Environmental Engineering Reference
In-Depth Information
L
= 0.5 r
V
r
C
L
c
D
= 0.5 r
V
r
C
D
c
(5-3)
where
L
= aerodynamic lift force per unit length of airfoil (N/m)
D
= aerodynamic drag force per unit length of airfoil (N/m)
C
L
, C
D
= lift and drag coefficients, respectively; functions of airfoil shape and a
a = angle of attack
Analysis of the airfoil as a
free body
yields the power extracted as
v
U
v
U
v
U
2
(5-4)
P
= 0.5 r
U
3
A
P
C
L
-
C
D
1 +
At maximum power
v
/
U
approximately equals (2/3)
C
L
/
C
D
(
i.e.
2/3 of the
lift-to-drag ratio
).
Therefore, the maximum power coefficient for an airfoil translating at right angles to the
wind is given by
C
L
C
D
2
=
2 9
C
L
C
L
C
D
C
P
, max
1 + 4 9
(5-5)
Figure 5-4 is a comparison of lift and drag as mechanisms to extract power from the wind
which readily shows the advantages or using lilting surfaces. Equations (5-2) and (5-4) are
used to construct the curves in this figure. The aerodynamic properties are
C
L
= 1.0 and
C
D
=
0.10 for the airfoil, and
C
D
, max
= 2.0 for the drag-driven device. The airfoil has a maximum
Figure 5-4. Comparison of typical power coefficients of a translating airfoil and a
translating drag device.
The airfoil is moving at right angles to the wind direction.
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