Biomedical Engineering Reference
In-Depth Information
L
V
res
V
h
α
D
V
F
p
h
FIGURE 5.16
Schematic of thrust production by a plunging airfoil in a freestream.
oscillatory pitching does not cause dynamic stall
to occur. In addition, the largest improvements
were observed at low pitching frequencies
(0.25-0.5 per revolution).
A further extension of this concept is to use
oscillatory flapping of the rotor blades to reduce
or eliminate the torque required to rotate the
rotor. This idea is based on the Knoller-Betz effect:
When an airfoil undergoes plunging motion in an
incident freestream velocity, it can produce thrust,
i.e., a force opposite the direction of the freestream
velocity. Flyers with flapping wings utilize this
effect to generate a propulsive force in flight. The
effect is summarized in
Figure 5.16
. The airfoil is
shown plunging in an incident freestream of
velocity
V
. The plunging displace ment of the
airfoil is
h
, and the apparent velocity of the air
is
V
h
=
dh
/
dt.
The resultant velocity incident on
the airfoil is
V
res
at an angle of attack
∝.
The lift
L
and drag
D
on the airfoil are perpendicular
and parallel, respectively, to the resultant inci-
dent velocity. The thrust or propulsive force
F
p
is given by the summation of horizontal compo-
nents of
L
and
D
, i.e.,
straight biplane-like wings located at the rear of
the vehicle, flapping in opposition to each other.
This gives the two wings an oscillatory pitching
and plunging motion with respect to each other
that results in both a lift force and a thrust force.
Heiligers
et al
.
[63]
developed a single-rotor
helicopter, called the Ornicopter, with a mecha-
nism that actively flapped the blades. The flap-
ping resulted in the production of a propulsive
force on the blades that created the torque
required to spin the rotor. As a result, there was
no reaction torque on the helicopter fuselage. A
radio-controlled model helicopter was modified
to accommodate the required flapping mecha-
nisms. A series of experiments was performed
to evaluate the yaw control authority and the
optimum settings of rotational speed and flap-
ping amplitude
[64]
.
The rotor diameter was 1.5 m and the flap-
ping was phased such that opposing pairs of
blades on the four-bladed rotor flapped with the
same phase and were out of phase with their
neighboring blades. In this way, oscillatory iner-
tial forces along the rotor shaft were eliminated.
The prototype was tested at a rotational speed of
500 rpm, over a range of collective pitch settings
and flapping amplitudes. Torque measurements
indicated a range of settings over which thrust
was produced at zero rotor torque. For example,
at 4° collective pitch and a flapping angle of 8.3°,
the rotor produced 8 N of thrust at zero torque.
Yaw control was achieved by varying the
F
p
=
L
SIN
α −
D
COS
α
.
(5.6)
Therefore, based on a specific range of values
of freestream velocity and plunging velocity, it is
possible to create a positive propulsive force. This
effect forms the basis of a unique microflyer devel-
oped by Jones and Platzer
[62]
in which the lift
and propulsive force are generated by a pair of
