Estimation of Aerodynamic Coefficients for Balls in Flight with Trajectory Data

Abstract

We present a method for estimating the aerodynamic coefficients of balls in flight by using position data on its trajectory. Since this approach is the inverse problem of solving the motion equation, it is possible to obtain instantaneous values of the aerodynamic coefficients along trajectories. Considering the motion equation of a particle including aerodynamic forces such as drag, lift and sideways force, and applying space-curve geometry to it, general expressions for the aerodynamic coefficients are derived. In order to validate the present approach, we apply the method to trajectory data of golf and soccer balls in flight. In the former data, time series of drag, lift and sideways force coefficients are estimated by using three dimensional data measured with TrackMan, and the results on drag and lift show good agreement with those of TrackMan's output. The 12 data in two dimensional ball trajectory are used in the latter, and also time series of drag and lift coefficients are estimated. The results reveal qualitative behaviour of the drag and lift coefficients in the Reynolds number.