Vehicle Velocity Relation to Slipping Trajectory Change: An Option for Traffic Accident Reconstruction

  • Vidas Žuraulis Vilnius Gediminas Technical University
  • Edgar Sokolovskij
Keywords: vehicle velocity, slipping trajectory, vehicle model, traffic accident, yaw marks


In this paper, the relation of the velocity of a vehicle in the slip mode to the parameters of the tire marks on the road surface is examined. During traffic accident reconstructions, the initial velocity of a sideslipping vehicle is established according to the tire mark trajectory radius, and calculations highly depend on the directly measured parameters of the tire marks, in particular cases known as yaw marks. In this work, a developed and experimentally validated 14-degree-of-freedom mathematical model of a vehicle is used for an investigation of the relation between velocity and trajectories. The dependence of initial vehicle velocity on tire yaw mark length and trajectory radius was found as a characteristic relation. Hence, after approximation of the permanent slipping part by a polynomial, the parameters of the latter were related to vehicle velocity. The dependences were established by specific experimental tests and computer-aided simulation of the developed model.


CARE Database/EC; 2012.

Safety net accident causation database 2005 to 2008 / EC; 2010.

Žuraulis V, Sokolovskij E, Matijošius J. The opportunities for establishing the critical speed of the vehicle on research in its lateral dynamics. Eksploatacja i Niezawodnosc – Maintenance and Reliability. Lublin: Polish Maintenance Society. ISSN 1507-2711. 2013; 15(4):312-318.

Muha R, Sever D. The impact of regulation 561/2006 on fleet management viewed through efficient use of drivers' working time. PROMET - Traffic&Transportation. Zagreb: University of Zagreb. ISSN 0353-5320. 2009; 21(1):61-67.

Crisman B, Roberti B. Tyre wet-pavement traction management for safer roads. Procedia - Social and Behavioral Sciences. 2012; 53:1055-1068.

Brach R M. An analytical assessment of the critical speed formula. SAE Paper No. 970957. 1997.

Echaveguren T, Bustos M, Solminihac H. Assessment of horizontal curves of an existing road using reliability concepts. Canadian Journal of Civil Engineering. 2005; 32(6):1030-1038.

Franck H, Franck D. Mathematical methods for accident reconstruction: a forensic engineering perspective. Taylor & Francis Group, LLC. ISBN 978-1-4200-8897-7. 2010; 302.

Wach W. Structural reliability of road accidents reconstruction. Forensic Science International. 2013; 228:83-89.

Wang Y W, Wu J, Lin Ch N. A line-based skid mark segmentation system using image-processing methods. Transportation Research Part C. 2008; 16:390-409.

Žuraulis V, Matuzevičius D, Serackis A. A method for automatic image rectification and stitching for vehicle yaw marks trajectory estimation. PROMET - Traffic&Transportation. 2016; 28(1):23-30.

Hoekwater J. Traffic accident reconstruction. Participant guide. 2008; 93.

Masory O, Gall E L, Bartlett W, Wright B. Experimental determination of the translational acceleration values for a spinning vehicle. Florida Conference on Recent Advances in Robotics, FCRAR 2006, Miami Florida. May 25-26. 2006; 1-4.

Seipel G, Winner H. Development and intensity of tyre marks - analysis of influencing parameters. 2013.

Reif K. Fundamentals of automotive and engine technology. Springer Vieweg. ISBN: 978-3-658-03971-4. 2014; 277.

Hirano Y, Inoue Sh, Ota J. Model-based development of future small EVs using modelica. Proceedings of the 10th International Modelica Conference Lund (Sweden). March 10-12. 2014; 63-70.

Sokolovskij E, Prentkovskis O. Investigating traffic accidents: the interaction between a motor vehicle and a pedestrian. Transport. Vilnius: Technika. ISSN 1648-4142. 2013; 28(3):302-312.

Shim T, Ghike Ch. Understanding the limitations of different vehicle models for roll dynamics studies. Vehicle System Dynamics. 2007; 45(3):191-216.

Sulaiman S, Samin P M, Jamaluddin H, Rahman R A, Burhaumudin M S. Modeling and validation of 7-DOF ride model for heavy vehicle. International Conference on Automotive, Mechanical and Materials Engineering (ICAMME'2012), Penang (Malaysia). May 19-20. 2012; 108-112.

ISO 8855:2011. Road vehicles. Vehicle dynamics and road-holding ability – Vocabulary.

ISO 8608:1995. Mechanical vibration – Road surface profiles – Reporting of measured data.

Feng J, Zhang X, Guo K, Ma F, Karimi H R. A frequency compensation algorithm of four-wheel coherence random road. Mathematical Problems in Engineering. 2013; 1-12.

Zhang Y, Chen W, Chen L, Shangguan W. Non-stationary random vibration analysis of vehicle with fractional damping. 13th National Conference on Mechanisms and Machines, Bangalore (India). December 12-13. 2007; 171-178.

Majdoub K E, Giri F, Ouadi H, Dugard L, Chaoui F Z. Vehicle longitudinal motion modelling for nonlinear control. Control Engineering Practice. 2012; 20:69-81.

Jazar R N. Vehicle dynamics: theory and application. Springer Science+Business Media, LLC. ISBN: 978-0-387-74243-4. 2008; 1015.

Brach R M, Brach R M. Tyre models for vehicle dynamic simulation and accident reconstruction. SAE Paper No. 0102. 2009.

Schramm D, Hiller M, Bardini R. Vehicle dynamics: modeling and simulation. Springer. ISBN: 978-3-540-36044-5. 2014; 405.

Bogdevičius M. Transporto priemonių dinamika: metodiniai praktinių uždavinių nurodymai. Vilnius: Technika. eISBN 978-609-457-276-0. 2012; 90.

Schiehlen W. Dynamical analysis of vehicle systems. CISM courses and lectures. SpringerWienNewYork. ISBN 978-3-211-76665-1. 2007; 497:304.

Pauwelussen J P. Essentials of vehicle dynamics. Butterworth-Heinemann, Published by Elsevier Ltd. 2015.

Corrsys-Datron. Instruction manual. A Kistler Group Company. 2012.

How to Cite
Žuraulis V, Sokolovskij E. Vehicle Velocity Relation to Slipping Trajectory Change: An Option for Traffic Accident Reconstruction. Promet [Internet]. 2018Jul.3 [cited 2022Jul.5];30(4):395-06. Available from: