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The theory of animal flight

In steady forward flight the forces acting on a flying animal are in equilibrium, which means there is no net force causing it to accelerate. The wings have to generate an aerodynamic force that counteracts the pull of gravity and the drag that tends to decelerate the animal. We usually separate this force into components that are aligned with the flight path (Drag and Thrust) and those that act perpendicular to the flight path (Lift). In gliding flight the analysis is simple with Lift (L) and Drag (D) acting perpendicular and parallel with the glide path, and together L and D balance the weight. Since the wings are not flapping they do not generate any thrust, which is the reason a gliding animal looses height at a steady rate.

A bat in flight

In flapping flight the complicated movement of the wings produce both Lift and Thrust because the aerodynamic force vector is tilted upward and forward during the downstroke. The overall drag during flapping flight can be divided into three main components, induced (Dind), profile (Dpro) and parasite (Dpar) drag. Dindis an inherent side effect of lift production: oncoming air is deflected downwards and in the process the air loses some of its momentum along the direction of the flight path. The effect is often illustrated as the downwash rotating the local flow vector, thereby also effectively tilting the lift vector backwards (hence causing drag). This component decreases with increasing forward flight speed (V). Dpro is caused by the interaction between the air and the surface of the wing and this component increases with increasing V. Dpar is the drag generated by the non-lifting surfaces of the animal (i.e. mainly the body) and increases with V. By multiplying the drag with flight speed we obtain the mechanical power required to fly, P = DV, which plotted against flight speed is known as the “power curve”. This is an important result used in many studies of animal flight, not least since it predicts certain “optimal flight speeds” that animals are expected to fly at depending on their ecological context. For example, the minimum power speed (Vmp) is associated with minimum rate of energy consumption, while the maximum range speed (Vmr) is associated with minimum cost to cover a distance (such as of interest during migratory flights).

Frontal view of a common swift in flight

Gliding flight performance can be described by the glide polar, which is a plot of forward speed versus sink rate. Also this curve can be used to calculate how birds should adjust their gliding flight speeds according to different requirements on performance.

Research carried out in the Lund University wind tunnel is partly designed to test and improve on the general fight mechanical theory of animal flight.

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A graph showing the U shaped power curve
A conceptual power curve of animal flight showing how the power requirement varies over the flight speed range.