WIND POWER CALCULATOR

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The single most important thing to determine when choosing your home power system is how much electricity it will generate. Wind turbines are usually listed by their rated power (or rated capacity). Unfortunately, this rating is pretty much useless or even misleading, because it represents just a potential wattage the system can generate at certain ideal conditions.



Wind generators are generally designed to yield maximum output at high air speeds. Likewise, the manufacturers rate their systems by the amount of power they can produce at a specific high wind speed, typically 24 mph (10.5 m/s) to 36 mph (16 m/s). In reality, in most areas you will rarely get these speeds. Note that the available energy of the moving air molecules is proportional to the cube of their velocity, so even small decrease in the speed results in large decrease in the energy. A turbine rated for example at 5000 watts at 30 mph will produce only 625 watts or less at 15 mph.

Besides rated wattage, wind generator manufactures also normally provide a so-called Power Curve (also known as a Performance Graph or Power Output Graph), that plots the output in watts or kilowatts as a function of instantaneous wind speed.

These curves have S-shape that starts with zero at a certain "cut-in" speed, and leveling off to a rated power at a rated speed. Above the rated speed the curve usually goes slightly down and then abruptly goes back to zero at a certain cut-out speed, where turbines shuts down to protect itself from a damage. Although the power curves are more useful than rated power values, they only tells you how much electricity you may generate at specific instantaneous air velocities. Since the air speed varies all the time, you need to know the net amount of electricity you can expect to generate over certain period of time, say in a year. There are various climate maps that provide data on mean air velocity for various geographical regions. However, you can't simply apply an average air speed to the turbine's power graphs to determine the annual output. The case is, it all depends on how that average speed came about, i.e. if winds in your site vary a lot, or if they blow at a relatively constant speed. In a hypothetical case, if the wind is always either below a turbine's cut-in speed, or above cut-out speed, you will not produce any electricity at all, even though the average air speed may look good. Also, the mean of the cubes of the speeds is greater than the cube of the mean speed.

To calculate an average amount of energy a system can generate annually, Battelle Laboratories estimated an actual average annual wind wattage density in various US regions, rather than simply mean air speed. They introduced a numerical rating that corresponds to one of the seven wind power classes. Each class represents a range of power density values based on the computer analysis of historical data. A similar mapping for Europe was done by Riso Laboratory.



Wind Power
Classes		 10 m (33 ft) 50 m (164 ft)
Wind Power Density (W/m2) Average Air Speed m/s (mph) Wind Power Density (W/m2) Average Air Speed m/s (mph)
1 0-100 0-4.4 (0-9.8) 0-200 0-5.6 (0-12.5)
2 100-150 4.4-5.1 (9.8-11.5) 200-300 5.6-6.4 (12.5-14.3)
3 150-200 5.1-5.6 (11.5-12.5) 300-400 6.4-7.0 (14.3-15.7)
4 200-250 5.6-6.0 (12.5-13.4) 400-500 7.0-7.5 (15.7-16.8)
5 250-300 6.0-6.4 (13.4-14.3) 500-600 7.5-8.0 (6.8-17.9)
6 300-400 6.4-7.0 (14.3-15.7) 600-800 8.0-8.8 (17.9-19.7)
7 400-1,000 7.0-9.4 (15.7-21.1) 800-2,000 8.8-11.9 (19.7-26.6)
These data provide annual average wind power density in watts per one square meter of a turbine sweep area. Average speeds in the table are based on the so-called Rayleigh speed distribution and are given for the sea level. To get the same density above sea level, the air speed has to increase by 3% per 1000 metre (1% per 1000 ft) elevation.

The table provides data only for 10 m and 50 m heights. To estimate the air speed and output for the actual height of your tower you can use an empirical 1/7 power law.
If you know the air speed V1 at a certain height h1, then the air speed V2 at a different height h2 can be estimated as: V2=V1×(h2/h1)1/7.
Efficiency (%)
Wind density watt/sq.m
Rated height (meters)
Turbine height (meters)
Rotor area (sq.m)
Power (watt)
This simple online wind power calculator lets you find average output wattage of your generator. Here is how it works. First you need to determine the wind class of your site from this online US wind resource atlas (look down their list and open the map for your state). Then find from the above table the average wind density in W/sq.m corresponding to your class at rated height (pick 10 m or 50 m whichever is the closest to actual height of your tower). To perform the calculation we need to find wind power density "P" at your tower height. This quantity is proportional to cube of the speed, and the speed in turn varies with altitude according to 1/7 power law. Therefore if we know P1 at a certain rated height h1 (such as at 10 m), we can calculate "P2" at the top of your tower h2 by using this formula: P2=P1×(h2/h1)3/7. This number is multiplied by the efficiency of your system (which is typically 20-25% for residential size designs) and by turbine swept area in sq.m. Note that for horizontal turbines the rotor sweep area is A=π(D/2)2, where D is the diameter of the blades, π=3.14 (see calculation of the energy in the wind).

Note that the values in the above table were obtained for the sites that are free of obstructions. If you have any objects such as a tree or a building within 300 feet (100 meters), it is generally recommended to place the turbine at least 10 feet (3 meters) plus the blade length above the top of the highest obstruction.




REFERENCES AND ADDITIONAL INFORMATION:
Wind Energy Resource Atlas of the United States.
Renewable Energy for home, farm, and business- a detailed book on making a wind-based system.

The information and calculators provided in this website are given AS IS without guarantee of any type, neither explicit or implicit. See a complete disclaimer linked below.




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