nautical mile

The nautical mile (symbol M, NM, Nm or nmi) is a unit of length corresponding approximately to one minute of arc of latitude along any meridian. It is a non-SI unit (although accepted for use in the SI by the BIPM) used especially by navigators in the shipping and aviation industries,^[1] and also in polar exploration. It is commonly used in international law and treaties, especially regarding the limits of territorial waters. It developed from the sea mile and the related geographical mile.

Definition

The international nautical mile was defined by the First International Extraordinary Hydrographic Conference, Monaco (1929) as exactly 1852 metres.^[1] This is the only definition in widespread current use, and is the one accepted by the International Hydrographic Organization and by the International Bureau of Weights and Measures (BIPM). Before 1929, different countries had different definitions, and the Soviet Union, the United Kingdom and the United States did not immediately accept the international value.

Both the Imperial and U.S. definitions of the nautical mile were based on the Clarke (1866) Spheroid: specifically, they were different approximations to the length of one minute of arc along a great circle of a hypothetical sphere having the same surface area as the Clarke Spheroid.^[2] The United States nautical mile was defined as 1853.248 metres (6080.20 U.S. feet, based on the definition of the foot in the Mendenhall Order of 1893): it was abandoned in favour of the international nautical mile in 1954.^[3] The Imperial (UK) nautical mile, also known as the Admiralty mile, was defined in terms of the knot such that one nautical mile was exactly 6080 feet (1853.184 m):^[4] it was abandoned in 1970^[4] and, for legal purposes, is now converted to metres on the basis of one UK nautical mile = 1853 metres exactly.^[5]

Sea mile

The sea mile (in English use) is often confused with the nautical mile. Strictly, the sea mile is the distance of one minute of arc of latitude at a given (current) latitude and along the current meridian: as such, it varies from approximately 1842.9 m at the Equator to approximately 1861.7 m at the Poles, with a mean value of 1852.3 m.^[4] The international nautical mile was chosen as the integer number of metres closest to the mean sea mile.

Geographical mile

The geographical mile is equal to one minute of arc of longitude along the Equator: it is equal to approximately 1855.4 m for the International (1924) Spheroid,^[4] or approximately 1855.325 m for the WGS 84 ellipsoid. The term "geographical mile" has also been used to refer to the mean sea mile, which would later become the international nautical mile.^[2]

Care must be taken not to confuse this with the similar-sounding German unit called the geografische Meile, if one is dealing with historical German measurements (or one is German). This unit is intended to signify four minutes of arc along the equator and is standardized as 7421.6 metres.

Tactical mile or data mile

As an approximation, designers of radar systems for ballistic, cruise and anti-ship missiles used by NATO navies use 6,000 feet (1,828.8 m) as their equivalent of a nautical mile. In the Royal Navy, this is also known as a data mile.

Unit symbol

There is no widely accepted international standard symbol for the unit nautical mile. The preferred abbreviation of the IEEE is nmi,^[6] while M is used by the BIPM^[1] and the maritime authorities of the USA^[7], Canada^[8] and the United Kingdom.^[4] For aviation use, the preferred abbreviation of the ICAO is NM.^[9] The abbreviation nm, though conflicting with the SI symbol for the nanometre, is also widely used. The SI symbol for the newton metre is N m.

History

Historical definition - 1 nautical mile

The nautical mile was historically defined as a minute of arc along a meridian of the Earth, making a meridian exactly 180×60 = 10,800 historical nautical miles.^[3] It can therefore be used for approximate measures on a meridian as change of latitude on a nautical chart. The originally intended definition of the metre as 10^-7 of a half-meridian makes the mean historical nautical mile exactly (2 × 10⁷)/10,800 = 1,851.851851… historical metres. Based on the current IUGG meridian of 20,003,931.4585 (standard) metres the mean historical nautical mile is 1,852.216 m.

The historical definition differs from the length-based standard in that a minute of arc, and hence a nautical mile, is not a constant length at the surface of the Earth but gradually lengthens with increasing distance from the equator, as a corollary of the Earth's oblateness, hence the need for "mean" in the last sentence of the previous paragraph. This length equals about 1,861 metres at the poles and 1,843 metres at the Equator. ^[10]

Other nations had different definitions of the nautical mile. This variety in combination with the complexity of angular measure described above along with the intrinsic uncertainty of geodetically derived units mitigated against the extant definitions in favor of a simple unit of pure length. International agreement was achieved in 1929 when the International Extraordinary Hydrographic Conference held in Monaco adopted a definition of one (1) international nautical mile as being equal to 1,852 metres exactly, in excellent agreement (for an integer) with both the above-mentioned values of 1,851.851 historical metres and 1,852.216 standard metres.

Conversions to other units

Visual comparison of a nautical mile, statute mile, and kilometre

One nautical mile converts to:

• 1,852 metres (exact)
• 1.150779 miles (statute) [1] (exact: 57,875/50,292 miles)
• 2,025.372 yards (exact: 2,315,000/1,143 yards)
• 6,076.1155 feet (exact: 2,315,000/381 feet or 1,822,831/300 survey feet)
• 1,012.6859 fathoms (exact: 1,157,500/1,143 fathoms)
• 10 international cables (exact)
• 10.126859 imperial (100-fathom) cables (exact: 11,575/1,143 imperial cables)
• 8.439049 US customary (120-fathom) cables (exact: 57,875/6,858 US customary cables)
• 0.998383 equatorial arc minutes (traditional geographical miles)
• 0.9998834 mean meridian arc minutes (mean historical nautical miles)

Associated units

The derived unit of speed is the knot, defined as one nautical mile per hour. The term "log" is used to measure the distance a vessel has moved through the water. This term can also be used to measure the speed through the water (see chip log), as the speed and distance are directly related.

The term knot and log are derived from the practice of using a "log" tied to a knotted rope as a method of gauging speed of a ship. The log would be thrown into the water and the rope trailed behind the ship. The number of knots that passed off the ship and into the water in a given time would determine the speed in "knots". The present day measurement of knots and log are determined using a mechanical tow, electronic tow, hull-mounted units (which may or may not be retractable), doppler, ultrasonics, or GPS.^[11][12] Speeds measured with a GPS differ from those measured by other means in that they are Speed Over Ground (including the effect of any current) while the others are all Speed Through the Water, which does not include current.

See also

Nautical portal

• conversion of units
• knot for the unit of speed
• mile for other types of mile
• orders of magnitude (length)

Notes

• Moritz, H. (1980). "Geodetic Reference System". Bulletin Geodesique 54 (3).  (IUGG/WGS-84 data)
• Taff, Laurence G. (1981). Computational Spherical Astronomy. John Wiley and Sons.  (IAU data)

External links

• National Bureau of Standards: Refinement of values for the yard and the pound (1959)
• Measure Distances on a map in Nautical miles
• Nautical Unit Converter Nautical miles converted to and from miles and kilometres