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

Abstract : The concepts of power law and critical speed (SCrit) have been applied to the analysis of individual running performances. We have analysed the results of two exceptional runners (Nurmi and Gebrselassie) and 11 physical education students (PES) who performed three exhausting running exercises. Power laws can accurately describe the relationships between exhaustion time (tlim) and distance (Dlim) or speed (S) [Dlim = ktlim and S = ktlim ] in elite runners and PES. However, the validity of the application of power laws must be verified for higher values of tlim in non-elite runners. Exponent γ is close to 1 in elite runners and lower in PES (from 0.625 to 0.872). The value of SCrit was computed from two values of tlim (3min-14min; 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 min (SCrit 3-14/S7min). The individual values of SCrit 3-14/S7min [0.945 for Gebrselassie, 0.919 for Nurmi and 0.764 ± 0.078 in PES] 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 PES]. The same results were observed when SCrit was computed for tlim equal to 6-28 min (SCrit 6-28) and MAS was the maximal velocity sustainable during 14 min (S14min). The fact that γ is linearly correlated and almost equal to SCrit 3-14/S7min or SCrit 6-28/S14min suggests that exponent γ can be considered as an index of aerobic endurance.