How much power can a small wind turbine produce?

How much power can a small wind turbine produce?

Warning: a little bit of math follows - not to hard, bear with us. We will give examples for 2 small turbines, 8 ft wind turbine at lakeone with 2 foot blades and one with 4 foot blades.

Power AVAILABLE in the wind = .5 x air density x swept area x (wind velocity cubed)

Air density = 1.23 kg per cubic meter at sea level. Swept area = pi x r squared. Our 2 foot blades = 0.609m, 4 ft = 1.219m. 10 mph = 4.4704 m/s, 20 mph = 8.9408 m/s.

How much power is in the wind: 2 ft blade, 10 mph winds = .5 x 1.23 x 3.14×0.609squared x4.4704 cubed

= .5 x 1.23 x 1.159 x 89.338 = 63.7 watts

With 4 foot blades and 10 mph winds = .5 x 1.23 x 4.666 x 89.338 = 256 watts

With 4 foot blades and 20 mph winds = .5 x 1.23 x 4.666 x 714.708 = 2051 watts

That’s the MAXIMUM power in the wind. However, it’s impossible to harvest ALL the power. The Betz Limit tells us that the maximum percentage of power we can harvest from the wind is 59.26%.

Thus our maximum power from these turbines would be:

2 ft blades, 10 mph wind = 37.7 watts

4 ft blades, 10 mph wind = 152 watts

4 ft blades, 20 mph wind = 1,215 watts

Keep these numbers in mind when a sales person starts to tell you their small wind turbine will meet all your needs….

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15 Responses to “How much power can a small wind turbine produce?”

  1. Would these systems be more effective by using a multi-blade unit, similar to the old farm windmills?
    Could you use more generators?

    Thank you for any information that you may provide.

    Lewis A. Morris

  2. Multi-blade wind turbines, like the old wind mills on farms that pump water, provide more torque. They generally start turning sooner and because of the torque, they can move something that’s providing a lot of pressure.

    Triple blade turbines, are easy to balance and provide more rpm, thus more voltage.

    If you want to pump water, use several blades. If you want to generate electricity, use fewer blades.

    I’m not sure what you mean, when you ask if you could use more generators. We use different sized DC generators (motors), based on the power you want to produce. Bigger motors required bigger towers and blades (more money) and produce more power.

    Did that answer your questions?

    Best regards,
    Bruce.

  3. Great information!
    What is the time frame?
    Hour? Day?

  4. These calculations are for watts per hour. Thus the maximum possible power a wind turbine with 4 foot blades in a 10 mph wind, could produce, is 152 watts. Homemade turbines will certinly produce less than this maximum hourly wattage.

  5. Hi Bruce im a student and im doing a report and i was hopeing that i could use some of this information in the report and i was wondering if you could tell me how you came across this info and what your title is are you an expert in the feild or what thank you
    Jeremy

  6. Hi Jeremy,

    The math, (Power AVAILABLE in the wind = .5 x air density x swept area x (wind velocity cubed), is public domain information. You are free to use any information you find on this site as part of a student report. If you post any info on another website, please make referrence to our site.

    My backgound is via hands on - the wind turbine in the picture on this site, is one that I built from scratch and now is running at my cottage.

    Note that the power numbers listed are the maximum available. In practice, a homebuilt turbine will likely get about 30% of this maximum.

    If you need more info, you can email me at:
    feedback @ greenterrafirma.com (take out the spaces).
    Regards
    Bruce (publisher - Greenterrafirma.com)

  7. Using a 1kw generator as an example, what is the relationship of torque to rotor speed to the torque required to turn the generator or (put another way) How much torque is necessary to turn a 1kw generator and how does that equate to wind speed?

    Thanks,
    Mark

  8. Mark, there are several 1.5 horsepower dc generators out there with a wide variety of specs. Does your generator produce 10 volts at 60 rpm or at 600 rpm? What is the max amps that the generator will support? Maybe you can provide the specs for your dc motor…

    Thanks,
    Bruce.

  9. Actually this is a due dilligence question in advance of me puchasing a 1kw turbine. The goal is to purchase a turbine that has a low startup speed with a rated speed at around 300 rpm. Hope this helps.

    Thanks,
    Mark

  10. Mark, what’s most important to you then, is the power curve for the particular wind turbine that you are looking at. And of course, the average windspeed for the location where it will be installed. However, given that the average windspeed will be the same, you’ll want to compare the power curves. These curves will show you at what wind speed the turbine starts to produce power and at what windspeed they achieve their rated output. There could be very significant differences in the power curves of different turbines.

    You can check the wind speed maps on the internet. Some will show your average windspeed at several different tower heights. You could also try the nearest airports to see if they have average windspeeds that are more specific to your site.

    The total power you can expect for that 1 kw wind turbine, will be determined by reading the power produced, at the average windspeed for your site. A turbine that starts soner, but produces less power at your average site windspeed, will still produce less power for you over a yearly period.

    One last note: if the people trying to sell you a wind turbine don’t have a documented power curve, one that shows the power DOWN at your average windspeed, then RUN, don’t walk, to the next dealership. I hate it when someone produces a power curve that starts at 10mph when my average windspeed is 6mph.

  11. what would be considered ‘best conditions’ for a wind turbine?

    if you could always control (i.e. it only blows in one direction) what direction the wind is coming from and its speed how much power could be produced?

  12. Cody,

    If you could control the wind, you would want it to always blow at the “rated speed” for the wind turbine that you have. Every wind turbine lists the power that it produces at it’s rated (highest) wind speed.

    A wind turbine that is advertised as a 2 kw wind turbine, will produce 2 kilowatts per hour at it’s rated speed. Rated windspeed for “small” wind turbines is usually around 20 mph.

    For example, the Skystream 3.7 is “rated” at 1.9 kw and only produces this much power at wind speeds of 20 mph. In many parts of North America, the average windspeed is much closer to 12 mph. At 12 mph, a small wind turbine produces about one tenth of it’s rated power level. Big drops in windspeed result in big drops in power output - or big increases in average windspeed mean big increases in power output.

    Hope that was clear.

    Here’s a link to the Skystream 3.7 data sheet:
    http://www.skystreamenergy.com/documents/datasheets/skystrea_%203.7t_datasheet.pdf

  13. Hey thanx for the info.

    Does generator size matter to the size of the turbine.. i.e could u have a small turbine with large generator or vise versa or do they need to be relatively the same?

    Would it be possible to make a turbine where the rated speed is variable.
    I need something than can be flexible.

    I’m actually thinking about a special kind of wind turbine where air direction and speed are always controlled. Any advice on patents?

    I wish I could go into more details but its too risky..

    Thanx again for your help.

  14. There is a formula for the maximum amount of power that you can get out of the wind. The 2 biggest variables are the sweep area and the speed of the wind. You can’t get any more power out of the wind, than what this formula states. Large commercial wind turbines can get very close to this theoretical maximum. Most wind turbine manufactures, will match the sweep area (blade length) to the generator in order to get the maximum amount of power. If either one is mismatched, you get less power output.

    Yes, in theory you could make a wind turbine with a variable rated wind speed, if that turbine’s sweep area was also variable. I would be concerned with the complexity of such a unit and cost, vs overall power output. Of course, new and improved models are designed everyday. Afraid I can’t comment on patents.

  15. thanx man youve been alot of help

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