Representation of Derived Units in UnitsML (revised December 8, 2006)
Peter J. Linstrom∗
December 8, 2006
∗phone: (301) 975-5422,DRAFT e-mail: [email protected] 1 INTRODUCTION 12/8/06
Contents
1 Introduction 1
2 Why this convention is needed 2
3 Information needed to define a unit 3
4 Proposed XML encoding 4
5 Important conventions 7
6 Potential problems 8
7 Possible alternatives 10
A Multiplicative prefixes 12
B SI units and units acceptable for use with the SI 14
C non-SI Units 19
1 Introduction
This document describes a proposed convention for defining derived units in terms of their base units. This convention is intended for use in the UnitsML markup language to allow a precise definition of a wide range of units. The goal of this convention is to improve interoperability among applications and databases which use derived units based on commonly encountered base units. It is understoodDRAFT that not all units can be represented using this convention. It is, however,
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anticipated that a wide range of scientific and engineering units of measure can be represented with this convention.
The convention consists of representing the unit in terms of multiplicative combinations of base units. For example the unit centimeter per second squared would be represented in terms of the following:
1. The unit meter with the prefix centi raised to the power 1.
2. The unit second raised to the power −2.
Please note that this convention seeks to address the problem of defining derived units, not to define conversion factors. For this reason it will only support multiplication by constants which have defined prefixes.
2 Why this convention is needed
Without this convention, there is no easy way to reliably compare unit definitions from different sources to see if they are the same. The proposed symbolic identifier for UnitsML can be used for this purpose, but it is not parsable XML, so it requires a specialized parser and cannot be validated against an XML schema. As will be noted later, other than syntax, this proposal is similar to the symbolic identifier; the need to enumerate a set of base units and multiplicative prefixes is the same for both approaches.
Other identifying data in the current XML schema lacks the qualities which would make them useful for comparing unit definitions from different sources. Numeric identifiers are assigned by the author of the definition and thus are only useful for comparison within the context in which they were assigned. Names are obviously language specific. Even within a given language there may be multiple names for a given unit, so names may not be unique identifiers.
Under this proposal, information about the definition is provided in a structured format based on enumerated and external base units combined with multiplicative prefixes. This will allow comparison of unit definitions from different sources; something essential for interoperability of applications with different unit definition databases. Such comparison will be done by comparing base units, multiplicativeDRAFT prefixes, and exponents of units to see if they match.
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3 Information needed to define a unit
In order to define a unit in terms of other units the following information is needed for each unit which will be used in the definition: identifier An identifier which specifies the unit. prefix A code which notes a factor by which to multiply the unit. exponent numerator Numerator of the exponent to which the unit and prefix is raised. The expo- nent is expressed as a separate numerator and denominator to restrict it to rational numbers (by restricting the numerator and denominator to integers). The exponent is applied to both the unit and the prefix. exponent denominator Denominator of the exponent to which the unit and prefix is raised.
Base units may be specified via a controlled vocabulary or reference to an external database. This proposal defines a controlled vocabulary for units likely to be found in a wide range of endeav- ors. The units for the controlled vocabulary were chosen to cover a wide range of base units encountered in practice. The codes used to identify units in the controlled vocabulary are internal representations to be used by UnitsML. They are not to be confused with symbols to be used in text documents or official abbreviations for the units. For convenience purposes, codes for the units were taken from CEFACT Recommendation 20 [1] where possible. In cases where Recommenda- tion 20 does not define an appropriate code a, code was constructed from the unit name. Unlike the Recommendation 20 codes, these codes contain lower case letters and are solely intended for use in this controlled vocabulary. In most applications, users should never see the codes defined in the appendix.
Since it is not practical to enumerate all possible base units in a fixed controlled vocabulary, this proposal also allows base units from external databases to be specified. It is envisioned that this facility would only be used when a base unit is not in the controlled vocabulary, since use of such identifiers may limit interoperability.
