by 19 joints. Default joint andbody characteristics fitted to pedestrian mass andheight are provided in the software. Eight specificmeasurements were used to define the front vehiclegeometry. Accident configuration was fixed thanksto side pedestrian injuries and vehicle drivingdirection. The pedestrian position on impact waschosen standing up without speed and with both feetnear each other on the ground. The simulation wasiteratively used changing impact vehicle velocityand mean vehicle deceleration in order to ob-tain pedestrian throw distance and impact points onfront vehicle measured by the in-depth investigation.

The last method concerns the pedestrian acci-dent reconstruction using a typical multibodysoftware which is commonly used in passive safety.The Madymo software V6.0 has been employed todevelop the numerical models and to perform thesimulations [16]. The whole multibody model isdivided into two parts: the car and the pedestrian(see Figure 7). The human body model has beendeveloped by the University of Chalmers (cf. Yanget al. [21]), Faurecia (cf. Glasson et al. [7]) andvalidated in collaboration with the Laboratory ofApplied Biomechanics (see Cavallero et al. [2]).The original model represents a human body close tothe 50th percentile male: 1.75 m, 78 kg. It includes35 bodies with 35 joints and it is represented by 85ellipsoids. Joint and body segment characteristicsare based mainly on available biomechanical data(cf. Yamada [20] and Kajzer et al. [8]). The specificcharacteristics of this model concern its lower legbecause it is predictive of fractures.

Depriester 7

This model has already been validated qualitativelybut also quantitatively in pedestrian configurationby comparison with PMHS experimental testsperformed at INRETS-LBA (cf. Cavallero et al.[2]).Concerning the real accident reconstruction, themultibody model was first adapted to the corre-sponding configuration of the accident: orientationof impact, anthropometry of the victim, front shapeof the car. A first simulation has been performedon this starting configuration provided as being themost probable one by the in-depth investigation.Next, effects of some parameters such as carvelocity or pedestrian position on impact havebeen numerically studied in order to find the bestcorrelations with all indications produced by thein-depth analysis. All simulations which were notin accordance with the in-depth investigation wererejected. Finally, the configuration retained is closeto the presumed real accident conditions because itreproduces in particular the same impact points onthe car, the same injuries, and is according to thedriver statement (cf. Serre et al. [14]).

RESULTS

Results Obtained With Simplest Models

Concerning the case No 1 (Xantia) which corre-sponds to a typical wrap trajectory, analytical andsemi-analytical models were applied. Ranges of ve-hicle impact speeds were calculated for each methodconsideringDt ∈ [16 m,18 m] and eventual bounds(only given by Searle’s method and semi-analyticalones). They are synthesized in table 1. With pa-

Table 1.Results for case No 1 obtained with simplest

methods.method name range of vehicle impact

speedsV0 (km/h)fall and slide [42,45]

Searle [42,54]Rau et al. [43,57]

Toor and Araszewski [37,56]Simms et al. [42,53]

rameter valuesµp = 0.66 andH2 = 1 m, projectionefficiency (or impact factor) was set to 1 for ”falland slide” and Searle’s models. Regarding Simmset al.’s model, lower bound (respectively upper) so-called probable was chosen with regression param-eters: C = 3.2, D = 0.47, S0 = 1.6 (respectivelyC = 3.7, D = 0.47,S0 = 1.2).Concerning the case No 2 (Twingo) which does not

correspond exactly to a typical wrap trajectory, an-alytical methods were rejected. ConsideringDt ∈[17 m,20 m] and lower and upper bounds, semi-analytical methods were used in the same conditionsas for case No 1. Ranges of vehicle speeds are sum-marized in table 2. According to driver statement

Table 2.Results for case No 2 obtained with simplest

methods (semi-analytical models).method name range of vehicle impact

speedsV0 (km/h)Rau et al. [45,60]

Toor and Araszewski [38,59]Simms et al. [44,56]

(time-lag braking) and lack of tire marks on ground,low part of vehicle impact speed range would be se-lected.

