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Re: Vexari post# 20672

Saturday, 07/23/2022 2:47:27 PM

Saturday, July 23, 2022 2:47:27 PM

Post# of 23061
Lol, all one has to do is learn to navigate.

Rhumb line is the simplest method but not the most efficient, because following a rhumb line will result in a loxodrome - a curving path. The reason for that is a spherical Earth.

Great circle navigation is the most efficient as it produces the shortest path between any two points on a sphere. Flying a path that is a circle segment will result in a geodesic - a straight arcing path between two points with the maximum arc at the mid-point. Again, the reason for that is a spherical Earth.

The shortest path between any two points on a sphere is part of a circle segment. If a Great Circle is drawn out on a flat map, it produces a sinusoidal graph with a period equal to the sphere's circumference and equal amplitudes that are determined by my path's inclination to the equator of that sphere. Why would a circle graph out as a sine wave? Because the flat map is an erroneous presentation.

An Example: Bangor, Maine is the closest major U.S. city to the continent of Africa. If I leave Bangor to fly to Tangier, Morocco I depart Bangor with a northerly vector even though Tangier lies considerably south of Bangor! The reason is because the maximum amplitude of the sine my circle graphs out on the flat map lies between those two points. If I fly that exact same great circle the other way, say to El Paso, Tx. I'll fly to the southwest and the path will graph out much straighter on the flat map as the amplitude of the sine is decreasing as I fly in that direction.

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