Are inertial forces ever of significance in cricket, golf and other sports?

Abstract

In previous papers we investigated the motion of a spherical projectile rotating about an arbitrary axis, subject to a drag force, a lift or Magnus force, and in the presence of a wind. The aim was to determine the motion of balls used in sporting games, primarily cricket. Newton's laws of motion apply in an inertial (unaccelerated) coordinate system, but the rotating Earth is not an inertial system. In such a non-inertial system two additional forces are present, the Coriolis force which produces a side-ways movement, and the centrifugal force. Generally these two inertial forces produce noticeable effects only on the large scale, when either the time of travel and/or the path length is large. In this paper we have added both of these forces to the equations of motion. In addition, we have also included a ground friction force in order to simulate a ball rolling over a surface or, more generally, a body moving through a resistive medium such as water. Here we quantitatively investigate the magnitude and direction of the effect of the inertial forces in a number of cases. It is found that, as expected, the effects of the inertial forces are generally small for ball games. In cricket the side-ways movement is ≲1 cm for a throw from the boundary and ≲1 mm for a slow bowler's delivery, and for a long drive in golf it is ≲10 cm. In lawn bowls the side-ways movement can be ∼2.8 cm, which may be significant, given the nature of this sport. The inertial forces are also potentially of relevance in sporting events not employing spherical projectiles. For example, in Olympic rowing we find that the side-ways movement can be more than 40 m for a 2 km race if it is not compensated for, and nearly 20 m for a 4 min mile event in athletics. The effect is also of significance in events such as swimming and horse racing. The importance of this is that athletes may not be aware of the effect and, in the case of rowing for example, may attribute it to side-ways currents, winds, or a deficiency in their rowing style. As a further complication, the magnitude of the side-ways movement is latitude dependent and its direction is hemisphere dependent, being to the right in the northern hemisphere and to the left in the southern hemisphere.