When a bird flaps its wings it generates thrust force which keeps it airborne, but how does this actually work? And how hard and how fast should they flap? As with most things the answer is not quite as simple as first thought… One possible explanation can be found in fluid dynamics, as Jun Zhang explained recently in his commentary article published in JFM discussing the work of Andersen et al. (2017).

Zhang compares the pattern of air left behind by a flapping wing to the footprints of animals – it gives a signature that tells us something about the animal that made it. In this instance, however, rather than trying to identify the bird, fluid dynamicists can use the air pattern to determine how the birds wing was moving.

The pattern of air left behind as an object moves through a fluid is called a wake. The most classical example is that of a stationary object sitting in a moving fluid. The fluid hits the object at the front and separates into two flows around the top and bottom, producing a pair of spiralling vortices which then separate away behind the object. Such a phenomenon is called a von Karman vortex street (a).

A slowly-flapping wing will produce a standard von Karman vortex street wake. However, by increasing the flapping speed the vortex street begins to look different. An increase in flight speed can be achieved by increasing the frequency of flapping or by increasing the amplitude of each flap. At higher speeds, the vortices generated at the end of the wing no longer spiral together in pairs but behave as a series of puffs of air which each generate a small amount of thrust. Such a feature is often called an inverted von Karman wake (b) and the thrust generated is used by the bird to aid flight.

The key question that Andersen et al. looked to address was to identify why the changes in the wake structure occur with an increase in flapping speed. They identified two main flapping methods that each left behind a different wake: pitching (c) and heaving (d). In the case of pitching the wing is aligned with the wind and pivots about the front edge. In the heaving case, the entire wing is moving up and down with no pivot.

For flight to be achieved the bird must cross what is known as the drag-thrust boundary: the flapping wing must create enough thrust to overcome the drag from the wind in order to stay airborne. The authors found that the change in the wake structure occurred as a result of the transition from drag to thrust. For example, a von Karman wake is always a drag wake, while a thrust wake is most likely an inverted von Karman wake (see Zhang (2017) for the fine details).

The authors also looked at both numerical simulations and experiments of a flapping wing and found that in general a pitching wing needs to flap 75% faster than a heaving wing to cross the drag-thrust boundary. This does not necessarily mean that the heaving wing is the best option for bird flight, however, as energy considerations need to be looked at; an area that Zhang identifies as the next step forward in the study of bird flight.

The following paper is freely available for 2 weeks from the date of this post:
A. Andersen , T. Bohr , T. Schnipper  & J. H. Walther (2017). Wake structure and thrust generation of a flapping foil in two-dimensional flow. J. Fluid Mech. 812, R4.

The following Focus on Fluids paper is freely accessible:
Zhang, J. (2017). Footprints of a flapping wing. J. Fluid Mech., 818, 1-4.