Estimation of running endurance by means of empirical models: A preliminary study

Abstract

Summary Purpose The relationships between distance (D lim ), speed (S) and exhaustion time ( t lim ) can be described by different empirical models: power laws (D lim = kt lim g , and S = kt lim ( g −1) in Kennelly's model); critical speed (S Crit ) (D lim = a + S Crit t lim ) and logarithmic model (S = 1–E*ln t lim in Peronnet–Thibault model). Methods These models have been applied to the performance of nine physical education students. In the first session, they performed the Montreal Track Test whose speed at the last stage (sMTT) is assumed to correspond to maximal aerobic speed. Thereafter, they performed 3 exhausting running exercises at 90, 100 and 110% sMTT, in different sessions with randomized order. The values of g and k were computed as ( g 1 , k 1 ) from t lim at 90 ( t lim90 ), 100 ( t lim100 ) and 110% sMTT ( g 1 , k 1 ) and also from t lim90 and t lim100 ( k 2 , g 2 ). The values of S Crit were normalized to sMTT. Results Significant correlations ( r > 0.999) of the relationships between the logarithms of D lim and t lim were observed. S Crit was not significantly correlated with g 1 , g 2 and E. In contrast, the correlations between the individual values of g 1 , g 2 and E were highly significant. Conclusion The high relationship between the logarithms of D lim and t lim suggested that power laws can be applied to subjects not-specialized in endurance. However, further studies with different protocols are necessary to determine if the power-law model is more accurate and useful than the logarithmic model in subjects who are not specialized in endurance.