## Choosing a Map Projection

Every map must begin, either consciously or unconsciously, with the choice of a map projection and its parameters. The cartographer’s task is to ensure that the right type of projection is used for any particular map. A well chosen map projection takes care that scale distortions remain within certain limits and that map properties match to the purpose of the map.

Generally, normal cylindrical projections are typically used to map the world in its entirety .In particular areas near the equator are shown well. Conical projections are often used to map the different continents. The mid-latitudes regions are shown well, while the polar azimuthal projections may be used to map the polar areas. Transverse and oblique aspects of many projections can be used for most parts of the world, though they are usually more difficult to construct.

The selection of a map projection for a particular area can be made on the basis of:

1. shape of the area,
2. location (and orientation) of the area, and
3. purpose of the map.

i.) Ideally, the general shape of the mapping area should match with the distortion pattern of a specific projection. If an area is approximately circular it is possible to create a map that minimizes distortion for that area on the basis of an azimuthal projection. The cylindrical projection is best for a rectangular area and a conic projection for a triangular area (figure below).

The choice of the map projection class (cylindrical, conical or azimuthal) depends largely on the general shape of the mapping area.

ii.) The choice of the aspect of a map projection depends largely on the location (and orientation) of the geographic area to be mapped. Optimal is when the projection centre coincides with centre of the area, or when the projection plane is located along the main axis of the area to be mapped .

An oblique Mercator projection is used for mapping the Alaska State (zone 5001). The cylindrical projection plane is located along the main axis of the area to be mapped (source: P. H. Dana).

iii.) Once the class and aspect of the map projection have been selected, the distortion property of the map projection has to be chosen. The most appropriate type of distortion property for a map depends largely on the purpose for which it will be used.

Map projections with a conformal distortion property represent angles and local shapes correctly, but as the region becomes larger, they show considerable area distortions. An example is the Mercator projection. Although Greenland is only one-eighth the size of South America, Greenland appears to be larger Maps used for the measurement of angles (e.g. aeronautical charts, topographic maps) often make use of a conformal map projection.

The Mercator projection is a cylindrical map projection with a conformal property. The area distortions are significant towards the polar regions. An example, Greenland appears to be larger but is only one-eighth the size of South America.

Map projections with a equal-area distortion property on the other hand, represent areas correctly, but as the region becomes larger, it shows considerable distortions of angles and consequently shapes . Maps which are to be used for measuring areas (e.g. distribution maps) often make use of an equal-area map projection.

The cylindrical equal-area projection after Lambert is a cylindrical map projection with an equal-area property. The shape distortions are significant towards the Polar Regions.

The equidistant distortion property is achievable only to a limited degree. That is, true distances can be shown only from one or two points to any other point on the map or in certain directions. If a map is true to scale along the meridians (i.e. no distortion in North-South direction) we say that the map is equidistant along the meridians (e.g. the equidistant cylindrical projection in the figure below). If a map is true to scale along all parallels we say the map is equidistant along the parallels (i.e. no distortion in East-West direction). Maps which require correct distances measured from the centre of the map to any point (e.g. air-route, radio or seismic maps) or maps which require reasonable area and angle distortions (several thematic maps) often make use of an equidistant map projection.

The equidistant cylindrical projection (also called Plate Carrée projection) is a cylindrical map projection with an equidistant property. The map is equidistant (true to scale) along the meridians (in North-South direction). Both shape and area are reasonably well preserved with the exception of the polar regions.

In summary, the ideal map projection for any country would either be an azimuthal, cylindrical, or conic projection, depending on the shape of the area, with a secant projection plane located along the main axis of the country or the area of interest. The selected distortion property depends largely on the purpose of the map.

Some map projections have rather special properties. The Mercator projection was originally designed to display accurate compass bearings for sea travel. Any straight line drawn on this projection represents an actual compass bearing. These true direction lines are rhumb lines (or loxodromes). Thus, the route of constant direction between two locations is a always a straight line. For navigation, this is the easiest route to follow, but not necessary the shortes route

The rhumb lines (lines of constant direction) are shown as straight lines on the Mercator projection. The shortest distance between two points – the great circle path – is shown as a curved line.

The gnomonic projection is a useful projection for defining routes of navigation for sea and air travel, because great circles – the shortest routes between points on a sphere – are shown as straight lines. Thus, the shortest route between any two locations is always a straight line. No other projection has this special property. In combination with the Mercator map where all lines of constant direction are shown as straight lines it assist navigators and aviators to determine appropriate courses. Changes in direction for following the shortest route can be determined by plotting the shortest route (great circle or orthodrome) from the Gnomonic map onto the Mercator map .

All great circles – the shortest routes between points on a sphere – are shown as straight lines on the gnomonic projection.

In the 15th, 16th and 17th centuries, during the time of great transoceanic voyaging, there was a need for conformal navigation charts. Mercator’s projection – conformal cylindrical – met a real need, and is still in use today when a simple, straight course is needed for navigation. Because conformal projections show angles correctly, they are suitable for sea, air, and meteorological charts. This is useful for displaying the flow of oceanic or atmospheric currents, for instance.

For topographic and large-scale maps, conformality and equidistance are important properties. The equidistant property, possible only in a limited sense, however, can be improved by using secant projection planes. The Universal Transverse Mercator (UTM) projection is a conformal cylindrical projection using a secant cylinder so it meets conformality and reasonable equidistance. Other projections currently used for topographic and large-scale maps are the Transverse Mercator (the countries of Argentina, Colombia, Australia, Ghana, S-Africa, Egypt use it) and the Lambert Conformal Conic (in use for France, Spain, Morocco, Algeria). Also in use are thestereographic (the Netherlands) and even non-conformal projections such as Cassini or the Polyconic.

Suitable equal-area projections for thematic and distribution maps include those developed by Lambert, whether azimuthal, cylindrical, or conical. These do, however, have rather noticeable shape distortions. A better projection is the Albers equal-area conic projection with two standard parallels, which is nearly conformal. In the normal aspect, they are excellent for mid-latitude distribution maps and do not contain the noticeable distortions of the Lambert projections.

An equidistant map, in which the scale is correct along a certain direction, is seldom desired. However, an equidistant map is a useful compromise between the conformal and equal-area maps. Shape and area distortions are often reasonably well preserved. An example is the equidistant cylindrical projection  (also called Plate Carrée projection), where the meridians are true to scale map (i.e. no distortion in North-South direction).

The projection which best fits a given country or region is always the minimum-error projection of the selected class. The use of minimum-error projections is however exceptional.

wikipedia

ITC Study Material

State Plane Coordinate System

Projections

Classes of Map Projection

Why Map Projection is an Issue in GIS

Datum,Ellipsoid,Rhumb Line,Secant, Spheroid, Tangent and Other Useful Terms

Celestial Sphere

Earth on Every Map Projection