Flow structure of knuckling effect in footballs

The flight trajectory of a non-spinning or slow-spinning soccer ball might fluctuate in unpredictable ways, as for example, in the many free kicks of C. Ronaldo. Such anomalous horizontal shaking or rapid falling is termed the ‘knuckling effect’. However, the aerodynamic properties and boundary-layer dynamics affecting a ball during the knuckling effect are not well understood. In this study, we analyse the characteristics of the vortex structure of a soccer ball subject to the knuckling effect (knuckleball), using high-speed video images and smoke-generating agents. Two high-speed video cameras were set at one side and in front of the ball trajectory between the ball position and the goal; further, photographs were taken at 1000 fps and a resolution of 1024×512 pixels. Although in a previous study (Taneda, 1978), shedding of horseshoe vortices was observed for smooth spheres in the Reynolds number (Re) range of 3.8×10⁵6, in the case of the soccer ball, the vortex structure, which consisted of distorted loop vortices, appeared in the wake behind the ball in the supercritical Re number region. Moreover, after the knuckleballs were airborne, large-scale undulations were observed in the vortex trail visualised with a smoke technique. On the other hand, aerodynamic forces acting on the ball were estimated from the data of the ball’s flight trajectory, and a statistically high correlation (r=0.94, p<0.01) between the fluctuation frequency of the lift and side forces and the undulation frequency of the vortex trail was shown to exist. This fact suggests that the phenomenon of large-scale undulations of the vortex trail is closely related to the cause of the unsteady aerodynamic forces acting on the knuckle ball.