Derivation of Closing Speed as a Function of Dissipated Energy

In accident reconstruction, a relationship frequently used for completely inelastic collisions is one between relative speed (or closing speed), vehicle weights and total energy dissipated in deforming the vehicles during collision (crush energy). Derivation of this equation is presented in various accident reconstruction literature, but always for collinear collisions, i.e. vehicles traveling along the same straight line. A derivation is presented here for the general case, which shows the same relationship is valid for any angle of approach between the vehicles, not just 0° or 180°. A supplemental derivation is presented which yields the relationship for all collisions, not just completely inelastic collisions.