# # This file is the units database for use with GNU units, a units conversion # program by Adrian Mariano adrianm@gnu.org # # May 2019 Version 3.04 # # Copyright (C) 1996-2002, 2004-2019 # Free Software Foundation, Inc # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 51 Franklin Street, Fifth Floor, # Boston, MA 02110-1301 USA # ############################################################################ # # Improvements and corrections are welcome. # # Fundamental constants in this file are the 2018 CODATA recommended values. # # Most units data was drawn from # 1. NIST Special Publication 811, Guide for the # Use of the International System of Units (SI). # Barry N. Taylor. 2008 # https://www.nist.gov/pml/special-publication-811 # 2. CRC Handbook of Chemistry and Physics 70th edition # 3. Oxford English Dictionary # 4. Webster's New Universal Unabridged Dictionary # 5. Units of Measure by Stephen Dresner # 6. A Dictionary of English Weights and Measures by Ronald Zupko # 7. British Weights and Measures by Ronald Zupko # 8. Realm of Measure by Isaac Asimov # 9. United States standards of weights and measures, their # creation and creators by Arthur H. Frazier. # 10. French weights and measures before the Revolution: a # dictionary of provincial and local units by Ronald Zupko # 11. Weights and Measures: their ancient origins and their # development in Great Britain up to AD 1855 by FG Skinner # 12. The World of Measurements by H. Arthur Klein # 13. For Good Measure by William Johnstone # 14. NTC's Encyclopedia of International Weights and Measures # by William Johnstone # 15. Sizes by John Lord # 16. Sizesaurus by Stephen Strauss # 17. CODATA Recommended Values of Physical Constants available at # http://physics.nist.gov/cuu/Constants/index.html # 18. How Many? A Dictionary of Units of Measurement. Available at # http://www.unc.edu/~rowlett/units/index.html # 19. Numericana. http://www.numericana.com # 20. UK history of measurement # http://www.ukmetrication.com/history.htm # 21. NIST Handbook 44, Specifications, Tolerances, and # Other Technical Requirements for Weighing and Measuring # Devices. 2011 # 22. NIST Special Publication 447, Weights and Measures Standards # of the the United States: a brief history. Lewis V. Judson. # 1963; rev. 1976 # 23. CRC Handbook of Chemistry and Physics, 96th edition # 24. Dictionary of Scientific Units, 6th ed. H.G. Jerrard and D.B. # McNeill. 1992 # 25. NIST Special Publication 330, The International System of # Units (SI). ed. Barry N. Taylor and Ambler Thompson. 2008 # https://www.nist.gov/pml/special-publication-330 # 26. BIPM Brochure, The International System of Units (SI). # 9th ed., 2019 # https://www.bipm.org/en/publications/si-brochure/ # ########################################################################### # # If units you use are missing or defined incorrectly, please contact me. # If your country's local units are missing and you are willing to supply # them, please send me a list. # ########################################################################### ########################################################################### # # Brief Philosophy of this file # # Most unit definitions are made in terms of integers or simple fractions of # other definitions. The typical exceptions are when converting between two # different unit systems, or the values of measured physical constants. In # this file definitions are given in the most natural and revealing way in # terms of integer factors. # # If you make changes be sure to run 'units --check' to check your work. # # The file is USA-centric, but there is some modest effort to support other # countries. This file is now coded in UTF-8. To support environments where # UTF-8 is not available, definitions that require this character set are # wrapped in !utf8 directives. # # When a unit name is used in different countries with the different meanings # the system should be as follows: # # Suppose countries ABC and XYZ both use the "foo". Then globally define # # ABCfoo # XYZfoo # # Then, using the !locale directive, define the "foo" appropriately for each of # the two countries with a definition like # # !locale ABC # foo ABCfoo # !endlocale # ########################################################################### !locale en_US ! set UNITS_ENGLISH US !endlocale !locale en_GB ! set UNITS_ENGLISH GB !endlocale !set UNITS_ENGLISH US # Default setting for English units !set UNITS_SYSTEM default # Set a default value !varnot UNITS_SYSTEM si emu esu gaussian gauss default !message Unknown unit system given with -u or UNITS_SYSTEM environment variable !message Valid systems: si, emu, esu, gauss[ian] !message Using SI !prompt (SI) !endvar !var UNITS_SYSTEM si !message SI units selected !prompt (SI) !endvar ########################################################################### # # # Primitive units. Any unit defined to contain a '!' character is a # # primitive unit which will not be reduced any further. All units should # # reduce to primitive units. # # # ########################################################################### # # SI units # # On 20 May 2019, the SI was revised to define the units by fixing the # values of physical constants that depend on those units. # # https://www.nist.gov/si-redefinition/ # # The BIPM--the International Bureau of Weights and Measures--provides a # succinct description of the new SI in its Concise Summary: # # https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-concise-EN.pdf # # The SI is the system of units in which: # # * the unperturbed ground state hyperfine transition frequency of the # caesium 133 atom is delta nu_Cs = 9 192 631 770 Hz, # * the speed of light in vacuum, c, is 299 792 458 m/s, # * the Planck constant, h, is 6.626 070 15 * 10^-34 J s, # * the elementary charge, e, is 1.602 176 634 * 10^-19 C, # * the Boltzmann constant, k, is 1.380 649 * 10^-23 J/K, # * the Avogadro constant, N_A, is 6.022 140 76 * 10^23 mol^-1, # * the luminous efficacy of monochromatic radiation of frequency # 540 * 10^12 Hz, K_cd, is 683 lm/W, # # where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, # J, C, lm, and W, respectively, are related to the units second, metre, # kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, # A, K, mol, and cd, respectively, according to Hz = s^–1, J = kg m^2 s^–2, # C = A s, lm = cd m^2 m^–2 = cd sr, and W = kg m^2 s^–3. # # These definitions specify the exact numerical value of each constant when # its value is expressed in the corresponding SI unit. By fixing the exact # numerical value the unit becomes defined, since the product of the # numerical value and the unit has to equal the value of the constant, # which is invariant. # # The defining constants have been chosen such that, when taken together, # their units cover all of the units of the SI. In general, there is no # one-to-one correspondence between the defining constants and the SI base # units. Any SI unit is a product of powers of these seven constants and a # dimensionless factor. # # Until 2018, the SI was defined in terms of base units and derived units. # These categories are no longer essential in the SI, but they are maintained # in view of their convenience and widespread use. They are arguably more # intuitive than the new definitions. (They are also essential to the # operation of GNU units.) The definitions of the base units, which follow # from the definition of the SI in terms of the seven defining constants, are # given below. # s ! # The second, symbol s, is the SI unit of time. It is defined second s # by taking the fixed numerical value of the unperturbed # ground-state hyperfine transition frequency of the # cesium-133 atom to be 9 192 1631 770 when expressed in the # unit Hz, which is equal to 1/s. # # This definition is a restatement of the previous one, the # duration of 9192631770 periods of the radiation corresponding # to the cesium-133 transition. c 299792458 m/s # speed of light in vacuum (exact) m ! # The metre, symbol m, is the SI unit of length. It is meter m # defined by taking the fixed numerical value of the speed metre m # of light in vacuum, c, to be 299 792 458 when expressed in # units of m/s. # # This definition is a rewording of the previous one and is # equivalent to defining the meter as the distance light # travels in 1|299792458 seconds. The meter was originally # intended to be 1e-7 of the length along a meridian from the # equator to a pole. h 6.62607015e-34 J s # Planck constant (exact) kg ! # The kilogram, symbol kg, is the SI unit of mass. It is kilogram kg # defined by taking the fixed numerical value of the Planck # constant, h, to be 6.626 070 15 * 10^-34 when expressed in # the unit J s which is equal to kg m^2 / s. # # One advantage of fixing h to define the kilogram is that this # affects constants used to define the ampere. If the kg were # defined by directly fixing the mass of something, then h # would be subject to error. # # The previous definition of the kilogram was the mass of the # international prototype kilogram. The kilogram was the last # unit whose definition relied on reference to an artifact. # # It is not obvious what this new definition means, or # intuitively how fixing Planck's constant defines the # kilogram. To define the kilogram we need to give the mass # of some reference in kilograms. Previously the prototype in # France served as this reference, and it weighed exactly 1 # kg. But the reference can have any weight as long as you # know the weight of the reference. The new definition uses # the "mass" of a photon, or more accurately, the mass # equivalent of the energy of a photon. The energy of a # photon depends on its frequency. If you pick a frequency, # f, then the energy of the photon is hf, and hence the mass # equivalent is hf/c^2. If we reduce this expression using # the constant defined values for h and c the result is a # value in kilograms for the mass-equivalent of a photon of # frequency f, which can therefore define the size of the # kilogram. # # For more on the relationship between mass an Planck's # constant: # # https://www.nist.gov/si-redefinition/kilogram-mass-and-planck s-constant # This definition may still seem rather abstract: you can't # place a "kilogram of radiation" on one side of a balance. # Metrologists realize the kilogram using a Kibble Balance, a # device which relates mechanical energy to electrical energy # and can measure mass with extreme accuracy if h is known. # # For more on the Kibble Balance see # # https://www.nist.gov/si-redefinition/kilogram-kibble-balance # https://en.wikipedia.org/wiki/Kibble_balance boltzmann 1.380649e-23 J/K # Boltzmann constant (exact) k boltzmann K ! # The kelvin, symbol K, is the SI unit of thermodynamic kelvin K # temperature. It is defined by taking the fixed numerical # value of the Boltzmann constant, k, to be 1.380 649 * 10^-23 # when expressed in the unit J/K, which is equal to # kg m^2/s^2 K. # # The boltzmann constant establishes the relationship between # energy and temperature. The average thermal energy carried # by each degree of freedom is kT/2. A monatomic ideal gas # has three degrees of freedom corresponding to the three # spatial directions, which means its thermal energy is # (3/2) k T. # # The previous definition of the kelvin was based on the # triple point of water. The change in the definition of the # kelvin will not have much effect on measurement practice. # Practical temperature calibration makes use of two scales, # the International Temperature Scale of 1990 (ITS-90), which # covers the range of 0.65 K to 1357.77K and the Provisional # Low Temperature Scale of 2000 (PLTS-2000), which covers the # range of 0.9 mK to 1 K. # https://www.bipm.org/en/committees/cc/cct/publications-cc.htm l # # The ITS-90 contains 17 reference points including things # like the triple point of hydrogen (13.8033 K) or the # freezing point of gold (1337.33 K), and of course the triple # point of water. The PLTS-2000 specifies four reference # points, all based on properties of helium-3. # # The redefinition of the kelvin will not affect the values of # these reference points, which have been determined by # primary thermometry, using thermometers that rely only on # relationships that allow temperature to be calculated # directly without using any unknown quantities. Examples # include acoustic thermometers, which measure the speed of # sound in a gas, or electronic thermometers, which measure # tiny voltage fluctuations in resistors. Both variables # depend directly on temperature. e 1.602176634e-19 C # electron charge (exact) A ! # The ampere, symbol A, is the SI unit of electric current. ampere A # It is defined by taking the fixed numerical value of the amp ampere # elementary charge, e, to be 1.602 176 634 * 10^-19 when # expressed in the unit C, which is equal to A*s. # # The previous definition was the current which produces a # force of 2e-7 N/m between two infinitely long wires a meter # apart. This definition was difficult to realize accurately. # # The ampere is actually realized by establishing the volt and # the ohm, since A = V / ohm. These measurements can be done # using the Josephson effect and the quantum Hall effect, # which accurately measure voltage and resistance, respectively , # with reference to two fixed constants, the Josephson # constant, K_J=2e/h and the von Klitzing constant, R_K=h/e^2. # Under the previous SI system, these constants had official # fixed values, defined in 1990. This created a situation # where the standard values for the volt and ohm were in some # sense outside of SI because they depended primarily on # constants different from the ones used to define SI. After # the revision, since e and h have exact definitions, the # Josephson and von Klitzing constants will also have exact # definitions that derive from SI instead of the conventional # 1990 values. # # In fact we know that there is a small offset between the # conventional values of the electrical units based on the # conventional 1990 values and the SI values. The new # definition, which brings the practical electrical units back # into SI, will lead to a one time change of +0.1ppm for # voltage values and +0.02ppm for resistance values. # # The previous definition resulted in fixed exact values for # the vacuum permeability (mu0), the impedance of free space # (Z0), the vacuum permittivity (epsilon0), and the Coulomb # constant. With the new definition, these four values are # subject to experimental error. avogadro 6.02214076e23 / mol # Size of a mole (exact) N_A avogadro mol ! # The mole, symbol mol, is the SI unit of amount of mole mol # substance. One mole contains exactly 6.022 140 76 * 10^23 # elementary entities. This number is the fixed numerical # value of the Avogadro constant, N_A, when expressed in the # unit 1/mol and is called the Avogadro number. The amount of # substance, symbol n, of a system is a measure of the number # of specified elementary entities. An elementary entity may # be an atom, a molecule, an ion, an electron, any other # particle or specified group of particles. # # The atomic mass unit (u) is defined as 1/12 the mass of # carbon-12. Previously the mole was defined so that a mole # of carbon-12 weighed exactly 12g, or N_A u = 1 g/mol # exactly. This relationship is now an experimental, # approximate relationship. # # To determine the size of the mole, researchers used spheres # of very pure silicon-28 that weighed a kilogram. They # measured the molar