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

Abstract

SUMMARY 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.

Aerodynamics of wing-assisted incline running in birds

“…U ind was probably greater, by some unmeasured amount, than the induced velocity at the wing (Ellington, 1984;Sane, 2006). We were unable to measure U ind at the wing because the wings and body, and reflection of laser light, obscured near-field flow patterns.…”

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor

“…We propose here an analytical method based on lifting line blade models. Sane [13] presented a lifting line blade model for hovering flapping wings; however, the model relied on empirical experimental data, and hence measurements are still required for the calculation. Leishman [14, ch.…”

“…Although this formula was originally developed for rotors with finite number of blades, Sane [13] showed that it can be used within the context of flapping flight, suggesting a value of 2 for N b to simulate a complete wing cycle and a value of 1 for a single up-or downstroke. For a hovering case, l is the ratio of the induced downwash velocity to the wing tip velocity rsif.royalsocietypublishing.org J. R. Soc.…”

“…[23], who used DPIV to measure the circulation around a revolving model fruitfly wing with a mean chord of 7 cm [13] in a typical hovering condition (J 1 ¼ 0). Because the wing has a planform shape of a fruitfly wing, we used the real fruitfly AR of 3.015 and non-dimensional radius of the first moment of wing area of 0.55 (table 1) to define the chord distribution based on the beta function.…”

“…The circulation distribution at the same experimental conditions was calculated using the lifting line model, and the result was compared with the experiment (figure 5). In figure 5, the semi-empirical treatment of Sane [13] for the same experiment is included for comparison. Excellent agreement between analytical model and experiment for the shape of variation, including both the peak value of circulation and the rate of decay of circulation towards zero is found.…”