Abstract The purpose of this study was to present a method to convert spatiotemporal ball tracking data into equations of motion, thereby facilitating a greater understanding in how different variables influence the trajectory of a tennis ball. Interpreting a tennis ball trajectory via equations of motion enables characterising a tennis shot based on only the initial launch parameters off the racket (speed, direction and spin) and accounting for the influence of the ball inertial and aerodynamic (drag and lift) properties. This study used spatiotemporal ball tracking data (used for electronic line-calling purposes) collected at the 2022 Australian Open for demonstration and validation, with a focus on the tennis serve. From an assessment of 8654 serves, the median Mean Absolute Error (MAE) between the spatiotemporal ball tracking data and the equations of motion trajectory solution was 4.8 mm for the ball trajectory from racket impact through to the bounce, and 2.4 mm for the rebound trajectory after the bounce. The derived trajectory parameters from the study were consistent with expectations from research literature for drag and lift coefficients for a tennis ball, as well as the expected spin profiles for flat, slice and kick serves. The results also enabled quantifying the influence on the ball drag coefficient from repeated impacts, a phenomenon characterised by tennis balls progressively becoming fluffier with use.
Eassom et al. (Tue,) studied this question.