Mathematics behind revolving door design

Using the circumference formula and estimation to design an efficient revolving door

This lesson tasks students with designing a functional and efficient revolving door. It tests practical maths skills such as estimation and calculating the circumference of a circle, while also challenging students with a fun design activity.

It’s one of a set of resources developed to aid the teaching of the secondary national curriculum, particularly KS3, supporting the teaching in maths.

Activity: Using the circumference formula and estimation to design an efficient revolving door

In this activity students will examine the design of revolving doors for maximum efficiency both in terms of reducing space and minimising heat loss.

They’ll firstly be tasked with calculating the idea entrance/exit arc length based on the door’s diameter. They’ll then be asked to estimate how many people can fit into each door section and how this will impact getting 200 people in and out of the building as the arrive and leave for work.

The GeoGebra file Revolving doors allows teachers to demonstrate the problem and check the solution to the first task.

Download our activity overview and Revolving door presentation for a detailed lesson plan on the maths behind designing a revolving door.

The engineering context
Revolving doors are energy efficient as they prevent drafts (via acting as an airlock), thus preventing increases in the heating or cooling required for the building. At the same time, revolving doors allow large numbers of people to pass in and out.

As such, architects and engineers need to apply mathematics to their designs, which can help to determine how they will work in practice and whether or not they’re fit for purpose.

Suggested learning outcomes
Students will learn how mathematical concepts like circumference and arc length are applied to solving real-world design problems.

Download our activity sheet and other teaching resources

The activity sheet includes teachers’ notes, useful web links, and links (where appropriate) to the national curriculum in each of the four devolved nations; England, Northern Ireland, Scotland and Wales.

All activity sheets and supporting resources are free to download, and all the documents are fully editable, so you can tailor them to your students’ and your schools’ needs.

Download our classroom lesson plan and presentation for free!

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