The aerodynamics of hovering insect flight. VI. Lift and power requirements

Abstract

The lift and power requirements for hovering insect flight are estimated by combining the morphological and kinematic data from papers II and III with the aerodynamic analyses of papers IV and V. The lift calculations are used to evaluate the importance in hovering of two distinct types of aerodynamic mechanisms: (i) the usual quasi-steady mechanism, where the circulation for lift is primarily determined by translation of the wing, and (ii) rotational mechanisms, where the circulation is largely governed by wing rotation at either end of the wingbeat. Power estimates are compared with the available measurements of metabolic rate during hovering to investigate the role of elastic energy storage, the maximum mechanical power output of the flight muscles, and the muscle efficiency. The quasi-steady mechanism proves inadequate for the lift requirements of hover-flies using an inclined stroke plane, and for a ladybird beetle and a crane-fly hovering with a horizontal stroke plane. Observed angles of attack rule out lift enhancement by unsteady modifications to the quasi-steady mechanism, such as delayed stall, but the rotational lift mechanisms proposed in paper IV seem consistent with the kinematics. The rotational mechanisms rely on concentrated vortex shedding from the leading edge during rotation, with attachment of that vorticity as a leading edge separation bubble during the subsequent half-stroke. Strong leading edge vortex shedding should result from delayed pronation for the hover-fly, a near fling and partial fling for the ladybird, and profile flexion for the crane-fly (the flex mechanism). The kinematics for the other insects hovering with a horizontal stroke plane are basically the same as for the anomalous crane-fly, and the quasi-steady mechanism cannot be accepted for them while rejecting it for the crane-fly. All of these insects flex their wings in a similar manner during rotation, and could use the flex mechanism for lift generation. The implication is that most, if not all, hovering animals do not rely on quasi-steady aerodynamics, but use rotational lift mechanisms instead. It is not possible to reconcile the power estimates with the commonly accepted values of both the mechanochemical efficiency of insect flight muscle (about 25%) and its maximum mechanical power output (about 20 W N -1 of muscle). Maximum efficiencies of 12-29% could be obtained only if there is no elastic storage of the kinetic energy of the flapping wings, but this would require more than twice the accepted value for maximum mechanical power output. The available evidence suggests that substantial elastic storage does occur, and that the maximum mechanical power output is close to the accepted value. If so, then the efficiency of both fibrillar and non-fibrillar flight muscle is likely to be only 5-9%.