North Most: 8,310 miles
South Most: 8,321 miles:
GCS_WGS_1984 has no distortion because everything is based on longitude and latitude: The distance between Washington, D.C. and Kabul was found to be 6,935 miles.
Conformal
Mercator projection: The distance between Washington, D.C. and Kabul was found to be 10,164 miles.
Gall Stereographic: The distance between Washington, D.C. and Kabul was found to be 7,166 miles.
Equidistant
Equidistant Conic: The distance between Washington, D.C. and Kabul was found to be 6,975 miles.
Equidistant Cylindrical: The distance between Washington, D.C. and Kabul was found to be 5,074 miles.
Equal Area
Bonne: The distance between Washington, D.C. and Kabul was found to be 6,706 miles.
Cylindrical Equal Area: The distance between Washington, D.C. and Kabul was found to be 10,695 miles.
The total layout
When a map of our round Earth is required, the most accurate representation is a three dimensional globe. However, a globe doesn’t always provide all the functionality needed in a map. It is therefore useful to be able to translate, or project, the Earth onto a flat surface like paper or digitally on a computer screen. Map projections are used to project the round Earth onto a flat surface. There are a variety of map projection types to choose from and which you choose depends on what parameters need to be the most accurate or to minimize distortion in a particular way. Examples of some parameters are distance, direction, shape, and area ratio. Three types of map projections will be discussed in the following paragraphs; these include Conformal, Equidistant, and Equal area map projections
A conformal projection maintains angular relationships and accurate shapes over small areas. It is used where angular relationships are important like with navigational or meteorological charts. The conformal maps that I chose to show are the Mercator and the Gall stereographic projections.. The sizes of areas are distorted on conformal maps even though shapes of small areas are shown correctly. A Mercator projection has straight rhumb lines, lines crossing all meridians of longitude at the same angle, which enables one to easily determine compass courses for marine navigation. Gall's stereographic cylindrical projection results from projecting the earth's surface from the equator onto a secant cylinder intersected by the globe at 45 degrees north and 45 degrees south. This projection moderately distorts distance, shape, direction, and area.
An equal area or equivalent projection maintains accurate relative sizes and is used where showing area accurately is important. Shapes are more or less distorted on every equal-area map. The equal area projections I chose to show are the Bonne and Cylindrical Equal Area Projections. The Bonne projection, shaped like a heart, is a pseudo-conical equal-area map projection that applies the true scale along the parallels of the Sinusoidal to the parallels of the Simple conic. It is used in atlases for equal-area maps.
An equidistant projection maintains accurate distances from the center of the projection or along given lines. It is used for radio and seismic mapping and for navigation. The equidistant map projections I chose to create are the Equidistant Cylindrical and Equidistant Conic projection. On an equidistant conic map, distances are true only along all meridians and along one or two standard parallels. Directions, shapes and areas are reasonably accurate, but distortion increases away from standard parallels.
Now that the different map projections have been discussed, without bias, their significance can now be fully explained. As has been explained in the above paragraphs every map projection has its own distortions. It is up to the creator and/or user of the map to decide which projection is best suited for a specific application. The example given in class was that if one wants to launch a missile from a given location, one should use an equidistant map with its center located at the launch site. This is because equidistant maps only preserve distance from a specific point to any point on the map, and not between two arbitrarily chosen points. If one were to choose a different type of map projection they would almost certainly not hit their target.
When studying the distance results one must not take the distances at face value. This is because if one were to use a map based on these result, they would be very disappointed. Based on the results the conic equidistant is the “best” at preserving the distance between it is the closest to the actual distance as was found from GCS_WGS_1984. However, this is very misleading because this map is not supposed to preserve the distance between these two locations because it is not centered about either one. Also the Bonne and Gall stereographic projections are fairly close to the actual distance, however, because of the distortions present they are still slightly off of the actual distance.
Also when looking at the maps one has to realize that many of them do not maintain correct area ratios. One of the worst is the Mercator projection. It distorts the poles so much that if someone who had never seen a map was told that this was what the world looked like they would get a very incorrect representation. So as has been said before, it is necessary to use these map projections as they are meant to be used.
In conclusion, there are an infinite number map projections that can be created and each comes with its own distortions. Map projections can be a very powerful tool but it is up to the user to choose the correct projection for their specific task. One may desire to use the map for navigation, distance, or representation. If one desired to it for navigation, or for any other purpose in which it was necessary to maintain the correct angular relationships then they would choose a conformal map projection. This map type is not concerned with preserving the distance or area. Two examples of this are the Mercator and Gall stereographic projections. If one was more concerned with preserving the distance from a point one should choose to use the equidistant map projection. The examples presented in this “report” are the Equidistant Conic, and Equidistant Cylindrical. In these maps it is not important to preserve the area or angular relationship. Finally if one wishes to keep the area ratio the same one should use an equal area map projection. This allows one to maintain proportionality and create maps that correctly portray the world. However, these maps should not be used for navigation or measuring purposes as they do not preserve angular or spatial relations. The examples presented are the Bonne and Cylindrical equal area map projections.
http://www.progonos.com/furuti/MapProj/Dither/CartProp/cartProp.html
http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html
http://www.nationalatlas.gov/articles/mapping/a_projections.html
http://www.quadibloc.com/maps/mps0402.htm (Bonne)
http://www.quadibloc.com/maps/mcy0102.htm (Gall’s Stereographic)
http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html
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