Mercator Projections

Figure 1. The Mercator Projection is conformal and shows loxodromes as straight lines.

The Mercator projection is one of the oldest, most influential, and most misunderstood projections of all time. This projection is so steeped in history that it is impossible to appreciate the Mercator projection without knowing something about its history.

Figure 2. Gerardus Mercator (1512 - 1594).

The Mercator projection was developed in 1569 by one of the most famous cartographers of all time, Gerardus Mercator (that's a 16^th century engraving of him in Figure 2). Mercator (whose birth name was Gerhard Kramer; in his day, if you wanted to present yourself as an educated person, you latinized your name; hence Gerhard Kramer became Gerardus Mercator) was born in Rupelmonde, Germany on March 5, 1512 and died in Duisburg, Germany on December 2, 1594. His works revolutionized ocean navigation. Prior to Mercator's 1585 publication of an atlas covering just about all of the known world (indeed, it was with this work that Mercator coined the word atlas to describe a collection of maps; the word did not exist prior to that time), ocean navigation was largely hit-or-miss. Sea captains navigated from point to point by either following landmarks visible on shore or by following incredibly vague verbal instructions (e.g., "sail into the summer wind for four hours to clear the rocks at the harbor's entrance, then turn to starboard and sail broad to the wind for a week or so to reach your destination"). This changed with the introduction of maps based on Mercator's projection. For the first time, sea captains had maps showing loxodromes as straight lines. All that a captain had to do was draw a line connecting his starting and ending points on a Mercator chart, measure the bearing of this line, and then sail that bearing until he reached his destination.

Because of its enormous influence, the Mercator projection became the de facto standard world map for centuries. Unfortunately, the Mercator projection suffers from compression to the extreme. South America is over eight times as large as Greenland, but the Mercator projection shown in Figure 1 shows Greenland as being larger than South America! No other projection in widespread use today suffers from compression to this extent. This excessive amount of compression makes the Mercator projection unsuitable for many uses, but that has not stopped many uninformed map users from applying the Mercator projection quite inappropriately.

• Form: Mercator projections are cylindrical.

• Case: The classic Mercator projection is tangent, but since about 1950 it has become accepted to lump a secant version of the same projection under the Mercator label as well.

• Aspect: The Mercator projection uses a normal aspect.

• Variation Within Mercator Projections: Mercator projections differ in the location of their line(s) of tangency. In the classic tangent case, a Mercator projection has one line of tangency, and this line falls along the equator. In its secant version, the Mercator projection has two lines of tangency, both following along lines of latitude, and both equally spaced on either side of the equator.

• Distortions
  • Shearing: The Mercator projection is conformal; small shapes are accurately represented.
  • Tearing: The Mercator projection produces maps shaped like simple rectangles; tearing occurs along the rectangle's outer edge. The Mercator projection can cover almost, but not quite, the entire Earth: It is impossible to map the poles using a Mercator projection. The map in Figure 1 extends from 85°N to 85°S latitude.
  • Compression: The compression in a Mercator projection can be enormous. There is no compression present along the map's line(s) of tangency, but compression increases extremely rapidly as you move away from these line(s) of tangency. The result of this rapid increase is that the Mercator projection can suffer from more compression than any other projection in widespread use today.
  • Conformality: The Mercator projection is conformal; small shapes are accurately represented.
  • Equidistance: The Mercator projection is not equidistant; there is no point from which all distances are shown accurately. The only places on the projection where true distances are accurately shown are along the projection's line(s) of tangency.
  • Azimuthality: The Mercator projection's greatest strength is its ability to show the loxodrome between any two points as a straight line. This implies that, in a fashion, the Mercator projection might be considered super-azimuthal, because instead of just showing accurate directions from a single central point to all other points, the Mercator projection shows accurate directions from all points to all other points! However, the true definition of azimuthality is a map that accurately shows the directions of the great circle routes between points, not the loxodrome routes between points. Under this more accurate definition of azimuthality, the Mercator projection is not azimuthal at all.
  
  
• Uses: If its extent is limited to a very small region around the map's line(s) of tangency (i.e., the region where the projection's compression is not extreme), the Mercator projection can produce a functional conformal map. However, given the severity of the Mercator projection's conformality problems, it is not a good choice for any sort of mapping project that requires a map that extends any great distance beyond the projection's line(s) of tangency. The only exception to this limited recommendation involves the ability of the Mercator projection to plot loxodromes as straight lines, which extends to all points on a Mercator map, regardless of distance from the line(s) of tangency. This still makes the Mercator projection a valuable aid to navigation.