How this is calculated
The power in moving air is half the air density, times the area the rotor sweeps, times the cube of the wind speed: the Department of Energy’s P = Cp × ½ ρ A V³. Speed is cubed, so small changes in it move everything.
Cp is the share a real machine takes. Betz’s law caps it at 16/27, 59.3 percent; the largest machines peak at 0.45 to 0.50, and small turbines average 0.25 to 0.35 across a year once generator and controller losses are folded in.
Hub-height speed comes from the logarithmic profile, scaling your quoted speed by the log of each height over the roughness length — the World Meteorological Organization’s terrain table, 0.0002 m for open sea up to 2 m for a town center.
Then the spread, because the cube of an average is not the average of the cubes. This integrates the power curve across a Weibull distribution in 0.05 m/s steps, times 8,760 hours, air density falling with elevation.
Worked example 10 mph at 33 ft over low crops, an 18 ft rotor on a 60 ft tower, 5 kW, Cp 0.30. The tower lifts the mean to 11.3 mph, the rotor sweeps 255 sq ft, and the year is 8,520 kWh — 19.5 percent of a nameplate claiming 43,800.
Worked example 4.5 m/s at 10 m over low crops, a 5.5 m rotor on an 18 m tower, 5 kW, Cp 0.30. The tower lifts the mean to 5.07 m/s, the rotor sweeps 23.8 m², and the year is 8,659 kWh — 19.8 percent of a nameplate claiming 43,800.
Checked against certified hardware: Bergey’s Excel 15, a 9.6 m rotor rated 15.6 kW, carries a Small Wind Certification Council rating of 29,800 kWh a year at a 5 m/s average. Fed the same machine at Cp 0.35, this page returns 28,900 kWh, three percent under the certificate.
Quick answers
How much wind does a small turbine need?
The Department of Energy’s handbook puts the line at 10 mph, about 4.5 m/s, grid-connected and 9 mph off grid. A 4 m/s site holds half the energy of a 5 m/s one.
Why does the average wind speed give the wrong answer?
Power goes with the cube of speed, and averaging first throws the spread away. A Rayleigh year carries 1.91 times the energy the cube of its mean suggests, and cut-in and the rated ceiling take part of that back.
What capacity factor should I expect?
Certified machines return 18 to 33 percent of nameplate at a 5 m/s average, and the spread says more about how each maker rates its generator than about the wind.
Is small wind cheaper than solar panels?
Rarely on capital. Small wind installed in 2021 averaged 5,120 dollars a kilowatt, several times what a kilowatt of panels costs, so the same money buys far more nameplate in solar.
Why five meters a second is where small wind starts
The cube law is brutal both ways: doubling the wind gives eight times the power, losing a quarter of it costs well over half. So a marginal site cannot be rescued with a bigger machine — energy per square meter of rotor is set by the wind, and the rotor only decides how many square meters you collect.
| Mean at hub height | kWh a year per m² of rotor | Share of a 5 m/s site | |
|---|---|---|---|
| 3.0 m/s | 6.7 mph | 75 | 20% |
| 3.5 m/s | 7.8 mph | 125 | 33% |
| 4.0 m/s | 8.9 mph | 191 | 50% |
| 4.5 m/s | 10.1 mph | 275 | 72% |
| 5.0 m/s | 11.2 mph | 380 | 100% |
| 5.5 m/s | 12.3 mph | 508 | 134% |
| 6.0 m/s | 13.4 mph | 661 | 174% |
| 7.0 m/s | 15.7 mph | 1,051 | 277% |
| 8.0 m/s | 17.9 mph | 1,558 | 410% |
| 9.0 m/s | 20.1 mph | 2,165 | 570% |
| 10.0 m/s | 22.4 mph | 2,825 | 743% |
Cp 0.30, Rayleigh spread, sea-level air, cut-in 3 m/s, cut-out 25 m/s, no generator ceiling. A 5 m rotor sweeps 19.6 m², so it takes 3,750 kWh a year from a 4 m/s site and 20,600 from a 7 m/s one.
Where the year’s energy actually arrives
A year at a 5 m/s average is not a year of 5 m/s wind. It is long calms, many mild hours, and a few strong ones carrying most of the energy.
Ratings assume a Rayleigh distribution, under which the wind holds 1.91 times the energy the mean cubed implies. The machine takes it back: nothing below cut-in, a ceiling above rated speed, a shutdown above cut-out.
What the certified machines actually return
The Small Wind Certification Council publishes one comparable number per machine: the kWh a year it would make at a 5 m/s annual average. Set against nameplate, the ratio runs wider than most people expect.
| Certified machine | Rated kW | Certified kWh a year at 5 m/s annual average | Share of nameplate |
|---|---|---|---|
| Kodair KW20 | 20.3 | 58,508 | 32.9% |
| Kodair KW30 | 29.3 | 81,050 | 31.6% |
| SkyWind NG | 0.31 | 615 | 22.6% |
| Bergey Excel 15 | 15.6 | 29,800 | 21.8% |
| Hi VAWT DS3000 | 1.4 | 2,460 | 20.1% |
| SD Wind SD6 | 5.2 | 8,950 | 19.6% |
| Skystream 3.7 | 2.1 | 3,420 | 18.6% |
| Kestrel e400nb | 2.5 | 3,930 | 17.9% |
Small Wind Certification Council listing, read September 2026. Ratings under AWEA 9.1 (2009) or ACP 101-1 (2021). The share column is the certified energy divided by rated power times 8,760 hours.
The high ratios are a rating artifact. A maker who fits a modest generator to a large rotor gets a flattering share of nameplate without making one extra kWh, which is why nameplate is the worst way to compare two turbines.
