How Wind Turbines Work

In a conventional power plant (fueled by coal or natural gas), combustion heats water to steam and the steam pressure is used to spin the blades of a turbine. The turbine is then connected to a generator, which is a giant coil of wire turning in a magnetic field. This action induces electric current to flow in the wire. The workings of a wind turbine are much different, except that instead of using a fossil fuel heat to boil water and generate steam, the wind is used to directly spin the turbine blades to get the generator turning and to get electricity produced.

The inner workings of a wind turbine consist of three basic parts, seen in the figure below. The tower is the tall pole on which the wind turbine sits. The nacelle is the box at the top of the tower that contains the important mechanical pieces – the gearbox and generator. The blades are what actually capture the power of the wind and get the gears turning, delivering power to the generator. The direction that the blades are facing can be rotated so that the turbine always faces into the wind, and the pitch of the blades (the angle at which the blades face into the wind) can also be adjusted. Pitch control is important, especially in very windy conditions, to keep the gearbox from getting overloaded.

Modern wind turbines sit upon towers that are typically 80 meters high or taller, with rotating blades that are 50 meters or longer.

Source: Wikipedia: Lamma wind turbine CC BY-SA 3.0 (Creative Commons)

The amount of power (in Watts) collected by a wind turbine is explained in the following equations:

The physics of wind power

Click here for a text description of the physics of wind power equation.

This figure explains the physics of wind power. So we begin with this notion of the moving wind having some kinetic energy which is 1/2 m v2. So that is kinetic energy. Power is related to energy in the following way: It is energy per unit of time. So if we want the power that we can get from that moving wind, we have to take the kinetic energy, and then the mass flux rate instead of just the mass. Mass flux rate is how much mass is moving per unit of time. That is dm over dt, change in mass over change in time. And that is equal to the air density times the area swept out by the windmill blades times the velocity, so that velocity and area multiplied together gives you something with the units of measure are cubic meters per second, and then you multiply that by the density and that gives you kilograms per second and that’s the mass flux rate. If you put all that together, you see the wind power is equal to one half times the air density times the area swept by the blade times the velocity cubed. So you see, the velocity is super important in this. Now then it turns out that there is an efficiency limit, something called the “ Betts Limit” that means that the power you can actually collect is 0.3 times the air density times the velocity cubed.

Source: David Bice

The Kinetic Energy (KE) of the wind is:

K E = \frac{1}{2} m v^{2}

Where m = mass, and v = velocity of wind.

Power (P) in the wind is the KE per unit time, so we replace the mass(m) with the mass flux rate dm/dt:

P = \frac{1}{2} \frac{d m}{d t} v^{2}

\frac{d m}{d t} = ρ A v

Where p = air density, and A = swept area of blades.

So the wind Power(P) is:

P = \frac{1}{2} ρ A v^{3}

If the wind turbine collected all of this power, the wind would have to stop and the blades would stop spinning. If you want the blades to keep spinning, it turns out that you can collect about 60% of the power (called the Betz limit).

So, collectible Power(P) is:

P = 0.3 ρ A v^{3}

How much power could we get with a turbine whose blades are 100m long, with a wind speed of 10m/s (about 22mpg>, with an air density of 1.2kg/m2?

P = 0.3 \times 1.2 \times π \times 100^{2} \times 10^{3} = 11, 304, 000 Watts = 11.3 MW

This is clearly a lot of power! But, mechanical inefficiencies related to the gears and the generator mean that we might only get 30% of this figure, but that is still a lot of power from one turbine.

All wind turbines have a minimum wind speed that differs depending on the size but is typically about 4-5 m/s (10 mph) and maximum wind speed above which they shut down to avoid damage, usually around 20-25 m/s (about 50 mph). Most wind turbines have a maximum spinning rate, reached a bit above the minimum velocity, and when the wind speeds up, the pitch of the blades is adjusted so that the rate of spinning remains more or less constant. The figure below shows a typical "power curve" for a small wind turbine.

