Wind energy is the kinetic energy of air in motion; see also wind power.
Total wind energy flowing through an imaginary area A during the time t is:
E = ½ m v2 = ½ (A * v * t * ρ) v 2
where v is the wind speed; ρ is the air density; (A * v * t) is the volume of air passing through A (which is considered perpendicular to the direction of the wind); (A * v * t * ρ) is therefore the mass m passing per unit time. Note that ( ½ ρ * v2) is the kinetic energy of the moving air per unit volume.
Power is energy per unit time, so the wind power incident on A (e.g. equal to the rotor area of a wind turbine) is:
P = E / t = ½ A * ρ * v3
Wind power in an open air stream is thus proportional to the third power of the wind speed; the available power increases eightfold when the wind speed doubles. Wind turbines for grid electricity therefore need to be especially efficient at greater wind speeds.
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