The nautical mile (symbol M, NM or nmi) is a unit of length that is about one minute of arc of latitude measured along any meridian, or about one minute of arc of longitude at the equator. By international agreement it is exactly 1,852 metres (approximately 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 are constructed on the Mercator projection whose scale varies by approximately a factor of six from the equator to 80° north or south latitude. It is, therefore, impossible to show a single linear scale for use on charts on scales smaller than about 1/80,000.^[2] The nautical mile circumvents this problem by being equal to a minute of latitude on a chart, which allows any distance measured with a chart divider to be simply converted using the chart's latitude scale.

Definition[link]

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: 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 1853.248 metres^[4] (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.^[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 6080 feet (1853.184 m):^[6] it was abandoned in 1970^[6] and, for legal purposes, old references to the obsolete unit are now converted to 1853 metres exactly.^[7]

Sea mile[link]

In English usage, a sea mile is, for any latitude, the length of one minute of latitude at that latitude. It 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).^[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 6000 feet or 1000 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.

Geographical mile[link]

The geographical mile is the length of one minute of longitude along the Equator, about 1855.4 m on the International (1924) Spheroid^[6] or about 1855.325 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 7421.6 metres. In Germany, the Mile, Uhr or Stunde typically refers to 24,000 of the local foot. This is the distance one might walk in an hour (Stunde).

Tactical mile or data mile[link]

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.

Radar mile[link]

In radar theory, the data mile (6,000 feet) is the length unit. A radar mile is the time it takes a radar pulse to travel one datamile forth and a data mile back again, which equals 12.277 μs. This value corresponds with the speed of light (c. 3×10⁸ m/s). A radar's range can be determined by dividing the listening time (pulse repetition time minus pulsewidth) by a radar mile.

Unit symbol[link]

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][10] The preferred abbreviation of the International Civil Aviation Organization is NM.^[11] 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.^[12]

History[link]

Historical definition - 1 nautical mile

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.^[13]

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 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.

Use of angle-based length was first suggested by E. Gunter (of Gunter's chain fame).^[14] 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[link]

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

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[link]

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.^[15][16] 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[link]

Nautical portal

• 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

Notes[link]

• 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[link]

• 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