This paper uses optimal periodic control (OPC) theory as a framework for assessing the relative efficiency of revolving versus flapping wing trajectories in insect-sized flight problems. The literature already offers both experimental and simulation-based comparisons between these two flight modes. A collective conclusion from these studies is that the potential advantages of flapping flight depend on many factors such as Reynolds number, wing size/morphology, wing kinematic constraints, aerodynamic efficiency metrics, etc. This makes it necessary to develop a unified framework for comparing these flight modes under various conditions. We address this need by using the π test from OPC theory as a tool for analyzing the degree to which one can improve the efficiency of steady rotary hovering flight through periodic trajectory perturbations. A quasi-steady insect flight model from the literature is adopted as a case study. The paper applies the π test to this model. It then concludes by solving for the optimal lift-power Pareto fronts for both flight modes, and using these Pareto fronts to confirm the results predicted by the π test.

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