Environmental Engineering Reference
In-Depth Information
dA
h
=
1
2
r
cV
rel
[
C
L
(a)
V
z
-
C
D
(a)
V
h
]
d
x
(11-21a)
dA
z
=
1
2
r
cV
rel
[
C
L
(a)
V
h
+
C
D
(a)
V
z
]
d
x
(11-21b)
a = q
h
- q
t
(11-21c)
q
h
= arctan(
V
z
/
V
h
)
(11-21d)
where
dA
h
,
dA
x
=
increments of aerodynamic loading normal to and parallel to the blade
reference plane (N/m)
q
h
= angle of the relative wind from the blade reference plane (rad)
q
t
= local twist angle relative to the blade reference plane; positive twist
rotates the trailing edge downwind, as does positive pitch, q
p
(rad)
Most HAWT blades and their pitch control mechanism (if they have one) are relatively stiff
in torsion about the spanwise axis, so aerodynamic pitching moments can be neglected.
However, if a blade has pitch flexibility (
e.g.
one that is
self-twisting
for controlling power
at high wind speeds) pitching moments must be included in the loading analysis, as follows:
q
x,
a
=
1
2
r
c
2
V
rel
C
M
,
a
.
c
.
d
x -
e
e
.
a
.
cdA
z
(11-22a)
x
a
.
c
.
-
x
e
.
a.
c
e
e
.
a
.
=
(11-22b)
where
dM
z
=
increment of aerodynamic pitch moment loading (N-m)
C
M
,
a.c.
=
pitch moment coefficient about the aerodynamic center of the airfoil
e
e.a.
= relative eccentricity of the elastic center of the airfoil; positive for
elastic center between leading edge and aerodynamic center
x
a.c.
= distance from leading edge to aerodynamic center; usually
c
/4
(m)
x
e.c.
=
distance from leading edge to elastic center (m)
Inertia Loading
The distributed inertia forces and moments acting along a unit length of the blade can
be computed using Newton's laws as follows:
x + 1/2
ò
ò
ò
-
a
P
r
b
d
h
d
z
p
I
=
-
a
p
dm
=
(11-23)
x
-
12
Section
x+1/2
ò
ò
ò
q
I
=
-
r
c
x
a
P
dm
=
(
r
c
x
a
P
)r
b
d
h
d
z
(11-24a)
x
-
1/2
Section
Search WWH ::
Custom Search