Animal flight dynamics I. Stability in gliding flight

Stability is as essential to flying as lift itself, but previous discussions of how flying animals maintain stability have been limited in both number and scope. By developing the pitching moment equations for gliding animals and by discussing potential sources of roll and yaw stability, we consider the various sources of static stability used by gliding animals. We find that gliding animals differ markedly from aircraft in how they maintain stability. In particular, the pendulum stability provided when the centre of gravity lies below the wings is a much more important source of stability in flying animals than in most conventional aircraft. Drag-based stability also appears to be important for many gliding animals, whereas in aircraft, drag is usually kept to a minimum. One unexpected consequence of these differences is that the golden measure of static pitching stability in aircraft--the static margin--can only strictly be applied to flying animals if the equilibrium angle of attack is specified. We also derive several rules of thumb by which stable fliers can be identified. Stable fliers are expected to exhibit one or more of the following features: (1) Wings that are swept forward in slow flight. (2) Wings that are twisted down at the tips when swept back (wash-out) and twisted up at the tips when swept forwards (wash-in). (3) Additional lifting surfaces (canard, hindwings or a tail) inclined nose-up to the main wing if they lie forward of it, and nose-down if they lie behind it (longitudinal dihedral). Each of these predictions is directional--the opposite is expected to apply in unstable animals. In addition, animals with reduced stability are expected to display direct flight patterns in turbulent conditions, in contrast to the erratic flight patterns predicted for stable animals, in which large restoring forces are generated. Using these predictions, we find that flying animals possess a far higher degree of inherent stability than has generally been recognized. This conclusion is reinforced by measurements of the relative positions of the centres of gravity and lift in birds, which suggest that the wings alone may be sufficient to provide longitudinal static stability. Birds may therefore resemble tailless aircraft more closely than conventional aircraft with a tailplane.