#3: Wind Turbines, Anyone?
Have you ever wondered how those giant spinny things actually work?
Today, we’ll be doing another engineering article, but instead of looking into solar energy for the third time, I’m instead going to switch gears and transfer over to wind turbines. Now, as a self-proclaimed sustainable energy fanatic, I have to admit that most of my work is concentrated onto solar energy (both thermal and photovoltaic), as well as some tinkering in tidal/hydroelectric systems.
So, this is a bit new for me, but I like it this way! We’ll be working to understand the basic functionality of how a wind turbine actually works, both from a logical perspective as well as a mathematical perspective. I’ll also direct you to some outside resources regarding the functionality of wind turbines because deep knowledge is sick. So, I won’t keep you waiting any longer–let’s get into the good stuff.
When you look at a wind turbine…it’s kind of easy to understand how the basic process works. Well, by a basic process, I mean the process leading up to the process…let me explain.
There are two things in play when we consider a wind turbine. First, we have the turbine itself. A giant stick planted in the ground with three large blades. Next, we have the wind. It can blow in any direction, in any way, at any speed.
Naturally, given the name of this technology as ‘wind turbine,’ we can tell that these two phenomena must combine in some sort of way. In essence, the wind hits the blades of the turbine and starts to spin them. Then, by some process we don’t actually know (by we, I mean us on this blog), this movement is converted into electricity.
Now, if you’ve ever taken a physics class, you probably know that energy is often transferred from one form to another. Whether you’re trying to light up a circuit, or trying to make a wind turbine work, it’s always one thing transforming into another…typical, but awesome.
So, for our wind turbine, we know that the blades are constantly spinning as a result of the air flowing through them, so all we need to work out is how this spin is converted into electricity. For this, we must consider another device, one that acts behind the scene for many different renewable energy technologies. That’s right, I’m talking about the electromagnetic generator.
If you’ve ever taken an advanced physics class, you’ll instantly recognize the item in the picture above. However, for those of you who haven’t allow me to explain (it’s actually really cool). That is an electric generator, which works with the principles of electromagnetic induction.
It’s got two main parts: a square circuit, and a giant magnet, set up so that the magnetic field flows through the square circuit. Simple, right?
Well, as it turns out, the square circuit is constantly spinning. This makes a lot of sense, considering that it’s attached to a spinning set of blades, as we had established earlier. So…why does this matter? To answer that, we need to consider the laws of electromagnetic induction.
Since this circuit is actually placed in a constant magnetic field, what ends up happening is that electricity (specifically an alternating current) can be produced in this way. It’s given in accordance with Faraday’s law of induction, as shown here.
So, if you’re confused by this, that’s completely understandable. It’s pure physics. Watch the video linked above if you need to learn it, or if you just want a refresher. Anyway, Faraday’s law above essentially states that the electromotive force E (which is kind of like the voltage, but still different) is equivalent to the rate of change of magnetic flux. Of course, flux is represented by the symbol.
For physics gearheads out there, you’ll know that flux can be represented by the following equation.
Since the circuit in question is spinning around due to the steam-powered turbine, that means that there is a rate of change in flux over time. At certain points, when the circuit is perpendicular to the magnetic field, the flux will be maximized, and when it’s parallel, there will be no flux.
If you’d like to get a better understanding of how this actually works click here to be taken straight to a PhET simulation that deals with understanding Faraday’s’ law of induction. After all, that is the process used to make this stuff work!
This, in turn, is able to create an electromotive force, and therefore create electricity. Isn’t that cool?
Although we could consider this to be set and done, we should also consider how to model the power generated by the wind turbine, using some physics. While we can technically just throw the equation mentioned above and use that as our explanation, we shouldn’t.
So, let’s begin. We know that the air flowing through the turbine has some kinetic energy, which is being transferred into electric energy. That tells us that to begin, the energy we have is actually equal to the following.
Okay, so now, we should also consider that the equation above actually represents energy and not power. To get from energy to power is quite simple, we just need to divide by time. So, we can do that really quickly.
Now, the key is to convert this into an equation we can actually understand. When we consider air, we can’t really know what the mass is. After all, it is a gas. However, we can derive it! For that, turn your attention to the diagram below.
As you can see here, we can break down the arbitrary mass that we don’t know into three other components: density, cross-sectional area, and displacement. Multiplying these three together can get us the mass of air actually being pushed through the wind turbine. It’s actually quite simple. What we can do now is modify our equation to consider this.
We can also modify one of our terms to consider velocity instead of displacement over time. Simple simplification.
From the equation above, we can see that the power depends on two of factors: cross-sectional area and wind speed. So, shouldn’t the best design be a giant wind turbine in a really windy area? Why do people invest so much money, time, and effort into designing the best possible wind turbines?
Well, it’s because our equation above assumes that the wind turbine we design has a perfect, or near-perfect efficiency. In reality, this is obviously not the case. Not all of the kinetic energy is transferred into the wind turbine, and a great deal of wind still leaves.
So, that means we need to add in another coefficient into our equation. It looks like this.
What does that mean? It represents the efficiency, and this depends on a bunch of factors. Some of these are listed below:
- Blade strength (material)
- Blade curvature
- Blade weight
- Gear assembly
- Generator material (conductivity)
…and many more. What wind turbine engineers do is try to change, manipulate and switch these factors around in order to make the efficiency value as high as possible. This, of course, depends on the environment in which the turbine is used, as well as other factors, such as the affordability, accessibility, and sustainability of the materials and designs used.
Today, the value of n tends to be approximately 0.40, which represents an efficiency of 40%. What does that tell us? There’s still a long way to go, and a lot of innovative design that could be implemented by future and current engineers. So, yes, the field of wind turbines is still growing exponentially!
Hope you enjoyed reading this article! I took an in-depth look at the functionality behind different wind turbines, trying to understand exactly how they work, why they’re important, and how we can continue to improve them. Wind turbines are often left in the shadow of solar power when we try to talk about renewable energy, but really, they deserve to be explored in their own right! Thanks for reading, and until next time…see ya!
