Page 22 - Wind Energy Handbook

xxii LIST OF SYMBOLS

÷ wake skew angle: angle between the axis of the wake of a yawed rotor
and the axis of rotation of rotor
÷ M1 weighted mass ratio defined in Section 5.8.6
ä a logarithmic decrement of aerodynamic damping
ä s logarithmic decrement of structural damping
ä logarithmic decrement of combined aerodynamic and structural
damping; width of tower shadow deficit region
ä 3 angle between axis of teeter hinge and the line perpendicular to both
the rotor axis and the low-speed shaft axis
å 1 , å 2 , å 3 proportion of time in which a variable takes the maximum, mean or
minimum values in a three-level square wave
ö flow angle of resultant velocity W to rotor plane
ª yaw angle; Euler’s constant (¼ 0:5772)
load factor
ª L
partial safety factor for material fatigue strength
ª mf
partial safety factor for material ultimate strength
ª mu
ˆ blade circulation; vortex strength
ˆ( ) gamma function
ç ellipsoidal parameter; shaft tilt; one eighth of Lock number (defined in
Section 5.8.8)
j impact factor in DS 472, defined as ratio of extreme moment to the
10 min mean
k von Karman’s constant
k L (s) cross-correlation function between velocity components at points in
space a distance s apart, in the direction parallel to the line joining
them
k T (s) cross-correlation function between velocity components at points in
space a distance s apart, in the direction perpendicular to the line
joining them
k u (r, ô) auto-correlation function for along-wind velocity component at radius
r on stationary rotor
0
k (r, ô) auto-correlation function for along-wind velocity component as seen
u
by a point at radius r on a rotating rotor
k u (r 1 , r 2 , ô) cross-correlation function between along-wind velocity components
at radii r 1 and r 2 (not necessarily on same blade), for stationary rotor
0
k (r 1 , r 2 , ô) cross-correlation function between along-wind velocity components
u
as seen by points (not necessarily on same blade) at radii r 1 and r 2 on
a rotating rotor
º tip speed ratio; latitude; ratio of longitudinal to transverse buckle half
wavelengths
tangential speed of blade element at radius r divided by wind speed:
º r
local speed ratio
¸ yaw rate
ì non-dimensional radial position, r=R; viscosity; coefficient of friction
ì i (r) mode shape of ith blade mode
ì i (z) mode shape of ith tower mode
ì T (z) tower first mode shape