John J. Videler

“4.1 Introduction A flying bird generates lift forces to counteract gravity and thrust forces to overcome drag. The magnitude of these forces can be crudely approximated using elementary physical principles. Steady flight in still air at a uniform speed and at one altitude is the simplest case. It requires balanced forces where lift equals weight and thrust equals drag as well as balanced moments of these forces about the centre of gravity. Under these relatively simple conditions the magnitude of the mechanical power involved in the generation of lift and thrust in relation to speed can be estimated. The power to generate lift is inversely proportional to flight speed and the power needed for thrust increases with the speed cubed. The total mechanical power is the sum of the lift and thrust powers and hence follows a U-shaped curve if plotted against speed. A U-shaped power curve implies that there are two optimal speeds, one where the power is minimal and a higher one where the amount of work per unit distance reaches the lowest value. The question is, does this U-shaped power curve really exist in birds?”
― John J. Videler, Avian Flight