Vol. IV No. 30   ·   13 April 2001

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I'm a baseball nut and have been watching it for years, but for the life of me I can't figure out how a curve ball curves. How does the pitcher do that?

CAS Physics Professor Emeritus George Zimmerman, who taught more than 10,000 students during his nearly four decades at BU, took a time-out between innings to answer this question.

"You can read an excellent book on the subject, The Physics of Baseball, in which you'll learn that a baseball curves because of the forces exerted on it during its motion," he says. "There is always the force of gravity, which makes the ball curve downward and eventually fall to the ground. Other forces are from the spin the pitcher puts on the ball and the interaction of this spin with air resistance. So how the ball is spun and its initial velocity, as well as the interaction of the air resistance with the seams of the ball, will characterize the various pitches.

"Now let's put a pitcher on the mound. He releases the ball and aims it towards home plate. As soon as he does this, the ball encounters air resistance, which tends to slow it down. This air resistance will be greater the greater the velocity of the ball, or the greater the relative velocity of the ball with respect to the air.

"Suppose that the pitcher, when he released the ball, gave it a spin. Let's assume the spin is counterclockwise when viewed from above. When you look along the path of the ball, from the point of view of the pitcher, the relative velocity of the ball with respect to the air on the right side will be greater than that on the left. Because the greater relative velocity implies a greater force, there will be a net force perpendicular to the path of the ball, to the left, and the ball will thus curve.

"To go one step further, according to Newton's laws of motion, the deflection from a straight line due to a steady force is proportional to the square of the distance the ball has traveled. Thus, assuming that the distance between pitcher and batter is 60 feet, if at 30 feet the ball has a deflection of 3.5 inches, by the time the ball gets to the batter the deflection will be 3.5 x 3.5, which equals 12.25 inches. This might account for the breaking phenomenon you see in a curve ball.

"But whether the pitcher's delivery results in a swing and a miss or an out-of-the-park home run depends on the batter."

13 April 2001
Boston University
Office of University Relations