DICKSON *, W.B.; DICKINSON , M.H.; California Institute of Technology; California Institue of Technology: Quantifying the effect of advance ratio on aerodynamic force generation during forward flight.

Recent studies have demonstrated that a quasi-steady model closely matches the instantaneous force produced by an insect wing during hovering flight. It is not clear, however, if such methods extend to forward flight. In this study we use dynamically-scaled robotic model of the fruit fly Drosophila melanogaster to investigate the forces produced by a wing revolving at constant angular velocity while simultaneously translating at velocities appropriate for forward flight. The results show that for a given Reynolds number the instantaneous force produced by a wing under these conditions depends upon three variables: the stroke position angle, the angle of attack, and the advance ratio. Parametric mappings of the lift and drag coefficients are compiled as functions of these three variables. Forces due to added mass make a small, but measurable, component of the total force and are in excellent agreement with theoretical values. The lift and drag coefficients, after subtracting the added mass contribution, obey simple trigonometric relationships with respect to angle of attack. Further, the amplitude and offset of the trigonometric relationships follow a simple second order polynomial relationship with respect to stroke position angle and advance ratio. In total the results confirm the utility of the quasi-steady models of insect flight and offer insight into how animals change wing motion to control flight speed.