Map Projections
The Great Circle Mapper uses the Azimuthal Equidistant, Lambert Azimuthal Equal Area (North and South), and Orthographic projections.
A Background to Map Projections
The only true representation of an actual area is a globe. Directions, distances, shapes, and areas are all true, and the shortest distance between two points can be easily found. However, globes have their disadvantages - even the largest globe has a very small scale, and shows relatively little detail. Its costly to reproduce and update, difficult to carry around or store. Consequently, some means was needed to transfer a curved map to a flat piece of paper or computer screen, and a large number of different map projections were devised to do this. The first thing to say is that there is no 'best' projection. Each have their own advantages and disadvantages. All have some distortion.
Specific Map Projections
An Equidistant Cylindrical projection is best visualised by imagining a sphere 'unwrapped' onto a cylinder, making a complete transformation to a flat surface. In a cylindrical projection, distortion increases away from the Equator, and is extreme in polar regions. Areas and shapes of large areas are distorted, but angles and shapes within any small area are essentially true. A cylindrical projection that we are all familiar with is the Mercator projection, used for navigation, or maps of equatorial regions. However, unlike the Equidistant Cylindrical projection, the latitudes in a Mercator map are not equally spaced.
Stereographic projections are used mainly for Arctic and Antarctic maps. Directions are true only from the point of projection. Scale increases away from the centre point, unlike the usual 'Great Circle' map (see below), where it is constant. Any straight line through the centre point is a great circle line. Distortion of large areas increase away from the centre point.
Conic projections distort scale and distance except along standard parallels. Areas are proportional and directions are true in limited areas. Used in the United States, Russia, and other large countries with a larger east-west than north-south extent and that require equal-area representation.
An Orthographic projection is best visualised as a view of the earth from deep space. It is used to obtain a perspective view of hemispheres. Area and shape are distorted. Distances are true along the equator and other parallels.
The projection most familiar to Radio Amateurs is the Azimuthal Equidistant projection, commonly know as the Great Circle Map. Distances and direction to all places on the map are true only from the centre point, normally the operator's QTH. Distortion of other properties increases away from the center point. A straight line drawn from the centre point indicates the shortest route to a point, and is used to determine the correct direction to point antennas. With the Global Overlay Mapping System, the same can be achieved on any of the maps by simply holding the cursor over the destination and reading the antenna direction from the status bar.
The Azimuthal Equidistant Projection, believed to be first used by Egyptians for star charts, preserves both distance and direction from the central point. The world is projected onto a flat surface from any point on the globe. Although all aspects are possible (equatorial, polar, and oblique), the one used most commonly is the polar aspect, in which all meridians and parallels are divided equally to maintain the equidistant property.
The Lambert azimuthal equal-area projection, developed by Johann H. Lambert in 1772, maintains land features at their true relative sizes while simultaneously maintaining a true sense of direction from the center. The world is projected onto a flat surface from any point on the globe. This projection is best suited for individual land masses that are symmetrically proportioned, either round or square. Although all aspects are possible (equatorial, polar, and oblique), the one used most commonly is the polar aspect. The Global Overlay Mapper provides both North and South polar aspects.
The Orthographic Projection, believed to be developed first by the Egyptians and the Greeks, is an azimuthal perspective projection, projecting the Earth's surface from an infinite distance to a plane. It gives the illusion of a three-dimensional globe so it is often used as inset map or for pictorial views of the Earth from space.
The Plate Carrée or Equidistant Cylindrical Projection, which was invented by Marinus of Tyre around A.D. 100, is a projection with the standard parallel located at the equator. A grid of parallels and meridians forms perfect squares from east to west and from pole to pole. It is one of the simplest and oldest map projections, and therefore its usage was more common in the past. The radius is used as a conversion factor between angular and linear units. Another usage of this projection is to display spatial data stored in a geographic coordinate system, known as the pseudo-plate carrée projection.