Here, ρ is the density of air (1.2 kg m–3), U is the flow
velocity (m s–1) and A is the projected area of the
soccer ball (r2, where r is the radius). The wind
velocity used in the tunnel experiment was within the
range of 7–35 m s–1 for non-rotating balls.
The balls were rotated using an air compressor
during the wind tunnel experiment. An air gun
connected to an air compressor was fired at the side of
each ball, and the number of rotations was measured
using a laser tachometer. The angular velocity became
unstable during low-speed rotation. Most curve kicks
produce a ball velocity of at least 20 m s–1 (Asai et al.,
2002). We therefore studied the aerodynamic properties
of a rotating ball with a flow velocity in the range
of 22–30 m s–1 and a rotational speed of 2–10 revolutions
per second (rev s–1). Sp was defined as the ratio of
the peripheral velocity to the velocity through the air,
as shown in eqn. 4