Foot (unit)

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1 foot =
US customary/Imperial units
12 in 1/3 yd
SI units
0.3048 m

A foot (plural: feet; abbreviation or symbol: ft or (the prime symbol)) is a unit of length. Since 1960 the term has usually referred to the international foot, defined as being one third of a yard, making it 0.3048 meters exactly. It is an integral part of both the imperial and United States customary systems of units. The foot is subdivided into 12 inches.

Historically the foot, which was used in Ancient Greece, Ancient Rome, England, Scotland and many Continental European countries and which varied from country to country and in some cases from city to city, was part local systems of units. 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 nation that uses the international foot and the survey foot (a customary unit of length) in preference to the meter in its commercial, engineering and standards activities.[1] The foot is still legally recognized as an alternative expression of length in Canada[2] officially defined as a unit derived from the meter[3] and still commonly used in the United Kingdom, although both have partially metricated their units of measurement. The measurement of altitude in the aviation industry is one of the few areas where the foot is widely used outside the English-speaking world.

Definition[edit]

International foot[edit]

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, the international foot is defined to be equal to exactly 0.3048 meters. This was 2 ppm shorter than the previous U.S definition and 1.7 ppm longer than the previous British definition.[4]

The international standard symbol for a foot is "ft" (see ISO 31-1, Annex A). In some cases, the foot is denoted by a prime, which is often marked by an apostrophe, and the inch by a double prime; for example, 2 feet 4 inches is sometimes denoted as 2′−4″, 2′ 4″ or 2′4″.

Survey foot[edit]

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 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 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.

The United States survey foot is defined as exactly 12003937 meter, approximately 0.3048006096 m.[5] In 1986 the National Geodetic Survey (NGS) released the North American Datum of 1983, which underlies the state plane coordinate systems and is entirely defined in meters. An NGS policy from 1991 has this to say about the units used with the new datum to define the SPCS 83:

In preparation for the adjustment of the North American Datum of 1983, 31 states enacted legislation for the State Plane Coordinate System of 1983 (SPCS 83). All states defined SPCS 83 with metric parameters. Within the legislation, the U.S. Survey Foot was specified in 11 states and the International Foot was specified in 6 states. In all other states the meter is the only referenced unit of measure in the SPCS 83 legislation. The remaining 19 states do not yet have any legislation concerning SPCS 83.[6]

Since then, 42 states have abandoned the non-metric versions of SPCS 83: 7 states continue to keep location data in survey feet as well as in meters, while one state keeps data in international feet as well as in meters.[7] State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2 ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). 24 states have legislated that surveying measures should be based on the U.S. survey foot, 8 have legislated that they be made on the basis of the international foot, and 18 have not specified the conversion factor from metric units.[7]

The Indian survey foot is defined as exactly 0.3047996 m,[8] 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,[9] which is also used by the Global Positioning System.

Pre-1959[edit]

In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 by 39.37 inches = 1 m. In Imperial units, the foot was defined as 13 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.[10] 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 as 0.9143969 m,[11] implying a pre-1959 foot in the UK of 0.3047990 m.

Historical units called the foot in different countries[edit]

Page from Austrian Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten – 1848[12]

Metric foot[edit]

In 1799 the meter 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 metrique, was defined as one third of a meter. This unit continued in use until 1837.[13]

Other "metric feet" were introduced into South Western Germany in 1806, when the Confederation of the Rhine was founded. Three different reformed feet were defined, all of which were based on the metric system:[14]

  • In Hesse, the Fuß (foot) was redefined as 25 cm.
  • In Baden, the Fuß was redefined as 30 cm.
  • In the Palatinate, the Fuß was redefined as being 3313 cm (as in France).

Other obsolete feet[edit]

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

  • Traite, Paris – 1769[15]
  • Palaiseau – Bordeaux: 1816 [16]
  • de Gelder, Amsterdam and 's-Gravenhage – 1824[17]
  • Horace, Brussels – 1840[18]
  • Noback & Noback (2 volumes), Leipzig – 1851[19][20]
  • Bruhns, Leipzig – 1881[21]

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.[22]

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 mesures usuelles under Napoleon[23] and the newly formed German Empire adopted the metric system in 1871.[24]

The palm (typically 200 mm to 280 mm) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was published[clarification needed] 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). In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.

