Measuring areas over the web - watch your projections!

Most maps you see served over the Internet, whether on Google Maps, Bing Maps, or from ESRI's ArcGIS Online, are provided in the "Web Mercator" map projection.   Map projections are important because the allow us to represent the round world on a flat map, whether that map is printed on a piece of paper or glowing on a computer screen.  The Mercator projection, developed by Gerardus Mercator (also known as Gerhard Kramer) in 1569, is a cylindrical projection.  Mercator's idea was to wrap the world (or at least a sphere representing the world) mathematically with a cylinder, and then "project" features from the round world onto the cylinder.  Uncurl the cylinder, and voila! a flat map on a plane!  (Imagine that the world is actually a round balloon.  Blow air into the balloon, the sphere expands, and as it touches the confining cylinder, it printing the pattern of land and water onto the plane.)  Mercator's genius was to imagine all this in the mind's eye, and then to develop the mathematics to describe it, which then created problems for mathematicians for several centuries.

Although computers handle most of the mathematics nowadays, we still need to be aware of the significance of map projections, including for our Mannahatta2409.org application.  In Mannahatta2409.org, every vision created by a user, we calculate the area:  the area of ecosystems, the area of floor space, and thus the area of residences, offices, transportation corridors, etc.  Area is a primary driver of all the other models of carbon, water, biodiversity, etc.

The world in Mercator projection, borrowed from Wikipedia.

The problem with Web Mercator, or indeed any may projection, is that they are subject to distortions.  In general the distortions increase from the place where the cylinder (or other representation of  a plane) touches the world.  In the case of Web Mercator, the place of minimal distortion is at the Equator.  And the Equator is a long way from New York City! 

As a result, we have to adjust the Web Mercator areas to the approximate equivalent in a projection used locally (like the Universal Transverse Mercator projection, zone 18).  The translation factor is about 0.57, so an area that reads as 100 square meters in Web Mercator is actually closer to 57 square meters when measured in New York City.  That must be why the apartments all seem so small!


To read more about the Mercator Project, read a nice page by Robert Israel at the University of British Columbia and a useful summary from ESRI.