Page 252 - Wind Energy Handbook

226 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

ó y1 ó u ð p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (Equation [N/A]
¼ 2 p ffiffiffiffiffiffi R u (n 1 ) K Sx (n 1 ) (5.6))
y 1 U 2ä
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffi
¼ 2 3 0:1225 3 9:935 3 0:0339 3 0:426
¼ 2 3 0:1225 3 9:935 3 0:184 3 0:652
¼ 2 3 0:1225 3 1:192 0.292
Root moment factor, º M1 0.579 (Equation [N/A]
(5.8))
Ratio of standard deviation of resonant root
moment to mean value,
0.169 (Equation [0.338]
ó M1 ó x1
¼ º M1 (5.7))
M x 1
Size reduction factor for quasistatic or background 0.926 (Equation [0.78]
(A5.40))
response, K SMB
Ratio of standard deviation of quasistatic root
moment response to mean value,
p ffiffiffiffiffiffiffiffiffiffiffi
ó MB ó u (Equation
¼ 2 K SMB ¼ 2 3 0:1225 3 0:962 0.236 [0.216]
M U (5.9))
Ratio of standard deviation of total root moment
response to mean value,
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2
ó M ó MB ó M1 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
2
¼ þ ¼ 0:236 þ 0:169 0.290 [0.402]
M M M
Zero up-crossing frequency of quasistatic response, 0.41 Hz (Equation [N/A]
n 0 (A5.57))
Zero up-crossing frequency of total root moment 1.02 Hz (Equation [N/A]
response, í (A5.54))
Peak factor, g, based on í 3.74 (Equation [3.9]
(5.12))
Ratio of extreme moment to mean value,

M max ó M
¼ 1 þ g ¼ 1 þ 3:74(0:290) 2.087 (Equation [2.57]
M M
(5.13))
Peak factor, g 0 , based on n 0 3.49 [3.5]
Ratio of quasistatic component of extreme moment
to mean value

ó MB (Equation
¼ 1 þ g 0 ¼ 1 þ 3:49(0:236) 1.823 [1.76]
M (5.15))
Dynamic factor, Q D ¼ 2:087=1:823 1.145 (Equation [1.46]
(5.17))
It is apparent that the DS 472 method yields a significantly larger value of the
extreme root bending moment. However, the DS 472 ratio of extreme to mean
bending moment is intended to apply at all points along the blade, so a conservative
value at the root is inescapable, as is shown in the next section which examines the
variation of bending moment along the blade.