Metric Tiger Paws

By The Metric Maven

Bulldog Edition

I recently took my car in for an oil change, and to have the dealer look it over and verify it as roadworthy for a trip back to the midwest. Above the desk of the person helping me was a flat panel monitor which was explaining “The Penny Test” for tires. Public service commercials years ago showed that if you put a penny into a tire tread with the top of Abraham Lincoln’s head in the tread, and the top of his head was not covered, the tires were worn and needed replacing. This video showed different lines along the coin, gave a value in terms of 1/32 of an inch and had red, yellow and green backgrounds for each value. I shook my head and thought: “Wow, that’s crazy, who knows how much 3/32ths of an inch is or how it compares to 7/32nds? Millimeters would actually mean something.”

I sat and waited for them to finish. A pleasant woman came with the inspection results. She showed me that my brakes were mostly ok, but close to needing to be changed on the front as there was only 3 mm left. On the back it was about 4 mm and could also wait. Ah, millimeters, no 32nds of an inch. But there was also some bad news. I had recently purchased new tires, and one of them had a screw puncturing the top, and a nail in the sidewall. The tire could not be fixed because of this. It was slowly leaking. It was down to about 20 PSI (138 Kilopascals) the normal value is about 32 PSI (221 Kilopascals).

I immediately drove my car to the local tire shop where I had purchased the tires. To my amazement, the tire was in warranty. The bad news?—the tire had been discontinued. This was the third time Michelin had discontinued the recommended tire. As I needed to go on a trip, I put a very similar tire on. The person helping me indicated that a new tire had been designed to replace the old version, but it was not of a compatible size. The next time I was in and needed all new tires, he suggested I purchase the new tire model. I asked what the difference was. I was told one important change was that it is 10 millimeters narrower than the other design. My mind screeched to a halt.

“Ten millimeters?—are tires all metric?”

“Well, mostly, most all of them are now.”

I asked the technician what he meant. He then escorted me over to a nearby wheel rim to explain. He pointed out that a 14 inch rim is measured from the diameter of the bead (the seal) and the width of the rim is also in inches. The bolt pattern is in metric, and the standoff of the mounting plate for the rim is in millimeters, in this case it was 41 mm. I asked if the bolts were all metric.

“Well, mostly, they are M12 x 0.5 but on older types of wheels like those still used on campers and trailers they are often 9/16″ and the wheels are all in standard.”

AHHHHHH!….there it was…that word standard again, for barleycorn inches. I told him “well, it’s standard for 5% of the worlds population.”

He smiled and said “only we could make it this complicated.”

How could I argue with that? The technician then explained that for common passenger tires one can read the set of numbers found on its side and determine important properties of the tire.

The designation I saw on a tire in the show room  was 215/55 R16 97H.  The 215 means the width of the tire is 215 millimeters. The number after the slash is the aspect ratio which
is 55. So the height of the sidewall is 0.55 X 215 mm or 118.25 mm. So far so good. The R means radial tire and the 16 means sixteen inches. So the tire designation is not all metric, but is a pigfish combination. Oh…the pain. Clearly with all the new cars, and new tires that have been designed over the years, the radius could have been changed to 400 mm with little problem. What I saw was that all the sales literature is in inches for the rims and tires. One would never see a millimeter where showroom information met the American consumer.

The number 97 is the load index of the tire, which in the typical indirect designation of which Americans make a fetish (like gauge numbers), it does not correspond directly to any known units. A load index table tells you that 92 actually means 1389 pounds. This sort of irrational designation is what makes America great! My mind kept nagging me with hope that perhaps the radius designation in inches is actually a metric value that was converted back to inches and rounded. I consulted Wikipedia about tire code, and unfortunately this appears not to be the case:

  • 2 digit number: Diameter in inches of the wheel that the tires are designed to fit. There is the rare exception metric diameter tires, such as the use of the 390 size, which in this case would indicate a wheel of 390 mm in diameter. Few tires are made to this size presently.[6]

Bummer.

With little else to do while waiting for the tire to be mounted, I asked about the “penny test” and the 32nds of an inch. I was told the “penny test” was mostly out of favor these days. I asked what the values were for red, yellow and green for tire tread in 32nds of an inch. There seemed to be some uncertainty. Finally one of the attendants tossed a gauge in front of me and said “here, you can keep this, it will tell you.”  Indeed it does. It is a six sided plastic polygon cylinder which has a scale in 32nds on it. Here is what it states:

0-3 32nds is Red
3-6 32nds is Yellow
6-32 32nds is Green

It was clear to me they used the gauge constantly, but the numbers on it remained foreign. This is probably because 1/32″ is not exactly a common unit and they just look at the color on the gauge. This caused me to look back at the print out I was given by my car dealer for the brakes as it had the same colors. When I looked, I was surprised. Here is the top line:

I had completely missed the tire tread data of 7/32nds for my tire tread. There it is, side by side, fractions of inches and millimeters. There is not even a designation for inches, it just has fractions! It also appears to disagree with the gauge I was given at the tire store–by 1/32 of an inch.

Let’s see how millimeters might work. For the tire shop:

0 to 2.5 mm is Red
2.5 mm to 5 mm is Yellow
5 mm to 25 mm is Green

For my car dealer:

0 to 3.0 mm is Red
3.0 mm to 5 mm is Yellow
5 mm to 25 mm is Green

Either set of values seems simple, provides dimensional meaning, and is easy to remember when compared with fractions of an inch. So, does having tread thickness in thirty-seconds of an inch make the tread thickness more understandable because it’s in “standard” units? I don’t see how having two sets of units, where one uses fractions and the others decimals makes any sense. Perhaps that’s why we in the US do this, to obscure any rational understanding.

Cars may be over 99% metric, but until the US switches and industry is compelled to exclusively use the metric system for commerce, there will never be 100% anything in the US, other than confusion.

Technical Presentation and Metric

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 Cm3/M2 (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/in2 x 1.55 = Cm3/M2

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 109 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/in2 is 12 µL/in2. 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/in2 is therefore 12 µL/(645.16 mm2). To keep with Naughtin’s convention, we shift to nanoliters and have 18.6 nL/mm2.

So instead of creating a ridiculous ad hoc pigfish measurement unit like BCM/in2 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/m2. This is also a unit that may be easily visualized. This numerical value, 18.6 mL/m2, is the same as  18.6 nL/mm2 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. cm3/m2 = 1 µm) rather than using a volume unit in the numerator to provide clarity.

Jargon combination units like BCM/in2, 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.