Hmm, that's a good question. I think the radius in scale_control is fine.

From Wikipedia:

for small scale (large region) applications the variation may be ignored, and mean values of 6,371 km and 40,030 km may be taken for the radius and circumference respectively

@andrewharvey I'm guessing that because you're calculating the circumference at the equator, you wanted a more exact radius than is needed for the spherical approximation in the scale, which I think is also fine. If we want to coordinate values like this, maybe it would be a good idea to pull them into a file that could be included elsewhere so we can define them once and not have inconsistencies in the code.

The figure in mercator_coordinate came from the EPSG:3857 definition.

@andrewharvey given how the value is used in MercatorCoordinate, I think we should change it to mean radius value rather than the equator one from EPSG:3857. The latter also defines inverse flattening (298.257223563) which defines how this radius varies across the globe.

@andrewharvey given how the value is used in MercatorCoordinate, I think we should change it to mean radius value rather than the equator one from EPSG:3857. The latter also defines inverse flattening (298.257223563) which defines how this radius varies across the globe.

@mourner Sorry I don't understand. What does "radius value" mean here?

At the equator (ie. along the semi-major axis) the inverse flattening won't matter or affect it right? And then we use the scale factor to account for larger latitudes being larger on the map.

@andrewharvey at the equator, it won't, but at other latitudes, it will — the Earth radius (the circumference is calculated from) will be smaller. You can either account for that with complicated formulas, or take a mean value across latitude range for simplicity — super-precision isn't important for the scale control anyway.

@andrewharvey at the equator, it won't, but at other latitudes, it will — the Earth radius (the circumference is calculated from) will be smaller. You can either account for that with complicated formulas, or take a mean value across latitude range for simplicity — super-precision isn't important for the scale control anyway.

Ok, maybe I misunderstood this then, I thought the scale factor formula I used accounted for this. But maybe that's just for the Mercator projection on a spherical datum instead of on the ellipsoidal datum which EPSG:3857 uses..

@andrewharvey yes, exactly. Standard Mercator formulas, including the scale factor one, assume spherical earth and so usually use the mean radius value as approximation.