E11 Non-stationary aerodynamics

Topic

This same unsteady aerodynamics describes, in general, how an insect's wing—specifically the one establishing the model in this set—generates both its final lift and thrust through a rapid, complex flapping motion, during which the airflow field changes radically throughout each flapping cycle.

Unlike an airplane wing, which operates under quasi-steady aerodynamics, this insect operates in a regime where the history of the airflow—specifically the vorticity generated during a previous flapping cycle—exerts a measurable effect on the force currently generated by the wing.

Wagner's function captures this temporal memory mentioned at the start of the paragraph: the insect wing's lift does not reach its final equilibrium value instantaneously but rather attains it gradually over the course of the flapping cycle.

The insect's specific Reynolds number implies that air viscosity is not negligible; consequently, the vortex generated by the wing persists longer and is considerably more intense relative to the wing's span. The fact that the insect flies with a much smaller wing results in an even lower Reynolds number, causing air viscosity to exert an even greater influence on the behavior of the vortex generated by the wing. Consequently, for this model—characterized by the lift and thrust generated by the rapid, complex wing-beating motion used to initiate flight—the insect's specific Strouhal number reflects an optimal flight efficiency that matches the optimal efficiency established by other models in this set for the oscillatory swimming of a fish and the oscillatory flight of a bird. The fact that this insect's Strouhal number aligns even more closely with the optimal range shared by the fish and the bird results in higher overall flight efficiency, thereby requiring less flight power than is predicted by another model in this set regarding the difference between flight metabolism and basal metabolism.

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