Different map projections can make a big difference. This project is designed to illustrate examples of 3 different kinds of map projection: conformal, equal-area and equidistant projections.
According to GCS WGS 1984, which is the current reference system being used by GPS, the distance between Washington D.C. and Kabul, Afghanistan is 6,934.478105 miles.
Notice the scale bars in some maps are different from others due to clarity concerns.
a) Equal-area projections
Mollweide Projection
“The Mollweide projection is a world map projection that minimizes area distortion while sacrificing the accuracy of shape and angle. It is a representation of the world map on an ellipse with a 2:1 ratio. Although it is not widely used today, the Mollweide projection has been influential in the development of other projections.” (Mollweide Projection page, wiki.gis.com) The distance measured on Mollweide projection between Washington D.C. and Kabul is 7,925.557346 miles.
Sinusoidal Projection
“The Sinusoidal projection is an equal-area world map projection that has straight, horizontal parallels spaced equally at their true distances. The central meridian is straight, and the others are curves that derive from a true division of each parallel.”(Sinusoidal Projection page, wiki.gis.com) The distance measured on Sinusoidal projection between Washington D.C. and Kabul is 8,098.076483 miles.
b) Equidistant projections
Azimuthal Equidistant Projection
“Azimuthal equidistant projection is a map projection in which all distances measured from the center of the map along any longitudinal line are accurate, however, distances and directions to all places are true only from the center point of projection. Distance measurements are accurate between points along straight lines through the center. All other distances are distorted and thus incorrect. Distortion of areas and shapes increases with distance from the center point.”(Azimuthal Equidistant page, wiki.gis.com) The distance measured on Azimuthal equidistant projection between Washington D.C. and Kabul is 8,341.411788 miles.
Two-point Equidistant Projection
“The two-point equidistant projection is a map projection first described by Hans Maurer in 1919. Distances from any point on the map to two control points scale to the geodesic distances of the same points on the sphere. The projection is commonly used in National Geographic Society atlases for maps of Asia, and it sometimes appears in diagrams of air routes.”(Two-point Equidistant Projection page, Wikipedia) The distance measured on Azimuthal equidistant projection between Washington D.C. and Kabul is 6,648.754559 miles.
c) Conformal Projections
Stereographic Projection
“In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point — the projection point. It is conformal, meaning that it preserves angles. It is neither an isometry nor area-preserving: that is, it preserves neither distances nor the areas of figures.” (Stereographic Projection page, wiki.gis.com) The distance measured on Stereographic projection between Washington D.C. and Kabul is 9,878.038997 miles.
Hotine Projection
“The Hotine (Oblique Mercator) world map projection is a cylindrical, conformal map projection.” (Hotine Projection page, wiki.gis.com) The distance measured on Hotine projection between Washington D.C. and Kabul is 9,628.552081 miles.
Different kinds of map projections preserve different properties. For instance, conformal projections preserve angles between two lines; equidistant projections preserve ratio of two distances; equal-area projections preserve ratio of two areas.
Map projections must have some distortion. For example, in two-point equidistant projection, the South Pole is bigger than Africa; in Hotine projection, the area of the US is much larger than that of Asia!
According to the properties of their projection, maps projected differently can be used in various circumstances. For example, Sinusoidal equal-area projection is frequently used in atlases to show distribution patterns and often used by the USGS to show prospective hydrocarbon provinces and sedimentary basins of the world; Stereographic projection is by the USGS for maps of Antarctica and American Geographical Society for Arctic and Antarctic maps; Azimuthal equidistant projection is useful for showing airline distances from center point of projection and useful for seismic and radio work.(Map Projections, USGS, http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html).
On the contrary, maps projected differently may be used by people such as businessmen and politicians to give the public a biased view of the world. For instance, politicians may have their maps projected to show the degree of poverty. Some maps would overestimate and some would underestimate the situation. In this case the public are not aware of the truth.
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