Forensic Science International

Forensic Science International 207 (2011) 135 144 Contents lists available at ScienceDirect Forensic Science International journal homeage: www.elsevier.com/locate/forsciint Analysis and alication of relationshi between ost-braking-distance and throw distance in vehicle edestrian accident reconstruction Tiefang Zou a, *, Zhi Yu b, Ming Cai b, Jike Liu b a School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410076, China b School of Engineering, Sun Yat-sen University, Guangzhou 510275, China ARTICLE INFO ABSTRACT Article history: Received 15 March 2010 Received in revised form 19 Setember 2010 Acceted 21 Setember 2010 Available online 30 October 2010 Keywords: Accident reconstruction Vehicle edestrian accident Post-braking-distance Throw distance Through theoretical analysis and introduction of some emirical arameters, the relationshi between ost-braking-distance and throw distance was studied concentratedly. Here, the ost-braking-distance is the distance a vehicle will travel from the imact osition to when it comes to a comlete sto. Two useful formulas which are meaningful in vehicle edestrian accident reconstruction were finally obtained. The first one can be used to calculate imact seed according to throw distance, while the other one can describe the relationshi between ost-braking-distance and throw distance. Their feasibility has been validated by comaring with other scholars emirical formulas and simulation results of software Pc-Crash, resectively. The relationshi between ost-braking-distance and throw distance has very bright alication ersective in vehicle edestrian accident reconstruction such as heling olicemen obtain more useful evidences, validating credibility of the throw distance, judging whether the vehicle is fully braked or not, determining the imact osition etc. Finally its alication was demonstrated by three cases, in which the imact seed was also calculated. All results until now have shown that conclusions obtained in this article are feasible and helful in vehicle edestrian accident reconstruction. ß 2010 Elsevier Ireland Ltd. All rights reserved. 1. Introduction In vehicle edestrian accident reconstruction, the two most imortant objectives are to determine imact osition and imact seed. In ractice, the imact osition is often determined according to traces in the accident scene and the imact seed can be calculated by many theoretical or emirical methods. These methods used for calculating the imact seed can be categorized by evidences they require. The categories are ost-braking-distance [1 2] (The ost-braking distance refers to the distance a vehicle will travel from the imact osition to when it comes to a comlete sto.), throw distance [2 7], vehicle damage [8 11], edestrian injury [11 15]. Here, ost-braking-distance reresents methods used for calculating the imact seed according to the ost-brakingdistance. In order to make the reconstruction results more credible, solutions of these methods are often used to validate each other, so the credibility of evidences needs to be validated firstly. In ractice, it is not easy to determine exact values of some useful arameters from the accident scene comletely. If relationshi between different evidences is known, it will be very * Corresonding author. Tel.: +86 731 85258633. E-mail address: zoutiefang@gmail.com (T. Zou). helful in validating credibility of evidences. Aart from that, it is ossible that some evidences cannot be measured easily or exactly, but the relationshi between different evidences can be measured easily. E.g., ost-braking-distance and throw distance can hardly be measured if the imact osition is unknown, but the distance between rest osition of the edestrian and the vehicle can be measured easily. Then their relationshi will be helful in determining the value of one arameter from the other one and then evaluating the imact seed further. It is a ity that until now, relationshi between different evidences has not been studied extensively. This article mainly focuses on the relationshi between throw distance and ostbraking-distance in vehicle edestrian accidents. Two useful formulas were obtained at last and their alication in vehicle edestrian accident reconstruction was also discussed and exlained by three cases. 1.1. Problem descrition The most common categories of vehicle edestrian collisions are forward rojection, wra, carry, roof vault and fender vault [1,2]. This article mainly focuses on the wra collisions, and the vehicle is assumed to move on a flat road. Fig. 1 shows a sketch of the wra collision sequence and indicates various variables in vehicle edestrian accident reconstruction. The imact seed is v. After a 0379-0738/$ see front matter ß 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.forsciint.2010.09.019

