# Quasi-steady aerodynamics predicts the dynamics of flapping locomotion

## TL;DR

This paper demonstrates that a quasi-steady aerodynamic model can effectively predict the key dynamics of flapping flight and swimming, capturing transitions and force behaviors without solving full flow equations.

## Contribution

It shows that quasi-steady models can explain unsteady locomotion phenomena across a broad range of parameters, extending their applicability.

## Key findings

- Reproduces transition from stationary to propulsive states with increasing Reynolds number.
- Strouhal number remains conserved across various parameters.
- Flow regimes are influenced by Reynolds number and attack angle.

## Abstract

The propulsion of a flapping wing or foil is emblematic of bird flight and fish swimming. Previous studies have identified hallmarks of the propulsive dynamics that have been attributed to unsteady effects such as the formation and shedding of edge vortices and wing-vortex interactions. Here we show that several key features of heaving flight are captured by a quasi-steady aerodynamic model that aims to predict stroke-averaged forces from wing motions without explicitly solving for the flows. We address the forward dynamics induced by up-and-down heaving motions of a thin plate with a nonlinear model which involves lift and drag forces that vary with speed and attack angle. Simulations reproduce the well-known transition for increasing Reynolds number from a stationary state to a propulsive state, where the latter is characterized by a Strouhal number that is conserved across broad ranges of parameters. Parametric, sensitivity, and stability analyses provide physical interpretations for these results and show the importance of accounting for the flow regimes which are demarcated by Reynolds number and angle of attack. These findings extend the phenomena of unsteady locomotion that can be explained by quasi-steady modeling, and they broaden the conditions and parameter ranges over which such models are applicable.