Charts represent the “reduced earth”.

The chart scale represents the relation between the length represented on the chart compared with the real distance on planet earth.

Chart Scale = Chart length / Earth distance

On a Mercator chart, the scale expands away from the Equator.

The scale expansion is proportional to the secant of the latitude.

Questions about scale in a Mercator chart, come in 1 of 4 basic types:

Given scale at the Equator, find Mercator scale at some other latitude.

Given Mercator scale at some latitude, find scale at the Equator.

Given Mercator scale at some latitude, find Mercator scale at some other latitude.

Given a fixed chart distance between meridians, find Mercator scale at a specific latitude.

The equation to remember to solve this question is the following one:

Scale denominator A x cos (Latitude B) = Scale denominator B x cos (Latitude A)

Distance on Earth, departure = 60 x 5º x cos (17º) = 287 nm

As the units of length are in different units, first we must convert them into the same units:

1 nm = 1 852 m
287 nm = 531 524 m = 53 152 400 cm
Chart scale at 17ºN = 5 / 53 152 400 = 1 / 10 630 480

With the scale at 17º N, we will determine the scale at 57º N:

Scale denominator 57º = 10 630 480 x cos (57º) / cos (17º) = 6 054 319
Scale at 57º = 1 / 6 054 319