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Accident Analysis and Prevention 45 (2012) 342– 353

Contents lists available at ScienceDirect

Accident Analysis and Prevention

jo ur n al hom ep a ge: www.elsev ier .com/ locate /aap

edestrian head translation, rotation and impact velocity: The influence ofehicle speed, pedestrian speed and pedestrian gait

.R. Elliotta, C.K. Simmsa,∗, D.P. Woodb

Department of Mechanical & Manufacturing Engineering, Trinity College, Dublin, IrelandDenis Wood Associates, Dublin, Ireland

r t i c l e i n f o

rticle history:eceived 16 June 2011eceived in revised form 21 July 2011ccepted 31 July 2011

eywords:ehicle–pedestrian collisionait cycleransverse offsetead rotationead impact speedehicle speed

a b s t r a c t

In road traffic collisions, pedestrian injuries and fatalities account for approximately 11% and 20% ofcasualties in the USA and the EU, respectively. In many less motorised countries, the majority of victimsare pedestrians. The significant influences of vehicle speed, pedestrian speed and pedestrian gait onpedestrian post-impact kinematics have been qualitatively noted in the literature, but there has been noquantitative approach to this problem. In this paper, the MADYMO MultiBody (MB) pedestrian model isused to analyse the influences of vehicle speed, pedestrian speed and pedestrian gait on the transversetranslation of the pedestrian’s head, head rotation about the vertical head axis and head impact velocity.Transverse translation has implications for injury severity because of variations in local vehicle stiffness.Head rotation is related to pedestrian stance at impact, which is known to affect the kinematics of acollision. Increased head impact velocity results in greater head injury severity. The results show thattransverse translation of the head relative to the primary contact location of the pedestrian on the vehicle

edestrian speedollision reconstruction

decreases with increasing vehicle speed and increases linearly with increasing pedestrian speed. Headrotation decreases with increasing vehicle speed and increases linearly with increasing pedestrian speed,but these variations are small. The range of head rotation values decreases with increasing vehicle speed.Head impact velocity increases linearly with vehicle speed and is largely independent of pedestrianspeed. Transverse translation, head rotation and head impact velocity all vary cyclically with gait inclearly definable patterns.

. Introduction

The World Health Organisation has reported that 1.2 millioneople die in road traffic accidents every year (WHO, 2009). Pedes-rians are a significant proportion of road fatalities (OECD, 2008).reventing or reducing the effects of these collisions requires a clearnderstanding of the collision events. This is generally pursuedhrough simulation using either physical or computational mod-ls. While physical testing using cadavers or dummies carries clearenefits (Kerrigan et al., 2005, 2009; Kerrigan and Crandall, 2007,008; Serre et al., 2007), the very high cost associated with thispproach means that only a limited number of collision scenar-os can be investigated. In contrast, sophisticated computational

odels allow complex vehicle–pedestrian collisions to be modelledver a broad range of input conditions to quantify the influence

f the many input parameters in vehicle pedestrian collisions. Inecent years, MADYMO has been the most popular modelling toolor pedestrian collision and injury evaluation.

∗ Corresponding author. Tel.: +353 877529208; fax: +353 16795554.E-mail address: csimms@tcd.ie (C.K. Simms).

001-4575/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.aap.2011.07.022

© 2011 Elsevier Ltd. All rights reserved.

The MADYMO pedestrian model (MADYMO, 2009) (hereafterreferred to as ‘the MADYMO pedestrian model’) implemented in theMultiBody (MB) software code Madymo is frequently employed forkinematic predictions (e.g. Simms and Wood, 2006a,b,c; Untaroiuet al., 2009), but other pedestrian models, with a different basis tothe Madymo pedestrian model, have also been implemented usingthe MADYMO environment (e.g. Svoboda et al., 2003; Andersonet al., 2005a,b; Linder et al., 2005a,b; Guo et al. 2006; Yao et al.,2008a,b). Pedestrian models in MADYMO have been comparedto data from staged tests using Post Mortem Human Subjects(PMHS), dummy and headform tests. The MADYMO pedestrianmodel response has been compared to PMHS test data for a varietyof impact conditions (van Hoof et al., 2003). The global kinemat-ics and body segment trajectories of the model generally showedgood agreement with the test data, with a ‘global correlation score’of over 90% achieved for head impact locations. For bumper forcesand accelerations (head, chest, pelvis, and legs), the global correla-tion scores were lower (47–64%). Leglatin et al. (2006) found that

the overall kinematics of the MADYMO pedestrian model matchedcollision sequences from PMHS tests. According to Anderson et al.(2005a,b), the response of their pedestrian model in MADYMOwas generally in accordance with head velocity corridors from

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For a pedestrian speed of 1.4 m/s, simulations were carried outat a greater number of vehicle speeds in order to obtain a set ofresults representative of vehicle–pedestrian impacts at a typicalpedestrian walking speed (Fugger et al., 2000). In all simulations,

J.R. Elliott et al. / Accident Analy

MHS tests. However, the results of this comparison were nothown. Pedestrian models implemented in MADYMO were used toeconstruct headform impact tests (Anderson et al., 2005a,b) and

dummy test (Svoboda et al., 2003). The head acceleration curvesrom these reconstructions had similar magnitudes and shapes tohe data from the tests.

Many attempts have been made to validate pedestrian models inADYMO by reconstructing real collisions. Linder et al. (2005a,b)

sed a pedestrian model formulated in MADYMO to reconstructix collisions. The responses were compared to the collision datan terms of head impact location (visual comparison), pedestrianhrow distances (within 20% of the estimated values from post-ollision data) and head injury severity trends (HIC and 3 ms linearcceleration). Yao et al. (2008a,b) used a pedestrian model inADYMO to reconstruct 10 collisions. The simulations comparedell with the collision data in terms of pedestrian wrap-aroundistance (errors of 2–4%) and pedestrian throw distance (errors of–16%). Guo et al. (2006) implemented a pedestrian model withhinese anthropometry in MADYMO and reconstructed a real-orld collision using CCTV footage of the event. The simulationatched the actual collision in terms of throw distance (6% error)

nd head impact location on the vehicle (visual comparison). A highIC score of 4328 for the head-ground impact was consistent with

he fatal brain injury sustained by the pedestrian.The MADYMO pedestrian model has very recently been com-

ared to staged tests and a real collision in terms of head trajectory,ongitudinal and transverse head translation relative to the primaryontact location of the pedestrian on the vehicle, impact location onhe head, head impact time and head impact velocity (Elliott, 2011).he model was shown to reproduce staged PMHS and dummy testsn terms of head trajectory (4 cases: mostly within 10%), longitu-inal offset (4 cases: all within 17%), transverse offset (2 cases: 0%nd 19% error, respectively), impact location on the head (7 cases:ithin 45◦ in the majority of cases), head impact time (19 cases:ean absolute difference of 9.3 ms) and head impact velocity (15

ases: mean absolute difference of 1.8 m/s). This is the first time thathe predictive capabilities of the MADYMO pedestrian model haveeen evaluated with regard to transverse motion and 3D rotationf the pedestrian, and the results show that, despite limitations,he model can be used to quantitatively test the influences of pre-mpact vehicle speed, pedestrian speed and pedestrian stance onedestrian kinematics during impact.

