The Determination of Vehicle Speeds from Delta-V in Two Vehicle Planar Collisions

Abstract

The change of a vehicle's velocity, delta-V (Δv), due to an impact is often calculated and used in the scientific investigation of road traffic collisions. In isolation, however, this figure does not yield any information concerning the actual velocities of the vehicles and such information is often of prime concern to those investigating collisions. In this paper a method is developed which uses the change in velocity sustained by a vehicle in a planar collision to estimate the velocities of the vehicle before and after a collision. The key equations are derived from conservation of momentum, conservation of energy, and restitution. As with the calculation of Δv, the method requires an initial estimate of the principal directions of force. The pre- and post-impact angles of the vehicles' velocities can be used to obtain better estimates of the principal directions of force and of the coefficient of restitution. In collisions where it is difficult to analyse the vehicles' post-impact motion, this method provides a way to estimate the actual speeds of vehicles. To demonstrate the method, it is used to analyse one of the RICSAC collisions. The results of an analysis of other staged collisions illustrate the accuracy of the method.