Model trajectories for a spinning tennis ball: II. The service stroke in the presence of a wind. (8th November 2018) - Robinson, Garry; Robinson, Ian
Abstract: In this paper we investigate, via model trajectory calculations, the effect of a horizontal wind on the path followed by a tennis ball resulting from the service stroke. The equations of motion employed included the effects of gravity, the drag force and, for a spinning ball, the lift or Magnus force. Spin about an arbitrary axis and spin-down of the ball in its flight are allowed for. Serve types treated are the flat serve (a serve delivered without spin), the sliced serve (a serve delivered with side-spin), the top-spin ('kicking') serve, the axial-spin serve (spin analogous to an off-spinner's delivery in cricket), and 'combination' spin serves (serves delivered with a mixture of spins). When a player is trying to deliver say a pure sliced serve or a pure top-spin serve, the result is actually likely to be a 'combination' spin serve, a serve consisting of a mixture of these spin types, perhaps with an 'axial' spin component as well. We focus mainly on a serve delivered towards the centre-line of the court. It is found that the court impact point for a flat serve or a top-spin serve is moved, not surprisingly, almost exclusively in the direction of the wind, with typical movements being in the range 0.1–1.0 m for a wind of strength 15 km h − 1 . A head wind causes the ball to impact the court shorter than it would in the absence of a wind, and a tail wind longer than it would with no-wind. A side-wind moves the ball towards the side of the court in the direction of the wind. However, a sliced serve, by the action of a wind, is moved in both directions relative to the no-wind situation. In this case the drag force causes movement in the direction of the wind, but the component of the lift force due to the wind, being perpendicular to the wind direction and spin vector, is in the horizontal plane, and therefore causes movement in this plane and perpendicular to the wind. The direction and amount of movement of a 'combination' spin serve in the presence of a wind is directly related to the individual components of the spin vector.