The MADYMO pedestrian model has previously been applied tovaluate the influence of stance on vehicle–pedestrian collisions.imms and Wood (2005, 2006a,b,c) predicted that, for pedestri-ns facing the vehicle or rotated 45◦ towards the vehicle, impactccurs with the face and/or front of the skull. For pedestrians fac-ng directly sideways to the vehicle with the legs together, theehicle impact with the head occurs with the side of the skull. Ifhe struck leg is lagging, the pedestrian tends to rotate such thathe front of the body contacts the front of the vehicle, i.e. ante-ior head injuries. If the struck leg is leading, the pedestrian tendso rotate in the opposite direction such that the back of the bodyontacts the front of the vehicle, i.e. posterior head injuries. How-ver, there was no quantification of these findings for intermediateait positions, since at the time the MADYMO pedestrian modelad not been validated for three-dimensional motion. Simms andood (2006a,b,c) found that the magnitude of head 3 ms accelera-

ion scores predicted by the MADYMO pedestrian model varies withre-impact stance by up to 30%. Anderson et al. (2005a,b) imple-ented a pedestrian model in MADYMO and found that the HIC

nd peak head acceleration are sensitive to the initial stance of a

edestrian model.

Although the above review shows that sophisticated modelsave been applied to give qualitative descriptions of 3D pedes-rian motion, the influences of vehicle speed, pedestrian speed

Prevention 45 (2012) 342– 353 343

and pedestrian gait on pedestrian post-impact kinematics havenot been quantified. Therefore, in this paper, the recently validatedMADYMO pedestrian model (Elliott, 2011) is used to evaluate theinfluences of vehicle speed, pedestrian speed and gait on the trans-verse translation of the pedestrian’s head, head rotation about thevertical head axis and head impact velocity. Transverse transla-tion has implications for injury severity because of variations inlocal vehicle stiffness (Simms and Wood, 2009). Head rotation isrelated to pedestrian stance at impact which is known to affect thekinematics of a collision (Simms and Wood, 2006a,b,c). Increasedhead impact velocity results in greater head injury severity (Mizunoet al., 2001). Head translation and head rotation can sometimesbe measured from post-accident vehicle damage and pedestrianinjury patterns, while head impact velocity is a key determinantof injury outcome. The results help to improve our understand-ing of the vehicle–pedestrian collision mechanism and subsequentpedestrian injury patterns. It is suggested that the estimated impactlocation on the head, combined with measurable post-collisionvehicle damage, could be used in future as additional informationfor reconstruction of the pre-impact speed of the pedestrian.

2. Methods

2.1. MADYMO pedestrian model

The MADYMO pedestrian model (MADYMO, 2009) consists of52 rigid bodies. The outer surface is described by 64 ellipsoids and2 planes. It is available in five body sizes: 3-year-old child, 6-year-old child, small female (5th‰), mid-size male (50th‰) and largemale (95th‰), and may also be scaled using stature and mass. Forthis paper, the standard 50th‰ male pedestrian model was used,with an orientation perpendicular to the direction of vehicle travel(i.e. the pedestrian was struck from the side).

2.2. Inferences from model: head rotation, translation and impactvelocity

MADYMO simulations of a side facing pedestrian struck by apassenger car were implemented for three pedestrian speeds andvehicle speeds ranging from 5 to 17.5 m/s as detailed in Table 1.

Fig. 1. MADYMO vehicle–pedestrian collision.

344 J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353

Table 1Setup of MADYMO simulations.

Pedestrian speed (m/s) Vehicle speed (m/s) Pedestrian stance Pedestrian type Vehicle type

10 stances fromUntaroiu et al.(2009)

50th‰ male Mid-sized sedan

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he pedestrian was struck laterally on the left side by an unbrakedid-sized sedan (similar to the mid-sized sedan reported in Subit

t al., 2008) consisting of four extruded cylinders and five ellip-oids (Fig. 1). The setup of the MADYMO simulations is describedn Appendix A.

Gait cycle stances from Untaroiu et al. (2009) were imple-ented. These are shown in Fig. 2. The start of the gait cycle (0%)

orresponds to right heel strike. The cycle can be broadly dividednto two regions as shown: 0–15% and 70–100% corresponding totruck (i.e. left) leg lagging (anterior head impact) and 15–70% cor-esponding to struck leg leading (posterior head impact).

The influences of vehicle speed, pedestrian speed and pedes-rian gait on the transverse translation of the pedestrian’s head,ead rotation about the vertical head axis and head impact veloc-

ty relative to the vehicle were evaluated. Due to the cyclic nature ofalking, periodic Fourier curve fitting was used to obtain a contin-ous variation of the output parameters over the entire gait cycle.

.3. Definitions of transverse offset, head rotation and headmpact velocity

The transverse offset between the primary and secondarympact locations of the pedestrian on the vehicle is defined ashown in Fig. 3.

The sign convention for head rotation about the vertical headxis is shown in Fig. 4, which shows that 0◦ corresponds to nootation, positive rotations correspond to anterior head impact andegative rotations correspond to posterior head impact. A rotationf +45◦ for a pedestrian struck on the left side is shown by way ofxample.

The head impact velocity is defined as the absolute value of theelocity difference between the head and the vehicle at the instantf head contact with the vehicle.