mass of Si-28 using mass spectrometry and # used X-ray diffraction interferometry to determine the # spacing of the silicon atoms in the sphere. Using the # sphere's volume it was then possible to determine the number # of silicon atoms in the sphere, and hence determine the # Avogadro constant. The results of this experiment were used to # define N_A, which is henceforth a fixed, unchanging quantity. cd ! # The candela, symbol cd, is the SI unit of luminous intensity candela cd # in a given direction. It is defined by taking the fixed # numerical value of the luminous efficacy of monochromatic # radiation of the frequency 540e12 Hz to be 683 when # expressed in the unit lumen/watt, which is equal to # cd sr/W, or cd sr s^3/kg m^2 # # This definition is a rewording of the previous definition. # Luminous intensity differs from radiant intensity (W/sr) in # that it is adjusted for human perceptual dependence on # wavelength. The frequency of 540e12 Hz (yellow; # wavelength approximately 555 nm in vacuum) is where human # perception is most efficient. # # The radian and steradian are defined as dimensionless primitive units. # The radian is equal to m/m and the steradian to m^2/m^2 so these units are # dimensionless. Retaining them as named units is useful because it allows # clarity in expressions and makes the meaning of unit definitions more clear. # These units will reduce to 1 in conversions but not for sums of units or for # arguments to functions. # radian !dimensionless # The angle subtended at the center of a circle by # an arc equal in length to the radius of the # circle sr !dimensionless # Solid angle which cuts off an area of the surface steradian sr # of the sphere equal to that of a square with # sides of length equal to the radius of the # sphere # # A primitive non-SI unit # bit ! # Basic unit of information (entropy). The entropy in bits # of a random variable over a finite alphabet is defined # to be the sum of -p(i)*log2(p(i)) over the alphabet where # p(i) is the probability that the random variable takes # on the value i. # # Currency: the primitive unit of currency is defined in currency.units. # It is usually the US$ or the euro, but it is user selectable. # ########################################################################### # # # Prefixes (longer names must come first) # # # ########################################################################### yotta- 1e24 # Greek or Latin octo, "eight" zetta- 1e21 # Latin septem, "seven" exa- 1e18 # Greek hex, "six" peta- 1e15 # Greek pente, "five" tera- 1e12 # Greek teras, "monster" giga- 1e9 # Greek gigas, "giant" mega- 1e6 # Greek megas, "large" myria- 1e4 # Not an official SI prefix kilo- 1e3 # Greek chilioi, "thousand" hecto- 1e2 # Greek hekaton, "hundred" deca- 1e1 # Greek deka, "ten" deka- deca deci- 1e-1 # Latin decimus, "tenth" centi- 1e-2 # Latin centum, "hundred" milli- 1e-3 # Latin mille, "thousand" micro- 1e-6 # Latin micro or Greek mikros, "small" nano- 1e-9 # Latin nanus or Greek nanos, "dwarf" pico- 1e-12 # Spanish pico, "a bit" femto- 1e-15 # Danish-Norwegian femten, "fifteen" atto- 1e-18 # Danish-Norwegian atten, "eighteen" zepto- 1e-21 # Latin septem, "seven" yocto- 1e-24 # Greek or Latin octo, "eight" quarter- 1|4 semi- 0.5 demi- 0.5 hemi- 0.5 half- 0.5 double- 2 triple- 3 treble- 3 kibi- 2^10 # In response to the convention of illegally mebi- 2^20 # and confusingly using metric prefixes for gibi- 2^30 # powers of two, the International tebi- 2^40 # Electrotechnical Commission aproved these pebi- 2^50 # binary prefixes for use in 1998. If you exbi- 2^60 # want to refer to "megabytes" using the Ki- kibi # binary definition, use these prefixes. Mi- mebi Gi- gibi Ti- tebi Pi- pebi Ei- exbi Y- yotta Z- zetta E- exa P- peta T- tera G- giga M- mega k- kilo h- hecto da- deka d- deci c- centi m- milli u- micro # it should be a mu but u is easy to type n- nano p- pico f- femto a- atto z- zepto y- yocto # # Names of some numbers # one 1 two 2 double 2 couple 2 three 3 triple 3 four 4 quadruple 4 five 5 quintuple 5 six 6 seven 7 eight 8 nine 9 ten 10 eleven 11 twelve 12 thirteen 13 fourteen 14 fifteen 15 sixteen 16 seventeen 17 eighteen 18 nineteen 19 twenty 20 thirty 30 forty 40 fifty 50 sixty 60 seventy 70 eighty 80 ninety 90 hundred 100 thousand 1000 million 1e6 twoscore two score threescore three score fourscore four score fivescore five score sixscore six score sevenscore seven score eightscore eight score ninescore nine score tenscore ten score twelvescore twelve score # These number terms were described by N. Chuquet and De la Roche in the 16th # century as being successive powers of a million. These definitions are still # used in most European countries. The current US definitions for these # numbers arose in the 17th century and don't make nearly as much sense. These # numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric # W. Weisstein. shortbillion 1e9 shorttrillion 1e12 shortquadrillion 1e15 shortquintillion 1e18 shortsextillion 1e21 shortseptillion 1e24 shortoctillion 1e27 shortnonillion 1e30 shortnoventillion shortnonillion shortdecillion 1e33 shortundecillion 1e36 shortduodecillion 1e39 shorttredecillion 1e42 shortquattuordecillion 1e45 shortquindecillion 1e48 shortsexdecillion 1e51 shortseptendecillion 1e54 shortoctodecillion 1e57 shortnovemdecillion 1e60 shortvigintillion 1e63 centillion 1e303 googol 1e100 longbillion million^2 longtrillion million^3 longquadrillion million^4 longquintillion million^5 longsextillion million^6 longseptillion million^7 longoctillion million^8 longnonillion million^9 longnoventillion longnonillion longdecillion million^10 longundecillion million^11 longduodecillion million^12 longtredecillion million^13 longquattuordecillion million^14 longquindecillion million^15 longsexdecillion million^16 longseptdecillion million^17 longoctodecillion million^18 longnovemdecillion million^19 longvigintillion million^20 # These numbers fill the gaps left by the long system above. milliard 1000 million billiard 1000 million^2 trilliard 1000 million^3 quadrilliard 1000 million^4 quintilliard 1000 million^5 sextilliard 1000 million^6 septilliard 1000 million^7 octilliard 1000 million^8 nonilliard 1000 million^9 noventilliard nonilliard decilliard 1000 million^10 # For consistency longmilliard milliard longbilliard billiard longtrilliard trilliard longquadrilliard quadrilliard longquintilliard quintilliard longsextilliard sextilliard longseptilliard septilliard longoctilliard octilliard longnonilliard nonilliard longnoventilliard noventilliard longdecilliard decilliard # The long centillion would be 1e600. The googolplex is another # familiar large number equal to 10^googol. These numbers give overflows. # # The short system prevails in English speaking countries # billion shortbillion trillion shorttrillion quadrillion shortquadrillion quintillion shortquintillion sextillion shortsextillion septillion shortseptillion octillion shortoctillion nonillion shortnonillion noventillion shortnoventillion decillion shortdecillion undecillion shortundecillion duodecillion shortduodecillion tredecillion shorttredecillion quattuordecillion shortquattuordecillion quindecillion shortquindecillion sexdecillion shortsexdecillion septendecillion shortseptendecillion octodecillion shortoctodecillion novemdecillion shortnovemdecillion vigintillion shortvigintillion # # Numbers used in India # lakh 1e5 crore 1e7 arab 1e9 kharab 1e11 neel 1e13 padm 1e15 shankh 1e17 ############################################################################# # # # Derived units which can be reduced to the primitive units # # # ############################################################################# # # Named SI derived units (officially accepted) # newton kg m / s^2 # force N newton pascal N/m^2 # pressure or stress Pa pascal joule N m # energy J joule watt J/s # power W watt coulomb A s # charge C coulomb volt W/A # potential difference V volt ohm V/A # electrical resistance siemens A/V # electrical conductance S siemens farad C/V # capacitance F farad weber V s # magnetic flux Wb weber henry V s / A # inductance H henry tesla Wb/m^2 # magnetic flux density T tesla hertz /s # frequency Hz hertz # # Dimensions. These are here to help with dimensional analysis and # because they will appear in the list produced by hitting '?' at the # "You want:" prompt to tell the user the dimension of the unit. # LENGTH meter AREA LENGTH^2 VOLUME LENGTH^3 MASS kilogram AMOUNT mole ANGLE radian SOLID_ANGLE steradian MONEY US$ FORCE newton PRESSURE FORCE / AREA STRESS FORCE / AREA FREQUENCY hertz VELOCITY LENGTH / TIME ACCELERATION VELOCITY / TIME DENSITY MASS / VOLUME LINEAR_DENSITY MASS / LENGTH VISCOSITY FORCE TIME / AREA KINEMATIC_VISCOSITY VISCOSITY / DENSITY CURRENT ampere CHARGE coulomb CAPACITANCE farad RESISTANCE ohm CONDUCTANCE siemens INDUCTANCE henry E_FIELD ELECTRIC_POTENTIAL / LENGTH B_FIELD tesla # The D and H fields are related to the E and B fields by factors of # epsilon and mu respectively, so their units can be found by # multiplying/dividing by the epsilon0 and mu0. The more complex # definitions below make it possible to use D_FIELD and E_FIELD to # convert between SI and CGS units for these dimensions. D_FIELD E_FIELD epsilon0 mu0_SI c^2 F / m H_FIELD B_FIELD / (mu0/mu0_SI) (H/m) ELECTRIC_DIPOLE_MOMENT C m MAGNETIC_DIPOLE_MOMENT J / T POLARIZATION ELECTRIC_DIPOLE_MOMENT / VOLUME MAGNETIZATION MAGNETIC_DIPOLE_MOMENT / VOLUME ELECTRIC_POTENTIAL volt VOLTAGE ELECTRIC_POTENTIAL E_FLUX E_FIELD AREA D_FLUX D_FIELD AREA B_FLUX B_FIELD AREA H_FLUX H_FIELD AREA # # units derived easily from SI units # gram millikg gm gram g gram tonne 1000 kg t tonne metricton tonne sthene tonne m / s^2 funal sthene pieze sthene / m^2 quintal 100 kg bar 1e5 Pa # About 1 atm b bar vac millibar micron micrometer # One millionth of a meter bicron picometer # One brbillionth of a meter cc cm^3 are 100 m^2 a are liter 1000 cc # The liter was defined in 1901 as the oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at L liter # the temperature of its maximum density l liter # under a pressure of 1 atm. This was # supposed to be 1000 cubic cm, but it # was discovered that the original # measurement was off. In 1964, the # liter was redefined to be exactly 1000 # cubic centimeters. mho siemens # Inverse of ohm, hence ohm spelled backward galvat ampere # Named after Luigi Galvani angstrom 1e-10 m # Convenient for describing molecular sizes xunit xunit_cu # Used for measuring x-ray wavelengths. siegbahn xunit # Originally defined to be 1|3029.45 of xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18 xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly # 1e-13 m, but was later found to be # slightly off. Current usage is with # reference to common x-ray lines, either # the K-alpha 1 line of copper or the # same line of molybdenum. angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965 to replace # the X unit. The wavelength of the # tungsten K alpha1 line was defined as # exactly 0.20901 angstrom star, with the # valule chosen to try to make the new # unit close to the angstrom. silicon_d220 1.920155716e-10 m # Silicon lattice spacing siliconlattice sqrt(8) silicon_d220# Silicon lattice parameter, (a), the side # length of the unit cell for the diamond # centered cubic structure of silicon. fermi 1e-15 m # Convenient for describing nuclear sizes # Nuclear radius is from 1 to 10 fermis barn 1e-28 m^2 # Used to measure cross section for # particle physics collision, said to # have originated in the phrase "big as # a barn". shed 1e-24 barn # Defined to be a smaller companion to the # barn, but it's too small to be of # much use. brewster micron^2/N # measures stress-optical coef diopter /m # measures reciprocal of lens focal length fresnel 1e12 Hz # occasionally used in spectroscopy shake 1e-8 sec svedberg 1e-13 s # Used for measuring the sedimentation # coefficient for centrifuging. gamma microgram # Also used for 1e-9 tesla lambda microliter spat 1e12 m # Rarely used for astronomical measurements preece 1e13 ohm m # resistivity planck J s # action of one joule over one second sturgeon /henry # magnetic reluctance daraf 1/farad # elastance (farad spelled backwards) leo 10 m/s^2 poiseuille N s / m^2 # viscosity mayer J/g K # specific heat mired / microK # reciprocal color temperature. The name # abbreviates micro reciprocal degree. crocodile megavolt # used informally in UK physics labs metricounce 25 g mounce metricounce finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light # with wavelength 296.7 nm. fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure # the energy incident on the receiving # body across a specified frequency # bandwidth. [12] jansky fluxunit # K. G. Jansky identified radio waves coming Jy jansky # from outer space in 1931. flick W / cm^2 sr micrometer # Spectral radiance or irradiance pfu / cm^2 sr s # particle flux unit -- Used to measure # rate at which particles are received by # a spacecraft as particles per solid # angle per detector area per second. [18] pyron cal_IT / cm^2 min # Measures heat flow from solar radiation, # from Greek work "pyr" for fire. katal mol/sec # Measure of the amount of a catalyst. One kat katal # katal of catalyst enables the reaction # to consume or produce on mol/sec. solarluminosity 382.8e24 W # A common yardstick for comparing the # output of different stars. # http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html # at mean earth-sun distance solarirradiance solarluminosity / (4 pi sundist^2) solarconstant solarirradiance TSI solarirradiance # total solar irradiance # # time # sec s minute 60 s min minute hour 60 min hr hour day 24 hr d day da day week 7 day wk week sennight 7 day fortnight 14 day blink 1e-5 day # Actual human blink takes 1|3 second ce 1e-2 day cron 1e6 years watch 4 hours # time a sentry stands watch or a ship's # crew is on duty. bell 1|8 watch # Bell would be sounded every 30 minutes. # French Revolutionary Time or Decimal Time. It was Proposed during # the French Revolution. A few clocks were made, but it never caught # on. In 1998 Swatch defined a time measurement called ".beat" and # sold some watches that displayed time in this unit. decimalhour 1|10 day decimalminute 1|100 decimalhour decimalsecond 1|100 decimalminute beat decimalminute # Swatch Internet Time # # angular measure # circle 2 pi radian degree 1|360 circle deg degree arcdeg degree arcmin 1|60 degree arcminute arcmin ' arcmin arcsec 1|60 arcmin arcsecond arcsec " arcsec '' " rightangle 90 degrees quadrant 1|4 circle quintant 1|5 circle sextant 1|6 circle sign 1|12 circle # Angular extent of one sign of the zodiac turn circle revolution turn rev turn pulsatance radian / sec gon 1|100 rightangle # measure of grade grade gon centesimalminute 1|100 grade centesimalsecond 1|100 centesimalminute milangle 1|6400 circle # Official NIST definition. # Another choice is 1e-3 radian. pointangle 1|32 circle # Used for reporting compass readings centrad 0.01 radian # Used for angular deviation of light # through a prism. mas milli arcsec # Used by astronomers seclongitude circle (seconds/day) # Astronomers measure longitude # (which they call right ascension) in # time units by dividing the equator into # 24 hours instead of 360 degrees. # # Some geometric formulas # circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi) spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \ cuberoot(spherevolume/4|3 pi) spherevol() spherevolume square(x) range=[0,) x^2 ; sqrt(square) # # Solid