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Sports Med. 1999 Jun;27(6):359-79.

Time in human endurance models. From empirical models to physiological models.

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  • 1Laboratoire des Sciences et Techniques des Activités Physiques et Sportives (STAPS), Université Paris 5, France. Veronique.Billat@wanadoo.fr


This article traces the study of interrelationships between power output, work done, velocity maintained or distance covered and the endurance time taken to achieve that objective. During the first half of the twentieth century, scientists examined world running records for distances from < 100 m to > 1000 km. Such examinations were empirical in nature, involving mainly graphical and crude curve-fitting techniques. These and later studies developed the use of distance/time or power/time models and attempted to use the parameters of these models to characterise the endurance capabilities of athletes. More recently, physiologists have proposed theoretical models based on the bioenergetic characteristics of humans (i.e. maximal power, maximal aerobic and anaerobic capacity and the control dynamics of the system). These models have become increasingly complex but they do not provide sound physiological and mathematical descriptions of the human bioenergetic system and its observed performance ability. Finally, we are able to propose new parameters that can be integrated into the modelling of the power/time relationship to explain the variability in endurance time limit at the same relative exercise power (e.g. 100% maximal oxygen uptake).

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