Looking into Chapman’s homer: The physics of judging a fly ball

How does a baseball player learn to judge a fly ball? An experienced outfielder, observing the initial stages of flight, can predict the landing point rapidly and accurately. In 1968, S. Chapman Am. J. Phys. 36, 868 (1968) proposed that an outfielder unconsciously uses trigonometry to determine the landing point. However, Chapman assumed incorrectly that the effects of aerodynamic drag could be ignored. The trajectory of a baseball is shown to be affected significantly by air resistance, so that the specific trigonometric factor cited by Chapman cannot provide useful cues to the fielder. In evaluating potentially useful cues, we take note not only of aerodynamic drag, but also of the specific neurophysiological processes used for the detection of distance and motion. This study shows that the angular acceleration of the fielder’s line of sight to the ball provides the strongest initial cue to the location of the eventual landing point. This suggests that the fielder’s vestibular system, responding to the acceleration of the fielder’s head as he observes the initial stages of flight, may play a key role in the judgment process.