Ball spin in the tennis serve: spin rate and axis of rotation

Abstract

The purpose of this study was to describe three-dimensional ball kinematics including spin axis and spin rate for the flat, slice, and kick serves executed by elite male tennis players. Trajectories of three retro-reflective markers attached to the surface of the ball were measured using a Vicon MX motion analysis system. The local coordinate system of the ball enabled the ball's angular velocity vector to be determined. Mean ( ± SD) spin rates recorded were 127.4 ( ± 56.3), 232.1 ( ± 34.8), and 336.5 ( ± 51.5) rad/s for the flat, slice, and kick serves, respectively. The resultant horizontal velocities of the ball were 52.0 ( ± 2.9), 46.4 ( ± 3.4), and 40.8 ( ± 2.8) m/s, respectively, and a clear tradeoff existed between the development of ball spin rate and horizontal ball velocity, with resultant horizontal velocities of 52.0 ( ± 2.9), 46.4 ( ± 3.4), and 40.8 ( ± 2.8) m/s, respectively, being recorded. The spin axis and ball velocity vector were close to perpendicular regardless of serve type. Mean angles between the spin axis and the horizontal plane (elevation angles) were 65.6° ( ± 10.2°), 68.4° ( ± 6.9°), and 54.5° ( ± 8.4°) for the flat, slice, and kick serves, respectively.