Wind energy is the kinetic energy of the air in motion. The kinetic energy of packet of air of mass m with velocity v is given by V: m v2 To find the mass of the packet passing through an area A perpendicular its velocity (which could be the rotor area of a turbine), we multiply its volume after time t has passed with the air density p, which gives us m=A v t p. So, we find that the total wind energy is:
E = ½ pAv3 t
Differentiating with respect to time to find the rate of increase of energy, we find that the total wind power is:
P=dE/dt = ½ pAv3
Wind power is thus proportional to the third power of the wind velocity.