Recently I spent some time going over ads for micro turbines, and there's lots of interesting claims out there. So before anybody parts with their hard earned cash some wind math is in order.
A case in point is an ad for a micro turbine:
"We build these wind turbines to provide 1200watts of power. They are suitable for charging 12/24/48 volt battery systems....in winds over 4-5mph (6.4-8kph or 1.7-2.2ms)...Brand new 24� (.61m) blades."
Wow, 1.2kW from a 48" (1.22m) diameter blade. Unless you live in a wind tunnel you'll never see that kind of an output.
The most energy you can extract is 59.3% of the total kinetic energy contained in the wind. Most small scale turbines operate much lower then that, while industrial turbines approach it, but still can't get there.
According to the Bertz co-efficient you would need a sustained wind of 27mph (43kph or 11.9ms) to get 1200w from a 48" (1.2m) or 4ft blade (Wind turbine diameter=8ft). To come to this number we need to use some wind math;
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First we need the swept area of the rotor;
Area = p x (blade diameter x blade diameter) / 4
Using the above ad - 3.1416 x (1.22 x 1.22) / 4 = 3.1416 x 1.4884 / 4 = 1.17m2
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Power in watts = .5 x air density x swept area x wind velocity3
Where - air density (@ sea level) = 1.23kg/m3
- swept area in m2
- velocity in meters per second
So.......... .5 x 1.23 x 1.17 x 5.5ms3 (5.5ms is my areas average wind speed)
.5 x 1.23 x 1.17 x 166.37 = 117.91 watts
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Now lets try doubling the blade area;
.5 x 1.23 x 2.34 x 5.5m/s3 = .5 x 1.23 x 2.34 x 166.37 = 239.42 watts
*Doubling the blade diameter roughly doubles the power output.
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Now lets use the original swept area and double the wind speed;
.5 x 1.23 x 1.17 x 11m/s3 = .5 x 1.23 x 1.17 x 1331 = 957.72 watts
*Doubling the wind speed roughly increases 8x the original power output. Yet we're still not at the 1200watts from the original ad.
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Using 43kph wind speeds;
.5 x 1.23 x 1.17 x 11.95m/s3 = .5 x 1.23 x 1.17 x 1706.49 = 1227.9 watts
Wind speeds like this happen very rarely in most areas of the world.
Below is a spreadsheet showing output at different wind speeds using the above 3meter (9ft) diameter wind mill.
A case in point is an ad for a micro turbine:
"We build these wind turbines to provide 1200watts of power. They are suitable for charging 12/24/48 volt battery systems....in winds over 4-5mph (6.4-8kph or 1.7-2.2ms)...Brand new 24� (.61m) blades."
Wow, 1.2kW from a 48" (1.22m) diameter blade. Unless you live in a wind tunnel you'll never see that kind of an output.
The most energy you can extract is 59.3% of the total kinetic energy contained in the wind. Most small scale turbines operate much lower then that, while industrial turbines approach it, but still can't get there.
According to the Bertz co-efficient you would need a sustained wind of 27mph (43kph or 11.9ms) to get 1200w from a 48" (1.2m) or 4ft blade (Wind turbine diameter=8ft). To come to this number we need to use some wind math;
---------------------------------------------------------------------------------------------------------
First we need the swept area of the rotor;
Area = p x (blade diameter x blade diameter) / 4
Using the above ad - 3.1416 x (1.22 x 1.22) / 4 = 3.1416 x 1.4884 / 4 = 1.17m2
---------------------------------------------------------------------------------------------------------
Power in watts = .5 x air density x swept area x wind velocity3
Where - air density (@ sea level) = 1.23kg/m3
- swept area in m2
- velocity in meters per second
So.......... .5 x 1.23 x 1.17 x 5.5ms3 (5.5ms is my areas average wind speed)
.5 x 1.23 x 1.17 x 166.37 = 117.91 watts
--------------------------------------------------------------------------------------------------------------------------
Now lets try doubling the blade area;
.5 x 1.23 x 2.34 x 5.5m/s3 = .5 x 1.23 x 2.34 x 166.37 = 239.42 watts
*Doubling the blade diameter roughly doubles the power output.
--------------------------------------------------------------------------------------------------------------------------
Now lets use the original swept area and double the wind speed;
.5 x 1.23 x 1.17 x 11m/s3 = .5 x 1.23 x 1.17 x 1331 = 957.72 watts
*Doubling the wind speed roughly increases 8x the original power output. Yet we're still not at the 1200watts from the original ad.
--------------------------------------------------------------------------------------------------------------------------
Using 43kph wind speeds;
.5 x 1.23 x 1.17 x 11.95m/s3 = .5 x 1.23 x 1.17 x 1706.49 = 1227.9 watts
Wind speeds like this happen very rarely in most areas of the world.
Below is a spreadsheet showing output at different wind speeds using the above 3meter (9ft) diameter wind mill.
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