Английская Википедия:Foot (unit)

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

Шаблон:Short description Шаблон:About Шаблон:Use mdy dates Шаблон:Use American English Шаблон:Infobox unit The foot (Шаблон:Plural form; standard symbol: ft)[1][2] is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, Шаблон:Char, is commonly used to represent the foot.[3] In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Since an international agreement in 1959, the foot is defined as equal to exactly 0.3048 meters.

Historically, the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16 digits.

The United States is the only industrialized country that uses the (international) foot in preference to the meter in its commercial, engineering, and standards activities.[4] The foot is legally recognized in the United Kingdom; road distance signs must use imperial units (however, distances on road signs are always marked in miles or yards, not feet; bridge clearances are given in meters as well as feet and inches), while its usage is widespread among the British public as a measurement of height.[5][6] The foot is recognized as an alternative expression of length in Canada.[7] Both the UK and Canada have partially metricated their units of measurement. The measurement of altitude in international aviation (the flight level unit) is one of the few areas where the foot is used outside the English-speaking world.

Historical origin

Шаблон:See also

Файл:Determination of the rute and the feet in Frankfurt.png
Determination of the rod, using the length of the left foot of 16 randomly chosen people coming from church service. Woodcut published in the book Шаблон:Lang by Jakob Köbel (Frankfurt, Шаблон:C.).

Historically, the human body has been used to provide the basis for units of length.[8] The foot of an adult European-American male is typically about 15.3% of his height,[9] giving a person of Шаблон:Convert a foot-length of about Шаблон:Convert, on average.

Archaeologists believe that, in the past, the people of Egypt, India, and Mesopotamia preferred the cubit, while the people of Rome, Greece, and China preferred the foot. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of Шаблон:Convert and a cubit of Шаблон:Convert.[10] The Egyptian equivalent of the foot—a measure of four palms or 16 digits—was known as the Шаблон:Lang and has been reconstructed as about Шаблон:Convert.

The Greek foot (Шаблон:Lang, Шаблон:Lang) had a length of Шаблон:Sfrac of a stadion,[11] one stadion being about Шаблон:Convert;[12] therefore a foot was, at the time, about Шаблон:Convert. Its exact size varied from city to city and could range between Шаблон:Convert and Шаблон:Convert, but lengths used for temple construction appear to have been about Шаблон:Convert to Шаблон:Convert; the former was close to the size of the Roman foot.

The standard Roman foot (Шаблон:Lang) was normally about Шаблон:Convert (97% of today's measurement),[13] but in some provinces, particularly Germania Inferior, the so-called Шаблон:Lang (foot of Nero Claudius Drusus) was sometimes used, with a length of about Шаблон:Convert. (In reality, this foot predated Drusus.)[14][15]

Originally both the Greeks and the Romans subdivided the foot into 16 digits, but in later years, the Romans also subdivided the foot into 12 Шаблон:Lang (from which both the English words "inch" and "ounce" are derived).

After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In AD 790 Charlemagne attempted to reform the units of measure in his domains. His units of length were based on the Шаблон:Lang and in particular the Шаблон:Lang, the distance between the fingertips of the outstretched arms of a man.[16] The Шаблон:Lang has 6 Шаблон:Lang (feet) each of Шаблон:Convert.

He was unsuccessful in introducing a standard unit of length throughout his realm: an analysis of the measurements of Charlieu Abbey shows that during the 9th century the Roman foot of Шаблон:Convert was used; when it was rebuilt in the 10th century, a foot of about Шаблон:Convert[Note 1] was used. At the same time, monastic buildings used the Carolingian foot of Шаблон:Convert.[Note 1][17]

The procedure for verification of the foot as described in the 16th century posthumously published work by Jacob Köbel in his book Шаблон:Lang is:[18][19] Шаблон:Blockquote

England

Файл:Imperial measurement standards, Greenwich.JPG
The unofficial public imperial measurement standards erected at the Royal Observatory in Greenwich in the 19th century

