The Cuprous Proxy

Stained GlassBy 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

The Metric Dream House

By The Metric Maven

Bulldog Edition

Many people have an idea what their ideal custom house might be. Retired Boiler and Pressure Vessel Inspector Holger Michelsen and his wife Madeleine have envisioned theirs. This vision includes the requirement that the house be dimensioned and constructed using the metric system. Holger retained a structural engineer who is sympathetic to the metric design of housing, and agreed help to make his vision a reality. The dimensions submitted are in millimeters, but also the drawing size was in ISO metric.  The Whatcom County (Washington State) staff rejected the  application but then proposed that for a fee of $100 per hour, they could translate the units to U.S. Customary. The two appealed the decision because the Whatcom County Code RCW 19.94.150   states that the system of weights and measures in customary use in the United States and the metric system of weights and measures are jointly recognized, and either one or both of these systems shall be used for all commercial purposes in this state. This is very similar to the State of Washington’s code.

It was argued that the action of applying additional fees to process a building permit application submitted in metric units “destroys the equality inherent in Whatcom County (Washington State) Code.” This proposed extra fee is in essence a penalty for the use of metric units. The County Engineering Staff attempted to justify the extra fees claiming that it would take more time to process a building permit request which was not submitted in U.S. Customary Units. The County officials remarked that other previous applications in metric units were all changed to U.S. customary by the applicants at the request of County Engineering staff. Apparently these County officials did not realize that according to Congress, the metric system is the “preferred” system of weights and measures in the US. The use of metric units for building construction is much more efficient than U.S. customary units. In my view, Whatcom County should have offered a discount for the submission of metric-only construction plans.

The other strange complaint from the County was the scale to be used. When I was told that the desired scale on the drawings is 1:48 or  ¼” = 1 foot, my first thought was was “feet and inches? Two units?” Because we use dual units for housing plans, it is a much less efficient process, which is prone to error. Holger had used 1:50 and 1:25 scales as seemed appropriate. There is no “base unit” with metric scaling, they are a true ratio. My second thought was: “in the age of Computer Aided Design (CAD) programs, they were asking for submissions of scaled paper drawings?”  Modern CAD programs work directly in the units involved, or are normalized, why on earth would anyone bother to use a scale?  All of my parts for my engineering work are 1:1. I have not made one scaled drawing in the last six years. How much time is being wasted because there has been no thought to reforming the process of submission?  Also why not demand A-Series paper sizes so that one can printout any size directly? Neither ANSI nor American Architectural paper sizes can do that. Why is The County Engineering Staff not thanking Holger for trying to set a useful precedent?—one which would make life easier for them?

Holger and Madeleine

The Board of Appeals on July 9th (2013-07-09) heard the case, and in a 3-2 ruling, found in favor of Holger and Madeleine. They can now submit their request for a Building Permit for review in metric at the same cost as Ye Olde English unit submissions are charged. Holger stated that the permit delay was worth the effort: “We were able to achieve true equality in recognition for metric and thereby lift metric units out of the parentheses to which they had been previously banished.” There was still one possible Olde English fly in the ointment. The County could appeal. Fortunately Holger received word on July 10th that they would not. We should all thank Holger and Madeleine for persevering and setting a metric-only precedent in US housing construction in Washington State. It is but a tiny crack in a solidly frozen glacier, but without them it would not be there at all.

Gasoline in US Dollars Per Liter (click to enlarge)

The area where Holger and Madeleine have decided to construct their metric house is unique. Point Roberts Washington is an exclave. It is an area of the US which according to Wikipedia is “legally or politically attached to a main territory  with which it is not physically contiguous because of surrounding alien territory.” That alien territory is Canada. Because they are surrounded on three sides by water and by Canada on the other, they have gasoline which is sold and priced in US Dollars per liter. Holger will now have a car designed in metric, into which he puts liters of gasoline, and then will be able to park in his metric garage—assuming he has a garage.

Point Roberts Washington

Holger and Madeleine thank you for your efforts on behalf of metric in the US.

Related essay:

Building a Metric Shed