The mechanics of lift and thrust generation by flying animals are studied by considering the distribution of vorticity in the wake. As wake generation is not continuous, the momentum jet theory, which has previously been used, is not satisfactory, and the vortex theory is a more realistic model.

The vorticity shed by the wings in the course of each powered stroke deforms into a small-cored vortex ring; the wake is a chain of such rings. The momentum of each ring sustains and propels the animal; induced power is calculated as the rate of increase of wake kinetic energy.

A further advantage of the vortex theory is that lift and induced drag coefficients are not required; estimated instantaneous values of these coefficients are generally too large for steady state aerodynamic theory to be appropriate to natural flapping flight.

The vortex theory is applied to hovering of insects and to avian forward flight. A simple expression for induced power in hovering is found. Induced power is always greater than simple momentum jet estimates, and the discrepancy becomes substantial as body mass increases.

In hovering the wake is composed of a stack of horizontal, coaxial, circular vortex rings. In forward flight of birds the rings are elliptic; they are neither horizontal nor coaxial because the momentum of each ring balances the vector sum of parasite and profile drag and the bird's weight. Total power consumption as a function of flight velocity is calculated and compared for several species. Power reduction is one of the major factors influencing the choice of flight style.

A large body of data is used to obtain an approximate scaling between stroke period and the body mass for birds. Together with relations between other morphological parameters, this is used to estimate the variation of flight speed and power with body mass for birds, and on this basis deviations from allometric scaling can be related to flight proficiency and to the use of such strategies as the bounding flight of small passerines.

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Present address: Department of Zoology, University of Bristol, Woodland Road, Bristol BS8 IUG, U.K.

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