In
navigation, a rhumb line (or loxodrome) is a line crossing all
meridians at the same angle, i.e. a path of constant
bearing. It is obviously easier to manually steer than the constantly changing heading of the shorter
great circle route.The idea of a loxodrome was invented by a
Portuguese mathematician Pedro Nunes in the 1500s.If you follow a given (
magnetic-deviation compensated) compass-bearing on Earth, you will be following a rhumb line. All rhumb lines spiral from one
pole to the other unless the bearing is 90 or 270 degrees, in which case the loxodrome is a line of constant latitude, such as the equator. Near the poles, they are close to being
logarithmic spirals (on a
stereographic projection they are exactly, see below), so they wind round each pole an infinite number of times but reach the pole in a finite distance. The pole-to-pole length of a rhumb line is (assuming a perfect
sphere) the length of the
meridian divided by the
cosine of the bearing away from true north.
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