The power law, and what alpha is doing
Wind speed rises with height because the ground drags on the air, and the standard way to describe it is a power law:
v₂ = v₁ × (h₂ / h₁)α
One measurement, two heights, one exponent. Since turbine power goes as the cube of speed, the power ratio is the same expression with the exponent tripled: (h₂/h₁)3α. That tripling is what makes tower height expensive to get wrong in either direction.
Alpha is a property of the ground upwind, not of the turbine. Smooth surfaces — open water, bare ground, short grass — hold the wind close to the surface and give low values. Rough surfaces — scrub, trees, buildings — slow the lower air far more and give higher ones. Ranges from about 0.10 to 0.40 get quoted for different terrain, but the page takes it as an input because published tables are generic and your particular tree line is not.
| Alpha | 30 ft → 100 ft, speed | Power ratio |
|---|---|---|
| 0.10 | +12.8% | 1.44× |
| 0.14 | +18.4% | 1.66× |
| 0.20 | +27.2% | 2.06× |
| 0.28 | +40.1% | 2.75× |
| 0.35 | +52.4% | 3.54× |
Read the middle column and the tower looks like a marginal improvement. Read the right-hand one and the same tower doubles or triples the plant. That gap between how the two columns feel is the single most common mistake in small wind.
How to measure alpha instead of guessing it
Two anemometers on the same mast at different heights give it directly. Take the ratio of the speeds and the ratio of the heights and:
α = ln(v₂/v₁) ÷ ln(h₂/h₁)
Averaged over weeks, not minutes, because shear is not constant. It is typically higher at night, when the air near the ground cools and stops mixing, and lower in the afternoon when convection stirs the layer. A single hour can give a value far outside anything you would design with.
If you only have one anemometer, put it at the height you actually intend to use. Every conversion between heights is an assumption, and the assumption is worth more error than the measurement.
Why the honest answer is often a taller tower rather than a bigger machine
Rotor power goes as the square of diameter. Height buys speed, which goes as the cube. On a site with alpha near 0.20, moving from 30 to 100 feet is worth about 2.06× the output; matching that with rotor diameter alone would take a rotor 1.44× as wide, sweeping twice the area, on the same short tower, in the same turbulent air.
Turbulence is the part the arithmetic does not show. Air close to broken ground is not just slower, it is unsteady in direction and speed, and a small machine yawing constantly to chase it produces less than the average speed suggests while wearing out faster. Getting the rotor into clean air above the obstructions is worth something the power law cannot express.
Against that: the tower is usually the larger share of the installed cost, taller towers need more foundation and more anchor, and everything that ever needs servicing is now further up. The cost per watt line on this page prices the height at one wind speed, which is a starting point rather than an answer.
What this does not tell you
It converts one speed to another speed. It does not know about the ridge that accelerates the flow over your site, the shelter belt that will be twenty feet taller in fifteen years, or the seasonal pattern that decides whether the good wind arrives when you need the energy. It also cannot give you annual output, because that needs a distribution of speeds rather than an average — the wind turbine power calculator covers why an average speed understates energy and by how much.
The other thing at the top of a tower is force. Wind loading on a mast is a structural question with its own arithmetic, and the antenna mast wind load calculator works that side. Sight lines and the fall radius are worth checking on the ground before any of this, and the antenna height and radio horizon calculator is a useful companion if the same structure is carrying anything else.
Anything that ties into house wiring is a licensed electrician job with a permit behind it. Back-feeding a line that the utility believes is dead can kill a lineman working on it, which is why the transfer arrangement is not a detail you improvise. Battery banks store real energy and can vent hydrogen. This page produces a number of watts and gives no wiring guidance whatsoever.
Questions people ask
What shear exponent should I use?
The one you measured, if you possibly can. Two anemometers at different heights on the same mast, averaged over weeks, give it directly from the ratio of the logs. Failing that, published values are grouped by terrain roughness, running low over open water and bare ground and considerably higher over scrub, trees and built-up ground, and this page deliberately states none of them because the useful number is site specific and generic tables mislead. If you must guess, guess a range and run the calculation at both ends. The spread you get is a fair picture of how much you actually know.
Why is the power gain so much larger than the speed gain?
Because the power law raises speed to alpha, and turbine power raises speed to the third power, so the height ratio ends up raised to three alpha. At alpha 0.20, going from 30 to 100 feet is a 27 per cent speed increase and a 106 per cent power increase. The speed figure is the one people look at and it makes the tower look like a modest improvement; the power figure is the one that pays for it. Whenever you see a small speed difference between two heights or two sites, cube it before deciding it does not matter.
Is a taller tower always better?
It is almost always better for output, and the question is whether it is better for the money and the risk. Taller means more speed, cleaner and less turbulent air, and less wear on the machine. It also means more tower cost, more foundation, longer guys on a bigger anchor radius, and every future service call happening higher up. The other constraint is not negotiable: the tower has to clear every power line by its full fall radius, and that often decides the location and sometimes the height before anything else does. What the height should be is a decision for you, the tower manufacturer and your building department, not for a calculator.
Does the power law work close to the ground?
Poorly, and this is where people get burned. Right down in and among obstacles the flow is not a smooth gradient at all; it is separated, turbulent and often reversed behind things. The power law describes a boundary layer over reasonably uniform ground, and it starts to mean something once you are clear of the local obstructions. Extrapolating a reading taken at ten feet in a yard with trees around it, up to a hundred feet, is stacking a bad measurement on a model that does not apply to it. Measure high, or at least clear of the obstructions.
Can I use this for a rooftop turbine?
The arithmetic will run and the answer will not mean much. A roof sits inside the disturbed flow around the building, where the wind is slower than the free stream in some places and accelerated in others, is turbulent nearly everywhere, and changes completely with wind direction. None of that is a smooth power law. Rooftop mounting also puts a vibrating machine in direct structural contact with a house, which is a separate problem with a separate specialist. If a rooftop is the only option, treat any number from this page as an upper bound with no confidence attached.