- Hold on mate

Last week I did some simple calculation to estimate how many solar panels are needed to run a small electric car for a year. There were some assumptions made, the car does 12,000 miles a year and it uses 200Wh per mile. I am going to stick to those same assumptions and have a look at wind turbines this week.

Wind turbines are the poster boy of the renewable energy, they are a very visual symbol that electricity can be generated in other ways. In reality though, wind turbines are really solar generators. This may seem an odd thing to say, especially as they work at night, but bear with me while I explain.

Wind is caused by air rushing from an area of high pressure to an area of low pressure, anyone that has blown up a balloon and then let the air out knows this. So how does the air in our atmosphere get to be at different pressures. Simple, the sun heats some parts more than others. This causes the local air pressure to increase and if it is surrounded by lower air pressure, it tries to equalise by moving hot air to the colder, lower pressure area. That is wind. Ok, it is a bit more complicated than that as hot air rises, the Earth spins, there are strange going ons around the poles, oceans and land have different characteristics, but basically wind starts in hot sunny places and blows to colder, darker places.

Now enough of that, so how does a wind turbine work.

Quite easy really, it is vectors.

A wind turbine blade is like a sail or aircraft wing. Wind, which has mass and velocity, hits one side of the blade, so is deflected away from it, this causes the velocity to slow.

As we all remember from science lessons at school, kinetic energy is ½ x velocity squared. So some energy has to have transferred to the blade. This causes the blade to move. Now as it is fixed to the generator shaft in the middle, all that can happen is that the blades spin. If the wind speed is high enough to overcome all the inertia and frictions, there is enough left to make some electricity. It really is that simple.

The trick is to design a wind turbine that is efficient. This is a problem as, and trust me on this, they do not have the same efficiency at all windspeeds. They tend not to work below about 4MPH and start to destruct above about 35MPH. We are totally stuck with the lower end, but can design a turbine blade to stall at a higher windspeed. This stalling is really just a self regulating mechanism and is similar to what limits the speed that propeller drive aeroplanes can travel at.

So when designing a wind turbine, we try to maximise the design to the available windspeeds for a given area. This has nothing to do with the number of blades, or whether it is a vertical or horizontal axis turbine, it is purely down to the design of the blade and the area presented to the wind. This is partly why blades have a variable profile, the centre bit is wider and at a steeper angle to the wind than the tip. Sailors can explain to you about ‘apparent wind’ better than I can, but it is just a vector issue.

Another thing that affects the output of a wind turbine is the overall diameter. If you think of this as a circle, doubling the diameter does not double the surface area, it quadruples it. It is what the squared in Pi x Radius Squared does (I wish I knew how do do superscript on the DriveTribe website).

There are two other things that affect the generation capacity, one is the height of the turbine above the ground. The higher they are, the faster the windspeed and the less turbulent the airflow.

The final thing is a limit to their efficiency, this is called Betz Limit and is just a calculation that shows that it is not possible to capture more than 59.3% of the kinetic energy in the wind hitting it. Very large turbines have percentage efficiencies in the mid 50s at optimal windspeeds. Small turbines are lucky to hit the mid 20s. That is why it is better to have one very large wind turbine than 4 smaller ones. Less is more.

So we can see that as air rushes from a hot place to a colder place, the wind blows, some of that wind energy can be captured and used to generate electricity. That electricity can be used to charge up your car.

So how big does this turbine need to be to generate enough power to run your car. And does the output change much during the year.

Second part first, yes, it is windier in the winter than the summer, but not in the way you think. In the winter we tend to get storms and gales that can be quite ferocious, in the summer we tend to have lighter winds, but they change less and summer storms are rarer. So there is not as great a difference as many people think.

There is a way to statistically calculate all this, which I may explain another time as it involves the Weibull Distribution. This shows that for any given mean windspeed, there is a skewed distribution. Higher windspeeds have a greater probability of more time above the maximum that the turbine can stand, lower windspeeds and there is a greater probability that there is not enough wind to get the wind turbine started. That nicely leads into the final point about wind turbines.

The generation capacity is set by the mass flow rate of the air and the diameter of the turbine. Due to some arithmetic cleverness, this means that power is proportional not to the windspeed, but to the cube of the windspeed, so for every doubling in windspeed, you can get eight times the energy out. Pretty useful to know that. Why we need to stick them on the top of high hills, they produce more energy up there.

So getting back to the purpose of this, how large does a turbine need to be to produce the 2,700 kWh needed to drive 12,000 miles.

Firstly you need to know the amount of time that the car will be at the charging place, we can call that home, but because a wind turbine is cheaper than battery storage we can dispense with that and just get a larger turbine. So say we have a good half day to charge the car, all we need to do is double the capacity of the wind turbine.

Using Leeds as my ‘base place’ only because it is in the middle of the country, I looked up the local mean annual windspeeds at 10 metres height, a pleasant 5.1 m/s.

Then I found an online turbine calculator that I knew was good (and I cannot find the spreadsheet I used at university to calculate all this). Plugged in some number and adjusted the diameter until I got the size I need to produce 5,400 kWh/year.

And now the bit you have been waiting for.

It has a diameter of 4.3 metres and would have an installed capacity, of around 5 kWp.

The nearest I can find to that is the Britwind R9000. No idea how much they cost now, probably not much change from £20,000 once installed.

And it is wider than my house, so would have to move again.

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