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As the great circle track crosses the various meridians at different angles the ship has to alter the course throughout the passage. Therefore rhumb line track is used even though the shortest distance between two points on Earth is the shorter arc of the great circle through those points.
Rhumb Line – A Rhumb Line or Loxodrome is a line on Earth’s surface, crossing all meridians at the same angle. For example the Equator, all parallel latitudes and meridians
Departure – The departure between two places is the east-west distance between them in nautical miles.
When the distance between the two latitudes is small the departure is taken as the distance between the two meridians measured along the mean latitude.
When the distance between the two latitudes is large the departure is taken as the east-west distance between the meridians measured along the middle latitude ( latitude in which true departure lies, when sailing between them ) between them.
PARALLEL SAILING
It is the same as the Departure between two places as the starting and destination position DOES NOT lie on the same latitude. The ship sails along the rhumb line, due east or west.
Dist = d’long (in min) cos lat
PLANE SAILING
Here the starting and the destination position are on the same latitude. Sailing is done along the Rhumb line.
SOME IMPORTANT FORMULAS
Dep = d’long cos (mean lat)
D’lat= dist cos (course)
Dep = dist sin (course)
Dep/d’lat(in min) = tan (course)