Wind Energy - Physics

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

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

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

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=\dot{E}=\frac{1}{2}\dot{m}v^2=\frac{1}{2}\rho A v^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.

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)

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 10^-12} 10^-12= p pico = 1/1000,000,000,000 10 -9 = n nano = 1/1000,000,000 10 -6 = µ micro = 1/1000,000 10 -3 = m milli = 1/1000 10 3 = k kilo = 1,000 = thousands 10 6 = M mega = 1,000,000 = millions 10 9 = G giga = 1,000,000,000 10 12 = T tera = 1,000,000,000,000 10 15 = P peta = 1,000,000,000,000,000