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Oracle – DBA

September 25, 2012

Posted by on 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 x 2)!

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:

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/m^{3} 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:

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:

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.

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 m^{2}! 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/m^{3}. 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.

If you are not mathematically minded you can quit now, however it is well worth trying to understand what is going on here.