October 2000 Newsletter - Naval Postgraduate School

MICRO-AIR VEHICLE AERODYNAMICS, continued from page 42
shown in Figure 4.
Since the resultant force must be normal to the incident
flow, the resultant force vector must be tilted forward, as
shown in Figure 4, which provides both a lift component and
a thrust component. Knoller and Betz went one step further,
and they noted that if the wing was flapped (plunging it up
and down vertically in an oscillatory fashion) while the lift
force would be both positive and negative during the cycle,
averaging to zero, the thrust force would always be
non-negative, so the average thrust would be a
positive value. (For an animated demonstration of
this phenomenon, visit our online version of this
article at www.aa.nps.navy.mil/~jones/research/
unsteady/propulsion/theory/).
Prandtl’s student Birnbaum (1924) first presented a
solution for incompressible flow past flapping airfoils,
while Katzmayr (1922) in Vienna produced the first
wind tunnel measurements which conclusively showed that
an airfoil mounted in an oscillating wind stream experiences a
thrust force. In the 1940’s and 50’s Schmidt (1965) in East
Germany started to conduct systematic experiments on
flapping foil propellers which led him to the development of
the wave propeller and its demonstration on a catamaran
boat. Classical oscillatory thin airfoil theory shows that the
propulsive efficiency of a single harmonically plunging airfoil
is only about 50 percent unless the airfoil oscillates rather
slowly (which in turn requires a large airfoil in order to obtain
Figure 5. Thrust Indicative Vortex Street.
FEATURED PROJECT
Figure 4. Induced velocity
and the resultant
tilting of the normal-force
vector.
significant thrust values). Schmidt sought to overcome this
deficiency by arranging two airfoils in tandem, where the
forward foil is oscillating and the rear-ward foil is stationary.
This makes it possible to convert the vortical energy generated
by the forward foil into additional thrust rather than being
wasted. Schmidt claimed that his wave propeller achieved
efficiencies comparable to those of conventional propellers
and had the additional advantage of enabling operation in
shallow waters.
Flapping Wings Generate Vortices
It is a well known fact that a vortex is generated
whenever an airfoil changes its angle of attack.
Therefore, a flapping airfoil continuously sheds
vortices from its trailing edge. We have made extensive
studies of this vortex shedding phenomenon. Two
examples are shown in Figures 5 and 6, where the
lower image is a photograph of the water-tunnel
experiment, and the upper image is a schematic
representation of the vortices. If one measures the
time-average of the flow at some station downstream
of the trailing edge (as we did using the previously
described LDV instrumentation), one obtains the jetlike
distribution schematically shown in the upper
part of Figure 5. Hence the flapping wing generates a
jet similar to the jet produced by a conventional
propeller or jet engine.
It is interesting to note, however, that when we flap
--continued on page 44
NPS Research page 43
October 2000