Dependence of a Coefficient of Restitution on Geometry for High Speed Vehicle Collisions 2001-01-0892

I investigate how a coefficient of restitution (CR) (the pre- to post-collision ratio of relative center of mass speeds) varies with collision geometry (vehicle orientation at contact and impulse direction). Based on the low CR’s measured for in-line collisions and barrier crash tests, I argue that in other collisions the CR will be close to the minimum value consistent with the collision’s geometry, and that this fact can be useful in reconstructing accidents.

I derive a general equation for calculating the CR’s lower bound, and investigate, for the particular case of a rear-impact collision, its variation with impulse direction (PDOF) relative to incident relative velocity (θ_J), offset, and the orientation of the collision contact surface. The minimum CR calculated here does not depend on the common-velocity assumption; it therefore offers promise for analyzing side-swipe collisions.

The minimum CR depends most strongly on θ_J, increasing with increasing θ_J. For many collisions the minimum CR can be approximately calculated from a knowledge of θ_J alone. For |θ_J| > 10°, the minimum CR is approximately equal to the lower bound (valid for all collisions) e ≥ sin (|θ_J|). The CR manifests a weaker dependence on vehicle offset and the direction of the inter-vehicle impulse, increasing with increasing offset, and increasing as the inter-vehicle impulse departs from the direction normal to the contact surface.

I demonstrate how this CR can be used to reconstruct a vehicle collision where lack of data prevents reconstruction by conservation of momentum.