Category Archives: Unit Proliferation

The Metric Mess is Hard Wired in The US

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Skeez

By The Metric Maven

Bulldog Edition

Skeez was a person who seemed to be born interesting. He obtained his nickname from a character called Skeezix in the comic strip Gasoline Alley. The comic strip itself is unusual in that Skeezix arrives as a baby on a doorstep and ages as time goes on. Skeez spent much time at his cottage on the shore of a nearby lake. One day I noticed a new bust among his eclectic collection of objects; it was Charles Dickens. Skeez then told me that Dickens had a story about an innkeeper who was so cheap he counted the number of beans he put into his soup, and that’s where the term “bean counter” arose. He was as close to a polymath as I have ever known. When he passed away I ended up with small gargoyles that he had brought back from France during World War II. I have an African shield with a weapon which was used to kill tigers, as well as other books and notes he left behind.

Recently I ran across a an RCA Radiotron Reference Book from 1940 which Skeez had owned. Inside, it contains a small snapshot of how the metric system was viewed by electrical engineers in 1940. It appears that US engineers saw the metric system as a simple drop-in substitute for Olde English measures. For instance, under pressure they equate pounds per square inch to Kilograms per square centimeter. No pascals. The equivalence of kilograms (mass) with pounds (force) is a strange misunderstanding in a reference like this—unless they meant Kilogram-force. It is clear that again Americans see the centimeter as a pseudo-inch and just substitute away without any measurement introspection. I’ve not found a millimeter mentioned in this reference.

It also has a list of miscellaneous conversions that have a couple of interesting aspects. First I had no idea there was a unit of metric horsepower. Apparently notion of horsepower was still considered so important in 1940 that a metric version needed to be defined. Apparently metric horses have less strength than Olde English horses. The definition does not seem to even involve a horse:

DIN 66036 defines one metric horsepower as the power to raise a mass of 75 kilograms against the earth’s gravitational force over a distance of one metre in one second;[13]

The other odd aspect is that meters show up with an er ending, but litre is spelled with re. I’ve often wondered when it was decided, and by whom that in the US we would use er rather than re. Here the situation is mixed.

What really caught my attention, and is the actual subject of this essay, are the tables on wire.  American copper wire is designated in American Wire Gauge (AWG). I have made my view known concerning the vacuous non-term gauge in a previous essay. We note that along the left column is the AWG number. AWG was first used as a designation in 1857. The diameter of the wire is then given using the informal feral unit known as the mil. A mil is a slang term for one-thousandth of an inch—at least in the US. In metric countries it’s a slang term for a millimeter as I understand it. As the gauge number increases, the diameter decreases.

There is also a column to the right of the diameter of the wire in mils, which is the area in circular mils. Let’s take an easy example, say AWG 10, which is a solid wire with  a diameter of 101.9 mils. Now we know the area of a circle is π multiplied by the radius squared.  The answer to the computation is 8155 square mils. But wait–the value in the area column is actually 10 380 circular mils. Well, that’s because apparently our engineering founding fathers, in their infinite wisdom, decided that dividing the area up into the number of circular areas of one mil was the best way to do it. To get circular mils you just square the wire diameter in mils. This produces a value that is not directly usable for any common engineering calculations. The resistance of a solid wire is proportional to the cross-sectional area, and circular mils are essentially a gauge number for area and not a defined area. We have inherited this strange way of determining the area of solid copper wire without questioning its sanity. It also illustrates once again that our Olde English set of measurements has nothing in common with a system. To make matters worse, Wikipedia decided to use the term kcmil for kilo-circular-mil in their wire table. I wish metric prefixes would only be used with metric units, and not feral ones, or medieval ones.

Another page in the RCA Radiotron Reference Book has the number of winding turns which make up a linear inch. For example, the Brown and Sharpe (i.e. AWG) Gauge Number is given on the left. We then see that for enamel coated wire one needs 7.6 turns of AWG 8 wire to have a coil which is one inch in length. This data is useful for computing how long an inductor might be for an electrical engineer.

If one were rationally using the metric system, one could easily compute any of these values from a table which gives the wire diameter in millimeters and the area in millimeters squared. If the wire manufactures were to use preferred numbers with metric diameters, then it would simplify matters further. Their would be no more indirect designation of sizes with meaningless gauge numbers. The values would be directly understandable in millimeters. Let’s suppose we have a wire of 1.25 mm diameter, we would know immediately that ten turns is 12.5 mm. We could use AWG 16 which after we consult the table is seen to have a diameter of 50.8 mils. We then know that ten turns is 500.8 mils, divide by 1000 to get the value in inches or 0.5008 inches. Alternatively, we could have started with a direct metric designation of 1.291 mm and ten turns is immediately seen to be 12.91 mm. Starting with the metric diameter, one knows this is the width of a single turn. Using this, one can quickly evaluate 1/1.291 mm on a calculator which is 0.775 turns per millimeter. To get 10 millimeters it would take 7.75 turns. start with a metric wire diameter and one can quickly compute anything one needs–using common mathematics.

