Lab 5

Equidistant Map Projections:

Equidistant Conic Distance from Washington DC to Kabul = 6,964 miles
Sinusoidal (World) Distance from Washington DC to Kabul = 8,111 miles

Equal Area Map Projections:

Bonne Distance from Washington DC to Kabul = 7,053 miles
Goode Homolosine (Land) Distance from Washington DC to Kabul = 10,025 miles

Conformal Map Projections:

Mercator (World) Distance from Washington DC to Kabul = 10,204 miles
North Pole Stereographic Distance from Washington DC to Kabul = 7,605 miles

Write 4 paragraphs about map projections be sure to reference your 6 maps:

In its most simple terms, a map projection is the representation of a 3-dimensional earth on a 2-dimensional surface. In order to construct a map projection it is necessary to select a datum to mathematically transform the earth into two-dimensions. When constructing a map projection, you have several developable surfaces to make use of: planes, cylinders, and cones. The selection of this developable surface and its center impact the resulting distortions. It is not possible to create a map projection without distorting certain map elements. Thus, map projections are categorized by the qualities in which they preserve. Conformal map projections preserve direction, equidistant map projections preserve distance, and equal area map projections preserve area.

The equidistant map projections map projections created in this lab were equidistant conic and sinusoidal. equidistant conic (or simple conic) map projection shown above, is neither equal-area nor conformal. Its distances are only preserved along the meridians and one or two standard parallels. As seen, the conic projection is unwrapped from a cone. Equidistant conic map projections are typically used in atlases to highlight regions around the middle latitudes. The distance from Washington D.C. to Kabul is 6,964 miles with the equidistant map projection compared with an actual distance of 6,956 miles. Since Washington D.C. and Kabul lie near the same latitude on the map, their distance is preserved without much distortion. In contrast, the sinusoidal (world) map projection seen above has a distance from Washington D.C. to Kabul of 8,111 miles. A sinusoidal projection is both an equal area and equidistant map projection. The distances between two points along the same meridian is preserved with this map projection. Thus, a sinusoidal map projection is effective for finding distances along the same meridian, but is problematic for measuring distances along parallels and far from the same meridian, which is the case with Washington D.C. and Kabul.

Equal area map projections are defined by preserving the same area proportionality on the map as on the ground. In this lab, Bonne and Goode Homolosine (Land) equal area map projections were constructed. The Bonne map projection is pseudoconical and has no distortion along the central meridian and standard parallel. The distance from Washington D.C. to Kabul is 7,053 miles, which is close to the actual value of 6,964 miles. Distortion primarily occurs along the edges of the map. Since Kabul and Washington D.C. are both near the central meridian, there is minimal distortion in their distances. In contrast, the distance between Washington D.C. and Kabul is 10,025 miles using the Good Homolosine (Land) projection. This projection is well suited to highlight spatial distributions of water and land, as it minimizes distortion throughout the world. The projection is a combination of Sinusoidal and Mollweide projections. Distances are not distorted close the standard parallel (equator) and the central meridian. Since both Washington D.C. and Kabul lie away from the center of the map, their distances are significantly distorted.

Conformal map projections are characterized by the preservation of angles locally. In other words, direction is maintained as it appears on earth. In this lab, Mercator (World) and North Pole Stereographic conformal map projections were constructed. Mercator map projections were a staple in nautical exploration, since lines represent constant directions. As a result, area is drastically distorted along the north and south poles, as evidenced by the blown-up size of Antarctica and Greenland. The distance from Washington D.C. to Kabul is 10,204 miles with the Mercator map projection, which shows significant distortion in distance. Since Washington D.C. and Kabul are not near the standard parallel (equator) their distance is significantly distorted. The North Pole Stereographic map projection shows lesser distortion in distance between Washington D.C. and Kabul (7,605 miles). All stereographic projections project spheres onto a plane from a single point, in this case the North Pole. The farther south you go along a meridian, the greater the distortion in distance and area becomes. Since Washington D.C. and Kabul are both near the north pole in the projection, their distances are minimally distorted.