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Mercator Sailings can be used when traveling in any direction for any distance, and are a lot easier
to solve if you've got a Bowditch handy. Mercator sailings are based on meridional parts, which are the length
of an arc of a meridian as drawn on a mercator chart between the equator and location, and are described in minutes of
longitude at the equator. Because Mercator projection charts distort the size of objects, we use meridional parts to describe
the relative distance from the equator to the latitude we are seeking. For example, from the equator to 30 N, there are 30
degrees or 1800 minutes of latitude, but 1876.9 meridional parts. As latitude increases on a mercator projection chart,
the relative "stretch" of the latitudes is greater than at lower latitudes. For example, between the equator and 60
N, there are 3600 minutes of latitude but 4507.4 meridional parts. The number of equivalent meridional parts can be found
in Table 6 of Bowditch, or a link to an online calculator can be found below.
Meridional Parts Calculator
To solve a Mercator sailing, a new triangle must be used with m (the
difference between the meridional parts of the two latitudes) substituted for l (the difference
in degrees between the two latitudes). From there, the simple plane sailing sine and cosine equations can be used to solve
for the missing parts.
To find m, use Bowditch Table 6 to find the meridional parts at both the
initial and final latitudes. Then, subtract the smaller M (meridional parts of one lat) from the larger
M (meridional parts of the other) if the two locations are within the same hemisphere, or add the values
if they are in opposite hemispheres.
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