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 (θJ), 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 θJ, increasing with increasing θJ. For many collisions the minimum CR can be approximately calculated from a knowledge of θJ alone. For |θJ| > 10°, the minimum CR is approximately equal to the lower bound (valid for all collisions) e ≥ sin (|θJ|). 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.