Lab 5

The above image is an map of the world based on the Geographic Coordinate System by the World Geodetic System of 1984.  Such a representation of the world is done by referencing a three-dimensional ellipsoid of the earth to calculate distances between two points.  This is the most accurate method to obtain distances between two points as it uses datum based on the actual curvature of the Earth.  Using the ArcMap's measurement tool, the distance from Washington D.C., United States of America to Kabul, Afghanistan is approximately 6, 954.752973 miles.  In this map, one can see that the sizes of the continents and respective countries are true to the real-world.  Although one is able to use this data in a computer or geographic positioning device, one must often utilize a physical map where an electronic version is unavailable.   The transformation of the world onto a two-dimensional, tangible map must unfortunately incur some distortion.  There is no "superior" map projection available; only those best suited to one's purpose.  Three categories of map projections were implemented in the ArcMap program: Conformal, Equal Area, and Equidistant to 1) compare the visual distortion and 2) compare the alteration of the true distance between the two cities.  

The two maps shown above are Conformal Projections based on the North America and South America Conics.  Lambert Conics, being one of the the most widely used in map making, preserve angular measurements.  The visual distortion of these two projections is remarkable.  The continents in the North America Conic have been significantly reduced in size and are barely visible whereas the South America Conic repairs this issues but in doing so, segments the European and Asian continents.  To produce such a projection, a cone is placed on the Earth and the information is transferred to the cone.  A cut is then made on the cone itself to flatten it, giving these maps a "pie shape."  Lambert conics are either 1) tangent to one parallel or 2) secant to two parallels of the Earth.  This type of map projection is very important when one needs to gain one's "heading" or direction of travel--an very important aspect in sea-faring or aeronautics.  Unfortunately using this system, one cannot gain an accurate measurement of distance.  The North America projection gives a distance between the two cities of 6, 702.869643 miles and is close to the true distance, off by a mere 3.62%.  However, the South America conic is very inaccurate.  It gives a distance of 13, 117.192883 miles, a substantial 88.61% difference.     

The above maps are Bonne and Goode's Homosoline Equal Area projections.  These projections, while preserving the relative sizes of the continents to their true values, produce very odd looking maps.  Although visually the Bonne Projection looks like a heart, it does preserve distance along each parallel and central meridian.  The approximate distance between the two cities from the Bonne Projection is 6, 765.256.451, a minuscule difference of 2.72%.  Due to the distortion, such projections are generally reserved for small areas and not global representations.  On the other hand, the Goode's Homosoline is preferred for global maps.  There are two versions of the Homosoline projection 1) land orientated and 2) ocean oriented.  For this context, the land oriented map was selected.  Despite the fact that the sizes of the land masses are correct, the map is very broken, almost if the globe was "unwrapped" or "peeled."  The distance between Washington D.C., USA and Kabul, Afghanistan is far from correct.  Goode's Homosoline calculated a distance of 15, 642.332504 miles, a massive 124.92% difference.  Equal Area projections are most often used for documenting changes in natural resources.  For example, the changes of foliage due to deforestation can be accurately measured due to the unwavering size of land masses in the map.          

Equidistant projections preserve distance along a given line, usually the meridians.  The Equidistant Conic projection can also be created along one parallel or two parallels using the same cutting method as the Lambert Conformal Projections.  However, the distortion in shape is significant.  The Antarctic continent is depicted as all encompassing and many countries, Australia in particular, have been "squished" vertically.   The Equidistant Conic projection gives a distance of 6, 994.945309 miles, a minuscule .58% difference, and the closest result by a projection to the actual distance given by the GCS WGS map.  Moreover, the Equidistant Cylindrical projection does the opposite of the Equidistant Conic.  Instead of compressing the continents, the cylinder appears to vertically stretch the shapes.  Horizontal distance seems to be fairly inaccurate, giving a distance of 5, 069.388001 miles, a difference of 27.21%.  Equidistant maps tend to be used for small areas to minimize the blatant visual distortion.