Map Projections

Map projections are important for many reasons. One of the main reasons is that map projections are necessary for creating maps. They take images from the 3D geoids of Earth and project them onto a 2D plane, thus making flat maps which are easier to carry, use, and digitize for GIS purposes. It is important that there is not only one type of map projection, but instead a variety of map projections since a different projection will be required depending on the purpose of the map. The maps purpose will also help decide what characteristics need to be preserved and what characteristics can be distorted, thus helping to find the proper projection. For example, for navigational purposes, one would want to use a conformal projection because it preserves direction, and for distance measuring, one would most likely want to use an equi-distant projection due to its equally spaced standard lines. For certain maps, however, it does not matter which projection you use especially if the purpose of the map is for thematic or illustrative purposes. One may also pick a different map projection based on what part of the world they are looking at, for different projections preserve and distort different parts of the globe.

The Mercator projection is a conformal projection that preserves direction and shape but varies in distance and area. In this projection, the N/S run of the map is longer than the E/W portion, thus possibly leading to more distortion in distance. When looking at the Mercator projection above, I believe this may be one of the reasons that the distance between Washington D.C. and Kabul is much larger than the true distance (10,098.61 miles [Mercator] v. 7,000 miles [True Distance]). Another reason that the projected distance on the Mercator map may be so different from the True Distance is that Mercator projections are many times used to examine Polar Regions and the cities under study in this map is located outside this region, thus causing a distortion in the distance. The Mercator projection does preserve distance, however, so this map could be very useful to a sailor or pilot for navigational purposes between the two cities. The other conformal map shown above is the Gall Stereographic projection. This projection is azimuthal, preserves angles and direction, while distorting area, object size and distance. Looking at the examples above, I thought that it was interesting that even though the Gall Stereographic projection distorts distance, the projected distance on the map was still very close to the True Distance (7,175.43 miles [Gall Stereographic] v. 7,000 miles [True Distance]). I believe this may be due to the lack of large distortions found at the poles, causing the continents to be properly spaced from one another and not squished together like in the Mercator Projection.

Equal Area maps preserve the area of the projected map surface. The Bonne projection preserves size, and has evenly spaced parallels that are true to scale along the concentric arcs. This projection also lacks distortion along the central meridians and parallel. I believe the Bonne projection’s distance (6,716.91 miles) is so closely related to the True Distance (7,000 miles) between the two cities due to the projections ability to preserve size. As seen in the conformal projections, the size of objects on the map greatly affects the spacing of the continents on the projections by causing them to converge or diverge. With the preserved size, however, all objects on the map are true to scale, thus allow for a more accurate measurement between the two cities. The Sinusoidal Projection is also an equal area projection. It is actually a special case Bonne projection. The Sinusoidal Projection preserves distances along horizontal lines, and all of its parallels are standard lines. This projection becomes distorted toward the poles and is slightly distorted along the equator. I believe the distance of the Sinusoidal Projection is relatively close to the True Distance between the two cities (8,100 miles [Sinusoidal] v. 7,000 miles [True Distance] for a couple of reasons. One of the main reasons is that both the N/S scale and the E/W scale are equal, therefore making distances more accurate. Also, in a Sinusoidal Projection, the true distance between two points on the same meridian corresponds to different points on the map between two parallels. This creates a larger projected distance between the two points on the map, hence explaining the above results.

Equidistant Projections preserve the distance between points on a projected surface. In the above examples, this is best seen in the Equidistant Conic projection, where due to its ability to preserve distance, out of all the other maps, this map’s projected distance is the most closely related to the True Distance on the ground (6,728.47 miles [Equidistant Conic] v. 7,000 miles [True Distance]). The Plate Carree equidistant projection, however, is a completely different story. Even though it is supposed to be an equidistant projection, the Plate Carree’s projected distance is much larger than the True Distance, coming in at 10,247.44 miles instead of around 7,000 miles (True Distance). I believe this may have occurred for a few reasons. First, the Plate Carree does not preserve shape or size. This may have caused the shapes of the continents to stretch out when projected, thus increasing the distance between the two cities. The Plate Carree’s inability to preserve size and shape are one of the main reasons it cannot be used for navigational purposes. Second, the Plate Carree also does not deal with complex relations between points on the map and their relation to points on the Earth, but rather uses simple relations which may make the distance less accurate.