136 T. Zou et al. / Forensic Science International 207 (2011) 135 144 Fig. 1. Sketch of wra collision sequence. duration time t 0, the edestrian is launched in an airborne trajectory with a velocity of v 0 at an angle u, the range of airborne trajectory is R. Then the edestrian imacts the ground with a velocity determined by the trajectory. After that it is assumed to be uniformly decelerated with a frictional drag coefficient f. And S is the distance between the oint where edestrian firstly contacts with ground and the rest osition of the edestrian, the throw distance S = R + S. At the same time, the vehicle is fully braked and it is assumed to be uniformly decelerated with a frictional drag coefficient f v, the braking distance after imact is S v. S v is named as ost-braking-distance in this aer, which is the distance a vehicle will travel from the imact osition to when it comes to a comlete sto. This article mainly concentrates on the relationshi between S and S v, which can be exressed as Sv ¼ f ðsþ (1) Now all tasks left are to determine f, and then alication of Eq. (1) in vehicle edestrian accident reconstruction will be also discussed. 2. The relationshi between ost-braking-distance and throw distance 2.1. Post-braking-distance The deceleration of vehicle is f v g if the vehicle is fully braked and moves on a flat road. According to the rincile of conservation of energy and conservation of momentum, the imact seed can be calculated by Eq. (2). v ¼ þ m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2f v gs v where is the mass of vehicle, kg; m is the mass of edestrian, kg; v is the imact seed of vehicle, m/s; f v is the vehicle ground friction drag coefficient; S v is the ost-braking-distance, m; g = 9.8 m/s 2. 2.2. Throw distance In order to obtain an analytical model for calculating S according to v, some hyotheses are made in this article as following. (1) The duration time t 0 in Fig. 1 is aroximately equal to zero. (2) The launched velocity v 0 is equal to v 0, where v 0 is the same velocity of the vehicle and the edestrian in ost-imact hase. (3) There is no vertical bounce or rebound of the edestrian after it imacts ground. (2) (4) The edestrian is uniformly decelerated with a frictional drag coefficient f on a dry and flat road. According to hyothesis 1, the rincile of conservation of momentum can be used in this section. According to hyothesis 2, v 0 can be calculated as v 0 ¼ v 0 ¼ v (3) þ m And R can be calculated as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v 0sinu þ v 02 sinu 2 þ 2gh R ¼ v 0 cosu (4) g where h is the height of edestrian center of gravity at launch, m. According to hyothesis 3 and 4, S can be calculated as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðv 0cosuÞ 2 þðf v 0 sinuþ 2 þ2ghf 2 2f v 0 cosu ðv 0 sinuþ 2 þ2gh S¼ 2gf (5) Now S can be calculated based on Eqs. (4) and (5) as S ¼ S þ R ¼ ðv 0cosu þ f v 0 sinuþ 2 2g f þ hf (6) And v can be obtained via Eqs. (3) and (6) as qffiffiffiffiffiffiffiffiffiffiffi v ¼ þ m 2g f qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S cosu þ f sinu f h (7) According to references [2,5,16,17], f obeys normal distribution. The mean value is about 0.6 and the standard deviation is 0.1. Generally h is aroximately equal to the height of hood, and then h < 1 m, and f h < 1 m. As a result, f h in Eq. (7) can be ignored and Eq. (7) can be simlified as qffiffiffiffiffiffiffiffiffiffiffi v ¼ þ m D ffiffiffiffiffi 2f g S ; where D ¼ (8) cosu þ f sinu Eq. (8) is still difficult to be alied to real accident reconstruction because the data in D is only artly available in a real collision. According to reference [2], u should be considered in the range 0 u 15 8 for reconstruction of tyical wra collisions. It is assumed to obey uniform distribution, and the lower and uer limit are 08 and 158, resectively. The distribution of D can be determined by Monte Carlo method according to the distribution of u and f, which can be found in Fig. 2. Fig. 2 shows that D obeys normal distribution, the mean value is 3.20 m 0.5 /s and standard deviation is 0.26 m 0.5 /s.

