Modeling of Running Performances in Humans: Comparison of Power Laws and Critical Speed

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Zinoubi, B, Vandewalle, H, and Driss, T. Modeling of running performances in humans: comparison of power laws and critical speed. J Strength Cond Res 31(7): 1859–1867, 2017—The concepts of power law and critical speed (SCrit) have been applied to the analysis of individual running performances. We have analyzed the results of 2 exceptional runners (Nurmi and Gebrselassie) and 11 physical education students (PESs) who performed 3 exhausting running exercises. Power laws can accurately describe the relationships between exhaustion time (tlim) and distance (Dlim) or speed (S) in elite runners and PES. However, the validity of the application of power laws must be verified for higher values of tlim in nonelite runners. Exponent γ is close to 1 in elite runners and lower in PESs (from 0.625 to 0.872). The value of SCrit was computed from 2 values of tlim (3–14 minutes; SCrit 3–14) and was expressed as a fraction of maximal aerobic speed (MAS) which was assumed to correspond to the maximal speed that can be sustained over 7 minutes The individual values of (0.945 for Gebrselassie, 0.919 for Nurmi, and 0.764 ± 0.078 in PESs) were linearly correlated with γ (r > 0.999) and almost equal to γ (0.952 for Gebrselassie, 0.918 for Nurmi, and 0.779 ± 0.076 for PESs). The same results were observed when SCrit was computed for tlim equal to 6–28 minutes (SCrit 6–28) and MAS was the maximal velocity sustainable during 14 minutes (S14min). The fact that γ is linearly correlated and almost equal to or suggests that exponent γ can be considered as an index of aerobic endurance.

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