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American Journal of Physics -- November 2003 -- Volume 71, Issue 11, pp. 1152

How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories

Gregory S. Sawicki1, Mont Hubbard1, and William J. Stronge2

1Department of Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, California 95616
2Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom

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Improved models for the pitch, batting, and post-impact flight phases of a baseball are used in an optimal control context to find bat swing parameters that produce maximum range. The improved batted flight model incorporates experimental lift and drag profiles (including the drag crisis). An improved model for bat–ball impact includes the dependence of the coefficient of restitution on the approach relative velocity and the dependence of the incoming pitched ball angle on speed. The undercut distance and bat swing angle are chosen to maximize the range of the batted ball. The sensitivity of the maximum range is calculated for all model parameters including bat and ball speed, bat and ball spin, and wind speed. Post-impact conditions are found to be independent of the ball–bat coefficient of friction. The lift is enhanced by backspin produced by undercutting the ball during batting. An optimally hit curve ball will travel farther than an optimally hit fastball or knuckleball due to increased lift during flight. © 2003 American Association of Physics Teachers.

© 2003 American Association of Physics Teachers

ERRATA AND EDITORIALLY RELATED

    Erratum

  1. Erratum: Reply to Comment on "How to hit home runs: Optimum baseball swing parameters for maximum range trajectories," by Gregory S. Sawicki, Mont Hubbard, and William J. Stronge [Am. J. Phys. 71 (11), 1152–1162 (2003)]
    G. S. Sawicki et al.
    Am. J. Phys. 73, 365 (2005)AJPIAS000073000004000365000001

    2. Related Articles

  2. Comment on "How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories," by Gregory S. Sawicki, Mont Hubbard, and William J. Stronge [Am. J. Phys. 71 (11), 1152–1162 (2003)]
    Robert K. Adair
    Am. J. Phys. 73, 184 (2005)AJPIAS000073000002000184000001
  3. Reply to Comment on "How to hit home runs: Optimum baseball swing parameters for maximum range trajectories," by Gregory S. Sawicki, Mont Hubbard, and William J. Stronge [Am. J. Phys. 71 (11), 1152–1162 (2003)]
    G. S. Sawicki et al.
    Am. J. Phys. 73, 185 (2005)AJPIAS000073000002000185000001

KEYWORDS and PACS

Keywords

sport, teaching, ballistics, optimal control, motion control

PACS

RELATED DATABASES

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History
Received Jun 2002
Accepted Jul 2003
Online Oct 2003

PUBLICATION DATA

ISSN

0002-9505 (print)  

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.1604384

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