Reconstruction model of vehicle impact speed in pedestrian–vehicle accident

International Journal of Impact Engineering 36 (2009) 783–788

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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng

Reconstruction model of vehicle impact speed in pedestrian–vehicle accident Jun Xu a, *, Yibing Li a, Guangquan Lu b,1, Wei Zhou a a b

State Key Laboratory of Automotive Safety and Energy, Department of Automotive Engineering, Tsinghua University, Beijing 100084, China School of Transportation Science and Engineering, Beihang University, Beijing 100191, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 May 2008 Received in revised form 11 November 2008 Accepted 12 November 2008 Available online 27 November 2008

Reconstruction of pedestrian–vehicle accident is a worldwide problem. Numerous previous studies have been carried out on accidents with vehicular skid marks or definite pedestrian throw distances. However, little could be done if marks or throw distances cannot be obtained in accident reconstruction. This paper first describes the physical model of dynamic process of pedestrian head impact on windshield glazing. Some simplifications are made to obtain a better and more practical model, including discussing the support boundary conditions. Firstly, the paper modeled the relations between pedestrian impact speed and deflection of windshield glazing based on the impact dynamics and thin plate theory. Later, the relations of vehicle impact speed and deflection are discussed. Therefore, a model of vehicle impact speed versus deflection of windshield glazing is developed. The model is then verified by ten real-world accident cases to demonstrate its accuracy and reliability. This model provides investigators a new method to reconstruct pedestrian–vehicle accidents. Ó 2008 Elsevier Ltd. All rights reserved.

Keywords: Accident reconstruction Pedestrian–vehicle accident Impact speed PVB windshield glazing Deflection

1. Introduction Worldwide significant efforts have been made to improve the protection of vulnerable road users against injuries and deaths, especially for pedestrians. However, the situation of pedestrian safety is still severe and worrying. China has been consistently ranked as a country with high percentage of pedestrian fatality rates because of its mixed traffic and transportation ways. According to the Road Traffic Accident Annual Census Report of China [1], more than 89,455 persons died in at least 378,781 accident cases in 2006, among which, pedestrian accounted for 26.01%, the highest proportion of all traffic fatalities. On the average, in China, a pedestrian is injured in every 5 min and one is killed in every 17 min. Even in a country where the traffic management is comparatively well organized, for example, the US, pedestrian safety is also the focus of public safety. In 1999 in the US, there were 4907 pedestrian killed, weighting 12% of all traffic fatalities [2]. While the age and state of health of the pedestrian, the nature of the impact and the vehicle shape all affect the outcome of injury, the prime factor in injury/fatality risk is the vehicle impact speed [3–5]. Vehicle impact speed is the prior focus of accident investigators.

At the very beginning, the reconstruction model used in vehicle speed estimation is based on energy conservation law: first a coefficient is determined by the pattern of skid mark according to previous experience and then the coefficient and the length of skid mark are employed to decide the initial velocity at the beginning of the mark [6–8], see Eq. (1)

vc ¼

pffiffiffiffiffiffiffiffiffiffi 2mgs

where mis the coefficient of tyre-to-road; s is the length of the skid mark; g is the acceleration of gravity; vc refers to the velocity of vehicle. However, many pedestrian–vehicle accidents are without skid marks. As the ABS (Antilock Break System) is widely used nowadays, fewer marks would be left when the vehicle breaks. In addition, the road surface under certain weather conditions, such as snow and rain, would have no marks left on it. Aiming to solve this problem, a pedestrian throw distance model to estimate the vehicle initial impact speed based on kinematics law was developed by Schmidt–Nageld [9]. Several passenger cars with different vehicle masses, dimensions and initial impact velocities were tested. The following empirical formula was obtained through data fitting:

X ¼ 0:0178mgvc þ 0:0271v2c =mg * Corresponding author. Tel./fax: þ86 10 62772721. E-mail addresses: [email protected] (J. Xu), [email protected] (Y. Li), [email protected] (G. Lu), [email protected] (W. Zhou). 1 Tel.: þ86 10 82317350 0734-743X/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2008.11.008

(1)

