Vector model of vehicle collisions for inferring velocity from loss of kinetic energy with restitution on residual crush surface

In the standard mathematical model that underpins the inference of velocity change from vehicle damage in road accident reconstruction, the point where the colliding bodies engage is taken to lie in the same location as the point of application of the average impact force, usually in the central region of the crush zone or on the residual crush surface. Mathematical and physical reasons suggest the fidelity of the model could be deepened by allowing for a separation of these points, for example by locating the impulse or average force in the central region of the crush zone and defining engagement (common velocity or rebound) relative to the crush surface. Refinement of the theory revealed that the solutions for the change of linear and angular velocity are unaffected. For long-running in-depth research studies, this means that historical calculations of velocity change (delta-V) and related analyses on such topics as injury risk curves, countermeasure effectiveness and accident scenarios are not potentially undermined. Relative and absolute velocity are however affected. This was illustrated using crash test data where adjustments of six and twelve centimetres resulted in changes of up to four percent in road speed.