T. Zou et al. / Forensic Science International 207 (2011) 135 144 137 Fig. 2. Density function of D. Fig. 4. Density function of A. Then Eq. (9) can be given as v min ¼ 2:42 ffiffiffiffiffi S ðmv þ m Þ v ¼ 3:2 ffiffiffiffiffi S ðmv þ m Þ v max ¼ 3:98 ffiffiffiffiffi S ðmv þ m Þ The robability of v 2½v min ; v max Š is 99.7%. If the mass of the edestrian or the vehicle is unknown, Eq. (9) can be aroximated to qffiffiffiffiffi v min ¼ 2:42 S v ¼ 3:2 ffiffiffiffiffi S (10) qffiffiffiffiffi v max ¼ 3:98 S Because many hyotheses were made to obtain Eq. (9), the feasibility of Eq. (9) should be validated. In order to make the comarison, the values of and m are set as = 1200 kg, m = 60 kg, resectively. Fig. 3 shows the validation of feasibility of Eq. (9), in which S reresents S, v reresents the imact seed v, vmin reresents v min, vmax reresents v max and vmean reresents (9) v. Fugger 2000 reresents the solution of Fugger s method [4], which is v = 8.3604S 0.6046, where v is the vehicle imact seed in km/h. Toor2003 reresents the solution of Toor s method [4], which is v = 9.84S 0.57. Fig. 3 shows that Eq. (9) is feasible in vehicle edestrian accident reconstruction, and then Eq. (8) is feasible too. 2.3. The relationshi between ost-braking-distance and throw distance After Eqs. (2) and (8) are available, the relationshi between ost-braking-distance and throw distance can be obtained easily S v ¼ AS ; where A ¼ f f v ðcosu þ f sinuþ 2 (11) Eq. (11) is difficult to be alied in real accident reconstruction because the data in A is artly available from a real collision too. In general, the vehicle-ground friction drag coefficient f v on a dry road is assumed to obey uniform distribution, the lower and uer limit is 0.7 and 0.9 resectively. Now the distribution of A can be obtained as D, which can be found in Fig. 4. Fig. 4 shows that A obeys normal distribution, the mean value is 0.66 and standard deviation is 0.12. So in general, a more convenient formula can be given as S v ¼ 0:66S (12) Fig. 3. Feasibility validation of Eq. (9). The robability of S v 2½0:3; 1:02ŠS is 99.7%. Then if a vehicle edestrian accident haened on a dry and flat road, and the vehicle is fully braked after imact, the rest osition of the edestrian must be ahead of the rest osition of the vehicle. In order to validate the feasibility of Eq. (12), the most oular accident reconstruction software Pc-Crash [17,18] was used here. Serial exeriments were designed, and the number of the test is 144. Imact seed, vehicle shae and vehicle edestrian contact lace were changed several times in these exeriments. And then all exeriments were erformed by Pc-Crash, the ostbraking-distance and the throw distance were recorded for each exeriment. Fig. 5 shows the relationshi between the ostbraking-distance and the throw distance. In Fig. 5, Observed value are values of numerical exeriments, and Svmean = 0.66S, Svmax = 1.02, Svmin = 0.3S. Fig. 5 also shows that Eq. (12) is feasible in vehicle edestrian accident reconstruction, and then Eq. (11) is feasible too.

