Back-of-the-envelope calculations: When close is good enough

Some engineers, professional and amateur, share something with Enrico Fermi: the ability to take rough data, pencil whip it through a few calculations, and decide if a project is possible or what it might take to get something done. Stefan Funk, a physicist at Stanford University is particularly good at tackling these types of problems, also known as Fermi problems, and teaches course on them, “Science on the Back of an Envelope.” The course is even mandatory for physics grad students at the university.

To make the course more interesting, he takes problems from popular culture. For example, taking a cue from the 1998 movie Armageddon, he had students determine if it would be possible to blow up an asteroid heading toward Earth if you knew the size, speed, and current position of the asteroid. Another problem came from James and the Giant Peach: How may seagulls would it take to carry a house-sized peach from England to New York. And you know peaches float, so they are less dense than water. (To see handwritten back-of-the-envelope calculations for these two problems, go to Asteroid or Peach.)

Taking seemingly nonsensical problems from movies and books lets students focus on solving the problem rather than getting the correct number to three decimal places. And they are more interesting.

“It’s about being able to step back and look at your results. Does it make sense? If you’re only off by a factor of two or three, that’s no big deal. If you’re off by, say 1020, that’s a big problem,” says Funk in an interview with Symmetry magazine.

I think Prof. Funk’s course would be great for all sorts of people, including politicians, screenwriters, , business folks off all stripes, and magazine editors.

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Stephen Mraz

Steve serves as Senior Editor of Machine Design.  He has 23 years of service and has a B.S. Biomedical Engineering from CWRU. Steve was a E-2C Hawkeye Naval Flight Officer in the U.S. Navy. He...
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