Description of Some Commonly Used Map Projections

There are many projections which have been developed and are available for use in both analogue and digital mapping. A number of standardized transformation processes have been developed to represent the earth’s surface in two dimensions. As you are already aware, every transformation will produce some sort of distortion, depending on which specific geographic properties are modified in the transformation process. I shall provide you with brief description of some commonly used map projections.

Developable surfaces give rise to various types of map projections and modified forms. These include

Mercator Equal Area, Transverse Mercator Universal Transverse Mercator Conformal Conic Stereographic Gnomic Projections.

Cylindrical projections

There are many types of the cylindrical projection. These include the original Mercator, Transverse Mercator and the Universal Transverse Mercator.

Mercator Projections

Figure… A cylindrical equal-area projection.

Figure .. A central-perspective cylindrical projection.

The projection of the grid has been parallel with the plane of the tangent great circle. The result is the cylindrical-equal area projection, but in it the shapes of areas in high latitudes are so stretched out east and west and so shortened north and south that they look odd – so odd, in fact, that the projection is little used in this form.

Figure

An equidistant cylindrical projection or plane chart

It was first published in 1969 and perhaps the most used of al projections. To balance that distortion, the position of the parallels of latitude are mathematically computed to produce north-south expansion which increases at the same rate as the east-west expansion.

It is a conformal projection (preservation of shape) and not equal area and as such the scale is constant all over the map. In the Mercator projection, the scale increases rapidly in the higher latitudes causing some great differences in size.

In this one the direction of the projection radiates from the centre of the earth to the tangent cylinder. In this central-perspective cylindrical projection there is also a great east-west expansion in high latitudes but a still greater north-south expansion. It is neither equal-area nor conformal.

The Mercator projection enlarges areas in higher latitudes (Disproportionate enlargement of areas). Note for example, that Alaska in North America appears about the same size as Brazil in South America, whereas in fact Brazil is more than five times larger than Alaska

Fig …

Parallels and meridians are straight lines intersecting art right angles. The meridians are spaces equally but the spacing between the parallels grow wider the further one moves from the Equator.

A compass course or compass bearing plotted on to a Mercator projection is a straight line. This is its biggest asset and of greatest convenience to navigators because of the characteristics of the Loxodrome (rhumb line) which is a line of constant compass bearing drawn on a map or navigational chart. This line cuts successive meridians at the same angle.

The projection is therefore ideally suited for navigation purposes. It can also be used for maps showing direction such as charts or wind or currents but it should never be use for distribution maps.

This projection is useful for marine navigation because a straight line drawn between two points has correct, constant directions or angles. In the Mercator projection, the lines of latitude and longitude are straight and they intersect with each other at 90º angles. The north-south scale in this projection increases from the equator at the same rate as the corresponding east-west scale. The main shortcoming of this projection is that size distortion increases with latitude in that middle and high latitude countries appear larger that they really are.

Transverse Mercator Projection

While the Mercator projection is based on the Equator as a standard parallel, the Transverse Mercator is “turned” mathematically so as to use a meridian as

a standard reference line. The projection is sometimes constructed, as others, as secant projection in order to average out the scale factor.

The Transverse Mercator projection is used as the basis for the Universal Transverse Mercator grid reference system (UTM) which I have also described in another topic below.

The Transverse Mercator projection is appropriate for areas of limited extent east-west, but with long extent north-south.

Universal Transverse Mercator (UTM) Projection

The system of UTM and UPS grid zone designations. Each quadrilateral is identified by its column number and row letter (I and O omitted). The tinted quadrilateral is designated 32N. The UPS grid zones in the polar areas are sectors on each side of the 0°-180° meridians.

The framework or basis for the UTM projection is the Transverse Mercator projection which in this case is “turned” or rotated mathematically so as to use a meridian as a standard reference line. It is an internationally accepted projection and used for topographic mapping and military manoeuvres.

This system was established to provide worldwide coverage by defining 6o

zones, each having a 6o longitude range. UTM zone 1 extends from 180o west longitude to 174o west longitude with a central meridian of 177o west. Zone numbers increase to the east, at an equal spacing of 6o longitude.

Conical Projections

Lambert Conformal Conic Projection

As the name implies, the Lambert Conformal conic projection uses a cone as its projecteable surface. The axis of the cone is made to coincide with the minor axis of the ellipsoid (spheroid) and will pass through the ellipsoid along two parallels of latitude, called the standard parallels as shown in Figure 5.18

Figure 5.18 Representation of the cone used in the Lambert Conformal conic projection.

Source:

Different Lambert conformal conic projections can be set up for specific local areas or “zones”. When a Lambert conformal conic projection is developed for a specific area, a central meridian is selected whose longitude is equal to that of the approximate centre of the zone. The origin for the map projection is also selected.

Some examples of the modified forms of the conical projection:

Simple Conic Projection

Figure Simple conic projection with two standard parallels at 20o and 60oN.

The parallels remain equidistant over the entire projection. This projection has been widely used in atlases for areas in middle latitudes.

It is a conformal projection which means that true shape is maintained. The projection is appropriate for areas of limited extent north-south, but wide extent east-west.

Bonne Projection

This is one of the earliest forms of the modified conical projection used for topographic maps. It is used occasionally used for maps of continents.

Figure 5.20 The Bonne Equal Area projection

The Albers Equal area projection.

This is also an example of a conical projection with two standard parallels on which the scale is true. The parallels are also mathematically arranged so as to give an equal area projection. Between the standard parallels the scale along the meridians is a little too large and outside the standard parallels the scale is a little too small.

Like the Lambert Conformal conical projection this projection is best suited for countries having a mainly east-west orientation. The meridians are straight lines radiating from a point beyond the mapped area towards the Pole. The parallels are arcs of par of concentric circle centered on that point. Parallels and meridians intersect at right angles.

In this projection all parallels are arcs of concentric circles, as they are in thee truly conical projections.

The Meridians, however, are not straight lines but curves which converge at the poles and pass through points on the parallels that are spaced in true proportion to their spacing on the globe.

It gives good shapes near the central meridian, but deformation increases rapidly away from the central meridian.

The projection is most appropriately used, therefore, for a land area which has its greater dimension north and south.

Azimuthal/Stereographic projection

There are many examples of an azimuthal. These result from projecting a spherical surface onto a plane as viewed from space. The five well-known azimuthal projection are stereographic, lambert’s equal-area, azimuthal equidistant, orthographic and gnomonic.

Figure 5.21 An azimuthal equidistant projection

The meridians are depicted as straight lines radiating out from the Pole and the parallels are a series of concentric circles intersecting the meridians at right angles.

The projection is conformal, the scale increasing away from the Pole whilst shape is preserved. It is not then, an equal area projection.

The drawbacks to this projection are that only one part of the Earth's surface can be displayed at a time and distance, shape and size are distorted. This projection is generally used for perspective views of hemispheres.