Lab - Week 6

Mercator (Conformal)
Distance measured between Washington DC and Kabul: 10,115 mi
Gall Stereographic (Conformal)
Distance measured between Washington DC and Kabul: 7,164 mi
Sinusoidal (Equidistant)
Distance measured between Washington DC and Kabul: 8,101 mi

Equidistant Conic (Equidistant)
Distance measured between Washington DC and Kabul: 6,971 mi

Bonne (Equal-area)
Distance measured between Washington DC and Kabul: 6,753 mi
Mollweide (Equal-area)
Distance measured between Washington DC and Kabul: 7,895 mi


Because a spherical object such as the Earth can not be flattened onto a plane, map projections are essential. Without map projections we would be limited to only spherical models of the Earth, which, while still useful, lack the flexibility and portability that 2D maps offer. 2D maps can be printed into books, displayed on computer screens, or hung on walls. 2D maps also can inherently display a greater amount of the Earth's surface simultaneously than globes, and consequently are useful for displaying a large amount of geographical data at once (for example, maps displaying worldwide GDP or quality of life.) Thus there is a desire to create accurate map projections.

However, map projections always include some element of distortion because the Earth is not a developable surface. As a result, a multitude of map projections exist, each designed to preserve a certain aspect of the Earth's geometry. Conformal map projections, such as the Mercator and Gall Stereographic projections above, preserve angles, and thus are useful for calculating bearings in navigation. However, conformal projections fail to preserve areas or distances, often with enormous size distortions. In the Mercator projection, for example, the size of areas far from the equator is greatly exaggerated: Greenland appears to be almost as large as the entire continent of Africa, and Antarctica dwarfs every other continent in size.

Equidistant map projections, as their name implies, preserve distances along certain lines or from certain points (since preserving distances from every point to every other point is impossible.) Equidistant map projections are obviously optimal for measuring distances or calculating travel times, but one must be aware of which points or lines conserve actually distance. Measuring the distance from Washington DC to Kabul, Afghanistan using the Sinusoidal projection gave a figure more than 1,000 miles greater than with the Equidistant Conic projection; clearly distance was not preserved along this path.

Equal-area map projections, such as the Bonne or Mollweide projections above, preserve areas. Area distortion is one of the most immediately obvious forms of distortion, and thus equal-area projections are often more visually pleasing than other types of map projections. These projections are useful in thematic maps, maps which associate certain attributes with geographic areas - such as maps of world religions or chloropleth maps like population density. Maintaining area is also useful in statistical analysis of the globe: observing geographic distributions of various phenomena.