DETERMINING THE SPEED OF VEHICLES BEFORE AND AFTER CRASH

Transcription

1 Number, Volume V, July 0 DETERMNNG THE SPEED OF VEHCLES BEFORE AND AFTER CRASH Bayarjaral Tseveennamjil, Anon Hudák, Vladimír Rievaj 3 Summary: Te aricle is represenin ypical example of cras analyical soluion. Tere are presenin basic principles and eir calculaions in e area of veicle moion durin e acciden. Key words: Cras, Analyical soluion, Traffic safey. NTRODUCTON n road raffic accidens occur on a differen ype. is a veicle crases - a barrier, e veicle - pedesrian, veicle - veicle, or a combinaion ereof. Afer impac, e movemen of veicles varies. n order o deermine e acciden, i is imporan o know e facs on wic i is deermined by e iniial speed of e veicle. Te impac is acion were e inerfacin of wo or more bodies in e sor erm sinificanly cane velociy a leas one of e bodies. We alk abou e process of mecanical acion of lare forces a sor noice. n is process e speed of poin objecs are caned. is obvious a e size of e common conac area is canin oo durin e life of caracer.. CENTRC MPACT mpac force direcion is line perpendicular o e oucpad, wic passes rou cener of raviy of is area. Has e same direcion as e impac force. mpac force is divided accordin o e posiion of impac force: o CENTRC MPACT - occurs wen e impac force direcion passes rou e ceners of raviy of inerfacin bodies o ECCENTRC MPACT - occurs wen e impac force direcion do no raverse rou e ceners of raviy of inerfacin bodies. CENTRC MPACT could be: srai line impac - velociy vecors lie on e same line as a impac force direcion, Mr. Bayarjaral Tseveennamjil, Univerziy of Zilina, Faculy of Operaion and Economics of ranspor and Communicaions, Deparmen of Road and Urban Transpor, Univerziná, 00 6 Žilina, Tel.: , bajra@fpedas.uniza.sk, n., Anon Hudák, PD., Univerziy of Zilina, Faculy of Operaion and Economics of ranspor and Communicaions, Deparmen of Road and Urban Transpor, Univerziná, 00 6 Žilina, Tel.: , anon.udak@fpedas.uniza.sk, 3 doc., n., Vladimír Rievaj, PD., Univerziy of Zilina, Faculy of Operaion and Economics of ranspor and Communicaions, Deparmen of Road and Urban Transpor, Univerziná, 00 6 Žilina, Tel.: , vladimir.rievaj@fpedas.uniza.sk, Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 55

2 Number, Volume V, July 0 bevelled impac - velociy vecors do no lie on e same line as a impac force direcion. Durin e wo pases of impac force increasin o e maximum unil an equal velociy of bo veicles will be reaced, en decreases o zero. As defined by Newon e impac of bodies can be divided ino bo pases: compression and resiuion.. Compression pase Consequence of impac force increasin is body deformaion (ram pars of veicles a e impulse poin are idenical. Te ceners of raviy of ineraced veicles are erefore muc closer. Compression pase ends a e momen e car body deformaion reaces a maximum "value. A is sae, e kineic enery is convered ino a car deformaion work.. Pase of resiuion - bein from e momen of maximum deflecion and e ime separaion. n is par of e deformaion enery convered ino kineic enery of e car, e disance beween e axes of cars is increasin and bodies (veicles) are ryin o resore is oriinal sape. Because e maerials ave cerain pysical caracerisics, complee sape recovery does no occurs. Afer e cras remains a permanen deformaion. is imporan o define e cane in impac sren over ime, wic is e impulse impac sren. mpac force decreases and e velociy of e veicles are differen. r R FRd RK + RR () 0 RK - mpulse impac sren in compression pase [N] RR - mpulse impac sren in pase of resiuion [N] K R R F R - compression pase ime [s] - resiuion pase ime [s] - mpac ime, k + R [s] - mpulse impac sren [N] - mpac sren [N].. Coefficien of Resiuion Te raio of impac sren RR pulse applied o e body in resiuion o e sae of mpulse impac sren RK forces acin on e body a e sae of compression is called e coefficien of resiuion known k. Due o elasiciy of e veicle srucure, e wo veicles will separae aain. Te coefficien of resiuion is defined as raio beween resiuion RR and compression RK impulse. RR k () RK Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 56

