Structural Dynamic Behavior of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 618

d 2
dt r P / B

d W
dt

x r P / B + 2W x d a P (a) = a B (a) +

dt r P / B (b ) + W x (W x r P / B ) +

(11-18)

The indicated operations of Equation (11-18) must be carried out, and the results must then
be transformed to the b coordinate system and linearized. This tedious activity gives the
expressions for the acceleration components in the x p -y p -z p coordinates. For the small-
deformation theory of this analysis, there is no difference between the x p -y p -z p and h-z-x
coordinate systems with respect to structural equations. For convenience, therefore, we will
use the same h-z-x notation for the accelerations as for the relative velocities. This gives

a P , h
a P , z
a P ,x

é
ê ë

a P = (11-19a)

a P , h = - s q p ( r W 2 b 0 + 2 f W rc y + f rs y + v W 2 c q p )
- zW 2 c q p s q p - hW 2 c q p

(11-19b)

a P , z = - c q p ( r W 2 b 0 + 2 fW rc y + f rs y) - v W 2 c q p
- z W 2 s q p - hW 2 s q p c q p + v

(11-19c)

a P , x = - r W 2 − 2W vs q p (11-19d)

where
a P,h , a P,z , a P,x = components of the acceleration vector at an arbitrary point P within the
blade, in the normal, chordwise, and spanwise directions, respectively
(m/s 2 )

Aerodynamic Loading

Referring to Figure 6-1, the lift and drag forces on an airfoil section are given by

dL = 1

2 r C L c V rel d x

(11-20a)

1

2 r C D cV rel d x

(11-20b)

dD =

where

dL = increment of lift force, normal to the relative wind (N)

dD = increment of drag force, parallel to the relative wind (N)
r = air density (kg/m 3 )