Lab 5

Bonne Projection - Equal Area Map

Cylindrical Equal Area Projection

Equidistant Cylindrical Projection

Azimuthal Equidistant Projection

Stereographic Conformal Projection

Eckert I Conformal Projection

Distances between Washington and Kabul, using the various map projections:

Projection	Distance  between Washington and Kabul (in miles)
Bonne (Equal Area)	6,730.70
Cylindrical Equal Area	10,108.05
Equidistant Cylindrical	5,061.58
Azimuthal Equidistant	8,341.41
Stereographic (Conformal)	9,878.03
Eckert I (Conformal)	7,410.47

 I chose these map projections because they seemed to be extremely interesting. Even among the same type of projection, there is a great difference between the maps: for example, the Bonne projection and the Cylindrical Equal Area projection are both equal area projections, but look extremely different and the distances do not coincide at all. I chose the Equidistant Cylindrical so I could compare it to the Cylindrical Equal Area, since they are both cylindrical projections. On the other hand, the Azimuthal equidistant contrasts with the equidistant cylindrical, but it looks similar to the stereographic conformal. The Eckert I looks interesting just by itself, so I included it to find out how it would measure against the other maps.

We can see that there are great differences between the three types of projections: the equal area projections preserve the areas in the map, but not distances. For example, notice how in the Bonne projection, the longitudinal lines get closer and closer together as they move away from the Prime Meridian; similarly, in the Cylindrical equal area projection, the parallels get closer and closer together as they get farther away from the Equator. This occurs so as to not overstretch the area, maintaining it as close as possible to the real one. The equidistant projections, on the other hand, preserve distances on the maps, but not angles between lines nor areas. This can be seen through the Cylindrical equidistant projection and the Azimuthal equidistant projections: in the former, we see that the distance between the parallels are constant, and this occurs with the lines of longitude as well; in the latter, we see that the intersection of the lines of longitude with the Equator occur at constant intervals, and parallels intersect the Prime Meridian at constant intervals as well, so distances are preserved. Lastly, conformal projections preserve angles between every line on the map, but it does not preserve distances nor areas. In the stereographic projection, we can clearly see that every interception occurs at right angles, and this occurs similarly in the Eckert I projection, except that distortions occur at the Equator.

So how do projections within these types differ from each other? Within the equal area projections, the Bonne and the Cylindrical equal area are significantly different: the Bonne seems to preserve areas from the center outward, with outliers (such as Australasia) being disproportionately large or small; the cylindrical projection appears to maintain areas more accurate for the shapes in the middle band, whereas areas in the utmost top or bottom bands (like Antarctica) are disproportionate in relation to other areas at the center. Aside from this fact, the cylindrical projection yields a rectangular map, precisely because it is cylindrical, so the longitudinal lines are equally spaces. For the equidistant projections, we see that the cylindrical equidistant (which is in fact quite different from the cylindrical equal area), preserves distances alone, since lines are equally spaced throughout the map. However, this leads to distortions in shapes and sizes. With the Azimuthal equidistant projection it is harder to tell whether lines are equidistant, but one can easily see this is true because lines intersect at regular intervals, similarly to the cylindrical equidistant projection. However, there are significant differences between the two: the cylindrical is a rectangular map, and lines are straight; in the azimuthal the map is circular, and the lines (except for the standard lines) are not straight, but rather circular and elliptical. This causes a difference which is similar to that of the Bonne/Cylindrical equal area: distances are preserved closer to the center in the azimuthal, and as one steers away from the center, we begin to see distortions. The stereographic (conformal) projection and the Eckert I projection are very different from each other. Both retain angles, yet the stereographic projection is similar to the azimuthal in the sense that lines are not straight (but neither are they equidistant in this case), and in the Eckert I they are. It also seems the stereographic has a much higher distortion of shapes that do not lie near the center (such as Australasia), and the Eckert I represents this more accurately, as well as the proportions of bodies of land to bodies of water.

Summing up, these projections yield extremely different maps, which we saw through the differences above. Yet, they also yield different distances between the same points. In our case, the discrepancies between distances of Washington - Kabul are seen in the table above. Taking into consideration that the real distance is about 6940 miles, we can see that this puts the Bonne as the most accurate concerning this information, but also tells us something about the other maps: the circular maps overshot on the distance, because distances flow from the center outward; the cylindrical maps are not accurate because the scale between latitudes is similar, and since longitudinal lines are equally spaced, this creates a distortion in distances. The Eckert I is close in calculating the distance, but sacrifices some of the accuracy by accurately portraying shapes and arrangements - which leads me to saying "you win some, you lose some". This tells us that we have to take into mind our purpose when choosing which map projection to opt for: are we looking for accurate distances? or perhaps accurate shapes and arrangements of the bodies of land and water? Are we more concerned with the fact that areas are portrayed accurately? All of these factors should be taken into account when choosing a projection, because most of the time, improving one will sacrifice the other, as it is impossible for all of these factors to remain accurate when projecting from a 3-dimensional spheroid to a flat surface.