Optimization of triple jump performance: A simple model
Abstract
A simple mathematical model was presented to simulate the motion of the center of gravity of a human body throughout the three flight phases of the triple jump. Equations of the three phases were used in one chain equation in which the independent input variable was the initial touchdown velocity to the hop phase. The final equation of motion was manipulated as a function of the three support times. The path of the center of gravity during the support and flight of an elite triple jumper was superimposed against the path generated from the model. Finally, the optimization routine was formulated. The results of the optimization of a particular subject indicated that increasing the hop phase distance ratio by 1.8% and decreasing the step phase distance ratio by 4.4% would allow the jumper to increase the jump phase distance ratio by 2.6%. This could be done by using the same amount of energy as in the original jump. By using this distribution of the three phases, the subject would gain about 0.56m compared to the original total distance. The results of optimization were found to be similar to actual changes made by athletes in performing over time in different competitions. Estimates of possible error indicate a high sensitivity to the force generated by the subject at takeoff from each phase and the vertical position of the center of gravity at takeoff of each phase. Further study and validation of the results are recommended.
Degree
Ph.D.
Advisors
Widule, Purdue University.
Subject Area
Mechanics|Physical education
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