Coefficient of Restitution

The coefficient of restitution (COR), or bounciness of an object is a fractional value representing the ratio of velocities after and before an impact. An object with a COR of 1 collides elastically, while an object with a COR < 1 collides inelastically. For a COR = 0, the object effectively "stops" at the surface with which it collides, not bouncing at all.

The coefficient of restitution likes lamp entered the common vocabulary, among golfers at least, when golf club manufacturers began making thin-faced drivers with a so-called "trampoline effect" that creates drives of a greater distance as a result of an extra bounce off the clubface. The USGA (America's governing golfing body) has started testing drivers for COR and has placed the upper limit at 0.83, golf balls typically have a COR of about 0.78. According to one article (addressing COR in tennis racquets), "for the Benchmark Conditions, the coefficient of restitution used is 0.85 for all racquets, eliminating the variables of string tension and frame stiffness which could add or subtract from the coefficient of restitution."

The COR is generally a number in the range [0,1]. Qualitatively, 1 represents a perfectly elastic collision, while 0 represents a perfectly inelastic collision. A COR greater than one is theoretically possible, representing a collision that generates kinetic energy, such as land mines being thrown together and exploding. For other examples, some recent studies have clarified that COR can take a value greater than one in a special case of oblique collisions. These phenomena are due to the change of rebound trajectory of a ball caused by a soft target wall. A COR less than zero would represent a collision that pulls two objects closer together instead of bouncing them apart.

An important point: the COR is a property of a collision, not necessarily an object. For example, if you had five different types of objects colliding, you would have different CORs (ignoring the possible ways and orientations in which the objects collide), one for each possible collision between any two object types.