(2)

where X is the throwing distance. Many authors have done numerous tests to determine the coefficients in the throw distance model and made some changes to the parameters [10–16]. What’s more, along with the model, comes

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783–788

another problem: it is a difficult task to determine the pedestrian throwing distance because traces or marks that indicate the contact point of vehicle and pedestrian are not easy to acquire in the accident scene. Therefore, Braun and Strobl [16,17] used throw distance of spinning fragment from windshield and lamp to estimate the impact velocity of vehicle. Following this work, Xu [8,18– 20] put forward a generalised fragment throw distance model to calculate the impact speed of vehicle by employing the dimensions of the glass fragment field, based on the kinematics law. According to authors’ accidents investigation experiences, exact values of parameters describing the glass fragments are difficult to gain. Windshield glazing on modern vehicle consisting of two soda lime glass plies adhered by a polymer interlayer. PVB (polyvinyl butyryl), a widely used windshield interlayer, has two major advantages over monolithic glass: energy-absorbing and fragment–glutinosity, indicating fewer fragments would spin on the ground. Therefore, the above-mentioned methods are limited in investigation and reconstruction. There are three phases in pedestrian–vehicle accidents according to the motion of pedestrian: vehicle bumper first impacts with pedestrian’s leg, defined as ‘‘contact phase’’; and then, pedestrian’s head impacts with windshield, engine hood or A-pillar, called ‘‘impact phase’’; pedestrian slides down onto the ground at last, named as ‘‘fall-over phase’’. 237 pedestrian–vehicle accidents were picked out from National Traffic Accident Database of Tsinghua University (NTADTU), among which, head impact on the windscreen accounted for 81.02% of all the vehicle part contacted with pedestrian head. It is obvious that windshield of vehicle contains much information about accidents. In this paper, a proper impact dynamics model is put forward describing impact between pedestrian head and windshield. A mathematical model characterizing the deflection of the impacted point and impact speed of pedestrian head is suggested. After combining the two models, a complete reconstruction model of vehicle impact speed calculation is developed. Finally, in order to demonstrate the validity of the model, ten real-world accidents are chosen to compare the results. 2. Methods 2.1. Abstract physical model As mentioned above, a typical composite PVB windshield glazing has two pieces of glass with an interlayer between them. When head crashes into the windshield plate, there is a clear deflection of the impacted point on the glazing, shown in Fig. 1. The deflection is much lager than the thickness of the entire glazing, indicating that it is a large deformation problem. Thus, we consider there is no slide between the layers for simplicity.

The shape of windshield glazing can be regarded as rectangle and the entire windshield glazing is considered as a composite thin plate. The comparative directions of pedestrian motion to that of vehicle are of various kinds. To make the problem simply, we ignore the prominence on the head, for instance, eyes, noses and ears. In other words, the head is treated as a sphere headform. Windshield glazing is usually supported by rubber bar made of polyurethane, a kind of elastic material. Without the loss of generality, in such boundary conditions, one border (y ¼ 0) is taken as example. The equations describing the boundary condition are [21]:

# "   v3 w ð2  nÞv3 w þ Vy y¼0 ¼ D vy3 vx2 vy # "   v2 w mv2 w My y¼0 ¼ D þ vy2 vx2

(3)

¼ K11 ½wy¼0 y¼0

¼ 0

(4)

y¼0

where Vy is the shear force of unite length, D ¼ Eh3 =12ð1  m2 Þ, E is theYoung’s modulus of the plate, h is the thickness of the plate, w is the deflection of the plate, (x, y) is the displacement of point on the plate in the global coordinate, n is thePoisson’s ration, K11 is the spring stiffness of the elastic foundation, My is the rotation moment of unite length. Obviously, K11 ¼ 0 represents free boundary and K11 ¼ N refers to simply support boundary. Then, we conduct finite element analysis (FEA) to show the difference in deflection of plate under different boundary conditions. A rectangular plate made of composite laminated glass material is analyzed in FEA method. Fig. 2 shows that there are only about 3% differences between two boundary conditions. Due to the brittleness of the glass material, the plate cannot bear much deflection and bending moment. As a result, the effect of boundary conditions on the deflection of plate is much less. For simplicity, we consider the support boundary as simply support one. Thus, an abstract physical model of impact between pedestrian head and windshield glazing is conceived, see Fig. 3. The above typical three-layered windshield glazing is considered. ti denotes the thickness of a certain layer. Subscripts ‘‘g’’and ‘‘PVB’’ refer to glass and PVB film separately. R is the radius of average pedestrian head (impactor/indenter). The head crashed into the windshield glazing with a velocity ofv0. We define the glass layer which would contact with the head as inner glass layer, and the other glass layer is called outer glass layer.

