Mathcad Brush Up: Convert Weird Units of Measurement




The Harvard Bridge, which spans the Charles River to connect Boston and Cambridge, Massachusetts, is 364.4 Smoots long (+/- 1 ear). How long would it take me to traverse the bridge if I were going 35 mph?

Harvard bridge was measured in Smoot units in 1958

Harvard bridge. Image Dvortygirl via Wikimedia commons.

That may not be an easy number to determine if you don't know how long one Smoot is. What is a Smoot anyway?

In 1958, as part of a fraternity prank at MIT, Oliver Reed Smoot was used as a measuring stick for the Harvard Bridge. He lay flat as fraternity members carried him along the bridge, marking the lengths of his body, 364.4 Smoots in total. Those measurements have become something of a legend in the area, with college students repainting the markings every year.

 Interestingly, having begun his college career as a standard of length measurement himself, Oliver Smoot "went on to head both the American National Standards Institute [ANSI] and the International Organization for Standardization [ISO]" according to the plaque on the Harvard Bridge that was installed to commemorate the 50th Anniversary of the advent of the Smoot unit.

Figuring the height of Oliver Smoot in 1958 …

In order to answer the initial question posed, we need to know how tall Oliver Reed Smoot was in October 1958. In other words, what is the conversion factor between Smoots and miles, or Smoots and feet?

Mark on Harvard bridge showing 100 smoots, a unique unit of measure

100-Smoots mark on Harvard Bridge. Image Dvortygirl via Wikimedia commons.

Of course, this problem is not relegated to Smoots. If I had given the length of the Harvard Bridge in meters, we would still need to know the conversion factor in order to determine how much time it would take me to cross the bridge. The only real difference is that meters are more well known, so it is more likely that you already know the conversion factor between meters and feet.

…without conversion factors.

I, however, do not know even that conversion. Given that (a) I agree with Sherlock Holmes’ notion (found in A Study in Scarlet, by Sir Arthur Conan Doyle) that we should not crowd our brains with useless information, and that (b) Mathcad eliminates my need to use unit conversion factors, thereby rendering those factors useless to me, “I shall do my best to forget” any conversion factors.

It turns out that Mathcad doesn’t just know about meters. Mathcad also has Smoot as a built-in unit (a fun little surprise). Thus, using Mathcad, we can see what the conversion factor is from Smoots to feet-inches-fraction:

Smoot units to classical units in Mathcad

There you have it. Oliver Reed Smoot was 5 feet 7 inches in 1958, thus making the Harvard Bridge just under 0.4 mile long (+/- 1 ear, which is on average 6.30 cm).

Smoot units to miles in Mathcad

Mathcad converting centimeters to inches

Going back to the original problem, Mathcad makes it easy. No unit conversions necessary.

Smoot unit problem converted in Mathcad

The takeaway? Mathcad's got your units covered

While I doubt you are using Smoots in your engineering calculations, you are still using units. And having to keep track of what units you have to use and how to convert between different units can be a waste of time and error prone. 

So whether you are still using Excel for your calculations, trying out Mathcad for the first time, or using Mathcad regularly but (inexplicably) not taking advantage of its unit sensitivity, I offer the same piece of advice: Start using units in Mathcad! (Did the bold and italics help? I thought ALL CAPS MIGHT BE TOO PUSHY)

Become a unit expert

I have been subtle, I know, but you should know that I feel very strongly about this. As such, I want to give you some resources as you familiarize yourself with units in Mathcad:

  • Visit our Engineering Unit Converter landing page. This is just a generally good place to start.
  • By default, Mathcad displays units italicized and blue, as part of Mathcad Prime’s labeling feature. But you can learn how to change the format of the Units label.
  • Read up on how not to get confused by pound mass and pound force.
  • Most units are pretty straightforward in terms of scaling and conversion. Temperature units are an important exception, since different temperature scales place zero at a different place. Thus, you can’t just apply a multiplicative factor to convert between temperature units, which means Mathcad has to approach them differently, too. But fear not, we have a blog post for that.
  • There is a secret keyboard shortcut for labelling units. Not to brag, but I found it all by myself. It’s the last shortcut on my list of Mathcad hacks.

I’ll leave you with this question: How many furlongs per fortnight would you have to travel in order to drive (or otherwise travel) from New York City to Boston in 4 hours? It’s easy to figure out with Mathcad.

converting miles per hour to furlongs in a fortnight

Not using Mathcad yet? 

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