A Bridge Too Far?

By The Metric Maven

Mini-Bulldog Edition

The view that “diversity in measures” is a good idea is absurd whether it is stated by George Orwell, or former NIST Director Gallagher.  The metric system was developed because all that “measurement diversity” offers society is at worst an opportunity for fraud, and at best an opportunity for conversion error.

A very important benchmark used to determine the vertical height of a position on Earth is sea level. One would think that in the age of GPS, and the metric system, that a universally agreed upon sea level  value would exist. Alas, it does not. The UK’s mapping agency measures altitude on the Earth with respect to mean sea level using a value determined during World War I at Newlyn in Cornwall.[1] Today this figure has increased by 200 millimeters.

GPS has a spherical “Earth model,” but alas the Earth is not a sphere. It is a lumpy and in-homogeneous solid that looks much like a sphere. Satellites were launched and have provided enough data to create an accurate geometric model of the Earth–warts and all. The model will be accurate within a few tens of millimeters. Combined with ground based measurements, the new model should provide millimeter accuracy. The value of altitude on Earth will not be in terms of sea level, but with respect to the Earth’s center. Currently, European countries each use their own definition of sea level. The new data shows how much sea level variation there is across European countries. Amsterdam’s vertical benchmark will be about 10 mm above the proposed European Vertical Reference System, Helsinki is 210 mm higher and Ostend is 2320 mm lower than the new benchmark. Tregde happens to be very close to zero offset from the new standard.

This farrago of vertical measurement references can have engineering consequences.[2]  In 2003 a bridge was constructed to span the Rhine River, and connect Laufenburg, Germany and Laufenburg Switzerland. Each country began construction on its respective side and were to meet in the middle. The German reference for sea level used the North Sea. The Swiss reference for sea level used the Mediterranean Sea. The two reference values differ by 270 millimeters. The two cities have always seen themselves as a single metropolis, and so they communicated this difference to one another so that it could be taken into account. A problem occurred when the simple conversion had a sign error, and the German side of the bridge was 540 millimeters higher than that constructed by the Swiss. The German side was lowered, and eventually the two sides connected.

With a costly error like that, it would seem obvious that the world should embrace the new single model of our Earth developed using the latest satellite data. The US, Canada and Mexico have all agreed to use a unified geoid-based height system in 2022. The International Union of Geodesy and Geophysics passed a resolution in 2015 to support the adoption of a single global model.

Mount Everest

This sounds all well and good, but often anatomical measurement contests interfere with rational ones. The development of an international standard for elevation could precipitate a “Pluto Controversy” here on Earth. We all know that Mount Everest is the tallest mountain on planet Earth. It is generally accepted to be 8848 meters above sea level. China and Nepal argue over whether the height of Everest should be measured in terms of its rock height, or snow height. The National Geographic Society has its own ideas of how to measure the peak and in 1999 argued it is 8850 meters high.

Chimborazo

When one starts to use the Earth’s center as a reference, considerable change can occur. The peak of  Ecuador’s Chimborazo is a mere 6310 meters above the local sea level, but because of the Earth’s deviation from a sphere, this peak is much farther from the Earth’s center. When using the Earth’s center as a reference point, Chimborazo is over 2 Kilometers taller than Mount Everest. One can only hope the political creatures that inhabit our planet can look past “who’s is bigger” and all agree on a single standard for elevation, but in the past, one country in particular has been incorrigible when it comes to international standardization of measures. We can hope this obstinate attitude is not contagious when it comes to altitude.

[1] New Scientist 2017-02-11 “Vertically Challenged” pp 38-41

[2] Heather A. Lewis (2015) Math Mistakes That Make the News,
PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 25:2,181-192

Spring Chicken

Chicken-ManBy The Metric Maven

Bulldog Edition

It is said that in 1960 Richard Leghorn coined the phrase “information age.” He founded a company that manufactured spy cameras and later worked at the Pentagon. The phrase “information explosion” was also in vogue at the time. In my view there has also been a “non-information explosion” depending on if one is concerned about the veracity of information presented. Klystron sent me a link to an online article where an automotive writer discusses the different types of compression springs one can use in car suspension. The article introduces the reader to “spring rate” which is proportional to the stiffness of a spring:

In simple terms, a spring’s rate is the amount of weight required to compress itself a single inch. It’s a universal measurement, it applies to everything from lowering springs to valve springs, and it’ll look something like this: 500 lbs/in. The bigger the number, the stiffer the spring.