angle measure # sphere 4 pi sr squaredegree 1|180^2 pi^2 sr squareminute 1|60^2 squaredegree squaresecond 1|60^2 squareminute squarearcmin squareminute squarearcsec squaresecond sphericalrightangle 0.5 pi sr octant 0.5 pi sr # # Concentration measures # percent 0.01 % percent mill 0.001 # Originally established by Congress in 1791 # as a unit of money equal to 0.001 dollars, # it has come to refer to 0.001 in general. # Used by some towns to set their property # tax rate, and written with a symbol similar # to the % symbol but with two 0's in the # denominator. [18] proof 1|200 # Alcohol content measured by volume at # 60 degrees Fahrenheit. This is a USA # measure. In Europe proof=percent. ppm 1e-6 partspermillion ppm ppb 1e-9 partsperbillion ppb # USA billion ppt 1e-12 partspertrillion ppt # USA trillion karat 1|24 # measure of gold purity caratgold karat gammil mg/l basispoint 0.01 % # Used in finance fine 1|1000 # Measure of gold purity # The pH scale is used to measure the concentration of hydronium (H3O+) ions in # a solution. A neutral solution has a pH of 7 as a result of dissociated # water molecules. pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol)) # # Temperature # # Two types of units are defined: units for converting temperature differences # and functions for converting absolute temperatures. Conversions for # differences start with "deg" and conversions for absolute temperature start # with "temp". # TEMPERATURE kelvin TEMPERATURE_DIFFERENCE kelvin # In 1741 Anders Celsius introduced a temperature scale with water boiling at # 0 degrees and freezing at 100 degrees at standard pressure. After his death # the fixed points were reversed and the scale was called the centigrade # scale. Due to the difficulty of accurately measuring the temperature of # melting ice at standard pressure, the centigrade scale was replaced in 1954 # by the Celsius scale which is defined by subtracting 273.15 from the # temperature in Kelvins. This definition differed slightly from the old # centigrade definition, but the Kelvin scale depends on the triple point of # water rather than a melting point, so it can be measured accurately. tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \ x K + stdtemp ; (tempC +(-stdtemp))/K tempcelsius() tempC degcelsius K degC K # Fahrenheit defined his temperature scale by setting 0 to the coldest # temperature he could produce in his lab with a salt water solution and by # setting 96 degrees to body heat. In Fahrenheit's words: # # Placing the thermometer in a mixture of sal ammoniac or sea # salt, ice, and water a point on the scale will be found which # is denoted as zero. A second point is obtained if the same # mixture is used without salt. Denote this position as 30. A # third point, designated as 96, is obtained if the thermometer # is placed in the mouth so as to acquire the heat of a healthy # man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724) tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \ (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 tempfahrenheit() tempF degfahrenheit 5|9 degC degF 5|9 degC degreesrankine degF # The Rankine scale has the degrankine degreesrankine # Fahrenheit degree, but its zero degreerankine degF # is at absolute zero. degR degrankine tempR degrankine temprankine degrankine tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \ x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur degreaumur 10|8 degC # The Reaumur scale was used in Europe and # particularly in France. It is defined # to be 0 at the freezing point of water # and 80 at the boiling point. Reaumur # apparently selected 80 because it is # divisible by many numbers. degK K # "Degrees Kelvin" is forbidden usage. tempK K # For consistency # Gas mark is implemented below but in a terribly ugly way. There is # a simple formula, but it requires a conditional which is not # presently supported. # # The formula to convert to degrees Fahrenheit is: # # 25 log2(gasmark) + k_f gasmark<=1 # 25 (gasmark-1) + k_f gasmark>=1 # # k_f = 275 # gasmark[degR] \ .0625 634.67 \ .125 659.67 \ .25 684.67 \ .5 709.67 \ 1 734.67 \ 2 759.67 \ 3 784.67 \ 4 809.67 \ 5 834.67 \ 6 859.67 \ 7 884.67 \ 8 909.67 \ 9 934.67 \ 10 959.67 # Units cannot handle wind chill or heat index because they are two variable # functions, but they are included here for your edification. Clearly these # equations are the result of a model fitting operation. # # wind chill index (WCI) a measurement of the combined cooling effect of low # air temperature and wind on the human body. The index was first defined # by the American Antarctic explorer Paul Siple in 1939. As currently used # by U.S. meteorologists, the wind chill index is computed from the # temperature T (in °F) and wind speed V (in mi/hr) using the formula: # WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4. # For very low wind speeds, below 4 mi/hr, the WCI is actually higher than # the air temperature, but for higher wind speeds it is lower than the air # temperature. # # heat index (HI or HX) a measure of the combined effect of heat and # humidity on the human body. U.S. meteorologists compute the index # from the temperature T (in °F) and the relative humidity H (as a # value from 0 to 1). # HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH # - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2 # - 0.0199 T^2 H^2. # # Physical constants # # Basic constants pi 3.14159265358979323846 light c mu0_SI 2 alpha h / e^2 c # Vacuum magnetic permeability mu0 mu0_SI # Gets overridden in CGS modes epsilon0 1/mu0 c^2 # Vacuum electric permittivity Z0 mu0 c # Free space impedance energy c^2 # Convert mass to energy hbar h / 2 pi spin hbar G 6.67430e-11 N m^2 / kg^2 # Newtonian gravitational constant coulombconst 1/4 pi epsilon0 # Listed as k or k_C sometimes k_C coulombconst # Physico-chemical constants atomicmassunit 1.66053906660e-27 kg # Unified atomic mass unit, defined as u atomicmassunit # 1|12 of the mass of carbon 12. amu atomicmassunit # The relationship N_A u = 1 g/mol dalton u # is approximately, but not exactly Da dalton # true (with the 2019 SI). # Previously the mole was defined to # make this relationship exact. amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of # the 3 naturally occuring neutral # isotopes of oxygen amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral # oxygen 16 atom gasconstant k N_A # Molar gas constant (exact) R gasconstant kboltzmann boltzmann molarvolume mol R stdtemp / atm # Volume occupied by one mole of an # ideal gas at STP. loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an # ideal gas at STP. Loschmidt did # work similar to Avogadro. molarvolume_si N_A siliconlattice^3 / 8 # Volume of a mole of crystalline # silicon. The unit cell contains 8 # silicon atoms and has a side # length of siliconlattice. stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a sigma stefanboltzmann # blackbody at temperature T is # given by sigma T^4. (exact) wiendisplacement (h c/k)/4.9651142317442763 # Wien's Displacement Law gives # the frequency at which the the # Planck spectrum has maximum # intensity. The relation is lambda # T = b where lambda is wavelength, # T is temperature and b is the Wien # displacement. This relation is # used to determine the temperature # of stars. The constant is the # solution to x=5(1-exp(-x)). (exact) K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until K_J 2e/h # recently, laboratories kept Weston cadmium cells as # a reference, but they could drift. In 1987 the # CGPM officially recommended the use of the # Josephson effect as a laboratory representation of # the volt. The Josephson effect occurs when two # superconductors are separated by a thin insulating # layer. A "supercurrent" flows across the insulator # with a frequency that depends on the potential # applied across the superconductors. This frequency # can be very accurately measured. The Josephson # constant K_J relates the measured frequency to the # potential. Two values given, the conventional # (exact) value from 1990, which was used until the # 2019 SI revision, and the current exact value. R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties. R_K h/e^2 # The old approach involved maintaining resistances # that were subject to drift. The new standard is # based on the Hall effect. When a current carrying # ribbon is placed in a magnetic field, a potential # difference develops across the ribbon. The ratio # of the potential difference to the current is # called the Hall resistance. Klaus von Klitzing # discovered in 1980 that the Hall resistance varies # in discrete jumps when the magnetic field is very # large and the temperature very low. This enables # accurate realization of the resistance h/e^2 in the # lab. The 1990 value was an exact conventional # value used until the SI revision in 2019. This value # did not agree with measurements. The new value # is exact. # The 2019 update to SI gives exact definitions for R_K and K_J. Previously # the electromagnetic units were realized using the 1990 conventional values # for these constants, and as a result, the standard definitions were in some # sense outside of SI. The revision corrects this problem. The definitions # below give the 1990 conventional values for the electromagnetic units in # terms of 2019 SI. ampere90 (K_J90 R_K90 / K_J R_K) A coulomb90 (K_J90 R_K90 / K_J R_K) C farad90 (R_K90/R_K) F henry90 (R_K/R_K90) H ohm90 (R_K/R_K90) ohm volt90 (K_J90/K_J) V watt90 (K_J90^2 R_K90 / K_J^2 R_K) W # Various conventional values gravity 9.80665 m/s^2 # std acceleration of gravity (exact) force gravity # use to turn masses into forces atm 101325 Pa # Standard atmospheric pressure atmosphere atm Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact) water gram force/cm^3 # Standard weight of water (exact) waterdensity gram / cm^3 # Density of water H2O water wc water # water column mach 331.46 m/s # speed of sound in dry air at STP standardtemp 273.15 K # standard temperature stdtemp standardtemp normaltemp tempF(70) # for gas density, from NIST normtemp normaltemp # Handbook 44 # Weight of mercury and water at different temperatures using the standard # force of gravity. Hg10C 13.5708 force gram / cm^3 # These units, when used to form Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate Hg23C 13.5386 force gram / cm^3 # because of considerations of the Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale. Hg40C 13.4973 force gram / cm^3 Hg60F 13.5574 force gram / cm^3 H2O0C 0.99987 force gram / cm^3 H2O5C 0.99999 force gram / cm^3 H2O10C 0.99973 force gram / cm^3 H2O15C 0.99913 force gram / cm^3 H2O18C 0.99862 force gram / cm^3 H2O20C 0.99823 force gram / cm^3 H2O25C 0.99707 force gram / cm^3 H2O50C 0.98807 force gram / cm^3 H2O100C 0.95838 force gram / cm^3 # Atomic constants Rinfinity 10973731.568160 /m # The wavelengths of a spectral series R_H 10967760 /m # can be expressed as # 1/lambda = R (1/m^2 - 1/n^2). # where R is a number that various # slightly from element to element. # For hydrogen, R_H is the value, # and for heavy elements, the value # approaches Rinfinity, which can be # computed from # m_e c alpha^2 / 2 h # with a loss of 2 digits # of precision. alpha 7.2973525693e-3 # The fine structure constant was # introduced to explain fine # structure visible in spectral # lines. bohrradius alpha / 4 pi Rinfinity prout 185.5 keV # nuclear binding energy equal to 1|12 # binding energy of the deuteron conductancequantum 2 e^2 / h # Planck constants planckmass sqrt(hbar c / G) m_P planckmass plancktime hbar / planckmass c^2 t_P plancktime plancklength plancktime c l_P plancklength plancktemperature hbar / k plancktime T_P plancktemperature # Particle radius electronradius coulombconst e^2 / electronmass c^2 # Classical deuteronchargeradius 2.12799e-15 m protonchargeradius 0.8751e-15 m # Masses of elementary particles electronmass 5.48579909065e-4 u m_e electronmass muonmass 0.1134289259 u m_mu muonmass taumass 1.90754 u m_tau taumass protonmass 1.007276466621 u m_p protonmass neutronmass 1.00866491595 u m_n neutronmass deuteronmass 2.013553212745 u # Nucleus of deuterium, one m_d deuteronmass # proton and one neutron alphaparticlemass 4.001506179127 u # Nucleus of He, two protons m_alpha alphaparticlemass # and two neutrons tritonmass 3.01550071621 u # Nucleius of H3, one proton m_t tritonmass # and two neutrons helionmass 3.014932247175 u # Nucleus of He3, two protons m_h helionmass # and one neutron # particle wavelengths: the compton wavelength of a particle is # defined as h / m c where m is the mass of the particle. electronwavelength h / m_e c lambda_C electronwavelength protonwavelength h / m_p c lambda_C,p protonwavelength neutronwavelength h / m_n c lambda_C,n neutronwavelength muonwavelength h / m_mu c lambda_C,mu muonwavelength # The g-factor or dimensionless magnetic moment is a quantity that # characterizes the magnetic moment of a particle. The electron g-factor is # one of the most precisely measured values in physics, with a relative # uncertainty of 1.7e-13. g_d 0.8574382338 # Deuteron g-factor g_e -2.00231930436256 # Electron g-factor g_h -4.255250615 # Helion g-factor g_mu -2.0023318418 # Muon g-factor g_n -3.82608545 # Neutron g-factor g_p 5.5856946893 # Proton g-factor g_t 5.957924931 # Triton g-factor # Magnetic moments (derived from the more accurate g-factors) # # The magnetic moment is g * mu_ref * spin where in most cases # the reference is the nuclear magneton, and all of the particles # except the deuteron have spin 1/2. bohrmagneton e hbar / 2 electronmass # Reference magnetic moment for mu_B bohrmagneton # the electron nuclearmagneton e hbar / 2 protonmass # Convenient reference magnetic mu_N nuclearmagneton # moment for heavy particles mu_e g_e mu_B / 2 # Electron spin magnet moment mu_mu g_mu e hbar / 4 muonmass # Muon spin magnetic moment mu_p g_p mu_N / 2 # Proton magnetic moment mu_n g_n mu_N / 2 # Neutron magnetic moment mu_t g_t mu_N / 2 # Triton magnetic moment mu_d g_d mu_N # Deuteron magnetic moment, spin 1 mu_h g_h mu_N / 2 # Helion magnetic moment # # Units derived from physical constants # kgf kg force technicalatmosphere kgf / cm^2 at technicalatmosphere hyl kgf s^2 / m # Also gram-force s^2/m according to [15] mmHg mm Hg torr atm / 760 # The torr, named after Evangelista # Torricelli, and is very close to the mm Hg tor Pa # Suggested in 1913 but seldom used [24]. # Eventually renamed the Pascal. Don't # confuse the tor with the torr. inHg inch Hg inH2O inch water mmH2O mm water eV e V # Energy acquired by a particle with charge e electronvolt eV # when it is accelerated through 1 V lightyear c julianyear # The 365.25 day year is specified in ly lightyear # NIST publication 811 lightsecond c s lightminute c min parsec au / tan(arcsec) # Unit of length equal to distance pc parsec # from the sun to a point having # heliocentric parallax of 1 # arcsec (derived from parallax # second). A distant object with # parallax theta will be about # (arcsec/theta) parsecs from the # sun (using the approximation # that tan(theta) = theta). rydberg h c Rinfinity # Rydberg energy crith 0.089885 gram # The crith is the mass of one # liter of hydrogen at standard # temperature and pressure. amagatvolume molarvolume amagat mol/amagatvolume # Used to measure gas densities lorentz bohrmagneton / h c # Used to measure the extent # that the frequency of light # is shifted by a magnetic field. cminv h c / cm # Unit of energy used in infrared invcm cminv # spectroscopy. wavenumber