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Comment by rootusrootus | Hacker News Reader

If it were to get technical enough to differentiate between rhumb and great circle, then maybe it should factor in elevation changes too.

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He does: 75.9km on the map, 77.0km when accounting for elevation. With the caveat: "Well, it's never as much as I'd think and it depends upon the accuracy of your terrain model"

That number surprised me, but because of how much extra it was rather than how little extra -- I always assume it's negligable, but in this case was over 1%

I also agree it seems like a lot. If there was 3000m of elevation gain and 3000m of elevation loss, I would only expect a couple or hundred extra meters of distance walked. 77.23 ≈ sqrt(77^2+(3+3)^2).

Reading total elevation gain/loss from his graph it hard but 3000m up and down seems about right.

The average gradient of Scotland is 19.3%.

Then it becomes a coastline problem, with different answers depending on the resolution of your elevation data.

Great video on this from Matt Parker (focusing on area in this case): https://youtu.be/PtKhbbcc1Rc

If you include elevation then you have to include tolerance for deviation. I live in an old house, so I can't even walk across the room without a vertical deviation of some sort :)

Edit: My point here is that if you try to plot a literal straight line through 3D space, it will be necessary to allow some amount of deviation in one axis. Else your longest 3D line will be the distance between your first two points.

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