Calculate the power of the wind hitting
There are many complicated calculations and
equations involved in understanding and constructing wind turbine generators
however the layman need not worry about most of these and should instead
ensure they remember the following vital information:
1) The power output of a wind generator is
proportional to the area swept by the rotor - i.e. double the swept area and
the power output will also double.
2) The power output of a wind generator is
proportional to the cube of the wind speed - i.e. double the wind
speed and the power output will increase by a factor of eight (2 x 2
If you are not mathematically minded you can quit
now, however it is well worth trying to understand what is going on here.
The Power of Wind
Wind is made up of moving air molecules which have
mass - though not a lot. Any moving object with mass carries kinetic energy in
an amount which is given by the equation:
Kinetic Energy = 0.5 x Mass x Velocity2
where the mass is measured in kg, the
velocity in m/s, and the energy is given in joules.
Air has a known density (around 1.23 kg/m3 at sea
level), so the mass of air hitting our wind turbine (which sweeps a known area) each second is given by the
Mass/sec (kg/s) = Velocity (m/s) x Area (m2) x
And therefore, the power (i.e. energy per
second) in the wind hitting a wind turbine with a certain swept area is
given by simply inserting the mass per second calculation into the
standard kinetic energy equation given above resulting in the following vital
Power = 0.5 x Swept Area x Air Density x Velocity3
where Power is given in Watts (i.e.
joules/second), the Swept area in square metres, the Air density in
kilograms per cubic metre, and the Velocity in metres per second.
Read World Wind Power Calculation.
The world's largest wind turbine generator has a
rotor blade diameter of 126 metres and so the rotors sweep an area of PI x
(diameter/2)2 = 12470 m2! As this is an offshore wind turbine, we know it is
situated at sea-level and so we know the air density is 1.23 kg/m3.
The turbine is rated at 5MW in 30mph (14m/s) winds,
and so putting in the known values
we get: Wind Power = 0.5 x 12,470 x 1.23 x (14 x 14
...which gives us a wind power of around 21,000,000
Watts. Why is the power of the wind (21MW) so much larger than the rated power
of the turbine generator (5MW)? Because of the Betz Limit and
inefficiencies in the system.