Paradoxical pop-ups: Why are they difficult to catch?

Michael McBeath, Alan M. Nathan, A. Terry Bahill, David G. Baldwin

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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 languageEnglish (US)
Pages (from-to)723-729
Number of pages7
JournalAmerican Journal of Physics
Issue number8
StatePublished - Aug 2008

ASJC Scopus subject areas

  • General Physics and Astronomy


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