Fundamental aerodynamics of the soccer ball

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 (C _d) rapidly decreases. However, the aerodynamic properties and boundary-layer dynamics of a soccer ball are not yet well understood. In this study we showed that the critical Reynolds number (Re _crit) of soccer balls ranged from 2.2 × 10⁵ to 3.0 × 10⁵. Wind-tunnel testing, along with visualisation of the dynamics of the boundary layer and the trailing vortex of a ball in flight, demonstrated that both non-spinning and spinning (curved) balls had lowC _d values in the super-critical region. In addition, theRe _crit values of the soccer balls were lower than those of smooth spheres, ranging from ∼ 3.5 × 10⁵ to 4.0 × 10⁵, due to the effects of their panels. This indicated that the aerodynamic properties of a soccer ball were intermediate between those of a smooth ball and a golf ball. In a flow visualisation experiment, the separation point retreated and theC _d decreased in a super-critical regime compared with those in a sub-critical regime, suggesting a phenomenon similar to that observed in other sports balls. With some non-spinning and spinning soccer balls, the wake varied over time. In general, the high-frequency component of an eddy dissipated, while the low-frequency component increased as the downstream vortex increased. The causes of the large-scale fluctuations in the vortex observed in the present study were unclear; however, it is possible that a ‘knuckle-ball effect’ of the non-rotating ball played a role in this phenomenon.