# Wind Turbine Power Lifter

Using skateboard bearings to reduce friction, build a wind turbine sturdy enough to lift a weight. Adjust your turbine’s blade design to investigate—and maximize—the power you can extract from the wind.

- Four 1/2-inch PVC slip joints or socket caps
- Four 1/2-inch PVC T-joints
- Six 1/2-inch pieces of PVC tubing cut to 6 inches (15 centimeters) long
- One 1/2-inch piece of PVC tubing cut to 18 inches (46 centimeters) long
- Two 608 sealed ball bearings (also known as skateboard bearings)
- One 5/16-inch x 4-inch (8-millimeter x 10-centimeter) bolt
- Two 5/16-inch (8-millimeter) fender washers
- One 5/16-inch (8-millimeter) nut
- Two 5/16-inch (8-millimeter) nut drivers or wrenches
- One 5/16-inch (8-millimeter) wooden dowel approximately 8 inches (20 centimeters) long
- One Tinkertoy™or similar wooden spool
- Masking tape
- Four pieces of cardboard approximately 3 inches x 6 inches (8 centimeters x 15 centimeters)
- Four 5/16-inch (8-millimeter) wooden dowels approximately 3 inches (8 centimeters) long or four dowels from a Tinkertoy™ set
- One small plastic bottle
- 100 grams of sand, water, BBs or similar
- Large paper clip
- Scale
- 20 inches (50 centimeters) of narrow ribbon or string
- Box fan (not shown)
- Optional: Sturdy lab stand with a clamp mount, to use instead of the PVC stand

*Build the PVC Stand:*

Note: If you have access to a sturdy lab stand with a clamp mount, you can use that instead of making the PVC stand.

- Insert a 6-inch (15-centimeter) PVC tube into each arm of a PVC T-joint. Repeat with a second PVC T-joint. Add a PVC slip joint or socket cap to the ends of the two tubes that make a straight line (see photo below).
- Connect the tubing in the center of each tee together with another PVC T-joint to make a large H (see photo below).
- Insert the 18-inch (46-centimeter) tube to make a vertical riser (see photo below).

*Assemble and attach the hub and axle:*

- Slide one fender washer onto the end of the bolt. Slide a 608 sealed bearing onto the bolt.
- Slide a T-joint onto the bolt, and place the other bearing onto the bolt. Add two more fender washers, as shown in the photo below. Twist the nut onto the bolt and hand tighten.
- You’ll be using the bolt, washers, and nut to squeeze the bearings into place. Make sure that the two bearings are aligned on the T-joint. Use the two wrenches to tighten the bolt and nut together (click to enlarge the left photo below); this will forcefully seat the bearings in the openings of the T-joint. Tighten until the bearings are about halfway inside the T-joint (click to enlarge the right photo below). If you push them all the way in, they are more likely to become misaligned.

- Push the wooden dowel through the center holes of the two sealed bearings (click to enlarge photo below). Wooden dowels are sometimes a little bit undersized. If the dowel is too loose and doesn’t cause the bearing to turn, wrap a tiny piece of tape around the dowel and push into the hole. You can add additional layers of tape to make the dowel even thicker if necessary.
- Attach a Tinkertoy™ spool to the end of the shaft (see photo below). Over the years the manufacturers of Tinkertoy™ sets have changed the diameter of the center hole. On older wooden sets, the hole can be too small. The hole can easily be widened by drilling a 5/16-inch (8-millimeter) hole. In current plastic sets, the holes are too large. Wrapping ten or so turns of masking tape around the dowel will make a snug fit.
- Attach the hub to the top of the stand.

*Make and attach the blades:*

- Tape the cardboard to the 3-inch (8-centimeter) wooden dowels as shown in the photo below or, if you have them, you can use the rods from a TinkerToy set. Wooden dowels are not always consistent in size. You may need to wrap masking tape over the end to tune the fit into the spool.
- Repeat until you have four blades.
- Attach each blade to the Tinkertoy™ spool to make your wind turbine.

*Make and attach the bottle as a weight:*

Note: If you have access to hanging weights, you can use them instead of making your own.

- Take a water or pill bottle, a cap, and a paper clip and place all of them on the scale. Fill the bottle with water or sand until the total mass is 100 grams.
- Bend the paper clip to the cap to make a hook and wrap the other end around the neck of the bottle (click to enlarge the photo below).
- Tape the ribbon to the axle. The attachment point on the axle should be as close as possible to the bearings, but far enough away to keep the bottle from hitting the stand (click to enlarge the photo below). Attach the ribbon to the paperclip so that the bottle swings freely from the axle.

