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A cartography question: you open an atlas and usually at the beginning of it there are some world maps showing various thematics. Let's say the world map uses Robinson projection and it says it has a scale of 1 : 120,000,000.

How is this scale determined? Are there any standard practices (measuring scale ratio of 10° longitude on equator or something similar)? Or is this an imprecise science left to each cartographer to figure out?

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2 Answers 2

In order to compute the scale, you need to work along the standard lines (which are not necessarily straight lines on the map). With cylindrical and conical projections, those standard lines are located at the intersection/tangent with the sphere/ellipsoid. For azimuthal equidistant, those all straight lines that converge to the points of tangency; for the sinusoidal projection, linear scale is true for the equator and the prime meridian; van der grinten, linear scale is true at the equator; for Eckert, it is true at two parallels ...

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Answering my own question. After thinking about it, the answer seems pretty obvious: map projection formulas. Let's take Natural Earth projection as an example.

In order to project the map to a 1 : 1 scale, you multiply the projected coordinates with Earth's radius (cca. 6371008 m). Such an (imaginary) map has a width of (roughly) 35,000 km (I'm using the test data provided by the author of Natural Earth projection). So in order to show such a map on a piece of paper with a width of 20 cm, you need to scale it down by 180,000,000. And this is the scale of the final map.

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