138 T. Zou et al. / Forensic Science International 207 (2011) 135 144 information for olicemen, which can hel them to obtain more useful evidences. 3.2. Alication 2: validating the credibility of the throw distance It is suosed that the vehicle edestrian accident haened on a flat road, the imact osition is known, and the vehicle is fully braked. Now is the robability that the edestrian is not imacted by other obstacles while sliding on a flat road. Then if is aroximately equal to 0, the robability that the edestrian is imacted by other obstacles is high, and then the throw distance is incredible. And if is aroximately equal to 1, the robability that the edestrian is not imacted by other obstacles is high, and then the throw distance is credible. Then the vehicle velocity can be calculated via Eq. (2). If the throw distance is roved to be credible, Eqs. (8), (9) or (10) can be used to validate the solution of Eq. (2). 3.3. Alication 3: judging whether the vehicle is fully braked 3. Alication Fig. 5. Feasibility validation of Eq. (12). After Eq. (11) is obtained, the robability that the vehicle is fully braked and the edestrian is not imacted by other obstacles while sliding on a flat road can be given as ¼ 1 PðmeanðAÞ r 0 < A < meanðaþþr 0 Þ r 0 ¼ A ractice meanðaþ (13) where A ractice ¼ S v ractice =S ractice, S vractice and S ractice reresent the ost-braking-distance and the throw distance measured from one true accident resectively; mean(a) reresents the mean value of A. Eq. (13) can be written as ¼ 1 þ FðmeanðAÞ r 0 Þ FðmeanðAÞþr 0 Þ (14) where F is the distribution function of A. Under conditions in this article, according to Fig. 5, A obeys normal distribution, and its mean value is 0.66, so Eq. (14) simlified as ¼ 1 þ F 0:66 A ractice 0:66 F 0:66 þ A ractice 0:66 (15-1) If some functions in some mathematical softwares are introduced, then Eq. (15-1) can be calculated easily, e.g., normcdf in matlab, then can be calculated as ¼ 1 þ normcd f 0:66 A ractice 0:66 ; 0:66; 0:12 normcd f 0:66 þ A ractice 0:66 ; 0:66; 0:12 (15-2) This will be helful in accident reconstruction, which can be used to judge whether the vehicle is fully braked or the edestrian is imacted by other obstacles while sliding on a flat road. Four kinds of otential alications of the relationshi between ostbraking-distance and throw distance in vehicle edestrian accident reconstruction will be exlained in the following sections. It is suosed that the vehicle edestrian accident haened on a flat road, the imact osition is known, and the edestrian is not imacted by other obstacles while sliding on the road. Now is the robability that the vehicle is fully braked. Then whether the vehicle is full braked or not can be evaluated based on. This will be helful for resonsibility confirmation of a traffic accident. And then, the vehicle velocity can be calculated via Eqs. (8), (9) or (10). If the ost-braking-distance is roved to be credible (the vehicle is fully braked), Eq. (2) can be used to validate the solution of Eqs. (8), (9) or (10). 3.4. Alication 4: determining the imact osition It is suosed that the vehicle edestrian accident haened on a flat road, the imact osition is unknown, the vehicle is fully braked and its moving direction is known, the edestrian is not imacted by other obstacles while sliding on the road. The sketch of the rest ositions of the edestrian and vehicle can be found in Fig. 6. Under the conditions of this section, the arameters S 1, S 2 and a in Fig. 6 are already known. If a is aroximately equal to zero, then S S v S 1 þ S 2 (16) According to Eq. (11) S ¼ S S v 1 A ¼ S 1 þ S 2 1 A (17-1) S v ¼ A S 1 þ S 2 (18-1) 1 A The reason why in Eq. (16) is relaced by = in Eq. (17-1) is that all measurements obtained from the accident scene are 3.1. Alication 1: heling olicemen to obtain more useful evidences It is suosed that the vehicle edestrian accident haened on a flat road, and the imact osition is known. But whether the vehicle is fully braked or not and whether the edestrian is imacted by other obstacles or not while sliding on the flat road are unknown. If is aroximately equal to 1, the robability of these two situations is high, while, the robability that the vehicle is not fully braked or the edestrian is imacted by other obstacles is high if is aroximately equal to 0. This will rovide helful Fig. 6. Rest ositions of articiators in accident.

