Drag and Lift Coefficient Modeling from Table Tennis Experiments

Spinning balls are used judiciously in sports like cricket, tennis, table tennis, and football. Table tennis is particularly interesting to study as it is the sport where both the aerodynamic forces, i.e., drag and lift, dominate gravity the most. We have built a high-speed stereo vision system to track the three-dimensional trajectory of spinning sports balls, including the bounce. In the current study, it is employed in table tennis to obtain the experimental trajectories for shots imparted with pure topspin, sidespin, backspin, and their combinations. For each recorded trajectory, the 3D position data is extracted from the two synchronized camera footages using Computer Vision, and the velocities are subsequently derived at every timestep. Furthermore, we developed a mathematical framework to obtain the instantaneous spin vector on the ball utilizing either of the camera footages. The algorithms for extracting position and spin are validated against ground-truth values. Using the trajectory and kinematic datasets, we ultimately model the drag and lift coefficients in the aerodynamic equation of motion for the table tennis ball.