Model trajectories for a spinning tennis ball: III. The effect of a light wind on ground strokes

Abstract

Theoretical models are presented for the trajectory of a rotating spherical projectile appropriate to the ground stroke in tennis, the ball being delivered in the presence of a light head wind, tail wind or side wind. The aim of the study is to determine, quantitatively, the amount of movement due to such light winds which are known to be present even in enclosed stadiums. The ball is assumed to be struck without spin (i.e., a ‘flat’ stroke), with top-spin or with under-spin (i.e., ‘slice’), with the ball being hit directly down the court or ‘cross-court’. Forces considered are the drag force, the lift force and gravity. It is found that a very modest wind can move the ball/court impact point by large amounts, of the order of tens of centimeters compared to the no-wind case. For example, a wind of 5 km h−1 (1.39 m s−1) may move the impact point by up to 1 m. The direction of movement of the impact point is, not surprisingly, normally in the direction to which the wind is blowing, although the exact direction depends, in-part, on the spin. An under-spun ball, for example, in the presence of a head wind can have its ‘range’ to the impact point actually increased, and in the presence of a tail wind the range can be decreased, a seemingly anomalous behaviour which at first sight seems surprising. Explanations for this behaviour are given. Actual movements due to the wind are compared with the product of the flight time and wind speed, since this quantity might be expected to provide an upper limit to such wind-induced movements. For a head or tail wind of 5 km h−1 and a 150 km h−1 full-court-length flat ground stroke with a flight time of 0.765 s, this product is 1.06 m and the shift in the impact point is 42.5% of this value, with larger shifts of up to 75% occurring for top-spin shots.