The two power limits conditioning step frequency in human running.

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Abstract
1. At high running speeds, the step frequency becomes lower than the apparent natural frequency of the body's bouncing system. This is due to a relative increase of the vertical component of the muscular push and requires a greater power to maintain the motion of the centre of gravity, Wext. However, the reduction of the step frequency leads to a decrease of the power to accelerate the limbs relatively to the centre of gravity, Wint, and, possibly, of the total power Wtot = Wext + Wint. 2. In this study we measured Wext using a force platform, Wint by motion picture analysis, and calculated Wtot during human running at six given speeds (from 5 to 21 km h‐1) maintained with different step frequencies dictated by a metronome. The power was calculated by dividing the positive work done at each step by the duration of the step (step‐average power) and by the duration of the positive work phase (push‐average power). 3. Also in running, as in walking, a change of the step frequency at a given speed has opposite effects on Wext, which decreases with increasing step frequency, and Wint, which increases with frequency; in addition, a step frequency exists at which Wtot reaches a minimum. However, the frequency for a minimum of Wtot decreases with speed in running, whereas it increases with speed in walking. This is true for both the step‐average and the push‐average powers. 4. The frequency minimizing the step‐average power equals the freely chosen step frequency at about 13 km h‐1: it is higher at lower speeds and lower at higher speeds. The frequency minimizing the push‐average power approaches the freely chosen step frequency at high speeds (around 22 km h‐1 for our subjects). 5. It is concluded that the increase of the vertical push does reduce the step‐average power, but that a limit is set by the increase of the push‐average power. Between 13 and 22 km h‐1 the freely chosen step frequency is intermediate between a frequency minimizing the step‐average power, eventually limited by the maximum oxygen intake (aerobic power), and a frequency minimizing the push‐average power, set free by the muscle immediately during contraction (anaerobic power). The first need prevails at the lower speed, the second at the higher speed.

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