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

Abstract

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) (Equation is included in full-text article.)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 (Equation is included in full-text article.)The individual values of (Equation is included in full-text article.)(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 (Equation is included in full-text article.)or (Equation is included in full-text article.)suggests that exponent γ can be considered as an index of aerobic endurance.

Modelling of Running Performances: Comparisons of Power-Law, Hyperbolic, Logarithmic, and Exponential Models in Elite Endurance Runners

“…However, in a previous study [ 61 ], some results were assumed to be the effect of submaximal performances on S Crit1 model whose sensitivity was discussed in a review on the critical power concept [ 16 ]. Similarly, the values of parameter k that is an index of maximal running speed were overestimated in several physical education students in a previous study [ 55 ], which was probably the effect of submaximal running performances. Indeed, in 4 physical education students, parameters k were largely overestimated since they were higher than 20 m.s −1 , whereas the maximal running speed is about 12.2 m.s −1 for the best world sprinter U. Bolt [ 62 ].…”

“…The curvature of the D lim -t lim equation depends on exponent g. In the elite endurance runners the D lim -t lim equation is almost perfectly linear ( Figure 2 ) whereas this equation is more curved in runners who are not endurance athletes. For example, exponent g was close to 1 in elite endurance runners and lower than 0.9 in physical education students [ 55 ]. It can be demonstrated that exponent g is equal to the ratio of the slope of the D lim -t lim equation to MAS when t lim is equal to t MAS .…”

Quantifying and modelling the game speed outputs of English Championship soccer players

“…The maximum value across each of the moving average window durations was then extracted and converted to units of metres per minute (m . min −1 ) for further statistical analysis (Delaney et al, 2018;Zinoubi et al, 2017).…”

Effects of Submaximal Performances on Critical Speed and Power: Uses of an Arbitrary-Unit Method with Different Protocols

“…Therefore, the effects of submaximal performance on S Crit and P Crit in the present study have been compared between a low-endurance athlete and a high-endurance athlete, i.e., athletes with low and high endurance indices (for example, exponent g or S Crit /MAS or P Crit /MAP). The values of exponent g were about 0.95 in the best elite endurance runners [15,31] as Gebrselassie whose ratio S Crit /MAS was equal to 0.945 (MAS corresponded to the maximal running speed during 7 min). In the low-endurance runners whose ratios S Crit /MAS were equal to 0.764 ± 0.078, exponent g was about 0.80 [31].…”

“…The values of exponent g were about 0.95 in the best elite endurance runners [15,31] as Gebrselassie whose ratio S Crit /MAS was equal to 0.945 (MAS corresponded to the maximal running speed during 7 min). In the low-endurance runners whose ratios S Crit /MAS were equal to 0.764 ± 0.078, exponent g was about 0.80 [31].…”