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Publication Title | Wind Generator Tower Height

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Wind

Wind Generator Tower Height Mick Sagrillo

Most of us are afraid of heights, or at least have a pretty healthy respect for heights. Not many folks fall into the Gonzo climbing category. For most people with generators, this poses a problem. Wind generators don't do very well on the ground. You've got to get them out of the box and way

up there. But how high is high enough?

There are two reasons to get your wind system way up there; wind speed and turbulence. We'll explain these and offer some reasonable guidelines for the proper placement of your wind generator somewhere between the ant hills and the ozone layer. The Cube Law

Let's get the math out of the way first. The power available to the blades of a wind generator can be expressed by the equation:

P = 1 d A S3 2

where P is power at the rotor (system efficiency is of no concern here); d is the density of the air mass (this will change from winter to summer); A is the swept area of the rotor (the solid disc that the rotating blades present to the wind); and S is the

velocity of speed of the wind. What we're concerned with here is the wind speed, S. The most important part in this equation for us is the "3" after the "S". The three stands for "cubed", or S X S X S. What this means is that very small increases in wind speed result in substantial increases in power available to the rotor. Doubling wind speed yields an eight-fold increase in power!

For example, say our wind generator produces 100 watts at 8 mph. If we were to double this to 16 mph, our wind generator would be capable of putting out 800 watts. That's an 800% increase in available power! Even small increases in wind speed result in big gains. Jumping from 8 mph to just 9 mph gives us a 42% increase in available power.

Applications

So what's this got to do with towers? Well, the higher you go off the ground, the stronger the wind becomes. Because there is less surface friction and fewer objects for the wind to bump into and move around, the air can flow freer and faster.

The figure to the right (compliments of Bergey Windpower Company) depicts the relationship of tower height to increase in wind speed. We can extrapolate from the diagram that going from a 30 foot tower (on level ground with no obstacles) to a 70 foot tower will increase the available wind by about 50%. Using our previous example, that would be like going from 8 mph to 12 mph. Using the cube law, this would give us a 338% increase in power available to the rotor.

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The Lesson

The bottom line to all this is that we can get radical increases in available power to our wind generator by just going higher. Using the above example and in terms of dollars and cents, we could have gotten a 300% increase in power by just installing two more wind generators and towers. It should be obvious to all but the most tower-fearful that going up is cheaper and less trouble than adding more wind generators. (Another way of increasing power is to put up a bigger wind generator. However, taller towers are usually cheaper than bigger wind generators.)

But how high is high enough? Using the above rationale, maybe we should go all the way to the stratosphere. Not so. Towers aren't free. There comes a point where the additional tower structure is not worth the gains in power. How do you determine

©1991 Mick Sagrillo

Home Power #21 • February / March 1991

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