. Results

.1. Transverse offset

The transverse offset (defined in Fig. 3) varies throughout theait cycle. The resulting mean transverse offset as a function of

ehicle speed and pedestrian speed is shown in Figs. 5 and 6,espectively. The transverse offset decreases with increasing vehi-le speed and increases with increasing pedestrian speed. In Fig. 5,he responses for a stationary pedestrian (0 m/s speed) show that

Fig. 2. Gait cycle stances adapted

Fig. 3. Transverse offset between primary (leg) and secondary (head) impact loca-tions of the pedestrian on the vehicle.

the mean transverse offset is practically independent of vehiclespeed. If the pedestrian is moving transversely across the vehi-cle, the mean transverse offset decreases with increasing vehiclespeed, as shown by the responses for pedestrian speeds of 1.4 m/sand 2.8 m/s. Fig. 6 shows that the relationship between mean trans-verse offset and pedestrian speed is highly linear at all pedestrianspeeds.

For a given vehicle and pedestrian speed, the transverse off-set responses vary cyclically with gait (Figs. 7 and 8). To obtain acontinuous variation of transverse offset over the entire gait cycle,third-order Fourier curves were fitted. The Fourier coefficients andR2 values are given in Appendix B (Table 2). The responses for astationary pedestrian struck by a vehicle at 5, 10 and 15 m/s are pre-sented in Fig. 7. As stated above, the transverse offset is practicallyindependent of vehicle speed in the case of a stationary pedestrian.Therefore, in this case a single Fourier curve was fitted to all thedata at the three vehicle speeds as shown (R2 = 0.95).

The Fourier curves for a pedestrian speed of 1.4 m/s are shownin Fig. 8. The direction of increasing vehicle speed is indicated by

an arrow. The Fourier patterns shown are seen to be similar at allvehicle speeds. For clarity, only the MADYMO responses for a vehi-cle speed of 5 m/s are shown, but the minimum R2 for the Fourierfitting was 0.99. The transverse offset response for a vehicle speed

from Untaroiu et al. (2009).

J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353 345

+90◦: front of head, −90◦: back of head.

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TF

Fig. 4. Head rotation (plan view)

f 5 m/s and 80% gait was unusually high due to the interactionetween the pedestrian’s abdomen and the bonnet, which causedhe pedestrian to roll across the bonnet, resulting in a higher trans-erse offset. This did not occur at any other vehicle or pedestrianpeeds. The case was therefore excluded from the Fourier curvetting.

.2. Head rotation

The amount of head rotation between first contact between theehicle and the legs and the time of head contact with the vehiclearies throughout the gait cycle. The resulting mean head rotation ishown in Figs. 9 and 10 as a function of vehicle speed and pedestrianpeed, respectively. A head rotation result of 0◦ means no rotation,.e. the location marked 0◦ on the left side of the head in Fig. 4 strikeshe vehicle. Positive rotations correspond to anterior head impactnd negative rotations correspond to posterior head impact. Theertical axis limits of ±90◦ represent rotations of 90◦, i.e. impactst the front or back of the head, as shown in Fig. 4.

Fig. 9 shows that the mean head rotation across the gait cycles largely independent of vehicle speed when the pedestrian is

tationary. The mean head rotation decreases with increasing vehi-le speed for a moving pedestrian, as shown by the responses foredestrian speeds of 1.4 m/s and 2.8 m/s. Fig. 10 shows that, for aiven vehicle speed, the relationship between head rotation and

able 2ourier coefficients and R2 values for transverse offset.

Vp Vc a0 a1 b1 a2

0.0 5 −9.301 9.517 −4.309 1.120.0 10 −6.84 10.95 −5.786 2.3

0.0 15 −7.478 11.02 −5.858 2.070.0 5, 10, 15 −7.873 10.49 −5.318 1.831.4 5 26.19 9.678 −6.61 1.071.4 7.5 17.55 11.37 −5.786 2.071.4 8.75 14.96 11.65 −6.356 2.251.4 10 12.04 11.06 −6.384 2.281.4 11.25 10.85 11.47 −6.239 2.611.4 12.5 8.686 11.63 −6.266 2.711.4 13.75 7.351 10.95 −6.239 2.631.4 15 6.011 11.2 −6.239 1.331.4 17.5 4.18 11.01 −5.858 1.392.8 5 60.4 9.85 −2.96 −1.682.8 10 30.81 10.14 −6.91 1.812.8 15 19.68 10.45 −5.506 0.80

Fig. 5. Variation of mean transverse offset as a function of vehicle speed.

pedestrian speed is linear and the variation of rotation with pedes-trian speed is small.

As in the case of transverse offset, the head rotation responsesvary cyclically with gait. The responses and corresponding thirdorder Fourier curves for head rotation across the gait cycle are

b2 a3 b3 R2

1 −3.022 −0.3221 −1.017 0.95−2.67 −0.00835 0.4213 0.98

6 −1.892 −0.8324 0.729 0.992 −2.528 −0.3876 0.04439 0.958 −2.619 0.4348 0.9309 0.996 −2.199 −0.4791 0.4213 0.994 −2.932 −0.4246 0.7739 0.995 −2.507 −0.7936 1.58 0.998 −2.127 −0.3846 0.9642 0.993 −2.317 −0.8894 1.77 0.99

−1.892 −0.4493 0.9642 0.991 −2.037 −0.6531 0.9642 1.003 −1.656 −0.3911 0.729 1.002 −0.0106 −1.554 −0.5363 0.945 −3.503 −0.817 2.43 0.9864 −1.757 −0.731 1.3 1.00

346 J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353

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Fig. 8. Transverse offset responses and Fourier curves for pedestrian speed of 1.4 m/s(arrow indicates increasing vehicle speed).

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Fig. 11. Head rotation responses and Fourier curves for vehicle speed of 10 m/s.Positive – anterior head impact. Negative – posterior head impact.

J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353 347

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Fig. 12. Head rotation vs. gait – Fourier curves for nine vehicle speeds (minR2 = 0.81).

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To obtain fundamental insights, the analysis was limited to

ig. 13. Variation of mean head impact velocity as a function of vehicle speed.

hown in Fig. 11 for pedestrian speeds of 0, 1.4 and 2.8 m/s and vehicle speed of 5 m/s (R2 = 0.92, 0.99 and 0.91, respectively).

The Fourier coefficients and R2 values are given in Appendix BTable 3). As stated above, the influence of pedestrian speed onead rotation at a given vehicle speed is small. Therefore, for vehi-le speeds of 5, 10 and 15 m/s, a single Fourier curve was fitted tohe data for all three pedestrian speeds. The Fourier curves for theine vehicle speeds are shown in Fig. 12 (minimum R2 = 0.81). Theatterns can be seen to be very similar for all vehicle speeds.