Assemble the wind turbine, but don’t attach the ribbon to the axle just yet. Place the fan in front of the turbine blades. Turn on the fan and adjust the fan blades until the turbine starts to spin. Turn off the fan.

Now attach the ribbon to the axle. Measure how much distance the weight has to move to reach the axle (from the top of the weight to the bottom of the axle). Turn the fan back on, and measure how much time it takes for the turbine to lift the weight to the top. Change the distance from the turbine to the fan. Measure the time to lift the bottle again.

The time to raise the weight is related to the rate at which energy is extracted from the wind and can be used as a reference to how powerful the turbine is. Everything else staying the same, shorter times mean a more powerful turbine.

See if you can improve the amount of power extracted from the air. Change the angle of the blades. Is there an optimum angle? Do all the blades need to have the same angle?

Other things you might consider changing:

- Number of blades
- Size of the blades
- Blade material
- Rotational symmetry of the blades around the center axle
- Distance to the fan
- Air speed coming out of the fan
- Angle of the wind turbine to the airflow

Keep track of how each modification changes the time to lift the weight. Use the data you collect to help you optimize the design of your wind turbine for maximum energy extraction.

Humans have been putting wind to work for well over a thousand years. Our reliance on this energy source is growing rapidly, increasing by 10% on average per year since 2010. Well-designed turbines that efficiently convert wind into energy are crucial to making wind power viable.

A wind turbine is usually rated by its *power*, the energy per second it can extract from the wind. While there are several ways to measure power, in this activity we’re using a physical approach. Lifting the weight a certain distance requires a certain amount of energy. (See Going Further.) If the wind turbine can lift the weight in a shorter amount of time, then it is producing more power.

The maximum amount of power that a wind turbine can extract from the air is proportional to the area that is swept by the blades, the density of the air, and the cube of the speed of the air.

$$\mathrm{P}=\frac{1}{2} \pi^* \mathrm{r}_{\text {blades }}^2{ }^* \text { density }_{\text {air }}{ }^* \mathrm{v}_{\text {air }}^3$$

(For a derivation, see Teaching Tips.)

Your own observations will likely be consistent with this formula: Increased wind speed from the fan has the biggest effect in the rate of lifting the weight, either by increasing the fan speed or putting the wind turbine closer to it. You probably also found that longer blades increased the wind turbine’s power.

The density of the air is not something easily changed, so this aspect of the relationship usually goes unnoticed. However, the fact remains that real wind turbines are less effective at higher elevations, where air density is reduced.

When it comes to the number of blades, you may have discovered a more complicated relationship. Most people find that four blades are better than two but worse than eight. While two blades sweep out the same area as four or eight blades, at low speeds some air will pass between the blades without hitting either one. More blades means more air can be hit, but at some point the extra blades aren’t running into “new” air, and so only add weight. Similarly, making the blades wider is useful at lower speeds and less effective at higher speeds.

If you experimented with asymmetric blade arrangements, you probably found they perform poorly. Like an unbalanced load of laundry in a clothes washer, unbalanced blades cause the center of mass of the hub to move up and down as the blades turn, jiggling the entire turbine.

You may also have noticed the importance of the angle of the blades with respect to the direction of the wind, called the *pitch*. A blade that is too perpendicular to the direction of the wind will just block the wind without turning the blades, while blades that are nearly parallel to the flow will allow the air to slip past the blades without applying any force. The optimum angle depends on the wind speed and the length of the blade. Many real wind turbines have actuators that change the pitch of the blades depending on the wind speed.

To make this activity into an engaging engineering project, have each group pick a goal. A group may decide that it wants to make the most powerful turbine, but there are other options. Other examples include making a turbine that

- can lift a heavier weight
- is more efficient in lower or higher wind speeds
- minimizes materials

While many teachers would be inclined to assign a single task for the class, letting each group set its own goal has many advantages. Students tend to be more invested in the design and work harder. Groups don’t just copy the work of other groups. Voices that are less often heard may be more likely to express themselves.

Help students to understand that this is the engineering process. Engineering uses a cycle of

determining a problem, identifying what’s needed to solve the problem, trying and testing possible solutions, optimizing, and iterating.

