Environmental Engineering Reference
In-Depth Information
The coordinate transformation that takes vector components from the fixed
X-Y-Z
system to the rotating
x
p
-y
p
-z
p
coordinates of the undeformed blade is as follows:
x
p
y
p
z
p
a
11
a
12
a
13
é
ç
ë
é
ç
ë
é
ç
ë
X
Y
Z
(11-1)
=
a
21
a
22
a
23
=
a
31
a
32
a
33
where
a
11
=
c
q
p
c
y + b
0
s
q
p
s
y + f
s
q
p
a
12
=
c
q
p
c
yf -
s
q
p
+ c
c
q
p
s
y
a
13
= - c
s
q
p
-
c
q
p
s
y + b
0
s
q
p
c
y
a
21
=
s
q
p
c
y - b
0
c
q
p
s
y - f
c
q
p
a
22
=
s
q
p
c
yf +
c
q
p
+ c
s
q
p
s
y
a
23
= c
c
q
p
-
s
q
p
s
y - b
0
c
q
p
c
y
a
31
=
s
y
a
32
= f
s
y + b
0
- c
c
y
a
31
=
c
y
c
q
p
= cos q
p
c
y = cos y
s
q
p
= sin q
p
s
y = siny
This transformation has been linearized by assuming a small yaw angle f, a small tilt
angle c, and a small coning angle b
0
. The angle of the principal axis, q
p
,
may be large.
Of course, the blade azimuth angle, y,
can vary from 0 to 2p
radians. The inverse trans-
formation taking the
x
p
-y
p
-z
p
components into the
X-Y-Z
system is given by the transpose
of the 3x3 matrix in Equation (11-1). The blade position for y = 0 is straight up.
Assuming small deformations, the transformation for obtaining h-z-x components is
é
ê
ë
h
z
x
é
ê
ë
1
0
0
é
ê
ë
x
p
y
p
z
p
(11-2)
=
0
1
-
v
0
v
1
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