Wind energy

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Wind energy is the kinetic energy of the air in motion. Total wind energy flowing through an imaginary area A during the time t is:
E = A . v . t . ρ . ½ v²,
where v is the wind velocity and ρ is the air density. The formula presented is structured in two parts: (A . v . t) is the volume of air passing through A, which is considered perpendicular to the wind velocity; (ρ . ½ v²) is the kinetic energy of the moving air per unit volume.
Total wind power is:
P = E / t = A . ρ . ½ v³
Wind power is thus proportional to the third power of the wind velocity.

History of usage by humans

The wind has been used for thousands of years as a source of energy. Sailors capture it in the sails of their ships, and weather has therefore had important historical consequences, for example, the Spanish Armada was defeated with the help of stormy weather around the British Isles. The Netherlands are famous for the use of windmills with four cloth sails. These were used for pumping water to drain polders forming agricultural land. In the UK, Norfolk borrowed this Dutch expertise to do the same, leaving distinctive features on the flat lowland landscape.

Electric energy

Theoretical power captured by a wind turbine

Total wind power could be captured only if the wind velocity is reduced to zero. In a realistic wind turbine this is impossible, as the captured air must also leave the turbine. A relation between the input and output wind velocity must be considered. Using the concept of stream tube, the maximal achievable extraction of wind power by a wind turbine is 59% of the total theoretical wind power^[1] (see: Betz' law).

Practical wind turbine power

Further insufficiencies, such as rotor blade friction and drag, gearbox losses, generator and converter losses, reduce the power delivered by a wind turbine. The basic relation that the turbine power is (approximately) proportional to the third power of velocity remains.