• A. Guskov
  • A. Vorobiev
  • G. Ariel


A mathematical model of a long jumper flight dynamics is proposed. The model incorporates the factor of the full aerodynamic force exerted during the flight phase under varying conditions. The full aerodynamic force is applied to the body at some angle to the vector of air speed and can be represented as vector sum of drag and lift forces. The magnitudes of the drag and lift components, as well as their role in the length of the jump are affected by a number of parameters, such as flight kinematics, wind velocity, mean altitude, etc., which vary from athlete to athlete, between attempts and competition grounds. Analysis of the video recordings of the jumps of the leading long jumpers were processed using computerized image processing schemes. As the result, the kinematics of the jumps and the aerodynamics of the athletes' bodies at various stages of the flight phase, drag and lift quotients were calculated as the function of the angle of attack of the body, using regression analysis approach. The results obtained make possible determining the influence of the wind velocity and mean altitude. Based on this, the forecast of results and comparable values, derived from the results obtained under specific conditions can be performed. Table gives the results of numerical analysis for three high performance attempts in trial conditions and recalculated to the normalized conditions (zero wind /zero mean elevation). The comparison of the actual and normalized data indicates that the absolute value of the results in long jump during last 24 years might be reconsidered. As another application of the developed model, a series of iso-energetic trajectories was emulated, in order to enhance the performance by optimizing the flight aerodynamics under average conditions.