How Much Power Does a Wind Turbine Produce
Are you thinking about building a wind turbine? If so, you’re probably asking yourself, “How much power does a wind turbine produce? In this article, I am going to explain exactly how much available power is in the wind.
Then I am going to explain how much of that power can actually be harnessed, and, finally, I am going to use real DIY wind turbine examples to explain how much electricity can be created with typical do-it-yourself wind power systems.
The Power in the Wind
The power in the wind is measured in watts. The formula is:
Watts = (.5) (rho) (A) (V^3)
Don’t worry, it’s simpler than it looks. “Rho” stands for air density, and, at sea level, one cubic meter of air weighs 1.23 kilograms: therefore, we insert 1.23 for “rho.”
“A” in the equation represents what is called swept area. Swept area is a representation of how much area your wind turbine blades cover. To figure out your particular wind turbine’s swept area, use this formula, A = pi x r^2.
Or, to keep things simple, A = 3.14 X the length of one turbine blade squared.
“V” in the equation represents the velocity of the wind. In this space, you would insert the average wind speed where you plan to install your wind turbine.
So, in simple terms, the power of the wind can be figured like this:
watts = .5 X air density X swept area X wind velocity ^3
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The Power Your Wind Turbine Can Take Out of the Wind
The above formula shows you how much energy is in the wind. It does not tell you how much energy you can extract from it. It is only possible to extract 59.26% of the energy available in the wind. I won’t go into the details here, but if you would like to know more, you can study the Betz Law.
So, does this mean that we can use a wind turbine to extract 59.26% of the total power of the wind, as described using the information above? No, it doesn’t. Why? Because there are inefficiencies in wind turbine blades and in the gears and motors used to generate electricity.
Okay, what’s the bottom line? The bottom line is that using a small, well built DIY wind turbine you should be able to extract about 30% to 35% of the power in the wind.
Your Wind Turbine
Okay, let’s dive into what’s really important. How much power is your own personal DIY wind turbine going to produce?
Well, let’s say that you are going to build a 6-foot wind turbine, meaning each of your blades is 3 feet long. The wind in your area blows at 12 MPH. Before we do anything, we need to convert our figures into metric numbers. Our blades are 3 feet long, which equals .914 m. 12MPH needs to be converted into meters per second, which is 5.36 meters/second.
Our formula is…
Watts = (.5) (rho) (A) (V^3)
Let’s fill in the easy numbers first.
Watts = (.5) (1.23) (A) (5.36^3)
Now we need to get our “swept area,” (A). To do that we use the simple equation A = 3.14 x length of one blade^2. Our blades are .914m long, so to get our swept area we use the equation…
A = 3.14 (.914 ^2)
A = 3.14 (.835)
A = 2.62
Now we go back into our original equation and insert 2.62 for our swept area (A).
Watts = (.5) (1.23) (2.62) (5.36^3)
Watts =(.5) (1.23) (2.62) (153.99)
Watts = (.615) (2.62) (153.99)
Watts = (1.61) (153.99)
Watts = 247.92
As you can see, there are 247.92 watts available for our wind turbine. Remember, though, that your wind turbine is only going to be able to extract about 30% to 35% of the power available. So, in reality, for your DIY wind turbine…
Watts = 247.92 (35%)
Watts = 86.77
So, what you’ve got is a wind turbine rated at 87 watts. What does that mean exactly? An 87-watt wind turbine produces 87 watts for each hour of operation. So, if the wind at your location blew 24 hours a day at 12 MPH, you would produce 2088 watts per day, or about 2 kw (kilowatts).
What would this power?
The average laptop uses about 35 watts per hour.
A CFL light bulb uses about 25 watts per hour.
A 42-inch ceiling fan on low uses about 24 watts.
So, under the above mentioned circumstances, with one small DIY wind turbine, you could sit in a room with a ceiling fan, a light bulb and a laptop computer and not have to use any power from the grid.
Of course, we don’t really live like this. Our wind turbine is not going to be spinning at 12 MPH for 24 hours a day, nor are we going to be sitting in our home with a light bulb on and a computer running for 24 hours a day. And, most importantly, there are wonderful things called batteries that we can use to store the energy our wind turbine makes.
This means that while we are sleeping, or at work, or playing outside, we can use our wind turbine to charge up our battery bank. Then, in the evening, for example, we can use that stored up energy to watch TV or surf the Internet.
How much energy would you need to produce to go off the grid? Well, that varies widely between households. In order to figure out exactly how much you would need to produce, head over to my home energy audit page.