Wind Energy - Physics

Unit abbreviations

m = metre = 3.28 ft.	HP = horsepower
s = second	J = Joule
h = hour	cal = calorie
N = Newton	toe = tonnes of oil equivalent
W = Watt	Hz = Hertz (cycles per second)

Wind Power

The power P of a wind-stream, crossing an area A with velocity v is given by

 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P=\frac{1}{2}\rho A v^3}

It varies proportional to air density Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} , to the crossed area A and to the cube of wind velocity v. 

The Power P is the kinetic energy

$E={\frac {1}{2}}mv^{2}$

of the air-mass m crossing the area A during a time interval

${\dot {m}}=A\rho {\frac {dx}{dt}}=A\rho v$.

Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation

$P={\dot {E}}={\frac {1}{2}}{\dot {m}}v^{2}={\frac {1}{2}}\rho Av^{3}$

The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power the air-mass would have to be stopped completely, leaving no space for the following air-masses.