.3. Head impact velocity

The head impact velocity on the vehicle varies throughout theait cycle. The resulting mean head impact velocity can be seenn Figs. 13 and 14 as a function of vehicle speed and pedestrianpeed, respectively. Fig. 13 shows that the relationship between

ean head impact velocity and vehicle speed is largely indepen-

ent of pedestrian speed and is highly linear. A single regressionine, fitted to all the data at the three pedestrian speeds, has an R2

Car 5m/s Car 10m/s Car 15m/s

Fig. 14. Variation of mean head impact velocity as a function of pedestrian speed.

value of 0.99. Fig. 14 shows that the mean head impact velocity ispractically constant for a given vehicle speed.

The head impact velocity varies cyclically with gait. Theresponses and third order Fourier curves for a vehicle speed of10 m/s are shown in (minimum R2 = 0.84).

The Fourier coefficients and R2 values are given in Appendix B(Table 4). As mentioned above, the head impact velocity is largelyindependent of pedestrian speed at a given vehicle speed. There-fore, for vehicle speeds of 5, 10 and 15 m/s, a single Fourier curvewas fitted to the data for all three pedestrian speeds. The Fouriercurves for the nine vehicle speeds are shown in Fig. 16 (5 m/s:R2 = 0.59, 10 m/s: R2 = 0.64, other speeds: minimum R2 = 0.86). Theshapes of the curves change with increasing vehicle speed. How-ever, in all cases the minimum head impact velocity occurs at about10% of the gait cycle and the maximum occurs at about 60% of thegait cycle.

4. Discussion

The influence of pedestrian pre-impact stance on post-impactkinematics has been reported previously in qualitative terms(Simms and Wood, 2005, 2006a,b,c), but the results presented inthis paper are the first quantitative analysis, and these are basedon a recent validation of the MADYMO pedestrian model for three-dimensional kinematics (Elliott, 2011). The MADYMO pedestrianmodel was used to evaluate the influences of vehicle speed, pedes-trian speed and pedestrian gait on the transverse translation ofthe pedestrian’s head occurring between first contact of the vehi-cle with the legs and the head strike on the vehicle. Similarly,the influences of vehicle speed, pedestrian speed and pedestriangait on the rotation of the head about the vertical head axis andthe head impact velocity relative to the vehicle were evaluated.The vehicle was modelled using multibody surfaces (see AppendixA) for simplicity, but it is not expected that the choice of vehiclerepresentation has a significant influence on the kinematic resultspresented.

a single vehicle type (mid-sized sedan) and a single pedestriansize (50th‰ male). Additionally, the vehicle was unbraked. Hence,the only variables in the current work were the vehicle speed,

348 J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353

Table 3Fourier coefficients and R2 values for head rotation.

Vp Vc a0 a1 b1 a2 b2 a3 b3 R2

0.0 5 −28.78 68.41 −28.42 19.66 −23.13 −15.44 23.35 0.920.0 10 −26.02 64.08 −33.12 7.132 −17.02 −9.041 10.22 0.990.0 15 −30.75 53.63 −24.26 3.941 −10.79 −12.33 12.63 0.961.4 5 −96.36 65.18 −43.14 5.091 −13.05 −7.653 34.28 0.991.4 7.5 −99.96 68.55 −31.95 9.04 −9.167 −13.07 23.16 0.991.4 8.75 −100.5 68.9 −29.02 7.894 −8.742 −11.15 21.09 0.991.4 10 −103.2 62.49 −33.96 2.728 −10.59 −9.067 18.63 1.001.4 11.25 −106.2 61.36 −30.21 1.651 −9.278 −13.55 15.78 0.991.4 12.5 −107 64.32 −29.9 2.239 −7.594 −11.04 15.85 1.001.4 13.75 −108.9 62.3 −30.78 −0.1623 −8.96 −9.699 16.13 0.991.4 15 −109.8 55.3 −27.18 0.3359 −7.701 −10.66 18.11 0.991.4 17.5 −116.3 51.23 −22.92 3.4 −13.14 −1.546 13.11 0.982.8 5 18.34 70.87 −34.01 −15.69 2.318 −19.91 27.06 0.912.8 10 1.927 69.52 −27.21 −7.512 4.895 −13.21 18.92 0.962.8 15 −16.61 55.54 −28.38 −2.706 −6.525 −9.087 20.43 0.990.0, 1.4, 2.8 5 −5.761 68.03 −34.91 3.231 −11.12 −14.13 28.06 0.810.0, 1.4, 2.8 10 −12.43 65.36 −31.43 0.7827 −7.574 −10.44 15.92 0.920.0, 1.4, 2.8 15 −22.39 54.82 −26.61 0.5236 −8.339 −10.69 17.06 0.96

Table 4Fourier coefficients and R2 values for head impact velocity.

Vp Vc a0 a1 b1 a2 b2 a3 b3 R2

0.0 5 −28.78 68.41 −28.42 19.66 −23.13 −15.44 23.35 0.990.0 10 −26.02 64.08 −33.12 7.132 −17.02 −9.041 10.22 0.950.0 15 −30.75 53.63 −24.26 3.941 −10.79 −12.33 12.63 0.971.4 5 −96.36 65.18 −43.14 5.091 −13.05 −7.653 34.28 0.991.4 7.5 −99.96 68.55 −31.95 9.04 −9.167 −13.07 23.16 0.941.4 8.75 −100.5 68.9 −29.02 7.894 −8.742 −11.15 21.09 0.861.4 10 −103.2 62.49 −33.96 2.728 −10.59 −9.067 18.63 0.841.4 11.25 −106.2 61.36 −30.21 1.651 −9.278 −13.55 15.78 0.871.4 12.5 −107 64.32 −29.9 2.239 −7.594 −11.04 15.85 0.911.4 13.75 −108.9 62.3 −30.78 −0.1623 −8.96 −9.699 16.13 0.931.4 15 −109.8 55.3 −27.18 0.3359 −7.701 −10.66 18.11 0.941.4 17.5 −116.3 51.23 −22.92 3.4 −13.14 −1.546 13.11 0.932.8 5 18.34 70.87 −34.01 −15.69 2.318 −19.91 27.06 0.772.8 10 1.927 69.52 −27.21 −7.512 4.895 −13.21 18.92 0.862.8 15 −16.61 55.54 −28.38 −2.706 −6.525 −9.087 20.43 0.960.0, 1.4, 2.8 5 −5.761 68.03 −34.91 3.231 −11.12 −14.13 28.06 0.590.0, 1.4, 2.8 10 −12.43 65.36 −31.43 0.7827 −7.574 −10.44 15.92 0.640.0, 1.4, 2.8 15 −22.39 54.82 −26.61 0.5236 −8.339 −10.69 17.06 0.90

6

7

8

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1009080706050403020100

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ocity

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/s)

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ocity

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rt v

ehic

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/s)

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1009080706050403020100

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d im

pact

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ocity

w

rt v

ehic

le (m

/s)

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Pedestrian 2.8m/s (R2 = 0.86)

Fig. 15. Head impact velocity responses and Fourier curves, vehicle speed of 10 m/s.

