A STUDY OF COMPUTER SIMUI,ATION SYSTEM FOR RECONSTRUCTING

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1 237 STUDY OF COMPUTER SIMUI,TION SYSTEM FOR RECONSTRUCTING CR.TO.CR COLLISION CCIDENTS INVOLVING THE SECOND IMPCT Lang Wei, Dr. Egn. Vice Professor Faculty of utomobile Engineering Xi'an Highway UniversitY Xi'an, Shaanxi, china Fax: Yinsan Chen Professor Faculty of utomobile Engineering Xi'an Highway UniversitY Xi'an, Shaanxi, 7loo64 China Fax: Hirotoshi Ishikawa ChiefResearcher Japan utomobile Research Institute 305 Japan Fax: l 1 35 Rui Fu, Dr. Egn. Vice Professor Faculty of utomobile Engineering Xi'an Highway UniversitY Xi'an, Shaanxi, 7l0064 China Fax: Tao Chen Graduate Student Faculty of utomobile Engineering Xi'an HighwaY UniversitY Xi'an, Shaanxi, China Fax: bstract: In this paper, based on the accident site information, a car-to-car accident reconstruction system is developed, which is used to simulate the impact velocity and trajectory of vehicles. The accidents concerned involve the second impact' Five collision tests involving second impact were used to evaluate the system. The simulation results are found to be in good agreement with real-world test results' 1. FOREWORI) In the field of traffic accidents authenticating, estimating the impact velocity and trajectory of vehicles is often the main goal of an accident analysis in order to establish accident course and transact accident responsibility justly in the light of the law Car-to-car collisions are a common tra{iic accident form. Its impact analytical solutions have aroused the attention of the accident investigators. The authors published a car-to-car analytical impact model not involving the second impact and the animate reconstructing program three years ago. The video and data of sixteen collisions tests provided by Japan utomobile Research Institute (JRI) was used to test and verify its validity. The second impact was found in some videos of collision tests provided by JRI. nd specifically this Journal ol thc Easlern sia Srciety lirr Transportation Studies, Vol.3, No.l, September, 1999

2 238 L,ang WEI,Hirotoshi ISHIKW, Yinsan CHEN, Rui FU and Tho CHEN kind of accident was called car-to-car impact accident involving the second impact. Car-to-car impact accident, as a special traflic accident form and its analytical simulation and reconstruction method has aroused great interest for the accident investigators. ut, many real-world car-to-car collisions involve the second impact (It can be deduced by check the mark on the car body whether the second impact occulred or not). For this kind of accidents, the second impact center position in the ground coordinate system can't be obtained by investigating the accident site, besides, the instantaneous motion state and velocity during the second impact is unknown. It is therefore much more complex to simulate and reconstruct car-to-car impact.accidents involving the second impact. Furthermore, it is difficult to verify through tests. The method used to simulate car-to-car impact accident involving second impact hasn't been found till now. This paper improves the algorithms [Lang, Hirotoshi and Takashi (1995)], [Lang, Yinsan, Takashi and Hirotoshi (1996)1, [Hirotoshi (1995)], and develops the methods dealing with reconstruction of carto-car collisions accidents involving the second impact, based on the analysis for a number ofcar-to-car collision tests. The video and data offive collision tests were used to test and veri$ its validity. 2.THE SIMULTION SYSTEM FOR CR-TO-CR IMPCT CCIDENT INVOLVING THE SECOND IMPCT The meaning of the notation and subscript is as follows: (NOTTTON) X, Y: the centroid coordinate of vehicle in the ground coordinate system r, 4 : the centroid coordinate of vehicle in the second impact coordinate system( r k 4) 0 : the angle between the longitudinal central line of vehicle and x axle m : vehicle mass V: velocity w: angular velocity p : radius of gytation P: impact momentum e : restitution coefficient L: wheel spacing : axle spacing Lr: distance from the centroid to fore axle L, : distance from the mark center of second impact to centroid (m) ( It is positive in the front of the centroid; negative behind the centroid.) L, : the total length of vehicle (m) u : road friction coefficient,: the width of vehicle (m) r x, E y, 0 : the permitted error of the centroid position along x axle, y axle and o angle. (Subscript) X, y, r, rl:the component of x axle, y ax1e, taxle (tangential), I axle (normal) k: the value at second impact center (or the second impact mark center) Journal oflhe Easlernsia Society for Transportation Studies, Vol.3, No.l, September, 1999

