Loxodrome
In navigation, a rhumb line (also rhumb () or loxodrome) is an arc crossing all meridians of longitude at the same angle. It is a path of constant azimuth relative to true north, which can be steered by maintaining a course of fixed bearing. When drift is not a factor, accurate tracking of a rhumb line course is independent of speed.
In practical navigation, a distinction is made between this true rhumb line and a magnetic rhumb line, with the latter being a path of constant bearing relative to magnetic north. While a navigator could easily steer a magnetic rhumb line using a magnetic compass, this course would not be true because the magnetic declination—the angle between true and magnetic north—varies across the Earth's surface.
To follow a true rhumb line, using a magnetic compass, a navigator must continuously adjust magnetic heading to correct for the changing declination. This was a significant challenge during the Age of Sail, as the correct declination could only be determined if the vessel's longitude was accurately known, the central unsolved problem of pre-modern navigation.
Using a sextant, under a clear night sky, it is possible to steer relative to a visible celestial pole star. The magnetic poles are not fixed in location. In the northern hemisphere, Polaris has served as a close approximation to true north for much of recent history. In the southern hemisphere, there is no such star, and navigators have relied on more complex methods, such as inferring the location of the southern celestial pole by reference to the Crux constellation (also known as the Southern Cross).
Steering a true rhumb line by compass alone became practical with the invention of the modern gyrocompass, an instrument that determines true north not by magnetism, but by referencing a stable internal vector of its own angular momentum.
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