Application of an exact energy theorem for surface sliding and crush energy in planar motor vehicle collisions. 2019-01-0422
This research is the adaptation of recently published research concerning energy and work principles consistent with a modal isotropic classical physics Impulse Momentum Planar Collision (IMPC) model. This model is based on Newton’s Laws of Motion, Coulomb's friction law and the temporal integral of the collision force and the vehicle accelerations, so the collision mechanics description becomes that of a collision impulse vector and corresponding delta-V components for each of the two colliding vehicles. Generally, IMPC models are known by various descriptions, including "Planar Impact Mechanics", "Classical Theory of Impact", "Classical Crash Model", "PC-Crash", "Stereomechanical Impact", "Rigid Body Theory for Planar Collisions", and so on. The equations presented here regarding work and energy are especially relevant to a motor vehicle collision reconstruction because some of the IMPC dissipated energy is commonly used to correlate with calculated vehicle crush energy. For glancing impact conditions this requires a mathematically consistent account of sliding energy dissipation, which has not been previously published for motor vehicle collision application. Previous research has not correctly identified the energy dissipated due to collision contact surface sliding. As such, previous methods commonly result in substantially inaccurate interpretations of the crush energy.
Also new and previously unpublished is the derivation of an equation, based on principles of structural dynamics, with which to calculate "relative collision time span" specific to the IMPC model. "Relative collision time span" correlates inversely to vehicle deformation, inversely to vehicle impact acceleration, and is consistent with the work energy principles presented in this paper. Therefore, for a given Delta V, the impact force to the vehicle and to the occupants is inversely proportional to the relative collision time span.
Nicholas Carpenter, Judson Welcher
Collision Dynamics Analysis, Biomechanical Research & Testing