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Simulation of movement dynamics at collision of vehicles
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Transportation Research Procedia 00 (2018) 000–000
Available online at www.sciencedirect.com
Transportation Research Procedia 00 (2018) 000–000
www.elsevier.com/locate/procedia
ScienceDirect
www.elsevier.com/locate/procedia
Transportation Research Procedia 36 (2018) 358–363 www.elsevier.com/locate/procedia
Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018) Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018)
Simulation of movement dynamics at collision of vehicles Simulation of movement dynamics at collision of vehicles * Valery Kovalev, Dmitry Morozov Valery Kovalev, Dmitry Morozov* Siberian Federal University, 26 Kirenskiy St., Krasnoyarsk, 660074, Russia Siberian Federal University, 26 Kirenskiy St., Krasnoyarsk, 660074, Russia
Abstract Abstract A method for calculating the number of rotations of vehicle after side collision made by the vehicle in its translational-rotational motion after road trafficthe accident is proposed. This method after allows taking into account friction work of tires on the road, A method fora calculating number of rotations of vehicle side collision made bythe thefull vehicle in its translational-rotational which a prerequisite foraccident calculating the speedThis of the hittingallows vehicle at theinto moment of the sidefull collision hit. motionisafter a road traffic is proposed. method taking account frictionwith workthe ofvehicle tires onbeing the road, In this iscase, the full friction work of tireson theofroad determined summing upoftheside work of translational motionbeing and turn which a prerequisite for calculating the speed the is hitting vehicleby at the moment collision with the vehicle hit. relative to thethe centre mass work of theofvehicle hit. Correct calculation of the number rotations ensures significant increase In this case, full of friction tiresonbeing the road is determined by summing up theofwork of translational motion and turn of reliability the reconstructed event and obtaining for a non-biased of the road trafficsignificant accident. increase relative to theofcentre of mass of the vehicle being hit.materials Correct calculation of theinvestigation number of rotations ensures of reliability of the reconstructed event and obtaining materials for a non-biased investigation of the road traffic accident. © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018). Peer-review responsibility of the scientific committee Traffic Safetyunder Management in Large Cities (SPbOTSIC 2018).of the Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018). Keywords: road traffic accident; side collision; angle of turn;longitudinal displacement;friction work of tires on the road; number of rotations. Keywords: road traffic accident; side collision; angle of turn;longitudinal displacement;friction work of tires on the road; number of rotations.
1. Introduction 1. Introduction The main factors that stipulate possibility of determining the cause of a road traffic accident are the values of the vehicle speedfactors at thethat moment of collision et al., 2015; Vasiliev, 2004, 2006; Abdel-Aty The main stipulate possibility(Lee of determining theEvtiukov cause of and a road traffic accident are the values of and the Radwan, 2000;at Yang et al., 2015; Mayou(Lee et al., 1993). The speed of at 2004, the moment of collisionand is vehicle speed the moment of collision et al., 2015; Evtiukov andvehicles Vasiliev, 2006; Abdel-Aty determined by the existing methods on et theal., friction work tires on road, taking account traces of Radwan, 2000; Yang et al., 2015; based Mayou 1993). Theofspeed ofthe vehicles at theinto moment of the collision is the brakingbypath (Ilarionov, 1980,based 1989;on Fedorov andwork Gavrilov, In many these methods determined the existing methods the friction of tires 2003). on the road, takingcases, into account the tracesare of insufficient. example,1980, there may no skidding when 2003). brakingInmodern vehicles, the the braking Thus, path for (Ilarionov, 1989;beFedorov andtraces Gavrilov, many ABS-equipped cases, these methods are schemes of road accidentsthere in some be compiled incorrectly, the totalABS-equipped angle of vehicle turn after insufficient. Thus,traffic for example, may cases be no might skidding traces when braking modern vehicles, the side collision is in mostaccidents cases determined by the angle directionsthe of total vehicles moment the schemes of road traffic in some cases might be between compiledthe incorrectly, angleatofthevehicle turnofafter collision and after side collision is init.most cases determined by the angle between the directions of vehicles at the moment of the collision and after it.