0

Central point deflection (mm)

784

Free support boundary Simply support boundary

-5

-10

-15

-20

-25

-30

0

2

4

6

8

10

Time (ms) Fig. 1. Windshield glazing under the impact of pedestrian head.

Fig. 2. Comparison of central point deflection under free support boundary and simply support boundary.

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783–788

785

Headform R

Head form v0

S Windshield

Inner glass layer tP

Windshield glazing

PVB film Outer glass layer

tg

2.2. Material model The stress–strain relations of PVB are influenced by time because PVB is a viscoelastic material. Ref. [22] pointed out that the time period of impact between pedestrian head and windshield glazing is comparatively short, about 0.1 s. In such a short time period, the shear modulus G(t) of PVB would not change a lot. Thus, we consider PVB is a linear elastic material during the impact. Both inner glass layer and outer glass layer are common float glass, so relations between shear modulus G(t), bulk modulus K, Young’s modulus E and Poisson’s ratio n are [24]:

E 2ð1 þ nÞ

E K ¼ 3ð1  2nÞ

Fig. 4. Headform impact on the windshield glazing.

If we denote by s the distance that the headform approaches the windshield, it is obvious to see that:

Fig. 3. Schematic illustration of a sphere pedestrian headform impacting on a windshield glazing.

G ¼

δp

tg

(5)

(6)

Same formulae could be used on calculating PVB material. Glass and PVB film both can be treated as orthotropic materials according to their physical and material properties. Therefore, we assume that each layer of composite windshield is orthotropic with respect to its material symmetry lines and obeys Hooke’s law. It then becomes reasonable to consider the composite windshield as integrity. As a result, an equivalent elastic modulus and Poisson’s ration should be introduced as follows [24]:

E ¼

2tg Eg þ tp Ep 2tg þ tp

(7)

n ¼

2tg ng þ tp np 2tg þ tp

(8)

s_ ¼ v0

(10)

Greszczuk [25] showed that if the contact duration between the impactor and the target is very long in comparison with their natural periods, vibrations of the system can be neglected. It can then be assumed that the impact force according to the Hertz contact law could be described as follows:

Fc ¼ ns2=3

(11)

where n is the contact stiffness defined by the shape of the impactor. Headform is sphere-shaped object, and then n can be written as

n ¼

pffiffiffi 4 R 3pðk1 þ k2 Þ

(12)

where

k1 ¼

1  n21 1  n2 ¼ pE1 pE

(13)

k2 ¼

1  n22 pE2

(14)

When studying the contact behavior of composite material, Sankar [26] indicated that Eq. (14) can be rewritten as follows:

k02 ¼

1

(15)

pE2

Impact force and the corresponding deflection have a certain relation in impact problem:

Fp ¼ Kp dp

where E and n are equivalent Young’s modulus and equivalent Poisson’s ration of windshield glazing. We are concerned about the dynamic response of windshield in this paper. Consequently, we don’t have to investigate many details about pedestrian head. Only values of physical parameters from references are substituted into the featureless spherical headform used in this study.

(16)

where Fp represents contact force; Kp is the ‘‘elastic property’’ of the windshield glazing, depending on the material of the glazing; dp is the curvature of the glazing. The governing equation can be acquired according to the system energy conservation law:

1 2 Mv ¼ 2 0

Z dmax 0

Fp ddp þ

Z

s 0

Fc ds

(17)

Substitution of (11) and (16) into (17) yields: 2.3. Dynamics model 2.3.1. Deflection versus pedestrian head impact speed model Usually, pedestrian head would intrude into the windshield and cause the glazing plate curving or even broken, shown in Fig. 4. Denoting the time period during the impact t, the impact force of the pedestrian head is

F ¼ M

dv0 dt

(9)

where M is the mass of headform; v0 is initial speed of headform.