Шаблон:See also

The Neolithic long foot, first proposed by archeologists Mike Parker Pearson and Andrew Chamberlain, is based upon calculations from surveys of Phase 1 elements at Stonehenge. They found that the underlying diameters of the stone circles had been consistently laid out using multiples of a base unit amounting to 30 long feet, which they calculated to be 1.056 of a modern international foot (thus 12.672 inches or 0.3219 m). Furthermore, this unit is identifiable in the dimensions of some stone lintels at the site and in the diameter of the "southern circle" at nearby Durrington Walls. Evidence that this unit was in widespread use across southern Britain is available from the Folkton Drums from Yorkshire (neolithic artifacts, made from chalk, with circumferences that exactly divide as integers into ten long feet) and a similar object, the Lavant drum, excavated at Lavant, Sussex, again with a circumference divisible as a whole number into ten long feet.[20]

The measures of Iron Age Britain are uncertain and proposed reconstructions such as the Megalithic Yard are controversial. Later Welsh legend credited Dyfnwal Moelmud with the establishment of their units, including a foot of 9 inches. The Belgic or North German foot of Шаблон:Convert was introduced to England either by the Belgic Celts during their invasions prior to the Romans or by the Anglo-Saxons in the 5th and 6th century.

Roman units were introduced following their invasion in AD 43. Following the Roman withdrawal and Saxon invasions, the Roman foot continued to be used in the construction crafts while the Belgic foot was used for land measurement. Both the Welsh and Belgic feet seem to have been based on multiples of the barleycorn, but by as early as 950 the English kings seem to have (ineffectually) ordered measures to be based upon an iron yardstick at Winchester and then London. Henry I was said to have ordered a new standard to be based upon the length of his own arm and, by the Шаблон:Circa Act concerning the Composition of Yards and Perches[21] traditionally credited to Edward I or II, the statute foot was a different measure, exactly Шаблон:Sfrac of the old (Belgic) foot. The barleycorn, inch, ell, and yard were likewise shrunk, while rods and furlongs remained the same.[22] The ambiguity over the state of the mile was resolved by the 1593 Act against Converting of Great Houses into Several Tenements and for Restraint of Inmates and Inclosures in and near about the City of London and Westminster, which codified the statute mile as comprising 5,280 feet. The differences among the various physical standard yards around the world, revealed by increasingly powerful microscopes, eventually led to the 1959 adoption of the international foot defined in terms of the meter.

Definition

International foot

The international yard and pound agreement of July 1959 defined the length of the international yard in the United States and countries of the Commonwealth of Nations as exactly 0.9144 meters. Consequently, since a foot is one third of a yard, the international foot is defined to be equal to exactly 0.3048 meters. This was 2 ppm shorter than the previous US definition and 1.7 ppm longer than the previous British definition.[23]

The 1959 agreement concluded a series of step-by-step events, set off in particular by the British Standards Institution's adoption of a scientific standard inch of 25.4 millimetres in 1930.

Symbol

The IEEE standard symbol for a foot is "ft".[1] In some cases, the foot is denoted by a prime, often approximated by an apostrophe, and the inch by a double prime; for example, 2Шаблон:Nbspfeet 4 inches is sometimes denoted as 2′Шаблон:Nbsp4″.[24]

Imperial units

In Imperial units, the foot was defined as Шаблон:Sfrac yard, with the yard being realized as a physical standard (separate from the standard meter). The yard standards of the different Commonwealth countries were periodically compared with one another.[25] The value of the United Kingdom primary standard of the yard was determined in terms of the meter by the National Physical Laboratory in 1964 to be Шаблон:Val,[26] implying a pre-1959 UK foot of Шаблон:Val.

