Baseball Bats

Hitting a baseball well is not easy. Even professional baseball players have difficulty consistently making solid contact with a pitched baseball. Once hit, the distance of flight of the ball is determined by its initial velocity that is, the initial speed and direction which depends on how hard the ball has been hit by the bat. All other factors being held constant, the initial velocity can be said to depend on the speed of the bat just before collision. A quicker swing would mean a faster bat speed during the collision to add distance to each hit and also allow the batter more time to judge the pitch.

There have been proposals to put shallow, pea-sized depressions dimples in the surface of a baseball bat to allow a greater swing speed. Another sports object, the golf ball, already is made with dimples on its surface. How would these dimples affect the bat’s swing speed?

Answer

The main source of drag on the swing of a baseball bat is not air friction but the retarding force produced by the pressure difference across the bat from front to back. As the bat carves its swath, the air in front gets separated into two boundary layers that pass around the bat and recombine behind the bat. In the wake of the bat, between the two separated boundary layers, the “lack of air” means a lower pressure immediately in back of the bat, with a resulting backward force due to the pressure difference. Therefore, some of the energy of the swing does work against this backward force.

A dimpled bat sends the boundary layers tumbling in turbulent eddies into the space behind the bat, reducing the pressure difference and cutting the drag. More swing energy is now available to accelerate the bat and to transfer to the ball, so the ball’s exit velocity will be increased.