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Lift force reduction due to body image of vortex for a hovering flight model. (English) Zbl 1275.76232
Summary: The effect of the body on the lift force in hovering flight is studied here by including the effect of image vortex rings (IVRs) in the inviscid vortex ring model proposed by J. M. V. Rayner [J. Fluid Mech. 91, 697–730 (1979; Zbl 0436.76019)] and used by X. X. Wang and Z. N. Wu [J. Fluid Mech. 654, 453–472 (2010; Zbl 1193.76031)] to study lift force due to wakes. The body is treated simply as an equivalent sphere following the data of C. P. Ellington [Philos. Trans. R. Soc. Lond., Ser. B 305, 17–40 (1984)]. It is shown that the body image reduces the lift by inducing a further downwash near the wing tip and an additional contraction to the real vortex rings (RVRs). The amount of force reduction due to body image is found to grow cubically with relative body size, defined by the equivalent radius relative to the wing span, and approximately linearly with the feathering parameter. For Apis and Bombus with large relative body size and large feathering parameter, the body images reduce lift by an amount near 8% according to the present simplified analysis.

76Z05 Physiological flows
76B75 Flow control and optimization for incompressible inviscid fluids
76B47 Vortex flows for incompressible inviscid fluids
92C10 Biomechanics
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