The aerodynamics of hovering insect flight. I. The quasi-steady analysis

Abstract The conventional aerodynamic analysis of flapping animal flight invokes the ‘quasisteady assumption’ to reduce a problem in dynamics to a succession of static conditions: it is assumed that the instantaneous forces on a flapping wing are equivalent to those for steady motion at the same instantaneous velocity and angle of attack. The validity of this assumption and the importance of unsteady aerodynamic effects have long been controversial topics. Weis-Fogh tested the assumption for hovering animal flight, where unsteady effects are most pronounced, and concluded that most insects indeed hover according to the principles of quasi-steady aerodynamics. The logical basis for his conclusion is reviewed in this paper, and it is shown that the available evidence remains ambiguous. The aerodynamics of hovering insect flight are re-examined in this series of six papers, and a conclusion opposite to Weis-Fogh’s is tentatively reached. New morphological and kinematic data for a variety of insects are presented in papers II and III, respectively. Paper IV offers an aerodynamic interpretation of the wing kinematics and a discussion on the possible roles of different aerodynamic mechanisms. A generalized vortex theory of hovering flight is derived in paper V, and provides a method of estimating the mean lift, induced power and induced velocity for unsteady as well as quasi-steady flight mechanisms. The new data, aerodynamic mechanisms and vortex theory are all combined in paper VI for an analysis of the lift and power requirements and other mechanical aspects of hovering flight. A large number of symbols are needed for the morphological, kinematic and aerodynamic analyses. Most of them appear in more than one paper of the series, and so a single comprehensive table defining the major symbols from all of the papers is presented at the end of this paper.