J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353 349

0

5

10

15

20

25

1009080706050403020100

Hea

d im

pact

vel

ocity

wrt

veh

icle

(m

/s)

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5m/s: R2 = 0.5858. 10m/s: R2 = 0.6388.Other speeds: minimum R2 = 0.8643

Car 5m/s Car 7.5m/s Car 8.75m/s

Car 10m/s Car 11.25m/s Car 12.5m/s

Car 13.75m/s Car 15m/s Car 17.5m/s

F

tftsspi

4

atcWavo(

arais

rcraocF(

R² = 0.99

-20

-10

0

10

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30

40

50

60

70

0.60.50.40.30.20.10.0

Mea

n tr

ansv

erse

off

set (

cm)

Pedestrian speed/Vehicle speed

tion data from Figs. 9 and 10 as a function of the ratio of pedestrianspeed to vehicle speed. The relationship is highly linear (R2 = 0.99),indicating that head rotation is directly related to pedestrian speed

R² = 0.99

-30

-20

-10

0

10

20

30

0.60.50.40.30.20.10.0

Mea

n he

ad r

otat

ion

(o )

Pedestrian speed/Vehicle speed

ig. 16. Head impact velocity vs. % gait – Fourier curves for nine vehicle speeds.

he pedestrian speed and the pre-impact pedestrian stance. Inuture work, the analysis will be expanded to investigate howhe results presented in this paper are influenced by pedestrianize, vehicle shape and vehicle braking. However, the results pre-ented here are the first quantitative analysis of these aspects ofedestrian kinematics, and as such they provide significant new

nsights.

.1. Transverse offset

The transverse offset decreases with increasing vehicle speednd increases linearly with increasing pedestrian speed. The meanransverse offset across the gait cycle is independent of vehi-le speed when the pedestrian is stationary at impact (Fig. 5).

hen the pedestrian is moving transversely across the vehiclet impact, the mean transverse offset decreases with increasingehicle speed (Fig. 5). The relationship between mean transverseffset and pedestrian speed is highly linear at all pedestrian speedsFig. 6).

Fig. 17 shows the mean transverse offset data from Figs. 5 and 6s a function of the ratio of pedestrian speed to vehicle speed. Theelationship is highly linear (R2 = 0.99) and there is very little scatterbout the linear regression line, indicating that the transverse offsets directly related to pedestrian speed and to the inverse of vehiclepeed.

Third-order Fourier curves were fitted to the transverse offsetesponses in order to obtain a continuous variation across the gaitycle (see Figs. 7 and 8 for pedestrian speeds of 0 m/s and 1.4 m/s,espectively). It is evident that the Fourier patterns are similar atll vehicle speeds (Fig. 8), indicating that the pattern of transverseffset is independent of vehicle impact speed. Gait has a signifi-

ant effect on transverse offset; for the Fourier curves shown inigs. 7 and 8, as well as the curves for a pedestrian speed of 2.8 m/snot shown), the average range (maximum–minimum) is 25 cm.

Fig. 17. Variation of mean transverse offset as a function of pedestrian speed/vehiclespeed.

4.2. Head rotation

The amount of rotation of the head about the vertical headaxis that occurs between first contact between the vehicle andthe legs and the time of head contact with the vehicle decreaseswith increasing vehicle speed and increases with increasing pedes-trian speed, but is not strongly dependent on either, as shown inFigs. 9 and 10. Fig. 9 shows that the mean head rotation is largelyindependent of vehicle speed when the pedestrian is stationary.For a given pedestrian speed, the amount of rotation does not varysignificantly with vehicle speed. For example, mean head rotationvaries from −22◦ to −27◦ (a range of 5◦) for a pedestrian speed of0 m/s and from 22◦ to −13◦ (a range of 35◦) for a pedestrian speedof 1.4 m/s. Fig. 10 shows that, for a given vehicle speed, the amountof head rotation does not depend strongly on pedestrian speed. Forexample, mean head rotation varies from −22◦ to 22◦ (a range of44◦) for a vehicle speed of 5 m/s and from −27◦ to −13◦ (a range of14◦) for a vehicle speed of 15 m/s. Fig. 18 shows the mean head rota-

Fig. 18. Variation of mean head rotation as a function of pedestrian speed/vehiclespeed.

350 J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353

egions of positive and negative regions at 15% and 70% gait.

ao

ticrthc

rocrgld(Gcisoa0sFiataa

clstv2haseiogu2v

0

1

2

3210M

ean

head

impa

ct

velo

city

/ Veh

icle

vel

ocity

Pedestrian speed (m/s)

Car 5m/s Car 10m/s Car 15m/s

Fig. 19. Fourier curves for head rotation divided into r

nd to the inverse of vehicle speed, as is also shown for transverseffset (Fig. 17).

The head rotation variations as a function of vehicle or pedes-rian speed are potentially of limited practical significance since,n a real collision case, it may not be feasible to determine a pre-ise amount of rotation as the head contact on the vehicle typicallyesults in injuries that cover quite a broad region of the pedes-rian’s head. In practice, it might at best be possible to describeead impact location in terms of being anterior or posterior to theoronal plane.

