Foot (unit)

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 in a number of different systems including Ancient Greek, Ancient Roman, English units, Imperial units, United States customary units and the units of many Continental European countries. Its size varied from system to system, but in each is around a quarter to a third of a metre and most but not all were subdivided into 12 inches. The U.S. is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities,[1] and uses the international foot (a customary unit of length) and the survey foot. The foot is still commonly used in the United Kingdom, which has partially metricated in some walks of life.

Contents

Definition

International foot

On July 1, 1959, the length of the international yard in the United States and countries of the Commonwealth of Nations was defined as 0.9144 metres. Consequently, the international foot is defined to be equal to exactly 0.3048 metres (equivalent to 304.8 millimetres). This was 2 ppm shorter than the previous U.S definition and 1.7 ppm longer than the previous British definition.[2]

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 approximated 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

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 a state plane coordinate system is used, 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 in use for surveying in the US 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 metres.

The United States survey foot is defined as exactly 1200⁄3937 metres, approximately 0.3048006096 m.[3] 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.[4]

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 metres, while one state keeps data in international feet as well as in meters.[5] 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.[5]

The Indian survey foot is defined as exactly 0.3047996 m,[6] 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,[7] which is also used by the Global Positioning System.

Pre-1959

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 1⁄3 yard, with the yard being realized as a physical standard (separate from the standard metre). The yard standards of the different Commonwealth countries were periodically compared with one another.[8] The value of the United Kingdom primary standard of the yard was determined in terms of the metre by the National Physical Laboratory in 1964 as 0.9143969 m,[9] implying a pre-1959 foot in the UK of 0.3047990 m.

Obsolete use in different countries

Metric foot

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 metrique" was defined as one third of a metre. This unit of measure continued in use until 1837.[11]

Other metric feet were introduced into what is now South Western Germany when, in 1806, the Confederation of the Rhine was founded. Three different reformed feet were defined, all of which were based on the metric system:[12]

Other obsolete feet

Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably: 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). A list of conversions between the various units of measure were catalogued 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 conversion factors varied, depending on who took them - for example, the English foot was measured 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.[20]

Most of the various feet in this list ceased to be used as the countries concerned adopted the metric system: the Netherlands and modern Belgium adopted the metric system in 1817 having used the mesures usuelles under Napoleon[21] and newly formed German Empire adopted the metric system in 1871 as its system of measure[22]

The palm (typically 200 mm to 280 mm) was used in many Mediterranean cities instead of the foot - Horace, whose reference was published in Belgium which had the smallest foot measurements groups both units together while Palaiseau devoted three chapters to units of length - one for linear measures (palms and feet), one for cloth measures (ells) and one for distances travelled (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 Fuß 316.11[19]
Tyrol Austria fuß 334.12[12]
Ieper/Ypres Belgium voet 273.8[23]
Brugge Belgium voet 274.3[23]
Brussels Belgium voet 275.75[23]
Hainaut Belgium pied 293.39[16]
Liege Belgium pied 294.70[16]
Kortrijk Belgium voet 297.6[23]
Aalst Belgium voet 277.2[23]
Mechelen Belgium voet 278.0[23]
Leuven Belgium voet 285.5[23]
Tournai Belgium pied 297.77[16]
Antwerp Belgium voet 286.8[23]
Moravia Czech Republic stopa 295.95[12]
Prague Czech Republic stopa 296.4[18] (1851) Bohemian foot or shoe
301.7[13] (1759) Quoted as "11 pouces 1¾ lignes"[Notes 1]
Denmark Denmark fod 313.85[19] Until 1835, thereafter the Prussian foot
330.5[13] (1759) Quoted as "2½ lines larger than the pied [de Paris]"[Notes 1]
France France pied du roi 324.84[24] [Notes 2]
Angoulême France pied d'Angoulême 347.008[25]
Bordeaux (urban) France pied de ville de Bordeaux 343.606[25]
Bordeaux (rural) France pied de terre de Bordeaux 357.214[25]
Strasbourg France pied de Strasbourg 294.95[25]
Württemberg Germany fuß 286.49[12]
Hanover Germany fuß 292.10[12]
Augsburg Germany Römischer Fuß 296.17[17]
Nürnberg Germany Fuß 303.75[17]
Meiningen-Hildburghausen Germany Fuß 303.95[12]
Oldenburg Germany Römischer Fuß 296.41[12]
Weimar Germany fuß 281.98[12]
Lübeck Germany fuß 287.62[19]
Aschaffenburg Germany fuß 287.5[16]
Darmstadt Germany fuß 287.6[16] Unitl 1818, thereafter the Hessen "metric foot"
Bremen Germany fuß 289.35[19]
Bavaria Germany fuß 291.86[12]
Aachen Germany fuß 282.1[17]
Leipzig Germany fuß 282.67[12]
Dresden Germany fuß 283.11[12]
Saxony Germany fuß 283.19[19]
Prussia Germany Rheinfuß 313.85[19]
Frankfurt-am-Main Germany fuß 284.61[12]
Venice & Lombardy Italy 347.73[12]
Rome Italy pied de Rome 297.896[25]
Amsterdam Netherlands voet 283.133[15] Divided into 11 duimen (inches)
Honsbossche en Rijpse Netherlands voet 285.0[15]
’s Hertogenbosch Netherlands voet 287.0[15]
Gelderland Netherlands voet 292.0[15]
Bloois (Zeeland) Netherlands voet 301.0[15]
Schouw Netherlands voet 311.0[15]
Rotterdam Netherlands voet 312.43[16]
Rijnland Netherlands voet 314.858[15]
Norway Norway fot 313.75[26] (1824 - 1835)[Notes 3] Thereafter as for Sweden
Warsaw Poland stopa 297.8[27] until 1819
288.0[16] (From 1819) Polish stopa
Lisbon Portugal Pé 330.0[17] (From 1835) [Notes 4]
South Africa South Africa Cape foot 314.858[15] Identical to the Rijnland foot
Burgos and Castile Spain Pie de Burgos/
Castellano		 278.6[13] (1759) Quoted as "122.43 lignes"[Notes 1]
Toledo Spain Pie 279.0[13] (1759) Quoted as "10 pouces 3.7 lignes"[Notes 1]
Sweden Sweden fot 296.9[19] = 12 tum (inches)
Galicia Ukraine stopa galicyjska 296.96[16] Part of Austria before World War I
Scotland United Kingdom Fuit, Fit, Troigh 305.287[28] [Notes 5]

