Induced airflow in flying insects I. A theoretical model of the induced flow.

A strong induced flow structure envelops the body of insects and birds during flight. This flow influences many physiological processes including delivery of odor and mechanical stimuli to the sensory organs, as well as mass flow processes including heat loss and gas exchange in flying animals. With recent advances in near-field aerodynamics of insect and bird flight, it is now possible to determine how wing kinematics affects induced flow over their body. In this paper, I develop a theoretical model based in rotor theory to estimate the mean induced flow over the body of flapping insects. This model is able to capture some key characteristics of mean induced flow over the body of a flying insect. Specifically, it predicts that induced flow is directly proportional to wing beat frequency and stroke amplitude and is also affected by a wing shape dependent parameter. The derivation of induced flow includes the determination of spanwise variation of circulation on flapping wings. These predictions are tested against the available data on the spanwise distribution of aerodynamic circulation along finite Drosophila melanogaster wings and mean flows over the body of Manduca sexta. To explicitly account for tip losses in finite wings, a formula previously proposed by Prandtl for a finite blade propeller system is tentatively included. Thus, the model described in this paper allows us to estimate how far-field flows are influenced by near-field events in flapping flight.