# Dimensional Analysis

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## Summary

This video leads students through the problem solving method of dimensional analysis. Students use dimensional analysis to determine the diameter of a parachute needed to slow a rover to 90m/s in order to safely land on Mars. Students see how the general formula found using dimensional analysis applies on any planet, allowing for the use of experimental data collected on Earth to Mars.

## Learning Objectives

After watching this video students will be able to use dimensional analysis to estimate the size of a parachute canopy that can slow a rover to 90 m/s on its descent to Mars.

Funding provided by the Singapore University of Technology and Design (SUTD)

Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD

## Related Resources

Instructor Guide

Dimensional Analysis Instructor Guide (PDF)

It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.

During the video, students will:

• Determine the dimension of energy.
• Identify independent variables for the parachute and rover system.
• Discuss why only diameter or surface area of the parachute canopy can be specified as an independent variable (and not both).
• Determine the dimensions of the variables in the parachute and rover system.
• Create dimensionless versions of the independent variables.
• Create expressions involving independent variables that have the same dimension as velocity. Then, determine how to define the real value function, phi, in the formula obtained through dimensional analysis in order to obtain those expressions.