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Aerodynamicists (people who study the dynamics of flight) propose that long-distance migratory birds, such as geese and swans, fly in a "V" formation in order to reduce the amount of energy needed for such long flights. According to theoretical calculations, birds flying in the "V" formation can fly about 10 percent farther than a lone bird can, while expending the same amount of energy. That's because formation flying lessens the air pressure that pushes against a bird's wings. The effect is similar to what occurs when an airplane encounters a current of rising air. In that situation, a plane can ascend to a higher altitude using less power than normal.
The reason why birds fly in a "V" and not in a single file is that when flying, each bird creates behind it a small area of disturbed air. If a bird were to fly directly behind another, it would be caught in this turbulence. The turbulence problem is avoided by assuming the "V" formation, in which each bird flies to the side of, or above, the bird in front.
Sources: Callahan, Philip S. Bird Behavior, pp. 133-34; Terres, John K. The Audubon Society Encyclopedia of North American Birds, p. 377.
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