The power required for flight in any flying animal is a function of flight speed. The power curve that describes this function has become an icon of studies of flight mechanics and physiology because it encapsulates the accessible animal's flight performance. The mechanical or aerodynamic power curve, describing the increase in kinetic energy of the air due to the passage of the bird, is necessarily U-shaped, for aerodynamic reasons, and can be estimated adequately by lifting-line theory. Predictions from this and related models agree well with measured mechanical work in flight and with results from flow visualization experiments. The total or metabolic power curve also includes energy released by the animal as heat, and is more variable in shape. These curves may be J-shaped for smaller birds and bats, but are difficult to predict theoretically owing to uncertainty about internal physiological processes and the efficiency of the flight muscles. The limitations of some existing models aiming to predict metabolic power curves are considered. The metabolic power curve can be measured for birds or bats flying in wind tunnels at controlled speeds. Simultaneous determination in European starlings Sturnus vulgaris of oxygen uptake, total metabolic rate (using labelled isotopes), aerodynamic power output and heat released (using digital video thermography) enable power curves to be determined with confidence; flight muscle efficiency is surprisingly low (averaging 15–18 %) and increases moderately with flight speed, so that the metabolic power curve is shallower than predicted by models. Accurate knowledge of the power curve is essential since extensive predictions of flight behaviour have been based upon it. The hypothesis that the power curve may not in fact exist, in the sense that the cost of flight may not be perceived by a bird as a continuous smooth function of air speed, is advanced but has not yet formally been tested. This hypothesis is considered together with evidence from variation in flight behaviour, wingbeat kinematics and flight gait with speed. Possible constraints on flight behaviour can be modelled by the power curves: these include the effect of a maximum power output and a constraint on maximum speed determined by downstroke wingbeat geometry and the relationship between thrust and lift.

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