Abstract
Professional baseball players occasionally find it difficult to gracefully approach seemingly routine pop-ups. We describe a set of towering pop-ups with trajectories that exhibit cusps and loops near the apex. For a normal fly ball the horizontal velocity continuously decreases due to drag caused by air resistance. For pop-ups the Magnus force is larger than the drag force. In these cases the horizontal velocity initially decreases like a normal fly ball, but after the apex, the Magnus force accelerates the horizontal motion. We refer to this class of pop-ups as paradoxical because they appear to misinform the typically robust optical control strategies used by fielders and lead to systematic vacillation in running paths, especially when a trajectory terminates near the fielder. Former major league infielders confirm that our model agrees with their experiences.
Original language | English (US) |
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Pages (from-to) | 723-729 |
Number of pages | 7 |
Journal | American Journal of Physics |
Volume | 76 |
Issue number | 8 |
DOIs | |
State | Published - Aug 2008 |
ASJC Scopus subject areas
- General Physics and Astronomy