Power curve for 1.5 MW wind turbine. Wind on x-axis, power on y-axis. Power increases with wind speed til 50 mph where power drops to 0

Power curve for a 1.5 MW wind turbine

Click here for a text description of the power curve for 1.5 MW wind turbine.

This figure shows the power curve for a 1.5 megawatt wind turbine. So on the Y-axis is the power and the X-axis is the wind speed in miles per hour. And what you can see is that there is sort of a threshold speed that is something like 6 miles per hour wind speed you start to get some power. And as the wind speed increases, the power output rises rapidly until you get to about 30 miles per hour. At that point the power sort of saturates and flattens out and with more wind you don’t get any more power. So it reaches its capacity at 1.5 megawatts and it generates that up until 50 miles per hour and above that the power drops off rapidly because the wind turbine has a shut off mechanism will turn off if the wind gets going to fast because of the turbulence that can cause damage to the wind turbine. So they just shut down if the winds get to great.

Source: US Department of Energy, Idaho Office

The wind, as you may have noticed, is highly variable in any given place, but as a general rule, it is stronger and steadier as you rise up above the ground. This is because friction between the wind and the land surface slows the wind. But there is also a lot of regional variation in the wind velocity. Both of these factors (elevation above the ground and location) can be seen in the maps below, showing the average wind speed in the US at two different heights.

graph showing annual average wind speed at 30 meters in U.S.

United States - Annual Average Wind Speed at 30 m

Click here for a text description of the U.S. Annual Average Wind Speed at 30 m.

These two maps of the United States show the average annual wind speed at two different heights above the surface. The upper map shows the wind speed at 30 meters height and the one below shows it at about a hundred meters. You can see a couple thing right away. One is that there is just a lot more wind at greater velocities at this higher elevation above the lands surface. You get to 100 meters and there are a lot of places in the central part of the US where you get wind speed from 8 to 10 meters per second, which is really moving along quit fast. And you also see this lower map of 100 meter of wind speeds of the offshore regions everywhere on the west coast and the east coast and around the Gulf of Mexico there are very high wind speeds. Also the Great Lakes are like this. The primary reasons these offshore regions have such high wind speeds and also why higher up you have such wind speeds are because there are less friction in those settings. So you go higher up from the surface there is less friction from the air and all the trees and the roughness of the land surface. That roughness slows the wind down and as you rise above that to 100 meters you get away from that disturbance and have higher wind velocities. You can also see that in the mid-continent region, both the 30 meter and the 100 meter heights, that’s the area with the greatest wind potential. You have these annual average wind speeds that are quit high and this is primarily because this is flat part of the country. There are not a whole lot of topography in those areas so the winds can really get going and be maintained. They do not encounter mountains and valleys and the sort of complexity that you see in other areas where further out west the wind speeds are not that high. So you can look at this and see right away that if you wanted to develop wind power, the best places are in the middle of the continent and at a high elevation 100 meters above the surface. That is why you see so many tall wind turbines to get up that high.

Credit: National Renewable Energy Laboratory (NREL)

graph showing annual average wind speed at 100 meters in U.S.

United States - Land-based and Offshore Annual Average Wind Speed at 100 m

Click here for a text description of the U.S. Land-based and Offshore Annual Average Wind Speed at 100 m.

These two maps of the United States show the average annual wind speed at two different heights above the surface. The upper map shows the wind speed at 30 meters height, and the one below shows it at about a hundred meters. You can see a couple thing right away. One is that there is just a lot more wind at greater velocities at this higher elevation above the land's surface. You get to 100 meters and there are a lot of places in the central part of the US where you get wind speed from 8 to 10 meters per second, which is really moving along quite fast. And you also see this lower map of 100 meter of wind speeds of the offshore regions everywhere on the west coast and the east coast and around the Gulf of Mexico there are very high wind speeds. Also, the Great Lakes are like this. The primary reasons these offshore regions have such high wind speeds and also why higher up you have such wind speeds are because there are less friction in those settings. So you go higher up from the surface, there is less friction from the air and all the trees and the roughness of the land surface. That roughness slows the wind down and as you rise above that to 100 meters you get away from that disturbance and have higher wind velocities. You can also see that in the mid-continent region, both the 30 meter and the 100-meter heights, that’s the area with the greatest wind potential. You have these annual average wind speeds that are quite high, and this is primarily because this is a flat part of the country. There are not a whole lot of topography in those areas, so the winds can really get going and be maintained. They do not encounter mountains and valleys and the sort of complexity that you see in other areas, where further out west the wind speeds are not that high. So you can look at this and see right away that if you wanted to develop wind power, the best places are in the middle of the continent and at a high elevation 100 meters above the surface. That is why you see so many tall wind turbines to get up that high.

