Wind turbines are not inefficient

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From the BBC last week,

Critics of wind turbines argue vehemently that they are ugly and inefficient – a blot on the landscape and an expensive folly to boot.

Efficiency has always been a strange critique given that the fuel driving turbines – wind – is free. And while electricity generated from wind may currently be more expensive than that from some fossil fuels, costs are coming down fast.

The BBC should consider running these pieces past an engineer. Wind turbines are not inefficient. And anyone who claims they aren’t generally doesn’t know what they are talking about. Alternatively, what they are normally referring to is the fact that wind itself is an intermittent source of power.

This of course is a totally different thing to wind turbines being inefficient.

How efficient are wind turbines?

Theoretically, a turbine cannot generate electricity at an efficiency greater than that defined by Betz’s Law, that is 59.3%.

So, that’s the theoretical maximum. Yet, last year a Daily Express headline informs us that “Wind turbines at 90 per cent efficiency LESS than 20 hours a year”. This laws of physics defying feat should have warranted a phone call from the Nobel committee and not the scorning of a British tabloid. But I guess there is no need to understand what you are talking about when  attacking wind farms.

Let’s look at the efficiency of a typical turbine, the Enercon E70.

The power output of a wind turbine varies with wind speed, something that is generally referred to as the power curve. Here it is for the Enercon E70, a 2.3 MW turbine:


As you can see, the output of the turbine increases very rapidly with wind speed initially, and then it reaches its maximum output at a wind speed of around 12 m/s. Further, the turbine switches off for safety reasons at a speed of 28-34 m/s. This cut off does not matter much, winds rarely reach that speed anyway.

How efficient is the turbine? If we want to know this we simply need to compare the kinetic energy that flows through the turbine at each wind speed and compare that with electrical energy that comes out the other end.

This requires some relatively straight forward physics, which I won’t go into here. But, all you really need to know is that kinetic energy equals half of mass times velocity squared, the typical mass of air, and the diameter of the turbine, in this case 71 metres.

After some simple calculations, you then get the efficiency of the turbine, which is shown below.


So, the turbines peak efficiency is 50%. This is excellent, and is 80% of the theoretical maximum. Similarly, over most relevant wind speeds the efficiency is greater than 30%. This is highly efficient, not inefficient as many ill informed opponents of wind farms will tell you.

It can also be compared with typical efficiency of coal and nuclear power plants, which is around 35-40%. So, clearly, by the standards of energy conversion wind turbines aren’t that bad.

But, it also shows that wind turbines cannot be improved that much in terms of efficiency. A doubling of efficiency is simply not physically impossible.

So, next time you here breathless headlines about massive improvements in the efficiency of wind turbines, try to keep in mind the laws of physics.


One thought on “Wind turbines are not inefficient

    jmdesp said:
    March 12, 2015 at 12:52 pm

    Thanks, that’s great information, I had no idea the available data actually allowed to calculate precisely how much of Betz’s Law is reached.


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