The UK adopted the international yard for all purposes through the Weights and Measures Act 1963, effective January 1, 1964.[27]

Survey foot

When the international foot was defined in 1959, a great deal of survey data was already available based on the former definitions, especially in the United States and in India. The small difference between the survey foot and the international foot would not be detectable on a survey of a small parcel, but becomes significant for mapping, or when the state plane coordinate system (SPCS) is used in the US, because the origin of the system may be hundreds of thousands of feet (hundreds of miles) from the point of interest. Hence the previous definitions continued to be used for surveying in the United States and India for many years, and are denoted survey feet to distinguish them from the international foot. The United Kingdom was unaffected by this problem, as the retriangulation of Great Britain (1936–62) had been done in meters.

US survey footШаблон:Anchor

In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 as 39.37 inches = 1 m (making a US foot exactly Шаблон:SfracШаблон:Nbspmeters, approximately Шаблон:Val).Шаблон:R[28] Out of 50 states and six other jurisdictions, 40 have legislated that surveying measures should be based on the US survey foot, six have legislated that they be made on the basis of the international foot, and ten have not specified.[29]

State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (two parts per million) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile).

The National Institute of Standards and Technology, National Geodetic Survey, and the United States Department of Commerce are phasing out the US survey foot beginning in 2023.[30][31][32] However, its relevance may persist, as the Federal Register Notice says:[33]

Шаблон:Quote

Indian survey foot

The Indian survey foot is defined as exactly Шаблон:Val,[34] presumably derived from a measurement of the previous Indian standard of the yard. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum,[35] which is also used by the Global Positioning System.

Historical use

Файл:Fußmaße1.jpg
Page from Austrian Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten – 1848[36] (Combined mathematics textbook for the fourth form of senior schools in the Imperial–royal states.)

Metric foot

An ISO 2848 measure of 3 basic modules (30 cm) is called a "metric foot",Шаблон:Cn but there were earlier distinct definitions of a metric foot during metrication in France and Germany.

France

In 1799 the metre became the official unit of length in France. This was not fully enforced, and in 1812 Napoleon introduced the system of mesures usuelles which restored the traditional French measurements in the retail trade, but redefined them in terms of metric units. The foot, or pied métrique, was defined as one third of a metre. This unit continued in use until 1837.[37]

Germany

In southwestern Germany in 1806, the Confederation of the Rhine was founded and three different reformed feet were defined, all of which were based on the metric system:[38]

Other obsolete feet

Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably in length: the Шаблон:Lang in Ypres, Belgium, was 273.8 millimeters (10.78Шаблон:Nbspin) while the Шаблон:Lang in Venice was 347.73 millimeters (13.690Шаблон:Nbspin). Lists of conversion factors between the various units of measure were given in many European reference works including:

Many of these standards were peculiar to a particular city, especially in Germany (which, before German unification in 1871, consisted of many kingdoms, principalities, free cities and so on). In many cases the length of the unit was not uniquely fixed: for example, the English foot was stated as 11 pouces 2.6 lignes (French inches and lines) by Picard, 11 pouces 3.11 lignes by Maskelyne, and 11 pouces 3 lignes by D'Alembert.[46]

Most of the various feet in this list ceased to be used when the countries adopted the metric system. The Netherlands and modern Belgium adopted the metric system in 1817, having used the Шаблон:Lang under Napoleon[47] and the newly formed German Empire adopted the metric system in 1871.[48]

The palm (typically 200–280 mm) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was publishedШаблон:Clarify in Belgium which had the smallest foot measurements, grouped both units together, while J. F. G. Palaiseau devoted three chapters to units of length: one for linear measures (palms and feet); one for cloth measures (ells); and one for distances traveled (miles and leagues).Шаблон:Citation needed