Location Modern Country Local name Metric
equivalent
(mm)
Comments
Vienna Austria Wiener Fuß 316.102[21][25]
Tyrol Austria Fuß 334.12[14]
Ieper/Ypres Belgium voet 273.8[26]
Bruges/Brugge Belgium voet 274.3[26]
Brussels Belgium voet 275.75[26]
Hainaut Belgium pied 293.39[18]
Liège Belgium pied 294.70[18]
Kortrijk Belgium voet 297.6[26]
Aalst Belgium voet 277.2[26]
Mechelen Belgium voet 278.0[26]
Leuven Belgium voet 285.5[26]
Tournai Belgium pied 297.77[18]
Antwerp Belgium voet 286.8[26]
China China tradesman's foot 338.3[27]
China China mathematician's foot 333.2[27]
China China builder's foot 322.8[27]
China China surveyor's foot 319.5[27]
Moravia Czech Republic stopa 295.95[14]
Prague Czech Republic stopa 296.4[20] (1851) Bohemian foot or shoe
301.7[15] (1759) Quoted as "11 pouces 1¾ lignes"[Notes 1]
Denmark Denmark Fod 313.85[21] Until 1835, thereafter the Prussian foot
330.5[15] (1759) Quoted as "2½ lines larger than the pied [de Paris]"[Notes 1]
France France pied du roi 324.84[28] [Notes 2]
Angoulême France pied d'Angoulême 347.008[29]
Bordeaux (urban) France pied de ville de Bordeaux 343.606[29]
Bordeaux (rural) France pied de terre de Bordeaux 357.214[29]
Strasbourg France pied de Strasbourg 294.95[29]
Württemberg Germany Fuß 286.49[14]
Hanover Germany Fuß 292.10[14]
Augsburg Germany Römischer Fuß 296.17[19]
Nürnberg Germany Fuß 303.75[19]
Meiningen-Hildburghausen Germany Fuß 303.95[14]
Oldenburg Germany Römischer Fuß 296.41[14]
Weimar Germany Fuß 281.98[14]
Lübeck Germany Fuß 287.62[21]
Aschaffenburg Germany Fuß 287.5[18]
Darmstadt Germany Fuß 287.6[18] Until 1818, thereafter the Hessen "metric foot"
Bremen Germany Fuß 289.35[21]
Rhineland Germany Fuß 313.7[27]
Berlin Germany Fuß 309.6[27]
Hamburg Germany Fuß 286.8[27]
Bavaria Germany Fuß 291.86[14]
Aachen Germany Fuß 282.1[19]
Leipzig Germany Fuß 282.67[14]
Dresden Germany Fuß 283.11[14]
Saxony Germany Fuß 283.19[21]
Prussia Germany, Poland, Russia etc. Rheinfuß 313.85[21]
Frankfurt-am-Main Germany Fuß 284.61[14]
Venice & Lombardy Italy 347.73[14]
Turin Italy 323.1[27]
Rome Italy pied de Rome 297.896[29]
Malta Malta 283.7[27]
Utrecht Netherlands voet 272.8[27]
Amsterdam Netherlands voet 283.133[17] Divided into 11 duimen (inches)
Honsbossche en Rijpse Netherlands voet 285.0[17]
’s Hertogenbosch Netherlands voet 287.0[17]
Gelderland Netherlands voet 292.0[17]
Bloois (Zeeland) Netherlands voet 301.0[17]
Schouw Netherlands voet 311.0[17]
Rotterdam Netherlands voet 312.43[18]
Rijnland Netherlands voet 314.858[17]
Norway Norway fot 313.75[30] (1824–1835)[Notes 3] Thereafter as for Sweden
Warsaw Poland stopa 297.8[31] until 1819
288.0[18] (From 1819) Polish stopa
Lisbon Portugal 330.0[19] (From 1835)[Notes 4]
Moscow Russia 334.5[27]
Riga Latvia 274.1[27]
Saint Petersburg Russia 349.2[27]
South Africa South Africa Cape foot 314.858[32] Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859.
Burgos and Castile Spain Pie de Burgos/
Castellano
278.6[15] (1759) Quoted as "122.43 lignes"[Notes 1]
Toledo Spain Pie 279.0[15] (1759) Quoted as "10 pouces 3.7 lignes"[Notes 1]
Sweden Sweden fot 296.9[21] = 12 tum (inches)
Zurich Switzerland 300.0[27]
Galicia Ukraine stopa galicyjska 296.96[18] Part of Austria before World War I
Scotland United Kingdom Fuit, Fit, Troigh 305.287[33] [Notes 5]

