Slartibartfast has just finished designing the fjords of Norway. He begins work on the volcanoes of Hawaii when he soon realizes that his work isn't matching up with his blueprints.

Finally the answer hits him; his once faithful meter-long aluminum ruler that served him so well in the -10°C temperature of the fjords, after entering the 40°C tropical islands of Hawaii has expanded, and become 1.0012 meters long.

This may not sound like a lot, but when you are designing a coastline, 1.2mm per meter turns into kilometers worth of difference. And when he is working in the deeper, hotter parts of the volcanoes, this expansion of the aluminum ruler is only going to get worse.

What material can our worldbuilder design a measuring stick out of so it will stay as close to one meter as possible, regardless of what temperature he is working in? What sort of tolerance will the measuring stick have?

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    $\begingroup$ Cool question (+1), but it doesn't seem to be about worldbuilding, just a tool a guy happens to have when building a world. $\endgroup$ – HDE 226868 Oct 25 '15 at 22:00
  • $\begingroup$ @HDE226868 You are right, it is a physics question, not necessarily world building. I was planning on asking this in Physics Stack Exchange, but I thought I would me more on topic, and get some more creative answers here. $\endgroup$ – IQAndreas Oct 25 '15 at 22:05
  • $\begingroup$ I know people often look to Worldbuilding for creativity, but our scope only goes so far. There must be a way to apply a question to worldbuilding, and I don't think there's a connection here. $\endgroup$ – HDE 226868 Oct 25 '15 at 22:09
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    $\begingroup$ what tech level? why didn't he consider laser because of your precision requirement for this trip to hell? $\endgroup$ – user6760 Oct 26 '15 at 2:27

The standard material to use for low thermal expansion is Invar Typical TCOE is about 1 ppm/deg K compared to aluminum's 22 ppm, so a shift of 50 C will change such a meter stick by about .005 mm.

At the temperature range specified, there are not many candidates which will do better. In principle, a composite ruler made out an 86 cm invar portion and a 14 cm cubic zirconium tungstate section could produce an overall thermal coefficient very close to zero, but at present CZT is only produced in a powder.

The obvious approach is not to depend on the material to maintain stability. A ruler with a built-in laser measurement system could be constructed which would use correcting mechanisms such as PZT stacks to produce a stability well under 1 micron.

  • $\begingroup$ I think the answer is the opposite; the ruler should be made with SIO2 so that it changes with the material it's being used to measure. $\endgroup$ – Joshua Apr 8 at 16:48

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