This took me back to my introductory physics class in college where I was introduced to Hooke’s Law. In 1678 Robert Hooke (1635-1703) offered a simple linear mathematical equation that relates the force produced by a spring in terms of its extension or compression (depending on the type of spring). The equation is simple: F = kX. The letter F stands for the force the spring produces, X is the distance you have compressed or stretched the spring. The value k is a number that converts the distance the spring has been compressed or stretched to the amount of force it produces. The value k is called the spring constant, and it is the same as the “spring rate”  offered by the automotive writer. In this case k is in pounds per inch or lbs/in. Indeed, the larger the spring constant k, the stiffer the spring. As I point out in my essay, The Count Only Counts—He Does Not Measure, this relationship was used to produce the first spring mass gauges. Springs often obey this relationship only over a given displacement range, but we will ignore that here and assume we are within the linear range.

The author then points out that the rest of the world is metric and converts the spring constant (rate) over to metric for his readers:

Metric_Car_Guy

Kilograms are not a force, and so Kg/mm when multiplied by a displacement distance in millimeters produces a mass value and not a force. This is very poor dimensional analysis on the part of this professional automotive writer. When one stands on a bathroom scale in the US, the readout is in pounds of force, but if one flips a switch to metric it instead offers mass in Kilograms. If the scale had a metric readout of force, the value would be in Newtons. If you have a mass of 75 Kg, then your metric weight would be 735 newtons, which is a force value.

A 500 lb/inch spring constant properly converted to metric would instead be 87.8 newtons/mm.

While springs appear rather prosaic they are used ubiquitously in our modern world. Their benefits are enthusiastically portrayed in this 1940s film about the benefits of springs.

Metric springs in the US apparently use non-SI for a spring constant:

PigFish-Springs

click to enlarge

The 60 mm inner diameter spring in the top line of the table above has a metric “spring rate” of 18 kgf/mm or 18 kilogram-force per millimeter. Kilogram force has never been a part of the metric system and is not accepted for use with the modern metric system. A “kilogram-force” is 9.806 newtons, so the spring constant when actually converted to metric is 9.806*18 = 176.5 newtons/mm.

We are a country that thinks it is technologically unmatched, yet everyday I see that most professions never think quantitatively or technically.

Spring-ColorsSome years back, one of the tension springs on my garage door snapped making it inoperable. The previous owner had taped a garage repair business card to the wall and I called the number. The fellow who showed up was friendly and had a large number of springs in his truck. He took one look and checked his truck to see if he had a replacement. The technician looked up from his pickup-bed and asked “is the color white or blue?” It was then that I realized the spring had a section along the middle painted white. He returned with a set of blue and a set of white springs, one of which had paint on one end. The workman indicated that both garage springs needed to be replaced so they would have the same “strength.” This made sense. He took out the broken spring and then the intact one, which he then put over a hook on the back of his truck and pulled. He next pulled on a new blue one, and then a new white one.

I asked why he was doing two colors. “They’re all different” he said, “the colors are meaningless. Every manufacturing company is different—I use feeling.”  I immediately suspected this was not a good idea. The interpretation of force (weight) on an object by humans is logarithmic. It struck me that it would be possible to create a device that would measure the spring constant of each spring so there would be no guessing. When I asked if such a device existed, the technician asserted he did not need it. His human measurement perception indicated white was needed as I recall. He put them into the garage door and after opening and closing it a time or two decided the blue spring was probably better. He installed the blue springs and then pronounced them the best. Indeed, my garage door has been fine over the last few years and works well.

It bothers me that people who support what is left of our infrastructure in the US seem so out of tune with the quantitative aspects of it. It would make a lot of sense to me that if one needs a pair of springs with the same spring constant for each side of a garage door that measuring this value would make sure the springs are the same. At the next level, those who write articles to inform the public are often no better. I see this as part of a cultural problem that promotes an anti-intellectual view in the US. The lack of the metric system appears to be but a symptom of this larger problem.

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The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.

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