Environmental Engineering Reference
In-Depth Information
Multiple Blades and Coning
For an idealized rotor with
B
blades, we assume again that q
R
=
q
T
=
p/ 2 and modify
Equation (9-18a) as follows:
|
E
R
,
S
|
I
= |
E
WT
,
D
|
B
E
lw
lz
sin(f
R
)
(9-20a)
B
i
=1
sinc
p
l
l
p
i
sin(W
t
)
i
B
E
=
(9-20b)
where
|
E
R, S
|
I
= idealized amplitude of the scattered signal field at the receiver (mV/m)
B
E
= effective number of blades, £
B
i
= blade index number, from 1 to
B
For a two-bladed rotor, blade 1 is placed in the horizontal, specular position as before, for
maximum scattering. The azimuthal angles f
R
and f
T
of blade 2 will then differ from
those of blade 1 by twice the coning angle, so that
2p
l
l
B
E
= 1 +
sinc
sin(2 q) cos(f
RT
/2)
(9-20c)
where q = coning angle between the blade axis and the plane of revolution (rad)
In an idealized three-bladed rotor, blades 1 and 2 are placed at W
t
=
p
/
6
and W
t =
5p
/
6
and
are assumed to be in a specular position with negligible coning effect. Blade 3 is then in
the same position as blade 2 in the idealized two-bladed rotor. Substitution of these angles
into Equation (9-20b) shows that Equation (9-20c) also applies to a three-bladed rotor.
Signal Scattering Efficiency of a HAWT Blade
Because the dimensions
l
and
w
in Equation (9-18) are those of an ideally-flat metal
plate, we can expect that their product will be less than the
planform area
of a general
blade airfoil (
i.e.
,
its maximum projected area) with the same signal-scattering capability.
To account for this, a
scatter efficiency factor
is included in our idealized HAWT rotor
scattering model. Laboratory tests [
e.g.
,
Sengupta and Senior 1978, 1980] have shown that
l
is very nearly equal to the physical length of an airfoil, so the following equations can be
used to convert plate dimensions to blade dimensions:
lw
=
h
s
A
P
(9-21a)
l
»
L w
»
S
(
A
P
/
L
)
h
(9-21b)
where
h
S
=
signal scattering efficiency of a blade compared to a flat metallic plate
A
P
= planform area of one blade (m
2
)
L
=
length of one blade (m)
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