A study of soccer ball aerodynamics

Abstract

When the boundary layer of a sports ball undergoes the transition from laminar to turbulent flow, a drag crisis occurs whereby the drag coefficient (Cd) rapidly decreases. However, the aerodynamic properties and boundary-layer dynamics of a soccer ball are not well understood. Here we showed that the critical Reynolds number (Re_crit) of a soccer ball was 2.2 - 3.0 × 10⁵. Wind-tunnel testing, along with visualization of the dynamics of the boundary layer and the trailing vortex of a ball in flight clearly demonstrated that both non-spinning and spinning curved balls had low Cd values in the supercritical region. We also showed that the R_ecrit of a soccer ball was lower than that (approximately 3.5 - 4 × 10⁵) of a smooth sphere, due to the effects of its panels; this indicated that the aerodynamic properties of a soccer ball were between those of a smooth ball and a golf ball. Lateral images taken during high-speed kicking of a spinning curve ball (26 m/s; 8 rps) revealed that the separation point was approximately 120° from the front-stagnation point. In addition, the boundary layer between the top and bottom surfaces of the ball became turbulent. Top-view images taken during curved kicking (27 m/s; 7 rps) showed vortex deflection due to the effects of a relative difference in fluid speed caused by the spinning. The curvature of the ball was largely attributed to a lateral force generated by vortex counteraction. However, although the separation point showed left-right asymmetry in relation to the direction of travel (top-bottom symmetry on the images), it was approximately 116° from the front-stagnation point, which was similar to the separation angle during high-speed kicking of a non-spinning ball. In addition, the boundary layer became turbulent and the vortex region shrank during high-speed kicking of a spinning ball.