A simplified model for analysis of the post-impact motion of vehicles

In a collision between vehicles, the post-impact phase, where they translate and rotate, often has significant importance in the analysis and reconstruction of road accidents. Indeed, the calculation of errors made in this analysis will be reflected in later stages, compromising the correct identification of the accident scenario. Because of the uncertainty in the initial data as well the lack of data, simplified models are used in order to calculate the kinematic parameters of the vehicles. The literature offers some of these simplified models, even though the most reliable models require iterative calculations or numerical integration of the equations of motion. In the present work a model for the calculation of both the linear velocity and the angular velocity of the vehicle, which are useful for analysing the post-impact phase between vehicles, is built. The model is based on the schematization of the trajectory of the individual wheels with a cycloid, which is lengthened or shortened depending on the magnitude of the ratio of the translational velocity to the rotational velocity of the vehicle. The work dissipated by friction along this trajectory is calculated and then made equal to the loss in kinetic energy, assuming that the ratio of the angular velocity to the linear velocity during motion is constant. The model gives results comparable with the numerical integration of the equations of motion, when schematizing the vehicle as a rigid body with three degrees of freedom. The model is suitable in the field of road accident reconstruction owing to its simplicity of use. Indeed, it is necessary to consider only the friction coefficient between the tyre and the road, and to use only two uncoupled equations to find the values of the angular velocity and the translation.