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Bird wings generally contain a 4-bar pantograph mechanism in the forearm that enables the wrist joint to be actuated from the elbow joint thus reducing the number of wing muscles and hence reducing the wing inertia and inertial drag. In this paper we develop a theoretical model of inertial power for flapping flight to estimate the advantage of the 4-bar pantograph mechanism by comparing the inertial power required for the case where wrist muscles are present in the forearm with the case where wrist muscles are not present in the forearm. It is difficult to predict how wrist muscles would look when there is no pantograph mechanism. Therefore a lower bound and upper bound case are defined. The lower bound case involves redistributing the elbow muscles with no increase in wing mass. The upper bound case involves replicating the biceps-triceps muscles near the wrist joint. At minimum power speed the model estimates that the 4-bar pantograph mechanism reduces the inertial power for the gull from between 6.1%-12.3% and reduces the overall power by 0.6%-1.2%. When account is taken of the tight margins involved in the design of a flying vehicle, the energy savings produced by the pantograph mechanism are significant. A ring-billed gull was chosen for the case study and an adult specimen was obtained to gather morphometric data. Lessons for the design of flapping micro air vehicles are discussed. [ABSTRACT FROM AUTHOR]

There has been an unresolved question of whether there is any significant degree of aerodynamic braking during wing deceleration in the flapping flight of birds, with direct analogies existing with flapping micro air vehicles. Some authors have assumed a complete conversion of kinetic energy into (useful) aerodynamic work during wing deceleration. Other authors have assumed no aerodynamic braking. The different assumptions have led to predictions of inertial power requirements in birds differing by a factor of 2. Our work is the first to model the aerodynamic braking forces on the wing during wing deceleration. A model has been developed that integrates the aerodynamic forces along the length of the wing and also throughout the wing beat cycle. Aring-billed gull was used in a case study and an adult specimen was used to gather morphometric data including a steady state measurement of the lift coefficient. The model estimates that there is a 50% conversion of kinetic energy into useful aerodynamic work during wing deceleration for minimum power speed. This aerodynamic braking reduces the inertial power requirement from 11.3% to 8.5% of the total power. The analysis shows that energy conversion is sensitive to wing inertia, amplitude of flapping, lift coefficient and wing length. The aerodynamic braking in flapping micro air vehicles can be maximised by maximising flap angle, maximising wing length (for a given inertia), minimising inertia and maximising lift coefficient. [ABSTRACT FROM AUTHOR]