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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