Residual Crush Energy Partitioning, Normal and Tangential Energy Losses

Residual damage caused during a collision has been related through the use of crush energy models and impact mechanics directly to the collision energy loss and vehicle velocity changes, ΔV₁ and ΔV₂. The simplest and most popular form of this crush energy relationship is a linear one and has been exploited for the purpose of accident reconstruction in the well known CRASH3 crush energy algorithm. Nonlinear forms of the relationship between residual crush and collision energy also have been developed. Speed reconstruction models that use the CRASH3 algorithm use point mass impact mechanics, a concept of equivalent mass, visual estimation of the Principle Direction of Force (PDOF) and a tangential correction factor to relate total crush energy to the collision ΔV values. Most algorithms also are based on an assumption of a common velocity at the contact area between the vehicles. The use of point mass mechanics, equivalent mass, a tangential correction factor and zero restitution are unnecessarily restrictive and their use reduces the accuracy of the crush energy methods in crash reconstruction.

This paper shows that planar impact mechanics can be adapted to significantly improve the rigor of using residual crush for crash reconstruction. Planar impact mechanics models the impulses and the changes in momentum of vehicles colliding in a plane including restitution of the collision at the intervehicular contact surface. Two impact coefficients are used, the (normal) coefficient of restitution and the (tangential) impulse ratio. The work of the normal component and tangential component of the crash impulse vector are individually associated with the crush energy and with the tangential energy loss and to each vehicle's ΔV. This work-energy association is referred to as partitioning of the collision energy loss. Partitioning is necessary in order to adapt planar impact mechanics to the CRASH3 measurement protocol. The paper also covers the proper approach to take restitution into account, both as it occurs in the barrier tests to determine each vehicle's crush stiffness coefficients and as it occurs in the impact between two vehicles. Data from oblique frontal barrier crash tests by Struble-Welsh Engineering are used to assess the use of planar impact mechanics and the partitioning of energy loss into crush energy and tangential energy. The process of using crush energy in reconstructions is discussed.