It is proposed that only well defined units which are not explicitly derived units be used for base units. This would mean that named derived units, such as newtons, could be used, but explicitly derived units, such as acre-feet could not. Units such as acre-feet can be defined as derived units. There is one importantDRAFT and potentially controversial unit listed in table 24. The item unit refers to a count of items and can be used to note derived units which included such counts (e.g. neutron
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flux). This concept is at odds with the SI which assigns such counts a unit of 1. In this proposal it was chosen to include counts as a named unit, because some communities may find the semantic precision provided by this unit of value. It is anticipated that individual groups will decide if the use of this unit is of value for their applications. Thus it is likely that this unit will be used in some fields of endeavor (commerce), but not in others.
The units defined in the appendix have been taken from several sources [2, 3, 4, 5, 6, 7].
It is important to remember that this is a working document and that the list of units in the appendix is only an initial attempt at enumerating units to be defined. It is envisioned that units will be added or removed from the list based on input from the UnitsML developers. In addition, it should be recognized that the codes defined in this document are solely for enumerating base units in the XML schema; they are not intended for use in any way outside of representing derived units in UnitsML.
Proposed codes for prefixes are provided in appendix A. Supported prefixes include those defined by the SI and multipliers based on powers of two which are defined by the IEC.
Exponents are specified by indicating both an integer numerator and denominator. This avoids the problems associated with using floating point numbers to specify fractional quantities.
4 Proposed XML encoding
As noted above, derived units can be expressed as the product of base units with a multiplicative prefix raised to a specified power. It is proposed that such definitions be contained in an element named baseUnits. This element would contain elements for each base unit in the definition. Each base unit would be noted in an enumeratedBaseUnit or externalBaseUnit el- ement depending on whether or not the enumerated list or an external definition is used. The enumeratedBaseUnit element would have the following attributes: multiplier One of the codes for the multiplicative prefixes defined in appendix A. If omitted there is no prefix. unit One of theDRAFT unit codes defined in the appendix. This attribute is required.
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Figure 1: Representation for a cubic international foot.
Figure 2: Representation for centimeters to the three-halves power. numerator The numerator of the exponent which the unit and prefix is raised. The value should be an integer. The default value is one. denominator The denominator of the exponent to which the unit and prefix is raised. The value should be an integer, but must not be zero. The default value is one.
The externalBaseUnit element would also have the multiplier, numerator, and de- nominator elements as defined above. To specify units this element would include the following mandatory attributes: source URN which specifies the namespace for the unit identifier. unit Identifier (textttnumericID attribute) for a unit definition (unit element) at the resource specified by the URN noted above.
These attributes specify a unit defined by an external resource.
The baseUnits element is a child of the unit element. Only one baseUnits element per unit element would be allowed.
The proposed markup is best illustrated with a few examples. The text in figure 1 shows the relevant markup for a cubic international foot. Another example (showing the use of rational number exponents is the markup for centimeters to the three-halves power given in figure 2. The advantages ofDRAFT the proposed markup can be seen by looking at an example. Figures 3 and 4 both show markup for kilojoules per cubic meter. The markup comes from different sources and uses
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...
Figure 3: XML markup for kilojoules per liter from an application with the name in English.
...
Figure 4: XML markup for kilojoules per liter from an application with the name in Spanish. names in different languages. The elements defined in this proposal are in boldface text; all other elements are present in the current definition of UnitsML. In the two figures, the existing UnitsML provides names and a numeric identifier, neither of which can be used to compare the units. The numeric identifier cannot be used because these are tied to specific data sets, and therefore cannot be relied on for inter-comparison. The names cannot be relied on because, in this case, they are in different languages. Even if the same language is used, names are not reliable identifiers because they may be constructed differently for the same unit (e.g., foot-pounds versus pound- feet). Without information provided in the baseUnits element, it would be impossible to determine if the units are different or the same. In this case it can be seen that the units are the same. Figure 5 shows another unit for energy per volume. Examination of the base units quickly shows that this unit is quite differentDRAFT from that noted in figures 3 and 4.
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...
Figure 5: XML markup for thermochemical BTUs per cubic foot.
A final example, shown in figure 6 shows markup for degrees Reaumur per minute. Since degrees Reaumur is not an enumerated unit, it is necessary to refer to an external source for this definition. The source given in the example is fictional.
5 Important conventions
A problem arises when a unit can be expressed in terms of more than one set of base units. In such cases it it possible that two identical units may not be recognized as such. There are two ways this problem can occur:
1. Dimensionless base units such as radians or steradians are omitted.
2. There is a choice between representations which use SI special (named) derived units and those which use the SI base units which correspond to the derived units.
