Board Thread:Speculation House/@comment-4830106-20141010002549/@comment-24891101-20141013020623

This analysis follows Advocate's, in assuming the location of Vale, based on the coastal band of red on Vytal which is Forever Fall. We know that Vale is coastal, and we know Forever Fall terminates at Vale, on account of it being coastal, and does continue past, as RWBY was in the southeast, where the trees were green. Therefore, it is reasonable to conclude that the water on which Vale is situated is not a bay, and is in fact the open ocean.

Another assumption is that Remnant is a planet of similar composition to Earth, and therefore has similar density, and as it has similar gravity, within .1g, then its radius is in the range .897 to 1.097 of Earth, via Wolfram, which should not throw calculations off too much.

A further simplifying assumption is that the map we have of Remnant is an equirectangular projection. Irritatingly, the geographical map does not correspond to the proportions of the projection, so I will assume that the map sweeps through the polar angle, and incompletely through the azimuthal (presumably that is just water).

Now, to the analysis. Vale is located on the prominent "spike" jutting into the ocean toward the Black Dragon off of the bulge. Using ImageJ, I rescaled an equirectangular projection of Earth to the size of the Remnant map. This allowed me to calibrate a global scale bar, since we know Earth's circumference. Here are the images:



Now that we have a global scale, we can move on to examining Vale and its environs. The approximate distance from the westernmost extent of Forever Fall to the sea is approximately 300 miles, though this does not account for the strip of forest between Vale and the coast, which would be too small to appear on the map. Further, a reasonable bounding box placed around the city measures approximately 500x400 miles, from its inside. This suggest that this region is quite large. Even if Vale only occupies one percent of that bounding box, which is a very conservative estimate, then it still occupies 2000 square miles, which is truly a megalopolis.

The population of Vale may not be quite as large as that would imply. That size likely includes, per Roman's map, all sorts of industrial and agricultural facilities, most of which would be located outside of cities on Earth. Remnant has not that luxury.

Any critique of specific methodology, math, or assumptions is welcome.