ArcMap Scale Bars for Geographic Coordinates
We just had a customer send us a GeoPDF created with Map2PDF for ArcGIS. The map was created using geographic coordinates, and covered an area around 32 degrees North latitude. Map2PDF for Reader was measuring the 12 km scale bar in GeoPDF to be 10 km -- what gives?
The Map2PDF for Reader/Acrobat paradigm doesn't really have a notion of maps in geographic coordinates, per se. We treat all maps as in projected coordinate systems. To resolve our impedance mismatch, we treat ArcGIS geographic coordinate maps as special cases of the equidistant cylindrical projection with a standard parallel passing through the middle of the map. We did this for a couple of reasons. First, since the map author didn't choose an explicit coordinate reference system for the map, there are no Cartesian coordinates to recover. Second, we wanted to make measurements as accurate and useful as possible.
It appears that ArcMap calculates a scale bar for a geographic coordinate map using something like a equidistant cylindrical projection with a standard parallel at the equator, but makes geodesic measurements. Indeed, the customer measuring the scale bar in ArcMap shows 10 km, not the 12 km marked on the map. To get the most functionality out of your GeoPDF coming out of ArcMap, pick a projected coordinate system. If want the look of the geographic coordinate system, pick equidistant cylindrical, and pick a standard parallel in the middle of your area of interest.