Unsteady aerodynamic force on a knuckleball in soccer

The purpose of this study is to analyze the fluid mechanics and frequency of forces acting on a knuckleball, specifically a soccer ball that was kicked and was in flight, was visualized using a smoke agent (titanium tetrachloride), and its unsteady aerodynamics were investigated. In the case of the knuckleball, the peak value of the vortex lift reached approximately 2.0 N, and the average vortex lift force frequency of approximately 3.5 Hz. A comparison of this vortex lift frequency and vortex oscillation frequency indicated that these frequencies tended to act in unison with a high statistical correlation (r=0.83,p<0.01).