Obsolete feet details

In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.Шаблон:Citation needed

Location Modern country Local name Metric
equivalent
(mm)
Comments
Vienna Austria Шаблон:Lang 316.102[45][49]Шаблон:Circular inline
Tyrol Austria Шаблон:Lang 334.12[38]
Ypres (Ieper) Belgium Шаблон:Lang 273.8[50]
Bruges/Brugge Belgium Шаблон:Lang 274.3[50]
Brussels Belgium Шаблон:Lang 275.75[50]
Hainaut Belgium Шаблон:Lang 293.39[42]
Liège Belgium Шаблон:Lang 294.70[42]
Kortrijk Belgium Шаблон:Lang 297.6[50]
Aalst Belgium Шаблон:Lang 277.2[50]
Mechelen Belgium Шаблон:Lang 278.0[50]
Leuven Belgium Шаблон:Lang 285.5[50]
Tournai Belgium Шаблон:Lang 297.77[42]
Antwerp Belgium Шаблон:Lang 286.8[50]
China China tradesman's foot 338.3[51]
China China mathematician's foot 333.2[51]
China China builder's foot 322.8[51]
China China surveyor's foot 319.5[51]
Moravia Czech Republic Шаблон:Lang 295.95[38]
Prague Czech Republic Шаблон:Lang 296.4[44] (1851) Bohemian foot or shoe
301.7[39] (1759) Quoted as "11 Шаблон:Lang Шаблон:Sfrac Шаблон:Lang"[Notes 1]
Denmark Denmark Шаблон:Lang 313.85[45] Until 1835, thereafter the Prussian foot
330.5[39] (1759) Quoted as "Шаблон:Sfrac Шаблон:Lang larger than the Шаблон:Lang [of Paris]"[Notes 1]
France France Шаблон:Lang 324.84[52] [Notes 2]
Angoulême France Шаблон:Lang 347.008[53]
Bordeaux (urban) France Шаблон:Lang 343.606[53]
Bordeaux (rural) France Шаблон:Lang 357.214[53]
Strasbourg France Шаблон:Lang 294.95[53]
Württemberg Germany Шаблон:Lang 286.49[38]
Hanover Germany Шаблон:Lang 292.10[38]
Augsburg Germany Шаблон:Lang 296.17[43]
Nuremberg Germany Шаблон:Lang 303.75[43]
Meiningen-Hildburghausen Germany Шаблон:Lang 303.95[38]
Oldenburg Germany Шаблон:Lang 296.41[38]
Weimar Germany Шаблон:Lang 281.98[38]
Lübeck Germany Шаблон:Lang 287.62[45]
Aschaffenburg Germany Шаблон:Lang 287.5[42]
Darmstadt Germany Шаблон:Lang 287.6[42] Until 1818, thereafter the Hessen "metric foot"
Bremen Germany Шаблон:Lang 289.35[45]
Rhineland Germany Шаблон:Lang 313.7[51]
Berlin Germany Шаблон:Lang 309.6[51]
Hamburg Germany Шаблон:Lang 286.8[51]
Bavaria Germany Шаблон:Lang 291.86[38]
Aachen Germany Шаблон:Lang 282.1[43]
Leipzig Germany Шаблон:Lang 282.67[38]
Dresden Germany Шаблон:Lang 283.11[38]
Saxony Germany Шаблон:Lang 283.19[45]
Prussia Germany, Poland, Russia etc. Шаблон:Lang 313.85[45]
Frankfurt am Main Germany Шаблон:Lang 284.61[38]
Venice & Lombardy Italy 347.73[38]
Turin Italy 323.1[51]
Rome Italy Шаблон:Lang 297.896[53]
Riga Latvia Шаблон:Lang 274.1[51]
Malta Malta Шаблон:Lang 283.7[51]
Utrecht Netherlands Шаблон:Lang 272.8[51]
Amsterdam Netherlands Шаблон:Lang 283.133[41] Divided into 11 Шаблон:Lang (inches, Шаблон:Literally)
Шаблон:Ill Netherlands Шаблон:Lang 285.0[41]
's-Hertogenbosch Netherlands Шаблон:Lang 287.0[41]
Gelderland Netherlands Шаблон:Lang 292.0[41]
Bloois (Zeeland) Netherlands Шаблон:Lang 301.0[41]
Schouw Netherlands Шаблон:Lang 311.0[41]
Rotterdam Netherlands Шаблон:Lang 312.43[42]
Rijnland Netherlands Шаблон:Lang 314.858[41]
Norway Norway Шаблон:Lang 313.75[54] (1824–1835)[Notes 3] Thereafter as for Sweden.
Warsaw Poland Шаблон:Lang 297.8[55] Until 1819
288.0[42] (From 1819) Polish Шаблон:Lang
Lisbon Portugal Шаблон:Lang 330.0[43] (From 1835)[Notes 4]
South Africa South Africa Cape foot 314.858[56] Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859.
Burgos and Castile Spain Шаблон:Lang 278.6[39] (1759) Quoted as "122.43 Шаблон:Lang"[Notes 1]
Toledo Spain Шаблон:Lang 279.0[39] (1759) Quoted as "10 Шаблон:Lang 3.7 Шаблон:Lang"[Notes 1]
Sweden Sweden Шаблон:Lang 296.9[45] = 12 Шаблон:Lang (inches). The Swedish Шаблон:Lang was also used in Finland (Шаблон:Lang).
Zürich Switzerland 300.0[51]
Galicia Ukraine, Poland Шаблон:Lang 296.96[42] Part of Austria–Hungary before World War I
Scotland United Kingdom 305.287[57] [Notes 5]