* *
Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail: [email protected] Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail: [email protected]
2352-1465 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018). 10.1016/j.trpro.2018.12.108
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Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, DmitryMorozov / Transportation Research Procedia 00 (2018) 000–000
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2. Methodology and calculations One of the methods that allow to obtain parameters of a road traffic accident is simulation of the dynamics of vehicle movement after collision (Vantsevich et al., 2001; Transport and Trace examination, 1988). Let us consider the dynamics of the vehicle after side collision. In most cases, the expert analysis of an accident requires determining the speed of the hitting vehicle at the moment of collision with the vehicle being hit. To solve the task, the design scheme of a road traffic accident will be compiled (see Figure 1). The kinetic energy of rotation of the vehicle being hit Vpreceived by it as a result of side collision from the hitting vehicle Vato the right front (to the front axis):
Wrot
J p p2 2
(1)
whereJpismoment of inertia of the vehicle being hit relative to the centre of mass, kgm2,
Jp
m p L2p 12
(2)
wherempis themass of vehicle Vp, kg; Lpis the base of vehicle Vp, m; ωpis theangular rate of rotation of vehicle Vp, rad/s,
p
2 Va Lp
(3)
whereVais the speed of vehicle Vaat the moment of collision, i.e. at the beginning of rotation of vehicleVp, m/s. Then equation (1) will be written as
Wrot p
m p Va2 6
(4)
Part of the kinetic energy of rotation of vehicle Vp passes into the work of tire scrubbing during rotation around the centre of mass, which can be defined as follows:
Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, Dmitry Morozov / Transportation Research Procedia 00 (2018) 000–000
360
3
Fig. 1. Calculation model:Vаis the hitting vehicle; α is the angle of application of the impact pulse; Vp is the vehicle being hit; Vаis the speed of vehicle Vaat the moment of collision; Vp is the speed of vehicle Vpat the moment of collision; Vp1is thespeed of displacement of the centre of mass of vehicleVp after collision; dSis the elementary way of displacement the front part of vehicle Vp; dyis the infinitely small angle of rotation of vehicle Vp with respect to the centre of mass; is the angular speed of rotation of vehicle Vprelative to the centre of mass; Sp1is the path of displacement of the centre of mass of vehicle Vp after collision; dSp1is the elementary small displacement of the centre of mass of vehicle Vp after collision for an infinitely small time interval; H is thearm of impact pulse relative to the centre of mass.
Wrot p G p b Lp
360
(5)
where: Wrot pis thefriction work of tires on the road road, kg m; Gpis theweight of vehicle Vp, kg; φbis thecoefficient coefficient of traction of the tire with the road in lateral direction direction; γis thetotal angle of rotation of vehicle Vpover the time of rotation, degr. Considering equations (4) and (5), we will obtain obtain:
m p Va2 6
G p b L p
360
(6)
From which:
60 m p Va2 G p b L p
(7)
The elementary small displacement dS1pof the centre of mass of vehicle Vp (see Figure 1) over the infinitely small time interval dt:
dS 1p Vp1 dt
(8)
Where V1pis thespeed of vehicle Vpafter collision,, m/s. When vehicle Vp is turning by an infinitely small angle dγ, its front will strike an elementary arc dS:
dS
Lp d 2
(9)
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Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, DmitryMorozov / Transportation Research Procedia 00 (2018) 000–000
361
Or
dS
Lp p 2
dt
(10)
From equation (8) we will obtain:
dS 1p
dt
(11)
V p1
Then, taking into account equation (10), we will obtain:
dS
Lp 2
p
1 dS 1p 1 Vp
(12)
From which:
S S 1p
Lp p 2 Vp1
(13)
Substituting the valueωpfrom equation (3) to equation (13), we will obtain:
S S 1p
Va V p1
(14)
From which:
Va V p1
S S 1p
(15)
Substituting the value Vafrom equation (15) to equation (7), we will obtain:
60 m p S 2 (V p1 ) 2 G p b Lp ( S 1p ) 2
(16)
In equation (16) we will determine the arc S through the angle of rotation of vehicle Vp:
S Lp
360
(17)
Substituting the value Sfrom equation (17) to equation (16), we will obtain:
60 m p (V p1 ) 2 2 L p 2 2 G p b Lp ( S 1p ) 2 360 2
