Lab 5 Projections

How many decimal degrees does the equator span? 

360.6DD

What about the northern- or southern-most graticule line on the map?
180.46DD

What do these two lines in fact represent?

(latitude, longitude)

From Washington D.C., USA to Kabul, Afghanistan
Spherical GCS Model Distance = 6932.4 miles

All distances posted below refers to the distance from Washington D.C. to Kabul in different map projections.

Conformal Map Projection

Mercator Projection Distance =10189.5 miles

Gall Stereographic Projection Distance = 7141.3 miles

Equal Area Map Projections
World Sinusoidal Projection Distance = 8112.8 miles
World Cylindrical Equal Area Projection Distance = 10066.6 miles

Equidistant Map Projections
Equidistant Conic Projection Distance = 6985.2 miles
Equidistant Cylindrical Projection Distance = 5079.6 miles

 

In this lab, we had to use project a three-dimensional spherical model of the Earth (Spherical GCS model) onto a two-dimensional planar model that falls into three main categories- the conformal, equidistant and equal area type map projections. Furthermore, as seen above, each category of map projection type can have more than one way to be projected: conformal projections include the Mercator and gall stereographic projections; equal area projections include the world sinusoidal and world cylindrical equal area projections; and lastly,  equidistant projections include the equidistant conic and equidistant cylindrical projections.

The purpose of this lab is to recognize the inevitable distortion that occurs whenever a 3D surface is projected onto a 2D surface, and this can be observed in the differences the projections look from the original spherical GCS model. The conformal projections preserves shapes and angles on a map- and this is important if the map is needed for bearings or angles in flight or ship navigation. The equal area projection preserves the proportionality of areas on the map- important if you want to calculate area. Lastly, the equidistant projection preserves distances from a certain point- which is important if distances are to be calculated correctly.

As seen above, each type of map above measures a different distance from Washington D.C., USA to Kabul, Afghanistan, which shows that if you blindly use one map projection without knowing how it is being distorted, it will give you a lot of inaccuracy in calculations. The perils could include getting wrong bearings while navigating, or choosing a projection that doesn't conserve areas when you are trying to do a comparison between two areas in the world, or choosing a projection that doesn't conserve local distances when you are trying to measure distance. For example, the spherical GCS model, which should be the most accurate because it has not been distorted, shows the distance between the two cities to be 6932.4 miles, and the most accurate map projection that shows this is the equidistant map projection which shows 6985 miles, whereas other map projections are up to hundreds of miles off.

The significance of map projection is the ability to project a 3D model of the Earth onto a planer 2D surface. This has mainly practical purposes because planar maps can be easily stored and read, whereas keeping a three dimensional globe is cumbersome and could be harder to read. However, with such practical improvements come with the drawback of distortion- in the areas of angles, distances and areas. The critical part is to know how each map projection distorts and conserves certain features, and on a case by case basis, depending on the task that the user wants to do, there is a most suited map projection.