Time-Velocity Equations and Oxygen Requirements of “All-Out” and “Steady-Pace” Running

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Abstract
Oxygen requirement is visualized theoretically as the sum of two exponential terms—oxygen intake and debt—both functions of the time required for running a unit distance. Estimates of requirement based on world record times are consistent with this theory and with measured requirements at lower speeds. An equation of motion, derived from acceleration and fatigue factors, describes the position and speed of the runner at any time t in either steady-pace or all-out runs. It has been verified by data on 24 track men and 30 inexperienced athletes who were timed with an automatic recorder on dashes and 300-yd. runs. The metabolic cost of running, computed from these two mathematical models, is considerably less for steady pace than for all-out or certain other coach-recommended velocity patterns. Percentage of time saved decreases with increased velocity. Although this finding disagrees with previous concepts, it is explainable on theoretical grounds. Tables and curves are given for simplified computation of time saved. Hand or foot reaction time and sprint speed are uncorrelated (r = 0.09 and 0.04).

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