On a possibility of complicating the mathematical model of a collision between two motor vehicles

In this paper, a survey on some selected problems of motor vehicle collisions modeling was undertaken. The aim of this paper was to replace the classic approach based on a planar motion with a more complex resultant motion to examine the potential additional factors affecting the process of a collision. In the case of a collision between two vehicles, especially for a large velocity, the colliding vehicles may break away from the road surface and perform a motion that requires including a more sophisticated approach to understand a road collision process, particularly in view of its short duration. Moreover, the most common frontal or rear collision model was replaced with the side impact collision model in which one vehicle struck the side of the other. Such approach makes the collision model even more complex. It was also necessary to consider other phenomena as well. Apart from adopting a simple momentum - impulse collision model, the authors took into account the friction between the bodies of the vehicles involved in a collision in order to analyze the possibility of the coefficient of restitution in the case of both normal and tangential directions versus the plane of collision common for both vehicles. In the case of a resultant motion during the collision the forces of inertia, transportation and Coriolis were included. Such analysis can be a tool to better understand the crucial parameters of any collision between motor vehicles, instead of performing a forensic expertise. The novelty and one of the most important results of this paper may be creation of the more complex mathematical model of a collision between two vehicles when compared to the regular models. Such model can include such factors as the resultant motion during a collision that enable providing more realistic description of a collision process than in a typical scenario. Of course, the paper deals with the momentary phenomena, which last for a very short period of time (e.g. 0.1 s), hence including the factors which make the collision model more complex may allow understanding its course and, what is more, the potential effect on the post-collision motion of the vehicles involved.