# Things of Physics: Structures

## Quantifying Experience: Estimation Problems

One of the well-known characteristics of professional physicists is the ability to do "back-of-the-envelope" estimation problems. This means using their personal knowledge to be able to get semi-quantitative order-of-magnitude estimates for almost anything under the sun (and for many things over it). This is an extremely valuable skill to learn but it takes some practice. It is not "just guessing" and it is not "I remember from somewhere else that the number is...".

These problems are sometimes called "Fermi problems" after Enrico Fermi, the famous Manhatten Project physicist who was an expert at them. His canonical example was "How many piano tuners are there in the city of Chicago?" Legend has it, that when he was watching the first A-bomb test at Alamagordo (from a reasonably safe distance), when he saw the flash, he dropped some torn up scraps of paper. As the shock wave went past, he estimated the energy of the explosion from how far they were blown back.

Learning estimation has many great benefits. If you get good at it, you will often be able to save yourself a lot of time by deciding that some correction you thought you ought to calculate is really negligible. If you go into business, the skill to do estimations is a critical one for developing a business plan. Finally, for any citizen, it is an extremely useful skill in filtering when some politician is trying to manipulate you using big numbers he thinks you can't possibly understand.

In this class, when we ask you to do an estimation problem, we are asking you to start developing this skill. This means that for estimation problems,

• Do not look up any data in books, on-line, or get it from friends. Learn to develop your own numerical estimation skills.
• Do not use your calculator. Do all calculations to one or two significant figure accuracy. You will lose credit if you give sig figs that you have no information about.
• Tell what physical principles you are using so we can see how you get from your starting assumptions to your results.
• Be sure you state your underlying assumptions and be sure they relate to some plausible personal experience.

The last point needs a bit of explaining. If you were asked on an exam: "How many blades of grass are there in a typical lawn in the Maryland suburbs in June?" you might decide you could estimate the size of the lawn, but you would need the density of the grass -- the number of blades per square meter. If you said, "Let's assume that there are a million blades of grass per square meter" you would receive no credit. If you said, "When I lie down on a grassy lawn, I can see the grass. Knowing that the last joint of my thumb is about 1 inch long, I can easily imaging the grass against it. I can then see about 10 blades of grass against half that thumb joint, or 10 per cm. This makes 100 (= 10x10) per square cm, or 102(102)2 = 106< or one million blades per square meter." That would receive full credit.

To see another example and solution, check out this problem.

For many more estimation problems, check the following websites.