A map projection is a way to represent the curved surface of the Earth on the flat surface of a map. A good globe can provide the most accurate representation of the Earth. However, a globe isn’t practical for many of the functions for which we require maps. Map projections allow us to represent some or all of the Earth’s surface, at a wide variety of scales, on a flat, easily transportable surface, such as a sheet of paper. Map projections also apply to digital map data, which can be presented on a computer screen.
There are hundreds of different map projections. The process of transferring information from the Earth to a map causes every projection to distort at least one aspect of the real world – either shape, area, distance, or direction.
Each map projection has advantages and disadvantages; the appropriate projection for a map depends on the scale of the map, and on the purposes for which it will be used. For example, a projection may have unacceptable distortions if used to map the entire country, but may be an excellent choice for a large-scale (detailed) map of a county. The properties of a map projection may also influence some of the design features of the map. Some projections are good for small areas, some are good for mapping areas with a large east-west extent, and some are better for mapping areas with a large north-south extent.
A Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre or a Sylvanus projection. Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l’Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter’s usages were approximate, however, and it is not clear they intended to be the same projection.
The projection is:
and φ is the latitude, λ is the longitude, λ0 is the longitude of the central meridian, and φ1 is the standard parallel of the projection.
Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the central meridian and the standard latitude shapes are not distorted.
The inverse projection is given by:
taking the sign of .
Special cases of the Bonne projection include the sinusoidal projection, when φ1 is zero, and the Werner projection, when φ1 is π/2. The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection; an alternative intermediate would be a Bottomley projection.
Examples of Bonne projection
The Werner projection is a pseudoconic equal-area map projection sometimes called the Stab-Werner or Stabius-Werner projection. Like other heart-shaped projections, it is also categorized as cordiform. Stab-Werner refers to two originators: Johannes Werner (1466–1528), a parish priest in Nuremberg, refined and promoted this projection that had been developed earlier by Johannes Stabius (Stab) of Vienna around 1500.
The projection is a limiting form of the Bonne projection, having its standard parallel at one of the poles (90°N/S). Distances along each parallel and along the central meridian are correct, as are all distances from the north pole.
Examples of Bonne projection