Flapping flight universal vortex formation (free pdf)

[Ben Creisler]

Ben Creisler

bcre...@gmail.com

A new paper:

Free pdf:

Yukun Sun, Emily Palmer, Christopher Doughert, Cade Sbrocco, Aspen Shih, Jena Shields, and Chris Roh (2025)
Universal vortex formation time of flapping flight
Proceedings of the National Academy of Sciences 122(35): e2501511122
doi: https://doi.org/10.1073/pnas.2501511122
https://www.pnas.org/doi/10.1073/pnas.2501511122

Free pdf:
https://www.pnas.org/doi/epdf/10.1073/pnas.2501511122


Significance

Through the action of flapping, biological flyers generate a vortex upon each wing known as the leading-edge vortex (LEV), which has been shown to enhance aerodynamic force production. However, the LEV does not grow indefinitely. Here, by examining the limits of LEV growth and its growth rate, we show that the animal’s wing stroke lasts until the LEV reaches its natural growth limit. These findings suggest that the flapping frequency of insects, birds, and bats is governed by this intrinsic constraint.

Abstract

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.

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[Michael Habib]

I just had a read of this paper, and it is some top notch dynamics. This is, frankly, a big deal and should rightfully be cited everywhere starting basically immediately. My one critique is of their “Significance” statement, which suggests that flapping frequency is the primary variable that is tuned by flapping flyers. In reality (as demonstrated and discussed expertly by the authors), it is the interaction of flapping frequency, flapping amplitude, and angle of attack that is tuned. Angle of attack is of particular note here because 1) the main contribution of this work was figuring out how to incorporate it 2) flapping flyers vary AoA over time and 3) flapping flyers also vary AoA span-wise (i.e., it’s not the same down the whole wing). This means that, from a functional anatomy standpoint, the degree of span-wise twist is part of the tuning process.

Why does that matter for paleo folks looking at fossil morphology? Well, there’s a couple of reasons, but one of them is that in birds, twist of the distal-most wing is dominated by passive feather properties, and that depends on feather morphology (including, but not limited to, rachis cross sectional shape and, for separated feathers, vane asymmetry).

Anyway… super cool, and one of the best things I’ve read all year, easily.

Cheers,

—Mike H.

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