(In Belgium, the words pied (French) and voet (Dutch) would have been used interchangeably.)

Notes

  1. ^ a b c d The source document used pre-metric French units (pied, pouce and lignes)
  2. ^ The original meter was computed using pre-metric French Units
  3. ^ The Norweigian fot was defined in 1824 as the length of a (theoretical) pendulum that would have a period 1238 s at 45° from the equator
  4. ^ Prior to 1835,the pé 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

Historical origin[edit]

See also: pous
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 Geometrei by Jakob Köbel (Frankfurt, c. 1536).

Historically the human body has been used to provide the basis for units of length.[34] The foot of a white male is typically about 15.3% of his height,[35] giving a person of 160 cm (5 ft 3 in) a foot of 245 mm and one of 180 cm (5 ft 11 in) a foot of 275 mm. These figures are less than the foot used in most cities over time, suggesting that the "foot" was actually a synonym for a "shoe".[original research?]

Archeologists believe that the Egyptians and Mesopotamians preferred the cubit while the Romans and the Greeks preferred the foot. 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 unciae (from which both the English words "inch" and "ounce" are derived). The Greek foot (ποὐς,pous) varied from city to city and ranged between 270 mm and 350 mm, but lengths used for temple construction appear to have been about 295 mm or 325 mm, the former being close to the size of the Roman foot. The standard Roman foot (pes) was normally about 295.7 mm, but in the provinces, the pes Drusianus (foot of Nero Claudius Drusus) with a length of about 334 mm was used. (In reality, this foot predated Drusus).[36]

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 toise and in particular the toise de l'Écritoire, the distance between the fingertips of the outstretched arms of a man.[37] The toise has 6 pied (feet) each of 326.6 mm (12.86 in).

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 296.1 mm was used; when it was rebuilt in the 10th century, a foot of about 320 mm[Note 1] was used. At the same time, monastic buildings used the Carolignian foot of 340 mm.[Note 1][38]

The procedure for verification of the foot as described in the 16th century by Jacob Koebel in his book Geometrei. Von künstlichem Feldmessen und absehen is:[39]

Stand at the door of a church on a Sunday and bid 16 men to stop, tall ones and small ones, as they happen to pass out when the service is finished; then make them put their left feet one behind the other, and the length thus obtained shall be a right and lawful rood to measure and survey the land with, and the 16th part of it shall be the right and lawful foot.

In England[edit]

Imperial measurement standards, Royal Observatory, Greenwich

The Roman foot was introduced to Britain in the 1st century AD. The length of the Roman foot has been estimated at 296 mm or 11.65 inches. In the 5th century, the Anglo-Saxons introduced the North German foot of 335 mm (13.2 inches). The new foot was used for land measurement, while the Roman foot continued to be used in the construction crafts. Some time between 1266 and 1303 the weights and measures of England were radically revised by a law known as the Composition of Yards and Perches (Compositio ulnarum et perticarum)[40] often known as the Compositio for short. This law, attributed to either Henry III or his successor Edward I, instituted a new foot that was exactly 10/11 the length of the old foot, with corresponding reductions in the size of the yard, ell, inch, and barleycorn. Miles, furlongs and rods, however, remained the same. The furlong remained an eighth of a mile, but changed from 600 old feet to 660 new feet. The rod remained the same length, but changed from 15 old feet to 1612 new feet.[41]