Third-order Fourier curves were fitted to the head rotationesponses at each vehicle speed to obtain a continuous variationf head rotation as a function of gait, as shown in Fig. 11 (vehi-le speed of 10 m/s) and Fig. 12 (all nine vehicle speeds). Theesults show that the patterns of variation of head rotation withait are very similar for all vehicle speeds, again indicating that,ike the transverse offset, the pattern of head rotation is indepen-ent of vehicle impact speed. The range of head rotation valuesmaximum–minimum) decreases with increasing vehicle speed.ait has a very significant effect on head rotation. For a given vehi-le speed, the range of head rotation responses across the gait cycles wide, e.g. 166◦ for a vehicle speed of 5 m/s, 115◦ for a vehiclepeed of 17.5 m/s. These Fourier curves can be divided into regionsf anterior impacts (positive rotations) and posterior impacts (neg-tive rotations) relative to the coronal plane. A head rotation of◦ forms the boundary between these two regions and this corre-ponds to gait values of approximately 15% and 70%, as shown inig. 19. The resulting gait ranges correspond to the lagging and lead-ng leg regions of the gait cycle as indicated in Fig. 2. Two full cyclesre shown in Fig. 19 to illustrate that there is variation in the pat-erns at the transitions between the two regions (±20◦ approx.),nd also in the gait values at which the transitions occur (±5%pprox.).

The results indicate that when the struck leg is lagging, headontact occurs anteriorly on the head, and when the struck leg iseading, head contact occurs posteriorly on the head. It has beenhown using a single segment momentum-based model that withinhese gait regions, different relationships exist between the trans-erse offset and the pedestrian speed (Elliott et al., 2010; Elliott,011). It is therefore possible that the location of the impact on theead (anterior/posterior) could be used to identify the gait region,nd in combination with the transverse offset (which may be mea-urable following a collision) this approach might in future facilitatestimation of pedestrian pre-impact speed. Here the analysis is lim-ted to a single pedestrian size (50th‰ male), and therefore the ratiof transverse offset to longitudinal offset may prove more useful for

eneral application to a range of pedestrian sizes. Previous worksing a momentum-based model has found that this ratio (Elliott,011) is linearly correlated with the ratio of pedestrian speed toehicle speed.

Fig. 20. Variation of mean head impact velocity/vehicle speed as a function of pedes-trian speed.

4.3. Head impact velocity

The velocity of head impact on the vehicle increases linearlywith increasing vehicle speed and is largely independent of pedes-trian speed, as shown in Figs. 13 and 14. In Fig. 14, the mean headimpact velocity data from Fig. 14 is divided by the vehicle speedand shown as a function of pedestrian speed. This effectively nor-malises the data and confirms that the head impact velocity is afunction of vehicle speed and is largely unaffected by pedestrianspeed (Fig. 20).

Third-order Fourier curves were fitted to the head impact veloc-ity responses at each vehicle speed, as shown in Fig. 15 (vehiclespeed of 10 m/s) and Fig. 16 (all nine vehicle speeds). Gait hasa considerable effect on head impact velocity; for the Fouriercurves shown in Fig. 16, the average range (maximum–minimum)is 4.6 m/s. The minimum and maximum values of these Fouriercurves were regressed as functions of vehicle speed (Fig. 21). Theregressions were found to be highly linear with R2 values of 0.98for both the minimum and maximum head impact velocity values.

Fig. 22 shows the ratio of maximum to minimum head impactvelocity as a function of vehicle speed. The ratio diminishes asymp-totically from 1.7 at a speed of 8 m/s to 1.3 at 25 m/s. As the severityof head injury is strongly correlated with head impact velocity,Fig. 22 shows that there is likely to be a substantial variation ininjury severity depending on the stage in the gait cycle when theimpact occurs.

The head injury severity is strongly correlated with the headimpact velocity. Therefore the MADYMO head impact velocity pat-terns presented here could provide some insight into head injury

severity patterns in real world conditions where the pre-impactstance of the pedestrian is generally not known. Detailed investi-gation of real life collision data is needed to confirm whether theinferences derived here actually occur.

J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353 351

R² = 0.98

R² = 0.98

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20151050

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)

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Maximum

Fig. 21. Minimum and maximum head impact velocity vs. vehicle velocity.

1.0

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/min

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rwiagTla

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Offset (c m) )Head rotation ( Vh (m/s)

10 m/s (for shape comparison purposes, the head impact velocity

ig. 22. Ratio of maximum to minimum head velocity as a function of vehicle speedpredicted from minimum and maximum head velocity regressions).

Fig. 16 shows that, unlike the transverse offset and head rotationesponses, the shapes of the head impact velocity curves changeith increasing vehicle speed. Nonetheless, the minimum head

mpact velocity always occurs between 10% and 20% of the gait cyclend the maximum always occurs at about 60% of the cycle. It is sug-ested that this arises because of the geometry of the pedestrian.

he gait cycle stances in Fig. 2 show that at 10% gait, the struck (left)eg is practically vertical. The pedestrian therefore does not rotatebout the vertical body axis as there is no moment arm to cause

Fig. 23. MADYMO snapshots – pedestrian pivots about cir

Fig. 24. Normalised Fourier curves for transverse offset, head rotation and headimpact velocity.

this. The pedestrian’s pelvis is impacted by the vehicle front and thepedestrian pivots about the contact point between the vehicle frontand the pelvis (circled in Fig. 23, left) such that the side of the bodycontacts the bonnet. At 60% gait, the struck leg is displaced forward,creating a moment arm that causes the pedestrian to rotate aboutthe vertical body axis. The back of the pedestrian’s body thereforecontacts the bonnet. Importantly, the pedestrian pivots about thecontact point between the vehicle front and the upper leg (circledin Fig. 23, right), which is lower on the vehicle front than the pelviscontact location at 10% gait. The moment arm causing the pedes-trian’s body to rotate towards the bonnet is therefore greater at 60%gait, causing the head impact velocity to be higher.

As the minimum head impact velocity occurs between 10% and20% of the gait cycle and the maximum head impact velocity occursat about 60%, this suggests that, all other factors remaining thesame, head injuries due to anterior head impacts will be less severethan those resulting from posterior head impacts.

4.4. Comparison of Fourier patterns

In order to compare the response patterns for transverse offset,head rotation and head impact velocity, the Fourier curves werenormalised, i.e. the curves were shifted and scaled so that the min-imum value was 0 and the maximum value was 1 in all cases. Thenormalised curves were overlaid for each combination of vehicleand pedestrian speed. Fig. 24 shows the normalised curves for atypical case of a pedestrian speed of 1.4 m/s and a vehicle speed of

curve has been inverted). The patterns for transverse offset andhead rotation are seen to be very similar across the entire gaitcycle. It was previously shown that the pattern of head rotation

cled contact locations. Left: 10% gait. Right: 60% gait.

