Reconstruction Model of Vehicle Impact Speed in Pedestrian

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Reconstruction model of vehicle impact speed in pedestrianvehicle accident

Jun Xu a,*, Yibing Li a, Guangquan Lu b,1, Wei Zhou a

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

a r t i c l e i n f o

Article history:

Received 21 May 2008

Received in revised form

11 November 2008

Accepted 12 November 2008

Available online 27 November 2008

Keywords:

Accident reconstruction

Pedestrianvehicle accident

Impact speed

PVB windshield glazing

Deflection

a b s t r a c t

Reconstruction of pedestrianvehicle 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 pedestrianvehicle accidents.

2008 Elsevier Ltd. All rights reserved.

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 acci-

dent 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 were4907 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

[35]. 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 coef-

ficient 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[68], see Eq.(1)

vcffiffiffiffiffiffiffiffiffiffi

2mgsp

(1)

wheremis the coefficient of tyre-to-road;s is the length of the skid

mark; gis the acceleration of gravity; vcrefers to the velocity of

vehicle.

However, many pedestrianvehicle accidents are without skid

marks. As the ABS (Antilock Break System) is widely used nowa-

days, fewer marks would be left when the vehicle breaks. In

addition, the road surface under certain weather conditions, such assnow 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

SchmidtNageld[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 0:0178mgvc 0:0271v2c=mg (2)where Xis 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 [1016]. Whats more, along with the model, comes

* Corresponding author. Tel./fax:86 10 62772721.E-mail addresses: [email protected] (J. Xu), [email protected]

hua.edu.cn (Y. Li), [email protected] (G. Lu), [email protected] (W.

Zhou).1 Tel.:86 10 82317350

Contents lists available atScienceDirect

International Journal of Impact Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j i m p e n g

0734-743X/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijimpeng.2008.11.008

International Journal of Impact Engineering 36 (2009) 783788
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/0734743Xhttp://www.elsevier.com/locate/ijimpenghttp://www.elsevier.com/locate/ijimpenghttp://www.sciencedirect.com/science/journal/0734743Xmailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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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 esti-

mate 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 majoradvantages over

monolithic glass: energy-absorbing and fragmentglutinosity,

indicating fewer fragments would spin on the ground. Therefore,

the above-mentioned methods are limited in investigation and

reconstruction.

There are three phases in pedestrianvehicle accidents accord-

ing to the motion of pedestrian: vehicle bumper first impacts with

pedestrians leg, defined as contact phase; and then, pedestrians

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 pedestrianvehicle accidents were

picked out from National Traffic Accident Database of Tsinghua

University (NTADTU), among which, head impact on the wind-

screen 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 gener-

ality, in such boundary conditions, one border (y 0) is taken asexample. The equationsdescribing the boundary condition are [21]:

Vyy0 D

"v

3w

vy32 nv

3w

vx2vy

#y0

K11wy0 (3)

Myy0 D

"v

2w

vy2mv

2w

vx2

#y0

0 (4)

where Vy is the shear force of unite length, D Eh3=121 m2, EistheYoungs modulus of the plate,his the thickness of the plate,wis

the deflection of the plate, (x,y) is the displacement of point on the

plate in the global coordinate, n is thePoissons ration, K11 is the

spring stiffness of the elastic foundation, My is the rotation momentof unite length.

Obviously, K11 0 represents free boundary and K11N refersto simply support boundary.

Then, we conduct finite element analysis (FEA) to show the

difference in deflection of plate under different boundary condi-

tions. 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, seeFig. 3.The above typical three-layered windshield glazing is consid-

ered. tidenotes the thickness of a certain layer. Subscripts gand

PVB refer to glass and PVB film separately. R is the radius of

average pedestrian head (impactor/indenter). The head crashed

into the windshieldglazing 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.

Fig. 1. Windshield glazing under the impact of pedestrian head.

0 2 4 6 8 10-30

-25

-20

-15

-10

-5

0

Time (ms)

Centralpointdeflection(

mm)

Free support boundary

Simply support boundary

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

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783788784


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Kp E2h3w

ab2 (20)

where hwis the thickness of the plate anda,bare the lengths of the

two sides, respectively.