1 2 1 2 2 Mv ¼ Kp dp þ ns2=5 2 0 2 5

(18)

Considering Fc ¼ Fp ¼ F, we are able to rewrite (18):

1 2 1 F2 Mv0 ¼ 2 2 Kp

! þ

2 F 3=5 5 n2=3

! (19)

Young [27] suggested that when a rectangular plate is simply supported, the above-mentioned ‘‘elastic property’’ can be determined:

786

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783–788

Fig. 5. Schematic of contact phase and impact phase.

Kp ¼

E2 h3w ab2

(20)

where hw is the thickness of the plate and a, b are the lengths of the two sides, respectively. Substitution of (12) and (20) into (19) yields:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !!!ffi ! u u2 ab2 2 ð3pðk1 þ k2 ÞÞ2=3 t 2 3=5 F þF v0 ¼ M 5 16R 2E2 h3w

(21)

(22)

4

PN

m¼1

wðx; yÞp4 E2 Iab mpx nph PN sin a sin b mpx npy  2 2 sin a sin b n ¼ 1   m 2þ n a b

(23)

(23)

where F is the contact force; h denotes to the height of contact point; a is the angular acceleration of pedestrian. During the impact time ti, h and I are constant. Integration for Eq. (23), we get:

Z

ti

Fdt ¼ I

Z

0

Z

ti

adt

(24)

0

Due to the momentum conservation law, we can also obtain: ti

0

where E2I is the flexural rigidity of windshield; x, h are the distances to the nearest side of windshield; I is the largest moment of inertia of the windshield. Therefore, we can obtain:

F ¼

Fh ¼ I a

h

Thus, base on Navier method [28], deflection of windshield glazing (rectangular plate) under the impact of pedestrian head is expressed as

mpx nph N X N sin sin X 4F mpx npy a b wðx; yÞ ¼ 4    2 2 sin a sin b p E2 Iab m ¼ 1 n ¼ 1 m 2 n a þ b

impact speed is not the same as pedestrian head impact speed for bonnet-type vehicles due to the revolution of pedestrian in impact. Such vehicles are involved most in pedestrian–vehicle accidents. There are two phases between vehicle first contact with pedestrian and pedestrian head impact with windshield: contact phase and impact phase. (see Fig. 5). Pedestrian is regarded as a single rigid body with initial momentum I; rotation radius Rp. Hence, the momentum of pedestrian is

  Fdt ¼ mp vp1  0

where vp1 and mp are velocity and mass of pedestrian, respectively. And it is also known to all that:

Z 0

ti

adt ¼ u1  0

(26)

where u1 is the angular velocity of pedestrian. Combination of (25) and (26) and substitution into (24) yields [12]:

mp vp1 h ¼ I u1

(27)

Because I ¼ mpR2p, the following equation can be acquired [12]:

Substituting (23) into (21), the first half of the entire model that describes the relations between deflection and head impact velocity can be developed. In this case, we can easily calculate the pedestrian head impact velocity if we obtain the exact measurement. 2.3.2. Pedestrian head impact speed versus vehicle impact speed model According to the front-end shape, mini-cars, small, midsize and large sedans, sports and specialty vehicles, wagons and SUVs can also be grouped together as bonnet-type vehicles [29]. Vehicle

vp1 h ¼ u1 R2p

(28)

The vehicle impact speed v0 can be expressed as [12]:

v0 ¼ vp1 þ u1 h

(29)

As a result of horizontal momentum conservation, the kinetic momentum of the pedestrian–vehicle system is [12]:

  mv v0 ¼ mp vp1 þ mv u1 h þ vp1 where mv is the mass of vehicle.

Windshield dimension Location of impact point Deflection of windshield panel Moment of inertia of windshield and pedestrian Young’ s modulus and Poisson’ s ratio of PVB, glass, pedestrian head

Reconstruction Model

Velocity of vehicle

Calculation

Output

Mass of vehicle Mass of pedestrian Mass and radius of pedestrian head

Input

(25)

Fig. 6. Illustration of the brief structure of the model.