352 J.R. Elliott et al. / Accident Analysis and Prevention 45 (2012) 342– 353

10%

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ig. 25. Fourier curve for transverse offset vs. Fourier curve for head rotation.

ould be divided into positive and negative regions at gait values ofpproximately 15% and 70% (Fig. 19). The higher and lower trans-erse offset responses therefore broadly fall within these same gaitegions, i.e. 0–15%/70–100% and 15–70%, respectively, (Fig. 8), ashe normalised transverse offset and head rotation patterns areery similar (Fig. 24). The head impact velocity pattern is different:or approximately the first half of the gait cycle, the inverted headmpact velocity response appears out of phase and lags behind theransverse offset and head rotation responses. For the remainder ofhe cycle, the inverted head impact velocity is largely in phase withhe transverse offset and head rotation responses.

To further illustrate this, the Fourier curves for transverse offsetnd head impact velocity are shown in Figs. 25 and 26 as functionsf head rotation (for these figures, the curves were not normalisednd the head impact velocity curve was not inverted). The positionsorresponding to 0% gait, 10% gait, etc. are shown. Fig. 25 shows aargely linear trend because the response patterns for transverseffset and head rotation are very similar, as seen in Fig. 24. Fig. 26an be divided into two regions. Firstly, there is a curved regionetween 0% and 50% gait, corresponding to the ‘out of phase’ region

s indicated in Fig. 24. Secondly, there is a relatively linear regionetween 50% and 100% gait corresponding to the ‘in phase’ regions indicated in Fig. 24. The pattern of head impact velocity variations a function of head rotation (i.e. location of impact on the head)

0

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Forc

e (N

)

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Bonnet loading

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Windscreen unloading

Forc

e (N

)

Fig. 27. Loading and unloading functions for windscreen, bonnet, bo

Fig. 26. Fourier curve for head impact velocity vs. Fourier curve for head rotation.

shows the positions on the head that are predicted to sustain lowand high impact velocities.

The patterns of transverse offset and head rotation are similarfor all pedestrian and vehicle speed combinations. At low vehiclespeeds, the head impact velocity curve is largely in phase with thetransverse offset and head rotation curves across the gait cycle. Athigher vehicle speeds, the head impact velocity curve goes out ofphase with the transverse offset and head rotation responses forthe first 50% of the cycle. This effect becomes more pronounced asthe vehicle speed increases.

5. Conclusion

In this paper, the 50th% male adult MADYMO pedestrian modelwas used to show (for a single vehicle shape) that the transversetranslation of the pedestrian’s head between primary and sec-ondary vehicle contacts decreases inversely with increasing vehiclespeed and increases linearly with increasing pedestrian speed.The extent of head rotation about the vertical axis also decreases

inversely with increasing vehicle speed and increases with increas-ing pedestrian speed, although these effects are small. The headimpact velocity on the vehicle increases linearly with increasingvehicle speed and is largely independent of pedestrian speed. The

0

2000

4000

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0.00 0.01 0.01

Deformation (m)

BLE loading

BLE unloading

Bumper loading

Bumper unloading

nnet leading edge and bumper (Simms and Wood, 2006a,b,c).

sis and

mw

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A

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J.R. Elliott et al. / Accident Analy

aximum and minimum head impact velocities increase linearlyith increasing vehicle speed.

It was found that all three quantities vary cyclically and signifi-antly with gait, in a manner that can be very well represented usinghird order Fourier curves. These results provide the first quantifica-ion of the influences of pedestrian speed and stance on transverseffset and head rotation, both of which may sometimes be availablen individual pedestrian accident cases.

ppendix A.

etup of MADYMO simulations

MADYMO is commercial multibody simulation software inhich systems of rigid bodies connected by kinematic joints

re allowed to contact each other according to specified contactharacteristics. The resulting equations of motion are integratedumerically to yield movements based on specified initial con-itions. The MADYMO vehicle model consisted of four extrudedylinders and five ellipsoids. The loading and unloading functionsor the bonnet, windscreen, BLE and bumper are shown in Fig. 27.he loading and unloading functions for the bonnet and windscreenere taken from Mizuno and Kajzer (2000). The linear stiffnessarameters for the BLE and bumper were taken from Liu et al.2002a,b). For the BLE and bumper, the unloading force-penetrationunction was 10 times less stiff than the loading function. Eulerntegration was used in all simulations.

It was previously found that a friction coefficient of 0.3 for theehicle–pedestrian contacts gave reasonable results (Simms andood, 2006a,b,c). The hysteresis slope was set to 108 for all vehi-

le contacts. The combined force-deformation characteristics ofoth contacting surfaces were used in all contacts except for theehicle–head contact, in which only the vehicle deformation char-cteristics were used.

The chosen time step used was 10−5. To check the dependencyf the results on the time step, the time step was halved and theesponses were compared to the responses at the original time step.t was found that halving the time step had a negligible effect on theesults. A time step of 10−5 was therefore considered acceptable.

MADYMO does not directly output contact locations. Therefore,he impact locations between the pedestrian and the vehicle wereound using a method employed by Untaroiu et al. (2009) in which

arkers are placed on the contacting surfaces and the positions ofhe markers are used to estimate the contact locations.

ppendix B.

ourier coefficients

The general form of a third-order Fourier series is:

0 + a1 cos(xω) + b1 sin(xω) + a2 cos(2xω) + b2 sin(2xω)

+ +a3 cos(3xω) + b3 sin(3xω)

here a0, a1, b1, a2, b2, a3 and b3 are the Fourier coefficients and is the frequency of the function. In all cases, a period of 100%

one gait cycle) was required. The period is equal to 2�/ω, therefore was set to 0.06283. The Fourier coefficients and R2 values for

ransverse offset, head rotation and head impact velocity are givenn Tables 2–4.

eferences

nderson, R., McClean, J., Dokko, Y., 2005a. Determining accurate contact defini-tions in multibody simulations for DOE type reconstruction of head impacts inpedestrian accidents. Experimental Safety Vehicles, ESV Paper No. 05-0175.

