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.

Topics
Bioacoustics of mammals, Friction, Rigid body dynamics, Mathematical optimization
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2003
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