In order to minimize these problems, the following conventions should be employed when devel- oping a representation for a derived unit:
Don’t cancel units or omit dimensionless units. Canceling units (e.g. converting m · m−1 to 1) causes information to be lost. Likewise, inclusion of base units such as radians retains infor- mation thatDRAFT would otherwise be lost.
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...
Figure 6: XML markup for thermochemical degrees Reaumur per minute.
Use SI units for dimensionless ratios. A dimensionless ratio (e.g. length divided by length) can be expressed equally well with many different units. By standardizing on SI units for such ratios, there will only be one way of expressing a given ratio, making it easier to compare units. It should be noted that multiplicative prefixes can be applied to ratios. In such cases it is advised that the prefix be applied to the numerator rather than the denominator. An example of a dimensionless ratio is given in figure 7. When possible, use SI derived units instead of base units. The derived units provide more in- formation because they provide a logical grouping of the base units. It is more meaningful to express torque units as a force unit times a distance unit than the SI base units which make up the force unit and distance unit. Use the appropriate SI derived units for the area of endeavor. When representing torque (force times distance), one should use newton meters, while energy should be represented by joules.
6 Potential problems
This proposal may provide two implementation problems: lack of specificity in unit definitions, and conflict with the symbolic identifier. One drawback ofDRAFT this proposal is that it does not support version numbers. Version numbers may be used by a units database to distinguish between different definitions of a unit that is used over
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...
Figure 7: XML markup for a scaled dimensionless ratio. time. This means, for example, that this convention cannot distinguish between different versions of the meter. This drawback is particularly significant in the case of units based on experimental values (such as the electron-volt). Conversions between such units and the corresponding SI units may change over time as better experiments or theory provide more accurate measurements of the unit. This drawback is inherent in this proposal because version numbers are tied to a specific database – this proposal seeks to provide interoperability so it cannot be tied to a single data source. It should be noted that this proposal supports well known changes in unit definitions such as the difference between survey feet and international feet.
This proposal attempts to do much of what the proposed symbolic identifier intended to do; so there will be redundant features if both items are adopted into UnitsML. This proposal is arguably better than the symbolic identifier for the following reasons:
• All data is marked up in XML, so no specialized parser is needed to extract the data.
• Because prefix and common unit codes are XML attributes they can be validated using XML schema. XML schema can also be used to require that exponent numerators and denomina- tors be integers.
• There is no pressure to reduce the size of unit codes, so more readable codes can be used. Since the symbolic identifier is a single string, long codes could result in unmanageable string lengths.
As noted above the symbolic identifier has the advantage of being able to specify a version number. It also has the advantageDRAFT of being readily used as a query string.
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7 Possible alternatives
In addition to the approach outlined above, it is useful to consider possible alternative approaches. Alternatives include the proposed symbolic identifier, referring users to a pre-defined set of base units in a public database, or mapping ID codes from one database to another.
As noted above, this proposal is arguably superior to the proposed symbolic identifier for UnitsML because it uses XML syntax. There are, however, some advantages to the symbolic identifier. These advantages include a compact format and the ability to use the identifier in non-XML aware applications. The symbolic identifier, for example, could be readily encoded into a URL while the proposed representation scheme could not.
Another alternative could be to refer to a recommended set of base units in the UnitsML docu- mentation and not use the enumeratedBaseUnit element. For example, one could state that base units should be taken from the NIST UnitsDB whenever possible. This approach would have the advantage of not requiring the UnitsML language to enumerate common base units. However, without such an enumeration, it would be impossible for XML validators to detect erroneous base unit specifications in documents that use the enumerated units.
A third alternative is to do nothing at all and allow users and organizations to construct lists which map units from one database to another. The goal of this proposal is to reduce the need for such maps, but it should be assessed if the reduction in effort in mapping one unit set to anther is worth the effort required by this proposal.
References
[1] CEFACT Information Content Management Group. Recommendation no. 20: Codes for units of measure used in international trade, revision 4. Technical report, United Nations Economic Comission For Europe, Geneva, Switzerland, 2006.
