A curve fitting methodology to determine impact location, timing, and instantaneous post-impact ball velocity in cricket batting

Abstract

This study aimed to develop a methodology for accurate determination of the impact location of a cricket ball on the bat face, as well as the identification of bat–ball contact timing and post-impact instantaneous ball velocity in a whole-body kinematic data collection environment. Three-dimensional kinematic data of bat and ball were recorded during 14 batting strokes: 8 hitting a static ball and 6 against a bowling machine. Curves were fitted separately to the pre- and post-impact phases of the ball position data against time in three axes according to logarithmic equations determined from mechanical principles. Separate Fourier series models were similarly fitted to the four corners of the bat face against time during the downswing prior to ball impact. Time of impact for the dynamic ball trials was determined based on the intersection of pre- and post-impact curves, with impact location calculated from ball and bat face curves at this time. R² values for the goodness of fit of the ball and bat curves averaged 0.99 ± 0.04 and 1.00 ± 0.00 with root mean square errors of 7.5 ± 2.6 and 0.8 ± 0.2 mm, respectively. Calculated impact locations were assessed against measured impact locations derived from the impression imparted to a fine powder coating on the bat face, finding absolute differences of 6.4 ± 4.2 and 7.1 ± 4.4 mm in the transverse and longitudinal axes of the bat, respectively. Thus, an automated curve fitting methodology enables the accurate determination of cricket bat–ball impact characteristics for use in experimental investigations.