Calculation of Wind Energy and Wind Power

basic calculation that needs to be done before calculating more detail when designing wind tubines is to calculate the power requirements and power that can be generated from wind turbine currently in design, some things that need to be considered in the calculation of wind power is
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)

picture above shows the direction and also a component of the wind turbine through which the wind well or not,

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.


However, there’s no way to harvest ALL of this available energy and turn it into electricity. In 1919 a gentleman named Betz calculated that there’s a limit to how much power a turbine blade can extract from the wind. Beyond the Betz Limit of 59.26% energy extraction, more and more air tends to go around the turbine rather than through it, with air pooling up in front. So 59.26% is the absolute maximum that can be extracted from the available power.
Simply put, if you capture 100% of the energy available in the wind, you stop the wind.  Obviously, the wind will stop flowing through such a turbine.  The opposite of that is that if you don't capture any energy in the wind, you don't need a turbine.  The wind is able to flow around any major obstruction.  The Betz limit says that essentially, if you capture 59.6% of the energy in the wind, that is the best compromise between stopping the air and forcing it to go around your machine.  You need to maintain the flow of air, that's the compromise any wind machine must make whether it is a horizontal axis (traditional style turbine) or vertical axis turbine, with many blades or few, or any such combination.  It's covered by the Betz limit.

More Detail in PDF Tutorial also available from Oklahoma University just Download Here

The design of blades attached with the rotor also contributes towards an effective wind turbine design. Apart from the shape and weight of these blades, it is also important to consider the material used for manufacturing them. As far as number of blades is concerned, two or three-blade wind turbines are the most popular ones in the industry.