Prevention 45 (2012) 342– 353 353

Anderson, R.W.G., McLean, A.J., Dokko, Y., 2005b. Determining accurate contact def-initions in multi-body simulations for DOE-type reconstruction of head impactsin pedestrian accidents. In: Proceedings of the 19th International Conference onthe Enhanced Safety of Vehicles (ESV), Washington, D.C, Paper No. 05-0175.

Elliott, J., Simms, C., Wood, D., 2010. Monte Carlo modeling to estimate pedestrianvelocity from post-accident vehicle damage. In: Proceedings of InternationalJournal of Crashworthiness Conference, Washington, D.C.

Elliott, J.R., 2011. Monte Carlo modelling to estimate pedestrian pre-impact velocityfrom post-accident vehicle damage. MSc. Thesis. Trinity College Dublin.

Fugger, T., Randles, B., Stein, A., Whiting, W., Gallagher, B., 2000. Analysis of pedes-trian gait and perception/reaction at signal-controlled crosswalk intersections.Pedestrian and Bicycle Transportation Research (1705), 20–25.

Guo, R., Yuan, Q., Sturgess, C., Hassan, A., Li, Y., Hu, Y., 2006. A study of an Asiananthropometric pedestrian in vehicle–pedestrian accidents using real-worldaccident data. International Journal of Crashworthiness 11 (6), 541–551.

Kerrigan, J., Arregui, C., Crandall, J., 2009. Pedestrian head impact dynamics: com-parison of dummy and PMHS in small sedan and large SUV impacts. In:Experimental Safety Vehicles Conference.

Kerrigan, J., Crandall, J., 2007. Pedestrian kinematic response to mid-sized vehicleimpact. International Journal of Vehicle Safety 2 (3), 221–240.

Kerrigan, J., Crandall, J., 2008. A comparative analysis of the pedestrian injury riskpredicted by mechanical impactors and post mortem human surrogates. StappCar Crash Journal 52.

Kerrigan, J., Murphy, D., Drinkwater, D., Kam, C., Bose, D., Crandall, J., 2005. Kinematiccorridors for PMHS tested in full-scale pedestrian impact tests. In: Proceedingsof 19th Conference on the Enhanced Safety of Vehicles (ESV).

Leglatin, N., Blundell, M., Blount, G., 2006. The simulation of pedestrian impact witha combined multibody finite elements system model. Journal of EngineeringDesign 17 (5), 463–477.

Linder, A., Douglas, C., Clark, A., Fildes, B., Yang, J., Otte, D., 2005a. Mathematicalsimulations of real-world pedestrian–vehicle collisions. In: Experimental SafetyVehicles Conference.

Linder, A., Douglas, C., Clark, A., Fildes, B., Yang, J., Otte, D., 2005b. Mathematical sim-ulations of real-world pedestrian–vehicle collisions. In: Proceedings of the 19thInternational Technical Conference on the Enhanced Safety of Vehicles (ESV),Washington, D.C, Paper No. 05-285.

Liu, X.J., Yang, J.K., Lovsund, P., 2002a. A study of influences of vehicle speed and frontstructure on pedestrian impact responses using mathematical models. TrafficInjury Prevention 3 (21), 42.

Liu, X.J., Yang, J.K., Lövsund, P., 2002b. A study of influences of vehicle speed and frontstructure on pedestrian impact responses using mathematical models. TrafficInjury Prevention 3, 31–42.

MADYMO, 2009. MADYMO, Human Models Manual, Version 7.0. TNO Delft, TheNetherlands.

Mizuno, K., Kajzer, J., 2000. Head injuries in vehicle pedestrian impact. Society ofAutomotive Engineers Conference, 24–40, SAE Paper No. 010157.

Mizuno, K., Yonezawa, H., Kajzer, J., 2001. Pedestrian headform impact tests for var-ious vehicle locations. In: Experimental Safety Vehicles Conference, ESV PaperNo. 278.

OECD, 2008. Organisation for Economic Co-operation and Development (OECD).Serre, T., Masson, C., Perrin, C., Chalandon, S., Llari, M., Cavallero, C., Cesari, D.,

2007. Real accidents involving vulnerable road users: in-depth investigation,numerical simulation and experimental reconstitution with PMHS. Journal ofCrashworthiness 12 (3), 227–234.

Simms, C.K., Wood, D., 2005. Pedestrian impact: the effect of pedestrian motion onhead contact forces with vehicle and ground. In: IRCOBI Conference, Prague.

Simms, C.K., Wood, D., 2006a. Effects of pre-impact pedestrian position and motionon kinematics and injuries from vehicle and ground contact. International Jour-nal of Crashworthiness 11 (4), 345–356.

Simms, C.K., Wood, D., 2006b. Pedestrian risk from cars and sport utility vehicles –a comparative analytical study. IMechE Journal of Automobile Engineering 220,1085–1100.

Simms, C.K., Wood, D., 2009. Pedestrian and Cyclist Impact – A Biomechanical Per-spective. Springer.

Simms, C.K., Wood, D.P., 2006c. Pedestrian risk from cars and sport utility vehicles– a comparative analytical study. Proceedings of the Institution of MechanicalEngineers, Part D: Journal of Automobile Engineering 220, Part D.

Subit, D., Kerrigan, J., Crandall, J., Fukuyama, K., Yamazaki, K., Kamiji, K., Yasuki, T.,2008. Pedestrian–vehicle interaction: kinematics and injury analysis of four fullscale tests. In: Proceedings of IRCOBI Conference, Bern, Switzerland.

Svoboda, J., Solc, Z., Cizek, V., 2003. Analysis of collision between pedes-trian and small car. International Journal of Crashworthiness 8 (3),269–276.

Untaroiu, C., Meissner, M., Crandall, J., Takahashi, Y., Okamoto, M., Ito, O., 2009.Crash reconstruction of pedestrian accidents using optimisation techniques.International Journal of Impact Engineering 36 (2), 210–219.

van Hoof, J., de Lange, R., Wismans, J., 2003. Improving pedestrian safety usingnumerical human models. Stapp Car Crash Journal 47, 401–436.

WHO, 2009. European Status Report on Road Safety. World Health Organization.Yao, J., Yang, I., Otte, D., 2008a. Investigation of head injuries by reconstruc-

tions of real-world vehicle-versus-adult-pedestrian accidents. Safety Science 46,1103–1114.

Yao, J., Yang, J., Otte, D., 2008b. Investigation of head injuries by reconstructionsof real-world vehicle-versus-adult-pedestrian accidents. Safety Science 46 (7),1103–1114.