(18)
Let us transform the equation (18):
2160 G p ( S 1p ) 2 b m p L p (V p1 ) 2
(19)
Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, Dmitry Morozov / Transportation Research Procedia 00 (2018) 000–000
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Where:
V p1 2 S 1p ja
(20)
wherejais thedeceleration in lateral movement (see Fig. 1), m/s2. Substituting the value V1pfrom equation (20) to equation (19), after transforming, we will obtain
1080 G p S 1p b m p L p ja
K rot cos
(21)
When transforming the equation (21), we will obtain
1080 G p S 1p b m p L p ja
K rot cos
(22)
From where:
1080 g S 1p b L p ja
K rot cos
(23)
whereКrotis thecoefficient taking into account the location of application of the impact pulse with respect to the centre of mass, 0 ≤ Кrot≤ 1; αis theangle of application of impact pulse (see Fig. 1). Knowing the total rotation of Vp over the rotation period, it is possible to calculate the number of rotationsfor the same period:
nrot
(24)
360
From which considering the equation (23), we will obtain:
nrot
3 g S 1p b Lp ja
K rot cos
(25)
Equation (25) allows to calculate the number of rotations made by vehicle Vpunder the influence of impact pulse from vehicle Va after the end of the contact at lateral movement on way S1p(see Fig. 1) and determining the full friction work of tires on the road. Accounting full friction work of tires on the road of vehicle Vpis required for calculation of the speed of Vaat the moment of collision. Full friction work of tires on the road is determined by summing the work of translational motion and rotation in relation to the centre of mass of vehicle Vp. In the translational movement, the friction work of tires on the road is calculated taking into account the linear displacement of the centre of mass of the vehicle. The work of turning of the vehicle relative to the centre of the mass under translational motion is determined by the number of rotations. Herewith, the method of determining the number of rotations can significantly affect reliability of the event. 3. Discussion and conclusions The proposed method for calculating the speed of a vehicle by the number of rotations in translational-rotational motion after collision enables more detailed study of the circumstances of the accident, identification and systematization of the factors that contribute to its emergence and development, revealing data that can be evidence for establishing the truth in a civil or criminal case. The known methods for simulating the dynamics of vehicle movement are based either on the visual perception
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363
of eyewitness (Podlotsky, 2014) or on the materials of the road experiment (Kislyakov, 2016). In the first case, the reliability of the coverage of an event is determined by psychophysical capabilities of the person (Golchevsky et al., 2014); in the second case, the simulation of the event is complicated by various technical and operational properties of vehicles used in the test and involved in the accident (Omurov, 2016). For this reason, development of the accident model based only on the physical laws (Balakin, Shchipan, 2014) is reasonable and should be of higher priority. References Balakin, V.D., Shchipan, I.V., 2014. Reconstruction of the mechanism of road traffic accident with collision of vehicles.Bulletin of SibADI 36, 7–12. Evtiukov, S.A., Vasiliev, Ya.V., 2006.Examination of road traffic accidents. DNK Publishing House, Saint Petersburg. Evtiukov, S.,A., Vasiliev, Ya.V., 2004. Investigation and examination of road traffic accidents. DNK Publishing House, Saint Petersburg. Fedorov, V.A., Gavrilov, B.Ya., 2003. Investigation of road traffic accidents. Examen Publishing House, Moscow. Golchevsky, V.F., Zhigalov, N.Yu., Karnovich, S.A., 2014. Individual aspects of the algorithm for solving the expert task of determining the speed of the pedestrian.Russian Investigator 11, 3–5. Ilarionov, V. A., 1980. Forensic automotive and technical examination: A guide for expert automotive maintenance technician, investigators and judges. VNIISE, Moscow. Ilarionov, V.A., 1989. Examination of road traffic accidents. Transport, Moscow. Kislyakov, S. V., 2016. Improving the procedure of an investigative experiment at the initial stage of accident investigation with bodily injury.Russian Legal Journal 