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Where V is the gliding speed between thermals, Vz is the sink component (negative downwards) and Vc is the climb rate in thermals (Pennycuick 1972, 1975, 1989).

Box 8.2 Calculation of theoretical energy and time costs of migration. From Alerstam et al. (2003)

Energy costs

Generally, if migration is subdivided into periods of movement, interspersed with periods of stopover, the total energy consumption during migration can be written as:

V 'dep where P is the power of locomotion (rate of energy consumption), D is the migration distance, V is the flight speed, Pdep is the rate of energy deposition at stopovers, and x is the field metabolic rate at stopovers. Equation (1) can be used to compare the total investment in migration among, for example, birds of different size and using different modes of flight. The ratio x:Pdep determines the ratio between energy consumed during stopovers and cost of flight, which in a typical passerine bird may be about 2:1 or larger. From Equation (1), it is also evident that minimising the ratio P:V, a measure closely related to cost of transport, will minimise the energy cost of migration.

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