A calculation of cricket ball trajectories

While a number of past investigations have measured the aerodynamic forces on cricket balls, in general these forces have not been used to calculate the trajectories of balls between bowler and batsman. This article presents such a calculation. It begins with the full trajectory equations as developed for the study of debris flight in extreme windstorms, which are adapted for the cricket ball case. A collation of earlier experimental data is then presented for drag and side force coefficients on cricket balls. From these data, which show considerable scatter, a small number of generic force characteristics are derived for use in the trajectory equations. These characteristics have constant force coefficients in the subcritical and supercritical Reynolds number regions, and a transition between these two regions with a variable gradient. An approximate analysis of the trajectory equations results in very simple forms for the trajectories in the sub-and supercritical Reynolds number regimes, which reveal the governing dimensionless parameters of the problem, and enable the effect of crosswinds to be quantified. The predicted parabolic profiles are in agreement with some very simple calculations carried out by earlier investigators, revealing the limited range of validity of such calculations, and with the limited real bowling trajectories that have been observed. A full solution of the trajectory equations is then presented for the generic force coefficient characteristics, and a study of trajectories through the Reynolds number range is carried out. In the transition region between sub-and supercritical flows, complex ball trajectories are shown to be possible.