# The case for the simple solution, sans protractor

DN Staff

April 10, 2010

By Drew Berding

There is a wonderful reality series on PBS called “Rough Science.” In episode 4 (”Ice”) one of the team’s assignments is to measure the speed of a glacier. They are in the wild in New Zealand and have almost no equipment except whatever they can scrounge from an abandoned sawmill.  However, they are given an old suitcase containing miscellaneous things that might be useful.

Of all strange things to find in the wild, the suitcase contains, among other less useful things, a scientific calculator, a protractor and a measuring tape. Ah ha!

These are brilliant people but at this point they make a classic mistake. They immediately get to work using the items in the suitcase. They don’t stop to consider that there might be an easier way to do the job. As the old saying goes, “If the only tool you have is a hammer, everything begins to look like a nail.” Since they have a trigonometric calculator and a protractor, of course they think they must use them.  We engineers often make the same mistake.

Because they know the glacier moves so slowly (glacially!), they know they need extreme accuracy. So they make a six-foot diameter copy of the protractor (!) using some scrap plywood found at the abandoned sawmill and they laboriously mark it in fractions of a degree. They plan to measure the angle from each end of a baseline to a stick imbedded in the rugged surface of the glacier then repeat the measurements the next day. From the two sets of measurements, using some incredibly difficult trigonometry, they expect to determine the distance the glacier has moved in one day.

Surprisingly, after three days of major effort, they actually got the right answer! The glacier’s velocity was approximately one meter per day.

Their effort reminds me of yet another saying, “Anyone can design something complicated but to design something simple takes genius.” Simple designs are much more likely to work reliably, cost less and be easier to maintain and upgrade.

Now, if  the team had stood back for a while rather than getting right to work, they might have realized that there is a much simpler and less error-prone way to do the same job that doesn’t require a scientific calculator, a protractor or several sheets of equations.

For example, on day one, establish fixed points on either side of the moving glacier.  Then go out on the glacier and embed a stick in the glacier in line with the two stationary points (this may require assistance from someone sighting from one of the fixed points to the other). The stick that is embedded in the glacier will move with the glacier by the next day.

On day two, go out on the glacier again and place a new stick in line with the two stationary points. Then measure the distance between the two sticks. This is how far the glacier traveled in one day.

Therefore the speed of the glacier is simply that distance divided by the elapsed time between measurements. We can do those calculations in our heads (especially if there is exactly one day between measurements) without needing any trig tables or calculator or fractional-degree, six-foot diameter protractors.