In the Mercator charts the degrees of longitude are made to appear the same length over the whole chart. It becomes necessary in order to preserve the direction between different locations to increase the North-South distance on the chart and such increase must become greater and greater the higher the latitude.
The length of the meridian as thus increased between the equator and any given latitude (L), expressed in minutes of longitude at the equator as a unit, constitutes the number of meridional parts (M) corresponding to that latitude.
The value for M is normally taken from a table of meridional parts, but now that we are in the computer age, the value for M can be calculated by a programmable calculator or computer. For normal navigational purposes the value of M is taken to one decimal place (NNNN.N), but for survey work greater precision may be required.
Meridional parts for the Clark spheroid of 1866.
M = 7915.704468 * log tan ( 45 + (L/2))
- 23.268932 * ( sin L )
- 0.052500 * ( sin L )^3
- 0.000213 * ( sin L )^5
When sailing from point 1 (L1, LO1) to point 2 (L2, LO2)
M1 = meridional distance for L1
M2 = meridional distance for L2
m = (M2 - M1) = (meridional difference)
C = course angle
DLO' = difference in longitude expressed in minutes
D = distance from point 1 to point 2
tan C = DLO' / m
D = 60 * ( L2 - L1 ) / cos C (nautical miles)When L1 is greater than L2, then the angle C will be negative (fourth quadrant). To put the answer into the second quadrant add 180 degrees.
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