Analysis of the wobble of a spinning disc at launch - Rae, W.; Hubbard, M. (The Engineering of sport 7, Volume 1, 2008)
Field observations (Hubbard and Hummel, 2000) and numerical simulations (Crowther and Potts, 2007) of spinning discs in flight often show a wobble of the disc immediately after launch. This component of the motion causes an undesirable drag penalty, and its source is not well understood, occurring for a wide range of initial conditions. The analysis presented in this paper succeeds in identifying, for a flat disc, the frequencies and amplitudes of the wobble and their connection to the launch conditions. The approach used to make this identification is to express the equations of motion in a two-Euler-angle reference frame, leading for small wind angles and Euler angles to a pair of eigensolutions containing the proper coupling of aerodynamic, gyroscopic, and Coriolis effects. This analysis of the disc motion shows two components; one member of the solution pair is strongly damped, while the other is a slightly unstable oscillation. The amplitude information in the solution shows the connection, in the small-angle limit, between the launch conditions and the initial wobble, and may be useful in minimizing the latter. The sections that follow contain descriptions of the coordinate frames and method of analysis used, and the conclusions reached.