Wind

P = \frac{1}{2} \rho A v^3

• P is the power in the wind
• \rho is the density of the air
• A is the cross-sectional area of the wind
• v is the speed of the wind

Air Density

Air density, \rho, depends on temperature, pressure, and altitude.

At 15C and 1 atmosphere of pressure, the density is 1.225 kg per cubic meter.

Air Pressure

Air pressure varies with exponentially with altitude

p = p_0 e^{\frac{h}{h_0}}

Fan/Cube Law

Air density

\rho = \frac{353.1}{T} \exp\left(-\frac{0.0342 z}{T}\right)

• Models the air density at an altitude z and a temperature T in Kelvin.
• Equation 7.17 in REEPS2

Height law

\frac{v}{v_0} = \left(\frac{H}{H_0}\right)^\alpha

• Models the wind speed v at a height H if you know the velocity v_0 at height H_0 and the friction coefficient \alpha.