Experimental aerodynamic analysis of finite flapping wings with chordwise flexibility

Classic two-dimensional aerodynamic results for a heaving and pitching airfoil are normally used for finite flapping wings, taking a reference amplitude at 1/3 of the wingspan from the wingtip. However, for the wings of actual flapping wing robots, flexibility also plays a significant role due to their light weight. For that reason, an analysis of the chordwise stiffness is provided with an experimental testbench, performing low-amplitude pitching motions in the absence of incoming airflow; this allows to obtain the resonance frequency of the structure, enabling the development of an analogy with the theoretical formulation for a deformable heaving airfoil. The beam stiffness term of the airfoil is substituted by that one derived from the resonance frequency. This analogy, which includes the effect of wing inertia through the mass ratio computed from the total mass of the wing, is compared with actual flapping wing experimental results in the wind tunnel. Experiments are performed with two wings of different stiffness characteristics to adequately validate the analysis. Results show excellent agreement with the proposed formulation with similar trends for the evolution of forces at different frequencies and airspeeds. As expected from previous results, the analogy fails when the stiffness term becomes too small (S<1). Results show how the amplitude of the lift oscillations decreases with flexibility, whereas the effects on the average thrust force depend on the reduced frequency, with a critical value around k∼0.6 beyond which the thrust increases with flexibility.