The Cuprous Proxy

Stained Glass

By The Metric Maven

Bulldog Edition

Many moons ago my father decided to construct a lehr, so he could print and decorate glassware as a part of his printing business.  A lehr is like a kiln, only it is designed for continuous use. One screenprints a decoration on a glass, which contains ceramic particles and oil.  The screenprinted glass is then placed on a chain conveyor. The glassware goes through warm-up, firing and cooldown zones inside the lehr. The ceramic printed image would fuse to the softened surface of the glass and become semi-permanent from this process. This lehr was unique because unlike most designs, it used electricity instead of natural gas. I recall many anecdotes about the design and development of the lehr. The one which is germane to this blog involves the firing of a considerable number of stemmed glasses. The glasses were placed at the entrance of the lehr, but as they emerged from the far end, to my father’s horror, the stems had all softened and the glasses came out looking like tulips which rather than seeking the sun, sought the ground.

The possible financial loss weighed on my father. He could not think of any way to fix the situation, so he stopped for a glass of ethyl alcohol at the  local pub to give the disaster some thought. My father knew the pub owner, to whom he related his problem. The owner knew exactly what to do. He told my father to bring in the glasses, and they would put them
up on a shelf and sell them. My father exclaimed “but who would buy them?” The owner replied “drunk people will buy anything.” Sure enough they did, to the eternal gratitude of my father.

I thought of this story when reading through the monograph Metrication in Australia by Kevin Wilks. A PDF of this work is available under the metrication tab on this web site. Wilks has summaries of how metrication was used as a unique opportunity to reform many trades, that had entrenched, long time traditional practices, that were clearly in need of change. He has a short note on Flat Glass: “Some rationalization of glass thicknesses was achieved and the opportunity was taken to eliminate mass per unit area as a measure of glass thickness.” In other words, before metrication, glass was sold not by thickness but by perhaps ounces/square foot, or ounces per square yard. Of course people would want to know the thickness for some applications, but it would not be sold that way, they would only guarantee the weight, and not the thickness. In other words ounces per square foot was a proxy “unit” for the thickness. One guesses that controlling the weight of the glass is easier than controlling the thickness?

One would think that in our enlightened age, proxy units like this would be a thing of the past in the United States. Well, not so for electronics and specifically not so for RF (Radio Frequency) / Microwave printed circuit boards. When I was in Engineering School we were presented with equations to calculate the important design values for RF circuits. One common parameter is called characteristic impedance. The design equations require one to know the thickness value of the copper on a printed circuit board. When I took my first Engineering position in industry, I asked how thick the copper was on some RF PCB material we had in stock. The surprising answer came back that  “it’s half-ounce copper.” My mind contorted. “But how thick is it?” None of the young engineers around me had a clue. Fortunately a classic Engineering Textbook on Microstrip Antennas has a table in the back to which I could refer:

The textbook explained that “The cladding material usually is designated in terms of weight per square yard.” By cladding they mean the copper foil. In those days (and now) in Aerospace, the thickness is expressed in a feral unit called a mil. This is 1/1000 of an inch in the US (in the UK it’s a term for a millimeter). The copper thicknesses were called out as 1/2 ounce with 0.7 mil thickness, 1 ounce has 1.4 mil thickness and so on. No metric was to be used in Aerospace–except when safely tucked away from view inside of computer programs. I asked my fellow engineers why the copper designation was in ounces/square yard. No one knew for certain, but it was speculated that weighing the finished product before and after cladding was easier than using a microscope, or micrometer to determine the final thickness.

An author, with whom I’m acquainted, produced a textbook in 2004 about microstrip antennas. It has the same table with the same information. The foil weight is asserted to be in ounces per square yard. The table is in a format which is perhaps more readable:

A second edition of the textbook was published in 2009. It has essentially the same table as shown above. By now I’m sure many readers are waving their arms in the air and saying “Look at the crazy number of decimal places on the metric thicknesses!” and he did not use micrometers to produce more easily comparable values.

The author has contemplated a third edition of his textbook, but (possibly through my influence) has become a metric advocate, and is now aware of Naughtin’s Laws. He decided to go back and start from first principles for the next edition. It makes very little sense to talk about grams/square yard as shown in parenthesis in the table. This is serious PigFish. The author started with the density of copper, ran through the calculation from first principles, and obtained a number for grams per square meter. There was just one problem, the numbers computed were not even close to those for grams per square yard found in the table. The value of grams/square yard and grams per square meter simply did not correlate at all. The calculations were checked over and over. There seemed to be no error. Then while researching the problem, he ran into this statement in a fairly obscure textbook:

Very thin copper foils, e.g., 1/8 oz/ft2 weight at 4μm thickness,

The 1/8 oz copper was divided by a square foot?!–and not a square yard? When the calculations were repeated using a square foot, and not a square yard they came out exactly perfect. That is they matched the values found in the original textbook table.

But what about how to designate the metric version of the mass/unit area for copper foil? Should it be re-done in all metric?  Should it be left in grams per square foot? He decided to go all metric. He converted from Ye Olde English to metric, and rounded the values so metric becomes rational. The metric copper foil information for the new edition of his textbook is below:

One can see the table is now all metric and Naughtin’s Laws have been applied—mostly.

