# Nautical mile

SI units | |
---|---|

1.852 km | 1,852 m |

US customary / Imperial units | |

1.151 mi | 6,076 ft |

A **nautical mile** (symbol **M**, **NM** or **nmi**) is a unit of distance, set by international agreement as being exactly 1852 meters (about 6,076 feet), compared with the 5,280 feet in a statute mile. Historically, it was defined as the distance spanned by one minute of arc along a meridian of the Earth (north-south), and developed from the sea mile and the related geographical mile.

It is a non-SI unit (although accepted for use in the International System of Units by the BIPM), which is generally used by navigators at sea and in the air,^{[1]} and also in polar exploration. It remains in use worldwide because of its convenience when working with charts.^{[2]} Most nautical charts use the Mercator projection, whose scale varies by about a factor of 6 from the equator to 80° latitude, so charts covering large areas cannot use a single linear scale.^{[3]} The nautical mile is nearly equal to a minute of latitude on a chart, so a distance measured with a chart divider can be roughly converted to nautical miles using the chart's latitude scale.

The nautical mile is commonly used in international law and treaties, especially regarding the limits of territorial waters.

## Definition

The **international nautical mile** was defined by the First International Extraordinary Hydrographic Conference, Monaco (1929) as exactly 1,852 meters.^{[2]} 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.

The Imperial (UK) and U.S. definitions of the nautical mile were based on the Clarke (1866) Spheroid: they were different approximations to the length of one minute of arc along a great circle of a sphere having the same surface area as the Clarke Spheroid.^{[4]} The United States nautical mile was defined as 1853.248 meters^{[5]} (6,080.20 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.^{[6]} The Imperial nautical mile, also known as the **Admiralty mile**, was defined in terms of the knot, such that one nautical mile was exactly 6,080 international feet (1853.184 m):^{[7]} it was abandoned in 1970^{[7]} and, for legal purposes, old references to the obsolete unit are now converted to 1,853 meters exactly.^{[8]}

### Sea mile

A **sea mile** or **nautical mile** is, strictly, the length of a minute of arc measured along a meridian (north-south distance). On a spherical model, this equals a minute of longitude (east-west distance) *only* at the equator; on an ellipsoid model these distances are different.

The length of one minute of arc along a meridian of the International (1924) Spheroid varies from about 1,842.9 metres (6,046 ft) at the equator to about 1,861.7 metres (6,108 ft) at the poles, with a mean value of 1,852.3 metres (6,077 ft).^{[7]} These figures can be obtained by multiplying the equivalent in radians of an arc-minute by the radius of curvature of the meridian at each given latitude. The international nautical mile was chosen as the integer number of meters closest to the mean sea mile.

American use has changed recently. The glossary in the 1966 edition of *Bowditch* defines a "sea mile" as a "nautical mile".^{[9]} In the 2002 edition, the glossary says: "An approximate mean value of the nautical mile equal to 6,080 feet; the length of a minute of arc along the meridian at latitude 48°."^{[10]}

The sea mile has also been defined as 6,000 feet (1,828.8 m) or 1,000 fathoms, for example in Dresner's *Units of Measurement*. Dresner includes a remark to the effect that this must not be confused with the nautical mile. Richard Norwood in *The Seamans Practice* (1637) determined that one-sixtieth of a degree of any great circle on Earth's surface was 6,120 feet (compare the modern value of 6,080 feet). He added: "if any man think it more safe and convenient in Sea-reckonings" he may assign 6,000 feet to a mile, relying on context to determine the type of mile.^{[11]}^{[12]}

### Geographical mile

The geographical mile is the length of one minute of longitude along the Equator (east-west distance), about 1,855.4 m on the International (1924) Spheroid^{[7]} or about 1,855.325 m on the WGS 84 ellipsoid. Bowditch defines it as 6,087.08 feet, which is 1,855.34 meters.^{[10]} The term "geographical mile" has also been used to refer to the mean sea mile, which would later become the international nautical mile.^{[4]}

This is not to be confused with the similar-sounding unit the *geografische Meile*, seen in historical German measurements. This unit was intended to be the length of **four** minutes of arc along the equator and is standardized as 7,421.6 meters. In Germany, the *Meile*, *Uhr* or *Stunde* typically refers to 24,000 local feet – the distance one might walk in an hour (Stunde).

## Unit symbol

The International Hydrographic Organization, whose membership includes essentially all seafaring nations, and the International Bureau of Weights and Measures use **M** as the abbreviation for the nautical mile.^{[2]}^{[13]} The preferred abbreviation of the International Civil Aviation Organization is **NM**.^{[14]} The preferred abbreviation of the IEEE and US GPO is **nmi**.^{[15]}^{[16]} The abbreviation **nm**, though conflicting with the SI symbol for the nanometre, is also sometimes used.

## History

The nautical mile was historically defined as the length that spans one minute of arc on the surface of the Earth, measured along any meridian, making a meridian exactly 180×60 = 10,800 historical nautical miles, and the length of a degree of latitude is exactly 60 historical nautical miles.^{[6]} 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 meter as 10^{−7} of a half-meridian arc makes the mean historical nautical mile exactly (2×10^{7})/10,800 = 1,851.851851… historical meters. Based on the current IUGG meridian of 20,003,931.4585 (standard) meters, 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 in the north-south direction 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 meters at the poles and 1,843 meters at the Equator.^{[2]}^{[17]} Eratosthenes of Cyrene was the first to divide the surface of the earth into lines of latitude and longitude. His theory was first applied by medieval Arabic geographers, who extended the Roman mile to 1.04 nautical miles.

