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Education and Careers

Harnessing the energy of the wind

How we extract energy from the wind

See also:
Calculating the energy in the wind
Calculations for wind energy statistics

When the wind blows over the blades of a wind turbine, their aerofoil shape makes them turn.

When air passes over an aerofoil section, it travels faster over the top of the blade than it does below. This makes the air pressure above the blade lower than it is below. Due to the unequal pressures the blade experiences a lifting force. You can see this for yourself if you hold a thin sheet of paper to your lips and blow over the top of it. This will make the paper rise more than if you blow underneath it. The opposite force is drag, due to surface friction and turbulence. Wind turbine designers use these forces generated by the wind to make the rotor blades rotate.

This rotational energy is transmitted either to an electrical generator or to a machine for mechanical work, such as a water pump. With electricity generating turbines, a gearbox is used to speed up the rotation, typically about 30 times. In mechanical turbines a shaft connects the turbine to the working machine (with or without a gear

Energy is extracted from the wind as it moves through the 'swept area' of the turbine's blades. On the down wind side of the turbine the wind moves more slowly, as some of its kinetic energy has been lost.

The amount of energy which is actually transformed by a wind turbine is:

Power delivered = Cp x swept area of wind turbine x ¹/₂ du³

where
Cp = the power efficiency of the rotor, explained below
swept area of a turbine = pi r ² (pi = 3.14) r = radius of swept area, i.e. blade length)
d = density of air
u = wind speed

CP, Power efficiency

The power efficiency of the rotor is the fraction of the total power available which the blades are able to convert. The theoretical maximum is 0.59. This is known as the Betz limit.

To get some understanding of why there is a limit to the amount of kinetic energy which can be extracted, it helps to consider the two extremes. At one extreme, a wind turbine could not extract 100% of the kinetic energy. To do this the blades would have to stop the wind completely, requiring all the swept area to be solid, like a disk. The wind would simply blow around the turbine, and the blades would not turn at all. At the other extreme, if there were no blades at all, then no kinetic energy would be extracted.

Ideally we want a wind turbine that operates at a Cp as close to the Betz limit of 0.59 as possible, over a wide range of wind speeds. The power output is then approximately proportional to u³, i.e. the cube of the wind speed. The power has to be limited at high wind speeds in order to protect the mechanical and electrical components of the machine from overloading. This is done by somehow reducing the Cp as the wind speed increases. An ideal wind turbine operates at maximum Cp until the wind speed corresponds to the rated power, then, with increasing wind speed operates at a reducing Cp, so that the power output remains constant at its rated value.