Credit: National Renewable Energy Laboratory (NREL)

The graphs above show annual average wind speeds in the US at 2 different heights above the ground surface. For reference, 10 m/s is 22.3 mph. You can see that the wind speeds at 100 m are far greater than at 30 m — this is the friction effect of the land surface (which is minimal above large water bodies). As you can see, the Great Plains have great wind potential, as do the Great Lakes and offshore areas on both coasts.

The area covered by the turbine’s blades is another important factor in determining power output. While wind turbines are available in a wide variety of capacities, from a few kilowatts to many thousands of kilowatts, it’s the larger turbine sizes that are being deployed most rapidly in wind farms. Several years ago the image on the right side of the figure below of a Boeing 747 superimposed on a wind turbine gave an astonishing representation of the scale of the state-of-the-art wind technology. Now, turbine rotor diameters are approaching the size of the Washington Monument!

Graph shows increase in wingspan of turbine blades over 10 years, explained in caption.

Over the past decade, wind turbine blades have grown from being about the size of the wingspan of a jumbo jet to being about as long as an American football field.

Click for a text description of the Wind Turbine graph.

The image is a graph that illustrates the progression of rotor diameters of wind turbines over time, comparing them to the wing span of an Airbus A380.

The x-axis represents the years from 1985 to 2010 and beyond, with specific years marked: '85, '87, '90, '91, '93, '95, '97, '99, '01, '03, '05, '10, and an estimated future point labeled as "1ˢᵗ year of operation" with a capacity range of 8 to 10 MW.
The y-axis represents the rotor diameter in meters (m), ranging from 15 meters to 250 meters.
The graph shows a series of circles, each representing the rotor diameter of wind turbines at different points in time. These circles increase in size as the timeline progresses, indicating the growth in rotor diameter over the years.
Each circle is labeled with its corresponding rotor diameter:
- 1985: 15 m
- 1987: 30 m
- 1990: 40 m
- 1991: 50 m
- 1993: 60 m
- 1995: 70 m
- 1997: 80 m
- 1999: 90 m
- 2001: 100 m
- 2003: 110 m
- 2005: 120 m
- 2010: 130 m
- Future (8-10 MW): 250 m
A red line runs through the centers of these circles, showing the trend of increasing rotor diameter over time.
On the right side of the graph, there is an illustration of an Airbus A380 with a wing span of 80 meters for comparison. An arrow points from the Airbus A380 to the largest circle (250 m), suggesting a comparison between the wing span of the airplane and the rotor diameter of future wind turbines.
The background of the graph is light blue, and the circles are shaded in orange with red outlines.

This graph visually demonstrates the significant increase in wind turbine rotor diameters over the years, projecting into the future with much larger sizes compared to current standards.

Credit: UpWind: Design Limits and Solutions for Very Large Wind Turbines, 2011. European Wind Energy Association

Activate Your Learning

Given that the area of wind captured by the turbine is proportional to the square of the radius (essentially the length of the blade), if you were to double the length of a wind turbine's blade, how much more power would that turbine generate? Assume that wind speed and all other variables remain the same.

Click for the answer.

ANSWER: The area of a circle is given by A=πr², where r is the radius of the circle. If the length of the blade, which defines the radius of the circular area over which wind is captured, was increased by a factor of 2, then the area would increase by a factor of 2². Therefore, if all other variables were held constant, then according to the wind power equation above, doubling the blade length will produce 4 times as much energy.