Publication Title

Sports Engineering

Document Type


Department or Program


Second Department or Program

Physics and Astronomy

Publication Date



The fourth-order Runge–Kutta method is used to numerically integrate the equations of motion for a fastpitch softball pitch and to create a model from which the trajectories of drop balls, rise balls and curve balls can be computed and displayed. By requiring these pitches to pass through the strike zone, and by assuming specific values for the initial speed, launch angle and height of each pitch, an upper limit on the lift coefficient can be predicted which agrees with experimental data. This approach also predicts the launch angles necessary to put rise balls, drop balls and curve balls in the strike zone, as well as a value of the drag coefficient that agrees with experimental data. Finally, Adair’s analysis of a batter’s swing is used to compare pitches that look similar to a batter starting her swing, yet which diverge before reaching the home plate, to predict when she is likely to miss or foul the ball.


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This is a post-peer-review, pre-copyedit version of an article published in Sports Engineering. The final authenticated version is available online at: