forward flight from harmonic flapping motion
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|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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