THE WIND POWER BOOK
(Page 9 of 9)
Available Power = 1/2 X P X V 3 X A
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Both energy and power are proportional to the cube of the
windspeed.
If all the available wind power working against a windmill
rotor could be harvested by the moving blades, this formula
could be used directly to calculate the power extracted.
But getting such an output would require that you stop the
wind dead in its tracks and extract every last erg of its
kinetic energy. This is an impossible task. Some non-zero
windspeed must occur downstream of the blades to carry away
the incoming air, which would otherwise pile up. Under
ideal conditions, the maximum power that can be extracted
from the wind is only 59.3 percent of the power available,
or
Maximum Power =
0.593X p X V 3 X A
2
In practice, a wind machine extracts substantially less
power than this maximum. For example, the windmill rotor
itself may capture only 70% of the maximum power. Bearings
will lose another few percent to friction ...generators,
gears, and other rotating machinery can lose half of
whatever power remains. Pushrods, wires, batteries, and
monitoring devices will lose still more. The overall
"system" efficiency of the entire wind machine is the
fraction of the wind power available that is actually
delivered to a load or to a storage device:
Efficiency =
Power Delivered
Available Power
Thus, the power extracted by a particular wind machine with
system efficiency E is given by the formula
Extracted Power = 1/2 X p XV 3 X A X E
The final output of a wind machine is greatly reduced from
the power that is really available in the wind. In
practice, values of E commonly range from 0.10 to 0.50,
although higher and lower values are possible.
One more factor is needed before the formula above can be
used in your calculations . . a conversion factor, K, that
makes the answer come out in the appropriate units, whether
metric or English (see chart below).
The final formula combines everything so far presented:
Power =1/2 X p XV 3 X A X E X K
This is a very important formula ...perhaps the most
important in The Wind Power Book.
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