Is there a windmill in your future?


Generating electricity


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Windmill Equation

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General Rules
Our web site receives many questions, most of which are about wind power.  Three general questions are of interest. 

1)  how is electricity generated by a windmill?
2)  What web sites can give me more information?
3)  What are the general rules about 

It is in the nature of electromagnetics that the faster things happen, the better, at least up to a point. Generators at steam-power stations turn at 3600 revolutions per minute (60 revolutions per second), generating 60-Hz electricity in each of three sets of coils. 

The alternator in your car turns about 2 to 3 times as fast as the engine, namely, in the range of (say) 2000-7500 RPM.   The alternator produces three-phase AC in a Delta-wound coil, but the output is rectified to produce the DC for supplying power to the automobile's electrical load and to keep the battery charged.

Generators in hydropower stations often turn slower, some as low as 600 RPM (10 revolutions per second).  To generate 60-Hz electricity, they use many poles (6, in this case) in the rotating magnetic field.

It is in the nature of large machinery, like windmills, that the larger they are the slower they should turn. Huge windmills that produce electricity for the California, for example, lumber along at 20 to 50 RPM (I'm estimating from having seen them in action). The speed of the tips of the windmill blades should be about 5 times the speed of the wind. For a 10 m/s wind (about 20 mph, more or less), the tips move at 50 m/s. If the windmill has a large diameter, then 20 RPM is adequate, but if the diameter is small, a high RPM is required.

Houston, we have a problem! Most things can't go fast and slow at the same time.

There is some ideal size for a windmill such that the windmill RPM and the generator RPM are pretty well matched; unfortunately, that size is in the range of one-meter diameter. That device won't produce a lot of power. (There is a commercial unit that produces about 400 watts (MAXIMUM) using a modified automobile alternator. It is used primarily for charging batteries in remote locations.)

If you want more power, you either gets lots of the smaller units or you use a larger diameter. But the larger diameter will imply a slower rotation rate, so you have to gear up the speed with some kind of transmission.  It is easier to use gears to increase theRPM of the generator than to build the generator with so many poles that it can generate electricity efficiently at (say) 1 or 2 RPM.  (These are the huge commercial windmills, not the kind for home and farm use.  The best large units also have an electronic control to produce 60-Hz regardless of the rotation rate.)

That much in mind, do some figuring. If you had the world's best windmill, the amount of power (in watts) you could get would be just under the square of the radius (in meters) multiplied by the cube of the windspeed (in meters per second). (See Equation below)

(Note that it is the *radius* not the *diameter*). For example, the commercial unit I mentioned has an actual radius of 0.57 m. At 28 miles per hour (=12.5 m/s), it should produce (.57^2)*(12.5^3) = 634 watts. (Well, it produces only 400 W. As I said, the formula is an overestimate. The unit doesn't get up to 600 W until a speed of about 40 mph, 18 m/s.)

Question: What do you intend to do with the electricity? The most expensive thing you can do is to try to tie it in to the power line to feed them electricity during the three days a month when you get enough wind. (High cost, peanuts in return.) If you just want some heat, you can do that fairly easily, simply by matching some resistive heating elements to your generator. If you want to charge batteries, then there *must be* (and is, in commercial units designed for the purpose) some regulating circuitry to avoid destroying your batteries. (A friend destroyed batteries with a flea-power solar unit that took the voltage too high.) If you're trying to supply yourself with power to run your computer, your microwave oven, and your house lights, it will involve a lot of work and expense, a lot of which is protecting yourself and your appliances from voltage variations. 

Here are some web sites of interest (for a wind map)

 One site Removed at request of  lout


There are a few general rules. 

1. The bigger the windmill, the more power you get. The power is proportional to the square of the radius of the windmill. Double the radius and you quadruple the power. 

2. The faster the wind, the more power you get. The power is proportional to the cube of the wind velocity. Double the velocity, and you octuple the power. Approximately, the formula for wind power is given below for a nearly perfect windmill (and it is an overestimate) 

3. The tip speed of the windmill blades is typically 5 times the wind speed. That is, in a ten-mph wind, the tip of the blades moves at 50 mph. (Think of the neighborhood kids getting into mischief.) 

4. Ideally, you should have two or three blades. The old farm windmill with lots of blades was pretty inefficient. 

5. If you're trying to generate 110-VAC to match the power line, you will need pretty sophisticated equipment. If you only want to generate heat with your electricity, things are easier. 

6. Electrical generators usually run at 3600 RPM, which would be screamingly fast for a large wind turbine. 

7. Unless you're in a very rural environment, your neighbors may object. 

8. If windmills were an easy solution, there would be tens of millions of them in the US.   There are closer to 20,000.

9.  Safety First!


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