Studies of Baseball Aerodynamics

Analysis of the aerodynamic forces acting on baseball pitches from major league games reveals a large variance in the measured coefficients of lift and drag. We have examined possible explanations for this effect and found that, while uncertainties introduced by measurement error and the method of reporting major league pitch trajectories do explain some of the spread, the reasons for the larger portion remain unknown. I. Background and Motivation Baseball contains a myriad of pitches, differentiated by appearance or behavior. While pitchers can describe how to throw these different pitches, the physical effects at work are not completely understood. Once a ball has been released, its path is determined by its momentum and the forces acting on it: gravity, lift, and drag. Previous research gives us equations for the lift and drag forces acting upon a baseball. The lift force is represented as L , and is expressed in terms of air density, ρ ; the coefficient of lift, CL ; angular velocity, ω ; crosssectional area, A ; and velocity, V . The drag force, represented as D , is expressed in terms of the previous variables, as well as the coefficient of drag, CD . The equations are: L = 1 2 ρCL AV 2 ω ×V ω × V (1) D = − 1 2 ρCD AVV (2) These equations indicate that, for constant coefficients of lift and drag, the respective forces are proportional to the square of velocity. However, it is believed that the coefficient of lift is inversely proportional to velocity. Therefore, the lift force would increase linearly with velocity. As may be seen in Figure 1, the force of drag opposes velocity while the lift force is perpendicular to both the direction of travel and the angular velocity vector, ω . Figure 1. Directions of aerodynamic forces acting on a baseball, relative to ball’s direction of travel and angular velocity vector. Most of the components of the lift and drag forces can be observed through common techniques used at baseball games.