Wind Turbine Power Equation

The Wind Turbine Power Equation is one of the most important equations a beginning wind enthusiast should memorize.

HWP = 0.5 x 1.23 x SA x WV³ x 0.25

(HWP) Harvestable Wind Power (w/hr) = 0.5 x AD (air density kg/cu m) x SA (sweep area m^2) x WV^3 (wind velocity m/s) x cP (coefficient of performance Betz limit 59.26%, R^1 or Copper loss, linear power curve to cubic curve matching — 0.25 for most systems)

Conversions:

1 square foot = 0.09290304 square meters
1 mile per hour = 0.44704 meters per second
1 kilometer per hour = 0.277777778 meters per second

Equation for a HAWT with 17′ diameter blades in 10mph wind.

17′ Diameter Blades (21.07m² ), 10mph average wind (4.47m/s)

HWP = 0.5 x 1.23 x 21.07 x 89.31 x 0.25

WPH = 289Wh

Another important considertion that can have a big impact on the enery that the wind turbine produces is it position in relation to hills and valleys. The wind speeds up as it nears the top of a hill and as the wind goes down the other side it slows down considerably. It is also important to get the proper height for the wind turbine tower — 30′ higher than any object with in 300′.

Wind Speed Changes During The Year

If the wind speed increases by 25% to 5.58 or 12.5mph and you get 1191Wh which is double the Wh. If the wind speed is reducd by 25% to 3.35m/s or 7.5mph and you get 257Wh which is half the Wh. So you need to make sure when you are sizing your wind turbine that you have your wind speeds right.

The Canadian Wind Energy Atlas provides not only the avearge annual wind speed but also breaks it down into the 4 seasons. The winter months the wind will be the fastest and in the summer months it will be the slowest.

For Aylmer, Ontario Canadian Wind Energy Atlas shows an annual wind speed of 5.14m/s. During the winter the average is 6.17m/s and in the summer it is 3.92m/s. In the winter the above 17′ wind turbine will produce 1.897kWh but in the summer it will only produce 416Wh.

So when you are sizing your wind turbine make sure you look at your summer wind speed and power requirements during the summer.

Related Links:

Wind Turbine Kit — Dan from OtherPower really seems to know his stuff. This link is to their 10′ wind turbine kit. They also have sold a number of 17′ kits for around $5k. Their prices seem to be very good.