[2] Barry N. Taylor, editor. Guide to the SI, with a focus on usage and unit conversions: NIST Special Publication 811. U.S. Government Printing Office, Washington, DC, 1995.
[3] Tina Butcher, Linda Crown, Richard Suiter, and Juana Williams, editors. Specifications, Toler- ances, and Other Technical Requirements for Weighing and Measuring Devices as adopted by the 88th National Conference on Weights and Measures 2003. National Institute of Standards and Technology,DRAFT Gaithersburg, MD, 2004.
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[4] Louis E. Barbrow and Lewis V. Judson. Weights and Measures Standards of the United States: A brief history. U.S. Government Printing Office, Washington, DC, 1976.
[5] The nist reference on constants, units, and uncertainty. http://physics.nist.gov/ cuu/index.html.
[6] Gunther Schadow and Clement J. McDonald. The unified code for units of measure. http: //aurora.rg.iupui.edu/˜schadow/units/UCUM/.
[7] I. M. Mills, B. N. Taylor, and A. J. Thor. Defnitions of the units radian, neper, bel and decibel. Metrologia, 38(4):353–361, 2001.
DRAFT
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A Multiplicative prefixes
Under this proposal multiplicative prefixes from the SI and IEC may be be applied to base units. The SI defines prefixes for powers of ten. These prefixes and codes to identify them are noted in table 1. IEC has defined for a series of prefixes based on powers of two. These prefixes and corresponding codes can be found in table 2
Prefix Symbol Code Factor yotta Y Y 1024 zetta Z Z 1021 exa E E 1018 peta P P 1015 tera T T 1012 giga G G 109 mega M M 106 kilo k k 103 hecto h h 102 deka da da 101 deci d d 10−1 centi c c 10−2 milli m m 10−3 micro µ u 10−6 nano n n 10−9 pico p p 10−12 femto f f 10−15 atto a a 10−18 zepto z z 10−21 yocto y y 10−24
Table 1: SI prefixes DRAFT
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Prefix Symbol Code Factor kibi Ki Ki 210 mebi Mi Mi 220 gibi Gi Gi 230 tebi Ti Ti 240 pebi Pi Pi 250 exbi Ei Ei 260
Table 2: IEC prefixes for binary multiples DRAFT
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B SI units and units acceptable for use with the SI
This proposal will support all SI units and those deemed acceptable for use with the SI. The tables noted below provide information on units and their proposed representation.
SI units and those which can be used with the SI fall into categories: base units These are units which are used to define other units. Proposed representations for these units are given in table 3. Please note that the gram is listed in place of the kilogram as the base unit. This deviation from the SI was done to make prefixes apply in a rational manner (since the kilogram already has a prefix applied). special derived units These are derived units which have been given a special name. These units are noted in table 4. derived units for human health These units are included in the SI for purposes of protecting human health. They are listed in table 5 units accepted for use with the SI These units, noted in table 6, are not part of the SI but can be used with the SI. units accepted for use with the SI in specific fields These units can only be used with the SI in specific fields of endeavor. They are noted in table 7. units temporarily accepted for use with the SI These units, listed in table 8 are allowed to be used with the SI on a temporary basis. DRAFT
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Unit name Symbol Code Quantity Comment meter m MTR length gram g GRM mass This is not an SI base unit; it is used here in place of the kilo- gram to make prefixes work as ex- pected. second s SEC time ampere A AMP electric current kelvin K KEL thermodynamic temperature mole mol C34 amount of substance candela cd CDL luminous intensity
Table 3: SI base units DRAFT
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Unit name Symbol Code Quantity Comment radian rad C81 plane angle m · m−1 steradian sr D27 solid angle m2 · m−2 hertz Hz HTZ frequency s−1 newton N NEW force m · kg · s−2 pascal Pa PAL pressure kg · m−1 · s−2 or N · m−2 joule J JOU energy kg · m2 · s−2 or N · m watt W WTT power kg · m2 · s−3 or J · s−1 coulomb C COU electric charge s · A volt V VLT electric kg · m2 · A−1 · s−3 or W / A potential farad F FAR capacitance A2 · s4 · kg−1 · m−2 or C / V ohm Ω OHM electric kg · m2 · A−2 · s−3 or V · A−1 resistance siemens S SIE electric A2 · s3 · kg−1 · m−2 or A · V−1 conductance weber Wb WEB magnetic flux kg · m2 · s−2 · A−1 or V · s tesla T D33 magnetic flux kg · A−1 · s−2 or Wb · m−2 density henry H 81 inductance kg · m2 · s−2 · A−2 or Wb · A−1 degree Celsius oC CEL temperature K −273.15 lumen lm LUM luminous flux cd · sr lux lx LUX illuminance cd · sr · m−2 or lm · m2 katal kat katal† catalytic mol · s−1 activity † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
