By The Metric Maven

Let’s suppose for a moment that I was interested in promoting myself as an expert in the use of the English language (which, for the record, I am definitely not) and specifically for technical explanation. Further suppose that in order to convince you of this literary expertise, I sent you a slick bit of advertising copy which has this for its lead sentence:

I is expert in english and know how to show people the ways best to write groups of words for understanding.

How persuaded would you be that my claim of expertise with the English language is true? I suspect you might in fact question my literacy. When you see this construction, the very structure of the sentence serves to disqualify the author, and calls his competence into question. To a majority of Americans it would be self-evident that this sentence was either a joke, or a sad commentary.

When I read technical trade magazines and other works written by those purporting to be technological guiding lights, I’m often very surprised that the measurement unit equivalent of the mangled sentence above is ubiquitous. Worse, its incongruous nature is often completely invisible to technical readers, and technical authors. I’m not here to cast blame on particular people, this poor practice is common, but I will uses specific examples from trade magazines for illustration. I will not directly cite the article, author, and title. The articles I cite are not the issue, it is the accepted use of poor measurement unit descriptions by people in the technical community that is the issue. My first example is from an article which is described as “Educational.” It describes a type of printing roller called an Anilox Roller. This roller has a large number of dimples etched into its surface which hold ink for printing. Here is what the author states:

Simply put, the anilox roller is a measuring cup made up of volume carrying pockets that have a particular unit of volume measurement called a “BCM/Square inch.” ….However, unlike measuring cups, there is no standard off the shelf anilox specification. Unfortunately, there is an infinite variety of anilox volumes…

So what is a BCM/Square inch? He explains:

Volume of ink available from an anilox is measured in BCM’s (billion cubic microns). Because the size of a micron (25,400 microns per inch) and the number of cells the laser can engrave into the ceramic, a second unit had to be added to get the volume unit up to an understandable number. BCM/square inch is the volume unit for North America.

The European anilox volume is measured in Cm^{3}/M^{2} (cubic centimeters per square meter). I will not go through the difference between a micron and a centimeter. I will just move to the down and dirty conversion factors. A BCM is converted to European unit by multiplying the BCM by 1.55. The European unit is converted to a BCM by multiplying by 0.6455. For example, 12 BCM/in^{2} x 1.55 = Cm^{3}/M^{2}

Yes, the C of centimeter and the M of meter are capitalized in the original. I have tortured you and myself enough. Lets pause and talk about this for a moment. The mixing of metric and Ye Olde English units is bad enough, but giving a separate name to a clearly defined metric quantity of volume is unit proliferation at its worst.

So a BCM is a *billion cubic microns*, and it is a volume. The metric system has a nice unit for volume called the liter. Those of us who do not live in the 19th century use the term micrometer rather than micron. My understanding is that a billion is 10^{9} and a cubic micrometer is 10^{-18} cubic meters, or, when the two are multiplied, they become 10^{-9} cubic meters. We know there are 1000 liters in a cubic meter. That means this volume is 10^{-6} liters or a microliter. Therefore a *BCM is a microliter*. Unless I’ve made a mistake converting, this means that 12 BCM/in^{2} is 12 µL/in^{2}. The “rationale” used is that they had to choose units that give numbers that are understandable. Pat Naughtin argued for numbers to be expressed as integers when possible. He calls this his *whole number rule* and I’m at one with this view. The author is trying to express a volume contained in small dimples over a given area. One square inch is 645.16 square millimeters. The 12 µL/in^{2} is therefore 12 µL/(645.16 mm^{2}). To keep with Naughtin’s convention, we shift to nanoliters and have 18.6 nL/mm^{2}.

So instead of creating a ridiculous ad hoc pigfish measurement unit like BCM/in^{2} one could easily use nanoliters/square millimeter. This actually gives me some feeling for the volume of ink contained in an area. The Europeans embraced the pseudo-inch, also known as the centimeter. They use a square meter as the unit to project upon the Anilox Roller, which seems odd for a roller. When viewed by a pressman, an ink roller would never present anything like that size of an area to him. A millimeter area makes considerable sense. Even so, if the European’s insist that the centimeter be used, why not write the cubic centimeter as a milliliter and use 18.6 mL/m^{2}. This is also a unit that may be easily visualized. This numerical value, 18.6 mL/m^{2}, is the same as 18.6 nL/mm^{2} and is so easy to convert—just multiply by 1. The rewriting of the European specification with mL would also eliminate the possible confusion caused by using a ratio of length units (i.e. cm^{3}/m^{2} = 1 µm) rather than using a volume unit in the numerator to provide clarity.

Jargon combination units like BCM/in^{2}, which is a mix of metric and Ye Olde English units, is like my poorly executed sentence in English above. When examined, the unit expression is very, very poor engineering practice. This is either from ignorance, or it’s from willful obfuscation, which acts as an intellectual barrier to those who might embrace the trade. It may accidentally be the latter, but I suspect it is born from the former.

I have spent enough time harping on this “Educational Article.” I will toss out one more example. There has been considerable excitement in recent years about the development of 3D printers. If one has a computer model of a 3D object, it is possible to have that object fabricated in plastic using this printing device which puts down layers of melted plastic. I came across an article which compares available low cost 3D printing units. First the volume of the object which may be fabricated is described:

…the MakerBot Replicator 2, with a build envelope of 11.22 x 6 x 6.12 inches and the Cubify CubeX, with a build envelope of 10.82 x 10.43 x 9.49 inches (basically the size of a basketball).

A basketball has a volume of about 7.5 liters. The MakerBot Replicator 2 has a build envelope of 285 mm x 152.4 mm x 155.4 mm and the Cubifiy Cube X is 275 mm x 265 mm x 241 mm.

