Rhumb Line - Usage

Usage

Its use in navigation is directly linked to the style, or projection of certain navigational maps. A rhumb line appears as a straight line on a Mercator projection map.

The name is derived from Old French: "rumb", a line on the chart which intersects all meridians at the same angle. 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. 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.

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 5,400 nautical miles (10,000 km). At 20 degrees North the great-circle distance is 4,997 miles (8,042 km) while the rhumb-line distance is 5,074 miles (8,166 km), about 1½ percent further. But at 60 degrees North the great circle distance is 2,485 miles (3,999 km) while the rhumb-line is 2,700 miles (4,300 km), a difference of 8½ percent. A more extreme case is the air route between New York and Hong Kong, for which the rhumb-line path is 9,700 nautical miles (18,000 km). The great-circle route over the North Pole is 7,000 nautical miles (13,000 km), or 5½ hours less flying time at a typical 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.

Early navigators in the time before the invention of the 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 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.