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.
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November 2003
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November 01 2003
How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories
Gregory S. Sawicki;
Gregory S. Sawicki
Department of Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, California 95616
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Mont Hubbard;
Mont Hubbard
Department of Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, California 95616
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William J. Stronge
William J. Stronge
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
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Am. J. Phys. 71, 1152–1162 (2003)
Article history
Received:
June 12 2002
Accepted:
July 03 2003
Connected Content
A correction has been published:
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)]
Citation
Gregory S. Sawicki, Mont Hubbard, William J. Stronge; How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories. Am. J. Phys. 1 November 2003; 71 (11): 1152–1162. https://doi.org/10.1119/1.1604384
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