Proficiency in Customary Units

Eduardo Kausel

With the notable exception of the U.S., most of the world has universally adopted the metric system of units, and this includes the United Kingdom, Canada, and Australia.  Nonetheless, some sectors in the U.S. went metric a while ago, such as the automobile industry, wine and spirits or beverages, and so on. However, the full conversion of the U.S. to the metric (or SI) system has consistently been held back by a vocal group of politically influential individuals who liken the changeover to an unpatriotic and un-American act, indeed, the possible cause for economic and cultural disaster.

I, for one, am fluent in, and use, both systems, so I won’t take sides – at least not herein – as to whether or not we should complete the conversion. Nonetheless, I can share at least one anecdote that may hint as to my preferences. When I took the license exam for professional engineer in Massachusetts some three decades ago, I had a memorable question that challenged my proficiency with units. The question went roughly like this:  Determine how many horsepower must an electrical motor of efficiency E have if it drives a water pump that elevates water at the rate of R gallons per minute over a height of H feet using a pipe of D inches in diameter and the head loss in the pipe is L inches per linear foot (where, of course, E, R, etc. were just numbers). What a mix of units! I first converted all the parameters to metric, computed the power in KW, and then back into HP, remembering from high-school days that one HP equals approximately 3/4  of a KW, and sure enough, it worked!

Personally, I use both systems depending on context, and my measuring tapes and calipers are dual metric and English. For technical work, I stick mainly to metric units, but at home, when I build or install artifacts such as cabinets or picture frames and the like, I primarily employ inches, mostly because of my need to accommodate the standard American sizes that permeate all dimensions in the house. Still, even there I also resort often to centimeters and millimeters, especially when I need high precision – e.g., in a saw cut – or when I divide a non-integer measurement in inches into some integer fraction. It is easier and faster for me to compute, say, one third of 13.8 cm than one third of 5 7/16 inches, and also, I can locate much faster the result of that division on the metric part of the tape.

To test this observation on others, I have on various occasions carried out an informal experiment in which I asked an American-born person (but not a carpenter or mason) to measure the length of some piece of wood to the nearest 1/16th of an inch, and in most cases that measurement demanded some fifteen seconds, if not more. Most of my test persons proceeded roughly as follows: let’s see, this line must be 1/2, 1/4, 1/8, 1/16 ... and then proceeded to count those lines one by one from left to right starting from the nearest full inch. Then I repeated the experiment with that same person, and asked him/her to give me the same measurement in centimeters, accurate to the nearest millimeter. The response was consistently instantaneous and with no delay whatsoever: 27.4 cm. Some of them then smiled and nodded affirmatively while admitting, “Yes, I read it right away, but I have no feeling for what I read.” Hmmm.

For all of their resistance to a change to the metric system in the U.S., you would believe that Americans are intimately familiar with their system and know their customary units like the palm of their hand. Further experiments with a pop quiz I carried out with two of my classes of both undergraduate and graduate students at MIT (a total of 46 students), and also with colleagues, friends, and neighbors, have shown me otherwise.

Yes, they all know what an inch or a gallon is, but after that it gets really murky. Not everybody could tell me how many feet are contained in a mile, fewer still how many square feet in an acre, what the boiling temperature of water is in degrees Fahrenheit, or the atmospheric pressure in psi, and I have yet to find anybody who can tell me accurately how many gallons fit in a cubic foot (please guess that for now, and I’ll give you the answer later on). For that matter, many could not even decide how many fluid ounces are contained in a pint, how many pints in a gallon, or how heavy a pint (or gallon) of water is. By contrast, most of my quiz takers knew the fundamental metric units reasonably well. I tallied the answers, distinguishing between American-born and/or educated and international students (about 60% vs. 40%), and also between males and females.  The table shows my 10-minute questionnaire on English and metric units together with its resulting statistics.

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As for the answers, there appeared to be no significant differences in scores between men and women, but there were big differences between U.S.- and foreign-born or educated. By and large, foreigners were wholly ignorant of U.S. customary units, with the exception of the mile and the temperature for freezing water, for which about half knew the correct answer.

Among American respondents to my quiz, 86% gave an answer within 10% of the actual length of the mile and 66% knew the correct boiling temperature of water, but less than half knew the number of fluid ounces in one pint, only about one-fifth knew the atmospheric pressure in pounds per square inch, and barely 17% knew the weight in pounds of one pint of water.

Likewise, only 10% could estimate even approximately the size of an acre. In case you wonder, an acre is the rectangular plot of land that can be plowed by an ox in one day, and its size is one chain by one furlong, the chain being 22 yards and the furlong 10 chains, which results in an area of 66x660 = 43,560  ft2.  Interestingly, this number has no integer square root, so there is no square plot of land of integer dimensions in feet that contains an acre.

Concerning the metric system, both Americans and foreigners knew pretty much most of the important units and equivalences, and not surprisingly, foreigners scored somewhat higher in this category. Overall, only 36% of respondents gave correct answers for U.S. customary units, but 71% did so for metric units. Interestingly, only 20% of American-born students at MIT prefer the use of U.S. customary units. The overwhelming majority prefers either the metric system (54%), or the use of both systems (25%). I’ll let you judge the practical and political implications of these results. And whatever your thoughts on the matter, we should also not forget the unfortunate loss of the $125 million Mars Climate Orbiter in September 1999, which occurred because the Lockheed-Martin engineering team used English units in their code of navigational commands for the orbiter, in lieu of NASA’s usual metric system. Click here to view the quiz.

And by the way – believe it or not – a cubic foot contains nearly seven and a half gallons, or 7.481 to be precise. Indeed, a gallon is exactly equal to 231 cubic inches, a cabalistic number that you shouldn’t soon forget.

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