In Belgium, the words Шаблон:Lang (French) and Шаблон:Lang (Dutch) would have been used interchangeably.Шаблон:Citation needed

Notes

  1. 1,0 1,1 1,2 1,3 The source document used pre-metric French units (Шаблон:Lang, Шаблон:Lang and Шаблон:Lang).
  2. The original meter was computed using pre-metric French units.
  3. The Norwegian Шаблон:Lang was defined in 1824 as the length of a (theoretical) pendulum that would have a period of Шаблон:Sfrac seconds at 45° from the equator.
  4. Prior to 1835, the Шаблон:Lang or foot was not used in Portugal; instead a palm was used. In 1835 the size of the palm was increased from 217.37 mm (according to Palaiseau) to 220 mm.
  5. The Scots foot ceased to be legal after the Act of Union in 1707.

Present day uses

International ISO-standard and other intermodal shipping containers

International Standards Organisation (ISO)-defined intermodal containers for efficient global freight/cargo shipping, were defined using feet rather than meters for their leading outside (corner) dimensions. All ISO-standard containers to this day are eight feet wide, and their outer heights and lengths are also primarily defined in, or derived from feet.
Quantities of global shipping containers are still primarily counted in Twenty-foot Equivalent Units, or TEUs.

Aviation

Everyday global (civilian) air traffic / aviation continues to be controlled in flight levels (flying altitudes) separated by thousands of feet (although typically read out in hundreds – e.g. flight level 330 actually means 33,000 feet, or about 10 kilometres in altitude).

Relation to shoe size

The length of the (international) foot corresponds to a human foot with shoe size of 13 (UK), 14 (US male), 15.5 (US female) or 48 (EU sizing).[58]Шаблон:Better source

Dimension

In measurement, the term "linear foot" (sometimes incorrectly referred to as "lineal foot") refers to the number of feet in a length of material (such as lumber or fabric) without regard to the width; it is used to distinguish from surface area in square foot.[59]

See also

Notes

  1. 1,0 1,1 The original reference was given in a round number of centimeters.

References

Шаблон:Reflist

Шаблон:Imperial units Шаблон:United States Customary Units Шаблон:Authority control

