Spherical Mercator projection invented by Google and not conformal?

I had some certitudes on the Google Spherical Mercator also known under EPSG code 900913 and 3857 before looking at this presentation, I was sure that this projection was in the Mercator family (so conformal).

With this input, I'm now not sure about conformal status of Spherical Mercator. I didn't dive enough in mathematical "stuff" here to be able to qualify validity of the doc.

I also want to confirm / infirm this exact projection was never there before Google Maps landing.

Any opinions on those 2 questions?

• – Mapperz
Commented Oct 17, 2013 at 23:54
• Thanks for the link but I already know this part ;) or I wouldn't have post this other question Commented Oct 18, 2013 at 9:51
• I've you're interested in an authoritative academic reference on Web Mercator, look for an upcoming issue of the journal Cartographica. The paper is by Sarah Battersby of UCSB and other co-authors. -Noel
– user28870
Commented Apr 5, 2014 at 12:45

The Mercator projection has been around for a few hundred years. I don't know when the ellipsoidal version of the algorithm came into being (I don't have my reference books at my current location), but certainly the spherical version is quite old. Both versions certainly pre-date the use for web-based map imagery. By ellipsoidal / spherical, I mean that the algorithm supports either an ellipsoidal or a spherical model of the Earth.

Google / Microsoft (and supposedly Yahoo) started using a spherical version of Mercator. For the spherical model of the Earth, they chose to use the semimajor axis of the WGS84/GRS80 ellipsoid, 6378137.0 meters, for the radius. This means that the sphere is much larger than the actual size of the Earth. There are many ways to calculate a sphere that's closer in size and/or shape to the Earth, but the radius value will be closer to 6371000 km.

There are ways to make a 'conformal' sphere from an ellipsoid (and some adjustments to the geodetic latitudes and longitudes), but that's not being done. Thus, the argument runs that the data in EPSG:3857 cannot be considered conformal.

• If I had to conclude from your assertion, EPSG 3857 not conformal and Google was the first to use this exact projection. Can I have exact sources? I wasn't able to be sure because not enough validated sources and your answer is not enough precise for this part. Commented Oct 18, 2013 at 10:00
• I don't understand what you want when you say exact sources. As far as I know, there are no academically published papers. Commented Oct 18, 2013 at 14:42
• I didn't expect official papers but I wanted more than one reference outside your feedback and the PDF paper link I provided. Reason: wikihow.com/Evaluate-the-Credibility-of-a-Source But you seem to be a credible source ;) when reviewing your signature. Thanks Commented Oct 18, 2013 at 17:20

Mercator projection from the sphere was developed by Mercator, Wright and others, in the period between 1569 and 1640, when logarithms were fully discovered and understood.

When, years later, the ellipsoidal shape of the earth was proven, other scientists (Murdock 1741, Lambert 1772) developed the ellipsoidal formulas. They are called direct Mercator formulas for the ellipsoid, but are not a Mercator's work, since Mercator died in 1594. The same thing can be said for some other projection invented later, for example transverse mercator projection, and first of all, Web Mercator projection.

Web Mercator projection was created by Google in 2005 (the number is acronym 900913=GOOGLE), with the specific porpouse of projecting their maps in a simple way.

Since Web Mercator goal was Web visualization and not accurate surveying computations, the loss of conformality implied when using directly the simpler and faster spherical formulas (developed to project from the sphere) to project from the ellipsoid WGS84 instead, didn't worry his creators.

I can confirm that Web Mercator is not conformal, because I am doing a master degree thesis on the subject, and I've checked all formulas, including the scale factor one, that can be found in the EPSG's Geomatics Guidance note.

Being the scale factor at a given point, not a constant, but a function of azimuth (direction), the projection is not conformal by definition, technically speaking. But it is almost conformal! An infinitesimal circle drowed on the ellipsoid surface, would become an ellipse on the map, but an ellipse with a very small flattening, and really similiar to a circle. For this reason deformation of shape is very small too when looking at small areas, and is not visually notable; a square building is projected as a (almost) square building.

The spherical Mercator projection is a conformal projection from the sphere to the plane but it is not a conformal projection from an (non-spherical) ellipsoid to the plane. However, the errors are moderate for an ellipsoid similar to our earth.

The elliptic Mercator projection is a conformal projection from the ellipsoid to the plane but it is not a conformal projection from the geoid to the plane. However, the errors are very small for a good fitting ellipsoid.