ABSTRACT
Before exploring the methods for expressing distortion quantitatively, it is necessary to consider the accuracy required to estimate the effect of distortions. This chapter suggests that two or three significant figures are all that are necessary to give a realistic estimate of distortion. It is evident that a spherical model of the Earth is all that is needed to obtain this degree of accuracy. The orthographic projection suffers distortion as the equator is approached. The distortion in the gnomonic projection is more severe, and the equator itself can never be portrayed. In all cases, distortion is independent of longitude. Quantitative values for distortion are needed for comparing distortions in length, area, and angle. Distortion in length can be rather simply estimated from geometric considerations. In order to describe distortion in length, the chapter considers a two-dimensional plotting surface and derives terms for distortion along the parallels and meridians, as compared to true distance along a sphere.
