Figure 1
From: The strange flight behaviour of slowly spinning soccer balls
Free-fall and free-flight ball trajectories of soccer balls and aerodynamic side force coefficients.
(a), A stroboscopic image of a 65 m free-fall experiment. The ball had a 250 fps high-speed camera located on a bridge plate facing the ground. The spin rate (N) was less than 1/16 rps and the spin parameter (Sp) was 0.002. Here, the Sp was defined as Sp = πNd/U. (b), The aerodynamic force coefficients (CL and CS) were calculated from the position image every second with a two-step time differentiation. The red arrows denote the time sequences from S: (observations start) to E; (final stage). CD, CL and CS represent the aerodynamic force coefficients of the drag, lift and side forces, respectively, at time t. (CD, CL, CS) = (D, L, S)/0.5ρ U2A. The directions include +drag (D, gravity force direction), +lift (L, upward in this figure and +side force (S, direction to the right). ρ represents air density, U represents the ball speed, and, A represents the ball area with diameter (d) = πd2/4. The origin of this diagram does not correspond to (a). (c–e), (f–h), Two examples of a three-dimensional flight using a shooting machine. (c) and (f) display stroboscopic images of balls launched by the machine; the initial speeds in (c) and (f) were U0 = 82 km/s (22.8 m/s) and 105 km/h (29.2 m/s), respectively. The spin rates were approximately 1 rps and the Sp was = 0.03. (d) and (g) present displacements in the Y-Z plane based on the stroboscopic image in (c) and (f). (e), (h), Time traces of the side force coefficient (Cs). The Cs amplitude and period were 0.10–0.15 and 1.3 s, respectively, in both cases. The accuracy of the measured ball position may be within +5.0 to −5.0 cm, due to the digitised pixel number.
