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# Nautical miles

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### Nautical miles

1 nautical mile =
SI units
1.85200 km 1,852.00 m
US customary / Imperial units
1.15078 mi 6,076.12 ft

The nautical mile (symbol M, NM or nmi) is a unit of length that is approximately one minute of arc measured along any meridian. By international agreement it has been set at 1,852 metres exactly (about 6,076 feet).

It is a non-SI unit (although accepted for use in the International System of Units 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.

The nautical mile remains in use by sea and air navigators worldwide because of its convenience when working with charts. Most nautical charts use the Mercator projection whose scale varies by about a factor of six from the equator to 80° latitude, so charts covering large areas cannot use a single linear scale.[2] 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.

## 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.

The Imperial 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.[3] The United States nautical mile was defined as 1,853.248 metres[4] (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.[5] 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 6,080 international feet (1,853.184 m):[6] it was abandoned in 1970[6] and, for legal purposes, old references to the obsolete unit are now converted to 1,853 metres exactly.[7]

### Sea mile

The sea mile is an ambiguous unit, with the following possible meanings:

In English usage a sea mile is, for any latitude, the length of one minute of latitude at that latitude (1 sea mile = Earth radius x one minute in radian). It varies from about 1,855.3 metres (6,087 ft) at the equator (equatorial radius × π / 180 / 60) to about 1,849.1 metres (6,067 ft) at the poles (polar radius × π / 180 / 60), with a mean value of 1,852.3 metres (6,077 ft).[6] The international nautical mile was chosen as the integer number of metres 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".[8] 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°."[9]

The sea mile has also been defined as 6,000 feet 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 1/60th of a degree of any great circle on Earth's surface was 6,120 feet (vs 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.[10][11]

### Geographical mile

The geographical mile is the length of one minute of longitude along the Equator, about 1,855.4 m on the International (1924) Spheroid[6] or about 1,855.325 m on the WGS 84 ellipsoid. Bowditch defines it as 6,087.08 feet, which is 1,855.34 metres.[9] The term "geographical mile" has also been used to refer to the mean sea mile, which would later become the international nautical mile.[3]

Do not confuse this 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 metres. In Germany, the Mile, Uhr or Stunde typically refers to 24,000 local feet - the distance one might walk in an hour (Stunde).

### Tactical mile or data mile

As an approximation, the designers of radar systems for ballistic missiles, cruise missiles, and antiship 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

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.[1][12] The preferred abbreviation of the International Civil Aviation Organization is NM.[13] 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 (with a space) or N·m, not nm, because only prefixes may abut a unit symbol.[14]

## History

The nautical mile was historically defined as a minute of arc along a meridian of the Earth (north-south), making a meridian exactly 180×60 = 10,800 historical nautical miles.[5] 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 arc 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 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 metres at the poles and 1,843 metres at the Equator.[15]

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, 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 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.

The use of an angle-based length was first suggested by Edmund Gunter (of Gunter's chain fame).[16] During the 18th century, the relation of a mile of, 6000 (geometric) feet, or a minute of arc on the earth surface, had been advanced as a universal measure for land and sea. The metric kilometre was selected to represent a centisimal minute of arc, on the same basis, with the circle divided into 400 degrees of 100 minutes.

## Conversions to other units

One international nautical mile converts to:

• 1.852 kilometres (exact)
• 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.[17][18] 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.