Calculate the power of the wind hitting your wind turbine generator
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 speedand the power output will increase by a factor of eight (2
x 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 following equation:
Mass/sec (kg/s)
= Velocity (m/s) x Area (m2) x Density (kg/m3)
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 equation:
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 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