Influence of slack-angle induced deformation and advance ratio on aerodynamic characteristics of flapping wings

Experimental investigations are conducted to examine the effect of wing flexibility on the unsteady aerodynamic forces, power consumption, and vortex dynamics of flapping wings over a range of flight speeds. Tests are conducted at advance ratios (J) from −0.25 to 1, covering backward, hovering, and forward flights. Wing flexibility is introduced via slack angles (β = 0°, 2.5°, 5°, and 7.5°) and compared to a rigid wing. The effects of J and β are systematically investigated in a water towing tank facility. This study reveals that β-induced flexibility produces enhanced upstroke lift at moderate β, reduces power consumption by 40.15%, dampens the abrupt change in center of pressure movement, and suppresses negative lift generation at high J compared to the rigid wing. Although flexible wings display a phase delay in force production, this delay diminishes as J increases. Flow visualizations reveal that flexibility-induced twist stretches the leading-edge vortex (LEV) and migrates the center of pressure outside the wing surface. Unlike rigid wings, which show strong LEV-tip vortex merging and a significant circulation loss of 57.34%, flexible wings avoid this merger and retain stronger outboard flow, which leads to lower circulation loss. Thus, flexible wings preserve outboard circulation and prevent severe lift loss with increasing J. Overall, wing flexibility enables passive adaptations that improve aerodynamic efficiency up to 49.22%, enhance system stability, and alter the wake dynamics. These benefits were evident at low-to-moderate J and are specific to the tested horizontal stroke plane configuration.