Rotor diameter is the number to compare, because that is what sets how much air the machine can reach. The Excel 15 takes its 29,800 kWh with a 9.6 m rotor; nothing with a 3 m rotor comes near it, whatever the badge on the generator says.
How much a taller tower buys
Ground drags on wind, and clearing that drag is the whole job of a tower. Rough ground slows the low air more, so height buys more over trees than over water — though wind over trees stays slower at every height.
| Hub height | Open grass z₀ 0.03 m | Low crops z₀ 0.10 m | Scattered obstacles z₀ 0.25 m | Suburb or forest z₀ 1.0 m |
|---|---|---|---|---|
| 10 m / 33 ft | 1.00 × | 1.00 × | 1.00 × | 1.00 × |
| 15 m / 49 ft | 1.07 × | 1.09 × | 1.11 × | 1.18 × |
| 20 m / 66 ft | 1.12 × | 1.15 × | 1.19 × | 1.30 × |
| 25 m / 82 ft | 1.16 × | 1.20 × | 1.25 × | 1.40 × |
| 30 m / 98 ft | 1.19 × | 1.24 × | 1.30 × | 1.48 × |
| 40 m / 131 ft | 1.24 × | 1.30 × | 1.38 × | 1.60 × |
Speed multiplier against a 10 m reading on the same ground. Cube each figure for energy: 1.30 on speed is 2.2 on energy.
The Small Wind Guidebook calls guyed towers the least expensive of the options, and they need a guy radius of half to three-quarters of the tower height, so the footprint is wide. Tilt-down towers cost more and are named there as the easy way to service a machine of 5 kW or smaller.
A rooftop mount undoes the whole argument. It is short, it sits inside the building’s own wake, and it puts a vibrating machine on the rafters.
Turbulence, trees and the 30-foot rule
Turbulence is speed arriving from the wrong direction. It makes little power and works the bearings, the yaw and the blade roots hard.
The Department of Energy’s rule is a rotor at least 30 feet, about 9 meters, above anything within a 500-foot radius; the handbook states it elsewhere against obstacles within 300 feet. Take the larger radius for a treeline.
Trees are the trap, because they grow. The windbreak that clears your rotor today is a turbulence generator in fifteen years, and tower height is fixed the day the concrete goes in.
Noise and the neighbors
Certified sound levels look mild. The Excel 15 certificate gives 49.3 dB(A) at 60 meters from the rotor center, and the certified machines carrying a published figure run from 41 to 56 dB(A) on the same test.
Complaints are about character rather than level. The sound modulates with every gust, carries downwind, and runs all night in the weather that keeps the windows shut.
In the US, turbine noise sits in local ordinance, and tower height limits usually live in the same zoning text.
Across Europe, noise limits and mast heights come through national planning consent, which a solar array rarely needs.
The maintenance a solar array never needs
A turbine is the only moving machine in an off-grid system that lives 60 feet up in the weather. The Small Wind Guidebook is plain about the consequence: many turbines require periodic lubrication, oil changes and replacement of wear surfaces such as brake pads, and bolts and electrical connections should be checked and tightened.
None of that is hard. All of it happens 60 feet up.
Add the yearly round of checking corrosion and guy tension. The same source expects the machine to last 20 years or longer with proper installation and maintenance, and says the blades or bearings may need replacing after 10 years. Panels over that period ask for washing.
Which is why a tilt-down tower earns its cost: if servicing needs a crane, the servicing does not happen.
Where wind genuinely wins
Wind wins on timing rather than volume. It runs at night, in December, and through the week of overcast that empties a battery bank.
Four site types make it work: coastal ground with sea fetch, ridges where flow speeds up over the crest, open plains with nothing upwind for miles, and high latitudes where the winter sun is gone but the wind is strongest.
The pairing beats either machine alone. A turbine that covers the dark months lets the solar array be sized for the rest of the year instead of for December, and that is where the money is saved.
Below about 5 m/s at hub height the arithmetic collapses, and the same capital in panels returns more for less work. Weigh the full set on solar against wind, hydro and a generator.
Finding your number: the Global Wind Atlas gives mean speed at 10, 50, 100 and 150 m, and NASA POWER returns MERRA-2 wind at 10 m and 50 m for any coordinate. Both model coarse ground; a year of mast data settles it and nothing else does. This page ships no location lookup, so type the figure in with its quoted height.
Sources
US Department of Energy, WINDExchange, Small Wind Guidebook: the 10 mph and 9 mph siting thresholds, the 30 ft clearance rule at both the 300 ft and 500 ft radius, tower types and guy radius, maintenance, expected life, and the capacity-weighted average of 5,120 dollars per kilowatt for small wind installed in 2021 — 16 projects in three states, 396 kW combined. Small Wind Certification Council, certified turbine listing and the Bergey Excel 15 certificate (29,800 kWh a year and 49.3 dB(A) at 60 m from the rotor center), ratings under AWEA 9.1 (2009) and ACP 101-1 (2021), all at a 5 m/s annual average. World Meteorological Organization WMO-No. 8, the Davenport–Wieringa roughness length classes. NASA POWER wind methodology, MERRA-2 at 10 m and 50 m. Betz limit 16/27 and the 0.45 to 0.50 peak for the largest machines. The Weibull and log-law arithmetic on this page is derived here rather than quoted from a source. The solar cost field carries a starting figure only; put your own installed price in it. Checked September 2026.
Go deeper
Take the yearly kWh above into the off-grid solar sizing calculator to see what the panel side would have to be. With falling water on the site, the micro-hydro calculator is the third option, and the peak sun hours atlas holds the solar figure used here. Then read the hidden costs of off-grid solar.