The resolution of the 3D printing is next described:

*Resolution:* Of the two machines we considered, the Replicator 2 can print to a layer height of 100 microns. The CubeX can only go as fine as 125 microns, but it has options for 250 and 500 micron layers.

Once again, we in the US have never reformed our measurements and gone metric, so we use a 19th century term for the micrometer—the micron. The article goes on to discuss printing speed:

*Speed:* We recently built one part that took about 20 hours to finish at the highest resolution of 125 microns; it measured 9 inches tall by about 3 inches square. The same piece took about four hours at 500 microns.

Again we see a mixture of metric and Olde English. The resolution he first used was 125 micrometers. The printed part is about 228 mm x 76 mm x 76 mm. One can quickly see this is about 608 layers when the dimensions are all given in metric. This is about 118.4 seconds per layer. The volume of each layer is 76 mm x 76 mm x 0.125 mm or 722 cubic mm. Each layer printed is 722 microliters, so the volume deposit rate for the 125 µm resolution setting is about 6.1 microliters/second.

When the resolution was changed to 500 micrometers, it took four hours to print. The number of layers is now 152 which comes out to 94.73 seconds per layer. Each layer has 2888 µL which gives us 30.48 µL per second.

Considering that 3D printing is creating a volume, it might make sense to describe the printing speed in terms of microliters/second (µL/s) deposited. When set to 125 µm resolution the deposition speed is about 6.1 µL/s and when set to 500 µm resolution its 30.48 µL/s.

The fact that the US has not changed to the metric system produces an isolation, both from our own understanding of technical issues, and from the rest of the technical world. This in turn freezes our metric usage in the past, which is demonstrated by the constant use of the micron in US industry, rather than the micrometer. It reflects poorly on the technical writers of this nation that they do not appear to understand, that from a measurements standpoint, they sound completely innumerate. We in the US like to pat ourselves on the back as technologically advanced. Well at this point it’s more like we use technologically advanced equipment, which even our technical writers can only describe to us with a mismatched set of metric and pre-scientific units. We flatter ourselves at the expense of numerical understanding, even if we can’t perceive that it is happening.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: *Our Crumbling Invisible Infrastructure*. It is a succinct set of essays that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website, but the book has them all in one place in print. The book may be purchased from Amazon here.

The second book is titled *The Dimensions of the Cosmos*. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.

The third book is called *Death By A Thousand Cuts, A Secret History of the Metric System in The United States*. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

It appears to me that someone of Indian origin came up with the BCM. If you ever encounter Indian technical literature, it is peppered with strange symbols and rarely if ever uses standard SI symbols.

Here is an example:

http://news.oneindia.in/2007/02/10/crude-petroleum-production-to-double-at-190-mcmpd-by-march-2009-1171114478.html

MCMPD = million cubic metres per day

Your report on the 3D printer is in error. You are assuming those rounded and semi-rounded inches are real and you converted them to exact metric decimal equivalents with decimal dust. If these products were made and designed outside the US, there dimensions would be round metric numbers, but when converted to inches the dimensions are often changed to reflect rounded inches or close fractions. Then at some future time the corrupted inch values are reconverted to millimetres with a handful of decimal dust that was not the original value.

A dimension that is ….”about 3 inches square” would not be 76 mm, but more like 75 mm or even 80 mm. Rounding does not mean just dropping the decimal point, but using figures that end in either a 5 or 0.

30.48 µL/s looks too much like some rounded USC value expressed in ugly metric. Rather than just back converting one must take the extra time to locate the original pure metric values that reflect the actual dimensions of the product and do the calculations from that. In most cases the only way to know for sure is to contact the producer and ask for the dimensional information direct from the mechanical drawings and not the fictional data they present to Luddite customers.

Oh, and if you read further through the linked article, you will see that BCM can also mean a billion cubic metres. So, how about a billion cubic metres per inch squared?

As for the comment about the US using outdated metric terms, like micron, how many Americans will falsely think a micron is a USC unit, like calorie?

BCM/in², that is some ugly pigfish. Given the random, madeup abbreviation and ad hoc mix of measurement systems, I’ll guess this is an American company that doesn’t understand metric very well, which also explains the units used for European marketing. I don’t find 18.6 nL/mm² all that intuitive, and would much prefer 18.6 mL/m² as a measure of how much ink I can throw down through an open area on the plate, or for estimating how much ink the job consumes (if I know the percent coverage, text is about 5% by area for example). However dividing out the powers of length and calculating the average thickness of the ink layer on the roller, 18.6 µm, is also insightful.

3D Printer: I’m confused on which way layers are oriented. The part is clearly 228 mm tall. If layers are horizontal shouldn’t it be 228 mm/125 µm = 1824 layers? If layers are vertical, you may be right. In any case, a part is “interesting” only if it is open (not a rectangular solid), so its actual volume is probably much less than its envelope volume (product of max dimensions). The machine may also move faster across open areas than where it is laying down plastic. I would be suspicious of the speed and volume calculations. For an “interesting” part, there could be deviations of an order of magnitude.

Micron: Maybe a 20th century term? Reviewing the historical decisions in the appendix of the SI Brochure:

1) In the 9th CGPM (1948), the length unit micron, symbol µ, was affirmed, 10^-6 m. So were the calorie, erg, dyne and some other now obsolete units.

2) In the 11 CGPM (1960), the prefix micro, symbol µ, was affirmed as 10^-6, no mention of action regarding the micron.

3) The 13th CPGM (1967/68) abrogated the micron, since its symbol was now a prefix (and dropped the degree symbol from the Kelvin, renamed the new candle the candela, as well as several other “cleanups”). 46 years is a while ago but not quite the same as a couple of centuries.

“Veahdy intahresting”