Page 20 - Wind Energy Handbook

xx LIST OF SYMBOLS

Q L loss torque
m
Q ( ) associated Legrendre polynomial of the second kind
n
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
2
R u (n) normalized power spectral density, n:S u (n)=ó , of longitudinal wind-
u
speed fluctuations, u, at a fixed 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
separation between two points measured in the along-wind direction
s 1
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
0
S (n) single-sided power spectrum of longitudinal wind-speed fluctuations,
u
u, as seen by a point on a rotating blade (also known as rotationally
sampled spectrum)
0
S (r 1 , r 2 , n) cross spectrum of longitudinal wind-speed fluctuations, u, as seen by
u
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 direction –
typically taken over a period of 10 min or 1 h
U ave annual average wind speed at hub height