Lesson Plan: Power, Energy, Dynamics- Wind Turbines

Here is a step-by-step guide to using this lesson plan in the classroom/laboratory. We have suggested these steps as a possible plan of action. You may customize the lesson plan according to your preferences and requirements.

Step 1: Topic introduction and discussion

1. Use the teaching module, ‘6: Power’ by LibreTexts^TM to bring together concepts we have learnt so far- energy, power, work, electrical energy, conservation of energy and transformers.
2. Play the video tutorial within the text, to teach how numerical problems can be solved for computing values such as energy generated, and work done.
3. Navigate to the next page (6.7), to read a case study on the World’s Energy Use.
4. Discuss how fossil fuel-based energy generation is undesirable in the context of climate change and the need to increase the use of renewable and cleaner sources of energy such as wind energy.

This can be accessed here.

Step 2: Extend understanding

1. Explain to your students that they will now apply their understanding of the different concepts learnt in physics in a real-world situation by looking at how wind turbines work and identify the physics principles behind this form of renewable energy.
2. Ask your students what they already know about wind turbines and about how they work. Allow the students to respond with their ideas and summarize their main points on the board.
3. Play the video, ‘How do Wind Turbines Work’ by LearnEngineering, to introduce the topic of using wind energy to generate electricity by wind turbines. Use this video to describe various aspects of wind turbines and the science involved in the electricity they produce.
4. Allow some time for a classroom discussion following the video. Draw attention to Betz’s Limit as a new idea.

The video can be accessed here.

Step 3: Classroom Activity

1. Ask your students: How can we determine the kinetic energy of a mass of air of density that is moving at the speed through a turbine of radius r?
2. Form groups and encourage your students to determine the general formula for calculating the kinetic energy of a mass of moving air. Students will need to combine density ( ρ=m/V) ) with the volume of airflow (V=Av ), the area of a circle ( A=πr²)with the kinetic energy formula (1/2 mv² ) to define the kinetic energy of a mass of air as (KE=1/2 πr² ρv³ ).
3. Play the video, ‘The Physics of Wind Power: how does a wind turbine work?’ by the European Energy Centre (EEC) to elucidate how the kinetic energy of a mass of air moving through a wind turbine can be determined. This can be accessed here.
4. Solve a word problem with guidance:

Consider a wind turbine with a span of 100 m is situated at a site, subjected to constant 8ms^(-1) wind. If the air density is 1.25 kgm^(-3), how much kinetic energy passes through the plane of the blades every second?
Solution: We can directly substitute in the formula KE=1/2πr² ρv³,  but instead we will use a different strategy.

Strategy:

1.  Determine the area of the plane
2.  Determine the volume of air passing through plane every second
3.  Determine the mass of air passing through plane every second
4.  Calculate the kinetic energy of the mass of air passing through the plane every second

A=πr²
A=π (50)²

A=7854 m²

At 8ms^(-1), volume through plane

V=Av
V=7854m² × 8 ms^(-1)
V=62,832 m³ s^(-1)
With density of ρ=1.25 kgm^(-3)

m=ρV
m=1.25 kg(m)^(-3) × 62,832 m³ s^(-1)
m=78,540 kgs^(-1)

Kinetic energy every second
KE=1/2 mv²
KE=1/2 (78,540 kg s^(-1) ) × 8²  m² s^(-2)
KE/s  = 2.513×(10)⁶ Js^(-1)

P = 2.513 × (10)⁶  W = 2513 kW

5. Give a word problem for independent practice
Consider a wind turbine with a span of 50 m is situated at a site, subjected to a constant 12 ms-1 wind. If the air density is 1.23 kgm^(-3), how much kinetic energy passes through the plane of the blades every second? Round your answer to 3 s.f.

Solution:
Kinetic Energy every second
(KE)/s =1/2 πr² ρv³

(KE)/s=1/2 π (50)² (1.23) (12³  ) (m² )(kg/m³) (m/s)³
(KE)/s=8,340,000 m²  kg s^(-3)
(KE)/s =8.34 × (10)⁶  J s^(-1)
P = 8.34 × (10)⁶ W = 8,340  kW

6. Wrap up the session with a discussion on ways other than wind energy to generate sustainable energy. Discuss their benefits and caveats in the context of climate change.

7. Learning Extensions:

Electricity in Households: Draw attention to how this energy can be used in homes. We wish to sell this energy to households, and we need a unit of measure that makes sense to the average person. The unit used is called a kilowatt-hour (kWh) and is defined as the energy delivered to a 1000 W appliance over 1 hour. Determine how much 1 kWh is in terms of joules.

Solution:
P=E/t
E=Pt
E=1000 J s^(-1) × 3600  s
E=3.6× (10)⁶ J

Cost of Electrical Energy: Students to research the cost of electrical energy by visiting power-company websites to get rates. Typical rates in Australia are 0.15-0.30 AUD/kWh.

Students to then determine the revenue generated by this wind turbine per day (by multiplying Energy _electrical with the rate they find).

Suggested questions/assignments for learning evaluation :

1. What is wind energy?
2. How can wind power be harnessed for electricity using wind turbines?
3. How can you compute the energy available due to wind?
4. What are the advantages and challenges of producing electricity from a wind turbine?

The tools in this lesson plan will enable students to:

1. apply the concepts of conservation of energy, electrical energy, and power together in a meaningful way.
2. explain the advantages and challenges of producing electricity from a wind turbine.
3. learn the physics of wind power.
4. compute the energy available from wind as a renewable and clean source of energy.
5. solve real-world problems in the context of climate change.

If you or your students would like to explore the topic further, these additional resources will be useful.