On aerodynamics of baseball pitches: reconstruction of spinning throws, and a lift force model for the knuckleball - Aguirre López, Mario Alberto (2016)
Baseball pitchers have a wide repertory of throws, which can be classified in two types: spinning and non-spinning balls. Dynamics of spinning balls is widely understood while only a few works about non-spinning balls are found in literature. On the other hand, there are some methods to reconstruct baseball trajectories, however, these methods do not usually deal with the movement equations, and if they do, its by knowing a lot of points of the real trajectory. This work consists of two parts, both of them focused on real baseball pitches. In the first part, a method to reconstruct trajectories by obtaining the initial conditions (velocity and angular velocity) from spinning throws is designed. It is based on considering Magnus effect can be separate from rest of forces that define the dynamics of the ball, such assumption is supporting by an energetic analysis. Thus, methodology consist in solving the two-point boundary value problem (BVP) of the movement equations without the Magnus force and then adding its effect. The second part deals with the lift force present in knuckleball pitches, which is caused by the asymmetries on the ball morphology and has an oscillatory behavior varying the seams orientation. We propose a model to compute said force for two-seams (2S) and four-seams (4S) orientations, by means of a coefficient (lift coefficient) depending on the positions of each stitch of the ball seams. As a result from the knuckleball study, a lift coefficient model is constructed by fitting a function to experimental data reported in literature. Deflections in knuckleball trajectories are calculated as a complement. Regarding spinning pitches, analyses mentioned above lead us to assume that only three points (ball position in function of time) for a trajectory to reconstruct all it. This is applied in an algorithm based on shooting method, which obtains the initial conditions of synthetic trajectories with a high accuracy in a low-time.