3 239 Study of Computer Simulatiou Syslem lbr Rcconstructiug Car-to-Car Collision ccidcnts Involving the Second lmpact so: (initial) the value at impact position su: the value at rest Position q : pre-impact instantaneous value g: post-impact instantaneous value T: test value S: simulation value, : the value of vehicle, vehicle The car-to-car accidents analytical impact model involving the second impact consists of the following subsystem: l) The subsystem used to calculate the second impact center position' 2) The subsystem used to calculate the post-impact instantaneous motion variables. 3) The computation model at the second impact instant. 4) The computation model for estimating the initial impact velocity' 2.1 The Subsystem used To calculate The second Impact Center Position Finding the second impact center position in ground coordinate system is key to analyzing the car-to-car collision accident involving the second impact. The reason that second impact occurs after the first impact is the sharp rotation of impact vehicles. It can be inferred that second impact mainly occured on the two sides of vehicle (including the end of the sides). dditionally, studying numerous data of collision tests, we can infer that the impulsive force of second impact is less than that of the first impact. In view of this, the method of asymptotic approximate which used to compute the second impact center position was presented. Firstly, under the condition of neglecting the second impact, on the basis of the method of reference [Lang, Yinsan, Takashi and Hirotoshi (1996)], the trajectory of the second impact mark center point can be computed in the light of the impact and rest position. Then, the approximate coordinate (X*, Y*) of second impact center can be obtained. The formula is as follows: Where I x,) ltx,;,^, * tr- i = it Y,^i * I = il{min(dr, + 0) U [mind*, 0minfl] dr,=m X *i\ l2\ Y*,i) t2 ), (i = 1,2,o o o,n)l (i =l,2,ooo,n) (l) (2) lkt^, f,=1 l[<a^, - ot')l - 0u,) -,rll lon, l0 n, - 0r,l< (r / 2) - 0r,l> (tr I 2) (i =l,2,ooc,n) Journal of lhc Eastern sia S<rcicly lirr Transportation Studies, Vol.3, No.l, September, 1999

4 240 Lang WEI,Hirotoshi ISHIKW, Yinsan CHEN, Rui FU and Tho CHEN 2.2The Subsystem Used to Calculate The Post-Impact Instantaneous Motion Variables The subsystem used to calculate the second post-impact instantaneous motion variables mainly consists of the following computation models:. iteration-convergence judge model. kinematics model of impact vehicles. tire-ground mechanics model (adopt G. Gim and P. E Nikavesh tire model [Gwanghun and Parviz (1990)], [Gwanghun and Parviz (1991)]) In this subsystem, the variables such as velocity and angular velocity can be obtained in the light of second impact center and the rest positions [Lang, Hirotoshi and Takashi (1995)], [Lang, Yinsan, Takashi and Hirotoshi (1996)]. Its computational flow diagram is shown in Figure l. (The second impact position) Tire-ground mechanics model + Kinematics model of impact vehi c I es Iteration-convergence judge model The instantaneous motion variables after the second impact Fig. I Thetomputational Flow Diagram of Motion Variables after the Second Impact 2.3 The Computation Model at the Second Impact Instant. This computational model is used to describe the relation of the motion variables between the instant pre-impact and post-impact. When the second impact center was obtained, the post-impact instantaneous velocity and angular velocity can be deduced from pre-impact velocity of the second impact. s shown in Figure 2, set the side of struck vehicle as the impact surface, and the second impact center k as origin. The t -axie is tangential to the impact surface, parallel to the longitudinal central line of vehicle body, then the second impact coordinate system t k 4 is built. The following instantaneous impact model is obtained based on the law of conservation ofnomentum. vorrn=rrr*-z (3) vor,n =vrr,n -fr Q) Journal ofthe Eastern sia Society for Transportation Studies, Vol.3, No.l, Seplcmber, 1999

5 241 Slldy of Computer Simulation System for Reconstructing Car-to-Car Collision ccidents Involving the Second Impact Po,r* - ok l = d rk 4 a =mtpe (5) Vq*ta =t'rrr, - b*, (6) n, Yo*a=Yekta-fi (7) Prrru - Prrrlu 0ok T maps (8) Where e,, = uj,-af',^"t' * L) * u,*a "'a + )-l) P" = o;-^.)l* '-*o'" * )) *''n"tr * lll Figure 2. The Coordinate SYstem of Second Impact Center Position Ra, = V e*4t - t rra) ru - V glat + t *,to stt i Xr, = V grra + s - Y g*r,t - q k/a) shl M,,"= m,m,m"i f qtfrtlqams ; ^-= ' 1/4mtl7qtms ^,=-Z:l!!-am-a-i /,tmtt/,ams ^o=tu' u-*fu+ mtpt mtpe r,,t=-+1, y*=-4-,r.,= f",. i t,,=-2;- pt +tu pr' +ru' / tlt pr' +qr' Pi +t\u- 2.4 The Computation Model for Estimating the Initial Impact Velocity In this subsystem, post-impact velocity and angular velocity of the first impact can be gained through the first and second impact center position. Furthermore, on the basis of impact velocity computational model, pre-impact velocity and angular velocity of the first impact can be obtained [Lang, Hirotoshi and Takashi (1995)], [Lang, Yinsan, Takashi and Hirotoshi (1996)1. Its computational flow diagram is shown in Figure THE SIMULTION SYSTEM FOR RECONSTRUCTING CR-TO-CR COLLISIONS INVOLVING SECOND IMPCT The flow diagram of the animated simulation system for reconstructing car-to-car collisions involving second impact is shown in Figure 4. The program automatically read and input the post-impact velocity and angular velocity calculated in the former section. fter the computations, it can display the instantaneous motional state at every time step and the second impact position, which shows the entire process of impact accident. Simulation can be visualized with the continuous animate. Journal o[ the Eastern sia Sociely lirr Transportation Studies, Vol.3, No.l, September, 1999

6 242 Lang WEI,Hirotoshi ISHIKW, Yinsan CHEN, Rui FU and Tho CHEN (lnitial impacr position) --l Tire-ground mechanics model +Kinematics model of impact veh ic les Iteration-convergence judge model.(the second impact position) and (The pre-impact motion variables of the secpnd impact) The post-impact motion variables of vehicles (first impact) Impact velocity computational model Pre-impact instantaneous velocity and angular velocity of vehicles ( first impact ) Fig. 3 The Computational Flow Diagram of Impact Vetocity The animation output of pre-impact vehicles'movement Impact position, post-impact motion variables of vehicles, other vehicle parameters Tire-ground mechanics model +Xinematics model of impact vehi c les The output of vehicles movement and position corresponding to the difference calculation step The second impact position The second impact position, The post-impact motion variables of vehicles (the second impact) Rest position (The entire process of impact accident and overall perspective) Figure 4. The Flow Diagram Of Simulation System for Reconstructing Car-To-Car Collisions Involving Second Impact 4. EVLUTION OF THE SYSTEM USING THE TESTS Under the common conditions, the data measured at the real-world accident site, especially the impact velocity from accident investigation, is not suitable to verify the validity of the Journal of the Easlern sia Srxiety for Transportation Studies, Vol.3, No.l, September, 1999

