An experimental comparative study of the efficiency of twisted and flat flapping wings during hovering flight

This work presents a parametric study to find a proper wing configuration for achieving economical flight using unsteady blade element theory, which is based on the 3D kinematics of a flapping wing. Power loading was first considered as a performance parameter for the study. The power loadings at each wing section along the wingspan were obtained for various geometric angles of attack (AoAs) by calculating the ratios of the vertical forces generated and the power consumed by that particular wing section. The results revealed that the power loading of a negatively twisted wing could be higher than the power loading that a flat wing can have; the power loading of the negatively twisted wing was approximately 5.9% higher. Given the relatively low average geometric AoA (α _A,root  ≈  44° and α _A,tip  ≈  25°), the vertical force produced by the twisted wing for the highest power loading was approximately 24.4% less than that produced by the twisted wing for the strongest vertical force. Therefore, for a given wing geometry and flapping amplitude, a flapping-wing micro air vehicle required a 13.5% increase in flapping frequency to generate the same strongest cycle-average vertical force while saving about 24.3% power. However, when force³/power² and force²/power ratios were considered as performance indices, the twisted wings for the highest force³/power² (α _A,root  ≈  43° and α _A,tip  ≈  30°) and force²/power (α _A,root  ≈  43° and α _A,tip  ≈  36°) required only 6.5% and 4% increases in flapping frequency and consumed 26.2% and 25.3% less power, respectively. Thus, it is preferable to use a flapping wing operating at a high frequency using the geometric AoAs for the highest power loading, force³/power² ratio, and force²/power ratio over a flapping wing operating at a low frequency using a high geometric AoA with the strongest vertical force. Additionally, by considering both aerodynamic and inertial forces, this study obtained average geometric AoAs in the range of 30° to 40°, which are similar to those of a typical hovering insect's wings. Therefore, the operation of an aerodynamically uneconomical, high AoA in a hovering insect's wings during flight is explainable.