  1. 1,0 1,1 Шаблон:Cite web
  2. Шаблон:Cite book
  3. Шаблон:Cite book
  4. Шаблон:Cite book
  5. Шаблон:Cite news
  6. Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey that Transformed the World. London: Abacus.
  7. Weights and Measures Act Шаблон:Webarchive, accessed January 2012, Act current to January 18, 2012. Basis for units of measurement 4.(1) All units of measurement used in Canada shall be determined on the basis of the International System of Units established by the General Conference of Weights and Measures. (...) Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefore are as added pursuant to subparagraph 6(1)(b)(ii).
  8. Шаблон:Cite book
  9. Шаблон:Cite journal
  10. Kenoyer JM (2010) "Measuring the Harappan world," in Morley I & Renfrew C (edd) The Archaeology of Measurement, 117; Шаблон:Cite web
  11. Шаблон:Cite web
  12. Шаблон:Cite web
  13. Hosch, William L. (ed.) (2010) The Britannica Guide to Numbers and Measurement New York, NY: Britannica Educational Publications, 1st edition. Шаблон:ISBN, p.206
  14. Шаблон:Cite book
  15. Шаблон:Cite journal
  16. Шаблон:Cite web
  17. Шаблон:Cite journal
  18. Шаблон:Cite book
  19. Шаблон:Cite web
  20. Шаблон:Cite journal
  21. Шаблон:Cite book
  22. Шаблон:Cite book
  23. Шаблон:Cite web
  24. Шаблон:Cite book
  25. See, for example, Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with the Imperial Standard Yard and the Imperial Standard Pound and with each other during the Years 1947 to 1948 (H.M.S.O., London, 1950). Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with each other during the Year 1957 (H.M.S.O., London, 1958).
  26. Шаблон:Cite journal
  27. Thoburn v Sunderland City Council [2002] EWHC 195 (Admin) (18 February 2002)
  28. A. V. Astin & H. Arnold Karo (1959). "Refinement of values for the yard and the pound". Шаблон:Webarchive. Washington DC: National Bureau of Standards. Republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, filed June 30, 1959)
  29. "State Plane Coordinate System", National Geodetic Survey, May 4, 2019.
  30. "U.S. Survey Foot | NIST - Putting the Best 'Foot' Forward: Ending the Era of the U.S. Survey Foot (1959 to 2022)"Шаблон:Fcn
  31. "Measuring Unit Change Coming in 2022", National Geodetic Survey, June 14, 2019.
  32. Шаблон:Cite news
  33. Шаблон:Cite web
  34. Schedule to the Standards of Weights and Measures Act, 1976.
  35. Survey of India, "National Map Policy – 2005" Шаблон:Webarchive.
  36. Dr. Franz Mozhnik: Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten. Im Verlage der k.k. Schulbücher Verschleiß-Administration bey St. Anna in der Johannisgasse – Wien 1848
  37. Шаблон:Cite web
  38. 38,00 38,01 38,02 38,03 38,04 38,05 38,06 38,07 38,08 38,09 38,10 38,11 38,12 Шаблон:Cite web
  39. 39,0 39,1 39,2 39,3 39,4 Шаблон:Cite book
  40. Шаблон:Cite book
  41. 41,0 41,1 41,2 41,3 41,4 41,5 41,6 41,7 Шаблон:Cite book
  42. 42,0 42,1 42,2 42,3 42,4 42,5 42,6 42,7 42,8 Шаблон:Cite book
  43. 43,0 43,1 43,2 43,3 43,4 Шаблон:Cite book
  44. 44,0 44,1 Шаблон:Cite book
  45. 45,0 45,1 45,2 45,3 45,4 45,5 45,6 45,7 Шаблон:Cite book
  46. Шаблон:Cite web
  47. Шаблон:Cite book
  48. Шаблон:Cite webШаблон:Dead linkШаблон:Cbignore
  49. File
  50. 50,0 50,1 50,2 50,3 50,4 50,5 50,6 50,7 Шаблон:Cite web
  51. 51,00 51,01 51,02 51,03 51,04 51,05 51,06 51,07 51,08 51,09 51,10 51,11 Шаблон:Cite book
  52. Шаблон:Cite web
  53. 53,0 53,1 53,2 53,3 53,4 Шаблон:Cite journal
  54. Шаблон:Cite news
  55. Шаблон:Citation needed – Information copied from pl:Stopa polska
  56. Шаблон:Cite web
  57. Шаблон:Cite web
  58. Шаблон:Cite web (12×3=36. US(m): 36−22=14, UK: 36−23=13, EU:30.5×1.5=45.75 then +2 "for comfort" plus rounding = 48)
  59. Шаблон:Cite web