Substitution of(12)and (20)into(19)yields:

v0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2

M

F2

ab2

2E2h3w

!F3=5

2

5

3pk1k22=3

16R

!!!vuut (21)Thus, base on Navier method [28], deflection of windshield

glazing (rectangular plate) under the impact of pedestrian head is

expressed as

wx;y 4Fp

4E2Iab

XNm 1

XNn 1

sin

mpx

a sin

nph

bma

2nb

22sinmpxa sinnpyb (22)where E2Iis the flexural rigidity of windshield; x, h are the distances

to the nearest side of windshield; Iis the largest moment of inertia

of the windshield.

Therefore, we can obtain:

F wx;yp4E2Iab

4PN

m 1PN

n 1sin

mpx

a sin

nph

bma

2nb

22sinmpxa sinnpyb(23)

Substituting(23)into(21), the first half of the entire model that

describesthe relations between deflectionand head impact velocitycanbe developed. In this case, we caneasilycalculate thepedestrian

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

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 pedestrianvehicle accidents.

There are two phases between vehicle first contact with

pedestrian and pedestrian head impact with windshield: contact

phase and impact phase. (seeFig. 5).

Pedestrian is regarded as a single rigid body with initial

momentum I; rotation radius Rp. Hence, the momentum of

pedestrian is

Fh Ia (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 Iare constant. Integration for

Eq.(23), we get:

h

Z ti0

Fdt IZ ti

0adt (24)

Due to the momentum conservation law, we can also obtain:Z ti0

Fdt mpvp1 0

(25)

wherevp1andmpare velocity and mass of pedestrian, respectively.

And it is also known to all that:

Z ti0

adt u1 0 (26)

whereu1 is the angular velocity of pedestrian.

Combination of (25) and (26) and substitution into (24)

yields[12]:

mpvp1h Iu1 (27)BecauseI mpRp2, the following equation can be acquired [12]:

vp1h u1R2p (28)

The vehicle impact speedv0can be expressed as[12]:

v0 vp1u1h (29)As a result of horizontal momentum conservation, the kinetic

momentum of the pedestrianvehicle system is[12]:

mvv0 mpvp1mvu1h vp1

(30)

wheremv is the mass of vehicle.

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

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

Mass of vehicle

Mass of pedestrian

Mass and radius of

pedestrian head

Reconstruction

ModelVelocity of vehicle

Input Calculation Output

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



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Substitute (27) into (28) and then into (30), the pedestrianimpact speedviis [12]:

v0mvvp1h

2mvmp

R2pmvh2

(31)

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

v0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2M

F2

ab2

2E2hw

F3=5

25

3pk1k22=316R

r mvmp

R2p mvh2

mvh2

(32)

where

F wx;yp4E2Iab

4PN

m 1PN

n 1sin

mpx

a sin

nph

bma

2nb

22sinmpxa sinnpyb

2.4. Model summary

Lets summarize the model for convenience. The whole model

can be illustrated asFig. 6. One may not worry about the burden to

input so many values of different variables. Some of them are of

constant values.

3. Results and discussion

3.1. Determination of parameters in the model

In real-world accident reconstruction, we are quite easy to

attain the stature and weight of pedestrian from police investiga-

tion 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 wind-

shield glazing are almost the same, in accident reconstruction, then

we consider nPVB const 0.49for simplicity. The parameters ofPVB and glass are determined in Table 1.

3.2. Real-world accidents for comparison

Because the exact impact velocity cannot be obtained in real-

world traffic accidents, we had to choose the real-world pedes-

trianvehicle accidents with skid marks and consider speed calcu-

lated by skid marks is the exact one. We picked up ten real-world

accidents from NTADTU which have both skid marks and wind-

shield deflection. Results after comparison are listed asTable 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

developedmodel is accurate and reliable enough for us to employ itin pedestrianvehicle 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 reli-

ability of the reconstruction results. This model provides us a new

and convenient method to investigate pedestrianvehicle 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 sup-

ported boundary plate,leading theresultsof modelsmaller. It canbe

concluded safely thatif moreexactelastic conditionis employed, the

results wouldbe better. Another reasonis that in relative highspeed

30 40 50 60 70 804

5

6

7

8

9

10

11

12

13

14

Speed (km/h)

Differenc

e(%)

Fig. 7. Differences increase if the vehicle impact speed increases.

