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# Why Elasticity is The Key To Flapping Flight

The first detailed measurements of flapping wings bending in flight should help aerodynamicists build more efficient bird-like flyers
March 2, 2010

Flap your arms for a while and you’ll soon notice that the constant cycle of acceleration and deceleration requires and even wastes huge amounts of energy. And yet for birds, wing flapping is a highly efficient means of propulsion. A questions that still puzzles aerodynamicists is how birds are able to minimise the energy costs involved in flight while generating useful aerodynamic forces.

Engineers have long realised that the elasticity of a flapping wing is part of the answer but have little more than hand-waving arguments to explain why. The thinking is that the wing stores elastic potential energy as it bends and later releases it in a favourable part of the flapping cycle. But the absence of good experimental evidence to quantify this process means that the understanding is still sketchy.

One problem is the difficulty of studying the complex interaction between flapping machines and air. Various experiments have measured the forces that a wing experiences as it flaps in the airflow generated in a wind tunnel. But this is a highly artificial situation in which the movement of air is entirely divorced from the flapping motion of the wing. It seems clear that in real flight, the nature of the interaction between the wing and the air is crucial and yet nobody has investigated this in detail.

Until today. Benjamin Thiria and Ramiro Godoy-Diana at Université Denis Diderot in Paris built a self-propelled flapping wing and studied the forces at work as it moves through the air and how this deforms the wing, which is attached to a “merry-go-round” so it goes round in circles as it flaps (see above).

The results provide an important insight into the mechanics of flapping flight. They say: “the effect of wing flexibility on the efficiency of flapping flyers can be thought of as a two-step process: a solid mechanics problem, where the balance between inertial and elastic forces determines the instantaneous shape of the flexible wings, followed by a fluid dynamics problem, where the boundary conditions set by the previous step govern the distribution of aerodynamic forces.”

Consequently, the ratio of the inertial forces deforming the wing to the elastic forces restoring its shape is an important structural parameter. They call this ratio the elasto-inertial number.

Understanding this ratio, which may change in different parts of a wing, could turn out to be a crucial part of the puzzle for engineers attempting to design and build better flapping flyers: the take home point is that the flexibility of the wings is important.

It also has important implications for the efficiency of flight. Thiria and Godoy-Diana say: “Our measurements show that the elastic nature of the wings can lead not only to a substantial reduction of the consumed power, but also to an increment of the propulsive force.” Which finally confirms the engineers’ suspicions about the storage and release of elastic energy.

Ref: arxiv.org/abs/1002.4890: Bending to fly

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