The most dispiriting thing about trying to live a more environmentally friendly lifestyle is that it is all about not doing things.

We are told we have to stop flying, stop driving, stop eating meat, stop heating our houses... the list goes on and on.

So it is a nice change to be told that there is something you can do which will reduce your impact on the environment AND requires that you buy yourself a nice bit of kit to boot.

Bring on the domestic wind turbine!

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What could be more environmentally friendly than harvesting electricity from the wind and what better ethical badge of honour than a turbine spinning on my roof?

That's certainly what I thought three years ago, when my family and I were challenged by the Newsnight editor to try to make our lifestyle greener.

Unfortunately, I wasn't the only wannabe ethical man to want to reap the wind. As I began exploring the possibility of erecting a turbine on my terraced London home the Tory leader David Cameron announced his ambition to do the same.

The question was, who would get theirs up first?

Three years on and neither I nor the Tory party leader have a turbine on our roof.

Why?

The answer is very simple. In most urban locations in Britain wind turbines simply do not work.

Yes, they spin, but they do not generate significant amounts of power. Why not?

Here's the science bit... (don't worry, you will be able to follow it).

A simple equation gives the power of the wind. Power = 0.5 x collection area x the wind speed cubed.

What it tells us is that the power of a turbine is related to two factors: the size of the turbine and the strength of the wind.

Let's look at size first.

Cast your mind back to your GCSE maths (I'm old enough to have done O-levels). No doubt you dimly remember that the area of the circle is equal to the constant pi (3.14) times the radius of the circle squared.

What that means is that as you increase the length of a turbine blade, the collection area increases disproportionately.

Take the micro turbine I was planning. Its blades were 1.75m long, giving a collection area of just under 10sq m. Tiny.

Compare that to the wind turbines I visited in Texas earlier this year. Some had turbine blades 45m long, giving a collection area of 6,358sq m. Huge.

The message is clear from the maths - small turbines have disproportionately smaller collection areas and therefore generate dramatically less power.

And what about wind speed?

The key here is that cube function on the wind speed. The power of the wind is related to the cube of the wind speed. So, at low wind speeds you get virtually nothing. When it really blows it you get a lot of power.

Here's why. Double the wind speed and you get eight times the power. Quadruple it and you get 64 times as much. Eight times the speed and we're talking more than 500 times the power.

The figures given by Windsave, the company that was going to install my wind turbine, confirmed that.

It boasted that its 1.75m turbine would generate 1kW of power at speeds of 12.5m per second.

Pretty good, but 12.5m per second is a force 6 wind, a decent breeze.

Halve the wind speed to six meters per second (a moderate breeze) and - thanks to that cube law - you now get just 120 Watts - that's two standard incandescent lightblubs (10 energy friendly compact fluorescents).

Hum, not bad.

My house is on the flanks of the highest hill in London and is relatively exposed but I'm told that average wind speeds are likely to be between 4m and 5m per second. (You can find out the wind speed in your area here.)

At those speeds I'd be lucky to get 25 Watts. That is barely enough for two energy saving light bulbs. Nowhere near enough to live up to the company's promise of reducing my electricity bills by "up to 30% a year".

The message is clear. In most UK locations micro wind turbines will never generate significant amounts of electricity.

It makes a nonsense of the claim made by the Energy Saving Trust, when I was planning my turbine, that domestic wind turbines could supply 4% of all the UK's electricity needs and cut carbon dioxide emissions by 6%.

It also suggests the government should think again about offering a generous feed-in tariff for power generated from micro wind turbines.

And, if any more proof of my point was needed, in September this year Windsave went bust.

Of course, not all wind energy is a dead end. What our calculations tell us is that power increases dramatically as you increase the size of the turbine and the wind speed. So, a 10m turbine in a 10 knot breeze generates 100,000 times the power of a 1m turbine in a 1 knot breeze.

Indeed, if Camden, my local council, gave me planning permission for one of those Texan whoppers it would generate significant power - something like 200kW - even at 4m per second.

But even these impressive figures can't disguise the inconvenient truth about wind power: except in storm conditions it is - compared to fossil fuels - a very dilute energy source.

Professor David MacKay, the new chief scientist at the Department for Energy and Climate Change, has done the maths on this. Instead of kW, he calculates power in kWh, and he estimates that if we put wind turbines across the windiest 10% of the country, we would generate only 20 kWh per day per person in Britain.

According to MacKay, it takes 40 kWh to drive the average car 50km.

Add in offshore turbines covering a third of the available shallow water locations (44,000 turbines) and installing deep water turbines in a 9km-wide strip all round the entire British coast and you get an additional 48kWh day per person.

That's a lot of power, but even on quite conservative estimates the average UK resident uses 125 kWh day.

It leads to a dispiriting conclusion. Wind is, at best, only a very partial solution to the problem of how to generate low-carbon energy.