T. Zou et al. / Forensic Science International 207 (2011) 135 144 139 uncertain, so equal to can be relaced by aroximately equal to to some extent. According to Eqs. (8) and (17-1), v can be calculated as v ¼ m rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v þ m S 1 þ S 2 D 1 A (19-1) And S, S v can be obtained from Eq. (17-1) or (18-1), then the imact osition can be obtained; and according to Eq. (19), the imact seed can be calculated. In consideration of the distribution of A and D, then Eqs. (17-1) (19-1) can be simlified as S ¼ 50 17 ðs 1 þ S 2 Þ (17-2) S v ¼ 33 17 ðs 1 þ S 2 Þ (18-2) According to the cosine theorem and Eq. (11) 8 < S 2 1 þ S2 0 S2 2S 1S 0 cosð aþ ¼0 : S 2 2 þ S2 0 S2 v 2S 2S 0 cosðaþ ¼0 S v ¼ AS (20) There are three deendent variables S 0, S v and S in equation set (20) and three equations, so these deendent variables can be determined. Then the imact seed can be determined by Eq. (2) or Eqs. (8) (10), and the imact osition can be determined by S 0 too. The influence of initial velocity of the edestrian on the throw distance was not considered in this article. If the initial edestrian velocity has great influence on the throw distance, all conclusions obtained in this section could not be alied in accident reconstruction before they are roved. 4. Cases study v ¼ 5:49 þ m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S 1 þ S 2 If a is not aroximately equal to zero (19-2) 4.1. Case 1 This case is the first case in Ref. [19], all information of this case can be found in Fig. 7, which is cited directly from Ref. [19]. Fig. 7. Information of case 1.

140 T. Zou et al. / Forensic Science International 207 (2011) 135 144 Fig. 8. Simulation results of Pc-Crash. In this case, there are skid marks on the road, so the vehicle must be fully braked. According to Eq. (2), the imact seed can be calculated as ð1322 þ 75Þ v ¼ 1322 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (21) 2 0:8 9:8 14 3:6 ¼ 56:3 km=h Now the throw distance and Eq. (9) are suosed to be used to validate the solution of Eq. (21). It is found that A ractice = 14/ 16 = 0.88; according to Eq. (15), = 0.067, which means the robability that the edestrian is not imacted by other obstacles is 6.7%. In this case, the imact osition is on the middle of the road, but the rest osition of the edestrian is on the cycle track. There is a ste between the road and the cycle track, so the edestrian may be imacted by this ste. So it can concluded that the throw distance in this case is incredible. And then Eq. (9) and the throw distance S = 16 m cannot be used to validate the solution of Eq. (21). According to Eqs. (9) and (12) rffiffiffiffiffiffiffiffiffi 1322 þ 75 14 v ¼ 3:2 3:6 ¼ 56:1 km=h (22) 1322 0:66 It will be found that solution of Eq. (22) is almost the same of Eq. (18), and all results are close to the declared imact seed which is about 60 km/h. It means Eq. (12) is feasible in vehicle edestrian accident reconstruction. This case is also simulated by Pc-Crash. In the simulation, the vehicle imact seed is 57 km/h, friction coefficient between edestrian and road is 0.5, friction coefficient between edestrian and vehicle is 0.2. The simulation results can be found in Fig. 8. The relative osition of vehicle and edestrian in simulation can be found in Figs. 9 and 10. Through comaring Fig. 9 and the deformation of the vehicle, and Fig. 8, the conclusion that the simulation is well accorded with the actual situation can be obtained. Fig. 10 shows the time the edestrian firstly imact the ground, obviously, the edestrian was imacted by the ste between the road and the cycle track. This is the reason why the throw distance in this case is incredible. Now, it can be concluded that Eq. (15) is reliable in vehicle edestrian accident reconstruction. 4.2. Case 2 This case is the second case in Ref. [19], all information of this case can be found in Fig. 11, which is cited directly from Ref. [19] too. In this case, the throw distance is 19 m and the ost-brakingdistance is 34 m, so A ractice ¼ 34 ¼ 1:79 (23) 19 According to Eq. (15) = 0, it can be concluded that the vehicle was not fully braked, Eq. (2) will not work here because the deceleration of vehicle is unknown. According to Eq. (9) v ¼ 3:2 Fig. 10. Relative osition of vehicle and edestrian (t = 1.320 s). 885 þ 60 60 ffiffiffiffiffi 19 3:6 ¼ 53:6 km=h (24) According to Eqs. (2) and (12) 885 þ 60 v ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0:8 9:8 ð19 0:66Þ 3:6 60 ¼ 53:9 km=h (25) The solution of Eq. (25) is almost the same as Eq. (24), and all results are close to the declared imact seed which is about 45 50 km/h. It means Eq. (12) is feasible in vehicle edestrian accident reconstruction. Fig. 9. Relative osition of vehicle and edestrian in simulation.

