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I can’t seem to find an answer that doesn’t involve more than a ton and a half of concrete. The manual for the wind turbine reports that the load on the turbine in a 110 mph wind is only 155 lbs. When I add the weight of the pole above ground that’s just over 200 lbs. Shouldn’t 3x or 4x that amount of weight in ballast be sufficient? The county won’t let me set up my alternative power system until I get a solid answer to this question.

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  • $\begingroup$ Basically, you need to imagine it's just sitting on your lawn with the pole in a disc of concrete. Design a disc of concrete that wont blow over. Don't forget the wind loading on the pole. When you get the size and weight, add in about 8-10% steel reinforcing by weight. All needs to be below frost line. Steel poles conduct the cold down to the concrete really well. The coefficients of thermal expansion for steel and concrete are nearly identical, but they have to be the same temp. So figure on a cast-in baseplate and insulated flange connection below grade. These are available off the shelf. $\endgroup$ – Phil Sweet Jan 4 '18 at 3:35
  • $\begingroup$ For a larger machine we had 90 tons of concrete buried in a top hat shape - from the side a larger disc and a smaller disc on top to reduce the amount showing out of the ground. $\endgroup$ – Solar Mike Jan 4 '18 at 9:01
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Using very conservative assumptions, it makes sense that you'll need massive ballast weights to stabilize your pole. This is because the ballast is extremely inefficient for this task. I won't go into the math itself, but here's a conceptual demonstration of what's going on.

enter image description here

Imagine your pole is a vertical lever, with the fulcrum at the soil level. At the top of the pole is a horizontal force, and at the bottom is a vertical force. When the pole is precisely vertical, the vertical force at the bottom won't do anything, but the horizontal force at the top will want to topple the pole, so it will rotate.

Once the structure has rotated a bit, the vertical force will start to work against the pole's rotation, restraining it. However, it is very inefficient in doing so. Without going into the math, the following equilibrium must be reached:

$$F_{ballast}\ell_{underground}\theta = F_{wind}\ell_{aboveground}$$

where $\theta$ is the pole's rotation in radians at stability. Therefore, the weight of the ballast must be equal to

$$F_{ballast} = \dfrac{F_{wind}\ell_{aboveground}}{\ell_{underground}\theta}$$

This shows us that the greater the aboveground/underground ratio, the heavier the ballast. Also, the less the structure is allowed to rotate to achieve stability, the heavier the ballast as well. Since structures aren't allowed to deflect far, $\theta$ can be assumed very small, so the ballast must be very, very large. Tons seems absurd, but is actually reasonable.

This, however, uses the very conservative assumption of ignoring any work done by the ground to restrain the pole's motion. Assume for a moment that your pole is embedded in solid diamond (or titanium, or whatever). Will any ballast be required? Of course not. The wind will try to rotate your pole, but that'll make the underground section push against the diamond, which will push right back and impede any such rotation.

The same applies to any type of soil. When something pushes it (like the pole trying to push the soil out of its way so it can rotate), the soil develops what's known as "passive pressure" and pushes back. The soil will do this until the pressure crosses its ultimate strength, at which point it collapses and loses any resistive capacity. Using the diagram from before, this becomes equivalent to:

![enter image description here

This distributed force is far more efficient and can dramatically reduce the necessary ballast. However, it is a function of the type of soil. If your pole is embedded into solid rock, you probably won't need any ballast. If your pole is embedded into a marsh, this force will probably be insignificant and you'll need your massive ballast.

To determine how much the soil can help you, you'll need to hire a qualified geotechnical engineer, who'll need to extract samples from the exact spot (and surrounding area) where you intend to plant your pole. This will need to be combined with a reasonable structural model, according to applicable codes, to determine the appropriate size of the ballast. All of this should be done by qualified engineers and this should not be considered a DIY project.

Obviously, another possibility would be to adopt a different structural model, such as support cables around your pole, which could be significantly more effective than simple ballast. To judge the feasibility of this, however, we'd need a lot more information regarding your "alternative power system", and it would probably be out-of-scope for this question anyway.

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Sounds about right for an unstayed structure. You can reduce the ballast somewhat if you stay your mast (probably 2/3 the way up, design to keep the blades well clear of the stays under worst case sag/vibration/bending. But now you need three or four ballast masses to hold the stays into the ground.

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