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.
-
(DragPower)
The formulas (CP) and (SpeedRatio) are applied to express (DragPower) in nondimensional form:
-
(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
Famous quotes containing the words maximum, power, drag, based and/or wind:
“Probably the only place where a man can feel really secure is in a maximum security prison, except for the imminent threat of release.”
—Germaine Greer (b. 1939)
“O God, protect me from my friends, that they have not power over me.
Thou hast giv’n me power to protect myself from thy bitterest enemies.”
—William Blake (1757–1827)
“I know those little phrases that seem so innocuous and, once you let them in, pollute the whole of speech. Nothing is more real than nothing. They rise up out of the pit and know no rest until they drag you down into its dark.”
—Samuel Beckett (1906–1989)
“Any reductionist program has to be based on an analysis of what is to be reduced. If the analysis leaves something out, the problem will be falsely posed.”
—Thomas Nagel (b. 1938)
“If there is nothing new on the earth, still the traveler always has a resource in the skies. They are constantly turning a new page to view. The wind sets the types on this blue ground, and the inquiring may always read a new truth there.”
—Henry David Thoreau (1817–1862)