T. Zou et al. / Forensic Science International 207 (2011) 135 144 141 Fig. 11. Information of case 2. 4.3. Case 3 This case is cited from ZEDATU Zentrale Datenbank tödlicher Verkehrsunfälle. Fig. 12 shows the accident scene, and Fig. 13 shows a sketch of the accident scene. In this case, the imact osition is unknown. There are skid marks on the road, so it can be concluded that the vehicle is fully braked in ost-imact hase. And Fig. 12 also shows that the edestrian is not imacted by other obstacles while it was sliding on the flat road. The vehicle and edestrian were almost in the same lane, so Eq. (19-2) can be alied v ¼ 5:49 þ m ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S 1 þ S 2 5:49 ffiffiffiffiffiffiffi 4:2 3:6 ¼ 40:5 km=h (26) According to Eq. (17-2), S = 12.35 m, combing with the direction of the vehicle, the imact osition can be determined, which is showed in Fig. 14. In Fig. 14, the imact osition is on the edge of the crosswalk. Through comaring Figs. 14 and 15, it can be concluded that this conclusion is reasonable and Eqs. (17) and (18) are reliable. It is assumed that the imact seed is 37.5 km/h, lag time is 0.22 s, and reaction time is 0.2 s. Then this case was reconstructed by Pc-Crash too, the results can be found in Fig. 16. Through comaring with the solutions of this article and Pc- Crash, it can be concluded that the imact osition obtained from Eq. (17) or (18) and the imact seed obtained from Eq. (19) are reliable.

142 T. Zou et al. / Forensic Science International 207 (2011) 135 144 Fig. 12. Accident scene. Fig. 13. Sketch of the accident scene. Fig. 14. Sketch of the imact osition. 5. Discussion From the study in this article, the imact seed in a vehicle edestrian accident can be calculated by Eqs. (2), (8), (9) or (10), and the relationshi between ost-braking-distance and throw distance can be described by Eq. (11) or (12). Generally, Eqs. (2), (9) and (12) are more convenient in ractice. Eq. (11) or (12) rovides a constraint condition for vehicle edestrian accident reconstruction, it will make the number of conditions needed for reconstructing an accident much less and it can be used to validate credibility of the evidences or reconstruction results. In vehicle edestrian accident reconstruction, the value of f v in Eq. (2) is hard to know if the vehicle is not fully braked, and Eqs. (8), (9) or (10) along with Eqs. (11) and (12) will not work if the accident is not a wra collision and a fully braked car on a dry, flat road. All these should be aid attention to when conclusions obtained in this aer are suosed to be emloyed in accident reconstruction.

T. Zou et al. / Forensic Science International 207 (2011) 135 144 143 Fig. 15. Marks made by olice. Fig. 16. Simulation results of Pc-Crash. The four alications discussed in this aer will be valuable and helful in vehicle edestrian accident reconstruction, but eole should also know that those conclusions will not work if conditions in a true accident are not in accord with those discussed in these four alications. One vehicle edestrian accident is too comlicated in reality, so conclusions obtained in this aer are roosed to combine other methods, e.g., simulation methods or exerts exerience, when they are emloyed in legal circumstances. the accident reconstruction results, which need to be studied in deth in the future. Acknowledgements This work is suorted by the National Natural Science Foundation of China (50808181). And case 3 is rovided by Dr. Ernst Tomasch, Graz University of Technology, Austria. References 6. Conclusions In this aer, two useful formulas were obtained, the first one can be used to calculate imact seed according to throw distance, while the other one can describe the relationshi between