Important Mathematical Formula

1. Simple Calculation of Wind Power

The power (i.e. energy per second) in the wind flowing into a wind turbine with a certain swept area is given by inserting the mass per second calculation into the standard kinetic energy equation (above) resulting in the following vital equation:

Power = 0.5 x Swept Area x Air Density x Velocity3

 

The units of measurement are:

Power - Watts (i.e. joules/second)

Swept area - square metres

Air density - kilograms per cubic metre

Velocity - metres per second

 

     2.   Actual Energy Exerted From the Wind by the Wind Turbine

 

No turbine can capture more than 16/27 (59.3%) of the kinetic energy of the wind according
to German physicist, Albert Betz. This limit is known as the Betz Limit and has nothing to
do with inefficiencies in the generator, but how turbines actually work.Wind turbines extract energy and so slow down the wind passing through them. For a wind turbine to extract 100% of the energy it would need to stop 100% of the wind. If it did this it would then stop working. Instead it extracts enough energy to still allow the wind to continue to pass through it.

To calculate the power more accurately the Betz Limit must be taken into consideration.

Power = 0.5 x Swept Area x Air Density x Velocity3 x Cp

 

Where Cp is the power coefficient of the wind turbine.