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

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

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

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 \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

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}