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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....
ABSTRACT Although the mathematical basis for rhumb lines on the ellipsoidal earth is well known, the earth's oblateness is usually neglected in dead-reckoning sailing calculations. This leads to si...
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
2401. Rhumb Lines and Great Circles. The principal advantage of a rhumb line is that it maintains constant true direction. A ship following the 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.
Calculating the distance between two points along a rhumb line. In the next diagram, A, B, C, D and Z are meridians of longitude; the lines aB, bC, and cD are different parallels of latitude; and the line ABCDZ is a rhumb line.
This paper provides simple formulas that include the earth's oblateness, which can be readily applied to sailing calculations. The accuracy of these formulas is assessed, and they are shown to be good to about 10 m over ranges up to 1000 km.
Formulas regarding the rhumbline sailing computation are given in a form convenient for calculations done with a use of commonly accessible electronic calculators.
