If solar works on your roof, surely wind does too? It's a fair instinct — the wind is free, turbines are proven, and Britain is one of the windiest countries in Europe. But put a small turbine on a house and the numbers collapse, and they collapse for a reason that's baked into the physics. Once you see the two equations involved, you can't unsee them.
The power you can pull from the wind comes down to one formula. Don't worry — we'll translate it:
Power = ½ × air density × swept area × (wind speed)³
— The wind power equationTwo parts of that equation do all the damage: the swept area (how big a circle the blades sweep) and the wind speed, which is cubed. Those two levers are why wind is a triumph at sea and a near-write-off on a rooftop.
Lever one: blade length, squared
The blades sweep a circle, and the area of a circle grows with the square of its radius. Double the length of the blades and you don't double the power — you quadruple it, because the swept area goes up four times. A turbine isn't really a machine for spinning; it's a machine for capturing area, and area scales brutally with size.
A home turbine might sweep a circle two metres across. A modern offshore turbine sweeps a circle 150 metres or more across. That alone — before the wind even blows — is a difference of over five thousand times the catching area.
Lever two: wind speed, cubed
This is the one people get wrong, and it's worse than most guesses. Power doesn't rise in step with wind speed, and it isn't a square root either — it rises with the cube of wind speed. Double the wind, and you get eight times the power (2 × 2 × 2). A site with twice the average wind speed isn't twice as good; it's eight times as good.
And here's the trap for home wind: wind speed depends enormously on height and on what's around you. High up and out at sea, the wind is fast and smooth. Down at roof height in a town, it's slow and churned into turbulence by every house, tree and fence around it. Because speed is cubed, that drop from a smooth 9 m/s offshore to a gusty 4 m/s over the rooftops isn't a minor handicap — it slashes the available power by more than ten times on its own.
Put the two together: the home turbine vs the giant
Now stack the levers. Compare a typical rooftop turbine in a town with a single big offshore machine:
| Rooftop turbine (town) | Offshore turbine | |
|---|---|---|
| Blades sweep a circle | ~2 m across | ~150 m across |
| Swept area | ~3 m² | ~17,700 m² |
| Typical wind speed | ~4 m/s (slow, turbulent) | ~9 m/s (fast, smooth) |
| Average power produced | ~30 watts | ~3.5 megawatts |
| How often it's usefully working | under 8% of the time | around half the time |
Thirty watts. That's less than a single old-fashioned lightbulb, on average, from a turbine bolted to your house. The offshore machine produces over one hundred thousand times more power — not because it's a hundred thousand times bigger, but because the two multipliers (area squared, speed cubed) compound on each other. Make it bigger and put it where the wind is faster, and the gains explode.
A home turbine loses on both levers at once: tiny blades, and slow, broken-up wind. Because one of those levers is cubed, the penalty isn't additive — it's catastrophic.
— The Decarbonarma viewWhy scale wins, every time
This is the whole story of modern wind power in one sentence: the economics push relentlessly towards taller towers, longer blades and windier sites, because both levers reward size and height. Lift the rotor 100+ metres into faster, smoother air (cube law), and make the blades enormous (square law), and a single turbine generates more in an hour than a rooftop unit manages in months.
There's a ceiling no one can beat — the Betz limit says you can never extract more than about 59% of the energy in the wind passing through the blades, because you'd have to stop the air completely to take it all, and then no more could flow through. But that cap applies to everyone equally, big and small. It doesn't rescue the home turbine; it just means the giants are working against the same physical limit, and still winning by a hundred thousand to one.
The real-world receipts
This isn't theory. When the Energy Saving Trust ran a year-long field trial of domestic turbines, every single building-mounted turbine returned a "load factor" below 8% — meaning they produced less than 8% of what their rating implied. Some urban units generated so little they barely covered the electricity their own electronics drew. Free-standing turbines on masts, away from buildings, did about six times better — but even those averaged only around 19%, and only on genuinely exposed sites.
So when does home wind ever make sense?
Rarely — but not never. The physics points to a narrow set of conditions where it can work: a pole-mounted turbine (never roof-mounted), on a genuinely exposed rural site with a high average wind speed and no nearby buildings or trees to break up the flow. A windy hilltop smallholding in Scotland or mid-Wales can make a freestanding turbine pay. A semi-detached house in a town cannot — the cube law has already decided.
For almost everyone reading this, the honest conclusion is the one the maths forces: spend the money on solar panels, which collect over a large fixed area regardless of how still the air is, and leave the wind to the giants doing it properly, out at sea, where the cube law is finally on their side.