cminv kcal_mol kcal_th / mol N_A # kcal/mol is used as a unit of # energy by physical chemists. # # CGS system based on centimeter, gram and second # dyne cm gram / s^2 # force dyn dyne erg cm dyne # energy poise gram / cm s # viscosity, honors Jean Poiseuille P poise rhe /poise # reciprocal viscosity stokes cm^2 / s # kinematic viscosity St stokes stoke stokes lentor stokes # old name Gal cm / s^2 # acceleration, used in geophysics galileo Gal # for earth's gravitational field # (note that "gal" is for gallon # but "Gal" is the standard symbol # for the gal which is evidently a # shortened form of "galileo".) barye dyne/cm^2 # pressure barad barye # old name kayser 1/cm # Proposed as a unit for wavenumber balmer kayser # Even less common name than "kayser" kine cm/s # velocity bole g cm / s # momentum pond gram force glug gram force s^2 / cm # Mass which is accelerated at # 1 cm/s^2 by 1 gram force darcy centipoise cm^2 / s atm # Measures permeability to fluid flow. # One darcy is the permeability of a # medium that allows a flow of cc/s # of a liquid of centipoise viscosity # under a pressure gradient of # atm/cm. Named for H. Darcy. mobileohm cm / dyn s # mobile ohm, measure of mechanical # mobility mechanicalohm dyn s / cm # mechanical resistance acousticalohm dyn s / cm^5 # ratio of the sound pressure of # 1 dyn/cm^2 to a source of strength # 1 cm^3/s ray acousticalohm rayl dyn s / cm^3 # Specific acoustical resistance eotvos 1e-9 Gal/cm # Change in gravitational acceleration # over horizontal distance # # Electromagnetic CGS Units # # For measuring electromagnetic quantities in SI, we introduce the new base # dimension of current, define the ampere to measure current, and derive the # other electromagnetic units from the ampere. With the CGS units one approach # is to use the basic equations of electromagnetism to define units that # eliminate constants from those equations. Coulomb's law has the form # # F = k_C q1 q2 / r^2 # # where k_C is the Coulomb constant equal to 1|4 pi epsilon0 in SI units. # Ampere's force law takes the form # # dF/dl = 2 k_A I1 I2 / r # # where k_A is the ampere constant. In the CGS system we force either k_C or # k_A to 1 which then defines either a unit for charge or a unit for current. # The other unit then becomes a derived unit. When k_C is 1 the ESU system # results. When k_A is 1 the EMU system results. Note that these parameters # are not independent of each other: Maxwell's equations indicate that # # k_C / k_A = c^2 # # where c is the speed of light. # # One more choice is needed to define a complete system. Using Coulomb's law # we define the electric field as the force per unit charge # # E = k_C 1 / r^2. # # But what about the magnetic field? It is derived from Ampere's law but we # have the option of adding a proportionality constant, k_B, that may have # dimensions: # # B = 2 k_A k_B I / r # # We can choose k_B = 1, which is done in the SI, ESU and EMU systems. But if # instead we give k_B units of length/time then the magnetic field has # the same units as the electric field. This choice leads to the Gaussian # system. # # The relations above are used to determine the dimensions, but the units are # derived from the base units of CGS, not directly from those formulas. We # will use the notation [unit] to refer to the dimension of the unit in # brackets. This same process gives rise to the SI units such as the tesla, # which is defined by # # B = 2 # # References: # # Classical Electrodynamics by John David Jackson, 3rd edition. # Cardarelli, Francois. 1999. Scientific Unit Conversion. 2nd ed. Trans. # M.J. Shields. London: Springer-Verlag. ISBN 1-85233-043-0 # # # All of these systems result in electromagnetic units that involve the square # roots of the centimeter and gram. This requires a change in the primitive # units. # !var UNITS_SYSTEM esu emu gaussian gauss sqrt_cm ! sqrt_centimeter sqrt_cm +m 100 sqrt_cm^2 sqrt_g ! sqrt_gram sqrt_g +kg kilo sqrt_g^2 !endvar # Electrostatic CGS (ESU) # # This system uses the statcoulomb as the fundamental unit of charge, with # derived units that parallel the conventional terminology but use the stat- # prefix. The statcoulomb is designed by setting k_C=1, which means # # dyne = statcoulomb^2 / cm^2. # # The statcoulomb is also called the franklin or esu. # # The ESU system was specified by a committee report in 1873 and rarely used. statcoulomb 10 coulomb cm / s c # Charge such that two charges esu statcoulomb # of 1 statC separated by 1 cm statcoul statcoulomb # exert a force of 1 dyne statC statcoulomb stC statcoulomb franklin statcoulomb Fr franklin !var UNITS_SYSTEM esu !message CGS-ESU units selected !prompt (ESU) +statcoulomb sqrt(dyne) cm +A 0.1 statamp c/(cm/s) +mu0 1/c^2 +coulombconst 1 !endvar statampere statcoulomb / s statamp statampere statA statampere stA statampere statvolt dyne cm / statamp sec statV statvolt stV statvolt statfarad statamp sec / statvolt statF statfarad stF statfarad cmcapacitance statfarad stathenry statvolt sec / statamp statH stathenry stH stathenry statohm statvolt / statamp stohm statohm statmho /statohm stmho statmho statweber statvolt sec statWb statweber stWb statweber stattesla statWb/cm^2 # Defined by analogy with SI; rarely statT stattesla # if ever used stT stattesla debye 1e-10 statC angstrom # unit of electrical dipole moment helmholtz debye/angstrom^2 # Dipole moment per area jar 1000 statfarad # approx capacitance of Leyden jar # Electromagnetic CGS (EMU) # # The abampere is the fundamental unit of this system, with the derived units # using the ab- prefix. The dimensions of the abampere are defined by assuming # that k_A=1, which # # [dyne / cm] = [2 abampere^2 / cm] # # where the brackets indicate taking the dimension of the unit in base units # and discarding any constant factors. This results in the definition from # base CGS units of: # # abampere = sqrt(dyne). # # The abampere is also called the biot. The magnetic field unit (the gauss) # follows from the assumption that k_B=1, which means # # B = 2 I / r, # # and hence the dimensions of the gauss are given by # # [gauss] = [2 abampere / cm] # # or rewriting in terms of the base units # # gauss = abampere / cm. # # The definition given below is different because it is in a form that # gives a valid reduction for SI and ESU and still gives the correct # result in EMU. (It can be derived from Faraday's law.) # # The EMU system was developed by Gauss and Weber and formalized as a system in # a committee report by the British Association for the Advancement of Science # in 1873. abampere 10 A # Current which produces a force of abamp abampere # 2 dyne/cm between two infinitely aA abampere # long wires that are 1 cm apart abA abampere biot abampere Bi biot !var UNITS_SYSTEM emu !message CGS-EMU units selected !prompt (EMU) +abampere sqrt(dyne) +A 0.1 abamp +mu0 1 +coulombconst c^2 !endvar abcoulomb abamp sec abcoul abcoulomb abC abcoulomb abfarad abampere sec / abvolt abF abfarad abhenry abvolt sec / abamp abH abhenry abvolt dyne cm / abamp sec abV abvolt abohm abvolt / abamp abmho /abohm gauss abvolt sec / cm^2 # The magnetic field 2 cm from a wire Gs gauss # carrying a current of 1 abampere maxwell gauss cm^2 # Also called the "line" Mx maxwell oersted gauss / mu0 # From the relation H = B / mu Oe oersted gilbert gauss cm / mu0 Gb gilbert Gi gilbert unitpole 4 pi maxwell # unit magnetic pole emu erg/gauss # "electro-magnetic unit", a measure of # magnetic moment, often used as emu/cm^3 # to specify magnetic moment density. # Electromagnetic CGS (Gaussian) # # The Gaussian system uses the statcoulomb and statamp from the ESU system # derived by setting k_C=1, but it defines the magnetic field unit differently # by taking k_B=c instead of k_B=1. As noted above, k_C and k_A are not # independent. With k_C=1 we must have k_A=c^-2. This results in the magnetic # field unit, the gauss, having dimensions give by: # # [gauss] = [2 (c^-2) c statamp / cm] = [statamp / c cm] # # We then define the gauss using base CGS units to obtain # # gauss = statamp / ((cm/s) cm) = statcoulomb / cm^2. # # Note that this definition happens to give the same result as the definition # for the EMU system, so the definitions of the gauss are consistent. # # This definition gives the same dimensions for the E and B fields and was also # known as the "symmetric system". This system was proposed by Hertz in 1888. !var UNITS_SYSTEM gaussian gauss !message CGS-Gaussian units selected !prompt (Gaussian) +statcoulomb sqrt(dyne) cm +A 0.1 statamp c/(cm/s) +mu0 1 +epsilon0 1 +coulombconst 1 # The gauss is the B field produced +gauss statcoulomb / cm^2 # 1 cm from a wire carrying a current +weber 1e8 maxwell # of 0.5*(c/(cm/s)) stA = 1.5e10 stA +bohrmagneton e hbar / 2 electronmass c +nuclearmagneton e hbar / 2 protonmass c !endvar # # Some historical electromagnetic units # intampere 0.999835 A # Defined as the current which in one intamp intampere # second deposits .001118 gram of # silver from an aqueous solution of # silver nitrate. intfarad 0.999505 F intvolt 1.00033 V intohm 1.000495 ohm # Defined as the resistance of a # uniform column of mercury containing # 14.4521 gram in a column 1.063 m # long and maintained at 0 degC. daniell 1.042 V # Meant to be electromotive force of a # Daniell cell, but in error by .04 V faraday N_A e mol # Charge that must flow to deposit or faraday_phys 96521.9 C # liberate one gram equivalent of any faraday_chem 96495.7 C # element. (The chemical and physical # values are off slightly from what is # obtained by multiplying by amu_chem # or amu_phys. These values are from # a 1991 NIST publication.) Note that # there is a Faraday constant which is # equal to N_A e and hence has units of # C/mol. kappline 6000 maxwell # Named by and for Gisbert Kapp siemensunit 0.9534 ohm # Resistance of a meter long column of # mercury with a 1 mm cross section. # # Printed circuit board units. # # http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm. # # Conductivity is often expressed as a percentage of IACS. A copper wire a # meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at # 20 deg C. Copper density is also standarized at that temperature. # copperconductivity 58 siemens m / mm^2 # A wire a meter long with IACS copperconductivity # a 1 mm^2 cross section copperdensity 8.89 g/cm^3 # The "ounce" measures the ouncecopper oz / ft^2 copperdensity # thickness of copper used ozcu ouncecopper # in circuitboard fabrication # # Photometric units # LUMINOUS_INTENSITY candela LUMINOUS_FLUX lumen LUMINOUS_ENERGY talbot ILLUMINANCE lux EXITANCE lux candle 1.02 candela # Standard unit for luminous intensity hefnerunit 0.9 candle # in use before candela hefnercandle hefnerunit # violle 20.17 cd # luminous intensity of 1 cm^2 of # platinum at its temperature of # solidification (2045 K) lumen cd sr # Luminous flux (luminous energy per lm lumen # time unit) talbot lumen s # Luminous energy lumberg talbot # References give these values for lumerg talbot # lumerg and lumberg both. Note that # a paper from 1948 suggests that # lumerg should be 1e-7 talbots so # that lumergs/erg = talbots/joule. # lumerg = luminous erg lux lm/m^2 # Illuminance or exitance (luminous lx lux # flux incident on or coming from phot lumen / cm^2 # a surface) ph phot # footcandle lumen/ft^2 # Illuminance from a 1 candela source # at a distance of one foot metercandle lumen/m^2 # Illuminance from a 1 candela source # at a distance of one meter mcs metercandle s # luminous energy per area, used to # measure photographic exposure nox 1e-3 lux # These two units were proposed for skot 1e-3 apostilb # measurements relating to dark adapted # eyes. # Luminance measures LUMINANCE nit nit cd/m^2 # Luminance: the intensity per projected stilb cd / cm^2 # area of an extended luminous source. sb stilb # (nit is from latin nitere = to shine.) apostilb cd/pi m^2 asb apostilb blondel apostilb # Named after a French scientist. # Equivalent luminance measures. These units are units which measure # the luminance of a surface with a specified exitance which obeys # Lambert's law. (Lambert's law specifies that luminous intensity of # a perfectly diffuse luminous surface is proportional to the cosine # of the angle at which you view the luminous surface.) equivalentlux cd / pi m^2 # luminance of a 1 lux surface equivalentphot cd / pi cm^2 # luminance of a 1 phot surface lambert cd / pi cm^2 footlambert cd / pi ft^2 # The bril is used to express "brilliance" of a source of light on a # logarithmic scale to correspond to subjective perception. An increase of 1 # bril means doubling the luminance. A luminance of 1 lambert is defined to # have a brilliance of 1 bril. bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100 # Some luminance data from the IES Lighting Handbook, 8th ed, 1993 sunlum 1.6e9 cd/m^2 # at zenith sunillum 100e3 lux # clear sky sunillum_o 10e3 lux # overcast sky sunlum_h 6e6 cd/m^2 # value at horizon skylum 8000 cd/m^2 # average, clear sky skylum_o 2000 cd/m^2 # average, overcast sky moonlum 2500 cd/m^2 # # Photographic Exposure Value # This section by Jeff Conrad (jeff_conrad@msn.com) # # The Additive system of Photographic EXposure (APEX) proposed in ASA # PH2.5-1960 was an attempt to simplify exposure determination for people who # relied on exposure tables rather than exposure meters. Shortly thereafter, # nearly all cameras incorporated exposure meters, so the APEX system never # caught on, but the concept of exposure value remains in use. Though given as # 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is # related to exposure parameters by # # A^2 LS ES # 2^EV = --- = -- = -- # t K C # # Where # A = Relative aperture (f-number) # t = Exposure time in seconds # L = Scene luminance in cd/m2 # E = Scene illuminance in lux # S = Arithmetic ISO speed # K = Reflected-light meter calibration constant # C = Incident-light meter calibration constant # # Strictly, an exposure value is a combination of aperture and exposure time, # but it's also commonly used to indicate luminance (or illuminance). # Conversion to luminance or illuminance units depends on the ISO speed and the # meter calibration constant. Common practice is to use an ISO speed of 100. # Calibration constants vary among camera and meter manufacturers: Canon, # Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while # Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use # a value of 250 for incident-light meters with flat receptors. # # The values for in-camera meters apply only averaging, weighted-averaging, or # spot metering--the multi-segment metering incorporated in most current # cameras uses proprietary algorithms that evaluate many factors related to the # luminance distribution of what is being metered; they are not amenable to # simple conversions, and are usually not disclosed by the manufacturers. s100 100 / lx s # ISO 100 speed iso100 s100 # Reflected-light meter calibration constant with ISO 100 speed k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax # Incident-light meter calibration constant with ISO 100 film c250 250 lx / lx s # flat-disc receptor # Exposure value to scene luminance with ISO 100 imaging media # For Kenko (Minolta) or Pentax #ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400) # For Canon, Nikon, or Sekonic ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250) EV100() ev100 # Exposure value to scene illuminance with ISO 100 imaging media iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250) # Other Photographic Exposure