Thanks to Albert Einstein's famous equation E=mc 2, we all know that a very small amount of mass can in theory be turned into a very large amount of energy. The speed of light, c, is big but the square of the speed of light? That's just off the scale.
Another equation, which is the key to understanding a very topical energy issue, is P=CAv 3. This is the calculation of a wind turbine's power output of a wind turbine. Turbines have become symbols of low-carbon lifestyles. Unfortunately, they have also become the focus of some very heated arguments and poorly informed comment.
Everyone seems to have a strong view on wind farms. The recent decision by B&Q to sell domestic turbines has added fuel to the fire, not least in green building circles where doubts about their viability have been voiced. At the heart of all this wrangling is the inescapable fact that wind turbines are sensitive beasts: their performance depends on where you live and where you put them.
It's obvious that the more wind you have, the more power a turbine will produce. But take a closer look at that equation. P, the power output, is proportional to the area A swept by the turbine blades (C is a constant defined in part by turbine efficiency). But P is proportional to the cube of the wind speed (v multiplied by v multiplied by v). So if you increase the length of your turbine blades and double the size of the area they sweep, you will double the power output, but if you take your turbine up a hill and double the wind speed, you will increase the power output eight-fold.
This explains why power companies are so keen to put wind farms on hilltops - and why the output of domestic turbines often fails to meet expectations, especially in urban areas. It doesn't take much to obstruct the wind in a city - and when the wind speed drops, your power output collapses.
To get an idea of how much power you might get from a domestic wind turbine, ignore what the salesperson says and ask for a copy of the turbine's power curve, which shows how its output varies with wind speed. Then look yourself up in the national wind speed database ( www.bwea.com/noabl). If your home has an unobstructed view of the wind, the figure you get is likely to be reasonably accurate. If there are buildings or trees around you, it is not. For example, an experienced turbine enthusiast in Scotland found the average measured wind speed on the roof of a house in Edinburgh to be one-third of the speed given in the database ( www.scoraigwind.com). Adjust accordingly.
Rooftops, buildings and trees also cause air turbulence. This forces the turbine to chase the wind, seriously affecting its output and shortening its life. Some models are designed with turbulence in mind, but there's a way to go before this problem is cracked.
My aim is not to put you off, merely to clarify when and where this technology is likely to be worthwhile and so limit the grumpy backlash. If you have lots of wind, exploit it (for suppliers and grants, see www.lowcarbonbuildings.co.uk). If you face obstructions, raise your turbine on a pole to get as steady a wind as you can. If you're surrounded by rooftops, there are better (if less trendy) ways to get a good eco-return on your money, such as improving insulation, air-tightness and lighting. And if you are using a roof-top turbine to power lots of incandescent light-bulbs, you've definitely got the wrong end of the eco stick.
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For accurate measurement of your rooftop wind, install an anemometer. The WS1600 weather station is available for £99.95 from The Weather Shop (01323 479 769; www.ukweathershop.co.uk).
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