Waveform geometry dictating optimal cruising in animals

Area of Science:

• Biomechanics
• Fluid Dynamics
• Animal Locomotion

Background:

• Vertebrates and insects use a narrow Strouhal number (St) range for efficient sustained locomotion.
• The reason for this conserved range across different sizes and fluids remains a puzzle.
• Previous interpretations have varied, lacking a unified explanation.

Purpose of the Study:

• To propose and validate that the optimal Strouhal number (St) range is primarily constrained by the power output efficiency of the caudal fin's trailing edge.
• To investigate the relationship between trailing edge wake dynamics and propulsive efficiency.
• To determine the factors influencing optimal cruising speed in aquatic and aerial locomotion.

Main Methods:

• Development of a mathematical model for the periodic wake generated by the trailing edge.
• Analysis of power loss proportion not contributing to propulsion.
• Evaluation of constraints across various Reynolds numbers relevant to cruising fish.
• Integration of morphological characteristics and drag properties.

Main Results:

• The mathematical model predicts minimal energy loss within the observed optimal Strouhal number (St) range for fish.
• These power efficiency constraints are applicable across a range of Reynolds numbers.
• The model demonstrates that these constraints, combined with morphology, dictate optimal swimming and flight speeds for diverse organisms.
• Trailing edge geometry of periodic waveforms is identified as a key factor for cruising optimality.

Conclusions:

• The power output efficiency of the caudal fin's trailing edge is a primary constraint on the optimal Strouhal number (St) range.
• This finding offers a unified explanation for the conserved St range in animal locomotion.
• The study provides a new perspective for understanding animal movement in fluids and for bioinspired robotics design.