Scale (map) - The Representative Fraction (RF) or Principal Scale

The Representative Fraction (RF) or Principal Scale

There are two conventions used in setting down the equations of any given projection. For example, the equirectangular cylindrical projection may be written as

cartographers:

mathematicians:

Here we shall adopt the first of these conventions (following the usage in the surveys by Snyder). Clearly the above projection equations define positions on a huge cylinder wrapped around the Earth and then unrolled. We say that these coordinates define the projection map which must be distinguished logically from the actual printed (or viewed) maps. If the definition of point scale in the previous section is in terms of the projection map then we can expect the scale factors to be close to unity. For normal tangent cylindrical projections the scale along the equator is k=1 and in general the scale changes as we move off the equator. Analysis of scale on the projection map is an investigation of the change of k away from its true value of unity.

Actual printed maps are produced from the projection map by a constant scaling denoted by a ratio such as 1:100M (for whole world maps) or 1:10000 (for such as town plans). To avoid confusion in the use of the word 'scale' this constant scale fraction is called the representative fraction (RF) of the printed map and it is to be identified with the ratio printed on the map. The actual printed map coordinates for the equirectangular cylindrical projection are

printed map:

This convention allows a clear distinction of the intrinsic projection scaling and the reduction scaling.

From this point we ignore the RF and work with the projection map.