Other nations had different definitions of the nautical mile. This variety, in combination with the complexity of angular measure described above and the intrinsic uncertainty of geodetically derived units, militated 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 international nautical mile as being equal to 1,852 meters exactly, in excellent agreement (for an integer) with both the above-mentioned values of 1,851.851 historical meters and 1,852.216 standard meters.

The use of an angle-based length was first suggested by Edmund Gunter (of Gunter's chain fame).^{[18]} During the 18th century, the relation of a mile of 6000 (geometric) feet, or a minute of arc on the earth's surface, had been advanced as a universal measure for land and sea. The metric kilometer was selected to represent a centisimal minute of arc, on the same basis, with the circle divided into 400 degrees of 100 minutes (4 quadrants of 100 degrees). Thus on this basis, a great circle is 400×100 kilometers or 360×60 nautical miles, and a quarter great circle is 100×100 kilometers or 90×60, so a kilometer is (90×60)/(100×100) = 54/100 = 0.54 nautical miles, and a nautical mile is (100×100)/(90×60) = 100/54 ≈ 1.852 kilometers.

## Conversions to other units

One international nautical mile converts to:

- 1.852 kilometers (exact) (or
^{463}⁄_{250}km) - 1.150779 miles (statute) (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 U.S. customary (120-fathom) cables (exact: 57,875/6,858 U.S. 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 terms "knot" and "log" are derived from the practice of using a "log" tied to a knotted rope as a method of gauging the speed of a ship. A log attached to a knotted rope was thrown into the water, trailing 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 (either ultrasonic or radar), or GPS.^{[19]}^{[20]} Speeds measured with a GPS differ from those measured by other means in that they are Speed Over Ground (accounting for the effect of current), while the others are Speed Through the Water, which does not account for current.

## See also

- Conversion of units
- Knot (unit) for the unit of speed
- Mile for the land-based unit of length
- Orders of magnitude (length)
- Nautical airmile for the wind-adjusted unit of length (used in aviation)
- Units of measurement

## References

- ↑ The United States Navy and the US Army Air Force officially adopted the nautical mile and the knot as their standard aeronautical unts for distance and speed on 26 July 1946. (Air & Space/Smithsonian, June/July 1987, p. 27)
- 1 2 3 4 International Bureau of Weights and Measures (2006),
*The International System of Units (SI)*(PDF) (8th ed.), p. 127, ISBN 92-822-2213-6 - ↑ Bowditch, Nathaniel, LLD; et al.,
*The American Practical Navigator*(PDF) (2002 ed.), Washington: National Imagery and Mapping Agency, pp. 34–35 - 1 2 Glazebrook, Richard (1922), "Measurement, Units of",
*Dictionary of Applied Physics***1**, pp. 580–88 - ↑ Aside from rounding this is the exact length of a great-circle minute on a sphere of radius 6,370,997.2406 meters, which is the sphere that has the same area as the Clarke 1866 spheroid as usually defined.
- 1 2 National Bureau of Standards (August 1954), "Adoption of International Nautical Mile" (PDF),
*Technical News Bulletin* - 1 2 3 4 Ministry Of Defence of the United Kingdom (1987),
*Admiralty Manual of Navigation*, London: HMSO, pp. 6–7, ISBN 0-11-772880-2 - ↑ "The Units of Measurement Regulations 1995". The National Archives. Retrieved February 2011.
- ↑ Bowditch, Nathaniel, LLD; et al. (1966),
*The American Practical Navigator*(Corrected Print ed.), Washington: U.S. Navy Hydrographic Office, p. 945 - 1 2 Bowditch, Nathaniel, LLD; et al.,
*The American Practical Navigator*(PDF) (2002 ed.), Washington: National Imagery and Mapping Agency, pp. 716–854 - ↑ Norwood, Richard (1637–1670). "The Seaman's Practice".
*Early English Books Online*. pp. 5, 48. - ↑ Eva Germaine Rimington Taylor (1934).
*Late Tudor and Early Stuart Geography, 1583–1650: A Sequel to Tudor Geography, 1485–1583*. Taylor & Francis. pp. 81–82. ISBN 978-0-374-97809-9. - ↑
*Chart No. 1, Positions, Distances, Directions, Compass*, Jointly by NOAA and Department of Commerce, USA The cited book incorporates IHO Chart INT 1 and therefore represents the practice of the members of the IHO, most of the seafaring nations - ↑ NOTIFICATION OF ANNEX DIFFERENCES (Presented by Australia), International Civil Aviation Organisation, Sixth Meeting of CNS/MET Sub Group of APANPIRG, Bangkok, Thailand, 15–19 July 2002
- ↑ "IEEE Symbols and Prefixes".
*ieee-pes.org*. - ↑ "U.S. Government Printing Office Style Manual".
*gpo.gov*. - ↑ "For a point on the spheroid of the IAU System at geodetic latitude (Φ): 1 degree of latitude [=] (110.575 + 1.110 sin
^{2}Φ) km." Seidelmann, P. K. (Ed.), (1992),*Explanatory supplement to the Astronomical almanac*, Sausalito, CA: University Science Books, 700 - ↑ W. Waters (1958).
*The Art of Navigation in England in Elizabethan and Stuart Times*. London. - ↑ Fairhall, David (2005),
*Pass your day skipper*(2nd ed.), A&C Black, ISBN 0-7136-7400-8

## Sources

- Moritz, H. (1980), "Geodetic Reference System",
*Bulletin Geodesique***54**(3): 388, doi:10.1007/BF02519014 (IUGG/WGS-84 data) - Taff, Laurence G. (1981),
*Computational Spherical Astronomy*, New York: John Wiley and Sons, Bibcode:1981csa..book.....T, ISBN 978-0-89464-478-8 (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 kilometers