Any practical map, spherical or flat, shrinks Earth features
down to a manageable size. The general rate of reduction,
the **scale**, can be
expressed graphically or numerically. The latter case is usually
a fraction; for instance, on a 1:100000-scale map, two points
separated by 1 unit could represent two cities actually 100000
units apart; 1 centimeter on the map means 1000 meters on Earth.
With a scale 10 times "larger", 1:10000, one inch on the map
corresponds to 10000 inches on Earth, and so on. Therefore, if the
same region is presented in different maps, smaller-scale
versions can be more portable but probably less precise and
detailed.

A graphic scale is, at a minimum, a small "ruler" tagged with absolute distances and directly superimposed on the map. Although a distance evaluation requires two measurements (one for the ruler, another for the map itself), it has an important advantage: the map may be reproduced at different sizes with no modifications, while a numerical scale must be recomputed for each size. Graphic scales are especially useful for electronic devices like computer screens (whose resolution/physical size ratios are seldom correctly calibrated) and presentation slides (where the display's dimensions depend on the distance to the projection screen).

Either graphic or numeric, only on a true
globe a scale can be directly applied to *any* pair of
points on its surface. In flat maps the reduction
rate is *not* actually constant, changing with direction and
location. Especially, it may be *nonlinear*: the
length ratio of two segments of a line on the map is not the
same for the corresponding segments on Earth.
Finally, the shortest
distance between two points on a sphere is rarely
represented by a straight line on a flat map, and measuring
distances along an arbitrary (not always marked) curve
is not a straightforward procedure.

Thus, depending on the range of the mapped region (the larger, the greater will be distance distortions), neither numbers nor rulers can be reliably used without knowledge of the projection's properties; they both can be just misleading.

The outer edges of some azimuthal, cylindrical, conic and flat-polar pseudocylindrical provide some striking examples of distance distortion, as single points on Earth become lines on the map; in general any full-world map's edge distorts distances because points are projected twice in places far apart.

Lines on the map, straight or not, with constant, linear scale
(with length proportional to that of corresponding lines on
Earth) are *lines of true scale* or **standard lines**. Map
projections with a well-defined, nontrivial set of standard
lines are sometimes referred to
as **equidistant**. Some well-known examples are
the equidistant
cylindrical (in the normal aspect, all
meridians and one or two parallels are standard),
azimuthal equidistant (in the
normal aspect all meridians are standard), and the
conic equidistant
(in the normal aspect, all meridians and one or two parallels
are standard).

A common source of gross mistakes is assuming a circle drawn on a map represents the same range of distances as the corresponding shape on Earth. This only happens if all straight lines radiating from the circle's center are standard lines.

www.progonos.com/furuti/MapProj/Normal/CartProp/DistPres/distPres.html — June 16, 2018

Copyright © 1996, 1997, 2008 Carlos A. Furuti