(30)

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783–788 Table 1 Parameters used in both constitutive relations and finite element analysis.

14 13 12

Difference(%)

11

Components

Parameters and values

Headform [23] Glass [30] PVB film [31] Windshield dimension

E ¼ 6.5 GPa, r ¼ 1412 kg/m3, n ¼ 0.22 E ¼ 74 GPa, r ¼ 2500 kg/m3, n ¼ 0.25, tg ¼ 2 mm K ¼ 20 GPa, r ¼ 1100 kg/m3, tp ¼ 0.76 mm Panel dimensions (a  b): 1320 mm  630 mm

10 9

3. Results and discussion 8

3.1. Determination of parameters in the model

7 6 5 4 30

40

50

60

70

80

Speed (km/h) Fig. 7. Differences increase if the vehicle impact speed increases.

Substitute (27) into (28) and then into (30), the pedestrian impact speed vi is [12]:

v0 ¼ 

h2

mv vp1  mv þ mp R2p þ mv h2

(31)

Combination of (21) and (23) and (31) yields:

v0 ¼

787

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi      2=3   ð3pðk1 þk2 ÞÞ 2 F2 ab2 2 3=5 þF mv þmp R2p þmv h2 M 5 16R 2E h 2 w

mv h2 (32)

where

F ¼ 4

PN

m¼1

wðx; yÞp4 E2 Iab mpx nph PN sin a sin b mpx npy sin  2 2 sin n ¼ 1   a b m 2þ n a b

2.4. Model summary Let’s summarize the model for convenience. The whole model can be illustrated as Fig. 6. One may not worry about the burden to input so many values of different variables. Some of them are of constant values.

In real-world accident reconstruction, we are quite easy to attain the stature and weight of pedestrian from police investigation files. Based on Ref. [32], masses, center of masses, inertias, and distance between inertias of every body part can be acquired. Parallel axis theorem is employed to calculate the rotation radius and inertia of entire pedestrian. PVB material properties in windshield glazing are almost the same, in accident reconstruction, then we consider nPVB ¼ const ¼ 0.49for simplicity. The parameters of PVB and glass are determined in Table 1. 3.2. Real-world accidents for comparison Because the exact impact velocity cannot be obtained in realworld traffic accidents, we had to choose the real-world pedestrian–vehicle accidents with skid marks and consider speed calculated by skid marks is the exact one. We picked up ten real-world accidents from NTADTU which have both skid marks and windshield deflection. Results after comparison are listed as Table 2. 3.3. Results discussion First of all, the differences, among which the maximum value is 10.78% and average value is 7.56%, showing us that this newly developed model is accurate and reliable enough for us to employ it in pedestrian–vehicle accidents without skid marks or pedestrian throw distances. Using this model to further verify the results of accidents reconstruction are able to enhance the accuracy and reliability of the reconstruction results. This model provides us a new and convenient method to investigate pedestrian–vehicle accidents. Secondly, ten speed values computed from the model are a little bit smaller than the exact speed values. One reason is that the simplicity of the supporting boundary is responsible for it. Exact deflection is larger than the deflection occurred with simply supported boundary plate, leading the results of model smaller. It can be concluded safely that if more exact elastic condition is employed, the results would be better. Another reason is that in relative high speed

Table 2 Comparison of exact speed with speed calculated from the model.

Length of skid mark (m) Road–tyre adhesion coefficient Deflection of windshield on the impacted point (mm) Location of impacted point (x mm, h mm) Dimensions of windshield (a mm, b mm) Bumper height (mm) Weight of pedestrian (kg) Mass of vehicle (kg) Stature of pedestrian (cm) Exact speed (km/h) Result of the model (km/h) Difference (%)

Case I

Case II

Case III

Case IV

Case V

Case VI

Case VII

Case VIII

Case IX

Case X

11.23 0.841 37

7.80 0.790 23

9.30 0.690 19

15.40 0.740 42

23.00 0.862 49

8.40 0.766 27

15.30 0.760 41

21.10 0.812 47

19.80 0.820 45

24.00 0.760 48

(145, 650)

(350, 600)

(230, 100)

(250, 400)

