A unified framework for the prediction of cricket ball trajectories in spin and swing bowling

Abstract

This paper builds on earlier work of the author that calculated the trajectories of cricket balls under fast swing bowling conditions, and develops a unified analytical framework for the consideration of both slow spin bowling and fast swing bowling. A classification of different types of bowling delivery, in so far as they relate to the flight of the ball through the air, is set out, and from this classification four generic cases of seam and spin plane angle are identified for further consideration. The force coefficient characteristics on spinning balls due to auto-rotational effects (due to the spin of the ball) are then derived, and these are used to develop the full equations of motion that can predict both swing and spin bowling trajectories. The four generic cases are then investigated using approximate solutions of these equations, the trajectories of spin bowling in lateral and vertical directions are explored and the relative magnitudes of flight displacements due to the boundary layer asymmetry (the cause of swing bowling displacements) and auto-rotational forces are discussed. Finally, the effects of cross winds on spin bowling trajectories are considered. In summary the paper presents an overall methodology that enables the various flow phenomenon associated with cricket ball flight to be considered in a unified manner.