LIKELY OUTPUT - BETZ'S LAW

A quantitative measure of the wind energy available at any location is called the Wind Power Density (WPD) It is a calculation of the mean annual power available per square meter of swept area of a turbine, and is tabulated for different heights above ground. Calculation of wind power density includes the effect of wind velocity and air density. Color-coded maps are prepared for a particular area described, for example, as "Mean Annual Power Density at 50 Metres". In the United States, the results of the above calculation are included in an index developed by the National Renewable Energy Laboratory and referred to as "NREL CLASS". The larger the WPD calculation, the higher it is rated by class. Classes range from Class 1 (200 watts per square metre or less at 50 m altitude) to Class 7 (800 to 2000 watts per square m). Commercial wind farms generally are sited in Class 3 or higher areas, although isolated points in an otherwise Class 1 area may be practical to exploit.

By way of example, let us take 100 watts per square meter as a realistic target for SolarNavigator. Multiply the diameter of the blade: 3.142 x 1.5 x 1.5  = 7.07 m2. Multiply  x 4 (turbines) = 28.28 m2 swept area.  Multiplied by 100watts = 2.828 Kw/hr. Or, multiplied by 200w = 5.656Kw/hr for a Class 1 area. Such turbines typically weigh 60Kg each. Thus the boom and and 4 turbines and hydraulics should come in under 500Kg.

That is quite a useful amount of energy. Sufficient to operate Wind turbines are classified by the wind speed they are designed for, from class I to class IV, with A or B referring to the local turbulence.

Betz's law calculates the maximum power that can be extracted from the wind, independent of the design of a wind turbine in open flow. It was published in 1919, by the German physicist Albert Betz. The law is derived from the principles of conservation of mass and momentum of the air stream flowing through an idealized "actuator disk" that extracts energy from the wind stream. According to Betz's law, no turbine can capture more than 16/27 (59.3 percent) of the kinetic energy in wind. The factor 16/27 (0.593) is known as Betz's coefficient. Practical utility-scale wind turbines achieve at peak 75% to 80% of the Betz limit.

The Betz limit is based on an open disk actuator; if a diffuser is used to collect additional wind flow and direct it through the turbine, more energy can be extracted. However, such shrouded turbines are costly to build in utility-scale units because of the extra structure required.

The Betz law means that wind turbines can never be better than 59.3% efficient. The law can be simply explained by considering that if all of the energy coming from wind movement into the turbine were converted into useful energy then the wind speed afterwards would be zero. But, if the wind stopped moving at the exit of the turbine, then no more fresh wind could get in - it would be blocked. In order to keep the wind moving through the turbine, to keep getting energy, there has to be some wind movement on the outside with energy left in it. There must be a 'sweet spot' somewhere - and there is, the Betz limit at 59.3%. It's better to have 60% of something than nothing at all.

A 2Kw three 3 meter diameter 3 blade turbine

DESCRIPTION

A wind turbine is a device that converts kinetic energy from the wind, also called wind energy, into mechanical energy; a process known as wind power. If the mechanical energy is used to produce electricity, the device may be called a wind turbine or wind generator. Similarly, it may be called wind charger when it is used to charge batteries.

If the mechanical energy is used to drive machinery, such as for grinding grain or pumping water, the device is called a windmill or wind pump. 

The technology has been developed over a millennium. With modern engineering, today's wind turbines are manufactured in a wide range of vertical and horizontal axis types. The smallest turbines are used for applications such as battery charging or auxiliary power on boats; while large grid-connected arrays of turbines are becoming an increasingly important source of wind power-produced commercial electricity. SolarNavigator sits somewhere in between.

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