Fundamental Aerodynamics of Soccer Ball in High Reynolds Number Region

Abstract

The aerodynamic properties and boundary-layer dynamics of a soccer ball are not well under-stood. Here we showed that the critical Reynolds number (Re_crit) of a soccer ball was 2.2-3.0×10⁵ in a wind tunnel test. The boundary layer and vortex-trail dynamics of a non-spinning soccer ball in flight were visualized using smoke of titanium tetrachloride, and were compared between the subcritical and supercritical regions. The separation angle between the front-stagnation point (that is, the tip of the ball in the direction of the oncoming flow) and the boundary layer-separation point was about 90°. The vortex rigion was comparatively large when the subcritical ball velocity was 5 m/s. By contrast, the separation point went backward to about 120° from the front-stagnation point and the vortex region shrank when the supercritical ball velocity was about 29 m/s. By counting the number of vortex blobs from smoke visualization images with a wide view angle, the Strouhal number (St) (wide view angle) was estimated to be about 0.5. However, when the vortex blobs seemingly accompanying a vortex ring directly behind the ball were counted from closed up visualization images with a narrower view angle, the frequency increased and St was estimated to be about 1.0. Behind the balls under a knuckle effect were airborne, large scale undulation of the vortex trail were observed when St was about 0.1 or less.