Power Plant Engineering

60 POWER PLANT ENGINEERING

2.15.2 Aerofoil Design

A wind turbine changes the kinetic energy of the wind into rotary motion (or torque) that can do
work. It could power a water pump, or turn a generator.

‘Swept area’

Blade length, b, metres

P (watts) = 0.6 b Vπ^32

Fig. 2.5
Winds are the motion of air caused by uneven heating of the earth’s surface by the sun and
rotation of the earth. There is a direct relationship between the swept area of the turbine blades and the
turbine’s power output (see above). The estimated total power capacity of the winds passing over the
land is about 1e^15 W. But the total exploitable wind power is only 2e^13 W.

The theoretical wind power can be estimated as:
Power density = 0.6 k. ρ.v^3 = 0.6πb^2 v^3
where; k = Energy pattern factor (depends on type of wind)
ρ = Wind density
v = The average wind velocity.
Of the theoretical quantity energy that can be extracted from the wind, large commercial wind
turbines are unlikely to get more than 25% of this. Small and less high-tech. designs might only get
15%. But the effect of this equation is that if the wind speed doubles, the power output increases eight-
fold. So small increases in wind velocity can create large increases in power output.

The large amounts of energy that are produced at very high wind speeds means that most wind
turbines have a pre-designed maximum power output to prevent the machinery ripping itself apart.
Large wind turbines rated 150 kW and above are very complex machines. All wind turbines must
‘feather’ the blades turning then slightly out of the wind as wind speed increases in order to prevent the
turbine running away. If this didn’t happen, the centripetal force could rip the blades off. But large
turbines also have complex automatic gearboxes that keep the generator turning at the optimum speed
for power generation. Rarely does the wind blow constantly. This means that the rated output of the
turbine will never be achieved as a constant output. On average turbines produce about 30% of their
rated capacity as continuous power. So, to compare wind turbines to continuous power sources, you
have to multiply the continuous capacity by 3.33 to get the amount of wind turbine capacity required to
produce the same power output. For example, a 1,000 mW coal-fired power station would require
3,333 mW of wind capacity to provide the same average power output. As yet there is no efficient form
of large scale power storage that would allow the variations in wind turbine output to be evened out