PubMed2003
The distance flown in gliding is proportional to the starting height, not to the starting potential energy, and it is independent of the body mass. By analogy, in powered flight, the quantity of stored fuel can be converted into a virtual "fuel energy height", defined as the height to which the fuel energy could lift the bird against gravity, if it were converted into work. This is a logarithmic function of the fuel fraction, not of the absolute amount of fuel, or of the body mass. It takes account of the strength of gravity, and of the efficiency with which fuel energy is converted into work. The "performance number" is the gradient on which a migrating bird comes "down" from its initial fuel energy height. It is mechanical (not physiological) in character, and corresponds to the lift:drag ratio in a fixed-wing aircraft. The concept of range as an initial energy height multiplied by a performance number can also be applied to swimming and running animals. Performance number, and also the related variable "cost of transport", are both independent of gravity in flying and running, but not in swimming. Migration by thermal soaring is analogous to powered flight with stopovers, except that the bird replenishes its potential energy by climbing in thermals, rather than replenishing fuel energy during stopovers. Rates of climb in thermals are typically higher than fuel energy rates of climb, but the available height band is two orders of magnitude smaller, and the intervals at which energy replenishment is needed are correspondingly shorter. Albatrosses replenish their kinetic energy by exploiting discontinuities in the wind flow over waves, requiring replenishment at intervals of tens of seconds, a further two orders of magnitude shorter than in thermal soaring. Fat energy height can be used as a measure of "condition", which is independent of the size or type of the animal. The fat energy height at which a migrant must arrive on the breeding grounds, in order to breed successfully, reflects the ecological characteristics of the habitat, not the size or character of the bird. Energy height expresses what an animal or machine can do with its stored energy, not the amount of energy.