Conversions # # As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities # related by # # Ev = Av + Tv = Bv + Sv # # where # Av = log2(A^2) Aperture value # Tv = log2(1/t) Time value # Sv = log2(N Sx) Speed value # Bv = log2(B S / K) Luminance ("brightness") value # Iv = log2(I S / C) Illuminance value # # and # A = Relative aperture (f-number) # t = Exposure time in seconds # Sx = Arithmetic ISO speed in 1/lux s # B = luminance in cd/m2 # I = luminance in lux # The constant N derives from the arcane relationship between arithmetic # and logarithmic speed given in ASA PH2.5-1960. That relationship # apparently was not obvious--so much so that it was thought necessary # to explain it in PH2.12-1961. The constant has had several values # over the years, usually without explanation for the changes. Although # APEX had little impact on consumer cameras, it has seen a partial # resurrection in the Exif standards published by the Camera & Imaging # Products Association of Japan. #N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961, # derived from ASA PH2.5-1960. #N_apex 0.30 lx s # rounded value in ASA PH2.5-1960, # ASA PH2.12-1961, and ANSI PH2.7-1986 #N_apex 0.3162 lx s # value in ANSI PH2.7-1973 N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100 K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961 K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in # footcandles; flat sensor?) C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in # footcandles; hemispherical sensor?) N_speed N_exif K_lum K_apex1971 C_illum C_apex1961 # Units for Photographic Exposure Variables # # Practical photography sometimes pays scant attention to units for exposure # variables. In particular, the "speed" of the imaging medium is treated as if # it were dimensionless when it should have units of reciprocal lux seconds; # this practice works only because "speed" is almost invariably given in # accordance with international standards (or similar ones used by camera # manufacturers)--so the assumed units are invariant. In calculating # logarithmic quantities--especially the time value Tv and the exposure value # EV--the units for exposure time ("shutter speed") are often ignored; this # practice works only because the units of exposure time are assumed to be in # seconds, and the missing units that make the argument to the logarithmic # function dimensionless are silently provided. # # In keeping with common practice, the definitions that follow treat "speeds" # as dimensionless, so ISO 100 speed is given simply as '100'. When # calculating the logarithmic APEX quantities Av and Tv, the definitions # provide the missing units, so the times can be given with any appropriate # units. For example, giving an exposure time of 1 minute as either '1 min' or # '60 s' will result in Tv of -5.9068906. # # Exposure Value from f-number and Exposure Time # # Because nonlinear unit conversions only accept a single quantity, # there is no direct conversion from f-number and exposure time to # exposure value EV. But the EV can be obtained from a combination of # Av and Tv. For example, the "sunny 16" rule states that correct # exposure for a sunlit scene can achieved by using f/16 and an exposure # time equal to the reciprocal of the ISO speed in seconds; this can be # calculated as # # ~Av(16) + ~Tv(1|100 s), # # which gives 14.643856. These conversions may be combined with the # ev100 conversion: # # ev100(~Av(16) + ~Tv(1|100 s)) # # to yield the assumed average scene luminance of 3200 cd/m^2. # convert relative aperture (f-number) to aperture value Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av) # convert exposure time to time value Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv) # convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed; # make arithmetic speed dimensionless # 'Sv' conflicts with the symbol for sievert; you can uncomment this function # definition if you don't need that symbol #Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv) Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval) # convert luminance value Bv in ASA PH2.12-1961 to luminance Bv(x) units=[1;cd/m^2] range=(0,) \ 2^x K_lum N_speed ; log2(Bv / (K_lum N_speed)) # convert illuminance value Iv in ASA PH2.12-1961 to illuminance Iv(x) units=[1;lx] range=(0,) \ 2^x C_illum N_speed ; log2(Iv / (C_illum N_speed)) # convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in # ASA PH2.5-1960; make arithmetic speed dimensionless Sx(S) units=[1;1] domain=(0,) \ log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s) # convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed # for convenience, speed is treated here as if it were dimensionless Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg)) Sdin() Sdeg # Numerical Aperture and f-Number of a Lens # # The numerical aperture (NA) is given by # # NA = n sin(theta) # # where n is the index of refraction of the medium and theta is half # of the angle subtended by the aperture stop from a point in the image # or object plane. For a lens in air, n = 1, and # # NA = 0.5 / f-number # # convert NA to f-number numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \ 0.5 / x ; 0.5 / numericalaperture NA() numericalaperture # # convert f-number to itself; restrict values to those possible fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber # Referenced Photographic Standards # # ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome, # Continuous-Tone) Speed of Photographic Negative Materials. # ASA PH2.12-1961. American Standard, General-Purpose Photographic # Exposure Meters (photoelectric type). # ANSI PH3.49-1971. American National Standard for general-purpose # photographic exposure meters (photoelectric type). # ANSI PH2.7-1973. American National Standard Photographic Exposure Guide. # ANSI PH2.7-1986. American National Standard for Photography -- # Photographic Exposure Guide. # CIPA DC-008-2010. Exchangeable image file format for digital still # cameras: Exif Version 2.3 # ISO 6:1993. International Standard, Photography -- Black-and-white # pictorial still camera negative film/process systems -- # Determination of ISO Speed. # # Astronomical time measurements # # Astronomical time measurement is a complicated matter. The length of the # true day at a given place can be 21 seconds less than 24 hours or 30 seconds # over 24 hours. The two main reasons for this are the varying speed of the # earth in its elliptical orbit and the fact that the sun moves on the ecliptic # instead of along the celestial equator. To devise a workable system for time # measurement, Simon Newcomb (1835-1909) used a fictitious "mean sun". # Consider a first fictitious sun traveling along the ecliptic at a constant # speed and coinciding with the true sun at perigee and apogee. Then # considering a second fictitious sun traveling along the celestial equator at # a constant speed and coinciding with the first fictitious sun at the # equinoxes. The second fictitious sun is the "mean sun". From this equations # can be written out to determine the length of the mean day, and the tropical # year. The length of the second was determined based on the tropical year # from such a calculation and was officially used from 1960-1967 until atomic # clocks replaced astronomical measurements for a standard of time. All of the # values below give the mean time for the specified interval. # # See "Mathematical Astronomy Morsels" by Jean Meeus for more details # and a description of how to compute the correction to mean time. # TIME second anomalisticyear 365.2596 days # The time between successive # perihelion passages of the # earth. siderealyear 365.256360417 day # The time for the earth to make # one revolution around the sun # relative to the stars. tropicalyear 365.242198781 day # The time needed for the mean sun # as defined above to increase # its longitude by 360 degrees. # Most references defined the # tropical year as the interval # between vernal equinoxes, but # this is misleading. The length # of the season changes over time # because of the eccentricity of # the earth's orbit. The time # between vernal equinoxes is # approximately 365.24237 days # around the year 2000. See # "Mathematical Astronomy # Morsels" for more details. eclipseyear 346.62 days # The line of nodes is the # intersection of the plane of # Earth's orbit around the sun # with the plane of the moon's # orbit around earth. Eclipses # can only occur when the moon # and sun are close to this # line. The line rotates and # appearances of the sun on the # line of nodes occur every # eclipse year. saros 223 synodicmonth # The earth, moon and sun appear in # the same arrangement every # saros, so if an eclipse occurs, # then one saros later, a similar # eclipse will occur. (The saros # is close to 19 eclipse years.) # The eclipse will occur about # 120 degrees west of the # preceding one because the # saros is not an even number of # days. After 3 saros, an # eclipse will occur at # approximately the same place. siderealday 86164.09054 s # The sidereal day is the interval siderealhour 1|24 siderealday # between two successive transits siderealminute 1|60 siderealhour # of a star over the meridian, siderealsecond 1|60 siderealminute # or the time required for the # earth to make one rotation # relative to the stars. The # more usual solar day is the # time required to make a # rotation relative to the sun. # Because the earth moves in its # orbit, it has to turn a bit # extra to face the sun again, # hence the solar day is slightly # longer. anomalisticmonth 27.55454977 day # Time for the moon to travel from # perigee to perigee nodicalmonth 27.2122199 day # The nodes are the points where draconicmonth nodicalmonth # an orbit crosses the ecliptic. draconiticmonth nodicalmonth # This is the time required to # travel from the ascending node # to the next ascending node. siderealmonth 27.321661 day # Time required for the moon to # orbit the earth lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds # Mean time between full moons. synodicmonth lunarmonth # Full moons occur when the sun lunation synodicmonth # and moon are on opposite sides lune 1|30 lunation # of the earth. Since the earth lunour 1|24 lune # moves around the sun, the moon # has to revolve a bit extra to # get into the full moon # configuration. year tropicalyear yr year month 1|12 year mo month lustrum 5 years # The Lustrum was a Roman # purification ceremony that took # place every five years. # Classically educated Englishmen # used this term. decade 10 years century 100 years millennium 1000 years millennia millennium solaryear year lunaryear 12 lunarmonth calendaryear 365 day commonyear 365 day leapyear 366 day julianyear 365.25 day gregorianyear 365.2425 day islamicyear 354 day # A year of 12 lunar months. They islamicleapyear 355 day # began counting on July 16, AD 622 # when Muhammad emigrated to Medina # (the year of the Hegira). They need # 11 leap days in 30 years to stay in # sync with the lunar year which is a # bit longer than the 29.5 days of the # average month. The months do not # keep to the same seasons, but # regress through the seasons every # 32.5 years. islamicmonth 1|12 islamicyear # They have 29 day and 30 day months. # The Hebrew year is also based on lunar months, but synchronized to the solar # calendar. The months vary irregularly between 29 and 30 days in length, and # the years likewise vary. The regular year is 353, 354, or 355 days long. To # keep up with the solar calendar, a leap month of 30 days is inserted every # 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This # gives leap years that last 383, 384, or 385 days. # Sidereal days mercuryday 58.6462 day venusday 243.01 day # retrograde earthday siderealday marsday 1.02595675 day jupiterday 0.41354 day saturnday 0.4375 day uranusday 0.65 day # retrograde neptuneday 0.768 day plutoday 6.3867 day # Sidereal years from http://ssd.jpl.nasa.gov/phys_props_planets.html. Data # was updated in May 2001 based on the 1992 Explanatory Supplement to the # Astronomical Almanac and the mean longitude rates. Apparently the table of # years in that reference is incorrect. mercuryyear 0.2408467 julianyear venusyear 0.61519726 julianyear earthyear siderealyear marsyear 1.8808476 julianyear jupiteryear 11.862615 julianyear saturnyear 29.447498 julianyear uranusyear 84.016846 julianyear neptuneyear 164.79132 julianyear plutoyear 247.92065 julianyear # Objects on the earth are charted relative to a perfect ellipsoid whose # dimensions are specified by different organizations. The ellipsoid is # specified by an equatorial radius and a flattening value which defines the # polar radius. These values are the 1996 values given by the International # Earth Rotation Service (IERS) whose reference documents can be found at # http://maia.usno.navy.mil/ earthflattening 1|298.25642 earthradius_equatorial 6378136.49 m earthradius_polar (-earthflattening+1) earthradius_equatorial landarea 148.847e6 km^2 oceanarea 361.254e6 km^2 moonradius 1738 km # mean value sunradius 6.96e8 m # Many astronomical values can be measured most accurately in a system of units # using the astronomical unit and the mass of the sun as base units. The # uncertainty in the gravitational constant makes conversion to SI units # significantly less accurate. # The astronomical unit was defined to be the length of the of the semimajor # axis of a massless object with the same year as the earth. With such a # definition in force, and with the mass of the sun set equal to one, Kepler's # third law can be used to solve for the value of the gravitational constant. # Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital # period, a is the size of the semimajor axis, G is the gravitational constant # and M is the mass. With M = 1 and T and a chosen for the earth's orbit, we # find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called the Gaussian # gravitational constant, apparently because Gauss originally did the # calculations. However, when the original calculation was done, the value # for the length of the earth's year was inaccurate. The value used is called # the Gaussian year. Changing the astronomical unit to bring it into # agreement with more accurate values for the year would have invalidated a # lot of previous work, so instead the astronomical unit has been kept equal # to this original value. This is accomplished by using a standard value for # the Gaussian gravitational constant. This constant is called k. # Many values below are from http://ssd.jpl.nasa.gov/?constants gauss_k 0.01720209895 # This beast has dimensions of # au^(3|2) / day and is exact. gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian # gravitational constant. This is a # fictional year, and doesn't # correspond to any celestial event. astronomicalunit 149597870700 m # IAU definition from 2012, exact au astronomicalunit # ephemeris for the above described # astronomical unit. (See the NASA # site listed above.) GMsun 1.32712440018e20 m^3 / s^2 # heliocentric gravitational constant solarmass GMsun/G # with uncertainty 8e9 is known more sunmass solarmass # accurately than G. sundist 1.0000010178 au # mean earth-sun distance moondist 3.844e8 m # mean earth-moon distance sundist_near 1.471e11 m # earth-sun distance at perihelion sundist_far 1.521e11 m # earth-sun distance at aphelion moondist_min 3.564e8 m # approximate least distance at # perigee 1901-2300 moondist_max 4.067e8 m # approximate greatest distance at # apogee 1901-2300 # The following