2, 108–113. Omurov, Zh. M., 2016. Operational properties of vehicles affecting the traffic mode.Bulletin of the Kyrgyz State Technical University named after I. Razzakov 3, 141–144. Podlotsky, I. N., 2014. Expert evaluation of the degree of subjectivity of perception by an eyewitness of characteristics of appearance of a person.Bulletin of the Moscow University of the Ministry of Internal Affairs of Russia 2, 8–9. Transport and Trace examination in cases of road traffic accidents, 1988. Diagnostic study: A guide for expert automotive maintenance technician, investigators and judges. VNIISE, Moscow. Abdel-Aty, M.A., Radwan, A.E., 2000. Modeling traffic accident occurrence and involvement: Accident Analysis and Prevention 32(5), 633– 642. Yang, J., Ren, S., Ma, Z., Wang, H., Luo, T., 2015. Modeling of road traffic collision accidents' causes and experimental analysis of influential factors: Dongnan Daxue Xuebao (ZiranKexue Ban). Journal of Southeast University (Natural Science Edition) 45(5), 1008–1012. Mayou, R., Bryant, B., Duthie, R., 1993. Psychiatric consequences of road traffic accidents. British Medical Journal 307(6905), 647–651. Vantsevich, V.V., Vysotski, M.S., Happawana, G.S., Nwokah, O.D.I., 2001. Vehicle dynamics as the second dynamics problem. International Journal of Vehicle Design 25(3), 165–169. Lee, J., Abdel-Aty, M., Jiang, X., 2015. Multivariate crash modeling for motor vehicle and non-motorized modes at the macroscopic level. Accident Analysis & Prevention 78, 146–154.
ScienceDirect ScienceDirect
Transportation Research Procedia 00 (2018) 000–000
Available online at www.sciencedirect.com
Transportation Research Procedia 00 (2018) 000–000
www.elsevier.com/locate/procedia
ScienceDirect
www.elsevier.com/locate/procedia
Transportation Research Procedia 36 (2018) 358–363 www.elsevier.com/locate/procedia
Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018) Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018)
Simulation of movement dynamics at collision of vehicles Simulation of movement dynamics at collision of vehicles * Valery Kovalev, Dmitry Morozov Valery Kovalev, Dmitry Morozov* Siberian Federal University, 26 Kirenskiy St., Krasnoyarsk, 660074, Russia Siberian Federal University, 26 Kirenskiy St., Krasnoyarsk, 660074, Russia
Abstract Abstract A method for calculating the number of rotations of vehicle after side collision made by the vehicle in its translational-rotational motion after road trafficthe accident is proposed. This method after allows taking into account friction work of tires on the road, A method fora calculating number of rotations of vehicle side collision made bythe thefull vehicle in its translational-rotational which a prerequisite foraccident calculating the speedThis of the hittingallows vehicle at theinto moment of the sidefull collision hit. motionisafter a road traffic is proposed. method taking account frictionwith workthe ofvehicle tires onbeing the road, In this iscase, the full friction work of tireson theofroad determined summing upoftheside work of translational motionbeing and turn which a prerequisite for calculating the speed the is hitting vehicleby at the moment collision with the vehicle hit. relative to thethe centre mass work of theofvehicle hit. Correct calculation of the number rotations ensures significant increase In this case, full of friction tiresonbeing the road is determined by summing up theofwork of translational motion and turn of reliability the reconstructed event and obtaining for a non-biased of the road trafficsignificant accident. increase relative to theofcentre of mass of the vehicle being hit.materials Correct calculation of theinvestigation number of rotations ensures of reliability of the reconstructed event and obtaining materials for a non-biased investigation of the road traffic accident. © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018). Peer-review responsibility of the scientific committee Traffic Safetyunder Management in Large Cities (SPbOTSIC 2018).of the Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018). Keywords: road traffic accident; side collision; angle of turn;longitudinal displacement;friction work of tires on the road; number of rotations. Keywords: road traffic accident; side collision; angle of turn;longitudinal displacement;friction work of tires on the road; number of rotations.
