Blade Element Theory for Wind Turbines - Small Wind Turbines: Analysis, Design, and Application - page 45

between the plane of rotation of the blade and the element's chord line. Sometimes
h P is termed the pitch angle, but, in this text, ''pitch'' will signify a constant, global
change in h P caused by alteration of the blade's attachment at the hub. Finally, / is
the inflow angle between U T and the plane of rotation. From the geometry

h P þ a ¼ / ð 3 : 8 Þ

Note very carefully that Fig. 3.2 does NOT indicate the location of the effective
velocity relative to the blade element or the line of action of the forces. In aero-
nautical applications this line of action can be very important, for example in
determining the longitudinal stability of an aircraft. For wind turbines, however, its
location has much less significance.
Figure 3.3 shows the resulting lift and drag. By definition, the lift acts at right
angles to U T and the drag acts in the direction of U T . Chapter 4 shows that the
magnitude of the lift is many times that of the drag for well-designed aerofoils. Since
the primary purpose of the forces on the blade element is to produce a torque about
the axis of rotation, or equivalently, a circumferential force in the direction of
rotation, the figure indicates the necessity of maximising the lift and minimising the
drag. Very simply, drag acts to reduce the torque produced by the lift: the key to wind
turbine performance is the ratio of the lift to drag, rather than the individual values.

Fig. 3.2 Velocities for blade
element at radius r

chord
line

U 1 = (1-a)U 0

wind
direction

U T

Ω r

φ

θ P

a ' Ω r

α

direction
of
rotation

Fig. 3.3 Lift and drag on a
blade element

DRAG

wind
direction

U T 90°

α + θ P

direction
of
rotation

LIFT