Page 352 - Wind Energy Handbook

326 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
n ó 2 þ n ó 2
í ¼ 0 MB 1 M1 (A5:54)
ó 2 þ ó 2
MB M1
where
ð 1
2
n S u (n)K SMB (n)dn
0
n 0 ¼ ð 1 (A5:55)
S u (n)K SMB (n)dn
0
N
Substituting ł (r, r9, n) ¼ exp[ C(r r9)n=U] into the expression for K SMB (n)in
uu
the numerator of Equation (A5.55) gives
ð ð
R R
ð 1 ð 1 exp[ C(r r9)n=U]c(r)c(r9)rr9 dr dr9
2
2
n S u (n)K SMB (n)dn ¼ n S u (n) 0 0 ! 2 dn
0 0 ð R
c(r)r dr
0
(A5:56)

For high frequencies, the double integral is, in the limit, inversely proportional to
2 5=3 1
2
frequency, so the integrand n S u (n)K SMB (n) is proportional to n n n ¼ n 2=3
and the integral does not converge. Consequently it is necessary to take account of
the chordwise lack of correlation of wind fluctuation at high frequencies and, if this
is done, it is found that, in the limit, the integrand is proportional to n 5=3 for which
Ð
1
2
the integral is finite. The evaluation of the integral n S u (n)K SMB (n)dn taking
0
chordwise lack of correlation into account is a formidable task, so the use of an
approximate formula for the frequency, n 0 , is preferable, especially as the influence
of n 0 on the peak factor, g, is slight. One formula is given in Eurocode 1 (1997), but
a simpler one due to Dyrbye and Hansen (1997) for a uniform cantilever is as
follows:
U
n 0 ¼ 0:3 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (A5:57)
p
ffiffiffiffiffiffi
L x Rc
u
Here R is the blade tip radius and c is the blade chord, assumed constant. For a
tapering chord, the mean chord, c, can be substituted.

A5.8 Bending Moments at Intermediate Blade Positions

A5.8.1 Background response

Denoting the standard deviation of the quasistatic or background bending moment

fluctuations at radius r as ó MB (r ), it is apparent that