Results Obtained With Wood’s SSM

Wood’s Single Segment Model assumes that the ve-hicle decelerates at impact. So it needs a vehicle co-efficient frictionµv to model the interaction betweenvehicles and pedestrians in terms of primary and sec-ondary segment impacts in vehicle-pedestrian sub-phase. Therefore, Wood’s SSM was only used forcase No 1. For this case, angleα was varied in therange [0.20 rad,0.30 rad] also using different valuesfor impact speedV0. Throw distancesDt calculatedbetween 16 m and 18 m allowed us to determine so-lutions in terms ofV0. Segment characteristics (lo-cation of gravity centre, radius of gyrationk) werefixed using the approach recommended by Burg andRau [1]. In this way,V0 was determined as belongingto the range [48 km/h,56 km/h].

Results Obtained With Multibody Models

Use of the PC-Crash Software

With PC-Crash software, the two cases were treatedusing its default multibody models. Two pedestrianmultibody models are included in the version 6.0 ofthis software. The one which was used has been val-idated with dummy crash-tests [9, 10] and seems togive for the two accident cases better results than theother one. The main differences are in the values ofthe friction coefficients between pedestrian/car andpedestrian/ground both equal to 0.6 for the modelwe have used and 0.4 and 0.2 for the second one.

Concerning the accident case No 1, the recon-struction results gave an impact speed of 48 km/h for

Depriester 8

Figure 8. Multibody simulation of the two real accidents with Madymo (line 1: case No 1 (Xantia), line 2:case No 2 (Twingo)) and PC-Crash (line 3: case No 1 (Xantia), line 4: case No 2 (Twingo)).

Table 3.synthetic table of vehicle impact speedV0 and pedestrian throw distanceDt obtained (or used) by the

different methods for real cases No 1 & 2.method method name case No 1 case No 2 comments

category V0 (km/h) Dt (m) V0 (km/h) Dt (m)

in-depth investigation 55 16 [40,45] 19 V0 evalued or calcu-lated, Dt measuredand evalued

simple

fall and slide [42,45] [16,18] rejected

Dt input,V0 output

Searle [42,54] [16,18] rejectedRau et al. [43,57] [16,18] [45,60] [17,20]

Toor and Araszewski [37,56] [16,18] [38,59] [17,20]Simms et al. [42,53] [16,18] [44,56] [17,20]

advanced Wood’SSM [48,56] [16,18] rejected

iterative process todetermineV0complicated

PC-Crash V6.0 48 16 35 20pedestrian modelMadymo V6.0 50 17 40 18

+ specific pedestrian model

Depriester 9

the car and a throw distance of 16 m for the pedes-trian. The calculated pedestrian final position wasquite good for the X axis (in the car way of travel-ling) but not so good for the Y axis (perpendicular tothe car way of travelling) with a difference of 3.5 mwith reality. In the simulation, the car stopped 3 mbefore the real rest position of the car. The calcu-lated pedestrian impact areas on the car were coher-ent with car deformations (see figures 1 and 8), ex-cept for the hip impact which was too high on thecar bonnet (T=40 ms). However, a relatively impor-tant penetration of the pedestrian into the car body(T=40 ms, for both cases) was observed showing thedifficulty of contact modelling. During the airbornesub-phase, the pedestrian trajectory corresponded toa somersault. Such pedestrian kinematics did notsquare with the Madymo simulation and neither withPMHS crash-tests for this range of impact speed.

For the accident case No 2, the impact speed ofthe car is calculated to 35 km/h and the pedestrianthrow distance to 20 m. For this case, both final po-sitions, car and pedestrian, were in good coherencewith the reality. The simulation provided impact ar-eas on the car coherent with those observed by in-depth investigation. As in the precedent case, thecalculated pedestrian trajectory corresponded also toan improbable somersault during the airborne sub-phase.

