Wind Energy - Physics

Wind Power

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

 $P={\frac {1}{2}}\rho Av^{3}$

It varies proportional to air density $\rho$, 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.