Creating drag and lift curves from soccer trajectories

Trajectory analysis is an alternative to using wind tunnels to measure a soccer balls 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 m/s to 29.9 m/s. 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. Average root mean square error between 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.