BotEC: The Scale of Earth's Atmosphere
Air is our most precious resource. Without food, we can live for weeks and without water, we can live for days. But without air to breathe, we survive about 4 minutes! If you visit the top of Mt. Lemmon in Arizona, you will probably notice a shortness of breath due to the thinner atmosphere at 8,000 ft. At the top of Mt. Everest at 29,000 ft. about 99% of the earth's atmosphere is below you. In a commercial jet, traveling across country, you would be dead in minutes without the pressurized cabin and supply of oxygen to breathe.
Relative to the planet earth, the atmosphere we survive in is extremely thin. Most people live at or close to sea level since most of the major cities of the world are along coastlines. Some cities and villages in Mexico, South America and China are at higher elevations from 8,000 to 12,000 ft. Few, if any, people actually live above 15,000 ft. Mt McKinley in Alaska is about 20,000 ft high and climbers do get to the top without oxygen tanks but they need tremendous determination due in part to the thin atmosphere.
Given that most people live below an altitude of 15,000 ft., calculate the thickness in miles of the atmosphere in which humans effectively live.
References and Resources
This SERC page describes the use of Back of the Envelope Calculations
The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.