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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.
The power coefficient, , expresses what fraction of the power in the wind is being extracted by the wind turbine. It is generally assumed to be a function of both tip-speed ratio and pitch angle. Below is a plot of the variation of the power coefficient with variations in the tip-speed ratio when the pitch is held constant:
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.
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.
The power coefficient is a representation of how much of the available power in the wind is captured by the wind turbine and can be looked up in the graph above. The torque, Q {\displaystyle Q} , on the rotor shaft is given by the ratio of the power extracted to the rotor speed:
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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.