The US information in Olde English is provided as the second table:

One lesson that emerges is the negative affect of “Engineering Folklore.” One text book after another can copy the same incorrect information. One of the reasons this was not discovered sooner, is that the value of interest, the copper thickness, was tied to a proxy unit (ounces) which, was never examined or directly used in engineering computations. The proxy started out as ounces/square foot, but was reduced to ounces with the area value suppressed. People could then make the incorrect assumption that it was ounces per square yard and publish. No error would be noticed as the area value was suppressed. The word ounce is as decanted of meaning as the word gauge.  If the manufacturer publishes a proxy value (i.e. ounces) on a data sheet, and the thickness is correct when the table is consulted, no one realizes that an error has occurred in the descriptive text. The odd way copper is designated on PCBs is not the only problem created by non-metrication, I’ve discussed the problems with electronic parts in an earlier blog.

The implementation of metrication in the US would allow for a complete review of technical practices throughout the economy, government, and our lives, with everlasting benefits to us all. We would have an opportunity to invest some time and money to save time and money indefinitely into the future. If only government would exercise its constitutional right to “fix the weights and measures” rather than ignoring it as they have for at least 230 years, we could all benefit.

Australians no longer have to purchase glass in ounces per square yard or foot, they now purchase it in thickness. I would like the opportunity to purchase RF/Microwave PCBs with a defined copper thickness in micrometers, or have a rational metric proxy if industry sees fit to remain with its current questionable proxy practices.

Related essay:

US Electronics: A Metric Peg in an Imperial Hole

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 not of direct importance to metric education. It 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.

7 thoughts on “The Cuprous Proxy

  1. This is quite interesting – I have from another source:

    Slightly thicker – I think this is the minimum thickness specified by some standard rather than the actual calculation?

    If you look at IPC-6012B They show 1oz to be 30.9um Minimum

    I have wanted to specify the copper on my boards in metric, but still see various thicknesses for 1oz material.

    This matters! I created a page some years ago that referred to my calculations for creating fuse traces on circuit boards.

    What I got delivered in the circuit boards varied a great deal and I think it goes back to the sloppy terminology. About the best I was able to do was a 4:1 variation of fusing current with soldermask over bare copper..

    So here is my question: When you order PCBs exactly how do YOU specify the copper thickness?

  2. I have a packet of photocopy paper described as “80 gsm” meaning 80 grams/square metre. As it is A4 paper I calculate that each sheet weighs 5 grams.

    Are there other proxy units in other industries?

    • Specifying the paper density as 80 g/m^2 (or “gsm”) is actually more useful than specifying the weight of an individual sheet, because it lets you compare the density of sheets of different sizes.

      You can immediately know that 80 g/m^2 A2 is the same density as 80 g/m^2 A4 paper. But, it’s a little harder to know that a 5 g A4 sheet is the same quality as a 40 g A2 sheet.

      But, in any case, whether specifying paper density of paper weight, either is more useful than what is apparently used for US paper sizes. The basis weight system provides a measurement that is only relevant at one point during its manufacture, and not at all useful once packaged and sold to the customer. It’s ridiculous measurement that is of no use to anyone except the paper manufacturer.

      • Hi, Lachlan,

        I realised that point some time after I had posted the comment. I suppose measuring the thickness alone isn’t enough to indicate the grade.

        However, it should properly be listed as g/m^2 (I can’t work out how to do a superscript “squared” symbol) but I suppose everyone know what it means and nit-picking pedants like me will have to get used to it.

  3. Hi all,
    One would hope that with change to SI that complete review of technical practices and recalculation of previous tables will occur not just blind conversion of existing numbers with old units. Recently I brought multipurpose paper at staples and it is clearly labeled 216 mm X 279 mm (8 1/2 ” X 11″) 75 g/ m^2 (20 lb). Of course the USC units are larger print.

  4. One question I have concerning Table A-1 is why the micrometres are not round numbers? How were they determined? They look like calculator conversions of inches. If you round the copper density to the hundreds of grams per square metre, how is it that the thickness ends up being a mathematical conversion of the inches?

    If you start out with 3 g of copper applied at a density of 150 g/m², the result is 20 μm. If you double the density and double the thickness, the result is 4 times the mass of 12 g. In metric countries wire sizes are stated in square millimetres. A 20 μm thick trace that is 5 mm wide will have a cross sectional area of 0.1 mm².

    A trace capable of carrying current for common household items may need to be 1 mm², and if it is say 10 mm wide, the thickness would need to be 0.1 mm or 100 μm. This would require 120 g of copper if the density is 1200 g/m².

    Another thing to consider is tolerances? What would be the tolerances when it comes to thicknesses and mass of copper?

  5. “One lesson that emerges is the negative affect of “Engineering Folklore.””

    This negative effect is prevalent in US industry. Dropping part of the unit seems to be more common than not. People talk about putting pounds of air in their tires and drop the square inch part. Cubic yards of cement is often shortened to just yards. BTU per hour for air conditioners is often stated as only BTUs. miles per hour is also shortened to miles.

    This problem exists because unlike metric units which have unit names for compound units, none exist in USC or imperial. Metric opponents will always insist they are not confused because they shorten names in context and understand what is missing. But those who are not aware will make mistakes and never be aware.

    I remember some years ago being told that an average adult requires about 2 L of water per 100 kg of body mass per day. This is now often misquoted as 8 cups (1.92 L based on an FDA 240 mL cup) per day. The 100 kg was dropped and the 2 L was changed to cups. As it is ended up, the assumption is every adult needs about 2 L per day and it isn’t true, as it depends on your body mass. A 50 kg man needs only half of what a 100 kg man needs.

    As a result some people may be flushing out to many essential vitamins and electrolytes because they are over-hydrating.

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