Synopsis: Flapping in the Wind

A simple analytical model may explain what causes the lift forces that keep a flapping flag from drooping.
Synopsis figure
J. Hœpffner and Y. Naka, Phys. Rev. Lett. (2011)

In calm weather, a flag droops, but on a windy day, it’s held aloft. Making an analogy to the physics of sails, two scientists in France propose a simple model to explain how wind-driven waves in a flapping flag give rise to lift forces.

Since gravity tends to collapse a flag along its diagonal, while wind tends to stretch it out, the wavelike motion of folds in a flag is at an oblique angle to its length. Efforts to describe this special case of a deformable interface separating two moving fluids—a problem relevant to the study of insect flight and the instabilities that form between two dissimilar gasses—date back to the late 1800s.

Writing in Physical Review Letters, Jérôme Hœpffner at the Pierre and Marie Curie University in Paris and Yoshitsugu Naka at École Centrale in Lille simplify the problem of the flapping flag by mapping its geometry to that typically used to describe a sail: a right triangle, plus some additional material extending from the hypotenuse, called the “roach.” This simplification allows them to make an analytical (as opposed to numerical) study of the balance of inertial and viscous forces, which they compare to preexisting numerical simulations for the case of laminar flow and their own experiments for the case of turbulent flow.

They show that the oblique waves in a flag are what create the necessary air streams to produce lift and hold up the flag. – Jessica Thomas


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