Energy from the Wind
Learning Objectives — Students will:
1. Be able to recount the historical use of wind energy to include power for boats and ships, pumping water, processing grain and sugar cane, and making electricity. Students will evaluate the impact of each of these technologies on the history of social development to include trade, agriculture, and human dispersal.
2. Be able to use data they collect to test the relationship between airfoil design and energy harnessed.
3. Be able to explain the basic principles involved in transferring wind energy to mechanical energy, to include the roles of lift, drag, velocity, and ways to link foils to rotating shafts.
4. Be able to use published data sets to evaluate specific locations for siting of wind turbines, to include fluctuations in wind velocity associated with altitude, latitude, and daily and seasonal cycles. Interpret US maps of wind fields—spatial and seasonal. Evaluate their state for wind farms.
5. Articulate the potential negative and positive environmental effects of wind turbines, including economic cost and environmental impacts of wind farms.
6. Compare electrical-generating capacity between a wind farm and natural gas-fired power plant to include the issue of reliable base load generation.
7. Be able to diagram the major circulation pattern of wind on the planet and to detail the underlying principles involved.
Humans began harnessing the kinetic energy of wind thousands of years ago. Evidence shows that Phoenicians used sails to propel boats as early as 4,000 years ago, but the practice may be much older. Later we used windmills to grind grain and pump water, and more recently to make electricity. But what really is wind and where does it come from?
What makes the wind blow?
Wind is the directional movement of air from one place to another. It is intuitive that gravity propels water downhill, causing it to flow. But what makes the air flow? Air is comprised of gases (78% nitrogen, 21% oxygen, and others in much smaller amounts). Gases, like all forms of matter,consist of molecules. And molecules are always in motion, unless they are at the coldest possible temperature, called absolute zero. It is never nearly that cold on Earth. How fast molecules move depends on temperature; the warmer it is, the faster they move. In a solid, that motion is mostly a vibration, but in a gas the molecules move so much they crash into each other. As a consequence of increased molecular motion, warm air expands. Think of it as each molecule moving faster, and crashing into adjacent molecules more frequently. The fast- crashing molecules drive each other apart. So when warmer, the same number of molecules will fill a larger volume. This results in decreasing density of air as it warms. Density is the mass of the substance divided by the volume it occupies.
For fluids (gases and liquids), less dense substances tend to float up and more dense substances tend to sink. Consider a glass of water. If you drop a penny in the glass, it will sink. That is because the penny is denser than the water. If you then dropped in the water a piece of cork with the same mass as the penny, the cork would float. Even though the cork weighs the same as the penny, its mass is in a much larger volume, and thus has a lower density than the water.
While it is easy to see the difference in density for solids like cork and coins, it is less obvious that liquids like air and water also differ in density. If you heated a pan on the stove and placed a feather above the hot pan, you would notice it float up. It is being carried up by a current of air warmed by the hot pan below. That warm air is less dense than the surrounding cooler kitchen air, so it floats up — just like the cork in the glass of water. But the warm air is different from the cork floating in water in an important way. As the warm air floats up, it cools and mixes with the other air in the kitchen. The feather that floated up will now sink off to the side of the hot pan.
The air in the atmosphere of Earth is warmed by the radiation of the sun. However, that solar radiation is not evenly distributed across the Earth’s entire surface. Earth is a sphere. The land surface near the equator, if flat, is nearly perpendicular to the sun’s rays. Going north or south from the equator, Earth’s surface begins to form a slope with respect to the sun’s rays. That means that the same amount of light energy then gets distributed over an increasingly larger area at higher latitudes (the equator is zero latitude and the North and South Poles are at 90 degrees latitude). It is cooler near Earth’s poles, since the same amount of sunlight has to warm about twice the area as would be the case near the equator. Recall that Earth spins on a tilted axis. This results in seasons. During summer in the northern hemisphere Earth is tilted toward the sun, and the opposite is true during winter. Putting this all together, on any given day the sun’s energy will be more concentrated in one portion of Earth than another. So parts of Earth are warmer and parts are cooler.
