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This content will become publicly available on August 29, 2026

Title: Universal vortex formation time of flapping flight
Biological flyers periodically flap their appendages to generate aerodynamic forces. Extensive studies have made significant progress in explaining the physics behind their propulsion in cruising by developing scaling laws of their flight kinematics. Notably Strouhal number (St; ratio of flapping frequency times stroke amplitude to cruising speed) has been found to fall in a narrow range for animal cruising flights. However, St exhibits strong correlation to flight conditions; as such, its universality has been confined to preferred flight conditions. Since the leading-edge vortices (LEV) on flapping appendages generate the majority of propulsive forces, here we take the perspective of LEV circulation maximization, which generalizes the dimensionless vortex formation time to flapping flight. The generalized vortex formation time scales the duration of vorticity injection with the rate of total vorticity growth inside the LEV and the maximum vorticity allowed inside it. By comparing the new scaling with St of previously reported animal cruising flights of 28 species, we show that the generalized vortex formation time is consistent across different animals and cruising locomotion, independent of flight conditions. This finding advances the fundamental principles underlying the complex wing kinematics of biological flyers and highlights a unifying framework for understanding biolocomotion.  more » « less
Award ID(s):
2442036 2042740
PAR ID:
10650180
Author(s) / Creator(s):
; ; ; ; ; ;
Publisher / Repository:
Proceedings of the National Academy of Sciences of the United States of America
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
122
Issue:
35
ISSN:
0027-8424
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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