ifferent map projections are suited to different purposes depending on how they distort properties of the real world such as size and shape. Here I use the same global population density map to illustrate one variation of each of the three main classes of projection (conic,cylindrical, and azimuthal).
As its name suggests, this is a conic projection, which means it does a poor job of preserving area, shape, distance and direction except along standard parallels. The projection can also display only a single hemisphere. The 'equidistant' in the name refers to the fact that this projection preserves distance to a constant scale along any given meridian, but the scale changes from meridian to meridian. These properties make Equidistant Conic ill suited for world maps but well suited to national or regional maps, especially at mid-latitudes with east-west extents. For this particular map, I set a single standard parallel at 60° N, along which there is no distortion. Transparent ellipses on the map, called Tissot's Indicatrices, help visualize how distortion is maximized toward the edges of the map. Note that if I had set two standard parallels (e.g. at 30° and 60°), distortion would be minimized but not absent between these lines.
This once common cylindrical projection is unpopular for world maps due to its distortion of area and distance, each of which become exaggerated toward the poles creating a false impression of the Earth. Where distortion is minimized closer to the equator Mercator maps do remain useful, especially for small areas and for navigation. Any line drawn on a Mercator map will will preserve direction, thus providing a true compass bearing. Tissot's Indicatrices also show the projection preserves local shapes quite well even though scale changes dramatically north and south of the mid-latitudes. Mercator is currently gaining popularity again due to its application to web mapping (Web Mercator projection). Nevertheless, like cylindrically projected maps in general, Mercator maps are not well suited for the purpose of displaying global population densities, particularly due to their misrepresentation of area.
This is actually not a true azimuthal (planar) projection, but is modified from the azimuthal form. The Winkel Tripel is a compromise projection used most commonly by the National Geographic Society. No part of a Winkel Tripel map is distortion-free for any single property, but it minimizes the combined distortion of area, shape and distance. Minimum distortion occurs at the centre of the map, maximum distortion occurs at the edges. Of the three projections shown here, the Winkel Tripel is the most appropriate for displaying global population densities because it does a better job of preserving area. Area is the most important property to preserve because population density is calculated based on number of people per unit of area (in this case square kilometers). Equal-area projections such as the Hammer-Aitoff would do an even better job of allowing viewers to compare results with an accurate understanding of each country's areal extent, but it distorts shape dramatically toward the poles and I prefer the overall look of the Winkel Tripel.