Editing Rhumb line (section)

==Application==
Its use in navigation is directly linked to the style, or ''[[map projection|projection]]'' of certain navigational maps. A rhumb line appears as a straight line on a [[Mercator projection]] map.<ref name="EOS">Oxford University Press [http://www.encyclopedia.com/doc/1O225-rhumbline.html Rhumb Line]. The Oxford Companion to Ships and the Sea, Oxford University Press, 2006. Retrieved from Encyclopedia.com 18 July 2009.</ref>

The name is derived from Old French or Spanish respectively: ''"rumb"'' or "rumbo", a line on the chart which intersects all meridians at the same angle.<ref name="EOS" /> On a plane surface this would be the shortest distance between two points. Over the Earth's surface at low latitudes or over short distances it can be used for plotting the course of a vehicle, aircraft or ship.<ref name="EOS" /> Over longer distances and/or at higher latitudes the [[great circle]] route is significantly shorter than the rhumb line between the same two points. However the inconvenience of having to continuously change bearings while travelling a great circle route makes ''rhumb line navigation'' appealing in certain instances.<ref name="EOS" />

The point can be illustrated with an east–west passage over [[90 degrees]] of longitude along the [[equator]], for which the great circle and rhumb line distances are the same, at {{convert|5400|nmi|km|abbr=off|order=flip}}. At 20 degrees north the great circle distance is {{convert|4997|nmi|km|abbr=on|order=flip}} while the rhumb line distance is {{convert|5074|nmi|km|abbr=on|order=flip}}, about 1.5% further. But at 60 degrees north the great circle distance is {{convert|2485|nmi|km|abbr=on|order=flip}} while the rhumb line is {{convert|2700|nmi|km|abbr=on|order=flip}}, a difference of 8.5%. A more extreme case is the air route between [[New York City]] and [[Hong Kong]], for which the rhumb line path is {{convert|9700|nmi|km|abbr=on|order=flip}}. The great circle route over the North Pole is {{convert|7000|nmi|km|abbr=on|order=flip}}, or {{frac|5|1|2}} hours less flying time at a typical [[Cruise (flight)|cruising speed]].

Some old maps in the Mercator projection have grids composed of lines of [[latitude]] and [[longitude]] but also show rhumb lines which are oriented directly towards north, at a right angle from the north, or at some angle from the north which is some simple rational fraction of a right angle. These rhumb lines would be drawn so that they would converge at certain points of the map: lines going in every direction would converge at each of these points. See [[compass rose]]. Such maps would necessarily have been in the Mercator projection therefore not all old maps would have been capable of showing rhumb line markings.

The radial lines on a compass rose are also called ''rhumbs''. The expression ''"sailing on a rhumb"'' was used in the 16th–19th centuries to indicate a particular compass heading.<ref name="EOS" />

Early navigators in the time before the invention of the [[marine chronometer]] used rhumb line courses on long ocean passages, because the ship's latitude could be established accurately by sightings of the Sun or stars but there was no accurate way to determine the longitude. The ship would sail north or south until the latitude of the destination was reached, and the ship would then sail east or west along the rhumb line (actually a [[Circle of latitude|parallel]], which is a special case of the rhumb line), maintaining a constant latitude and recording regular estimates of the distance sailed until evidence of land was sighted.<ref>A Brief History of British Seapower, David Howarth, pub. Constable & Robinson, London, 2003, chapter 8.</ref>