Chamberlin Projections

Figure 1. The Chamberlin projection is one of the standard projections used by the National Geographic Society for mapping continents. The three input points for this map are highlighted, and are located at -150° 0' 0"E, 65° 0' 0"N; -101° 0' 0"E, 23° 0' 0"N; and -66° 0' 0"E, 54° 0' 0"N.

The Chamberlin projection (also called the Chamberlin Trimetric projection) was developed by Wellman Chamberlin in 1947. Wellman Chamberlin was the chief cartographer of the National Geographic Society (this was and still is a very prestigious position for cartographers). The Society still uses the projection he developed in the production of maps covering continents or larger areas.

The Chamberlin projection has the interesting quality that distances from three input points to any other point on the map are approximately correct. Note that this does not imply that the Chamberlin projection is equidistant. Equidistance means that the distances between certain pairs of points are shown accurately. In the Chamberlin projection, it is possible that there are no pairs of points between which distances are shown correctly. Consider this example: Call the three input points used in the Chamberlin projection points A, B and C, and call some other point on the map point X. Suppose that in the real world, the distances between these points were AX = 12 units, BX = 10 units and CX = 8 units. These three distances total to 12 + 10 + 8 = 30 units. All that the Chamberlin projection ensures is that when these same three distances are measured on the map, their total will be approximately 30 units. Thus, a Chamberlin map may show these distances as AX = 18 units, BX = 6 units and CX = 6 units. These distances total to 18 + 6 + 6 = 30 units, but none of the distances between individual pairs of points is accurate.

In reality, the distances between each of the input points to all other points on a Chamberlin map are almost always close to correct, so the Chamberlin projection is usually close to being equidistant. Furthermore, while the Chamberlin projection is neither equivalent nor conformal, the distortions in the region between the three input points are relatively minor. This make the Chamberlin a good compromise projection that is not perfect in any way, but pretty good in just about every way. This is why the National Geographic Society still uses this projection in its general-purpose mapping tasks.

• Form: Chamberlin projections are almost planner. Technically, the Chamberlin projection is called "modified planner," which means that the developable surface used in a Chamberlin projection is slightly curved, and not completely flat as it is in a projection with a true planner form. The degree of curvature in a Chamberlin projection's developable surface is determined by how close together the projection's three input points are to one another -- the farther the points are from one another, the more curved the developable surface.

• Case: Chamberlin projections are secant. The location of the projection's line of tangency is determined by the precise location of the projection's three input points.

• Aspect: Chamberlin projections can use any possible aspect; normal, transverse, or oblique.

• Variation Within Chamberlin Projections: Chamberlin projections differ in the locations of their three input points. These point locations, in turn, determine the projection's form and aspect.

• Distortions
  • Shearing: Chamberlin projections do distort shapes; but the amount of distortion is relatively low in the triangular region between the map's three input points. The amount of distortion in this region depends on the region's size; larger triangular regions will suffer more distortion than smaller regions.
  • Tearing: Chamberlin maps tend to have rounded edges, and are typically used to cover areas the size of continents. Mathematically, the projection could be used to map half the Earth (i.e., a single hemisphere), but it is very rare to use the Chamberlin projection to map areas that large. Tearing occurs along the map's edges. It would be extremely difficult to build an interrupted map using the Chamberlin projection.
  • Compression: Chamberlin projections do distort areas; they are not equivalent. However, the amount of area distortion is relatively low in the triangular region between the map's three input points. The amount of area distortion in this triangular region depends on the region's size; larger triangular regions will suffer more distortion than smaller regions.
  • Equivalence: Chamberlin projections do distort areas; they are not equivalent. However, the amount of area distortion is relatively low in the triangular region between the map's three input points. The amount of area distortion in this triangular region depends on the region's size; larger triangular regions will suffer more distortion than smaller regions.
  • Conformality: Chamberlin projections do distort shapes; but the amount of distortion is relatively low in the triangular region between the map's three input points. The amount of distortion in this region depends on the region's size; larger triangular regions will suffer more distortion than smaller regions.
  • Equidistance: Chamberlin projections are close to being equidistant in the sense that distances from each of its three input points to all other points on the map are usually close to being accurate. However, these distances are not completely accurate (and under some unusual conditions, they can be very inaccurate), and hence the Chamberlin projection cannot be considered truly equidistant.
  • Azimuthality: Chamberlin projections are close to being azimuthal in the sense that directions from each of its three input points to all other points on the map are usually close to being accurate. However, these directions are not completely accurate (and under some unusual conditions, they can be very inaccurate), and hence the Chamberlin projection cannot be considered truly azimuthal.
  
  
• Uses: The Chamberlin projection is the quintessential compromise. It is not perfect in any way; it distorts area, distance and direction. However, the amount of each type of distortion in the triangular region between the projection's input points is quite slight. This overall low level of distortion makes the Chamberlin an excellent choice for general purpose mapping where perfect equivalence, conformality, azimuthality or equidistance are not required, but general accuracy is desired.