Use of the Madymo Software

With regard to the more complicated method basedon the Madymo software, the accident reconstruc-tion can be decomposed into two phases: the nu-merical model adaptation and the parametric study.Time consumed to perform both works is about 1week and numerical simulations last less than 1 houron a classical PC computer.Model adaptation concerns the representation of thecar, the pedestrian and the definition of an initialaccident configuration. Input data are thus a shortdescription of the anthropometry of the pedestrian(height and weight), geometry and mechanical char-acteristics of the car and an initial impact speed ofthe car to start the parametric study. This parametricstudy concerns mainly the velocity of the car, theposition of the pedestrian at impact and the pitchangle during the braking phase. Output data con-cerns qualitative information such as injuries butalso quantitative ones such as an accurate impactspeed of the car, impact areas of the pedestrian withthe car and the throw distance.Concerning the case No 1 (Xantia), a first simula-tion was performed on the configuration provided bythe in-depth investigation. Car speed was fixed to55 km/h. Pedestrian was placed in a walking posi-

tion from the left to the right side of the car in orderto be impacted on the right side of his body. Theconfiguration retained during the parametric studywas the one which reproduced closely the same im-pact area and the same injuries reported by the in-depth investigation. Four impacts during the simu-lated kinematic were observed: the lower leg on thebumper, the upper leg on the low bonnet, the shoul-der on the high bonnet, the head on the windscreen(see figure 8). Compared to the real injuries, tibiafractures were observed numerically on the third su-perior part but not on the femur. The retained impactspeed for the car was finally 50 km/h and the throw-ing distance 17 m.For case No 2 (Twingo), initial car speed was fixed to45 km/h and the pedestrian position placed in walk-ing posture with the right leg put forwards. Afterthe parametric study, the retained configuration pro-vided a kinematic in accordance with the in-depthaccident investigation (see figure 8). Same impactareas were found and fracture on the superior thirdof the lower leg was simulated. Car speed was fi-nally found equal to 40 km/h and the throw distanceclose to 18 m.

DISCUSSION

In order to compare the methods in terms of qualityof real accident reconstruction, their numericalresults corresponding to the case No 1 and No 2were reported on table 3.The case No 1 corresponds to a typical wrap tra-jectory for which skid marks of emergency brakingallow us to have a good estimation of the vehicleimpact speed (55 km/h). All the methods - exceptthe fall and slide model - provide a solution forvehicle speed on impact compatible or close to thein-depth investigation estimation.For the case No 2, the vehicle impact speed hasbeen chosen by in-depth investigation as equal to40-45 km/h. These values have been evaluated fromcomparison of vehicle damage with those observedon a crash-test (same vehicle, impact speed 32 km/h,PMHS) performed by INRETS-LBA. This caseNo 2 represents a non typical wrap trajectory (novehicle deceleration at impact or time-lag after im-pact) for which the analytical simple and advancedmodel (e.g. Searle’s model) are not suited in term ofsub-phase modelling. Therefore, they have not beenused contrary to the others methods (semi-analyticalsimple models and 3D multibody model). From atheoretical point of view, this case highlights limitsof the analytical methods (simple and advanced)which didn’t take into account enough the contactphase.

Depriester 10

Table 4.Comparative matrix for the different methods.

Complication method inputs outputs precision operation computer field applicationlevel name preconised bringing calculation

by author’s method time (rough) time

simple fall and slide [4] H2, D1 +D3, µp, PE V0 no element few minutes immediate typical wrap and for-ward trajectory

simple Searle [13] H2, D1 +D3, µp, PE min{V0}, max{V0} mathematical lowerbound and arbitraryupper ground

few minutes immediate typical wrap and for-ward trajectory

simple Rau et al. [11] Dt V0 ±5 km/h (corridor) few minutes immediate wrap trajectorysimple Toor and Araszewski

[17]Dt V0 ±7.7 km/h for the

15th and 85th per-centile predictioninterval,±12.2 km/hfor the 5th and 95th

one (corridor)

few minutes immediate wrap trajectory

simple Simms et al. [15] Dt , mv, mp, set of re-gression parameters

min{V0}, max{V0} upper and lowerbounds dependingon degree of cer-tainty (probable,normal, overall)

few minutes immediate wrap trajectory

advanced Wood’SSM [18] V0, mv, mp, α, h, dh,bw, k, µp, µv

V0, Dt see statistical modelsderived from it (e.g.[15])

half an hour few seconds for onestep of the iterationprocess

typical wrap trajec-tory

complicated PC-Crash V6.0pedestrian model[9, 10]

veh. geometry,mv,veh. deceleration,V0, impact areas,veh. and ped. posi-tions on impact, ped.height,mp, Dt

