Baseball–bat collisions and the resulting trajectories of spinning balls

The collision between a baseball and a bat has been analyzed using the classical theory of rigid body collisions. Also computed are the ranges of batted balls for a variety of launch angles and rotation rates, accounting for both drag and lift forces. If the coefficient of friction is not too small, the batter can give the ball fairly large backspin without fouling it off by swinging under the ball by as much as 1 to 2.5 cm. The increased range resulting from backspin is large, of the order of several tens of meters. The effect of the weather on the ranges has been analyzed briefly and it is found that under extreme conditions it can be surprisingly large.