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Waveform geometry dictating optimal cruising in animals.

Kazuko Yoshizawa1,2,3, Ryosuke Motani2

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Summary
This summary is machine-generated.

The optimal Strouhal number (St) range for efficient swimming and flight is dictated by the power efficiency of the caudal fin

Keywords:
Strouhal numberoptimal swimmingswimming speed

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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.