Introduction to Modern Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 72

V Y = r W

(2-11c)

F X = L cos f + D sin f

(2-11d)

F Y = L sin f - D cosf (2-11e)

L = 0.5r V R c C L (a)

(2-11f )

D = 0.5r V R c C D ( )

a

(2-11g)

where
V R = relative airspeed (m/s)
V X = steady axial airspeed; wind speed at plane of rotation (m/s)
V Y = airfoil tangential speed (m/s)
a = wind speed axial induction (retardation) factor
U = free-stream wind speed (m/s)
r = radial distance from rotor axis to station (m)
W = rotor shaft speed (rad/s)
F X = axial airload intensity (N/m)
F Y = tangential airload intensity (N/m)
L = lift force intensity (N/m)
D = drag force intensity (N/m)
f = relative wind inlow angle; measured clockwise from plane of rotation to local
relative airspeed vector (deg)
r = air density (kg/m 3 )
c = chordline length (m)
C L = airfoil lift coeficient; function of angle of attack
C D = airfoil drag coeficient; function of angle of attack
a = angle of attack; angle from relative airspeed vector to chordline (deg)

The term intensity designates forces and loads per unit length along the blade axis. Rotor
shaft thrust and torque are calculated by integrating the effects of the relevant airload intensi-
ties over the lengths of all blades, as follows:

R

T = B

ò

F X dr

(2-12a)

R 0

R

Q = B

ò

F Y rdr

(2-12b)

R 0

where
T = rotor shaft thrust (N)
Q = rotor shaft torque (m-N)
B = number of rotor blades
R = rotor tip radius (m)
R 0 = rotor hub radius; inner end of active airfoils (m)