3 Number, Volume V, July 0 Te idenificaion of coefficiens of resiuion in veicle o veicle collisions is impracical since eac veicle o veicle combinaion as is unique resiuion response. Veicle o barrier coefficiens of resiuion can be measured for specific veicles. Coefficiens of resiuion beween wo veicles for wic e veicle o barrier coefficiens of resiuion are known may be prediced. Expressed in a more useful and more common form, e coefficien of resiuion k is e raio of e pos (afer)-impac separain velociy v a of e collidin bodies o eir (before) pre-impac closin velociy v b - v b. k v v a a (3) b v v b v a - Te coefficien of resiuion varies from zero for a perfecly plasic impac o uniy for a perfecly elasic collision, and as been sown o depend upon e impac velociy and e sape and size of e collidin bodies. Te coefficien of resiuion lies in e rane beween 0. and 0.3 in real veicle o veicle collisions. Bumper-o-bumper collisions a low closin velociy are primarily elasic. Te bumpers deform o some deree durin impac and en rebound o nearly eir pre-impac condiion, coefficien of resiuion values ier an 0,3. Teoreically, ere may be e followin cases:. k, elemens are compleely flexible - ere is perfecly elasic caracer. k0, perfecly plasic caracer 3. Pracically, e coefficien of resiuion in e rane 0 <k <, i is an imperfec elasic caracer - e mos common case Based on e eory of mpac is possible o deermine e speed of moor veicles before and afer e collision of e: law on e conservaion of linear momenum, conservaion of enery, oer laws of pysics.. DETERMNATON OF SPEED ON CRASH BETWEEN TWO CARS Procedure for solvin e soluion can be documened incidens of fi.. A e crossroads wi no verical raffic sins crased lorry () in a passener car (). A fooprin of e acciden sie secured by ranspor police afer a car cras caned e direcion of ravel, wen six meers a an anle and i e lef weel o curb road. Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 57

4 Number, Volume V, July 0 Fi - Acciden floorplan Source: Auors Lorry () afer e cras also caned is course, and sood up in is final posiion. Tere are recorded racks durin brakin of e ruck afer e collision. Usually is disance is measured. Accordin e police file any serious damae as been occurred on e ruck (). Tere is appeared door deformaion on veicle (). is possible o conclude impac of veicles ad elasic caracer. Veicle () was carryin,78k of caro. Te saus of e surface was paved and dry. To deermine e iniial velociy of veicles is necessary o find ou anles α and α. Fi - Sceme of collision Source: Auors Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 58

5 Number, Volume V, July 0 Accordin e sceme fi. eccenric bevelled impac arises and coefficien of resiuion is neaive. Te acciden floor-plan is calculaed e anle of speed vecor of e car o e impac sren vecor n: T ( M + S) 7 ( +,5) Sinα 0,58 ; > α (4) S 6 3 T - wid of e roadway in e direcion of movemen of veicle (); T 7m; M m; S- wid of veicle (); S,5m; S3 - bevelled rack of veicle () raviy movemen ; S 3 6m. Now calculae e anle of velociy vecor of e lorry () and impac force direcion vecor: S, N 4 α 0,6; > α (5) T M + l + L 7 + 0,5 + 5,7 N - disance from e ri roadside and loniudinal axis of e lorry (); N 4m; S - wid of e lorry (); S,m; L - len of e lorry (); L 5,7m; roadway l - disance o e rear of e veicle from roadway; l 0,5m; Te anles α and α is necessary o esablis precisely because of eir basis is deermined by e movemen of veicles afer e collision. Track moion of e lorry () raviy from e collision o final posiion can be deermined by e followin equaion:, S4 (7 + 0,5 + 5,7) + 4,55m; (6) Nex, we need o address bo veicles in one reference frame. Trou e impac poin creae y - axis defined in e direcion of movemen of a veicle () and x - axis defined in e direcion of lorry () moion. Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 59

6 Number, Volume V, July 0 Accordin o e eory of impulse of impac sren for veicle (): m υ 0 υ m F d R ; (7) for lorry (): m υ 0 υ m F d R ; (8) Wen a collision is fulfilled law of conservaion of linear momenum: m m m + m ; (9) υ + υ υ υ Based on e previous equaions we use decomposiion ino x and y coordinaes, we e: ; m υ. x + mυ. x mυ. x + mυ. x +. m υ. y mυ. y mυ. y + mυ. y υ - velociy of veicles before collision [m.s - ] υ - velociy of veicles afer collision [m.s - ] m - mass of veicle (); G 6700 m 700k ; 9,8 G 6700 N raviy of veicle () includin passeners, drivers and sorae; 9.8m. s raviae acceleraion; G 5630 N immediae wei of lorry (), includin passeners, drivers and sorae, e mass is 78k; m - lorry mass (), G 5630 m 5750k ; 9.8 υ.x - componen speed of veicle () before e collision axis x ; υ.y - componen speed of veicle () before e collision axis y ; υ.x - componen speed of lorry () before e collision axis x ; υ.y - componen speed of lorry () before e collision axis y ; Velociy of veicle afer collision may be deermined usin enery conservaion law. Comparin e kineic enery and work consumed by sideways skid of e veicle () and also work consumed in canin e amoun of cener of raviy afer impac. Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 60

