The Dynamics of Discus Throw

Abstract

The analysis contains the derivation and a solution method for six nonlinear differential equations of motion which describe the c.g. position and orientations of the principal axes of a spinning discus moving in air. The aerodynamic pressure on the discus is obtained from existing experimental data on inclined plates and disk-shaped bodies; the effect on the moment due to the spinning motion is derived from the classical hydrodynamics of a rotating ellipsoid in a flow field. A case study, analyzed in the context of the 1972 World Olympics discus throw (which recorded 64.39 m or 211 ft 3 in.), showed that a fast-spinning discus will go farther than one not spinning by 13.8 m in this range. The optimum angle and optimum initial discus inclination are 35° and 26°. This combination of angles is found to be superior to the commonly accepted combination of 35° and 35°. The 35°/26° combination produced a gain in distance of 1.55 m over the 35° /35° combination. The results of the analyses presented here, including the effect of wind, agree closely with the experience of expert discus throwers.