An improved Peronnet-Thibault mathematical model of human running performance

Area of Science:

• Exercise Physiology
• Sports Science
• Biophysics

Background:

• Understanding maximal power output during exercise is crucial for athletic performance.
• Previous models have limitations in accurately describing the dynamics of aerobic and anaerobic energy systems.
• The aerobic-to-total energy ratio (ATER) provides insight into the interplay between energy systems during prolonged exertion.

Purpose of the Study:

• To analyze maximal power available during exercise using an improved Peronnet-Thibault model.
• To accurately describe the decreasing dynamics of aerobic power.
• To investigate the aerobic-to-total energy ratio (ATER) and its relationship with exercise duration.

Main Methods:

• Application of an improved Peronnet-Thibault model.
• Analysis of world track records and ATER data.
• Modeling of a 3rd-order relaxation process for aerobic power dynamics.

Main Results:

• A 3rd-order relaxation process accurately describes aerobic power dynamics.
• Estimated time-scales for decreasing aerobic power range from 2.12 hours to 7.8 days.
• ATER rapidly increases within the first 300 seconds, plateauing near 100% after 1,000 seconds.
• Maximal aerobic power is achieved between 300-400 seconds, with a plateau lasting approximately 5,000 seconds.

Conclusions:

• The improved Peronnet-Thibault model provides accurate insights into exercise power dynamics.
• Aerobic power exhibits a complex decreasing dynamic influenced by long-term metabolic processes.
• The ATER dynamics suggest a transition point around 100 seconds (approx. 800m race distance) for significant aerobic contribution.