Incidentally the gauge designations for copper wire are not standard across types of wire, so one can’t be certain what diameter other wires might be when  given a gauge number. Clearly,  if the diameter of a wire in milimeters is given, or another appropriate metric length (e.g. micrometers), this allows one to immediately compute any appropriate parameter. Here is an illustration from a vendor who sells wire in Australia:

The wire industry in the US has been using this kludged up system since 1857 and has done nothing to introduce reform. This clearly shows to me that one needs to have a government mandate, like that implemented by Australia, which mandates metric. The voluntary part for industry is how they will introduce metric. If they have any sense they would take the opportunity to reform their industry with preferred numbers, or in some other rational manner. Standard DIN Sizes using ISO6722 in terms of mm² look like a good idea to me. But how they would implement the change would would be up to them—and in ‘merica they just might use “soft” metric and preserve familiarity over simplicity along with 19th century measurement practice. Until then, this mess is hard wired in the US.

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.

Milliards and Milliards

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Carl_Sagan_Planetary_Society

By The Metric Maven

Bulldog Edition

A seminal advance that allowed for the development of the modern world seems never to be consciously noted by most persons. That advance was when people began to identify groups of objects with the abstract idea of numbers. The concept that 1, 2, 3, 4 and so on could be mapped with a one-to-one correspondence to a group of skins or fruit or whatever, took a considerable amount of abstraction, and can be counted as one of the great conceptualizations humans embraced.

Francis Galton (1822-1911) is reported to have made this observation about a tribe in Southwest Africa:

When inquiries are made about how many days’ journey off a place may be, their ignorance of all numerical ideas is very annoying. In practice, whatever they may possess in their language, they certainly use no numeral greater than three. When they wish to express four, they take to their fingers, which are to them as formidable instruments of calculation as a sliderule to an English schoolboy. They puzzle much after five, because no spare hand remains to grasp and secure the fingers that are required for units. Yet they seldom lose oxen; the way in which they discover the loss of one is not by the number of the herd being diminished, but by the absence of a face they knew.

I don’t know if Galton felt sanctimonious about this lack of numeracy, but if he was, it was not particularly justified. Isaac Asimov (1920-1992) was the person who led me to this realization. In his book Fact and Fancy he states:

It was 1300 A.D. before the word “million” was invented. Until then, the largest number word was “myriad,” which was Greek for 10,000. Even Archimedes, in calculating the number of poppy seeds in the entire Universe as he knew it, used expressions meaning “myriads of myriads of myriads. …

It was only seven centuries ago that a word to describe 1 000 000 was created, which is equivalent to the modern metric prefix Mega—and adopted only in 1960.

In 1871, Fredrick A.P. Barnard (1809-1889) gave a speech which was expanded into a book called The Metric System of Weights and Measures. Barnard had done his best to make the metric system the exclusive system of measure in the US, but Charles Davies managed to derail this initiative. In his book Barnard presents this table:

Myriametre

The largest metric prefix used with a meter is a myriametre. The myriad apparently continued to remain an upper value limit for the everyday person. This is true even though the word million existed at that time, and Friedrich Bessel (1784-1846) determined in 1831 that the star 61 Cygni was about 98 Petameters from Earth, or 9 800 000 000 000 myriametres. The early metric system was provincial and still mired with numerical magnitudes from the time of Archimedes. It would not be until 1960 when a prefix larger than myria would be adopted, which is of course Mega. The prefixes Giga and Tera were also adopted that year. The use of myria as a prefix, despite its ancient origin, seems to have been eschewed without much difficulty, and the better by 1000 approach began. The seldom used prefix cluster around unity has proven much more difficult to eradicate.

While the numerical value for the word million was agreed upon after 1300 A.D., a fork occurred when English words were chosen for larger numbers. The word billion is used for Giga in the short scale; in the long scale, the word milliard is used. The word billion is used for Tera in the long scale, but it is called trillion in the short scale. The history of the changing values of words used to describe large numbers is considerable and meanders. This prefix table provides succinct documentation of the differences between short and long scale words:

Metric-Prefixes-Long and Short Scale
Cover of New Scientist November 8-14 2014 which describes the Rosetta Probe
Cover of New Scientist November 8-14 2014 which describes the Rosetta Probe as travelling 6 billion Kilometers and not 6000 Gigameters . The distance to Pluto is about 5419 Gigameters. (click on image to enlarge)

Douglas Adams’ The Hitchicker’s Guide to The Galaxy has a computer called the Milliard Gargantubrain, which shows that long scale usage is still with us. The use of the short and long scales has allowed for very poor literary numerical expression, which was long ago forbidden in the metric system, but is ignored when long and short scale words are combined with metric prefixes. The statement that a celestial object is one million Kilometers from Earth does not meet with objection, but if it is a KiloMegameter away, that would be laughable. The proper term Gigameters would probably also cause heartburn for the provincial literary crowd who are proudly literate and willfully innumerate, but it is the most succinct prose expression, and does not contain any numerical ambiguity. If we have a billion meters, it could be a Gigameter or Terameter. Carl Sagan (1934-1996) used the term billions and billions. But which billion? Alternatively he could have said milliards and milliards, which would have been unambiguous by comparison—even if it is a metaphor.

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.