Table 4: SI special derived units
Unit name Symbol Code Quantity Comment becquerel Bq BQL radionuclide s−1 activity gray Gy A95 absorbed dose m2 · s−2 or J · kg−1 sievert Sv D13 dose m2 · s−2 or J · kg−1 equivalent
DRAFTTable 5: SI derived units for human health
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Unit name Code Quantity Comment minute MIN time 60 seconds hour HUR time 60 minutes day DAY time 24 hours degree DD plane angle (π/180) radians minute D61 plane angle 1/60 of a degree second D62 plane angle 1/60 of a minute liter LTR volume 1 dm3 metric ton TNE mass 103 kg (synonym: tonne)
Table 6: Units accepted for use with the SI
Unit name Code Quantity Comment electron volt A53 energy The kinetic energy acquired by an electron in passing through a po- tential difference of 1 volt in a vac- uum. unified atomic D43 mass 1/12 of the mass of an atom of car- mass unit bon 12. astronomical unit A12 length Based on the mean earth sun distance, approximately 1.49597870 × 1011 meters DRAFTTable 7: Units accepted for use with the SI in specific fields
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Unit name Code Quantity Comment nautical mile NMI length 1852 meters knot KNT length 1 nautical mile per hour angstr˚ om¨ A11 length 10−10 meters are ARE area 100 square meters hectare HAR area 100 are or 104 square meters barn A14 area 10−28 square meters bar BAR pressure 105 pascals gal A76 velocity 1 cm · s−2 curie CUR radionucleotide 3.7 × 1010 becquerels activity roentgen 2C radiation 2.58 × 10−4 coulombs per kilo- exposure gram of air rad C80 absorbed dose 10−2 grays rem D91 dose 10−2 sieverts equivalent
Table 8: Units temporarily accepted for use with the SI DRAFT
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C non-SI Units
Several types of non-SI units are supported. Types of units supported include CGS (tables 9, 10, and 11), U.S. customary (tables 12, 13, 14, and 15) imperial (table 15), nutrition (tables 16, 17), and other (tables 18, 19, 20, 21, 22, 23, and 24)
The intent is not to support all such units, but to support ones widely used in current and historical practice. Units such as the perm which have poorly defined or conflicting definitions are omitted from these tables.
DRAFT
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Unit name Code Quantity Comment erg A57 energy 10−7 joules dyne DU force 10−5 newtons barye barye† pressure 1 dyne per square centimeter poise 89 viscosity 0.1 pascal seconds rhe rhe† inverse 10 inverse pascal seconds viscosity stoke 91 kinematic 10−4 square meters per second (synonym: viscosity stokes) darcy darcy† permeability The permeability of a one cen- timeter thick solid with a cross section of one square centimeter through which one cubic centime- ter of fluid, having a viscosity of one centipoise, will flow in one second when exposed to a pres- sure difference of one atmosphere. kayser kayser† wavenumber The number of wavelengths per centimeter. lambert lambert† luminance The luminance of a surface that emits or reflects one lumen per square centimeter. phot phot† illumination 1 lumen per square centimeter or 104 lux thermochemical D35 energy 4.184 joules calorie international R4 energy 4.1868 joules steam table calorie debye debye† dipole 10−18 statcoulomb centimeters moment † There is no corresponding code for this unit in UN CEFACT Recommendation 20. DRAFTTable 9: Some CGS units
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Unit name Code Quantity Comment abampere abampere† electric 10 amperes (synonym: biot) current abcoulomb abcoulomb† electric charge 10 coulombs abfarad abfarad† capacitance 109 farads abhenry abhenry† inductance 10−9 henrys abohm abohm† electric 10−9 ohms resistance abmho abmho† electric 109 siemens conductance abvolt abvolt† electric 10−8 volts potential abwatt abwatt† power 10−7 watt maxwell B65 magnetic flux 10−8 webers (synonyms: line, abweber) gauss 76 magnetic flux 10−4 teslas (synonym: density abtesla) gilbert gilbert† magnetic Defined as magnetic potential dif- potential ference around a closed path en- difference closing a surface through which flows a current of 1/(4π) abam- peres. oersted 66 magnetic field Defined as the strength of the mag- strength netic field at a distance of 1 cen- timeter from a straight conductor of infinite length and negligible circular cross section which car- ries a current of 0.5 abamperes. stilb stilb† luminance 1 candela per square centimeter † There is no corresponding code for this unit in UN CEFACT Recommendation 20. DRAFTTable 10: Units from the CGS electromagnetic system
