Extending the Theory of Dash Running

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Abstract
I extend the theory of dash running by allowing resisting force to be proportional to any positive power of speed and by allowing the runner to be tractive-force-limited at the beginning of the dash and developable-force-limited subsequently. I solve the equation of motion and express the maximum value of developable force as a function of limiting dash velocity, resisting-force/velocity exponent, and indoor and outdoor-track asymptotic intercept times (the intercepts with the time axis of asymptotic lines that are fitted to the distance-time curves) and limiting tractive coefficients. For a 20-yr-mean world record limiting dash velocity of 10.33 m/s and indoor and outdoor asymptotic intercept times of 0.617 and 0.265 s, I find that a composite dash world record holder is tractive-force-limited on indoor tracks, that limiting indoor tractive coefficient is about 0.9, and that the maximum value of developable force exceeds 2.0 times the record holder’s weight.

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