Ordinatum est, quod tria grana ordei sicca et rotunda faciunt pollicem, duodecim pollices faciunt pedem, tres pedes faciunt ulnam, quinque ulnae et dimidia faciunt perticam, et quadraginta perticae in longitudine et quatuor in latitudine faciunt unam acram. — Compositio ulnarum et perticarum

"It is ordained that three dry round grains of barley make an inch, 12 inches make a foot, three feet make a yard, five yards and a half make a perch, and 40 perches in length and four in breadth make one acre."

See also[edit]

Notes[edit]

  1. ^ a b The original reference was given in a round number of centimeters

References[edit]

  1. ^ "Appendix G – Weights and Measures". The World Factbook. Washington: Central Intelligence Agency. January 17, 2007. Retrieved February 4, 2007. 
  2. ^ Weights and Measures Act, accessed January 2012, Act current to 2012-01-18. 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).
  3. ^ Weights and Measures Act
  4. ^ "On what basis is one inch exactly equal to 25.4 mm? Has the imperial inch been adjusted to give this exact fit and if so when?". National Physical Laboratory. Retrieved July 24, 2012. 
  5. ^ A. V. Astin & H. Arnold Karo, (1959), Refinement of values for the yard and the pound, Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, June 30, 1959, 8:45 am)
  6. ^ National Geodetic Survey (January 1991), Policy of the National Geodetic Survey Concerning Units of Measure for the State Plane Coordinate System of 1983.
  7. ^ a b National Geodetic Survey (undated), "What are the "official" conversions that are used by NGS to convert 1) meters to inches, and 2) meters to feet?", Frequently Asked Questions about the National Geodetic Survey, retrieved May 16, 2009 
  8. ^ Schedule to the Standards of Weights and Measures Act, 1976.
  9. ^ Survey of India, "National Map Policy – 2005".
  10. ^ 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).
  11. ^ Bigg, P. H.; Anderton, Pamela (1964), "The United Kingdom standards of the yard in terms of the meter", Br. J. Appl. Phys. 15: 291–300, Bibcode:1964BJAP...15..291B, doi:10.1088/0508-3443/15/3/308 
  12. ^ 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
  13. ^ Denis Février. "Un historique du mètre" (in French). Ministère de l'Economie, des Finances et de l'Industrie. Retrieved March 10, 2011. 
  14. ^ a b c d e f g h i j k l m "Amtliche Maßeinheiten in Europa 1842" [Official measures in Europe 1842] (in German). Retrieved September 22, 2012. 
  15. ^ a b c d e d' Anville, Jean Baptiste Bourguignon (1769). Traité des mesures itinéraires anciennes et modernes [Treatise of ancient and modern measures of distance] (in French). Paris: de l'Imprimerie Royale. Retrieved October 24, 2011. 
  16. ^ Palaiseau, JFG (October 1816). Métrologie universelle, ancienne et moderne: ou rapport des poids et mesures des empires, royaumes, duchés et principautés des quatre parties du monde. Bordeaux. Retrieved October 30, 2011. 
  17. ^ a b c d e f g h Jacob de Gelder (1824). Allereerste Gronden der Cijferkunst [Introduction to Numeracy] (in Dutch). 's-Gravenhage (The Hague) and Amsterdam: de Gebroeders van Cleef. pp. 163–176. Retrieved March 2, 2011. 
  18. ^ a b c d e f g h i Doursther, Horace (1840). Dictionnaire universel des poids et mesures anciens et modernes. Bruxelles: M. Hayez. pp. 402–418. Retrieved October 25, 2011. 
  19. ^ a b c d e Noback, Christian; Noback, Friedrich Eduard (1851). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze [Comprehensive pocketbook of money, weights and measures for all counties and trading centres] (in German) I. Leipzig: F. А. Вrockhaus. Retrieved October 24, 2011. 
