Page 250 - Wind Energy Handbook

224 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

350 0.035

300 0.03

250 0.025

Mass per unit length (kg/m) 200 0.02 Second moment of area (m 4 )

0.015
150

100 0.01
Mass per unit length
Second moment
50 0.005
of area

0 0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Radius (m)
Figure 5.2(b) Blade ‘TR’ Mass and Stiffness Distributions

Figure 5.3. The first mode shape for a blade of constant cross section (i.e., a uniform
cantilever) is also shown for comparison purposes, and it is evident that the high
stiffness of the inboard portion of the tapered blade results in dramatically reduced
deflections there as a proportion of tip deflection. For a fibreglass blade, typical
2
values of the Young’s modulus and material density would be 40 000 N=mm and
3
1:7 Tonnes=m respectively, resulting in a first mode natural frequency of 1.65 Hz,
and a second mode natural frequency of 5.72 Hz.
Values of the other parameters assumed are:
Blade height, z 35 m
50 year return 10 min mean wind 45 m=s
speed at blade height, U
Eurocode 1 Terrain Category I (Roughness length, z o ¼ 0:01 m)
Turbulence intensity, 0.1225
I(z) ¼ 1=ln(z=z 0 )

The corresponding integral length scale for longitudinal turbulence is 227 m accord-
ing to Eurocode 1 (1997).