# What CRS to use for cylindrical raster world map?

I've drawn a cylindrical world map for a fictional planet. Exported it as png and scaled it, so one pixel corresponds to one km at the equator and from north to south pole.

I tried several cylindrical crs on it but it does never work out as I want and I can't find out why.
My goal: When I use the measure tool it should give me the following outputs:

• Horizontal length of equator (width of my png) = 38,211km
• Vertical distance from north to south pole (height of my png) = 19,105.5km
• When I measure the horizontal distance where the poles are (top and bottom rim of my png) it should show 0 km because of the cylindrical projection.

How can I georeference my png to get these results?

• You would need a world projection that maps the pole as a point, not a line. That would be sinusoidal. Most world projections map pole as line somewhat shorter than equator--various Eckerts for example. Dec 19, 2017 at 0:01
• Check out Furuti's pages or the Esri ArcGIS pages. Some projections may not be supported in QGIS/PROJ.4. Dec 19, 2017 at 0:03
• @mkennedy thanks for your comment! Is there any list as the "Esri ArcGis pages" for QGIS? Would help quite a lot to know what crs to use in what occasion. Furuti's page is quite helpful. But it isn't that easy to convert a raster map into another projection using gimp or photoshop, or is there any easier method? Dec 19, 2017 at 10:02

``````+proj=eqc +lat_ts=0 +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +a=6081469.53 +b=6081469.53 +units=m +no_defs
where `+a` and `+b` are equal to `equator_km / 2PI * 1000` (meters).