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 fourteen batting strokes; eight hitting a static ball and six 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 upon the intersection of preand post-impact curves, with impact location calculated from ball and bat face curves at this time. R 2 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.

The relationships between impact location and post-impact ball speed, bat torsion, and ball direction in cricket batting

“…The mean R 2 and RMSE values for pre-and post-impact ball curves (0.99 ± 0.04 and 9.8 ± 4.3 mm), and pre-impact bat curves (0.99 ± 0.03 and 1.0 ± 0.9 mm,) were found to be similar to those achieved during the validation of the impact location methodology (Peploe et al, 2017). This indicates a similar quality of curve fitting, and thus comparable errors in terms of impact location.…”

“…The effects of impact location in the longitudinal direction on bat torsion and ball direction were assumed to be negligible (King et al, 2012) and so were not assessed. Initially the rate of bat polar rotation (about the midline of the bat face) was calculated from 3D bat marker positions, and the absolute peak between impact (timing determined using Peploe et al, 2017) and 0.02 s after impact was defined. A measure of post-impact bat torsion was then determined as the difference between the peak measured rate of bat polar rotation, and the mean pre-impact rate of bat polar rotation during a similar period prior to impact.…”

“…A measure of post-impact bat torsion was then determined as the difference between the peak measured rate of bat polar rotation, and the mean pre-impact rate of bat polar rotation during a similar period prior to impact. Both the angle of the bat face and post-impact ball direction were calculated relative to the global coordinate system, from bat displacement curves at the time of impact, and the post-impact ball displacement curves respectively (Peploe et al, 2017). Finally, the relationship between peak change in the rate of bat polar rotation and post-impact ball direction was assessed.…”

“…Bat and ball marker position data were manually labelled and processed for each trial. The single ball displacement equation methodology of Peploe et al (2017) was then used to determine the impact location of the ball on the bat face (accurate to within 7.4 ± 4.8 mm medio-laterally and 9.2 ± 4.3 mm longitudinally of measured locations). Curves were fitted separately to the pre-and post-impact phases of the unfiltered ball position data against time in three axes according to logarithmic equations determined from mechanical principles.…”

“…The advent of a novel curve fitting methodology to determine the impact location of a cricket ball on a bat face from three-dimensional marker data, allows researchers scope to investigate the relationships between impact location and post-impact bat and ball kinematics during a dynamic hitting action. This methodology (Peploe et al, 2017) has been found to accurately establish impact location to within 6.4 ± 4.2 and 7.1 ± 4.4 mm in the medio-lateral and longitudinal directions of the bat face respectively, while also estimating impact timing and instantaneous post-impact ball speed and direction. As such, the aim of this study was to assess the effects of medio-lateral and longitudinal bat-ball impact location on post-impact ball speed, and in the medio-lateral direction on peak change in rate of bat polar rotation and on ball direction, during a dynamic hitting task.…”