  20. ^ a b Noback, Christian; Noback, Friedrich Eduard (1851). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze [Comprehensive pocketbook of money, weights and measures for all counties and trading centres] (in German) II. Leipzig: F. А. Вrockhaus. Retrieved October 24, 2011. 
  21. ^ a b c d e f g h Bruhns, Carl (1881). new manual of logarithms to seven places of decimals. Leipzig: Bernhard Tauchnitz. p. 610. Retrieved October 26, 2011. 
  22. ^ Thomas Jefferson (July 13, 1790). "Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States". United States House of Representatives. Retrieved November 8, 2011. 
  23. ^ Jacob de Gelder (1824). Allereerste Gronden der Cijferkunst [Introduction to Numeracy] (in Dutch). 's-Gravenhage (The Hague) and Amsterdam: de Gebroeders van Cleef. pp. 155–157. Retrieved March 2, 2011. 
  24. ^ Andreas Dreizler et al (April 20, 2009). "Metrologie" (in German). Technische Universität Darmstadt. Retrieved March 28, 2011. 
  25. ^ File
  26. ^ a b c d e f g h "Maten en gewichten" [Weights and measures] (in Dutch). Vlaamse Vereniging voor Familiekunde (Flemish Association for Family History). 2011. Retrieved October 24, 2011. 
  27. ^ a b c d e f g h i j k l m n Rose, Joshua (1900). Pattern Makers Assistant (9th ed.). New York: D. van Nostrand Co. p. 264. 
  28. ^ "Les anciennes unités et leurs équivalences" [Old units and their equivalences] (in French). Le Cybergroupe Généalogique de Charente Poitevine. 2011. Retrieved February 25, 2011. 
  29. ^ a b c d e Guilhiermoz, P (1913). "De l'équivalence des anciennes mesures. A propos d'une publication récente" [Values of ancient measures quoted in recent publications]. Bibliothèque de l'École des chartes (in French) 74: 267–328. 
  30. ^ halbo, leif (July 21, 2005). "Mål, vekt og norsk selvstendighet" [Dimensions, weight and Norwegian independence]. Aftenposten. 
  31. ^ [citation needed] – Information copied from pl:Stopa polska
  32. ^ Tomasz Zakiewicz (April 2005). "The Cape Geodetic Standards and Their Impact on Africa". FIG, Cairo. Retrieved January 4, 2012. 
  33. ^ "Scottish Weights and Measures: Distance and Area". Scottish Archive Network. Retrieved January 28, 2010. 
  34. ^ Oswald Ashton Wentworth Dilke (May 22, 1987). Mathematics and measurement. University of California Press. p. 23. ISBN 978-0-520-06072-2. Retrieved February 2, 2012. 
  35. ^ Fessler, Daniel M; Haley, Kevin J; Lal, Roshni D (January–February 2005). "Sexual dimorphism in foot length proportionate to stature". Annals of Human Biology, 32 (1): 44–59. 
  36. ^ Oswald Ashton Wentworth Dilke (May 22, 1987). Mathematics and measurement. University of California Press. p. 26. ISBN 978-0-520-06072-2. Retrieved February 2, 2012. 
  37. ^ Russ Rowlett. "How Many? A Dictionary of Units of Measurement". Center for Mathematics and Science Education, University of North Carolina at Chapel Hill. Retrieved February 28, 2011. 
  38. ^ Sutherland, Elizabeth R (May 1957). "Feet and dates at Charlieu". Journal of the Society of Architectural Historians 16 (2). JSTOR 987740. 
  39. ^ Jacob Koebel (16th century). Geometrei. Von künstlichem Feldmessen und absehen (in German). 
  40. ^ Great Britain (1762). The statutes at large: from the Magna Charta, to the end of the eleventh Parliament of Great Britain, anno 1761 (continued to 1807). The statutes at large 1. Printed by J. Bentham. p. 400. Retrieved November 30, 2011. 
  41. ^ Zupko, Ronald Edward (1977). British Weights and Measures: A History from Antiquity to the Seventeenth Century. University of Wisconsin Press. pp. 6, 10, 20. ISBN 978-0-299-07340-4.