A method for calculating and interpreting the ratio of friction force to normal force imparted on a spherical object: Application to a cricket ball during bowling

Abstract

The coefficient of friction (COF) is usually calculated from a force ratio or a translational velocity ratio. We developed a new method for calculating the COF between fingers and a thrown ball from the spin parameter (angular over translational velocity). We used triad data obtained from a motion analysis system. We rigidified the triad data with a new method by force-fitting a master triangle (obtained from average side lengths) to each triad, where the three distances between each pair of corresponding vertices are three virtual forces that are in force and moment equilibrium. We also applied a low-pass filter to the data. The following data were calculated: helical axis between two consecutive master triangles, angular velocity, translational velocity, and COF. We applied this method to cricket ball deliveries (finger-spin topspin Ft, finger-spin backspin Fb, wrist-spin topspin Wt, wrist-spin backspin Wb). The standard deviations of the triad side lengths were smaller without than with low-pass filter. The COF showed smaller interquartile and total ranges when force fitting the raw data than when force-fitting the filtered data; or filtered data without force fitting; or neither force-fitting nor filtering. The delivery finger-spin backspin exhibited the smallest COF, whereas wrist-spin backspin had the highest. Finger-spin deliveries had a smaller COF than wrist-spin ones. There was no significant difference between topspin and backspin in terms of the COF. Deliveries with the palm pointing medially (Ft, Wb) had a greater COF than deliveries with the palm pointing laterally (Fb, Wt). In conclusion, the force-fitting method was superior compared to low-pass filtering with the latter worsening the data because of filtering along the time axis rather than spatially. The COF imparted on cricket ball led to a new classification system of deliveries and to a proposal for a new bowling strategy.