Geographical mile

Geographical mile
Conversions
1 geographical mile in ...... is equal to ...
   SI units   ~1855.3 m
   imperial/US units   ~1.1528 mi or ~6,087 ft

The geographical mile is an international unit of length determined by 1 minute of arc1/60 degree—along the Earth's equator. For the international ellipsoid 1924 this equalled 1855.4 metres.[1] The American Practical Navigator 2017 defines the geographical mile as 6087.08 feet (1855.342 m).[2] Greater precision depends more on choice of ellipsoid than on more careful measurement: the length of the equator in the World Geodetic System WGS-84 is 40075016.6856 m, which makes the geographical mile 1855.3248 m,[3] while the IERS Conventions (2010) takes the equator to be 40075014.1723 m, making the geographical mile 1855.3247 m,[4] 0.1 millimetres shorter. In any ellipsoid, the length of a degree of longitude at the equator is thus exactly 60 geographical miles.

The shape of the Earth is a slightly flattened sphere, which results in the Earth's circumference being 0.168% larger when measured around the equator as compared to through the poles. The geographical mile is slightly larger than the nautical mile (which was historically linked to the circumference measured through both poles); one geographic mile is equivalent to approximately 1.00178 nautical miles.

Historical units

Historically, certain nations used slightly different divisions to create their geographical miles.

The Portuguese system derived their miles (milha geográfica) as one third of their league of three separate values. When each equatorial degree was divided into 18 leagues, the geographical mile was equal to 1/54 degree or about 2.06 km; when divided into 20 leagues, the geographical mile was equal to 1/60 degree, approximating the values provided above; and when divided into 25 leagues, the geographical mile was equal to 1/75 degree or about 1.48 km.

The geographical miles of the traditional Dutch (geografische mijl), German (geographische Meile or Landmeile), and Danish systems (geografisk mil) all approximated their much longer miles—equivalent to English leagues—by using a larger division of the equatorial degree. Instead of using one minute of arc, they all used four—1/15 degree—to produce a distance now notionally equal to 7408 m but actually differing slightly depending on official measurements and computations. (For example, the Danish unit was computed as equivalent to about 7,421.5 m by the astronomer Ole Rømer.)[5]

Relationship with the nautical mile

The geographical mile is closely related to the nautical mile, which was originally determined as 1 minute of arc along a great circle of the Earth[6] but is nowadays defined by treaty as exactly 1852 m.[1] The US National Institute of Standards and Technology notes that "The international nautical mile of 1,852 meters (6,076.115 49... feet) was adopted effective July 1, 1954, for use in the United States. The value formerly used in the United States was 6,080.20 feet = 1 nautical (geographical or sea) mile."[7][8] This deprecated value of 6080.2 feet is equivalent to 1853.24 m. A separate reference identifies the geographic mile as being identical to the international nautical mile of 1852 m and slightly shorter than the British nautical mile of 6080 feet (1853.18 m).[9]

Scandinavians used their own version of the geographical mile as their nautical mile up to the beginning of the 20th century, causing it to be more well known as the sea mile in Danish (sømil), Norwegian (sjømil), and Swedish (sjömil).

Use

The unit is not used much in English-speaking countries but is cited in some United States laws. For example, Section 1301(a) of the Submerged Lands Act defines state seaward boundaries in terms of geographic miles. While debating what became the Land Ordinance of 1785, Thomas Jefferson's committee wanted to divide the public lands in the west into "hundreds of ten geographical miles square, each mile containing 6,086 and 4-10ths of a foot" and "sub-divided into lots of one mile square each, or 850 and 4-10ths of an acre".[10]

See also

References

  1. ^ a b Ministry of Defence Staff, Navy Dept, Great Britain Ministry of Defence (1987). Admiralty manual of navigation. H.M. Stationery Office. p. 7. ISBN 9780117728806.{{cite book}}: CS1 maint: multiple names: authors list (link)
  2. ^ "Glossary of Marine Navigation", The American Practical Navigator, vol. II (2017 ed.), National Geospatial-Intelligence Agency, p. 346
  3. ^ Department of Defense World Geodetic System 1984 (third ed.), National Imagery and Mapping Agency, 2004, p. 3-2. Equatorial radius = 6,378,137 m.
  4. ^ Petit, Gérard; Luzum, Brian, eds. (2010), "General definitions and numerical standards", IERS Conventions (2010), p. 18. Equatorial radius = 6,378,136.6 m.
  5. ^ Rabounski, Dmitri (2008). "Biography of Ole Rømer" (PDF). The Abraham Zelmanov Journal. 1: 2. Archived (PDF) from the original on 2011-07-15. Retrieved 1 February 2018.
  6. ^ David Greenhood; Gerard L. Alexander (1964). Mapping. University of Chicago Press. pp. 51–52. ISBN 9780226306971.
  7. ^ "NIST Handbook 44, Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices, General Tables of Units of Measurement (PDF). NIST (Report). November 2014. p. C-15 (Appendix C, footnote 14). Archived (PDF) from the original on 2017-05-05. Retrieved April 9, 2019.
  8. ^ "Units of Weight and Measure (United States Customary and Metric) Definition and Tables of Equivalents" (PDF). National Bureau of Standards (Report). July 1, 1955. p. 4. Archived (PDF) from the original on 2017-02-01. Retrieved May 5, 2021.
  9. ^ Weast, Robert C. (ed.). CRC Handbook of Chemistry and Physics, 62nd edition, 1981-1982. Boca Raton, Florida: CRC Press. p. F-297. ISBN 978-0849304620.
  10. ^ "Journal of Continental Congress, Vol. 27". A Century of Lawmaking for a New Nation: U.S. Congressional Documents and Debates, 1774 - 1875. Library of congress. May 28, 1784. p. 446. Retrieved April 9, 2019.
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