Aerodynamics of the curve-ball : an investigation of the effects of angular velocity on baseball trajectories

In this dissertation the aerodynamic force and initial conditions of pitched baseballs are estimated from high-speed video data. Fifteen parameters are estimated including the lift coefficient, drag coefficient and the angular velocity vector using a parameter estimation technique that minimizes the residual error between measured and estimated trajectories of markers on the ball’s surface and the center of mass of pitched baseballs. Studies are carried out using trajectory data acquired from human pitchers and, in a more controlled environment, with a pitching machine. In all 58 pitch trajectories from human pitchers and 20 pitching machine pitches with spin information are analyzed. In the pitching machine trials four markers on the ball are tracked over the first 4 ft (1.22 m) and the center of mass of the ball is tracked over the last 13 ft (3.96 m) of flight. The estimated lift coefficients are compared to previous measured lift coefficients of Sikorsky (Alaways & Lightfoot, 1998) and Watts & Ferrer (1987) and show that significant differences exists in the lift coefficients of twoand four-seam curve balls at lower values of spin parameter, S . As S increased the twoand four-seam lift coefficients merge becoming statistically insignificant. The estimated drag coefficients are compared to drag coefficients of smooth spheres and golf-balls and show that these data sets bound the drag-coefficient of the baseball. Finally, it is shown that asymmetries of the ball associated with the knuckleball can influence the trajectory of the more common curve and fastball.