7 243 Sr[dy of compurer Simularion System a. u:::rjffitl"l Car-to-car collisior ccidents hvolving the simulation model. In this paper, under the accurate control and test conditions, five car-tocar collision tests involving second impact (see Table l) were used to verify and assess the simulation system. Table 1. The Data of Real world collision Tests Involving Second Impact -MoL,L 16r cil {tg (m) (m) (m) T1 n R T4 15 lo l5 t.t2 rod 125 l.l7 sl ln l{ IID lrts 124 l.l0 lrc9 t ltr l04t 124 l.l0 lgl 124 l.l0 9t l l.l5 lm 18 l Ll E E5 E5 E5 X* (m) t# 0m ld off tfi o.l0 t6-182 tfi 0g t6-115 t# 058 th 030 t6 {X5 Yro (m) -1fi 056 -lre 068 0m 067 a4 tn -1.'70 0.o Xru 0 (m) Y,u (m) s4n5%m l&,.10 3# 33 s l & l& : fr 6 0 2n5 041 y5 3 { % :15 llsl m $vl 49n $ 0r, P Lr 0(rn) (at) 065 (L)l3s (R)r65 (L)l2s (L)145 (R)l6s (1i20 (Rll6 (LRI Notes: Hm, Mm, Hg and Mg present the motion state of left-front wheel, right-front wheel, left-rear wheel and right-rear wheel respectively. ppoint: the value was set to I when the locked wheel can't roll' the value was set to 0 when the wheel can roll freely. 4.1 Verification of Simulation Computation The observed value Vr and calculated value V. of initial impact velocity, observed value and calculated value of the second impact center position are shown in Table 2' The absolute error of velocity is within 7.4krnlh, and the relative elror is within 12.2loh except for the car in T2 case (221l%) and car in T3 case (28'83%)' Table 2 Impact center Position and velocity comparison between Test and Simulation value Test Car ',(m) ',(m). r() &(m)yrr(m) ft(m) Y(m) TI T2 T3 T4 o.25-3r l9r5 otr 4D fi? -r7r 2& 2g t0 t.d vr km/h & a8 5l.l 45.0 V. absolute enor m/h\ Gm/h) 4t t7 47 2l 47 I q relative error (%) t2.2t 22.1t I il.ll 1 'r7 4.2 TheContrast Verilication for Simulation Reconstruction The trajectory comparison between the simulation and collision tests are shown in Figure Figure 9. The second impact simulation trajectories were found to be in good 5 - agreement with real-world test results. Journal ofthe Eastern sia Society tbr Transportation Studies, vol.3, No.l, September, 1999

8 244 l-aug WEI,Hirotoshi ISHIKW, Yirran CHEN, Rui FU aud Tho CHEN Ki,r W :ffi ffi rtll Fig. 5 Tl Test Result (Left) and Simulation Resutt Fig. 6 T2 Test Result (Left) and Simutation Resutt (Right) Journal of the Eastern sia Society tirr Transporlation Studies, Vol.3, No. l, September, I 999

9 245 Stttdy of Computer Simulation Systcm for Reconstrucling Car-to-Car Collision ccidcnts Involving the Second Impacl s e cond. imdact Fig. 7 T3 Test Result (Left) and Simulation Result (Right) b\ q Fig. 8 T4 Test Result (Left) and Simulation Result (Right) /* Fig. 9 T5 Test Result (Left) and Simulation Result (Right) Journal ol'lhc Eastcrn sia Sociely lirr Transportation Sludics, Vrl.3, No. l, Scptcmbcr, 1999

10 246 L:ngWEI,Hirotoshi ISHIKW, Yinsan CHEN, Rui FU andtho CHEN 5. CONCLUSIONS ased on the simulation model for car-to-car single impact accidents and quoted normal and tangential restitution coeffrcients in this paper, the simulation system for reconstructing car-to-car collisions involving second impact is described. Using the field data such as impact position, rest position, impact marks on the car body, this system can obtain the kinematic state of accident vehicles, the second impact position and impact velocity. Five collision tests involving second impact were used to evaluate this system, and the simulation results were found to be in good agreements with the real-world test results. REFERENCES Lang Wei, Hirotoshi Ishikawa and Takashi Nakatsuji (1995) Study on ccident Reconstruction Model, utomobile-research, I 7- I 0. Lang Wei, Yinsan chen, Takashi Nakatsuji and Hirotoshi Ishikawa (1996) Study of Computer Simulation System for Reconstructing Car{o-car Collisions ccidents, China Journal of Highway, Vol.9 No.4, l4-21' Hirotoshi ishikawa (1995) Restitution Coeffrcients in Car-to-car Collisions, utomobile- Research, l7-1. Lang Wei and Takashi Nakatsuji (1995) Study on ccident nimate Reconstruction Model, 30th nniversary of JCTS, Tokyo,Japan,S6-89. Gwanghun Gim and Parviz E.Nikravesh (1990) n nalytical Model of Pneumatic Tyres for Vehicle Dynamic Simulations. Part l:pure Slips, International Journal of Vehicle Design, Vol.ll, No.6, 589'618. Gwanghun Gim and Parviz E.Nikravesh (1991) n nalytical Model of Pneumatic Tyres for Vehicle Dynamic Simulations. Part 2:Comprehensive Slips, International Journal of Vehicte Design, Vol.l2, No.l, l9-39. Journal ol thc Easlcrtt sia Socicty tirr Transportation Studies, Vol.3, No.l, September, 1999

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