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The wind imparts a torque on the wind turbine, thrust is a necessary by-product of torque. Newtonian physics dictates that for every action there is an equal and opposite reaction. If the wind imparts torque on the blades, then the blades must be imparting torque on the wind.
According to Betz's law, no wind turbine of any mechanism can capture more than 16/27 (59.3%) of the kinetic energy in wind. The factor 16/27 (0.593) is known as Betz's coefficient. Practical utility-scale wind turbines achieve at peak 75–80% of the Betz limit. [2] [3] The Betz limit is based on an open-disk actuator.
When rotor power or torque coefficient is assumed constant, the weighing function is: = and the corresponding weighted solidity ratio is known as the power or torque-weighted solidity ratio. This solidity ratio is analogous to the activity factor used in propeller design and is also used in wind turbine analysis.
Whereas the streamtube area is reduced by a propeller, it is expanded by a wind turbine. For either application, a highly simplified but useful approximation is the Rankine–Froude "momentum" or "actuator disk" model (1865, [1] 1889 [2]). This article explains the application of the "Betz limit" to the efficiency of a ground-based wind turbine.
The instantaneous hub torque is found by summing all the torques from all the blades of the wind turbine at any instant in time. Consider an bladed wind turbine. Each blade is separated angularly from a neighboring blade by / degrees. That is, for a 3-bladed wind turbine, the blades are 120 degrees apart.
A wind turbine with a variable rotor speed is called a variable-speed wind turbine. Whilst this does mean that the wind turbine operates at or close to C p max for a range of wind speeds, the frequency of the AC voltage generator will not be constant. This can be seen in the equation =,
If torque is in newton-metres and rotational speed in revolutions per second, the above equation gives power in newton-metres per second or watts. If Imperial units are used, and if torque is in pounds-force feet and rotational speed in revolutions per minute, the above equation gives power in foot pounds-force per minute.
P is power; A device which converts the translational energy of the fluid into rotational energy of the axis or vice versa is called a Rankine disk actuator. The real life implementations of such devices include marine and aviation propellers, windmills, helicopter rotors, centrifugal pumps, wind turbines, turbochargers and chemical agitators.