Creating drag and lift curves from soccer trajectories

Abstract

Trajectory analysis is an alternative to using wind tunnels to measure a soccer ball’s aerodynamic properties. It has advantages over wind tunnel testing such as being more representative of game play. However, previous work has not presented a method that produces complete, speed-dependent drag and lift coefficients. Four high-speed cameras in stereo-calibrated pairs were used to measure the spatial co-ordinates for 29 separate soccer trajectories. Those trajectories span a range of launch speeds from 9.3 to 29.9 m s−1. That range encompasses low-speed laminar flow of air over a soccer ball, through the drag crises where air flow is both laminar and turbulent, and up to high-speed turbulent air flow. Results from trajectory analysis were combined to give speed-dependent drag and lift coefficient curves for the entire range of speeds found in the 29 trajectories. The average root mean square error between the measured and modelled trajectory was 0.028 m horizontally and 0.034 m vertically. The drag and lift crises can be observed in the plots of drag and lift coefficients respectively.