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Unit name Code Quantity Comment statampere statampere† electric 1 statcoulomb per second. (synonym: current esampre) statcoulomb statcoulomb† electric charge The point charge which repels an (synonyms: equal point charge at a distance of escoulomb, 1 centimeter with a force of one franklin) dyne. statfarad statfarad† capacitance The capacitance such that a charge of 1 statcoulomb results in a po- tential increase of 1 statvolt. stathenry stathenry† inductance The self inductance of a circuit with a potential of 1 statvolt when subjected produced by a current change of one statampere per sec- ond. statohm statohm† electric The amount of electrical resis- resistance tance such that 1 statvolt of poten- tial across the circuit produces 1 statampere of current. statmho statmho† electric The amount of electrical conduc- conductance tance such that 1 statvolt of poten- tial across the circuit produces 1 statampere of current. statvolt statvolt† electric The potential such that the amount potential of work needed to move 1 stat- coulomb of electric charge is 1 erg. statwatt statwatt† power 10−7 watts statweber statweber† magnetic flux The magnetic flux which when linearly reduced to zero in a sin- gle turn circuit results in a e.m.f. of one statvolt. stattesla stattesla† magnetic flux 1 statweber per square centimeter density † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
DRAFTTable 11: Units from the CGS electrostatic system
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Unit name Code Quantity Comment long ton LTN mass 2240 avoirdupois pounds short ton STN mass 2000 avoirdupois pounds gross CWI mass 112 avoirdupois pounds hundredweight hundredweight CNT mass 100 avoirdupois pounds, also known as a cental avoirdupois LBR mass 4.5359237 × 10−1 kilograms pound avoirdupois OZ mass 1/16 of an avoirdupois pound ounce avoirdupois dram DRI mass 1/16 of an avoirdupois ounce. UN CEFACT Recommendation 20 refers to this unit as a dram (UK). troy pound LBT mass 144/175 of an avoirdupois pound, same as an apothecaries pound troy ounce APZ mass 1/12 of a troy pound, same as an apothecaries ounce pennyweight DWT mass 1/20 of a troy ounce apothecaries DRA mass 1/8 of a troy or apothecaries dram ounce. UN CEFACT Recommen- dation 20 refers to this unit as a dram (US). scruple SCR mass 1/3 of an apothecaries dram grain GRN mass 1/24 of a pennyweight or 1/5760 of a troy pound or 1/7000 of an avoirdupois pound; grains are the same in the avoirdupois, troy, and apothecaries systems. slug slug† mass The mass that one pound-force ac- celerates at one foot per second. † There is no corresponding code for this unit in UN CEFACT Recommendation 20. DRAFTTable 12: Customary units for mass
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Unit name Code Quantity Comment pound-force C78 force The force exerted by an avoirdupois pound when sub- jected to the standard acceleration of earth’s gravity (9.80665 m · s−2). poundal poundal† force The force required to accelerate an avoirdupois pound at 1 foot per second. kip kip† force 1000 pounds-force ton-force ton force† force 2000 pounds-force kilogram-force B37 force The force exerted by a kilo- gram when subjected to the stan- dard acceleration of earth’s gravity (9.80665 m · s−2). † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
Table 13: Customary units for force DRAFT
