On the Aerodynamics of Birds' Tails

Adrian L. R. Thomas

Abstract

The aerodynamic properties of a bird's tail, and the forces produced by it, can be predicted by using slender lifting surface theory. The results of the model show that unlike conventional wings, which generate lift proportional to their area, the lift generated by the tail is proportional to the square of its maximum continuous span. Lift is unaffected by substantial variations in tail shape provided that the tail initially expands in width along the direction of flow. Behind the point of maximum width of the tail the flow is dominated by the wake of the forward section. Any area behind this point therefore causes only drag, not lift. The centre of lift is at the centre of area of the part of the tail in front of the point of maximum width. The moment arm of the tail, about its apex, is therefore more than twice the moment arm of a conventional wing about its leading edge. The drag of the tail is a combination of induced drag proportional to lift, and profile drag proportional to surface area. Induced drag can be halved by drooping the outer tail feathers to generate leading edge suction. This may be used for control, particularly in slow flight when both wings and tail are generating maximum lift. The slender lifting surface model is very accurate at angles of attack below about 15$^{\circ}$. At higher angles of attack vortex formation at the leading edge can stabilize the flow over the tail and thereby generate increased lift by a detached vortex mechanism. Asymmetry in the orientation of the leading edges with relation to the freestream (either in roll, yaw or caused by asymmetry in the planform) is amplified in the flow field and leads to large rolling and yawing forces that could be used for control in turning manoeuvres. The slender lifting surface model can be used to examine the effect of variations in tail shape and tail spread on the aerodynamic performance of the tail. A forked tail that has a triangular planform when spread to just over 120$^{\circ}$ gives the best aerodynamic performance and this may be close to a universal optimum, in terms of aerodynamic efficiency, for a means to control pitch and yaw. However, natural selection may act to optimise the performance of the tail when it is not widely spread. The tail is normally only widely spread during manoeuvres, or at low speeds, selection may act to improve the efficiency of the tail when it is spread to only a relatively narrow angle - for example to maximize the bird's overall lift to drag ratio - the optimum shape at any angle of spread is that which gives a straight trailing edge to the tail. This will always give a slightly forked planform, but fork depth will depend on how widely the tail is spread when selection acts, and this depends on the criteria for optimization under natural selection. A forked tail is more sensitive to changes in angle of attack and angle of spread, than other tail types. Forked tails are more susceptible to damage than other tail morphologies, and suffer a greater loss of performance following damage. Forked tails also confer less inherent stability than any other type of tail. Aerodynamic performance may not be an important optimization criterion for birds that fly in a cluttered environment, or do not fly very much. Natural selection, under these conditions, may favour tails of other shapes. The aerodynamic costs of sexually selected elongated tails can be predicted from the model. These predictions can be used to distinguish between the various models for the evolution of elongated tails. Elongated graduated tails and pintails could have evolved either through a Fisherian or Handicap mechanism. The evolution of long forked tails can be initially favoured by natural selection, the pattern of feather elongation seen in sexually selected forked tails is predicted by the Fisher hypothesis (Fisher 1930) but not by any of the other theories of sexual selection.