1. Introduction 1. Introduction The main factors that stipulate possibility of determining the cause of a road traffic accident are the values of the vehicle speedfactors at thethat moment of collision et al., 2015; Vasiliev, 2004, 2006; Abdel-Aty The main stipulate possibility(Lee of determining theEvtiukov cause of and a road traffic accident are the values of and the Radwan, 2000;at Yang et al., 2015; Mayou(Lee et al., 1993). The speed of at 2004, the moment of collisionand is vehicle speed the moment of collision et al., 2015; Evtiukov andvehicles Vasiliev, 2006; Abdel-Aty determined by the existing methods on et theal., friction work tires on road, taking account traces of Radwan, 2000; Yang et al., 2015; based Mayou 1993). Theofspeed ofthe vehicles at theinto moment of the collision is the brakingbypath (Ilarionov, 1980,based 1989;on Fedorov andwork Gavrilov, In many these methods determined the existing methods the friction of tires 2003). on the road, takingcases, into account the tracesare of insufficient. example,1980, there may no skidding when 2003). brakingInmodern vehicles, the the braking Thus, path for (Ilarionov, 1989;beFedorov andtraces Gavrilov, many ABS-equipped cases, these methods are schemes of road accidentsthere in some be compiled incorrectly, the totalABS-equipped angle of vehicle turn after insufficient. Thus,traffic for example, may cases be no might skidding traces when braking modern vehicles, the side collision is in mostaccidents cases determined by the angle directionsthe of total vehicles moment the schemes of road traffic in some cases might be between compiledthe incorrectly, angleatofthevehicle turnofafter collision and after side collision is init.most cases determined by the angle between the directions of vehicles at the moment of the collision and after it.
* *
Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail: [email protected] Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail: [email protected]
2352-1465 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the Thirteenth International Conference on Organization and Traffic Safety Management in Large Cities (SPbOTSIC 2018). 10.1016/j.trpro.2018.12.108
2
Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, DmitryMorozov / Transportation Research Procedia 00 (2018) 000–000
359
2. Methodology and calculations One of the methods that allow to obtain parameters of a road traffic accident is simulation of the dynamics of vehicle movement after collision (Vantsevich et al., 2001; Transport and Trace examination, 1988). Let us consider the dynamics of the vehicle after side collision. In most cases, the expert analysis of an accident requires determining the speed of the hitting vehicle at the moment of collision with the vehicle being hit. To solve the task, the design scheme of a road traffic accident will be compiled (see Figure 1). The kinetic energy of rotation of the vehicle being hit Vpreceived by it as a result of side collision from the hitting vehicle Vato the right front (to the front axis):
Wrot
J p p2 2
(1)
whereJpismoment of inertia of the vehicle being hit relative to the centre of mass, kgm2,
Jp
m p L2p 12
(2)
wherempis themass of vehicle Vp, kg; Lpis the base of vehicle Vp, m; ωpis theangular rate of rotation of vehicle Vp, rad/s,
p
2 Va Lp
(3)
whereVais the speed of vehicle Vaat the moment of collision, i.e. at the beginning of rotation of vehicleVp, m/s. Then equation (1) will be written as
Wrot p
m p Va2 6
(4)
Part of the kinetic energy of rotation of vehicle Vp passes into the work of tire scrubbing during rotation around the centre of mass, which can be defined as follows:
Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, Dmitry Morozov / Transportation Research Procedia 00 (2018) 000–000
360
3
Fig. 1. Calculation model:Vаis the hitting vehicle; α is the angle of application of the impact pulse; Vp is the vehicle being hit; Vаis the speed of vehicle Vaat the moment of collision; Vp is the speed of vehicle Vpat the moment of collision; Vp1is thespeed of displacement of the centre of mass of vehicleVp after collision; dSis the elementary way of displacement the front part of vehicle Vp; dyis the infinitely small angle of rotation of vehicle Vp with respect to the centre of mass; is the angular speed of rotation of vehicle Vprelative to the centre of mass; Sp1is the path of displacement of the centre of mass of vehicle Vp after collision; dSp1is the elementary small displacement of the centre of mass of vehicle Vp after collision for an infinitely small time interval; H is thearm of impact pulse relative to the centre of mass.
