Calculation of Long Jump Performance by Numerical Integration of the Equations of Motion

Abstract

The aerial phase of the long jump is calculated by numerical integration of the equations of motion. Consideration is given to the effects on performance of the horizontal and vertical components of velocity at takeoff, aerodynamic drag, wind assistance and the vertical displacement of the center of mass which occurs during the course of the jump. For still air conditions it is shown that an analytical solution due to Lamb [6] compares very favorably with the numerical solution, providing an excellent description of the trajectory. Calculations neglecting the effect of aerodynamic drag are shown to overestimate the jump distance of world-class athletes by from 9 to 11 cm under still air conditions.