Table 1

Parameters used in both constitutive relations and finite element analysis.

Components Parameters and values

Headform [23] E 6.5 GPa,r 1412 kg/m3,n 0.22Glass[30] E 74 GPa,r 2500 kg/m3,n 0.25,tg 2 mmPVB film[31] K 20 GPa,r 1100 kg/m3,tp 0.76 mmWindshield dimension Panel dimensions (a b): 1320 mm 630 mm

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

Case I Case II Case III Case IV Case V Case VI Case VII Case VIII Case IX Case X

Length of skid mark (m) 11.23 7.80 9.30 15.40 23.00 8.40 15.30 21.10 19.80 24.00

Roadtyre adhesion coefficient 0.841 0.790 0.690 0.740 0.862 0.766 0.760 0.812 0.820 0.760

Deflection of windshield on the

impacted point (mm)

37 23 19 42 49 27 41 47 45 48

Location of impacted point

(xmm,h mm)

(145,650) (350, 600) (230, 100) (250,400) (240, 470) (135, 460) (735, 160) (135, 695) (635, 395) (715, 480)

Dimensions of windshield

(amm,b mm)

(1320, 620) (1310, 730) (1350, 730) (1280, 630) (1200, 680) (1310, 670) (1400, 710) (1350, 660) (1295, 625) (1380, 690)

Bumper height (mm) 505 495 525 495 505 499 530 512 501 510

Weight of pedestrian (kg) 46 53 75 65 78 69 79 76 69 74

Mass of vehicle (kg) 1325 1880 1225 1480 1290 1340 2105 1890 1450 1655

Stature of pedestrian (cm) 175 168 172 166 173 158 176 173 166 169

Exact speed (km/h) 48.98 39.56 40.37 53.80 70.97 40.42 54.34 65.97 64.22 68.07

Result of the model (km/h) 45.94 37.42 38.18 50.20 63.72 37.31 51.29 60.99 57.81 60.73

Difference (%) 6.20 5.40 5.42 6.70 10.22 7.69 5.61 7.55 9.98 10.78

J. Xu et al. / International Journal of Impact Engineering 36 (2009) 783788 787


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accidentswindshield is broken because of largedeformation 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 wouldincrease a lotif pedestrian is impactedby vehicle in high

speed and then rotated a lot. To conclude, this model may not be

suitable to reconstruct high speed pedestrianvehicle accident.

Thirdly, this model excludes the consideration for curvature and

thickness of thewindshield as well as the windshield angle. In most

cases,curvature in windshield is small so we treat thewindshield 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. 7shows that the relation

between the speed anddifference may be: speed differencea. Thisrelation 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 themodel 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, should-

ers impact on the windshield would add the deflection of wind-

shield 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 simplifi-

cations were made. Material model was then chosen. The mostimportant part of the paper is the development of the dynamic

model of vehicle impact speed versus windshield deflection. Based

on impact dynamics and rectangular platetheory,the entire process

of pedestrianvehicle 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 maynot be suitable tocalculate thevehicle impactvelocity 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 notshould impactingon thewindshield 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 Peoples Republic of China and a part

of the project titled Dynamic response of PVB laminated wind-

shield subjectedto head impact supported by State Key Laboratory

of Automotive Safety & Energy, Tsinghua University.

The authors also thank the anonymous referees useful

comments and suggestions.

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Jun Xu: Graduate student of Department of Automotive Engineering, TsinghuaUniversity. Research interests: vehicle impact safety, traffic accident reconstructionand driver behavior.

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 Engi-neering, Beihang University, China. Research interests include road traffic safety, driverbehavior, accident reconstruction, and application of computer vision in road trafficsystem.

Wei Zhou: Master, graduated from Department of Automotive Engineering, TsinghuaUniversity. Research interests: traffic accident reconstruction and simulation.


Reconstruction Model of Vehicle Impact Speed in Pedestrian

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