The warmer places will have warmer air floating above the land. And warmer air has low density. The cooler places on Earth will have cooler air above. And the cooler air will have higher density. The amount of pressure exerted by the columns of air is dependent on the temperature. Warmer air will exert less pressure than colder air. The columns of cooler air will exert more pressure, owing to their higher density. The higher-pressure air will tend to flow toward the lower-pressure air. Think of blowing up a balloon. The air in the inflated balloon is under high pressure from the elastic rubber of the balloon. As soon as you let your fingers open the balloon, the high-pressure air will rush out. In nature, the flow of cooler, high-pressure air toward the warmer, low-pressure air creates wind.
The picture gets a bit more complicated on a global scale. Look at the figure below. It shows the location of the prevailing winds around the planet. Note that the winds come from the east in the tropics and near the Arctic and Antarctic Circles, and from the west in the mid temperate zone (around 40 degrees). Why?
To understand these prevailing winds you need to apply your knowledge of rising and sinking air on a global scale. Near the equator, Earth gets maximal solar radiation and it is hot. This causes a constant rising column of hot air. As the air floats up, it cools and becomes denser, but it cannot fall directly down, as more warmer air is constantly on the rise below. So the cooling air flows to a higher latitude (north or south) before it starts to descend. When the now cooler air comes back down to ground level, it is under high pressure, so it will flow in the direction of the lower-pressure warm air, essentially going back to where it started its journey. Once there, it too will warm, and flow back up to continue the cycle. This pattern of circulation is called a convection cell; three such cells are found in the Northern Hemisphere, and another three in the Southern Hemisphere. The two circulations in the tropical regions are called Hadley Cells.
Image Credit: Wikipedia
Image Credit: Wikimedia Commons
How does this up and down circulation of the convection cells translate in the lateral movement of air we know as wind? Understand that Earth is spinning around its axis, completing a full rotation every day. Indeed that is how we define a day. The circumference of Earth is about 25,000 miles or 40,000 km. Imagine an object sitting on the equator. As Earth spins, it takes one day to travel 25,000 miles to return to where it started. So it is going 25,000 miles/24 hours = 1,040 miles per hour on its daily trip around Earth’s axis. Now consider an object at the Arctic Circle. The circumference of Earth there is about 9,945 miles. The object there is spinning around Earth’s axis at 9,945 miles/ 24 hours = 414 miles per hour. This is less than half as fast as the object is going on the equator. Recall that the sun rises in the east, so Earth is spinning toward the east. Now suppose you moved the first object from the equator north toward the Arctic Circle at a rate of 100 miles an hour. As you watch it, you notice that it does not go in a straight line north, but instead begins to veer off to the right. Why? Because it may be going 100 mph north, but it is still traveling 1,040 mph east, while Earth below it is traveling east at a slower and slower rate on its journey north. This is called the Coriolis effect. Objects traveling north will veer to the right, and those traveling south will veer to the left.
With your new knowledge of the Coriolis effect you can understand how the up and circulation of the convection cells results in the winds moving from the side. Look at the Northern Hemisphere Hadley Cell, the convection cell in the northern tropics. Note that the cool air that descended to Earth’s surface is now traveling south. But due to the Coriolis effect, it does not go directly south, but veers toward the west. Since we name winds by where they come from, this is called an easterly wind.Now look at the next convection cell going north. Note that the air near the ground is headed north and the Coriolis effect will send it to the right (toward the east); therefore, it is a westerly wind.
Now you know the origin of the prevailing easterlies and westerlies. Understand that landforms like mountain ranges will alter these flows in many places. There also are seasonal effects, and in some places, daily cycles in wind, like sea breezes and land breezes along coastlines. Storms also create temporary changes in wind patterns. In the end, the thermal energy that drives the wind comes from the sun, so wind energy is in its essence solar energy.
Harnessing the energy of wind
Humans depend on the environment to provide their energy needs. Like all animals, we eat food to supply energy for metabolism (cell and body function). Many animals have evolved to obtain non-food energy from the environment, called an energy subsidy. Eagles use rising columns of warm air to stay aloft without beating their wings. The tiny plants and animals of the sea called plankton let ocean currents power their journeys. Snakes and lizards will bask in the sunshine after a meal; the solar energy warms them so they can digest their food faster.
When humans harnessed fire to warm themselves and cook their food, they took the first step toward our current situation of dependence on energy subsides from the environment. Perhaps the next step came when early boaters used sails to capture the energy of wind. These early sails assisted the boats in moving downwind. Oars or paddles powered by muscle enabled the boats to move against the wind.A big advance in sailing technology emerged about 2,000 years ago. This was the triangular sail of Egyptian boats that could be trimmed to allow the boats to sail toward the wind.
