Induced Drag of a Bird Flock

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Abstract
It is likely that birds such as geese, which migrate in horizontal V formation, save appreciable energy from the mutual aerodynamic interaction which can decrease their induced drag, an effect recently analyzed in some detail by Lissaman and Shollenberger (1970). Many species, however, migrate in large 3-dimensional flocks, so the simplest aerodynamic theory was used to estimate the change in total induced drag for both 2 and 3-dimensional lattices of birds, compared with the same numbers flying individually. For a large dilute flock, a novel approximation is introduced, representation of a vertical array of trailing-vortex pairs as a continuum of dipole strength. This relatively simple method shows a total drag decrease when the flock extends farther laterally than vertically. A more detailed (3-dimensional) analysis, using a horseshoe-vortex pattern to represent each bird and neglecting the disturbance due to flapping, adds the information that extension in the flight direction can be helpful or harmful, depending upon precise position of the following birds relative to the vortex wakes of those ahead of them. A high, narrow flock actually will experience an increase in drag. A tentative conclusion is that improved flight efficiency is not an important reason for migration in large 3-dimensional flocks.

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