Maximum Power of A Drag Based Wind Turbine
Equation (1) will be the starting point in this derivation. Equation (CD) is used to define the force, and equation (RelativeSpeed) is used for the relative speed. These substitutions give the following formula for power.
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(DragPower)
The formulas (CP) and (SpeedRatio) are applied to express (DragPower) in nondimensional form:
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(DragCP)
It can be shown through calculus that equation (DragCP) achieves a maximum at . By inspection one can see that equation (DragPower) will achieve larger values for . In these circumstances, the scalar product in equation (1) makes the result negative. Thus, one can conclude that the maximum power is given by:
Experimentally it has been determined that a large is 1.2, thus the maximum is approximately 0.1778.
Read more about this topic: Wind Turbine Aerodynamics
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