Stiffness and Crush Energy Analysis for Vehicle Collision and its Relationship to Barrier Equivalent Velocity (BEV) 2001-01-0500

Accident reconstruction typically requires estimating the change of velocity (Delta-V) imparted to vehicles during collision. Estimating Delta-V commonly involves measuring or estimating the deformation of the vehicles involved in a collision. Material coefficients, which relate barrier equivalent velocity (BEV) to deformation for the two vehicles, are then interpolated or extrapolated from barrier crash test data. Finally, the Delta-V for each of the two vehicles is usually calculated using single-degree-of-freedom (SDOF) impact mechanics formulas.

This paper presents a derivation of SDOF impact mechanics formulas applicable to one-dimensional vehicle collisions. The governing equations presented are new, more complete and more efficient than previously published efforts. In particular, Newton's third law of physics concerning collision force is proportionally expressed as the product of vehicle weight, crush progression behavior and BEV. Relative closing speed and Delta-V are then related to BEV by a factor that is efficiently a function of relative vehicle weight and relative crush progression behavior. The mechanics derivations reveal the proper relationship for predicting coefficient of restitution for vehicle-to-vehicle collision. Previous literature has assumed that restitution can depend on relative vehicle weight. It is shown that the prediction of restitution depends strictly on relative vehicle stiffness, not relative weight.