Wrot p G p b Lp
360
(5)
where: Wrot pis thefriction work of tires on the road road, kg m; Gpis theweight of vehicle Vp, kg; φbis thecoefficient coefficient of traction of the tire with the road in lateral direction direction; γis thetotal angle of rotation of vehicle Vpover the time of rotation, degr. Considering equations (4) and (5), we will obtain obtain:
m p Va2 6
G p b L p
360
(6)
From which:
60 m p Va2 G p b L p
(7)
The elementary small displacement dS1pof the centre of mass of vehicle Vp (see Figure 1) over the infinitely small time interval dt:
dS 1p Vp1 dt
(8)
Where V1pis thespeed of vehicle Vpafter collision,, m/s. When vehicle Vp is turning by an infinitely small angle dγ, its front will strike an elementary arc dS:
dS
Lp d 2
(9)
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Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, DmitryMorozov / Transportation Research Procedia 00 (2018) 000–000
361
Or
dS
Lp p 2
dt
(10)
From equation (8) we will obtain:
dS 1p
dt
(11)
V p1
Then, taking into account equation (10), we will obtain:
dS
Lp 2
p
1 dS 1p 1 Vp
(12)
From which:
S S 1p
Lp p 2 Vp1
(13)
Substituting the valueωpfrom equation (3) to equation (13), we will obtain:
S S 1p
Va V p1
(14)
From which:
Va V p1
S S 1p
(15)
Substituting the value Vafrom equation (15) to equation (7), we will obtain:
60 m p S 2 (V p1 ) 2 G p b Lp ( S 1p ) 2
(16)
In equation (16) we will determine the arc S through the angle of rotation of vehicle Vp:
S Lp
360
(17)
Substituting the value Sfrom equation (17) to equation (16), we will obtain:
60 m p (V p1 ) 2 2 L p 2 2 G p b Lp ( S 1p ) 2 360 2
(18)
Let us transform the equation (18):
2160 G p ( S 1p ) 2 b m p L p (V p1 ) 2
(19)
Valery Kovalev et al. / Transportation Research Procedia 36 (2018) 358–363 Valery Kovalev, Dmitry Morozov / Transportation Research Procedia 00 (2018) 000–000
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5
Where:
V p1 2 S 1p ja
(20)
wherejais thedeceleration in lateral movement (see Fig. 1), m/s2. Substituting the value V1pfrom equation (20) to equation (19), after transforming, we will obtain
1080 G p S 1p b m p L p ja
K rot cos
(21)
When transforming the equation (21), we will obtain
1080 G p S 1p b m p L p ja
K rot cos
(22)
From where:
1080 g S 1p b L p ja
K rot cos
(23)
whereКrotis thecoefficient taking into account the location of application of the impact pulse with respect to the centre of mass, 0 ≤ Кrot≤ 1; αis theangle of application of impact pulse (see Fig. 1). Knowing the total rotation of Vp over the rotation period, it is possible to calculate the number of rotationsfor the same period:
nrot
(24)
360
From which considering the equation (23), we will obtain:
nrot
3 g S 1p b Lp ja
K rot cos
(25)
Equation (25) allows to calculate the number of rotations made by vehicle Vpunder the influence of impact pulse from vehicle Va after the end of the contact at lateral movement on way S1p(see Fig. 1) and determining the full friction work of tires on the road. Accounting full friction work of tires on the road of vehicle Vpis required for calculation of the speed of Vaat the moment of collision. Full friction work of tires on the road is determined by summing the work of translational motion and rotation in relation to the centre of mass of vehicle Vp. In the translational movement, the friction work of tires on the road is calculated taking into account the linear displacement of the centre of mass of the vehicle. The work of turning of the vehicle relative to the centre of the mass under translational motion is determined by the number of rotations. Herewith, the method of determining the number of rotations can significantly affect reliability of the event. 3. Discussion and conclusions The proposed method for calculating the speed of a vehicle by the number of rotations in translational-rotational motion after collision enables more detailed study of the circumstances of the accident, identification and systematization of the factors that contribute to its emergence and development, revealing data that can be evidence for establishing the truth in a civil or criminal case. The known methods for simulating the dynamics of vehicle movement are based either on the visual perception
