Untersuchungen über die Strömungsvorgänge bei rotierenden glatten Kugeln und Fußbällen

The interaction of spherical bodies with the flow surrounding them plays a very important role in ball aerodynamics. In soccer shots on goal and free kicks are often performed without or with little spin in order to generate a swerve from the expected trajectory, the so-called knuckling effect. A second strategy involves applying spin to the ball around an axis perpendicular to the flight direction, which generates a curved trajectory due to the Magnus force. In the present study a basic understanding of the flow phenomena observed is established. Furthermore it is pointed out where more research on sphere and ball aerodynamics is needed. Additionally it is made clear, that experimental results often vary to a great extent even if the boundary conditions are the same due to the experimental set-up. Thus, the conceptual design of the wind tunnel set-ups of the present work was to reduce the flow interference of the supporting device with the sphere or soccer ball.

Investigations in the non-rotating state show that for soccer balls the critical Reynolds number range is shifted to considerably lower Reynolds numbers than for a smooth sphere. Simultaneously very high lateral forces are observed in this critical Reynolds number range. For a smooth sphere in the supercritical Reynolds number range, lateral forces are non-zero when averaged over an appropriate time interval. The reason is that the wake is inclined with respect to the flow axis. In the supercritical Reynolds number regime of a soccer ball the magnitude and direction of the lateral forces depend on the ball orientation relative to the approaching flow.

The investigations in the rotating state show the following: The results obtained on a sphere driven by a shaft passed through the sphere center are influenced to a great extent by the flow interaction with the supporting device. When a rear mounted supporting device is used, the results are less affected. Aerosol visualizations and wind tunnel balance measurements show that for a rotating sphere mainly reverse Magnus effect occurs when the Reynolds number is in a range of 125.000 to 450.000 and the spin parameter is based on rotational frequencies lower than 10 [Hz]. Considerable lateral forces and lateral force fluctuations occurring simultaneously prove that the Magnus effect for a sphere in the critical Reynolds number range is three-dimensional. For a model of a soccer ball a general shift of the Reynolds number range to lower Reynolds numbers is observed. Reverse Magnus effect occurs in a Reynolds number range of 96.000 to 248.000 whereas lateral forces are low.

Soccer ball trajectory simulations without spin show that lateral forces do not significantly change the flight time, but cause a scattering of the coordinates in the goal plane. The reverse Magnus effect obtained on smooth spheres leads to lateral deviations from a straight trajectory opposite to those observed for soccer balls.