# Energy, Society, and the Environment/Wind Energy in Canada's Arctic

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## Useful Formulas for Wind Power

Maximum power output of a wind turbine (Pmax):

Pmax = ${\displaystyle {\frac {pV^{3}}{4}}}$  watts per m2 of swept area [1]

p = air density, kg/m3 (Air density varies based on pressure and temperature, both of which vary depending on elevation, so it needs to be adjusted to the site location.)

V = velocity of the air, m/s (Wind velocity will also need to be adjusted to the site location.)

Rotor swept area of a horizontal axis turbine:

${\displaystyle A={\frac {{\text{π}}D^{2}}{4}}}$[1]

D = rotor diameter

Approximate land area required for a single onshore wind turbine:

${\displaystyle A=(4.375D)^{2}}$[2]

D = rotor diameter

## Potential Obstacles

ICE BUILDUP[3]:

Although there is more wind available in northern climates, due to air density, they also provide their own challenges. One of these challenges is ice buildup on the wind turbines. Ice accumulation can cause multiple issues such as: errors measuring the wind speeds, loss of power, overproduction, mechanical/electrical failures, and safety issues. When choosing a site for a wind farm the icing conditions need to be measured and/or calculated in order to design an appropriate facility. The design must incorporate a way to prevent ice buildup or remove the ice enough to mitigate the unwanted effects.

For those purposes there are two different strategies:

1. Anti-icing to prevent the ice from forming.

2. De-icing to remove the ice when it has formed.

1. Patel, Mukund R. (1999). Wind and solar power systems. Boca Raton: CRC Press. ISBN 0-8493-1605-7. OCLC 40174790.
2. Jacobson, Mark Z.; Delucchi, Mark A.; Bauer, Zack A. F.; Goodman, Savannah C.; Chapman, William E.; Cameron, Mary A.; Bozonnat, Cedric; Chobadi, Liat et al. (2017-09-06). "100% Clean and Renewable Wind, Water, and Sunlight All-Sector Energy Roadmaps for 139 Countries of the World". Joule 1 (1): 108–121. doi:10.1016/j.joule.2017.07.005. ISSN 2542-4785.
3. "Anti-icing and de-icing techniques for wind turbines: Critical review". Cold Regions Science and Technology 65 (1): 88–96. 2011-01-01. doi:10.1016/j.coldregions.2010.01.005. ISSN 0165-232X.