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of eyewitness (Podlotsky, 2014) or on the materials of the road experiment (Kislyakov, 2016). In the first case, the reliability of the coverage of an event is determined by psychophysical capabilities of the person (Golchevsky et al., 2014); in the second case, the simulation of the event is complicated by various technical and operational properties of vehicles used in the test and involved in the accident (Omurov, 2016). For this reason, development of the accident model based only on the physical laws (Balakin, Shchipan, 2014) is reasonable and should be of higher priority. References Balakin, V.D., Shchipan, I.V., 2014. Reconstruction of the mechanism of road traffic accident with collision of vehicles.Bulletin of SibADI 36, 7–12. Evtiukov, S.A., Vasiliev, Ya.V., 2006.Examination of road traffic accidents. DNK Publishing House, Saint Petersburg. Evtiukov, S.,A., Vasiliev, Ya.V., 2004. Investigation and examination of road traffic accidents. DNK Publishing House, Saint Petersburg. Fedorov, V.A., Gavrilov, B.Ya., 2003. Investigation of road traffic accidents. Examen Publishing House, Moscow. Golchevsky, V.F., Zhigalov, N.Yu., Karnovich, S.A., 2014. Individual aspects of the algorithm for solving the expert task of determining the speed of the pedestrian.Russian Investigator 11, 3–5. Ilarionov, V. A., 1980. Forensic automotive and technical examination: A guide for expert automotive maintenance technician, investigators and judges. VNIISE, Moscow. Ilarionov, V.A., 1989. Examination of road traffic accidents. Transport, Moscow. Kislyakov, S. V., 2016. Improving the procedure of an investigative experiment at the initial stage of accident investigation with bodily injury.Russian Legal Journal 2, 108–113. Omurov, Zh. M., 2016. Operational properties of vehicles affecting the traffic mode.Bulletin of the Kyrgyz State Technical University named after I. Razzakov 3, 141–144. Podlotsky, I. N., 2014. Expert evaluation of the degree of subjectivity of perception by an eyewitness of characteristics of appearance of a person.Bulletin of the Moscow University of the Ministry of Internal Affairs of Russia 2, 8–9. Transport and Trace examination in cases of road traffic accidents, 1988. Diagnostic study: A guide for expert automotive maintenance technician, investigators and judges. VNIISE, Moscow. Abdel-Aty, M.A., Radwan, A.E., 2000. Modeling traffic accident occurrence and involvement: Accident Analysis and Prevention 32(5), 633– 642. Yang, J., Ren, S., Ma, Z., Wang, H., Luo, T., 2015. Modeling of road traffic collision accidents' causes and experimental analysis of influential factors: Dongnan Daxue Xuebao (ZiranKexue Ban). Journal of Southeast University (Natural Science Edition) 45(5), 1008–1012. Mayou, R., Bryant, B., Duthie, R., 1993. Psychiatric consequences of road traffic accidents. British Medical Journal 307(6905), 647–651. Vantsevich, V.V., Vysotski, M.S., Happawana, G.S., Nwokah, O.D.I., 2001. Vehicle dynamics as the second dynamics problem. International Journal of Vehicle Design 25(3), 165–169. Lee, J., Abdel-Aty, M., Jiang, X., 2015. Multivariate crash modeling for motor vehicle and non-motorized modes at the macroscopic level. Accident Analysis & Prevention 78, 146–154.