The mechanics of bird migration
A theory is presented for calculating the relation between mechanical power required to fly and forward speed, for a bird flying horizontally. The significance of this for migration is explained, and quick methods are given (and summarized in the Appendix) for calculating key points on the curve. Speed ranges and effective lift: drag ratios are calculated for a number of different flying animals. Factors affecting migration range are discussed, and the effects of head- and tailwinds are considered. Still-air range depends on effective lift: drag ratio, but not on size or weight as such. The relation of power required to that available from the muscles is considered. Small birds have a greater margin of power available over power required than large ones, and tend to run their flight muscles at a lower stress, or lower specific shortening, or both. There is an upper limit to the mass of practicable flying birds, represented approximately by the Kori Bustard Ardeotit kori. The effect of adding extra weight (food or fuel) is to increase both minimum-power speed, and maximum-range speed, in proportion to the square root of the weight, and to increase the corresponding powers in proportion to the three-halves power of the weight. Birds up to about 750 g (fat-free) can double their fat-free mass, and still have sufficient power to fly at the maximum-range speed. Larger birds are progressively more severely limited in the maximum loads they can carry, and this reduces their range. Many large birds migrate by thermal soaring, thus economizing on fuel at the expense of making slower progress. During a long flight both speed and power have to be progressively reduced as fuel is used up. A formula is given for calculating the still-air range of a bird which does this in an optimal fashion. The only data required are the effective lift: drag ratio, and the proportion of the take-off mass devoted to fuel. Increase of height has no effect on the still-air range, but the optimum cruising speed (and power) is increased. The optimum cruising height is reached when the bird can absorb oxygen just fast enough to maintain the required power. The optimum height increases progressively as fuel is used up. No range is lost as a result of the work done in climbing to the cruising height.