ArcMap Projections

Above: Equidistant Map Projections preserve distance.from a given point.
Above: Equal Area Map Projections preserve area.

Above: Conformal Map Projections preserve angles.

Significance:

Map projections take a three-dimensional object, the earth which is a sphere, and project it onto a two-dimensional surface. Regardless of the method used, distortions always occur. This is why we different types of projections are used: equidistant projections preserve distance; equal area projections preserve area; and conformal projections preserve shape. No projection is perfect however, and depending upon the purpose of the map, the element that needs to be preserved must be identified. In preserving distance, often times, area and shape are sacrificed. This is true of the other two variables as well; therefore, different map projections serve specific purposes and should not be used for other purposes because they are inaccurate.

Perils:

Map projections can preserve area, shape, distance, scale or other factors. However, no map projection is perfect enough to preserve all properties. Because of this, distortion occurs. In changing the surface of the projections, different properties are preserved.

The conformal projections were the Mercator and the Gall Stereographic. The Mercator uses a cylindrical projection and is often used for navigation because it preserves linear scale and angle. However, it distorts shape and makes large objects seem larger than they are; the scale increases towards the poles. This is why Russia and Greenland, for example, appear inordinately large. The estimation of distance was inaccurate: standard error (the difference between the true value and the estimate divided by the true value and the result multiplied by 100) was 45.9%. The Gall Stereographic however, was far more accurate, with only 3.2% error. It projects the sphere onto a plane; it does not preserve angles, nor distances or areas of figures. It does preserve angles.

The equal area map projections were the Sinusoidal and the Mollweide. The Sinusoidal uses a pseudocylindrical projection to preserve scale along the Meridian. Area is preserved on the map. The error for the Sinusoidal projection was 16.9%. The Mollweide is also a pseudocylindrical projection that is often used to model the sky. It does not preserve angles or shape, only area. This is reflected in the curvature of the continents. Error for the Mollweide was 14.4%.

The equidistant projections were the Equidistant Conic and the Plate Caree. The Equidistant Conic is projected onto a cone and has equally spaced parallels. Area and angles are not preserved, only distances. Distortion increases below the equator. Error for the conic is 0.61%. The Plate Caree projection is a simple grid that spaces meridians and horizontals by circles of latitude. This map is highly inaccurate, but useful for thematic mapping, due to easy translation to pixels. The projection appears to be highly distorted horizontally; error is 46.8%.

Potential:

In representing distance from D.C. to Kabul, the most accurate map projection was the Equidistant Conic; it had the lowest value for standard error. The most inaccurate map projection was the Plate Caree, which had the highest error. If the time is not taken to make these comparisons among maps, reported data, such as distances, angles and area can be highly inaccurate. It is important to use projections that will best represent the properties studied.