V0, impact areas,veh. and ped. posi-tions on impact,Dt ,3D kinematics anddynamics

qualitative and quan-titative validationbased on input/ouputparameters compari-son

one day few minutes for onestep of the iterationprocess

frontal impact + pos-sible use for otherconfigurations withattention to the vali-dation

complicated Madymo V6.0 +specific pedestrianmodel [16, 21, 7]

veh. geometry,mv,veh. deceleration,V0, impact areas,veh. and ped. po-sitions on impact,ped. height,mp, Dt ,injuries

V0, impact areas,veh. and ped. posi-tions on impact,Dt ,3D kinematics anddynamics, injuries

qualitative and quan-titative validationbased on input/ouputparameters compari-son

one week less than an hour fora step of the iterationprocess

frontal impact + pos-sible use for otherconfigurations withattention to the vali-dation

Depriester

11

Reconstructions performed with PC-Crash andMadymo allow us to compare also kinematics. Ithas been observed good accordance in the bothtiming of the vehicle-pedestrian sub-phases (cf.figure 8).

Concerning the comparison of the differentmethodologies, some criteria have been reported ina general matrix and summarized in table 4. It con-cerns their requirements (inputs, outputs, computertime, into operation bringing time), their precision(if it is defined by their reference authors) and theirfield of application (validity domain). Concerningthe operation bringing time, it includes, if necessary,the time for measuring specific element such asthe vehicle geometry, preparing the adaptation ofthe pedestrian multibody model, performing theparametric study with the simulation tool, operatingresults. This general matrix illustrates the relationbetween the complication increase of mechanicalmodel and the improving of findings related toparticular car-pedestrian collisions with a wraptrajectory.

In the first category of methods, analytical andsemi-analytical models with simple formalism andvery few inputs propose relations (sometimes withlower and upper bounds) between vehicle impactspeed and pedestrian throw distance projection. Inthese relations, the pedestrian position on impactand the vehicle geometry for example are not explic-itly used. They rather contribute to the formulationassumptions (e.g. definition of the collision type asa wrap trajectory) which allows us to utilize thesesimple methods.

In the second category, some more advancedtwo-dimensional methods like the Wood’s SSMtry to relate vehicle impact deceleration and speedon impact, throw distance and a few parametersconcerning respectively pedestrian and vehiclegeometry. The equations obtained in that way aresolved iteratively in order to determine an accuratevehicle impact speed. Their assumptions are toosimplistic to describe exactly the sub-phase wherethe pedestrian is in contact with the vehicle. Astheir equations are moreover difficult to solve, eitherthey are used as a theoretical base for statisticalmethods (with simpler formalism), or the use ofmore complicated methods is preferred.

In the third category, the most complicated meth-ods, i.e. the three-dimensional multibody models(used in biomechanics applied to the vehicle passivesafety), allows us to relate directly: pedestrianthrow distance, vehicle acceleration and velocityduring the vehicle-pedestrian contact sub-phase,collision configuration, impact areas on the vehicle

front, pedestrian injuries. Their solution in thecontext of a real accident reconstruction impliesan iterative process which is due to a parametricstudy. This parametric study has been done for thePC-Crash method only for the car impact speedwhen it has been done for more variables for theMadymo method: car speed, pitch angle of the cardue to braking phase, pedestrian position on impact[14]. Validation of real accident reconstructionsperformed by these softwares is made mainly withthe pedestrian throw distance and the location of theimpact points on the car. The Madymo method canallow us to add a validation regarding pedestrianinjuries with specific biomechanics models. Theapplication of PC-Crash and Madymo methods intwo simple real cases of wrap trajectory highlighted:

- the three-dimensional multibody models are thebest-fitted methods to describe the complexityof these collision events,

- they are rather time consuming,

- their accurate and complete utilization is stillthe appanage of parameterization specialists (invehicle design, in biomechanics, in medicine,...) who know about or take part in their exper-imental validation.

