Page 327 - Wind Energy Handbook
P. 327
TOWER LOADING 301
speed will be augmented by inertial moments resulting from the excitation of
resonant tower oscillations by turbulence. As before, it is convenient to express this
augmentation in terms of a dynamic factor, Q D , defined as the ratio of the peak
moment over a 10 min period, including resonant excitation of the tower, to the
peak quasistatic moment over the same period. Thus
þ 1þ2Æ
1
M Max ¼ rU 2 H C f z dA:Q D (5:124)
2 e50 H
where U e50 is the 50 year return gust speed at hub height, z is height above ground,
H is the hub height, C f is the force factor (lift or drag) for the element under
consideration, Æ is the shear exponent, taken as 0.11 in IEC 61400-1, and
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
ó u ð 2
1 þ g 2 K SMB þ R u (n 1 )K Sx (n 1 )º M1
U 2ä
Q D ¼ (5:17)
ó u p ffiffiffiffiffiffiffiffiffiffiffi
1 þ g 0 2 K SMB
U
Þ
The integral sign signifies that the integral is to be undertaken over each blade
and the tower.
The derivation of Equation (5.17) is explained in Section 5.6.3 and the Appendix
in relation to a cantilevered blade. The essentially similar procedure for a tower
supporting a rotor and nacelle is as follows.
(1) Calculate the resonant size reduction factor, K Sx (n 1 ), which reflects the effect of
the lack of correlation of the wind fluctuations at the tower natural frequency
along the blades and tower. Adopting an exponential expression for the normal-
ized co-spectrum as before, Equation (A5.25) becomes:
þþ
2
exp[ Csn 1 =U]C c(r)c(r9)ì 1 (r)ì 1 (r9)dr dr9
f
K Sx (n 1 ) ¼ þ 2 (5:125)
C f c(r)ì 1 (r)dr
Þ
where the integral sign denotes integration over the blades and the tower, r
and r9 denote radius in the case of the blades and depth below the hub in the
case of the tower, s denotes the separation between the elements dr and dr9, C f
is the relevant force coefficient, c(r) denotes chord in the case of the blades and
diameter in the case of the tower, and ì 1 (r) denotes the tower first mode shape.
This expression can be considerably simplified by setting ì 1 (r) to unity for the
rotor and ignoring the tower loading contribution entirely. This is not unreason-
able, as only loading near the top of the tower is of significance, and this does
not add much to the spatial extent of the loaded area.