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Unit name Code Quantity Comment international inch INH length 1/12 of an international foot international foot FOT length 0.3048 meters international YRD length 3 international feet yard international mile length 5280 international feet mile U.S. survey inch survey inch† length 1/12 of a U.S. survey foot U.S. survey foot survey foot† length 1200/3937 meters U.S. survey yard survey yard† length 3 U.S. survey feet U.S. survey survey fathom† length 6 U.S. survey feet fathom U.S. survey rod survey rod† length 16.5 U.S. survey feet (synonyms: pole, perch) U.S. survey chain survey chain† length 4 U.S. survey rods (synonym: Gunter’s chain) U.S. survey link survey link† length 1/100 U.S. survey chain (synonym: Gunter’s link) U.S. survey survey furlong† length 40 rods or 660 U.S. survey feet furlong U.S. survey mile survey mile† length 5280 U.S. survey feet or 8 fur- (synonym: longs; known as a statute mile statute mile) in the U.S. The CEFACT Rec- ommendation 20 refers to a unit called mile (statute mile) with an SI equivalent value of 1609.344 m (which is the conversion factor for an international mile). Because of this ambiguity, the code from Rec- ommendation 20 is not used for the survey mile or the international mile. acre ACR area 43560 square U.S. survey feet † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
DRAFTTable 14: Customary units for length and area
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Unit name Code Quantity Comment imperial gallon GLI volume 4.54609 × 10−3 cubic meters imperial quart QTI volume 1/4 of an imperial gallon imperial pint PTI volume 1/2 of an imperial quart imperial gill GII volume 1/4 of an imperial pint imperial fluid OZI volume 1/5 of an imperial gill ounce U.S. liquid GLL volume 231 cubic international inches gallon U.S. liquid quart QTL volume 1/4 of a U.S. liquid gallon U.S. liquid pint PTL volume 1/2 of a U.S. liquid quart U.S. cup cup† volume 1/2 of a U.S. liquid pint U.S. gill GIA volume 1/4 of a U.S. liquid pint U.S. fluid ounce OZA volume 1/8 of a U.S. cup U.S. fluid dram fluid dram† volume 1/8 of a U.S. fluid ounce U.S. minim minim† volume 1/60 of a U.S. fluid ounce U.S. tablespoon tablespoon† volume 1/2 of a U.S. fluid ounce U.S. teaspoon teaspoon† volume 1/3 of a U.S. tablespoon U.S. bushel BUA dry volume 2150.42 cubic international inches U.S. peck PY dry volume 1/4 of a U.S. bushel U.S. dry quart QTD dry volume 1/8 of a U.S. peck U.S. dry pint PTD dry volume 1/2 of a U.S. dry quart † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
Table 15: Imperial and customary units for volume
Unit name Code Quantity Comment thermochemical E15 energy 4184 joules kilogram calorie international E14 energy 4186.8 joules steam table kilogram calorie DRAFTTable 16: Units used in nutrition.
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Unit name Code Quantity Comment label teaspoon label teaspoon† volume 5 mL label tablespoon label tablespoon† volume 15 mL label cup label cup† volume 240 mL label fluid ounce label fluid ounce† volume 30 mL label ounce label ounce† mass 28 g † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
Table 17: Units specified in U.S. regulations for food labels (21CFR101.9 b 5 viii).
Unit name Code Quantity Comment horsepower horsepower† power 550 pound-force per second. UN CEFACT Recommendation 20 de- fines a code (BHP) for a unit called brake horse power. Al- though the term brake horse power implies a specific quan- tity, it is probable that this unit is equivalent to the one specified in Recommendation 20. However, since this cannot be established with certainty, the Recommenda- tion 20 code is not used here. electric electric horsepower† power 746 watts horsepower boiler boiler horsepower† power defined by ASME horsepower metric HJ power horsepower water 5J power horsepower U.K. horsepower uk horsepower† power † There is no corresponding code for this unit in UN CEFACT Recommendation 20. DRAFTTable 18: Miscellaneous units for power
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Unit name Code Quantity Comment degree FAH temperature 9/5 × K − 459.67 Fahrenheit degree Rankine A48 temperature 9/5 × K
Table 19: Miscellaneous units for temperature
DRAFT
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Unit name Code Quantity Comment standard ATM pressure atmosphere technical ATT pressure atmosphere millimeter of Hg HN pressure (conventional) centimeter of Hg cm Hg† pressure (conventional) 0oC centimeter 0C cm Hg† pressure of Hg inch of Hg in Hg† pressure (conventional) 32oF inch of Hg 32F in Hg† pressure 60oF inch of Hg 60F in Hg† pressure foot of Hg ft Hg† pressure (conventional) millimeter of HP pressure water (conventional) centimeter of cm water† pressure water (conventional) 4oC centimeter 4C cm water† pressure of water inch of water IF pressure (conventional) 39.2oF inch of 39F in water† pressure water 60oF inch of 60F in water† pressure water foot of water ft water† pressure (conventional) 39.2oF foot of 39F ft water† pressure water † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
DRAFTTable 20: Miscellaneous units for pressure.
