Biomedical Engineering Reference
In-Depth Information
1.4
The best airfoils to use for microflyers and
for propellers at the microscale are circular-arc
profiles. However, these profiles still have a
significant profile drag. Micro-helicopter
rotors of diameter around 6 in., with blades
having circular-arc airfoils and a tip Reynolds
number on the order of 20,000, have a hover-
ing efficiency of around half that of a full-scale
helicopter rotor
[24]
. By modifying the plan-
form in specific ways, sharpening the leading
edge, and moving the maximum camber loca-
tion forward of the airfoil mid-chord, the hov-
ering efficiency can be improved to around
0.65
[25, 26]
. In comparison, a modern full-
scale helicopter rotor has a hovering efficiency
of more than 0.8
[27, 28]
.
1.2
1.0
0.8
C
L
Rounded-nose
0.6
Circular arc
0.4
0.2
0
0.04
0.08
0.12
C
D
FIGURE 5.7
Comparison of drag polars of thin circular
arc airfoil, and rounded-nose airfoil at Reynolds number of
120,000. Adapted from Ref.
21
.
5.4 UNSTEADY AERODYNAMICS
IN ANIMAL FLIGHT
1.8
The wings of birds, insects, and bats reflect the
behavior of airfoils at low Reynolds numbers.
Bird wings have a thin, cambered cross-section,
which gives optimum performance at their flight
Reynolds number. This fact was recognized early
on by the pioneers of manmade flyers: Sir George
Cayley, Otto Lilienthal, and the Wright broth-
ers, who used thin, cambered airfoils for their
airplane wings. However, as the flight speed
of airplanes increased and their representative
Reynolds number increased, thin cambered
airfoils made way for the higher-performing,
thicker, rounded-nose airfoils that are ubiquitous
on airplanes today.
The wings of natural flyers continuously flap
and deform, making their aerodynamic environ-
ment highly unsteady. The wing tips trace out
complex patterns that change depending on
flight speed and maneuvers. These paths are
quite complex, and can be executed at a high
frequency; this flapping frequency depends on
the body mass and can range from around 900 Hz
for a mosquito (mass ~ 1 mg ) to around 1 Hz for
a large bird such as a pelican (mass ~ 10 kg)
[30]
.
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
-4
-2
0
2
4
6
8
10
12
14
Angle of attack, degrees
FIGURE 5.8
Lift coefficient as a function of angle of attack
for an 8% cambered circular-arc profile when the Reynolds
number
=
3.14
×
10
5
. Adapted from Ref.
17.
higher than the Reynolds number typical of
microflyers, it is still much lower than that of
full-scale aircraft and shows significant nonlinear
behavior. In general, at low Reynolds numbers,
airfoils exhibit a lower maximum lift coefficient
and a higher profile drag coefficient.
