Unsteady aerodynamic force on a knuckle ball in soccer

Abstract

In this study, the unsteady aerodynamics of a knuckle ball in soccer were investigated. The characteristics of the fluid force, i.e. the magnitude and frequency acting on the knuckle ball, were analyzed through comparison with those of the straight ball using high-speed video cameras. Furthermore, the fluid flow around the knuckleball in flight was visualized using a smoke agent (titanium tetrachloride), and an attempt was made to clarify the fundamental fluid mechanics expressed by the knuckle ball as well as to analyze the vortex dynamics. It was found that the vertical acceleration of the knuckle ball tended to vary greatly (oscillate) in comparison with the acceleration of a straight ball, despite the fact that both are influenced by gravity. Moreover, in the case of the knuckle ball, the peak value of the vortex lift reached approximately 2.0 N, which was larger than the value of approximately 0.5 N for an instep kick. This vortex lift fluctuated greatly with time and was thought to be a highly unstable phenomenon. When the large-scale vortex structure of the knuckle ball was studied, successively shed vortex loops transformed and merged, and a few massive vortices formed an extended vortex street structure. Moreover, when the vertical fluctuation along the wake axis of the large-scale vortex structure was studied, evidence of unsteady wave oscillation (undulation) was observed. This large-scale structure of the far wake was conjectured to indicate traces of vortex motion at the time of vortex shedding, and the effect of this motion was thought to have a direct influence on the motion of the ball. Furthermore, the knuckle ball was observed to have an average vortex lift force frequency of approximately 3.5 Hz. A comparison of this vortex lift frequency and a vortex oscillation frequency indicated that these frequencies tended to act in unison with a high statistical correlation (r=0.83, p<0.01). Thus, it is considered that the oscillation of the large-scale vortex structures of the knuckle ball was the fundamental mechanism responsible for creating the fluctuating forces acting on the knuckle ball.