How much power can a small wind turbine produce?
Warning: a little bit of math follows – not to hard, bear with us. We will give examples for 2 small turbines, one with 2 foot blades and one with 4 foot blades.
Power AVAILABLE in the wind = .5 x air density x swept area x (wind velocity cubed)
Air density = 1.23 kg per cubic meter at sea level. Swept area = pi x r squared. Our 2 foot blades = 0.609m, 4 ft = 1.219m. 10 mph = 4.4704 m/s, 20 mph = 8.9408 m/s.
How much power is in the wind: 2 ft blade, 10 mph winds = .5 x 1.23 x 3.14×0.609squared x4.4704 cubed
= .5 x 1.23 x 1.159 x 89.338 = 63.7 watts
With 4 foot blades and 10 mph winds = .5 x 1.23 x 4.666 x 89.338 = 256 watts
With 4 foot blades and 20 mph winds = .5 x 1.23 x 4.666 x 714.708 = 2051 watts
That’s the MAXIMUM power in the wind. However, it’s impossible to harvest ALL the power. The Betz Limit tells us that the maximum percentage of power we can harvest from the wind is 59.26%.
Thus our maximum power from these turbines would be:
2 ft blades, 10 mph wind = 37.7 watts
4 ft blades, 10 mph wind = 152 watts
4 ft blades, 20 mph wind = 1,215 watts
Keep these numbers in mind when a sales person starts to tell you their small wind turbine will meet all your needs….
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Filed under: Wind Turbines