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Summary of Formulas. The formulas so far derived in this appendix are summarized below: Ddist = Dlong x Cos Lat. Dlong = Ddist ÷ Cos Lat = Ddist x Sec Lat. . dep.= d.long cos(mean lat) (for distances 600 n.m. or less). Dep. = d.long cos(mid lat). (for distances over 600 n.m.). The Rhumb Line Formulas.
The rhumb line connecting any two points of the great circle on the same side of the equator is a chord of the curve. If the two points are on op-posite sides of the equator, the direction of curvature of the great circle relative to the rhumb line changes at the equa-tor. The rhumb line and great circle may intersect each
rhumb line between two places does not change its true course. A rhumb line makes the same angle with all meridians it crosses and appears as a straight line on a Mercator chart. For any other case, the difference between the rhumb line and the great circle connecting two points increases (1) as the latitude increases, (2) as the difference
The formulas enable to solve the tasks with a use of electronic calculator and application of traditional methods on plane and sphere, and they also take the Earth’s ellipsoidal shape into consideration. Keywords: loxodrome (rhumb-line sailing), plane (or middle latitude) sailing, Mercator triangle (Mercator sailing) 1. Introduction
The formulas for determining a ship's dead-reckoned position, given an initial known location, the vessel's course and speed, and the time elapsed, are referred to as the sailing formulas....
Rhumb line calculation: Departure position (latitude, longitude) + Course and Distance, to compute Arrival position; Departure position + Arrival position, to compute Course and Distance; Path of constant course between Departure position and Arrival position. Great Circle calculation
The initial rhumb line course (θ T) is then altered by an incremental value of r0.1D(converted into radians) and evaluated as T Tc. After few iterative steps (Newton-Raphson method), T Tc reaches the free turning point I’ on the same great circle, thus determining the optimized distance (D TI’V) (Petrović, 2015). Detailed mathematical ...
