The way the baseball bounces.

The way the baseball bounces

Sometimes the difference between a fly ball that's caught and a home run is a matter of inches. One factor influencing how far a player can hit a baseball is the amount of "bounce" the ball has. Measured as the coefficient of restitution (the ratio of an object's velocity after a collision to its velocity before the collision), the bounce factor affects a well-hit ball's launch velocity and hence a fly ball's range.

The rules of major-league baseball specify that a baseball's coefficient of restitution must lie between 0.514 and 0.578. That's enough leeway to make a difference on teh order of 15 feet -- roughly the width of a baseball field's warning track -- in the horizontal distance a well-hit fly ball may travel, says David T. Kagan of California State University in Chico. Kagan describes his calculation in the February AMERICAN JOURNAL OF PHYSICS.

Kagan makes a number of assumptions and approximations in his calculations that limit the accuracy of his estimate. He assumes, for example, that the collision between a bat and a ball has the same coefficient of restitution as that measured officially by firing a baseball at 85 feet per second at a wall of ash. However, a bat may absorb energy differently, and the actual relative velocities in typical ball-bat collisions are considerably higher than 85 feet per second, which could lower the effective coefficient of restitution. It's also difficult to quantify the amount of drag, which varies considerably throughout a ball's flight as the air passing the ball becomes more or less turbulent. Furthermore, real baseballs may not vary as much as the rules allow.

Is the difference between a warning-track out and a home run really influenced by slight variations in the baseball? Kagan replies, "Probably not."