It is amazing that we can get electricity from the wind, but that is exactly what happens with a wind farm. This is a collection of wind turbines in a particular place where the wind is plentiful. And as for many things, the bigger it is, the better it is. The Hornsea windfarm, for example, is under construction 75 miles off the coast of Yorkshire, England, and once completed, it should be the largest offshore wind farm in the world Here are some big wind turbines: The video indicates that the diameter of the wind turbine is 154 meters (more than 500 feet).

But here is the part that interests me. They claim that only one tower of these giant wind turbines can generate enough energy To power a house for a whole day. You know what comes next, right? An estimation. Let's see if the numbers add up for this claim.

I guess we should start with the basic physics that makes this wind turbine create electricity. Like most other methods of producing electricity, it is a matter of transforming a wire into a magnetic field. When a changing magnetic field passes through a coil, it generates an electric current. But then, how do you get that reel to spin? For a wind turbine, air entering the large blades pushes them in a rotational motion.

Of course, you will not have to use the wind to turn you into a turbine. You can use running water by placing a type of propeller dawn in moving water, such as a stream or dam (hydroelectric plants of this type). Another popular option is to heat water and let the steam turn into a turbine. This is how coal and natural gas power plants operate. This is also how the nuclear power plant works. The only difference between nuclear and coal power generation is that a fossil fuel is used to heat water and the other uses a nuclear reaction. The parts of the turbine are the same. It's crazy if you think about it. In reality, the only method of producing different energy is the solar panel. It works with a different method.

It's good and everything, but how do you estimate the power (then the energy) of a wind turbine? All energy comes from the kinetic energy of the moving air. The kinetic energy can be calculated as follows:

In this expression, *m* is the mass of air and *v* is the speed of the air. Suppose the air enters the turbine with a speed of v_{1} and then leave at a slower speed of v_{2}. This decrease in speed leads to a decrease in the kinetics of energy, that is to say this energy which is transformed into electricity. Speeds can be easy to estimate, but what about the air mass?

Suppose that a large cylinder of air enters the turbine. The section of this cylinder is a circle of the same size as the rotating accessories and the length of the cylinder is simply a value. For the moment, I will call him *The*. This diagram should help.

What is the mass of this giant air cylinder? Well, if I know the density of air (I know) and the volume of a cylinder (yeah), I can calculate the mass of air. Do not forget that a good estimate of the density of air (ρ) is about 1.2 kilograms per cubic meter.

One more thing is missing, the length of this cylinder of air (*The*). If the air moves with a speed of *v*_{1} For a time interval (Δt), the length of this cylinder would then be:

It just comes from the definition of speed in a dimension. Now, instead of estimating the length, I can estimate the time interval. Do not forget that we are trying to find the energy of a rotation of this wind turbine. I can just watch the video and see a real rotating turbine. My guess is that it takes about 4 seconds to perform a rotation.

There are only a few things left to estimate:

- Initial air speed = 5 meters per second (11.2 mph)
- Final air speed = 2.5 meters per second (5.6 mph)
- Efficiency (fraction of kinetic energy going to electrical energy) = 0.25
- Average power of a house = 2,000 watts.

Now for the calculation. Here it is (you can change the values if you disagree with my estimates). If you want to see and change the code, click on the pencil icon. Click the Play button to run it.

So, that did not work. Using my values, the single turn of the wind turbine creates 291 watt hours (an energy unit), but a house consumes around 48,000 watt hours. I am a factor of 100 or more. This means that you would need 100 turbines (or 100 rotations) to get enough energy to run a house for a day. OK, so what went wrong? There are several options. Obviously, my estimates could be wrong. But why would they be by a factor of 100? Even if I double the wind speed and I put the final air speed to 0 m / s, it is still not enough energy.

The other option is that there was an error in the video. Hey, that's possible. We all make mistakes. Maybe they wanted to say that a rotation was enough to run a house for two hours, or something like that. Who knows What I know is that even though my calculations do not match the video, wind turbines can produce quite a bit of energy.

### More great cable stories

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. (tagsToTranslate) Dot Physics (t) Energy (t) estimate (t) Python</pre></pre>
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