All grades should be able to get something out of building a wind turbine. Younger children will be less able to build components and may need to have more things already sturdily built. They may also struggle to understand the process of optimizing, and so their goals for the project may need to be left fairly wide open.

Middle grade students may struggle with narrowing down their ideas. Encourage them to write down what they have done so that they can figure out what is successful.

Older high school students should be able to follow the derivation of the wind power equation. A wind turbine extracts energy from the air. The rate that it can extract energy is called the wind turbine’s power. Power is energy extracted per unit of time.

$$\mathrm{P}=\frac{\mathrm{E}}{\mathrm{t}}$$

Since almost all of the available energy is from the motion of the air, the turbine extracts kinetic energy from the air.

$$\mathrm{E}_{\text{kinetic}}=\frac{1}{2}\mathrm{m}_{\text{air}} \mathrm{v}_{\text{air}}^2 $$

The power is how fast that energy is removed per second.

$$\mathrm{P}=\frac{\mathrm{E}_{\text {kinetic }}}{\mathrm{t}}=\frac{\frac{1}{2} \mathrm{m}_{\text {air }} \mathrm{v}_{\text {air }}^2}{\mathrm{t}}$$

Looking at the equation, the hardest part is figuring out how much mass of air passes through the turbine’s blades per second.

So, let's imagine a parcel of air that is about to move through the turbine.

The mass of air in it is proportional to the volume of the cylinder of air and the density of the air.

$$\mathrm{m}_{\text{air}}=\pi\mathrm{r}^2{ }^*\text{length}_{\text{air}}{ }^*\text{density}_{\text{air}}$$

Substituting back into the power equation

$$\mathrm{P}=\frac{\frac{1}{2}\left(\pi \mathrm{r}^2{ }^* \text { length }_{\text {air }}{ }^* \text { density }_{\text {air }}\right){ }^* \mathrm{v}_{\text {air }}^2}{\mathrm{t}}$$

The equation can be rearranged.

$$\mathrm{P}=\frac{\frac{1}{2}\pi \mathrm{r}^2{ }^* \text { density }_{\text {air }}{ }^* \mathrm{ v }_{\text {air }}^2{ }^* \text{length}_{\text {air }}}{\mathrm{t}}$$

Length divided by time is speed, so the equation can be rewritten as

$$\mathrm{P}=\frac{1}{2}\pi \mathrm{r}^2{ }^*\text{density}_{\text{air}}{ }^* \mathrm{ v }_{\text {air }}^2{ }^* \mathrm{v}_{\text {air }} $$

$$\mathrm{P}=\frac{1}{2}\pi\mathrm{r}^2{ }^*\text{density}_{\text{air}}{ }^* \mathrm{ v }_{\text {air }}^3 $$

This equation is known as the *wind power equation,* an expression of the maximum power a wind turbine can produce. Real turbines can’t extract all of the available energy. If such 100% efficiency were possible, the air would stop moving altogether and block any additional air from coming in. In reality, only about half the energy that is in the moving air can be extracted.

If you’d like to calculate the power of your turbine exactly, start by measuring the potential energy gained when the bottle is lifted, which is equal to *mgh*, or mass * strength of gravity * change in height. (Tip: Use units of kilograms, meters, and seconds to get your answer for the energy gained in units called Joules.) Then divide this energy by the time it took to lift the bottle and you’ll have a measure of your turbine’s power in units of joules/second, or watts.

You can take your calculations a step further and calculate your turbine’s *efficiency*, defined as the actual power produced divided by the maximum available power, and expressed as a percentage. Divide the calculated power of your turbine by the maximum available power, given by the wind power equation. (See Teaching Tips.) Then multiply by 100 to turn this ratio into a percentage.

You can also use your turbine to create a makeshift *anemometer*, a device for measuring wind speed. To do this, first remove the ribbon and weight so that the blades can spin as freely as possible. You’ll need a long straight path with no wind, such as a hallway. Measure and record the distance. Start walking down the hallway at steady speed while someone else records the time it takes. Meanwhile, another person should measure the number of revolutions that the blades make. Using the distance and time, you can compute your speed. Do this for several more speeds and graph the average speed versus the number of revolutions per second. The graph probably won’t be linear, but with a fair number of points, you’ll be able to fit a good enough curve that you can use to estimate the speed of wind for points that you didn’t measure.