In order for a sailboat to sail in any direction other than downwind, it must include a device to keep it from sliding sideways (making leeway). A keel, centerboard, or daggerboard provides this necessary lateral resistance.
How airfoils work
For a boat to go toward the wind, the sails must provide “lift” from their airfoil shape. Flying insects, birds, and bats mastered this long before human sailors and aviators. Lift comes from the airfoil having an asymmetrical shape. As wind passes around the foil, it must go faster as it goes along the longer side, and according to Bernoulli’s principle, higher velocity wind creates lower pressure.This is the basic explanation of the phenomena of lift that informed the thinking of scientists and aeronautical engineers for most of the twentieth century. And it was good enough to facilitate the design of all sorts of aircraft and sails for boats. However, it was not really correct. While Bernoulli’s principle does add to the lift of an airfoil, we now know that most of the work is done by the wing of sail redirecting the flow of air (or wind) at an angle down and backward. We call this redirecting the thrust.
Consider the example of the sailboat. Most lift is generated by shaping the sails to direct the thrust of the wind backward, driving the boat forward. To flow around the sails, the wind has to deviate in direction, as shown by the arrows for initial velocity vi and final velocity vf, which are given with respect to the boat. The change of velocity dv is in the direction shown. The acceleration aa of the air is dv/dt, so the force Fa that sails exert on the air is in the same direction. (Newton's first and second laws: F = ma.) The force Fw that the wind exerts on the sails is in the opposite direction.
Lift, or the amount of force generated by a sail (of foil) depends on various factors. If the lift coefficient for a wing at a specified angle of attack is known, then the lift produced for specific flow conditions can be determined using the following equation:
where
- L is lift force,
- ρ is air density
- v is true airspeed,
- A is planform (sail) area, and
- is the lift coefficient at the desired angle of attack
Note that lift goes up with the square of the wind velocity — so a doubling of wind velocity will create four times the lift.
Using the formula, would it be easier for an airplane to take off on a day when the air is cold, or when the air is hot? Why?
The formula also shows that larger sails or wings will create more lift. There is a downside to a larger airfoil. The air of thrust that exits the foil starts to swirl around.If you move your finger or hand through water, you can see such swirls forming behind it. The same is true for air. This disturbed airflow creates drag, a force opposite to the direction the boat or airplane is moving. Larger sails and wings create more drag. If there is plenty of wind, a smaller sail can actually make a boat go faster, as it has plenty of lift and less drag. Large jumbo jets have relatively small wings because their engines are so powerful that sufficient lift is generated by their fast speeds through the air. A small and slow propeller airplane has to have proportionally larger wings, since velocity of the air passing over the wings is so low.
From sailboats to windmills and wind turbines
The Persians used sails to power vertical windmills around 400 AD. These mills turned grindstones and possibly some sort of water pump. Circa 1300 AD, Europeans modified the design by making the mills vertical, much like the water wheels already in use there. These tower mills used wooden cogs to turn shafts, just like the water wheel mills of the day. The Dutch, who were famous mariners, essentially modified sails from their boats to form the cloth-covered blades of their windmills. These first windmills and the modern wind turbine rely on the same principles of lift that powered sailing vessels for millennia.The sail on a boat is designed to make it move, while the purpose of an airfoil on a windmill is to turn a shaft. That shaft can then do work, such as rotating a grindstone over grain, or powering a water pump.
Image Credit: Wikimedia Commons
Would wind turbines work where you live?
Some places are windier than others. If a community is considering installing wind turbines to make electricity, it needs to know if the investment is worthwhile. Will there be sufficient wind to make the desired power at a reasonable cost? To help answer this, the US Department of Energy publishes maps that show average wind speeds. Go to the US D.O.E. website: Note that according to their work, a location needs an average wind speed of 6.5 m/sec (14.5 miles per hour) at a height of 80 m (262.4 feet) for wind energy to be an economic practical investment. Click on your state and then find your community. What is the average annual wind speed in m/s? Is your community a good candidate for wind turbines?
Having sufficient wind energy to invest in wind turbines is only part of the puzzle. Is the windy land really available for development? Do current land uses prevent building wind generators? Some development, like farms, is compatible with wind power, while others like cities and protected parklands are not. Go to open the tab for the Excel table shown in the second paragraph.