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These resources have been reviewed and selected by STEM Learning’s team of education specialists for factual accuracy and relevance to teaching STEM subjects in UK schools.

The Mathematics of Satellite Design - Coolant tank, fuel tank and engine design

All the resources listed here are aimed at the age group 14 to 16, except for the "Space for Engine" resource. 

Coolant tank design

Making efficient use of physical space and of materials is a central theme of many engineering problems. In this challenge students investigate the relationship between the volume of a cylinder and its surface area. 

Mathematical topics used in this challenge:

• Volume of a cylinder

• Surface area of a cylinder

• Substitution

• Trial and improvement

Fuel tank design

This challenge looks at a fuel tank in the shape of a cylinder with ends in the shape of hemispheres. Students look at what changes are needed to the dimensions of the fuel tank in order to double the capacity of the tank. 

Mathematical topics used in this challenge:

• Volume of a cylinder

• Volume of a sphere

• Surface area of a cylinder

• Surface area of a hemisphere

• Trial and improvement

• Substitution

• Setting up equations

• Algebraic manipulation

Space for the fuel tanks

Trading off one aspect of a design against another is a common theme in engineering. In this challenge students look at the consequence that increasing fuel capacity has on the amount of space available for the satellite’s positioning engine.

Mathematical topics used in this challenge:

• Pythagoras’ theorem

• Expressions

• Manipulating surds

Space for the fuel tanks - An algebraic model

The trade-off between fuel capacity and the amount of space for a satellite’s positioning engine is an important consideration in design. In this challenge students develop an algebraic model that will allow them to apply their findings to satellites of varying dimensions.

Mathematical topics used in this challenge:

• Pythagoras’ theorem

• Surds

• Solving equations

• Ratios

Space for engine

For larger satellites, being able to reposition in orbit is an important aspect of their design. For this they need an engine. This challenge looks at the considerations to be made when incorporating the engine in the satellite design. This is for the age range: 11 to 13.

Mathematical topics used in this challenge:

• Expressions

• Ratio

• Area of a square

• Area of a circle

• Pythagoras’ theorem

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