week 6 lab - map projections

Conformal Projection

The distance between Washington and Kabul:

Lambert Conformal Conic

Line measurement (Planar)

Segment: 7,234.594867 Miles

Length: 7,234.594867 Miles

Line measurement (Geodesic)

Segment: 6,934.478105 Miles

Length: 6,934.478105 Miles

Line measurement (Loxodrome)

Segment: 8,112.060673 Miles

Length: 8,112.060673 Miles

Line measurement (Great Elliptic)

Segment: 6,934.483772 Miles

Length: 6,934.483772 Miles

[We can notice that the distance between Washington and Kabul measures the same under geodesic and great elliptic measurement methods.]

Transverse Mercator Complex

Line measurement (Planar)

Segment: 8,056.146836 Miles

Length: 8,056.146836 Miles

Line measurement (Geodesic)

Segment: 6,939.629965 Miles

Length: 6,939.629965 Miles

Line measurement (Loxodrome)

Segment: 8,154.936147 Miles

Length: 8,154.936147 Miles

Line measurement (Great Elliptic)

Segment: 6,940.273134 Miles

Length: 6,940.273134 Miles

Equidistant Projection

The distance between Washington and Kabul:

Equidistant Conic

Line measurement (Planar)

Segment: 6,857.024332 Miles

Length: 6,857.024332 Miles

Line measurement (Geodesic)

Segment: 6,934.478105 Miles

Length: 6,934.478105 Miles

Line measurement (Loxodrome)

Segment: 8,112.060673 Miles

Length: 8,112.060673 Miles

Line measurement (Great Elliptic)

Segment: 6,934.483772 Miles

Length: 6,934.483772 Miles

Azimuthal Equidistant

Line measurement (Planar)

Segment: 9,476.289268 Miles

Length: 9,476.289268 Miles

Line measurement (Geodesic)

Segment: 6,952.220838 Miles

Length: 6,952.220838 Miles

Line measurement (Loxodrome)

Segment: 27.200859 Miles

Length: 9,486.93483 Miles

Line measurement (Great Elliptic)

Segment: 6,921.222224 Miles

Length: 6,921.222224 Miles

Equal Area Projection

The distance between Washington and Kabul:

Lambert azimuthal equal area

Line measurement (Planar)

Segment: 6,241.499534 Miles

Length: 6,241.499534 Miles

Line measurement (Geodesic)

Segment: 6,898.234813 Miles

Length: 6,898.234813 Miles

Line measurement (Loxodrome)

Segment: 8,068.046878 Miles

Length: 8,068.046878 Miles

Line measurement (Great Elliptic)

Segment: 6,903.044743 Miles

Length: 6,903.044743 Miles

Cylindrical_Equal_Area

Line measurement (Planar)

Segment: 10,108.051114 Miles

Length: 10,108.051114 Miles

Line measurement (Geodesic)

Segment: 6,934.478105 Miles

Length: 6,934.478105 Miles

Line measurement (Loxodrome)

Segment: 8,112.060673 Miles

Length: 8,112.060673 Miles

Line measurement (Great Elliptic)

Segment: 6,934.483772 Miles

Length: 6,934.483772 Miles

Comments:

Map projection is the way to transfer the 3 dimensional the Earth into a 2 dimensional map. Basically there’re three categories of map projections: conformal, equidistant and equal area. Conformal projection maps such as Lambert Conformal or Transverse Mercator maps preserve angular relationships, which makes conformal maps good for navigation. Equidistant projection maps such as Azimuthal Equidistant or Equidistant Conic maps preserve distance from the center or origin of the map to all other places. The trait enables us to measure distance between two places accurately. Equal area projection maps such as Cylindrical Equal Area or Lambert Azimuthal Equal Area maps preserve relative sizes of geographic features, which give us a better idea of the relative sizes of regions and avoids misunderstandings.

Conformal maps are widely used in daily lives, especially the Mercator projection map. Conformal maps were used to be a navigational tool for sailors in the Age of Discovery. However, while the angular relationships are preserved, conformal maps change sizes and shapes of areas so that people develop a misleading idea about the relative sizes of regions. For example, it seems on the map that Alaska is bigger than Brazil, but the truth is just the adverse. Alaska appears bigger because it’s close to the North Pole and distances and area are exaggerated near the poles.

Equidistant maps present all points on the map are at proportionately correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. It is useful for showing airline distances from center point of projection and for seismic and radio work. However, distances and directions to all places are true only from the center point of projection, and distortion of areas and shapes increases dramatically away from center point. For example, distance between Washington and Kabul in Equidistant Conic and Azimuthal Equidistant projection maps differs greatly from other projection maps and the real distance, even in equidistant maps themselves, different measure methods’ results vary dramatically.

Equal area projection maps accurately represent the relative size of areas, but it does not accurately represent angles. For example, unlike conformal or equidistant maps, Alaska and Brazil in equal area maps represent the right relative sizes, thus equal area maps are used to display information in the online Map Maker application by the National Atlas of the US, and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. However, equal area maps cannot be used as navigation tool since they distort angles.

There's no "perfect map", we choose map based on our ultimate goal. Sometimes we may need more than one projection so that we can get more accurate details that tell us what's the real world like.