Teaching sequence

Work through this resource material in the following sequence:

10 minutes

Tune In: Optimising solar using maths

20 minutes

Find Out: Trigonometry and angles of elevation

25 minutes

Take Action: Powering your school with solar

5 minutes

Reflection

Learning intentions and success criteria

Students will:

understand how to apply trigonometry to real-world contexts by investigating the optimal direction and tilt angle for solar panels and exploring how these factors impact energy efficiency in a solar farm design.

Students can:

calculate unknown side lengths and unknown angles in right-angled triangles using trigonometry
apply trigonometric principles to determine the height of objects using their shadow lengths and the sun’s angle of elevation in order to design a small-scale solar farm layout that maximises energy efficiency by selecting the appropriate direction and tilt angle for the panels.
apply mathematical reasoning to a real-world context and communicate findings

Tune In: Optimising solar using maths

Preparation

In this lesson, students will use trigonometry to undertake problem-solving activities related to optimum solar panel locations and tilt. Before completing this lesson, it is recommended that your students have an understanding of how to use trigonometry to calculate unknown side lengths and unknown angles.

Step 1

Facilitate a discussion with your class by posing the following questions to them and discussing students' ideas and responses.

What is something you have observed that all solar panel systems, like rooftop solar or solar farms, have in common?
Does the direction that solar panels face make a difference?
How do you think the angle of the solar panels affects how much electricity is produced?
Do you think the direction and the angle would change depending on where you are on Earth?

Some possible responses from students and ideas to discuss include:

rooftop solar and solar farms are always tilted at an angle

the solar panels would ideally be facing the sun at all times of the day, so if they were facing directly east or west there would be portions of the day where they wouldn’t see the sun
the angle it is tilted at is likely designed so the panel will collect the most amount of sunlight
the sun reaches different heights in the sky at different places around the world which may affect the most optimal tilt angle, which may also affect the direction the panel needs to face.

Step 2

Distribute the Optimising Solar Panel Tilt and Location Factsheet to your students.

Give students a few minutes to read the factsheet. After they have finished prompt discussion by asking the following questions.

Why is it important to optimise solar power?
What are the two main things to consider when optimising solar panels for maximum efficiency?
What are some other factors to consider when installing solar panels?
How do you find your optimum solar panel angle, and why is this important?
How do you know which way a solar panel should face?

Suggested answers

By improving how solar panels perform, we can boost the amount of energy they produce. This helps meet the energy needs of homes and businesses while reducing dependence on traditional energy sources, saving money, and benefiting the environment.
Orientation/location of the solar panel and angle of tilt.
Shading from nearby trees, buildings, or even other solar panels can significantly impact solar panel performance.
The ideal panel angle is equal to your location's latitude. When solar panels are tilted at an angle equal to your location’s latitude, they will face exactly midway between the sun’s highest point in the sky in summer and its lowest point in winter, obtaining the most possible solar exposure.
The ideal orientation/location for a solar panel is facing north. This way the sunlight exposure is maximised throughout the day.

Step 3

Explain to students that this lesson will involve them designing a small-scale solar farm for the school. In order to make it as efficient as possible, we need to know the optimal direction and angle of the solar panels for the school’s location.

Note: The direction will most likely be facing North, but the optimal tilt will be decided depending on the school's latitude.

Step 4

Distribute the Student Worksheet to your class. Have students complete the first question by heading to https://www.google.com/maps and finding their school. They should right-click on the school, and the latitude and longitude will be displayed. The first number is the latitude. The latitude will be negative, which signifies that we are in the Southern Hemisphere, below the Equator. Ask students to write this number down, but do not worry about the negative. This will be the maximum tilt angle for the solar panels at your location.

Find Out: Trigonometry and angles of elevation

Step 1

Explain to students that before they move on to the problem-solving aspect of this lesson, they need to refresh their trigonometry skills.

Show students the following video, which explains how trigonometry and the sun’s altitude angle (angle of elevation) can be used to calculate shadow lengths from an object’s height and vice versa. Students can copy this example into their Student Worksheet to help with their calculations later in the lesson.

