How a long tail and changes in mass and wing shape affect the cost for flight in animals

1. Relationships between foraging strategy, flight performance and wing shape in animals can be demonstrated with the use of aerodynamic theory. The optimal morphology is dictated not only by foraging behaviour and habitat selection but also by size of prey and migratory habits, as well as flight display. Here I demonstrate how changes in body size and structure of wings and tail affect the optimal flight speeds and power required to fly. 2. Long-tailed birds flying with their tails hanging downwards-backwards (e. g. widowbirds) are predicted to fly more slowly than short-tailed birds to save energy or to have larger wings (broader and/or longer wings giving lower wing loading) to compensate for increased tail drag during flight. Assuming that the tail length is five times as long in a long-tailed bird than in a short-tailed (normal) one, the minimum power and maximum range power would be about 30% higher in the long-tailed bird and the corresponding speeds about 40% slower. Ignoring wing inertial loads as a cost (inertial power) the corresponding percentages would become 16-18% higher powers and slower speeds. 3. I predict that members of a bird family that display in hovering or vertical take-off flights should not have elongated wings if wing inertia is important. In contrast to most other widowbird species, males of Jackson's widowbird (Euplectes jacksoni) do not have elongated wings (Anderson 1992), although they have particularly costly tails (Thomas 1993). This species has abandoned forward flight display and instead uses a vertical take-off and hovering flight display. Inertial costs appear to explain this result. 4. An increase in weight causes an increase in wing loading, which in turn requires higher flight speed for production of enough lift. A 50% increase in body mass (as fat, an egg or a fetus inside the body), would increase P mr and P mp by about 45-50% and V mr and V mp by about 20-25% (symbols defined in Fig. 1), when inertial power is taken to be zero. 5. A bird or bat carrying prey in the beak/mouth or claws should use about the same speed for minimization of flight costs as when flying without prey. 6. For low flight costs, and assuming a perfect elastic storage (zero inertial power), fast-flying species should benefit from short, narrow, high-aspect-ratio wings, hovering species should have long wings and slow-flying species should have larger wings (lower wing loadings) but with no particular demands on the aspect ratio. Ignoring inertial power the best flight economy is attained by the combination of a low wing loading (enabling slow flight) and high aspect ratio (Norberg & Rayner 1987; Norberg 1990). If we assume that inertial power is an important cost in hovering, a hovering animal should have short wings to minimize mechanical power