Optimizing running a race on a curved track.

Area of Science:

• Sports Science
• Biomechanics
• Mathematical Modeling

Background:

• Athletic race performance is influenced by track geometry and lane assignment.
• Centrifugal forces on curved tracks necessitate strategic adjustments for optimal velocity and energy expenditure.
• Psychological interactions between runners can impact race dynamics.

Purpose of the Study:

• To determine optimal race strategies based on lane number and track design.
• To analyze the impact of track straights length on performance.
• To model psychological interactions between two runners during a race.

Main Methods:

• Development of a differential equation model incorporating velocity, propulsive force, and anaerobic energy.
• Inclusion of centrifugal force and track-specific straights lengths in the model.
• Numerical simulations of race strategies and psychological interactions.

Main Results:

• Tracks with shorter straights yield better overall performances.
• Longer straights, particularly on double-bend tracks, result in poorer performances and greater lane disparities.
• Psychological effects, such as attraction and delayed benefit after overtaking, were simulated.

Conclusions:

• The findings align with International Association of Athletics Federations (IAAF) lane draw rules, favoring higher-ranked athletes in center lanes.
• Track design significantly impacts race outcomes and fairness across lanes.
• Psychological dynamics play a crucial role in two-runner race scenarios.