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UBC Theses and Dissertations

Optimum bird flock size in formation flight Kshatriya, Mrigesh


A theoretical model of flock size in migrating birds is developed. Although previous models of formation flight in birds show improved flight performance, they do not explain flock size variation across bird species or at different times of the year for a given bird species. This model captures some of the diversity in flock size observed in nature by incorporating energetic costs of flight and energy income from foraging. It turns out that within a myriad of possible flock sizes there - is one that is optimal for maximizing energetic efficiency (net energetic gain/energy expenditure) for a given maximum range speed, which minimizes flying cost per unit distance flown, and under certain migration conditions (i.e. flight distance and total time to complete the journey). Net energetic gain from foraging equals the rate of prey encountered times the time spent foraging. Energy expenditure from flying is determined from formation flight theory for a fixed wing aircraft. The benefit of formation flight, as derived from an approximation technique, is represented in close-form. This expression is a function of flock size and wing-tip spacing (WTS) and simplifies flight cost calculations. Under certain WTS, a good approximation to the induced drag for a member of a flock of size n is 1/nth of the induced drag of a single bird. In addition, optimum flight speed of a flock is (1/n)⅟₄ of the optimum flight speed of a single individual. The approach taken here allows the prediction of flock size in migrating birds. Model results are discussed in relation to observation of flock size under various migration conditions. If migration is constrained by hours of daylight, seasional variation in flock size is expected if the start time of the north and southward migration are asymmetrical with respect to the summer solstice (June 21). Under certain conditions, such as long non-stop migration, solo flight is an optimum migratory strategy.

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