An improved Peronnet-Thibault mathematical model of human running performance

Abstract.

Using an improved Peronnet-Thibault model to analyse the maximal power available during exercise, it was found that a 3rd-order relaxation process for the decreasing dynamics of aerobic power can describe accurately the data available for world track records and aerobic-to-total energy ratio (ATER). It was estimated that the time-scales for the decreasing dynamics are around 25 s for anaerobic power output and that they range from 2.12 h to 7.8 days for aerobic power output. In agreement with experimental evidence, the ATER showed a rapid increase during the first 300 s of exercise duration, to achieve an asymptote close to 100% after 1,000 s. In addition, the transition time when the ATER rose above 50% was found to be at a race duration of about 100 s, which would correspond to race distances of about 800 m. The results suggest that the aerobic power output achieves its maximal value at 300–400 s, and reaches a plateau at 26–28 W·kg^–1 that lasts about 5,000 s. After this period, the aerobic power output decreases slowly due to the contribution of long time-scale metabolic processes having smaller energy contributions (about 30% to 40% of the total aerobic power output).