Dienstag, 23. Februar 2016

Interlude: Sailing from Valparaíso (Chile) to Shanghai (China)

Wikipedia gives us an easy and straightforward example of how to sail from Valparaíso to Shanghai using the "great-circle navigation".
https://en.wikipedia.org/wiki/Great-circle_navigation#Example


It turns out that the computed distance (18743 km) is merely 0.05% off from what you experience in the real world (18752 km). Not bad I must say, as the model didn't even factor in ellipsoidal shape. Here's what it looks like on a globe. The plotted distance and angles are quite consistent with real world experience:



Here's my plot of the exact same journey on a flat earth (azimuthal) projection:

I've drawn in the "shortest distance", which would lead you directly over South America, North America and Asia mainland. I've also plotted the actual journey using waypoints for each 30° step in longitude.
It looks pretty much like a half-circle. So we could estimate that it is roughly π/2 longer than the straight line (around 57% longer).

Now, looking at the angles and distances on both plots, please tell me which plot you would prefer if you were sitting in a boat and trying to navigate from Valparaíso to Shanghai.

It is my understanding that one of the two is absolute bollocks for very simple mathematical reasons. (as described in the blog #34,35,43).
The two following links can be a good starting point for your own research:

https://en.wikipedia.org/wiki/List_of_map_projections
https://en.wikipedia.org/wiki/Theorema_Egregium

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