  We report on experimental and numerical studies aimed at developing an
improved paradigm for modeling avian flights at moderate Reynolds numbers. 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 incidence angles, {\alpha}. We demonstrate that, while the drag
coefficient curve, CD({\alpha}), can be accurately modeled solely by a simple
trigonometric function, the evolution of lift coefficient curve, CL({\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 the
incidence angle, which can be used in conjunction with the proposed aerodynamic
formulas (i.e. CL and CD) to evaluate the pitching moment coefficient, CM
({\alpha}), about any arbitrary axis. These quasi-steady formulations are then
utilized to simulate forward flight of a model that possesses dynamical
characteristics of a pigeon across various flight speeds, and the results are
compared against previously-reported experimental data on pigeons. We
successfully demonstrate that the proposed formulas yield accurate predictions
of the wing-beat frequency, at least over a range of Reynolds numbers spanning
from approximately 70,000 to 150,000.