(240, 470)

(135, 460)

(735, 160)

(135, 695)

(635, 395)

(715, 480)

(1320, 620)

(1310, 730)

(1350, 730)

(1280, 630)

(1200, 680)

(1310, 670)

(1400, 710)

(1350, 660)

(1295, 625)

(1380, 690)

505 46 1325 175 48.98 45.94 6.20

495 53 1880 168 39.56 37.42 5.40

525 75 1225 172 40.37 38.18 5.42

495 65 1480 166 53.80 50.20 6.70

505 78 1290 173 70.97 63.72 10.22

499 69 1340 158 40.42 37.31 7.69

530 79 2105 176 54.34 51.29 5.61

512 76 1890 173 65.97 60.99 7.55

501 69 1450 166 64.22 57.81 9.98

510 74 1655 169 68.07 60.73 10.78

788

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783–788

accidents windshield is broken because of large deformation in most cases. Measurements of deflection cannot be accurate enough, usually smaller than the exact measurements. Therefore, the results would be smaller in some extent. Moreover, the effective mass of head would increase a lot if pedestrian is impacted by vehicle in high speed and then rotated a lot. To conclude, this model may not be suitable to reconstruct high speed pedestrian–vehicle accident. Thirdly, this model excludes the consideration for curvature and thickness of the windshield as well as the windshield angle. In most cases, curvature in windshield is small so we treat the windshield as a plate, not a shell. Most of the windshields on modern passenger vehicles have the same thickness according to the automotive industrial standard. Actually, the windshield angle may vary from one vehicle to another. Thus, the impact speed of the pedestrian head would decrease slightly according to the exact angle, affecting the accuracy of the model. In addition, the comparison results show that with the speed increasing, the differences increase. Fig. 7 shows that the relation between the speed and difference may be: speed ¼ differencea. This relation suggests that this vehicle impact speed reconstruction model might not be suitable for high-speed accidents. Deflection of windshield is difficult to measure and difficulty in determining the deflection of windshield in high-speed accidents suggesting the model not suitable for such cases as well. Last but not the least, in some cases, not only did the pedestrian head impact on the windshield glazing, but also the shoulder of pedestrian impacted on the glazing. In the latter scenario, shoulder’s impact on the windshield would add the deflection of windshield that is hard to distinguish. It is suggested not to employ this model under such circumstances. 4. Conclusion In this paper, we first constructed the abstract physical model describing dynamic process that the pedestrian head impacts on the composite PVB windshield glazing. Some necessary simplifications were made. Material model was then chosen. The most important part of the paper is the development of the dynamic model of vehicle impact speed versus windshield deflection. Based on impact dynamics and rectangular plate theory, the entire process of pedestrian–vehicle accident excluding the slide down phase was discussed. The results of new model showed good agreement with those calculated from skid marks considered as exact speed in ten real-world accidents. Therefore, a new and reliable method of accident reconstruction method is established. However, this new model may not be suitable to calculate the vehicle impact velocity in high speed collision accident between pedestrian and vehicle as mentioned above. In addition, one should check the impact point to ensure that it is head not should impacting on the windshield before using this new calculation method. Acknowledgement This work is a part of the project titled ‘‘Road Traffic Accident Reconstruction Analysis Platform’’ (No. 20052DGGBJSJ002) in support of Police Ministry of People’s Republic of China and a part of the project titled ‘‘Dynamic response of PVB laminated windshield subjected to head impact’’ supported by State Key Laboratory of Automotive Safety & Energy, Tsinghua University. The authors also thank the anonymous referees’ useful comments and suggestions. References [1] Traffic management bureau of Police Ministry. Road traffic accident annual census report of China. Beijing; 2007.

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Yibing Li: Professor of Department of Automotive Engineering, Tsinghua University. Research interests: traffic accident reconstruction and measurement technology. Guangquan Lu: Associate professor of School of Transportation Science and Engineering, Beihang University, China. Research interests include road traffic safety, driver behavior, accident reconstruction, and application of computer vision in road traffic system. Wei Zhou: Master, graduated from Department of Automotive Engineering, Tsinghua University. Research interests: traffic accident reconstruction and simulation.