Stress and strain in the flight muscles as constraints on the evolution of flying animals

The minimum mechanical power needed for an animal to maintain level flight can be estimated, as can the wingbeat frequency, from measurements of the animal's mass, wing span and wing area, and of the strength of gravity and the air density. Dividing the power by the frequency gives the work done per cycle, and dividing this by the muscle mass gives the specific work, meaning the work done in each contraction by unit mass of muscle. This in turn is the product of the average stress during shortening and the strain, divided by the muscle density. The minimum specific work for level flight is strongly size dependent. To account for even minimum performance in the largest species known to be capable of prolonged, aerobic flight (whooper swan), the specific work of the myofibrils needs to be 57 J kg-1, which could be achieved, for example, by a stress of 240 kN m-2 combined with a strain of 0.25. The upper limits of stress and strain for sustained exercise are not known, but are not likely to be much higher than these figures. Much larger birds, such as the Miocene fossil Argentavis, would require improbably high values of stress and strain for level flight, unless the air density were much higher in Miocene times than at present, and/or the strength of gravity were much less. Birds of small and medium size have more than the minimum amount of muscle required for level flight. This opens a wide range of possibilities for different species to be specialised for different types of activity. The potential diversity for evolution in large species is less than for medium-sized or small ones, and dwindles to zero above a body mass of about 14 kg. There is also a strong positive trend in the aerobic scope, from about 3 in small, long-winged passerines such as swallows, to 47 in the whooper swan.