No abstract

A state-space formulation for the aerodynamics of flapping flight is presented. The Duhamel's principle, applied in linear unsteady flows, is extended to non-conventional lift curves to capture the LEV contribution. The aspect ratio effects on the empirical formulae used to predict the static lift due to a stabilized Leading Edge Vortex (LEV) are provided. The unsteady lift due to arbitrary wing motion is generated using the static lift curve. Then, state-space representation for the unsteady lift is derived. The proposed model is validated through a comparison with direct numerical simulations of Navier-Stokes on hovering insects. A comparison with quasi-steady models that capture the LEV contribution is also performed to assess the role of unsteadiness. Similarly, a comparison with classical unsteady approaches is presented to assess the LEV dominance. Finally, a reduced-order model that is more suitable for flight dynamics and control analyses is derived from the full model.

No abstract

Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.

No abstract