The formula commonly used to calculate velocity change in vehicle collisions

Abstract

A vehicle's velocity change in a crash, Δ v, is helpful in the scientific investigation of road traffic accidents. This note discusses the formula commonly used to calculate Δ v. A new derivation of this formula for planar motion is given here. The derivation is based upon the conservation laws and leads to an extension of the existing formula. It is not necessary to assume any deformation law for the vehicles in order to obtain the results. The new derivation clarifies the conditions under which the commonly used formula is valid. It shows that the masses and yaw moments of inertia of the vehicles must not be significantly changed by the collision. Further, tyre and other forces must be negligible when compared with the impulsive forces generated by the impact. Finally, there is a condition on the components of the velocities at the point where the resultant impulses act. The analysis shows that the commonly used formula neglects restitution effects and so tends to underestimate the actual velocity change. In fact, restitution effects are important for low-speed impacts. Impact speed calculated from the commonly used formula is not as accurate as speeds obtained by other methods. Nevertheless, in the absence of any marks on the road, such calculations may be the only way of scientifically estimating a vehicle's speed.