are masses for planetary systems, not just the planet itself. # The comments give the uncertainty in the denominators. As noted above, # masses are given relative to the solarmass because this is more accurate. # The conversion to SI is uncertain because of uncertainty in G, the # gravitational constant. # # Values are from http://ssd.jpl.nasa.gov/astro_constants.html mercurymass solarmass / 6023600 # 250 venusmass solarmass / 408523.71 # 0.06 earthmoonmass solarmass / 328900.56 # 0.02 marsmass solarmass / 3098708 # 9 jupitermass solarmass / 1047.3486 # 0.0008 saturnmass solarmass / 3497.898 # 0.018 uranusmass solarmass / 22902.98 # 0.03 neptunemass solarmass / 19412.24 # 0.04 plutomass solarmass / 1.35e8 # 0.07e8 moonearthmassratio 0.012300034 # uncertainty 3e-9 earthmass earthmoonmass / ( 1 + moonearthmassratio) moonmass moonearthmassratio earthmass # These are the old values for the planetary masses. They may give # the masses of the planets alone. oldmercurymass 0.33022e24 kg oldvenusmass 4.8690e24 kg oldmarsmass 0.64191e24 kg oldjupitermass 1898.8e24 kg oldsaturnmass 568.5e24 kg olduranusmass 86.625e24 kg oldneptunemass 102.78e24 kg oldplutomass 0.015e24 kg # Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in # turn cites Global Earth Physics by CF Yoder, 1995. mercuryradius 2440 km venusradius 6051.84 km earthradius 6371.01 km marsradius 3389.92 km jupiterradius 69911 km saturnradius 58232 km uranusradius 25362 km neptuneradius 24624 km plutoradius 1151 km moongravity 1.62 m/s^2 # The Hubble constant gives the speed at which distance galaxies are moving # away from the earth according to v = H0*d, where H0 is the hubble constant # and d is the distance to the galaxy. hubble 70 km/s/Mpc # approximate H0 hubble # Parallax is the angular difference between the topocentric (on Earth's # surface) and geocentric (at Earth's center) direction toward a celestial body # when the body is at a given altitude. When the body is on the horizon, the # parallax is the horizontal parallax; when the body is on the horizon and the # observer is on the equator, the parallax is the equatorial horizontal # parallax. When the body is at zenith, the parallax is zero. lunarparallax asin(earthradius_equatorial / moondist) # Moon equatorial moonhp lunarparallax # horizontal parallax # at mean distance # Light from celestial objects is attenuated by passage through Earth's # atmosphere. A body near the horizon passes through much more air than an # object at zenith, and is consequently less bright. Air mass is the ratio of # the length of the optical path at a given altitude (angle above the horizon) # to the length at zenith. Air mass at zenith is by definition unity; at the # horizon, air mass is approximately 38, though the latter value can vary # considerably with atmospheric conditions. The general formula is # E = E0 # exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value # seen by an observer, X is the air mass and c is the extinction coefficient. # A common value for c in reasonably clear air is 0.21, but values can be # considerably greater in urban areas. Apparent altitude is that perceived by # an observer; it includes the effect of atmospheric refraction. There is no # shortage of formulas for air mass # (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to # variations in local atmospheric conditions. The formula used here is simple # and is in good agreement with rigorously calculated values under standard # conditions. # # Extraterrestrial illuminance or luminance of an object at a given altitude # determined with vmag() or SB_xxx() below can be multiplied by # atm_transmission() or atm_transmissionz() to estimate the terrestrial value. # # Kasten and Young (1989) air mass formula. alt is apparent altitude # Reference: # Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables # and Approximation Formula." Applied Optics. Vol. 28, 4735–4738. # Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735. airmass(alt) units=[degree;1] domain=[0,90] noerror \ 1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364) # zenith is apparent zenith angle (zenith = 90 deg - alt) airmassz(zenith) units=[degree;1] domain=[0,90] noerror \ 1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364) # For reasonably clear air at sea level; values may need adjustment for # elevation and local atmospheric conditions # for scotopic vision (510 nm), appropriate for the dark-adapted eye # extinction_coeff 0.26 # for photopic vision, appropriate for observing brighter objects such # as the full moon extinction_coeff 0.21 atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \ exp(-extinction_coeff airmass(alt)) # in terms of zenith angle (zenith = 90 deg - alt) atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \ exp(-extinction_coeff airmassz(zenith)) # Moon and Sun data at mean distances moonvmag -12.74 # Moon apparent visual magnitude at mean distance sunvmag -26.74 # Sun apparent visual magnitude at mean distance moonsd asin(moonradius / moondist) # Moon angular semidiameter at mean distance sunsd asin(sunradius / sundist) # Sun angular semidiameter at mean distance # Visual magnitude of star or other celestial object. The system of stellar # magnitudes, developed in ancient Greece, assigned magnitudes from 1 # (brightest) to 6 (faintest visible to the naked eye). In 1856, British # astronomer Norman Pogson made the system precise, with a magnitude 1 object # 100 times as bright as a magnitude 6 object, and each magnitude differing # from the next by a constant ratio; the ratio, sometimes known as Pogson's # ratio, is thus 100^0.2, or approximately 2.5119. The logarithm of 100^0.2 is # 0.4, hence the common use of powers of 10 and base-10 logarithms. # # Reference: # Allen, C.W. 1976. Astrophysical Quantities, 3rd ed. 1973, reprinted # with corrections, 1976. London: Athlone. # # The function argument is the (dimensionless) visual magnitude; reference # illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside # Earth's atmosphere. Illuminance values can be adjusted to terrestrial values # by multiplying by one of the atm_transmission functions above. # Illuminance from apparent visual magnitude vmag(mag) units=[1;lx] domain=[,] range=(0,] \ 2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx)) # Surface brightness of a celestial object of a given visual magnitude # is a logarithmic measure of the luminance the object would have if its # light were emitted by an object of specified solid angle; it is # expressed in magnitudes per solid angle. Surface brightness can be # obtained from the visual magnitude by # S = m + 2.5 log(pi pi k a b), # where k is the phase (fraction illuminated), a is the equatorial # radius, and b is the polar radius. For 100% illumination (e.g., full # moon), this is often simplified to # S = m + 2.5 log(pi k s^2), # where s is the object's angular semidiameter; the units of s determine # the units of solid angle. The visual magnitude and semidiameter must # be appropriate for the object's distance; for other than 100% # illumination, the visual magnitude must be appropriate for the phase. # Luminance values are for outside Earth's atmosphere; they can be # adjusted to terrestrial values by multiplying by one of the atm_transmission # functions above. # luminance from surface brightness in magnitudes per square degree SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ vmag(sb) / squaredegree ; \ ~vmag(SB_degree squaredegree) # luminance from surface brightness in magnitudes per square minute SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ vmag(sb) / squareminute ; \ ~vmag(SB_minute squareminute) # luminance from surface brightness in magnitudes per square second SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ vmag(sb) / squaresecond ; \ ~vmag(SB_second squaresecond) # luminance from surface brightness in magnitudes per steradian SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ vmag(sb) / sr ; \ ~vmag(SB_sr sr) SB() SB_second SB_sec() SB_second SB_min() SB_minute SB_deg() SB_degree # The brightness of one tenth-magnitude star per square degree outside # Earth's atmosphere; often used for night sky brightness. S10 SB_degree(10) # Examples for magnitude and surface brightness functions # Sun illuminance from visual magnitude # You have: sunvmag # You want: # Definition: -26.74 = -26.74 # You have: vmag(sunvmag) # You want: lx # * 126134.45 # / 7.9280482e-06 # # Moon surface brightness from visual magnitude and semidiameter at 100% # illumination (full moon): # You have: moonvmag # You want: # Definition: -12.74 = -12.74 # You have: moonsd # You want: arcsec # * 932.59484 # / 0.001072277 # You have: moonvmag + 2.5 log(pi 932.59484^2) # You want: # Definition: 3.3513397 # # Similar example with specific data obtained from another source (JPL # Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in # arcseconds # # You have: -12.9 + 2.5 log(pi 2023.201|2^2) # You want: # Definition: 3.3679199 # You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2)) # You want: # Definition: 4858.6547 cd / m^2 # # If surface brightness is provided by another source (e.g., Horizons), # it can simply be used directly: # You have: SB_second(3.3679199) # You want: cd/m^2 # * 4858.6546 # / 0.0002058183 # The illuminance and luminance values are extraterrestrial (outside # Earth's atmosphere). The values at Earth's surface are less than these # because of atmospheric extinction. For example, in the last example # above, if the Moon were at an altitude of 55 degrees, the terrestrial # luminance could be calculated with # You have: SB_second(3.3679199) # You want: cd/m^2 # * 4858.6546 # / 0.0002058183 # You have: _ atm_transmission(55 deg) # You want: cd/m^2 # * 3760.6356 # / 0.0002659125 # If desired, photographic exposure can be determined with EV100(), # leading to acceptable combinations of aperture and exposure time. # For the example above, but with the Moon at 10 degrees, # You have: SB_second(3.3679199) atm_transmission(10 deg) # You want: EV100 # 13.553962 # The Hartree system of atomic units, derived from fundamental units # of mass (of electron), action (Planck's constant), charge, and # the Coulomb constant. # The Hartree energy can be derived from m_e, e, hbar, and coulombconst by # hartree = coulombconst^2 m_e e^4 / hbar^2 # but due to correlations between the measurements for m_e and coulombconst # this results in a significant loss of precision. So we use an alternate # equivalent definition for the hartree and derive then use energy instead # of the Coulomb constant to derive the other units. This method retains the # precision. hartree 2 rydberg # Approximate electric potential energy of # the hydrogen atom in its ground state, # and approximately twice its ionization # energy. # Fundamental units atomicmass electronmass atomiccharge e atomicaction hbar atomicenergy hartree # Derived units atomicvelocity sqrt(atomicenergy / atomicmass) atomictime atomicaction / atomicenergy atomiclength atomicvelocity atomictime atomicforce atomicenergy / atomiclength atomicmomentum atomicenergy / atomicvelocity atomiccurrent atomiccharge / atomictime atomicpotential atomicenergy / atomiccharge # electrical potential atomicEfield atomicpotential / atomiclength # # These thermal units treat entropy as charge, from [5] # thermalcoulomb J/K # entropy thermalampere W/K # entropy flow thermalfarad J/K^2 thermalohm K^2/W # thermal resistance fourier thermalohm thermalhenry J K^2/W^2 # thermal inductance thermalvolt K # thermal potential difference # # United States units # # linear measure # The US Metric Law of 1866 legalized the metric system in the USA and # defined the meter in terms of the British system with the exact # 1 meter = 39.37 inches. On April 5, 1893 Thomas Corwin Mendenhall, # Superintendent of Weights and Measures, decided, in what has become # known as the "Mendenhall Order" that the meter and kilogram would be the # fundamental standards in the USA. The definition from 1866 was turned # around to give an exact definition of the yard as 3600|3937 meters This # definition was used until July of 1959 when the definition was changed # to bring the US and other English-speaking countries into agreement; the # Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it # was approximately halfway between the British and US values; it had the # added advantage of making 1 inch = 25.4 mm (exactly). Since 1959, the # "international" foot has been exactly 0.3048 meters. At the same time, # it was decided that any data expressed in feet derived from geodetic # surveys within the US would continue to use the old definition and call # the old unit the "survey foot." The US continues to define the statute # mile, furlong, chain, rod, link, and fathom in terms of the US survey # foot. # Sources: # NIST Special Publication 447, Sects. 5, 7, and 8. # NIST Handbook 44, 2011 ed., Appendix C. # Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014. US 1200|3937 m/ft # These four values will convert US- US # international measures to survey- US # US Survey measures geodetic- US int 3937|1200 ft/m # Convert US Survey measures to int- int # international measures inch 2.54 cm in inch foot 12 inch feet foot ft foot yard 3 ft yd yard mile 5280 ft # The mile was enlarged from 5000 ft # to this number in order to make # it an even number of furlongs. # (The Roman mile is 5000 romanfeet.) line 1|12 inch # Also defined as '.1 in' or as '1e-8 Wb' rod 5.5 yard perch rod furlong 40 rod # From "furrow long" statutemile mile league 3 mile # Intended to be an an hour's walk # surveyor's measure surveyorschain 66 surveyft surveychain surveyorschain surveyorspole 1|4 surveyorschain surveyorslink 1|100 surveyorschain chain 66 ft link 1|100 chain ch chain USacre 10 surveychain^2 intacre 10 chain^2 # Acre based on international ft intacrefoot acre foot USacrefoot USacre surveyfoot acrefoot intacrefoot acre intacre section mile^2 township 36 section homestead 160 acre # Area of land granted by the 1862 Homestead # Act of the United States Congress gunterschain surveyorschain engineerschain 100 ft engineerslink 1|100 engineerschain ramsdenschain engineerschain ramsdenslink engineerslink gurleychain 33 feet # Andrew Ellicott chain is the gurleylink 1|50 gurleychain # same length wingchain 66 feet # Chain from 1664, introduced by winglink 1|80 wingchain # Vincent Wing, also found in a # 33 foot length with 40 links. # early US length standards # The US has had four standards for the yard: one by Troughton of London # (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent # with the definition of the meter in the metric joint resolution of # Congress in 1866, but defining the yard in terms of the meter; and the # international yard (1959), which standardized definitions for Australia, # Canada, New Zealand, South Africa, the UK, and the US. # Sources: Pat Naughtin (2009), Which Inch?, www.metricationmatters.com; # Lewis E. Barbrow and Lewis V. Judson (1976). NBS Special Publication # 447, Weights and Measures Standards of the United States: A Brief # History. troughtonyard 914.42190 mm bronzeyard11 914.39980 mm mendenhallyard surveyyard internationalyard yard # nautical measure fathom 6 ft # Originally defined as the distance from # fingertip to fingertip with arms fully # extended. nauticalmile 1852 m # Supposed to be one minute of latitude at # the equator. That value is about 1855 m. # Early estimates of the earth's circumference # were a bit off. The value of 1852 m was # made the international standard