The PC-Crash software uses an important numberof parameters to model a pedestrian accident. Mostof them are given by default with the software andthe results of the accident reconstruction are verysensible to their variations. The apprehension ofwhat they represent of the reality of these complexphenomena is often difficult. Thus the use, ap-parently ”easy”, of the PC-Crash software by nonspecialist users can be dangerous. The PC-Crashtechnical guideline should be more detailed onthe definitions, descriptions, and influences ofthe numerous parameters needed to compute areconstruction. The Madymo software methodneeds also and even more numerous parameters.But because this software is more complicated, itsuse is reserved to experts in the field of accidentanalysis and biomechanic.

From a general point of view, the increasein complication of the models corresponds so to thedirect use of supplementary material data either asinput data (e.g. very detailed geometrical vehicleand pedestrian description) or as validation param-eters (e.g. calculated impact areas on the vehicle)which are the simulation results at a step of an itera-tive process. This approach is particularly pertinentfor the in-depth investigation and the forensic fieldin order to take advantage of the most material

Depriester 12

evidence possible by means of hypothetic-deductivemodels. The adequate use of the multibody modelscorresponds however to update, multidisciplinaryand extensive knowledge with regard to input data(e.g. human body segment inertial parameters) andvalidity domain of different modellings (e.g. contactmodelling between ellipsoids, parts of multibodymodel).

CONCLUSION

This work was focused on the comparison of differ-ent methods allowing real pedestrian accident recon-structions corresponding to a wrap trajectory. Thiskind of trajectory can be modelled in terms of ve-hicle impact speed and throw distance with simpleformalism models. Methods with different levels ofcomplication were tested with two sets of real dataissued from in-depth investigation. They have beenclassified into three categories: simple, advancedand complicated. For this well-known configura-tion of vehicle pedestrian collision, the aim was toillustrate in what proportion the increase in compli-cation of a model can improve results in terms ofquality. Simple and advanced methods give good re-sults but their validity domain are restrictive (wraptrajectory and forward projection). The increase incomplication of the models corresponds to the di-rect use of supplementary material data either as in-put data (e.g. very detailed geometrical vehicle andpedestrian description) or as validation parameters(e.g. calculated impact areas on the vehicle). In par-ticular the 3 dimensional multibody models initiallydeveloped for passive safety research allow us to re-late most of relevant parameters (speed vehicle, im-pact areas, injuries, ...) of the pedestrian accident.Their applications to the reconstruction are very in-teresting in the in-depth investigation and forensicfields. It would enable us to achieve reconstructionof other types of collision involving pedestrian (e.g.vehicle frontal impact with fender vault post-impacttrajectory, vehicle corner impact), even if there is alack of material evidence (e.g. no skid mark for anABS equipped vehicle). That could be possible if themultibody models could be refined and validated forthese sorts of real collision configurations. This val-idation could be based on experimental tests (for ex-ample crash-tests using PMHS) reproducing real ac-cident configuration instead of standard ones. Con-nected to the complementary vehicle primary andpassive safety, and the forensic road accident recon-struction, this work would lead to the improvementof the pedestrian safety. It also could be extended toother vulnerable road users such as bicyclists.

ACKNOWLEDGEMENTS

This work is partly supported by the French Trans-port Ministry (DSCR) and is partly included in theframework of the APPA project (Amlioration de laProtection du Pieton lors de collision par des Auto-mobiles).

REFERENCES

[1] BURG and RAU. 1981. Handbuch derVerkehrsunfallrekonstruktion. Verlag Informa-tion Ambs Gmbh.

[2] C. CAVALLERO , D. CESARI, M. RAMET,P. BILLAULT , J. FARISSE, B. SERIAT-GAUTIER, and J. BONNOIT. 1983. Improve-ment of pedestrian safety: Influence of shapeof passenger car-front structures upon pedes-trian kinematics and injuries: Evaluation basedon 50 cadaver tests.ASME Paper, (830624).

[3] Dr. Steffan Datentechnik, LINZ AUSTRIA. july1999. PC-CRASH- A simulation program forvehicle accidents - Version 6.0, 6th edition.

