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| Rhumb line |
Rhumb lines are tracks with a constant track direction between two points on a sphere and therefore must be a longer distance than a great circle track. A rhumb line between any two points will always lie on the equatorial side of the equivalent great circle. At the mid point the rhumb line track and the great circle track are parallel.
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Example:
Imagine you are navigating a ship or plane using only a compass. The simplest and least error-prone method would be to maintain a constant heading throughout the entire trip.From Portugal, if you continuously sail south-west, you will reach Brazil. It won't be the shortest or fastest route, but it will be the easiest.
The Mercator Projection map (the "evil one", that makes Greenland look larger than Africa) was designed specifically for this purpose. Draw a straight line from your start to your destination and that course will have a constant heading all the way. Without any adjustments along the route, your compass will always indicate the same direction to go.
Every straight line on a Mercator Projection map is a rhumb line.
Except when following the equator (which is both a rhumb line and a great circle), any rhumb line will eventually reach either the north or south pole.
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