What projection is this? Is it van der Griten?

I am trying to convert some maps that came in .dra format from MapMaker to shapefiles. My problem is that the original files have no projection information, which complicates their use after exporting them using MapMaker. The map of the original data looks like this:

…which looks very similar to the van der Grinten projection, as can be seen here:

I also compared it to Robinson but that one does not look that similar. Neither does Eckert II.

One major complication is that the units of the original map do not seem to be meters, but some multiple. Specifically, if I import the world map from natural earth and compare bounds with the bounds of the exported shapefile I get different multiples, so it is not clear which unit it really is. Here’s some python code that shows the issue

import geopandas as gp

# Import World shapefile from Natural Earth in WGS84
world_wgs84 = gp.read_file('https://www.naturalearthdata.com/http//www.naturalearthdata.com/download/10m/cultural/ne_10m_admin_0_countries.zip')
world_wgs84 = world_wgs84.loc[world_wgs84.NAME.str.find('Antar')==-1].reset_index(drop=True)
world_wgs84.plot()

# Import MapMaker shapefile
mapmaker_shp = gp.read_file('https://www.dropbox.com/s/cxuoqh8msn9184o/8000.zip?dl=1')
mapmaker_shp.plot()

# Project to van der Grinten for comparison
world_vdg = world_wgs84.to_crs('ESRI:54029')
world_vdg.plot()

# compare bounds
wb = world_vdg.total_bounds # array([-19917658.38747369,  -8308978.01939191,  19974342.14947391, 14122774.74128915])
mb = mapmaker_shp.total_bounds # array([-9053.47050001, -4725.776     , 11509.66949999,  7034.509     ])
wb / mb # array([2200.00257221, 1758.2251083 , 1735.44011403, 2007.64186118])

If I define the van der Grinten projection and use different units, e.g., 1600 meters, the maps are more similar and they overlap quite closely, but not exactly as if the units in the x and y direction are different.

# Define Van der Grinten
vanDerGrinten = 'PROJCS["World_Van_der_Grinten_I", GEOGCS["GCS_WGS_1984", DATUM["WGS_1984", SPHEROID["WGS_1984",6378137,298.257223563]], PRIMEM["Greenwich",0], UNIT["Degree",0.017453292519943295]], PROJECTION["VanDerGrinten"], PARAMETER["False_Easting",0], PARAMETER["False_Northing",0], PARAMETER["Central_Meridian",0], UNIT["Meter",1600], AUTHORITY["EPSG","54029"]]'

world_vdg1600 = world_wgs84.to_crs(vanDerGrinten)
ax = world_vdg1600.plot(); mapmaker_shp.plot(ax=ax, color='r')

as shown here:

.

So the questions are

• whether this is really the van der Griten projection and if so how can I transform this into WGS84 correctly
• if it is not van der Griten then which projection is it?