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
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