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forward flight from harmonic flapping motion
(click on images below for larger views)
From our daily experience (and movies), we see that birds fly with apparent ease. They seem to flap their wings effortlessly to realize forward flight. During their flight, the wings appear to be only moving up and down as a somewhat rigid plate; very minor maneuvers are made to help this locomotion.

This observation naturally leads to the following question: can a rigid wing that is flapped up and down spontaneously generate lateral thrust? If the answer is "yes", is there a threshold that one has to overcome before such thrust is produced?

Bearing these questions in mind, we performed the following experiment. A rigid rectangular, stainless steel plate ---- a symmetric wing ---- is mounted onto a shaft that drives the plate up and down in a sinusoidal fashion. The wing and the shaft are attached through two low friction ball bearings --- the wing is allowed to freely-rotate. It is apparent that the wing's motion depends entirely on the interaction between the flapped plate and the fluid that surrounds it. We choose a rotational geometry to allow infinite length of "runway" that accommodates any possible instability. (A design with linear setting for this experiment would otherwise provide a limited space for a "forward flight" to reach a steady state.)

Indeed, somewhat surprisingly, the symmetric wing spontaneously set off a rotational motion from a stationary state, when a flapping frequency or Reynolds number is exceeded. It quickly reaches a steady-speed state once a flapping frequency is chosen. Figure 2 below shows the relation between the flapping frequency and its rotational speed, in the form of their corresponding Reynolds numbers. To find out the full details about this work, please read article "Symmetry breaking leads to forward flight" that is published in Journal of Fluid Mechanics Vol. 506, P. 147, 2004 and "On unidirectional flight of a free flapping wing" 18, 014102, 2006 (most recent works are listed under "publications"). As one can imagine, that there are still many open questions about flight locomotion that remain to be answered. Among those, for example, we are currently investigating the optimal flapping amplitude involved in a forward flapping flight.
Figure 1: The experimental set up of the flapping wing in a rotational geometry. The shaft is driven up and down in a simple harmonic motion. A flat, rigid, rectangular, stainless steel plate is mounted to the shaft that can freely rotate in the horizontal plane (no external force is applied onto it, in the horizontal plane). The rotational motion of the wing depends entirely on the interaction between the wing and the surrounding fluids.
Figure 2: The relationship between the flapping frequency and the rotational speed. The bifurcation that leads to the instability appears to be a sub-critical one. It is possibly due to the finite friction at the shaft.
Figure 3. Flow visualization of the flow structure around the flapping wing. When the flapping frequency is low (Reynolds number small), no vortex shedding is observed; fluid eddies stay attached to the flapping wing (both photos at the top). At a higher Reynolds number, when the wing starts to produce thrust, an inverted von Karman vortex street is seen trialing off the flying wing (bottom).
Figure 4. The threshold for forward flight is found to be within a window of 20-50 in Reynolds number. This window is obtained using extrapolation by increasing the fluid viscosity in the tank that relatively reduces the frictional effect from the shaft. The exact threshold, however, depends on the precise nature of the bifurcation.
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