Environmental Engineering Reference
In-Depth Information
Table 8-5. Statistical Factors,
F
s
, for Calculating Extreme Rust Magnitudes
[Frost
et al.
1978; data from Kaufmann 1977]
Ref. wind
speed,
U
r
(m/s)
Standard
deviations
above mean
Elevation,
z
(m)
10
20
40
80
160
300
5
1
1.19
1.25
1.31
1.37
1.43
1.49
2
1.37
1.52
1.68
1.85
2.04
2.24
3
1.64
1.88
2.16
2.52
2.91
3.32
10
1
1.37
1.40
1.45
1.48
1.53
1.57
2
1.48
1.56
1.64
1.73
1.83
1.93
3
1.60
1.73
1.87
2.01
2.17
2.34
15
1
1.07
1.09
1.12
1.14
1.16
1.19
2
1.15
1.20
1.25
1.30
1.36
1.41
3
1.23
1.31
1.39
1.48
1.57
1.67
25
1
1.05
1.06
1.07
1.09
1.11
1.12
2
1.11
1.15
1.20
1.24
1.29
1.33
3
1.17
1.23
1.29
1.36
1.43
1.49
Discrete Gusts for Fatigue Analysis
The gust magnitudes described in Equation (8-23) are based on statistics of hourly peak
wind speeds. In this sense they are expected to be extreme values and most useful for the
analysis of ultimate loads. For fatigue analysis, however, one is interested in smaller but
more numerous gusts which occur routinely throughout the life of the structure. Analysis
of gust fatigue loadings on the NASA/Boeing 2.5-MW Mod-2 HAWT was performed with
what has been termed the
NASA Lewis gust model
[Spera and Richards 1977, Powell and
Connell 1980]. In this model, fatigue gust amplitudes are determined by first computing
the wind turbulence intensity at a given elevation and steady wind speed for a given wind
turbine by means of the following equation:
n
max
ò
s
0,
x
(
z
,
U
) =
f
x
(
z
,
U
,
n
)
dn
(8-24)
n
min
where the frequency limits,
n
min
and
n
max
, are obtained from known or assumed dynamic
response characteristics of the turbine being analyzed.
The turbulence of the wind is then assumed to consist of a set of discrete gusts with
Gaussian random amplitudes
but with the deterministic shape given by Equation 8-20.
Thus, the population of gust magnitudes, D
u
, has a
normal distribution
based on s
0
,x
in this
model. To complete this definition of the set of discrete gusts, a duration must be specified,
and this is selected as follows: Let t
0
(D
u
) be the most probable period of a gust with
magnitude D
u
, determined from the data in Table 8-4. Then,
Search WWH ::
Custom Search