Simulation of a spin-stabilised sports disc - Crowther, W. J.; Potts, J. R. (Sports Engineering, 2007)
The spin-stabilised sports disc, more commonly known as the Frisbee, is used for a variety of recreation and sporting activities. Frisbees have unique flying characteristics compared to other sports projectiles because they depend on spin for stability during flight and, at typical launch speeds, aerodynamic lift is greater than or equal to the weight of the disc. In this paper, a six degree of freedom mathematical model of a spinning disc wing is developed and a simple analytical expression derived for the disc roll rate in straight and level flight. It is shown that dimensionless disc trajectories will be similar for similar values of a parameter based on the ratio of the disc static margin to the disc advance ratio. The mathematical model is implemented as a simulation in Matlab using steady model parameters obtained from wind tunnel tests and unsteady parameters from flight tests. Simulation results are shown to be in reasonable agreement with limited available experimental flight data. The effect of launch conditions has been investigated using a series of numerical experiments. It is found that flight path curvature in the horizontal plane increases with decreasing advance ratio, as expected. Pitch angles at launch for maximum range and maximum duration are approximately 10° and 20° respectively. Also, the locus of disc landing position as a function of launch roll angle has been shown to be an`S` shaped curve, with the straightest flight occurring for an initial roll angle of -6°. Finally, the simulation has been extended to include the effects of hypothetical control inputs, enabling simulation of novel Frisbee manoeuvres.