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

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