coefficient of restitution
A dimensionless number e between 0 and 1 characterising how elastic a collision is: ratio of post-collision to pre-collision relative speed.
Definition
The coefficient of restitution, usually written e, is the ratio of the relative speed of the two bodies after a collision to their relative speed before. e = 1 corresponds to a perfectly elastic collision (no KE lost); e = 0 to a perfectly inelastic one (maximum KE lost, bodies stick together). Everything real falls in between.
Typical values: a tennis ball on a hard court, e ≈ 0.75; a baseball on a wooden bat, e ≈ 0.55; a hard rubber superball on concrete, e ≈ 0.9; a basketball on a gym floor, e ≈ 0.75; two billiard balls, e ≈ 0.95. Sports equipment is often specified with a maximum allowed e — the NCAA caps baseball bats at e ≈ 0.55 to keep the game from turning into a parade of home runs.
For 1-D collisions, given initial velocities v_A and v_B and masses m_A and m_B, momentum conservation combined with v_A' − v_B' = −e·(v_A − v_B) uniquely determines the outgoing velocities for any 0 ≤ e ≤ 1. The formulation generalises smoothly to oblique 2-D and 3-D collisions by applying it only to the component of velocity along the collision normal. Engineers use it to model everything from ball-mill milling to golf-club design to railway buffer behaviour.