Chapter 03: Units, Dimensions, and Conversions
- Page ID
- 89907
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| Figure 3.1: The important part is to understand when you need to convert units. |
Although it seems basic, one of the first steps of becoming a successful engineer is having an intuitive understanding of units and dimensions. Intuitive means that when you see \(4 \: inches \) or \(4 \: millimeters \) you can “see” the difference between those two and understand how they are different. Intuitive means that when someone says that they are 6 meters tall, you raise your eyebrows and likely reply “I don’t think meters means what you think it means”. Unfortunately, it takes practice and time to have an intuitive understanding of anything (that is one of the reasons why we expect engineers to spend 4 years in school!). Therefore, the goal of this chapter is not that you will have an intuitive understanding by the time you are finished. It is important to understand that the learning process does not end at the completion of each chapter but instead is a lifelong process. The goal is that by the end of the chapter you will know how to appropriately look things up and that you understand how to be careful when converting units.
Learning Goals
In this chapter, we will learn a ton! We are going to learn the difference between units and dimensions and how you will be expected to manipulate them as an engineer. We will explore the following:
- The metric system
- Inferior unit systems (aka US Customary Units and why we should switch!)
- How to convert between unit systems
- The fundamental dimensions of the universe! (Grandiose but true!)
- Dimensional homogeneity (a fancy way of saying dimensional consistency) and analysis
- How to intuit the difference between precision and accuracy
Motivation - The Gimli Glider
On July 22, 1983, Air Canada flight 143 took off from Montreal to Edmonton. Before takeoff, routine checks showed all systems were functional and that everything was ready to go. While cruising at \(12,500 \: meters\), an alarm started blaring in the cockpit, warning the pilots that the fuel pressure on the left side of the airplane was low. The pilots silenced the alarm, figuring it was a fuel pump problem, and they knew gravity could handle moving the fuel around until they landed. The fuel gauges were not working correctly (or so it seemed), but the flight computer let the pilots know they had plenty of fuel to make the flight. A few minutes later, the right-side fuel pressure alarm went off. Seconds after that, the left engine shut down. The pilots called air traffic control and prepared to land with a single engine in Winnipeg. As they were discussing the plan with air traffic control in Winnipeg, the “all engines down” alarm went off and the cockpit went blank. The pilots consulted the manual and couldn’t find a section that told them what to do when all engines fail. Luckily, the pilots managed to safely crash land the plane, and no one was hurt.