Page 19 - Wind Energy Handbook

LIST OF SYMBOLS xix

K P power coefficient based on tip speed
K SMB size reduction factor accounting for the lack of correlation of wind
fluctuations over structural element or elements
K Sx (n 1 ) size reduction factor accounting for the lack of correlation of wind
fluctuations at resonant frequency over structural element or elements
K í ( ) modified Bessel function of the second kind and order í
K(÷) function determining the induced velocity normal to the plane of a
yawed rotor
L length scale for turbulence (subscripts and superscripts according to
context); lift force
L x u integral length scale for the along wind turbulence component, u,
measured in the longitudinal direction, x
m mass per unit length, integer
generalized mass with respect to the ith mode
m i
generalized mass of tower, nacelle and rotor with respect to tower
m T1
first mode
M moment; integer
M mean bending moment
teeter moment
M T
blade in-plane moment (i.e., moment causing bending in plane of
M X
rotation); tower side-to-side moment
M Y blade out-of-plane moment (i.e., moment causing bending out of
plane of rotation); tower fore-aft moment
M Z blade torsional moment; tower torsional moment
M YS low-speed shaft moment about rotating axis perpendicular to axis of
blade 1
M ZS low-speed shaft moment about rotating axis parallel to axis of blade 1
M Y N moment exerted by low-speed shaft on nacelle about (horizontal) y-
axis
M Z N moment exerted by low-speed shaft on nacelle about (vertical) z-axis
n frequency (Hz); number of fatigue loading cycles; integer
n 0 zero up-crossing frequency of quasistatic response
n 1 frequency (Hz) of 1st mode of vibration
N number of blades; number of time steps per revolution; integer
N(r) centrifugal force
N(S) number of fatigue cycles to failure at stress level S
p static pressure
P aerodynamic power; electrical real (active) power
m
P ( ) associated Legrendre polynomial of the first kind
n
q(r, t) fluctuating aerodynamic lift per unit length
Q rotor torque; electrical reactive power
aerodynamic torque
Q a
_
Q Q rate of heat flow
Q mean aerodynamic lift per unit length
Q D dynamic factor defined as ratio of extreme moment to gust quasistatic
moment
Q g load torque at generator