7 Number, Volume V, July 0 Cener of raviy is moved over a disance S3 from e oriinal direcion inclined a an anle α: m υ Gυ + G. S3. μb G. (0) Modified e equaions (0) we obain e relaionsip o deermine e speed of a car afer a collision in e form: ( S ) υ. μ + 3 b () S3 6m - disance of beveled moion of cener of raviy from e collision poin o e final posiion of e veicle (); μb 0,6 - coefficien of weel adesion (road surface was dry aspal); - cane in e cener of raviy due o il a car collision [m]; amoun of veicle s cener of raviy [m], - maximum amoun of cener of raviy on e border overurnin [m] To wa level is possible rise cener of raviy of veicle () (wiou reaenin is flip)? We can deermine from equaion of momens around e axis of e weel wi endency o flip a car, FG. 3. We can wrie equaion m b m x () x is e orizonal disance from e cener of raviy ilin ede [m] b veicle moion deceleraion [m.s - ] can be deermined as a funcion of laeral rip of ire and anle α, wic akes ino accoun diversion of veicle movemen away from e oriinal direcion of movemen b μ sinα (3) subsiue b for a deceleraion in equaion (3) and e modificaion we are ein: x μ sinα Fracion on e lef side of e equaion is a funcion of an γ. Value of a fracion on e ri side we can calculae. Valid an γ,873. is easy o deermine a e anle γ as a value of Based on e value of anle γ is impossible o deermine e maximum allowable amoun of cener of raviy, because e size of ypoenuse c ri rianle in Fi. 3 is e disance from e cener of raviy ilin ede (if we nelec e deformaion of e weel) and i can be calculaed usin e Pyaorean eory: (4) S c + (5) Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 6

8 Number, Volume V, July 0 Te maximum allowable cener of raviy is deermined by e equaion: sinγ S c + sinγ (6) Subsiuin ino equaion (4) allowable level of raviy reaces,5 0,65 sin 70,8 0, 94m + (7) usin equaion we find a e focus durin e acciden could raise eir posiion on 0,94 0,65 0, 9m. Subsiuin e speed of a car afer e collision is: ( S μ + ) 9,8 ( 6.0,6 + 0,9) 8, 74 υ. 3 b m.s - 3,46km. -. Now we deermine e speed of e lorry () afer e collision usin e law of conservaion of kineic enery: G. υ G. f. S 4 S,55 4 m veicle s () cenre of raviy disance from e collision poin o is final posiion; (8) f 0,0 - coefficien of fricion; final velociy of veicle deerminaion afer e collision of veicle () afer adjusin: υ f S 9,8 0,0,55,3 m.s - 7,66km. - 4 Now i is necessary o deermine iniial velociies before e collision. We assume as a lorry before e cras did no pass in e direcion of axis y. Terefore componen velociy of veicle () for y - axis afer e collision is:. y υ cosα ; υ. υ sinα υ y ; (9) Afer reamen in e previous equaion: m υ y m υ. α + m υ α (0). cos. cos wence we e suc a condiion and find e iniial velociy of veicle () before e collision: mυ cosα + mυ sinα 700.8,74.0, ,3.0,5 υ. y 8,9m.s - 3, m 700 km. -. Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 6

9 Number, Volume V, July 0 We can deermine e iniial velociy of e lorry () before e collision in e same way. υ. x 0, we assume as a veicle () before e cras did no pass in e direcion of e x-axis. Terefore e calculaion of x-wall componen of e final velociy afer e collision is:. x υ sinα; υ. υ cosα υ x ; () Afer reamen in e previous equaion: m υ x. α ; (). mυ sinα + mυ. cos wence we find e iniial velociy of e lorry () before e collision: mυ sinα + mυ cosα 700 8,74 0, ,3 0,9676 υ.. x 3,58 m.s - m 5750,9 km. - ; n is case, accordin o our calculaion values of iniial velociy before e collision are in veicle () 33km. - and lorry (),9 km. -. Te acciden record is no indicaion as o e brakin disance of e lorry (). Te driver in e noice says a before e cras e could no pus e brake pedal, wic, accordin o calculaions is no rue. Based on e observed daa we conclude a e lorry () is ampered and wen free moion afer e cras in e final posiion. is impossible o inore esimony of e lorry driver () on is brakes. Te absence of brakin marks, does no assume full brakin effec. f e arumen abou brakin of e lorry was rue, e iniial velociy of () would be ier an,9 km. -. n e case of veicle () we know cener of raviy laeral sif from e collision o e final posiion. f you would noice e driver was rue, e iniial velociy of e veicle () before impac ad o be reaer an 3,46 km. -. Te final locaion of lorry () would be furer an e calculaed values. REFERENCES () А.Р. Шляховым., Б.Л.Зотовым., А.В.Бекасовым., Г.Я. Боградом., Г.Г. Индиченко.: Роль судебной автотехнической экспертизы в предупреждении и расследовании дорожно-транспортных происшествий. Москва, 980 г. () Kasanický a kol.: Teória poybu a rázu pri analýze a simulácii neodovéo deja, ŽU v Žiline/EDS 00; SBN Tseveennamjil, Hudák, Rievaj: Deerminin e Speed of Veicles before and afer Cras 63