Q
L
loss torque
Q
m
n
( ) associated Legrendre polynomial of the second kind
Q
1
(t) generalized load, defined in relation to a cantilever blade by Equation
(A5.13)
r radius of blade element or point on blade; correlation coefficient
between power and wind speed; radius of tubular tower
r9 radius of point on blade
r
1
, r
2
radii of points on blade or blades
R blade tip radius; ratio of minimum to maximum stress in fatigue load
cycle; electrical resistance
Re Reynold’s number
R
u
(n) normalized power spectral density, n:S
u
(n)=
2
u
, of longitudinal wind-
speed fluctuation s, u, at a fixe d point
s distance inboard from the blade tip; distance along the blade chord
from the leading edge; separation between two points; Laplace
operator; slip of induction machine
s
1
separation between two points measured in the along-wind direction
S wing area; autogyro disc area; fatigue stress range
S electrical complex (apparent) power (bold indicates a complex
quantity)
S( ) uncertainty or error band
S
jk
(n) cross spectrum of longitudinal wind-speed fluctuations, u, at points j
and k (single sided)
S
M
(n) single-sided power spectrum of bending moment
S
Q1
(n) single-sided power spectrum of generalized load
S
u
(n) single-sided power spectrum of longitudinal wind-speed fluctuations,
u, at a fixed point
S
0
u
(n) single-sided power spectrum of longitudinal wind-speed fluctuations,
u, as seen by a point on a rotating blade (also known as rotationally
sampled spectrum)
S
0
u
(r
1
, r
2
, n) cross spectrum of longitudinal wind-speed fluctuations, u, as seen by
points at radii r
1
and r
2
on a rotating blade or rotor (single sided)
S
v
(n) single- sided power spectrum of lateral wind speed fluctuations, v,ata
fixed point
S
w
(n) single-sided power spectrum of vertical wind-speed fluctuations, w,
at a fixed point
t time; gear tooth thickness at critical root section; tower wall thickness
T rotor thrust; duration of discrete gust; wind-speed averaging period
u fluctuating component of wind speed in the x-direction; induced
velocity in x-direction; in-plane plate deflection in x-direction; gear
ratio
u
friction velocity in boundary layer
U
1
free stream velocity
U, U(t) instantaneous wind speed in the along-wind direction
U mean component of wind speed in the along-wind directi on –
typically taken over a period of 10 min or 1 h
U
ave
annual average wind speed at hub height
xx LIST OF SYMBOLS