ostbraking-distance and throw distance. And the alication ersective of these formulas in vehicle edestrian accident reconstruction are discussed. Conclusions obtained in this aer can make eole gain an elementary cognition on the accident; and some initial values, e.g., initial imact velocity, the imact osition and so on, can be obtained through these conclusions, which will be helful in analyzing the accident in detail. One vehicle edestrian accident is too comlicated in reality, many factors are not considered in this aer, e.g., the influence of the initial velocity of the edestrian and the shae of the vehicle on [1] J.J. Eubanks, Pedestrian accident reconstruction, Lawyers & Judges Publishing Comany, Tucson, AZ, 1994. [2] M. Raymond, R. Brach, Matthew, Brach, Vehicle Accident Analysis and Reconstruction Methods, SAE International Publisher, Pennsylvania, USA, 2005. [3] Amrit Toor, Michael Araszewski, Ravinder Johal, et al., Revision and Validation of Vehicle/Pedestrian Collision Analysis Method, SAE Paer No. 2002-01-0550,. 101 112. [4] Amrit Toor, Michael Araszewski, Theoretical vs. Emirical Solutions for Vehicle/ Pedestrian Collisions, SAE Paer No. 2003-01-0883,. 117 129. [5] Inhwan Han, Raymond M. Brach, Throw Model for Frontal Pedestrian Collisions, SAE Paer No. 2001-01-0898,. 1115 1127. [6] D.P. Wood, C.K. Simms, D.G. Walsh, Vehicle edestrian collisions: validated models for edestrian imact and rojection, Proc. ImechE. Part D: J. Automob. Eng. 219 (2) (2004) 183 195. [7] I. Han, R.M. Brach, Imact throw model for vehicle edestrian collision reconstruction, Proc. ImechE. Part D: J. Automob. Eng. 216 (6) (2002) 443 453. [8] Jun Xu, Yibing Li, Model of vehicle velocity calculation in vehicle edestrian accident based on deflection of windshield, J. Mech. Eng. 45 (2009) 210 215 (in Chinese).

144 T. Zou et al. / Forensic Science International 207 (2011) 135 144 [9] Jun Xu, Yibing Li, Guangquan Lu, et al., Reconstruction model of vehicle imact seed in edestrian vehicle accident, Int. J. Imact Eng. 36 (2009) 783 788. [10] Xiaoyun Zhang, Xianlong Jin, Wenguo Qi, et al., Vehicle crash accident reconstruction based on the analysis 3D deformation of the auto-body, Adv. Eng. Software 39 (2008) 459 465. [11] Xianlong Jin, Xiaoyun Zhang, Jiaotong Shigu Shuzihua Chonggou Lilun yu Shijian (Theory and Practice of Traffic Accident Digital Reconstruction), China Communications Press, 2007 (in Chinese). [12] Teresiński Grzegorz, Madro Roman, Evidential value of injuries useful for reconstruction of the edestrian vehicle location at the moment of collision, Forensic Sci. Int. 128 (2002) 127 135. [13] K. O Riordain, P.M. Thomas, J.P. Phillis, et al., Reconstruction of real world head injury accidents resulting from falls using multibody dynamics, Clin. Biomech. 18 (2003) 590 600. [14] Lei Guo, Xianlong Jin, Xiaoyun Zhang, et al., Study of injuries combining comuter simulation in motorcycle car collision accidents, Forensic Sci. Int. 177 (2008) 90 96. [15] Madro Roman, Teresiński Grzegorz, Neck injuries as a reconstructive arameter in car-to-edestrian accidents, Forensic Sci. Int. 118 (2001) 57 63. [16] Wood Denis, Simms Ciaran, Coefficient of friction in edestrian throw, Imact-J. ITAI 9 (2000) 12 14. [17] Andreas Moser, Hermann Steffan, et al., Validation of the Pc-Crash Pedestrian Model, SAE Paer No. 2000-01-0847,. 1336 1339. [18] A. Moser, H. Steffan, et al., The Pedestrian Model in Pc-Crash-The Introduction of a Multi Body System and Its Validation, SAE Paer No. 1999-01-0445,. 794 802. [19] Jean-Philie Deriester, Christohe Perrin, Thierry Serre, et al., Comarison of Several Methods for Real Pedestrian Accident Reconstruction, Paer No. 05-0333, 2006, htt://www.mathlab.mtu.edu/struther/dro/modeling/05-0333-o.df.