Dynamics of the baseball–bat collision

A model is developed for the collision between the baseball and bat, taking into account the transverse bending vibrations of the bat. By coupling the flexible bat to the ball via a parametrized force that each mutually exerts on the other, a complete description of the collision process is obtained, including the exit speed of the ball vf. It is shown that vibrations play an important role in determining vf. The model is in excellent agreement with experimental data at low impact velocities. At the higher velocities more appropriate to the game of baseball, vf is shown to coincide with the rigid-body value only over a very small region in the barrel of the bat and to drop off sharply for impacts removed from that region. Some interesting insights into the collision process are obtained, including the observation that for impacts in the barrel of the bat, the momentum transferred to the ball is essentially complete by the time the elastic wave first arrives at the handle and that any clamping action of the hands will affect the bat at the impact point only after the ball and bat have separated. This suggests that vf is independent of the size, shape, and method of support of the bat at distances far from the impact location.