Analysis of the Wobble of a Spinning Disc at Launch (P117)

  • William Rae
  • Mont Hubbard
Conference paper


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.

Key Words

Spinning Discs Flight Dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Crowther, W.J. and J. R. Potts, Simulation of a spin stabilized sports disc, Sports Engineering, vol. 10, pp. 3–21, 2007.Google Scholar
  2. M. Hubbard and K. B. Cheng, “Optimal Discus Trajectories”, Journal of Biomechanics, vol. 40, pp. 3650–3659, (2007)CrossRefGoogle Scholar
  3. M. Hubbard and S. A. Hummel, Simulation of Frisbee flight, In Proceedings of 5th Conference on Mathematics and Computers in Sport, G. Cohen, Ed., University of Technology, Sidney, New South Wales, Australia, 14–16 June, 2000.Google Scholar
  4. Kreyszig, E. Advanced Engineering Mathematics, Fifth Edition, John Wiley and Sons, New York, 1983.MATHGoogle Scholar
  5. W. J. Rae, Flight dynamics of an American football in a forward pass, Sports Engineering, vol. 6(3), pp. 149–164, 2003.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France, Paris 2009

Authors and Affiliations

  • William Rae
    • 1
  • Mont Hubbard
    • 2
  1. 1.University at Buffalo, State University of New YorkBuffaloUSA
  2. 2.University of California at DavisDavisUSA

Personalised recommendations