# The effectiveness of wind turbines(Activity)

### Adding some quantitative values to the debate

What the activity is for

In this activity the power input to the wind stream driving a wind turbine is compared with the power delivered to an external load in order to estimate the effectiveness of the device. Inevitably much of the input power is not switched successfully, but the reasons for this may lead to fruitful discussions about the siting of wind turbines in the UK. This in turn will support discussion regarding the practicality of utilising wind turbines to satisfy significant fractions of the power requirements of the UK.

What the activity is for

• an electric fan that can be set in one position (rather than rotating from side to side)
• a model wind turbine with motor attached (ideally of similar diameter to the fan)
• a G clamp
• a mains energy meter
• an SEP energy meter
• a fixed resistor of 47 ohm (or any value between 10 ohm and 40 ohm)
• a laboratory jack

• What happens during this activity

Set up the wind turbine directly in front of the fan, and 0.35 metre from it. Ensure the centre of the fan and the centre of the wind turbine are aligned with one another. You may need to raise the height of the fan with a jack or other suitable object. Connect the fan to the mains supply through a mains energy meter set to read power. The wind turbine is wired across a fixed resistor through an SEP energy meter set to read average power.

Introduce the activity with a discussion about using wind turbines in the UK. The students will be familiar with the idea that using renewable resources is one way of helping to reduce the consumption of fossil fuels. They will also know that many places in the UK offer a good windy location for such turbines.

### Connecting how much questions to real measurements and concerns

Teacher: Let's imagine we live in a very windy place on the coast of England. A local company has been able to calculate the power available from the wind in the place where we live. We know how much power we are likely to require to keep our heating system working through the winter (around 2 kW). The company tells us that there's more than enough power available from wind for all of our requirements if only we can harness it. The question the company seeks to answer is How much of this available power are we able to usefully divert for our use?

Explain that you'll use a model to investigate the efficiency with which a wind turbine can shift the estimated energy from the kinetic store of the wind along the electrical working pathway to the final thermal store in a load resistor. Suggest working with power rather than energy–perhaps discussing why this is a more practical approach. Using the suggested scenario, the load represents the heating system of the house.

Teacher: Before we try to compare input and output power of this system, could you estimate the fraction that we might divert?

It's a good idea to record some of the guesses before doing the measurements. Revisit them at the end to compare the two sets of values.

Switch the fan on, making sure that it remains stationary.

Teacher: The fan generates a channel of flowing air directly incident upon the wind turbine. We can see from the mains energy meter what power is being delivered to the fan.

Lucy: Yes, the fan is shifting 28 joule inverse second as the power is 28 watt.

Teacher: Good. Now can it be that the fan is shifting all of the 28 joule inverse second into the energy store of the moving wind?

Liam: No, because the internal parts of the fan are getting hot.

Lucy: Also the fan is making a noise.

Teacher: Yes. This means that the thermal and vibration store are also filling. The fan is not shifting all of its energy to the energy store of the moving air. But to get started let's just say that it is. This is a useful strategy in physics–make things simple enough to get started.

Lucy: OK then. So are we saying that the fan is delivering 28 joule inverse second to the energy store of the moving air?

Teacher: Yes. Especially since the diameter of the fan is about the same as the diameter of the wind turbine.

### Concluding the discussion–checking the numbers

Now switch the energymeter on, which is connected to the load resistor, to see that the power delivered to the load is much smaller.

Lucy: It's only 19.55 milliwatt.

Liam: That is tiny!

Teacher: It is small.

Lucy: That's so much lower than I expected. It's a tiny fraction.

Teacher: I thought you might find this surprising. Now let's make this calculation more realistic. Again physics at work–after getting started we gradually make things more complicated.

Teacher: Let's now imagine that the fan was able to shift 30 % of the energy from the original store to the energy in the kinetic store of the moving air, and let's imagine that the wind turbine is only able to switch 50 % of the energy in this store to the electrical pathway. Maybe we'd get a bigger fraction?

Lucy: Well the fraction would certainly be higher.

Teacher: Let's work it out. Power available to wind turbine is 28 watt  × 0.3  × 0.5, which is 0.42 watt

Lucy: Wow. That is still so small.

Teacher: Yes, but these are pretty realistic when trying to extract the energy from the wind flow over the UK! There's not much energy at all reaching the target store. Most energy will be dissipated and will fill up the store of the surroundings through the heating by particles pathway.

Now you could lead a discussion about the practicality of utilising wind turbines solely to satisfy the energy requirements of the UK.

You might then like to investigate how various factors, such as the number of blades, the wind turbine design and the total blade area, affect the fraction at a given distance from the fan. You could also vary the wind speed by moving the fan closer to or farther from the wind turbine.