How to Find the Angles of Elevation of the Sun Using the Shadows of Objects: Physics & Math - eHowEducation - (https://www.youtube.com/watch?v=KqpTDK3s70I)

You might like to explain this process to students using your usual methods instead of using the video. You can use the first two slides on the attached Visual Explainer to share with students the process of calculating unknown heights and angles using trigonometry. Ensuring that students are confident in calculating unknown angles and unknown side lengths will ensure they can complete the following parts of this lesson.

This GeoGebra Activity, Sunrise Trigonometry, may be helpful for students requiring support to investigate how changing the sun's position affects the size of the shadow that different objects cast.

Step 2

Ask your students to visit SunCalc.org and locate your school to determine the sun’s current altitude angle (angle of elevation). Students can input the school's name or address in the top left hand corner of the webpage and find this value in the ‘solar data for the selected location’ section, next to ‘altitude’. Encourage students to note this value down in their Student Worksheet.

Step 3

The next step involves students heading outside to use the angle of elevation of the sun they have just noted down in order to calculate the heights of objects using their shadows. To ensure students are ready for this task, ask them to write down the following formulas in their worksheets before heading out. Suggested answers are provided below, but you may like students to use the example image (on their Student Worksheet) and their knowledge of trigonometric ratios to work these out themselves.

Step 3

Take students outside to find a sunny area where you can cast clear shadows. Pair students up and ensure students have access to measuring tapes as well as their Student Worksheet.

Step 4

First, ask students to measure the height of their partner and note this down on the Student Worksheet. This will be their reference point for the next question.

Students will now check the value they obtained for the angle of elevation of the sun by using the altitude value they had written down and measuring the length of the shadow their partner creates to calculate their height. Students will be able to check if the altitude value of the sun is correct if they are able to calculate their partners' height and it matches their measurement.

Note: The sun will have moved during this time period, so you might like to check the altitude again using your personal device for students to use while you are outside. Otherwise, you can compare the values when you head back into the classroom.

Extension opportunity: task students requiring extension or early finishers with calculating the height of other objects by measuring their shadow length with a tape measure, and using the sun’s altitude angle as was done in the YouTube video.

Take Action: Powering your school with solar

Step 1

Head back inside and invite your students to head to the final part of their Student Worksheet - Powering Your School with Solar: Problem-Solving Activity.

Step 2

Read out the introduction and the key information in the worksheet to the class. Explain to students that they will need to apply their prior knowledge of trigonometry and area to solve the problems in the activity.

Introduction
Your job is to create a design proposal for a small-scale solar farm that will power all of your school’s energy needs.

Key information
A few assumptions will be made to simplify the calculations, along with some solar panel information.

If you are based in Queensland, you can find out how much electricity, in kWh, your school used in the 2011-2012 financial year in this document: Queensland State Schools Utility Usage Data _ 2011-2012. You can assume that your school’s energy consumption has remained the same since 2011-2012. In fact, this assumption agrees with the fact that Australia’s total energy consumption has remained mostly constant throughout this time period. (Source: Australian Energy Update 2022). If your school isn’t in Queensland you might like to choose a school from the list or try to find out how much electricity your own school uses!
Assume that your school receives 8 hours of sunlight per day which is suitable for solar panels to produce energy.
The solar panels you are installing have a power rating of 400W, and are 2.1m tall x 1.1m wide.
Rows of panels will need to be spread out so they do not block the sun from each other. The separation distance between the solar panels will need to be calculated based on the chosen tilt angle.

Step 3

Provide time for students to complete the worksheet, depending on your class, you can tackle this in pairs or individually.

See the Teacher Content Information for suggested responses to the questions to help you guide students through the task and scaffold if needed.

Extension opportunity: invite students to look into the Future Energy Jobs Guide to work out what types of careers and jobs exist in this sector and who is responsible for engineering the efficiency of solar panels and farms.

Step 4

Bring groups back together to discuss their findings.

Reflection

Engage students in a discussion around the following points:

How did you decide how many solar panels would be in each row?
Was the total area affected by how many rows were used?

Once the total number of solar panels needed and the tilt angle are decided on, the configuration of the solar panels should not affect the total area needed. This discussion may give students a different perspective on how number arrays work.

Designing Solar Farms Using Trigonometry

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