[4] Jerry J. EUBANKS et Paul F. HILL . 1998.Pedestrian Accident Recontruction and Litiga-tion. Lawyers & Judges Publishing Co, Inc.,second edition.

[5] F. FERRANDEZ, T. BRENAC, Y. GIRARD,D. LECHNER, J.-L. JOURDAN, J.-E. MICHEL,and C. NACHTERGAELE. 1995. L’ etudedetaillee d’accidents orientee vers la securiteprimaire. Presses de l’Ecole Nationale desPonts et Chaussees.

[6] Y. G IRARD. 1993. In-depth investigation ofaccidents: the experience of INRETS at Salon-de-Provence. InInternational congress onSafety evaluation of traffic systems: traffic con-flicts and other measures, ICTCT Congress, inSalzburg.

[7] E. GLASSON, J. BONNOIT, C. CAVALLERO ,and F. BASILE. 2000. A numerical analysisof the car front end module regarding pedes-trian lower limb safety. InPart of VehicleSafety 2000, International Conference, num-ber C567/016/2000, pages 79–91. Institutionof Mechanical Engineers.

[8] Janusz KAJZER, Yasuhiro MATSUI, HirotoshiISHIKAWA , Gunter SCHROEDER, and UlrichBOSCH. 1999. Shearing and bending effectsat the knee joint at low speed lateral loading.ASME Paper, (1999-01-0712).

Depriester 13

[9] Andreas MOSER, Heinz HOSCHOPF, HermannSTEFFAN, and Gustav KASANICKY . 2000.Validation of the PC-Crash pedestrian model.ASME Paper, (2000-01-0847).

[10] Andreas MOSER, Hermann STEFFAN, andGustav KASANICKY . 1999. The pedestrianmodel in PC-Crash - the introduction of a multibody system and its validation.ASME Paper,(1999-01-0445).

[11] Hartmut RAU, Dietmar OTTE, and BurkhardSCHULZ. 2000. Pkw-Fußgangerkollisionenim hohen Geschwindigkeitsbereich Ergeb-nisse von Dummyversuchen mit Kollisions-geschwindigkeiten zwischen 70 and 90 km/h.Verkehrsunfall und Fahrzeugtechnik, 12:341–350.

[12] B. RAVANI , D. BROUGHAM, and R. T. MA-SON. 1981. Pedestrian post-impact kinematicsand injury patterns.ASME Paper, (811024).

[13] John A. SEARLE and Angela SEARLE. 1983.The trajectories of pedestrians, motorcycles,motorcyclists, etc., following a road accident.ASME Paper, (831622).

[14] T. SERRE, C. PERRIN, M. BOHN, and C. CAV-ALLERO. 2004. Detailed investigations andreconstructions of real accidents involving vul-nerable road users. InExpert Symposium onAccident Research 2004.

[15] C.K. SIMMS, D.P. WOOD, and D. G. WALSH.2004. Confidence limits for impact speedestimation from pedestrian projection dis-tance. International Journal of Crashworthi-ness, 9(2):219–228.

[16] TNO Automotive. 2001. Theory manual -Madymo V6.0.

[17] Amrit TOOR and Michael ARASZEWSKI.2003. Theoretical vs. empirical solutions forvehicle/pedestrian collisions.ASME Paper,(2003-01-0883).

[18] D.P. WOOD. 1988. Impact and movement ofpedestrians in frontal collisions with vehicles.In Proceedings of Institution Mechanical Engi-neer, volume 202 noD2, pages 101–110.

[19] D.P. WOOD and C.K. SIMMS. 2000. A hy-brid model for pedestrian impact and projec-tion. International Journal of Crashworthi-ness, 5(4):393–403.

[20] YAMADA . 1970. Strength of biological mate-rials. Williams & Wilkens.

[21] J.K. YANG, Heinz LOVSUND, C. CAVALLERO ,and J. BONNOIT. 2000. A human body3D mathematical model for simulation of car-pedestrian impacts.Journal of Crash Preven-tion and Injury Control, 2(2):131–149.

Depriester 14