An Improved Aerodynamic Model for Quasi-Steady Simulations of Animal Flight at Moderate Reynolds Numbers

We present experimental and numerical studies aimed at improving models of animal flight at moderate Reynolds numbers ( $20k$ - $50k$ ). Quasi-steady aerodynamic force and moment data were collected using a rectangular wing across various angles of attack, α. The drag coefficient, $C_D\left(\alpha \right)$ , is well described by a simple trigonometric function, while the lift coefficient, $C_L\left(\alpha \right)$ , combines trigonometric and exponential terms-the latter capturing the linear behavior at small α predicted by inviscid theory. We also derive an empirical relation for the center of pressure as a function of α, allowing evaluation of the pitching moment coefficient, $C_M\left(\alpha \right)$ , about any axis. These formulas are integrated into a dynamic flapping wing model to simulate forward flight of a pigeon and a bat at different speeds. Compared to prior models, our approach yields better agreement with wingbeat frequency data, particularly at high speeds. The small α angle regime proves especially beneficial, offering higher $C_L/C_D$ , which translates to reduced power demands and smaller body pitch variation-key considerations for the design of flapping wing robots.