A new measure of roughness for defining the aerodynamic performance of sports balls

A new analysis is presented of the major findings in sports ball aerodynamics over the last 20 years, leading to a new method for defining surface roughness and its effects on the aerodynamic performance of sports balls. It was shown that the performance of balls in soccer, tennis, and golf are characterized by the position of the separation points on the surface of the ball, and that these are directly influenced by the roughness of the surface at a given Reynolds number and spin rate. The traditional measure of roughness k/D (the ratio of surface asperity dimension to diameter) was unable to predict the transition from laminar to turbulent flow for different sports balls. However, statistical measures of roughness commonly used in tribology were found to correlate well with the Reynolds number at transition and the minimum Cd after transition. It was concluded that this new measure and a further one of dimension should allow the complete characterization of the aerodynamic performance of sports balls. The effects of surface roughness on spin rate decay were also considered, and it was found that tennis balls had spin decay over six times that of golf balls and was due to the increased skin friction of the nap.