Wind Power Generation - Renewable Energy: Technology, Economics and Environment - page 303

is thus dependent on inflow angle α and angle β between the chord and the arc of
the circle.
The relation expressed by the simplified Equation (7.14) applies well to the
common profiles if inflow angles are not too elevated. Lift increase - and thus
also force F R resulting from lift and drag forces - is thus linear to the angle of at-
tack and the relative curvature f/l .

c l c l

c l c l

Stall Stall l l

v I v I

α α

c l,operation c l,operation

c l, 0 c l, 0

l l

v I v I

α α

c d,operation c d,operation

c d c d α operation α operation α α

Chord of wing Chord of wing

Curved profile Curved profile

Fig. 7.6 Lilienthal polar curves (left) and isolated profile polar curves (centre) of a sym-
metrical (right, top) and a curved profile (right, bottom) (for an explanation of symbols see
text)

Symmetrical profile Symmetrical profile

l c2 i (

= παβ πα + 2)2( 2f ≈ + l )

(7.14)

For wind energy converters, usually almost symmetrical profiles are applied, as
they normally produce low drag for low angles of attack ( α = 0°) and thus almost
no lift force. Lift and drag coefficients - and consequently lift and drag force- in-
crease with an increasing angle of attack ( α > 0°). From a certain point onwards
lift is no longer increased but disrupts eventually (so-called "Stall effect"; Fig. 7.4,
bottom, and Fig. 7.6, centre). This reveals that the flow incident on the profile
breaks down as streamlines can no longer follow the rotor blade contour (Fig. 7.4,
bottom). The lift break down involves considerable mechanical strain (i.e. strong
shaking) of the rotor - and of all other rotor components, and leads to high mate-
rial stress and may cause mechanical failures.
Fig. 7.7 on the left once more illustrates the correlation between the angle of at-
tack α and the lift and drag coefficients ( c l respectively c d ) using exact figures.
According to the given example the lift coefficient - and thus the lift force - in-
creases up to an angle of attack of approximately 13°, reaches its peak at about
15° and subsequently decreases due to flow break down on the topside of the pro-
file. The drag coefficient, by contrast, reaches its minimum at an angle of attack of
-4° and increases almost squarely to both sides.
Fig. 7.7, right shows the polar curves of the profile pertaining to Fig. 7.7, left.
The ratio of lift to drag coefficient (i.e. c d to c l ) is abbreviated as L/D ratio ε . The
more flow favourable the profile design, the higher the lift coefficient in compari-
son to the drag coefficient. The optimum angle of attack is reached at a minimum