An improved aerodynamic model for quasi-steady simulations of animal flight at moderate Reynolds numbers

TL;DR

This paper develops an improved aerodynamic model for animal flight at moderate Reynolds numbers, combining experimental data and formulas to better predict lift, drag, and pitching moments, enhancing flight simulation accuracy.

Contribution

The study introduces novel empirical formulas for aerodynamic coefficients and center of pressure location, improving quasi-steady flight modeling for animals and bio-inspired robots.

Findings

Enhanced agreement with experimental wingbeat data at various speeds.

Better prediction of lift-to-drag ratio in small-angle regimes.

Reduced power consumption and pitching variation in simulations.

Abstract

We report on experimental and numerical studies aimed at developing an improved paradigm to model animal flight at moderate Reynolds numbers ($ 20 k - 50k $). A series of experiments were performed to characterize the behaviors of aerodynamic forces and moment associated with a quasi-steady rectangular wing over a range of angle of attack, $\alpha$. We demonstrate that, while the drag coefficient curve, $C_D(\alpha)$, can be accurately modeled solely by a simple trigonometric function, the evolution of lift coefficient curve, $C_L(\alpha)$, is governed by the sum of trigonometric and exponential functions, where the latter captures the linear variation in lift coefficient within the small-angle regime, as predicted by the linear inviscid theory. In addition, we establish an empirical relation between the location of the center of pressure and $\alpha$, which can be used in conjunction with the proposed aerodynamic formulas (i.e., $C_L$ and $C_D$) to evaluate the pitching moment coefficient, $C_M(\alpha)$, about any arbitrary axis. These quasi-steady formulations are then utilized within a previously tested flapping-wing code to simulate the forward flight of a pigeon and a bat at various flight speeds, and the results are compared against previously reported experimental data. We successfully demonstrate that the proposed formulas yield much better agreement with wingbeat frequency for both animals, especially at higher flight speeds. In addition, the small-angle regime proves critical in offering higher $C_L/C_D$, leading to solutions with lower power consumption and body pitching variation, both of which are important aspects in designing future flapping wing robots.