# Calculation of Wind Power

# Calculation Of Wind Power

## Calculate the power of the wind hitting your wind turbine generator

wind | educationThere 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)!

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 Velocity**

^{2}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:

**Mass/sec (kg/s) = Velocity (m/s) x Area (m**

^{2}) x Density (kg/m^{3})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 Velocity**

^{3}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 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.

Article Last Modified: 23:20, 24th Sep 2014