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Universal vortex formation time of flapping flight.

Yukun Sun1, Emily Palmer2, Christopher Dougherty1

  • 1Department of Biological and Environmental Engineering, Cornell University, Ithaca, NY 14853.

Proceedings of the National Academy of Sciences of the United States of America
|August 29, 2025
PubMed
Summary
This summary is machine-generated.

A new scaling law, the generalized vortex formation time, explains biological flight across species and conditions. This principle, based on maximizing leading-edge vortex circulation, offers a universal framework for understanding animal locomotion.

Keywords:
biolocomotionflapping flightleading-edge vortexvortex formation

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Area of Science:

  • Aerodynamics
  • Biomechanics
  • Fluid Dynamics

Background:

  • Biological flyers generate propulsion through appendage flapping, with flight kinematics studied via scaling laws.
  • The Strouhal number (St) is a common metric for cruising flight but is condition-dependent.
  • Leading-edge vortices (LEV) are crucial for generating propulsive forces in flapping flight.

Purpose of the Study:

  • To develop a universal scaling law for biological flight independent of specific flight conditions.
  • To generalize the concept of vortex formation time for flapping flight.
  • To provide a unifying framework for understanding biolocomotion.

Main Methods:

  • Developed a generalized vortex formation time based on LEV circulation maximization.
  • Scaled the duration of vorticity injection with vorticity growth and maximum allowed vorticity.
  • Compared the new scaling law with the Strouhal number from 28 species' flight data.

Main Results:

  • The generalized vortex formation time is consistent across diverse animal flyers and cruising gaits.
  • This new metric is independent of specific flight conditions, unlike the Strouhal number.
  • Demonstrated a unifying framework for analyzing flapping flight dynamics.

Conclusions:

  • The generalized vortex formation time offers a fundamental principle for understanding biological flight.
  • This finding advances the study of complex wing kinematics in nature.
  • Highlights a universal approach to biolocomotion analysis.