in 1929. # The US did not accept this value until # 1954. The UK switched in 1970. cable 1|10 nauticalmile intcable cable # international cable cablelength cable UScable 100 USfathom navycablelength 720 USft # used for depth in water marineleague 3 nauticalmile geographicalmile brnauticalmile knot nauticalmile / hr click km # US military slang klick click # Avoirdupois weight pound 0.45359237 kg # The one normally used lb pound # From the latin libra grain 1|7000 pound # The grain is the same in all three # weight systems. It was originally # defined as the weight of a barley # corn taken from the middle of the # ear. ounce 1|16 pound oz ounce dram 1|16 ounce dr dram ushundredweight 100 pounds cwt hundredweight shorthundredweight ushundredweight uston shortton shortton 2000 lb quarterweight 1|4 uston shortquarterweight 1|4 shortton shortquarter shortquarterweight # Troy Weight. In 1828 the troy pound was made the first United States # standard weight. It was to be used to regulate coinage. troypound 5760 grain troyounce 1|12 troypound ozt troyounce pennyweight 1|20 troyounce # Abbreviated "d" in reference to a dwt pennyweight # Frankish coin called the "denier" # minted in the late 700's. There # were 240 deniers to the pound. assayton mg ton / troyounce # mg / assayton = troyounce / ton usassayton mg uston / troyounce brassayton mg brton / troyounce fineounce troyounce # A troy ounce of 99.5% pure gold # Some other jewelers units metriccarat 0.2 gram # Defined in 1907 metricgrain 50 mg carat metriccarat ct carat jewelerspoint 1|100 carat silversmithpoint 1|4000 inch momme 3.75 grams # Traditional Japanese unit based # on the chinese mace. It is used for # pearls in modern times and also for # silk density. The definition here # was adopted in 1891. # Apothecaries' weight appound troypound apounce troyounce apdram 1|8 apounce apscruple 1|3 apdram # Liquid measure usgallon 231 in^3 # US liquid measure is derived from gal gallon # the British wine gallon of 1707. quart 1|4 gallon # See the "winegallon" entry below pint 1|2 quart # more historical information. gill 1|4 pint usquart 1|4 usgallon uspint 1|2 usquart usgill 1|4 uspint usfluidounce 1|16 uspint fluiddram 1|8 usfloz minimvolume 1|60 fluiddram qt quart pt pint floz fluidounce usfloz usfluidounce fldr fluiddram liquidbarrel 31.5 usgallon usbeerbarrel 2 beerkegs beerkeg 15.5 usgallon # Various among brewers ponykeg 1|2 beerkeg winekeg 12 usgallon petroleumbarrel 42 usgallon # Originated in Pennsylvania oil barrel petroleumbarrel # fields, from the winetierce bbl barrel ushogshead 2 liquidbarrel usfirkin 9 usgallon # Dry measures: The Winchester Bushel was defined by William III in 1702 and # legally adopted in the US in 1836. usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5 bu bushel # inch diameter (rounded) peck 1|4 bushel uspeck 1|4 usbushel brpeck 1|4 brbushel pk peck drygallon 1|2 uspeck dryquart 1|4 drygallon drypint 1|2 dryquart drybarrel 7056 in^3 # Used in US for fruits, vegetables, # and other dry commodities except for # cranberries. cranberrybarrel 5826 in^3 # US cranberry barrel heapedbushel 1.278 usbushel# The following explanation for this # value was provided by Wendy Krieger # based on # guesswork. The cylindrical vessel is # 18.5 inches in diameter and 1|2 inch # thick. A heaped bushel includes the # contents of this cylinder plus a heap # on top. The heap is a cone 19.5 # inches in diameter and 6 inches # high. With these values, the volume # of the bushel is 684.5 pi in^3 and # the heap occupies 190.125 pi in^3. # Therefore, the heaped bushel is # 874.625|684.5 bushels. This value is # approximately 1.2777575 and it rounds # to the value listed for the size of # the heaped bushel. Sometimes the # heaped bushel is reported as 1.25 # bushels. This same explanation gives # that value if the heap is taken to # have an 18.5 inch diameter. # Grain measures. The bushel as it is used by farmers in the USA is actually # a measure of mass which varies for different commodities. Canada uses the # same bushel masses for most commodities, but not for oats. wheatbushel 60 lb soybeanbushel 60 lb cornbushel 56 lb ryebushel 56 lb barleybushel 48 lb oatbushel 32 lb ricebushel 45 lb canada_oatbushel 34 lb # Wine and Spirits measure ponyvolume 1 usfloz jigger 1.5 usfloz # Can vary between 1 and 2 usfloz shot jigger # Sometimes 1 usfloz eushot 25 ml # EU standard spirits measure fifth 1|5 usgallon winebottle 750 ml # US industry standard, 1979 winesplit 1|4 winebottle magnum 1.5 liter # Standardized in 1979, but given # as 2 qt in some references metrictenth 375 ml metricfifth 750 ml metricquart 1 liter # Old British bottle size reputedquart 1|6 brgallon reputedpint 1|2 reputedquart brwinebottle reputedquart # Very close to 1|5 winegallon # French champagne bottle sizes split 200 ml jeroboam 2 magnum rehoboam 3 magnum methuselah 4 magnum imperialbottle 4 magnum salmanazar 6 magnum balthazar 8 magnum nebuchadnezzar 10 magnum solomon 12 magnum melchior 12 magnum sovereign 17.5 magnum primat 18 magnum goliath 18 magnum melchizedek 20 magnum midas 20 magnum # The wine glass doesn't seem to have an official standard, but the same value # is suggested by several organization. # https://www.rethinkingdrinking.niaaa.nih.gov/ # http://www.rethinkyourdrinking.ca/what-is-a-standard-drink/ # https://www.drinkaware.co.uk/ # https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/5459 37/UK_CMOs__report.pdf # http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/content/drinksguide- cnt wineglass 150 mL # the size of a "typical" serving # A unit of alcohol is a specified mass of pure ethyl alcohol. # The term is used officially in the UK, but other countries use the same # concept but with different values. For example, the UK value of 8 g is # nominally the amount of alcohol that a typical adult can metabolize in # one hour. Values for several countries, converted to a volumetric basis: alcoholunitus 14 g / ethanoldensity alcoholunitca 13.6 g / ethanoldensity alcoholunituk 8 g / ethanoldensity alcoholunitau 10 g / ethanoldensity # Example: for 12% ABV (alcohol by volume) # alcoholunitus / 12% = 147.8 mL, close to the “standard” serving of 150 mL. # Coffee # # The recommended ratio of coffee to water. Values vary considerably; # one is from the Specialty Coffee Association of America # http://scaa.org/?page=resources&d=brewing-best-practices coffeeratio 55 g/L # ± 10% # other recommendations are more loose, e.g., # http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee # # Water is "hard" if it contains various minerals, expecially calcium # carbonate. # clarkdegree grains/brgallon # Content by weigh of calcium carbonate gpg grains/usgallon # Divide by water's density to convert to # a dimensionless concentration measure # # Shoe measures # shoeiron 1|48 inch # Used to measure leather in soles shoeounce 1|64 inch # Used to measure non-sole shoe leather # USA shoe sizes. These express the length of the shoe or the length # of the "last", the form that the shoe is made on. But note that # this only captures the length. It appears that widths change 1/4 # inch for each letter within the same size, and if you change the # length by half a size then the width changes between 1/8 inch and # 1/4 inch. But this may not be standard. If you know better, please # contact me. shoesize_delta 1|3 inch # USA shoe sizes differ by this amount shoe_men0 8.25 inch shoe_women0 (7+11|12) inch shoe_boys0 (3+11|12) inch shoe_girls0 (3+7|12) inch shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \ (shoesize_men+(-shoe_men0))/shoesize_delta shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \ (shoesize_women+(-shoe_women0))/shoesize_delta shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \ (shoesize_boys+(-shoe_boys0))/shoesize_delta shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \ (shoesize_girls+(-shoe_girls0))/shoesize_delta # European shoe size. According to # http://www.shoeline.com/footnotes/shoeterm.shtml # shoe sizes in Europe are measured with Paris points which simply measure # the length of the shoe. europeshoesize 2|3 cm # # USA slang units # buck US$ fin 5 US$ sawbuck 10 US$ usgrand 1000 US$ greenback US$ key kg # usually of marijuana, 60's lid 1 oz # Another 60's weed unit footballfield usfootballfield usfootballfield 100 yards canadafootballfield 110 yards # And 65 yards wide marathon 26 miles + 385 yards # # British # # The length measure in the UK was defined by a bronze bar manufactured in # 1844. Various conversions were sanctioned for convenience at different # times, which makes conversions before 1963 a confusing matter. Apparently # previous conversions were never explicitly revoked. Four different # conversion factors appear below. Multiply them times an imperial length # units as desired. The Weights and Measures Act of 1963 switched the UK away # from their bronze standard and onto a definition of the yard in terms of the # meter. This happened after an international agreement in 1959 to align the # world's measurement systems. UK UKlength_SJJ UK- UK british- UK UKlength_B 0.9143992 meter / yard # Benoit found the yard to be # 0.9143992 m at a weights and # measures conference around # 1896. Legally sanctioned # in 1898. UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and # Johnson found the yard to be # 0.91439841 meters. # Used starting in the 1930's. UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio # for the meter and inch. This # value was used as the legal # conversion ratio when the # metric system was legalized # for contract in 1864. UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter # to be 1.09362311 yards. This # conversion was legalized # around 1878. brnauticalmile 6080 ft # Used until 1970 when the UK brknot brnauticalmile / hr # switched to the international brcable 1|10 brnauticalmile # nautical mile. admiraltymile brnauticalmile admiraltyknot brknot admiraltycable brcable seamile 6000 ft shackle 15 fathoms # Adopted 1949 by British navy # British Imperial weight is mostly the same as US weight. A few extra # units are added here. clove 7 lb stone 14 lb tod 28 lb brquarterweight 1|4 brhundredweight brhundredweight 8 stone longhundredweight brhundredweight longton 20 brhundredweight brton longton # British Imperial volume measures brminim 1|60 brdram brscruple 1|3 brdram fluidscruple brscruple brdram 1|8 brfloz brfluidounce 1|20 brpint brfloz brfluidounce brgill 1|4 brpint brpint 1|2 brquart brquart 1|4 brgallon brgallon 4.54609 l # The British Imperial gallon was # defined in 1824 to be the volume of # water which weighed 10 pounds at 62 # deg F with a pressure of 30 inHg. # It was also defined as 277.274 in^3, # Which is slightly in error. In # 1963 it was defined to be the volume # occupied by 10 pounds of distilled # water of density 0.998859 g/ml weighed # in air of density 0.001217 g/ml # against weights of density 8.136 g/ml. # This gives a value of approximately # 4.5459645 liters, but the old liter # was in force at this time. In 1976 # the definition was changed to exactly # 4.54609 liters using the new # definition of the liter (1 dm^3). brbarrel 36 brgallon # Used for beer brbushel 8 brgallon brheapedbushel 1.278 brbushel brquarter 8 brbushel brchaldron 36 brbushel # Obscure British volume measures. These units are generally traditional # measures whose definitions have fluctuated over the years. Often they # depended on the quantity being measured. They are given here in terms of # British Imperial measures. For example, the puncheon may have historically # been defined relative to the wine gallon or beer gallon or ale gallon # rather than the British Imperial gallon. bag 4 brbushel bucket 4 brgallon kilderkin 2 brfirkin last 40 brbushel noggin brgill pottle 0.5 brgallon pin 4.5 brgallon puncheon 72 brgallon seam 8 brbushel coomb 4 brbushel boll 6 brbushel firlot 1|4 boll brfirkin 9 brgallon # Used for ale and beer cran 37.5 brgallon # measures herring, about 750 fish brwinehogshead 52.5 brgallon # This value is approximately equal brhogshead brwinehogshead # to the old wine hogshead of 63 # wine gallons. This adjustment # is listed in the OED and in # "The Weights and Measures of # England" by R. D. Connor brbeerhogshead 54 brgallon brbeerbutt 2 brbeerhogshead registerton 100 ft^3 # Used for internal capacity of ships shippington 40 ft^3 # Used for ship's cargo freight or timber brshippington 42 ft^3 # freightton shippington # Both register ton and shipping ton derive # from the "tun cask" of wine. displacementton 35 ft^3 # Approximate volume of a longton weight of # sea water. Measures water displaced by # ships. waterton 224 brgallon strike 70.5 l # 16th century unit, sometimes # defined as .5, 2, or 4 bushels # depending on the location. It # probably doesn't make a lot of # sense to define in terms of imperial # bushels. Zupko gives a value of # 2 Winchester grain bushels or about # 70.5 liters. amber 4 brbushel# Used for dry and liquid capacity [18] # British volume measures with "imperial" imperialminim brminim imperialscruple brscruple imperialdram brdram imperialfluidounce brfluidounce imperialfloz brfloz imperialgill brgill imperialpint brpint imperialquart brquart imperialgallon brgallon imperialbarrel brbarrel imperialbushel brbushel imperialheapedbushel brheapedbushel imperialquarter brquarter imperialchaldron brchaldron imperialwinehogshead brwinehogshead imperialhogshead brhogshead imperialbeerhogshead brbeerhogshead imperialbeerbutt brbeerbutt imperialfirkin brfirkin # obscure British lengths barleycorn 1|3 UKinch # Given in Realm of Measure as the # difference between successive shoe sizes nail 1|16 UKyard # Originally the width of the thumbnail, # or 1|16 ft. This took on the general # meaning of 1|16 and settled on the # nail of a yard or 1|16 yards as its # final value. [12] pole 16.5 UKft # This was 15 Saxon feet, the Saxon rope 20 UKft # foot (aka northern foot) being longer englishell 45 UKinch flemishell 27 UKinch ell englishell # supposed to be measure from elbow to # fingertips span 9 UKinch # supposed to be distance from thumb # to pinky with full hand extension goad 4.5 UKft # used for cloth, possibly named after the # stick used for prodding animals. # misc obscure British units hide 120 acre # English unit of land area dating to the 7th # century, originally the amount of land # that a single plowman could cultivate, # which varied from 60-180 acres regionally. # Standardized at Normon conquest. virgate 1|4 hide nook 1|2 virgate rood furlong rod # Area of a strip a rod by a furlong englishcarat troyounce/151.5 # Originally intended to be 4 grain # but this value ended up being # used in the London diamond market mancus 2 oz mast 2.5 lb nailkeg 100 lbs basebox 31360 in^2 # Used in metal plating # alternate spellings gramme gram litre liter dioptre diopter aluminium aluminum sulphur sulfur # # Units derived the human body (may not be very accurate) # geometricpace 5 ft # distance between points where the same # foot hits the ground pace 2.5 ft # distance between points where alternate # feet touch the ground USmilitarypace 30 in # United States official military pace USdoubletimepace 36 in # United States official doubletime pace fingerbreadth 7|8 in # The finger is defined as either the width fingerlength 4.5 in # or length of the finger finger fingerbreadth palmwidth hand # The palm is a unit defined as either the width palmlength 8 in # or the length of the hand hand 4 inch # width of hand shaftment 6 inch # Distance from tip of