Notes

  1. ^ a b c d The source document used pre-metric French units (pied, pouce and lignes)
  2. ^ The original metre 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 12⁄38 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

Historically the human body has been used to provide the basis for units of length.[29] The foot of a Caucasian male is about 15.3% of their height,[30] giving a person of 160 cm (5 ft 3 in) a foot of 245 mm and one of 180 cm (5 ft 10 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".

Archeologists believe that the Egyptians, Mesopotamians favoured the cubit while the Romans and the Greeks favoured 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 unica (from which both the English words "inch" and "ounce" are derived). The Greek foot (pous) varied from city to city and ranged between 270 mm and 350 mm, but lengths used for temple construction appear to be about 295 mm and 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) having a length of about 334 mm was used. (In reality, this foot predated Drusus).[29]

After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In 790 AD Charlemagne attempted to reform the units of measure in his domains by placing them on a sound basis. 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.[31] 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 ninth century, the Roman foot 296.1 mm was used, during its rebuilding in the tenth century a foot of 320 mm[Note 1] was used. At the same time, monastic buildings used the Carolignian foot of 340 mm.[Note 1][32]

The verification of the foot as described in the 16th century by Jacob Koebel in his book Geometrei. Von künstlichem Feldmessen und absehen is:[33]

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

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)[34] 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. 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 16 1/2 new feet.[35]

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

See also

Notes

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

References

  1. ^ "Appendix G - Weights and Measures". The World Factbook. Washington: Central Intelligence Agency. January 17, 2007. https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html. Retrieved February 4, 2007. 
  2. ^ "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. http://www.npl.co.uk/reference/faqs/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-(faq-length). Retrieved 2010-07-13. 
  3. ^ 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 a.m.)
  4. ^ National Geodetic Survey, (January 1991), "Policy of the National Geodetic Survey Concerning Units of Measure for the State Plane Coordinate System of 1983.
  5. ^ a b National Geodetic Survey (undated), "What are the 'official' conversions that are used by NGS to convert 1) metres to inches, and 2) metres to feet?", Frequently Asked Questions about the National Geodetic Survey, http://www.ngs.noaa.gov/faq.shtml#Feet, retrieved May 16, 2009 
  6. ^ Schedule to the Standards of Weights and Measures Act, 1976.
  7. ^ Survey of India, "National Map Policy – 2005".
  8. ^ 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).
  9. ^ Bigg, P. H.; Anderton, Pamela (1964), "The United Kingdom standards of the yard in terms of the metre", Br. J. Appl. Phys. 15: 291–300, doi:10.1088/0508-3443/15/3/308, http://www.iop.org/EJ/abstract/0508-3443/15/3/308/ 
  10. ^ 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
  11. ^ Denis Février. "Un historique du mètre" (in French). Ministère de l'Economie, des Finances et de l'Industrie. http://www.industrie.gouv.fr/metro/aquoisert/metre.htm. Retrieved 2011-03-10. 
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  19. ^ 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. http://books.google.co.uk/books?id=GoMNAQAAIAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false. Retrieved 26 October 2011. 
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  21. ^ Jacob de Gelder (1824) (in Dutch). Allereerste Gronden der Cijferkunst [Introduction to Numeracy]. 's Gravenhage and Amsterdam: de Gebroeders van Cleef. pp. 155–157. http://books.google.co.uk/books?id=XYVbAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false. Retrieved 2011-03-02. 
  22. ^ Andreas Dreizler et al (20 April 2009). "Metrologie" (in German). Technische Universität Darmstaft. http://www.csi.tu-darmstadt.de/media/csi/institutes/nearwallreactiveflows/bilderdateien_1/messtechnik/mtmnormen.pdf. Retrieved 2011-03-28. 
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  27. ^ - Information copied from pl:Stopa polska
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  34. ^ 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. http://books.google.com/books?id=iPQuAAAAIAAJ&pg=PA400&dq=Compositio+ulnarum+et+perticarum&hl=en&ei=_VnWTprrH6eliQKV2-irDA&sa=X&oi=book_result&ct=result&resnum=10&ved=0CGAQ6AEwCQ#v=onepage&q=Compositio%20ulnarum%20et%20perticarum&f=false. Retrieved 30 November 2011. 
  35. ^ 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 978-0299073404. http://books.google.com/books?ei=3qnTTpOjBqqRiALly43SCw&ct=result&id=pWUgAQAAIAAJ&dq=zupko&q=millimeters#search_anchor. 

External links