Gliding Birds: The Effect of Variable Wing Span

Abstract

The equilibrium gliding performance of a bird is described by the relationship between sinking speed (V8) and air speed (V). When V9 is plotted against V, the points fall in a ‘performance area’ because the wing span is changed during gliding. The lowest V3 for each V in the performance area defines a ‘maximum performance curve’. This curve can be predicted by a mathematical model that changes the wing span, area and profile drag coefficient (CD, pr) of a hypothetical bird to minimize drag. The model can be evaluated for a particular species given (a) a linear function relating wing area to wing span, and (b) a ‘polar curve’ that relates CDpr and the lift coefficient (CL) of the wings. For rigid wings, a single polar curve relates CDpr to CL values at a given Reynolds number. The position and shape of the polar curve depend on the aerofoil section of the wing and the Reynolds number. In contrast, the adjustable wings of a laggar falcon (Falco jugger) and a black vulture (Coragyps atratus) gliding in a wind tunnel have CL, and CD,pr values that fall in a ‘polar area’ rather than on a curve. The minimum values of CD,pr at each CL bound the polar area and define a polar curve that is suitable for evaluating the model. Although the falcon and the vulture have wings that are markedly different in appearance, the data for either bird are enclosed by the same polar area, and fitted by the same polar curve for minimum CD,pr at each CL value. This curve is a composite of the polar curves for rigid wings with aerofoils similar to those found in avian wings. These observations suggest that the polar curves of other gliding birds may be similar to that of the falcon and the vulture. Other polar curves are defined by CL and CD,pr values for the falcon and the vulture gliding at a constant speed but at different glide angles. Each speed has a different polar curve; but for a given speed, the same polar curve fits the data foreither bird. The falcon and the vulture gliding in the wind tunnel at a given speed were found to increase their drag by decreasing their wing span. This change increases induced drag and probably increases CD,pr for the inner parts of the wing because of an unusual property of bird-like aerofoil sections: wings with such sections have minimum values of CDpr at CL values near 1, while conventional wings have minimum values of CD,Pr at CL values near 0.