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Why Mercator?

Here is a Mercator projection of the world:

Source: Wikipedia

A quick glance at an actual globe should convince you that this map deserves its poor reputation: Europe, the United States and Canada are way too big, and Antarctica should certainly not be bigger than South America and Africa combined. Check out this Mercator puzzle and see for yourself how each country’s size changes as you move it on the map. So, how comes this map became so widespread? And why was it even invented in the first place? The key to the answer lies on the original map designed by the Flemish geographer Gerardus Mercator: the map, which was published in 1569, is entitled "Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata" (New and augmented depiction of Earth properly adjusted for sailing). Thus, the map was designed as a global sea chart, not as an accurate depiction of Earth’s surface. What makes it so well suited for sailing? And if it is just a sea chart, why did Google’s employees choose this specific projection for Maps?

Mercator’s original map (1569). Source: Wikipedia

Drawing a map of the whole world means coming up with a method for mapping each point of the globe onto some point of the plane. Such a method is called a projection. Different projections yield different world maps, here are some examples:

Mollweide projection. Source
Goode projection. Source
Robinson projection. Source
Stereographic projection. Source
Lambert conformal conic projection. Source
Orthographic projection. Source

All these maps display a distorted surface: they have to! Admittedly, a small surface, such as a city, can be accurately mapped onto a flat surface: even though Earth is curved, it appears almost flat on large scales (disregarding terrain). However, on a global scales, distortions are inevitable. Indeed, on a sphere, one can draw a triangle whose angles add up to more than 180°. Such a shape cannot exist on a flat surface, thus any projection is bound to distort it: either its sides appear curved (so the image is not a triangle anymore), or its angles appear smaller (so they do add up to 180°), or both.

The angles add up to 230°. On a large scale, no distortions occur. Source

Therefore, any world map must give a distorted view of the world. Hence, choosing a projection is a matter of choosing which kinds of distortions are acceptable, and which ones should be limited. This choice depends on how the map is going to be used.

For example instance, one might expect the projection to preserve relative areas, as do the Mollweide and Goode projections: Saudi Arabia does appear roughly the same size as Greenland, instead of several times smaller, as on the Mercator projection.

Consider a world map obtained through any projection. Now zoom in on a particular city. You should obtain a more or less usable map of the city (assuming the projection is “smooth” enough). However, depending on the projection you chose, the map could be distorted: for example, the streets of Manhattan might meet not at right angles, but instead at 30°, 45°, or any other value (they would, however, all meet at the same angle).

If such distortions do not occur anywhere on the map, the projection is said to be conformal. Examples of conformal projections include the stereographic projection, the Lambert conformal conic projection and the Mercator projection. To sum up, a projection is conformal if it represents Earth’s surface faithfully on large scales.

Once again, consider a world map obtained through any projection and zoom in on a particular city in order to obtain a local map. North need not be at the top: it can be in any direction, depending both on the projection and on where the city is located.

In fact, very few projections always put north at the top. Among them, only the Mercator projection is conformal.

Because of these two properties, if a ship keeps a constant bearing relative to north (for example, 30° towards east), its course will appear on the Mercator map as a straight line in the same direction. Thus, in order to know in which direction to sail, a navigator can simply draw a straight line on the map between the ship’s position and her destination and measure the line’s direction with a protractor. This gives a course with constant heading, which makes the Mercator projection a useful tool when navigating with a compass. Indeed, in order to follow a course with non constant heading, a navigator would need to know their position at all times and to be constantly computing the heading they need to follow. Nowadays, GPS navigation devices can do both, and indeed they have made Mercator maps obsolete.

For short trips, and sacrificing accuracy, one can use any conformal projection in the way described above (not just the Mercator projection). However, the projection has to be conformal: conformity is actually so important that navigators do not use any non-conformal map other than the gnomonic projection, whose use is explained below.

Gnomonic projection. Source

The Mercator projection allows navigators to find the route with constant heading between two points on the globe. But this is by no means the shortest route, especially so for long trips and at high latitudes. The shortest route between two points is an arc of great circle (that is, a circle whose center is the center of Earth). However, when navigating with a compass, keeping a constant bearing is easier. Therefore, for long voyages, it is common practice to draw the ideal, shortest route on a map, set waypoint on this route and then navigate with a constant bearing between consecutive waypoints.

Route with constant bearing β. Source

However, drawing the shortest route on a Mercator map is no easy task. This is where the gnomonic projection comes into play. Indeed, on this map, the shortest route between any two points always appears as a straight line. Unfortunately, the gnomonic projection is not conformal, so it cannot be used directly for navigation. The navigator must draw the shortest route and the waypoints on the gnomonic map and carry the waypoints on the Mercator map. Again, GPS navigation systems have made this method obsolete.

This covers the use of the Mercator projection as a sea chart. But what about Google Maps? A major asset of this application is that zooming in on any city will give you a useable map. This is only possible because the projection is conformal and (to a lesser extent) because the north is always at the top of the screen. As mentioned above, only the Mercator projection meets these two criteria, which is why it has been chosen, at the cost of a distorted zoomed-out view of the world1.

In fact, the following comment was published on april 8th 2009 by Joel Headley, manager of the customer support team at Google Maps: “ […] Maps uses Mercator because it preserves angles. The first launch of Maps actually did not use Mercator, and streets in high latitude places like Stockholm did not meet at right angles on the map the way they do in reality. While this distorts a 'zoomed-out view' of the map, it allows close-ups (street level) to appear more like reality. The majority of our users are looking down at the street level for businesses, directions, etc... so we're sticking with this projection for now. […] ”2.

Notes


  1. In fact, it might be possible to use a better-looking projection for the zoomed-out view and progressively switch to Mercator as the user zooms in. However, the map would rotate and get distorted (or straightened) every time the user zooms in or out. 

  2. http://productforums.google.com/forum/#!topic/maps/A2ygEJ5eG-o/discussion