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Unit name Code Quantity Comment light year B57 length parsec C63 length printer’s pica R1 length computer pica computer pica† length 1/6 of an international inch printer’s point N3 length 1/72.27 of an international inch computer point computer point† length 1/72 of an international inch † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
Table 21: Miscellaneous length units. DRAFT
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Unit name Code Quantity Comment thermochemical thermo btu† energy British thermal unit international BTU energy 1.05505585262 joules steam table British thermal unit mean BTU mean btu† energy 1/180 of the quantity of heat needed to raise the temperature of one avoirdupois pound of water from 32oF to 212oF. 39oF British 39F btu† energy The amount of heat needed to thermal unit raise the temperature of one avoirdupois pound by one degree Fahrenheit at 39oF. 59oF British 59F btu† energy The amount of heat needed to thermal unit raise the temperature of one avoirdupois pound by one degree Fahrenheit at 59oF. 60oF British 60F btu† energy The amount of heat needed to thermal unit raise the temperature of one avoirdupois pound by one degree Fahrenheit at 60oF. tons of TNT tons of tnt† energy 4.184 × 109 joules E.C. therm TD energy 105 international steam table BTU. U.S. therm us therm† energy 105 59oF BTU. † There is no corresponding code for this unit in UN CEFACT Recommendation 20. DRAFTTable 22: Miscellaneous energy units.
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Unit name Code Quantity Comment year ANN time 365 days tropical year D42 time The time for the Earth to complete one revolution of its orbit, as mea- sured in the frame defined by the intersection of the ecliptic and the equator. sidereal year sidereal year† time The time for the Earth to complete one revolution of its orbit, as mea- sured in a fixed frame of reference. sidereal day sidereal day† time The time for the Earth to com- plete one rotation, as measured in a fixed frame of reference. sidereal hour sidereal hour† time 1/24 of a sidereal day sidereal minute sidereal minute† time 1/60 of a sidereal hour sidereal second sidereal second† time 1/60 of a sidereal minute shake shake† time 10−8 seconds † There is no corresponding code for this unit in UN CEFACT Recommendation 20.
Table 23: Miscellaneous time units. DRAFT
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Unit name Code Quantity Comment item item† count Used to note cases where discrete items are counted. The SI does not recognize a unit for this purpose. denier A49 linear density grams per 9000 meters tex D34 linear density 10−6 kilograms per meter gon A91 plane angle 1/400 of a revolution (synonyms: grade, gradian) mil (NATO) NATO mil† plane angle 1/6400 of a revolution. Other mil- (synonym: itaries have used other definitions angular mil) for the mil. pound mole pound mole† amount of The amount of substance such that substance its mass in avoirdupois pounds is equal to its molecular (or atomic weight) in unified atomic mass units. ton of ton refrigeration† heat flow rate 12000 international steam table refrigeration BTUs per hour circular mil circular mil† area the area of a circle that is 1 mil (1/1000 of an inch) in diameter bel bel† ratio Common logarithm of an intensity or power ratio. neper C50 ratio Natural logarithm of an amplitude ratio. pH pH† concentration Negative common logarithm of moles per liter. petroleum barrel BLL volume 42 U.S. gallons footlambert footlambert† luminance 1/π candela per square foot footcandle footcandle† illuminance the illuminance at 1 foot from a 1 candela point source of light metric carat CTM mass 0.2 grams † There is no corresponding code for this unit in UN CEFACT Recommendation 20. DRAFTTable 24: Miscellaneous units.
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