Figure 4
From: The strange flight behaviour of slowly spinning soccer balls
Ω-shaped and two longitudinal vortices of a smooth sphere by Taneda4 and the relationships between the unsteady forces and flow around a soccer ball.
(a), An image obtained by Taneda4 of the flow around a smooth sphere at the supercritical Re number, Re = 3.8 × 105. This flow is an integrated streak line of the surface boundary layer into a Ω-shaped or U-type vortex and two-line flows of the longitudinal vortices. (b), The colour image was reproduced from the research notebook of Dr. Taneda with permission from his bereaved family. This figure was dated March 9, 1976. (c), The flow around the delta wing in his sketch. This figure was dated February 24, 1976. (d), Typical twin longitudinal vortices as shown in a. U = 26.0 m/s with 25 integrated frames during a 0.1 s period. (e–f), Unsteady aerodynamic force coefficients (CL and Cs) at 4–8 s, in Figure 3a. (g), The flow pattern observed in multiple images in 25 frames during the 0.1 s period of 6.75–6.85 s centred around the red lines of e and f. A longitudinal vortex exists in the lower-right directions. The resultant aerodynamic force (F), which is indicated by the arrow in (g), was oriented in the opposite direction of the vortex position at the symmetrical position of the ball centre axes.
