Achieving hover equilibrium in free flight with a flexible flapping wing

Recent discoveries in the fields of flapping wing aerodynamics and fluid-structure interaction have demonstrated that flexible wings can generate more lift than rigid wings. However, the implications of wing flexibility on the flight dynamics of flapping wing flyers is still an open research question. The main difficulty is that the free flight of flapping flyers with flexible wings is a result of the dynamic balance between unsteady aerodynamics, fluid-structure interaction, and flight dynamics. This study presents a fully coupled three-way flight simulator that solves the two-dimensional Navier-Stokes equations, tightly coupled to the Euler-Bernoulli beam equations of the wing and the nonlinear multi-body equations of motion for the dynamics at the fruit fly scale. A novel trim algorithm is used to determine the hover equilibrium in the longitudinal plane. The control inputs, i.e. the flapping amplitude, stroke plane angle, and flapping offset angle as well as the initial conditions are determined that effectively eliminate average body accelerations to less than 3% of gravitational acceleration. The resulting hover equilibrium control parameters flapping amplitude, stroke plane angle and the total power required agree well with the biological observation of fruit flies. Body oscillations in hovering free flight affect the flexible response of the wing compared to prescribed body motion without oscillation. The affected wing motion reduces the lift coefficient by up to 8.7% for the stiffest wing, necessitating slightly different control inputs to achieve trim. Finally, the power required to achieve hover equilibrium is 32%-94% lower for flexible wings than for rigid wings that are actively rotated to match the same passive pitch schedule.