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A formula for mechanical power is:
Power_W = (torque_N.m x 2pi x RPM) / 60
The turbine extracts power from the wind, and converts it to mechanical rotational power. A formula for power provided by the wind (not the turbine):
Power_W = 0.5 x AreaSweptByRotor_m^2 x Air Density_kg/m^3 x Velocity_m/s^3
Note that the wind velocity is very important. Doubling the speed of the wind give 8 times more power (proportional to the cube of wind speed). Halving the wind speed gives 1/8 the power. Air density is approx. 1.23 kg/m^3. The power from the turbine is less than this as it cannot be 100% efficient.
Turbines are similar to an engine starter. They have a number of brushes on the inside that make contact to the inside walls. As they spin inside a magnetic field they generate a current which is sent to a storage facility (usually batteries) to be used later.
It's mechanically connected. The rotating turbine turns the generator. usually they are on the same shaft, but they can be connected via gears.
a rotating turbine can be set up as an electrical generator. the rotating part is put in the middle of a magnetic field.
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