Page 23 - Wind Energy Handbook

LIST OF SYMBOLS xxiii

ì TJ (r) normalized rigid body deflection of blade j resulting from excitation
of tower first mode
ì z mean value of variable z
í ellipsoidal co-ordinate; mean zero up-crossing frequency
Ł wind-speed direction change; random phase angle; cylindrical panel
co-ordinate; brake disc temperature
r air density
0
r (r 1 , r 2 , ô) normalized cross-correlation function between along-wind velocity
u
components as seen by points (not necessarily on same blade) at radii
0
2
r 1 and r 2 on a rotating rotor (i.e., k (r 1 , r 2 , ô)=ó )
u
u
ó blade solidity; standard deviation; stress
ó mean stress
ó M standard deviation of bending moment
standard deviation of first-mode resonant bending moment, at blade
ó M1
root for blade resonance, and at tower base for tower resonance
standard deviation of quasistatic bending moment (or bending
ó MB
moment background response)
standard deviation of hub dishing moment
ó Mh
standard deviation of teeter moment for rigidly mounted, two-bladed
ó MT
rotor
ó standard deviation of mean of blade root bending moments for two-
M
bladed rotor
ó Q1 standard deviation of generalized load with respect to first mode
ó r rotor solidity
ó u standard deviation of fluctuating component of wind in along-wind
direction
ó v standard deviation of wind speed in across-wind direction
ó w standard deviation of wind speed in vertical direction
ó x1 standard deviation of first-mode resonant displacement, referred to
blade tip for blade resonance, and to nacelle for tower resonance
ô time interval; non-dimensional time; shear stress
ı Poisson’s ratio
ø angular frequency (rad=s)
ø d demanded generator rotational speed
ø i natural frequency of ith mode (rad=s)
generator rotational speed
ø g
induction machine rotor rotational speed
ø r
induction machine stator field rotational speed
ø s
Ù rotational speed of rotor; earth’s rotational speed
î damping ratio
ł angle subtended by cylindrical plate panel
ł uu (r, r9, n) real part of normalized cross spectrum (see Appendix 1, section A1.4)
Ø blade azimuth
æ teeter angle

Subscripts
a aerodynamic