1. Pennycuick's (1969) theory for the energetic requirements of avian flight predicts the metabolic rates of budgerigars and laughing gulls flying level at intermediate speeds in a wind tunnel with an accuracy of 10% or better. However, its predictions appear to be low for most birds with masses less than 0·1 kg and high for most birds with masses greater than 0·5 kg.
2. Four modifications are made to Pennycuick's theory: (1) a different computation of induced power; (2) a different estimate of equivalent flat plate area that includes Reynolds number effects, and is based on additional measurements; (3) a different estimate of profile power that includes Reynolds number effects; and (4) the addition of power terms for respiration and circulation. These modifications improve the agreement between the theoretical predictions and existing measurements for flying birds and bats.
3. The metabolic rates of birds and bats in level flight at various speeds can be estimated by the modified theory if body mass alone is measured. Improved estimates can be made if wing span is measured as well. In the latter case the theory predicts measured values with a mean absolute error of 8·3%.
4. The results of the modified theory are presented by approximate equations that can be solved quickly for metabolic rate and flight speed with a slide rule.
Reynolds number effects on mixing due to topological chaos