outstretched thumb to the # opposite side of the palm of the hand. The # ending -ment is from the old English word # for hand. [18] smoot 5 ft + 7 in # Created as part of an MIT fraternity prank. # In 1958 Oliver Smoot was used to measure # the length of the Harvard Bridge, which was # marked off in Smoot lengths. These # markings have been maintained on the bridge # since then and repainted by subsequent # incoming fraternity members. During a # bridge renovation the new sidewalk was # scored every Smoot rather than at the # customary 6 ft spacing. # # Cooking measures # # Common abbreviations tbl tablespoon tbsp tablespoon tblsp tablespoon Tb tablespoon tsp teaspoon saltspoon 1|4 tsp # US measures uscup 8 usfloz ustablespoon 1|16 uscup usteaspoon 1|3 ustablespoon ustbl ustablespoon ustbsp ustablespoon ustblsp ustablespoon ustsp usteaspoon metriccup 250 ml stickbutter 1|4 lb # Butter in the USA is sold in one # pound packages that contain four # individually wrapped pieces. The # pieces are marked into tablespoons, # making it possible to measure out # butter by volume by slicing the # butter. legalcup 240 ml # The cup used on nutrition labeling legaltablespoon 1|16 legalcup legaltbsp legaltablespoon # Scoop size. Ice cream scoops in the US are marked with numbers # indicating the number of scoops required to fill a US quart. scoop(n) units=[1;cup] domain=[4,100] range=[0.04,1] \ 32 usfloz / n ; 32 usfloz / scoop # US can sizes. number1can 10 usfloz number2can 19 usfloz number2.5can 3.5 uscups number3can 4 uscups number5can 7 uscups number10can 105 usfloz # British measures brcup 1|2 brpint brteacup 1|3 brpint brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon brdessertspoon 2 brteaspoon dessertspoon brdessertspoon dsp dessertspoon brtsp brteaspoon brtbl brtablespoon brtbsp brtablespoon brtblsp brtablespoon # Australian australiatablespoon 20 ml austbl australiatablespoon austbsp australiatablespoon austblsp australiatablespoon australiateaspoon 1|4 australiatablespoon austsp australiateaspoon # Italian etto 100 g # Used for buying items like meat and etti etto # cheese. # Chinese catty 0.5 kg oldcatty 4|3 lbs # Before metric conversion. tael 1|16 oldcatty # Should the tael be defined both ways? mace 0.1 tael oldpicul 100 oldcatty picul 100 catty # Chinese usage # Indian seer 14400 grain # British Colonial standard ser seer maund 40 seer pakistanseer 1 kg pakistanmaund 40 pakistanseer chittak 1|16 seer tola 1|5 chittak ollock 1|4 liter # Is this right? # Japanese japancup 200 ml # densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum # so you can convert '2 cups sugar' to grams, for example, or in the other # direction grams could be converted to 'cup flour_scooped'. butter 8 oz/uscup butter_clarified 6.8 oz/uscup cocoa_butter 9 oz/uscup shortening 6.75 oz/uscup # vegetable shortening oil 7.5 oz/uscup cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the cakeflour_spooned 4 oz/uscup # measuring method. "Scooped", or cakeflour_scooped 4.5 oz/uscup # "dip and sweep" refers to dipping a flour_sifted 4 oz/uscup # measure into a bin, and then sweeping flour_spooned 4.25 oz/uscup # the excess off the top. "Spooned" flour_scooped 5 oz/uscup # means to lightly spoon into a measure breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top. cornstarch 120 grams/uscup dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa dutchcocoa_spooned 92 g/uscup dutchcocoa_scooped 95 g/uscup cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa cocoa_spooned 82 g/uscup cocoa_scooped 95 g/uscup heavycream 232 g/uscup milk 242 g/uscup sourcream 242 g/uscup molasses 11.25 oz/uscup cornsyrup 11.5 oz/uscup honey 11.75 oz/uscup sugar 200 g/uscup powdered_sugar 4 oz/uscup brownsugar_light 217 g/uscup # packed brownsugar_dark 239 g/uscup baking_powder 4.6 grams / ustsp salt 6 g / ustsp koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt koshersalt_morton 4.8 g / ustsp # Morton kosher salt # Values are from the nutrition info # on the packages # Egg weights and volumes for a USA large egg egg 50 grams # without shell eggwhite 30 grams eggyolk 18.6 grams eggvolume 3 ustablespoons + 1|2 ustsp eggwhitevolume 2 ustablespoons eggyolkvolume 3.5 ustsp # Alcohol density ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition alcoholdensity ethanoldensity # # Density measures. Density has traditionally been measured on a variety of # bizarre nonlinear scales. # # Density of a sugar syrup is frequently measured in candy making procedures. # In the USA the boiling point of the syrup is measured. Some recipes instead # specify the density using degrees Baume. Conversion between degrees Baume # and the boiling point measure has proved elusive. This table appeared in one # text, and provides a fragmentary relationship to the concentration. # # temp(C) conc (%) # 100 30 # 101 40 # 102 50 # 103 60 # 106 70 # 112 80 # 123 90 # 140 95 # 151 97 # 160 98.2 # 166 99.5 # 171 99.6 # # The best source identified to date came from "Boiling point elevation of # technical sugarcane solutions and its use in automatic pan boiling" by # Michael Saska. International Sugar Journal, 2002, 104, 1247, pp 500-507. # # But I'm using equation (3) which is credited to Starzak and Peacock, # "Water activity coefficient in aqueous solutions of sucrose--A comprehensive # data analysis. Zuckerindustrie, 122, 380-387. (I couldn't find this # document.) # # Note that the range of validity is uncertain, but answers are in agreement # with the above table all the way to 99.6. # # The original equation has a parameter for the boiling point of water, which # of course varies with altitude. It also includes various other model # parameters. The input is the molar concentration of sucrose in the solution, # (moles sucrose) / (total moles). # # Bsp 3797.06 degC # Csp 226.28 degC # QQ -17638 J/mol # asp -1.0038 # bsp -0.24653 # tbw 100 degC # boiling point of water # sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \ # /(tbw+stdtemp)) / (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp) # # To convert mass concentration (brix) to molar concentration # # sc(x) (x / 342.3) / (( x/342.3) + (100-x)/18.02); \ # 100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1) # # Here is a simplified version of this equation where the temperature of boiling # water has been fixed at 100 degrees Celsius and the argument is now the # concentration (brix). # # sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \ # / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K # # # The formula is not invertible, so to implement it in units we unfortunately # must turn it into a table. # This table gives the boiling point elevation as a function of the sugar syrup # concentration expressed as a percentage. sugar_conc_bpe[K] \ 0 0.0000 5 0.0788 10 0.1690 15 0.2729 20 0.3936 25 0.5351 \ 30 0.7027 35 0.9036 40 1.1475 42 1.2599 44 1.3825 46 1.5165 \ 48 1.6634 50 1.8249 52 2.0031 54 2.2005 56 2.4200 58 2.6651 \ 60 2.9400 61 3.0902 62 3.2499 63 3.4198 64 3.6010 65 3.7944 \ 66 4.0012 67 4.2227 68 4.4603 69 4.7156 70 4.9905 71 5.2870 \ 72 5.6075 73 5.9546 74 6.3316 75 6.7417 76 7.1892 77 7.6786 \ 78.0 8.2155 79.0 8.8061 80.0 9.4578 80.5 9.8092 81.0 10.1793 \ 81.5 10.5693 82.0 10.9807 82.5 11.4152 83.0 11.8743 83.5 12.3601 \ 84.0 12.8744 84.5 13.4197 85.0 13.9982 85.5 14.6128 86.0 15.2663 \ 86.5 15.9620 87.0 16.7033 87.5 17.4943 88.0 18.3391 88.5 19.2424 \ 89.0 20.2092 89.5 21.2452 90.0 22.3564 90.5 23.5493 91.0 24.8309 \ 91.5 26.2086 92.0 27.6903 92.5 29.2839 93.0 30.9972 93.5 32.8374 \ 94.0 34.8104 94.5 36.9195 95.0 39.1636 95.5 41.5348 96.0 44.0142 \ 96.5 46.5668 97.0 49.1350 97.5 51.6347 98.0 53.9681 98.1 54.4091 \ 98.2 54.8423 98.3 55.2692 98.4 55.6928 98.5 56.1174 98.6 56.5497 \ 98.7 56.9999 98.8 57.4828 98.9 58.0206 99.0 58.6455 99.1 59.4062 \ 99.2 60.3763 99.3 61.6706 99.4 63.4751 99.5 66.1062 99.6 70.1448 \ 99.7 76.7867 # Using the brix table we can use this to produce a mapping from boiling point # to density which makes all of the units interconvertible. Because the brix # table stops at 95 this approach works up to a boiling point elevation of 39 K # or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy # making. The "hard crack" stage continues up to 310 F. # Boiling point elevation sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \ brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe)) # Absolute boiling point (produces an absolute temperature) sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \ range=[0.99717,1.5144619] \ brix(~sugar_conc_bpe(T-tempC(100))) ;\ sugar_conc_bpe(~brix(sugar_bp))+tempC(100) # In practice dealing with the absolute temperature is annoying because it is # not possible to convert to a nested function, so you're stuck retyping the # absolute temperature in Kelvins to convert to celsius or Fahrenheit. To # prevent this we supply definitions that build in the temperature conversion # and produce results in the Fahrenheit and Celsius scales. So using these # measures, to convert 46 degrees Baume to a Fahrenheit boiling point: # # You have: baume(45) # You want: sugar_bpF # 239.05647 # sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\ brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\ ~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100)) sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\ brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\ ~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100)) # Degrees Baume is used in European recipes to specify the density of a sugar # syrup. An entirely different definition is used for densities below # 1 g/cm^3. An arbitrary constant appears in the definition. This value is # equal to 145 in the US, but was according to [], the old scale used in # Holland had a value of 144, and the new scale or Gerlach scale used 146.78. baumeconst 145 # US value baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \ (baumeconst/(baumeconst+-d)) g/cm^3 ; \ (baume+((-g)/cm^3)) baumeconst / baume # It's not clear if this value was ever used with negative degrees. twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \ (1 + 0.005 x) g / cm^3 ; \ 200 (twaddell / (g/cm^3) +- 1) # The degree quevenne is a unit for measuring the density of milk. # Similarly it's unclear if negative values were allowed here. quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \ (1 + 0.001 x) g / cm^3 ; \ 1000 (quevenne / (g/cm^3) +- 1) # Degrees brix measures sugar concentration by weigh as a percentage, so a # solution that is 3 degrees brix is 3% sugar by weight. This unit was named # after Adolf Brix who invented a hydrometer that read this percentage # directly. This data is from Table 114 of NIST Circular 440, "Polarimetry, # Saccharimetry and the Sugars". It gives apparent specific gravity at 20 # degrees Celsius of various sugar concentrations. As rendered below this # data is converted to apparent density at 20 degrees Celsius using the # density figure for water given in the same NIST reference. They use the # word "apparent" to refer to measurements being made in air with brass # weights rather than vacuum. brix[0.99717g/cm^3]\ 0 1.00000 1 1.00390 2 1.00780 3 1.01173 4 1.01569 5 1.01968 \ 6 1.02369 7 1.02773 8 1.03180 9 1.03590 10 1.04003 11 1.04418 \ 12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \ 18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \ 24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \ 30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \ 36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \ 42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \ 48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \ 54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \ 60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \ 66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \ 72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \ 78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \ 84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \ 90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876 # Density measure invented by the American Petroleum Institute. Lighter # petroleum products are more valuable, and they get a higher API degree. # # The intervals of range and domain should be open rather than closed. # apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \ 141.5 g/cm^3 / (x+131.5) ; \ 141.5 (g/cm^3) / apidegree + (-131.5) # # Average densities of various woods (dried) # Data from The Wood Database https://www.wood-database.com # # North American Hardwoods wood_cherry 35 lb/ft^3 wood_redoak 44 lb/ft^3 wood_whiteoak 47 lb/ft^3 wood_blackwalnut 38 lb/ft^3 wood_walnut wood_blackwalnut wood_birch 43 lb/ft^3 wood_hardmaple 44 lb/ft^3 wood_bigleafmaple 34 lb/ft^3 wood_boxeldermaple 30 lb/ft^3 wood_redmaple 38 lb/ft^3 wood_silvermaple 33 lb/ft^3 wood_stripedmaple 32 lb/ft^3 wood_softmaple (wood_bigleafmaple \ + wood_boxeldermaple \ + wood_redmaple \ + wood_silvermaple \ + wood_stripedmaple) / 5 wood_poplar 29 lb/ft^3 wood_beech 45 lb/ft^3 # North American Softwoods wood_jeffreypine 28 lb/ft^3 wood_ocotepine 44 lb/ft^3 wood_ponderosapine 28 lb/ft^3 wood_loblollypine 35 lb/ft^3 wood_longleafpine 41 lb/ft^3 wood_shortleafpine 35 lb/ft^3 wood_slashpine 41 lb/ft^3 wood_yellowpine (wood_loblollypine \ + wood_longleafpine \ + wood_shortleafpine \ + wood_slashpine) / 4 wood_redpine 34 lb/ft^3 wood_easternwhitepine 25 lb/ft^3 wood_westernwhitepine 27 lb/ft^3 wood_whitepine (wood_easternwhitepine + wood_westernwhitepine) / 2 wood_douglasfir 32 lb/ft^3 wood_blackspruce 28 lb/ft^3 wood_engelmannspruce 24 lb/ft^3 wood_redspruce 27 lb/ft^3 wood_sitkaspruce 27 lb/ft^3 wood_whitespruce 27 lb/ft^3 wood_spruce (wood_blackspruce \ + wood_engelmannspruce \ + wood_redspruce \ + wood_sitkaspruce \ + wood_whitespruce) / 5 # Other woods wood_basswood 26 lb/ft^3 wood_balsa 9 lb/ft^3 wood_ebony_gaboon 60 lb/ft^3 wood_ebony_macassar 70 lb/ft^3 wood_mahogany 37 lb/ft^3 # True (Honduran) mahogany, # Swietenia macrophylla wood_teak 41 lb/ft^3 wood_rosewood_brazilian 52 lb/ft^3 wood_rosewood_honduran 64 lb/ft^3 wood_rosewood_indian 52 lb/ft^3 wood_cocobolo 69 lb/ft^3 wood_bubinga 56 lb/ft^3 wood_zebrawood 50 lb/ft^3 wood_koa 38 lb/ft^3 wood_snakewood 75.7 lb/ft^3 wood_lignumvitae 78.5 lb/ft^3 wood_blackwood 79.3 lb/ft^3 wood_blackironwood 84.5 lb/ft^3 # Krugiodendron ferreum, listed # in database as the heaviest wood # # Modulus of elasticity of selected woods. # Data from The Wood Database https://www.wood-database.com # # North American Hardwoods wood_mod_beech 1.720e6 lbf/in^2 wood_mod_birchyellow 2.010e6 lbf/in^2 wood_mod_birch wood_mod_birchyellow wood_mod_cherry 1.490e6 lbf/in^2 wood_mod_hardmaple 1.830e6 lbf/in^2 wood_mod_bigleafmaple 1.450e6 lbf/in^2 wood_mod_boxeldermaple 1.050e6 lbf/in^2 wood_mod_redmaple 1.640e6 lbf/in^2 wood_mod_silvermaple 1.140e6 lbf/in^2 wood_mod_softmaple (wood_mod_bigleafmaple \ + wood_mod_boxeldermaple \ + wood_mod_redmaple \ + wood_mod_silvermaple) / 4 wood_mod_redoak 1.761e6 lbf/in^2 wood_mod_whiteoak 1.762e6 lbf/in^2 wood_mod_poplar 1.580e6 lbf/in^2 wood_mod_blackwalnut 1.680e6 lbf/in^2 wood_mod_walnut wood_mod_blackwalnut # North American Softwoods wood_mod_jeffreypine 1.240e6 lbf/in^2 wood_mod_ocotepine 2.209e6 lbf/in^2 wood_mod_ponderosapine 1.290e6 lbf/in^2 wood_mod_loblollypine 1.790e6 lbf/in^2 wood_mod_longleafpine 1.980e6 lbf/in^2 wood_mod_shortleafpine 1.750e6 lbf/in^2 wood_mod_slashpine 1.980e6 lbf/in^2 wood_mod_yellowpine (wood_mod_loblollypine \ + wood_mod_longleafpine \ + wood_mod_shortleafpine \ + wood_mod_slashpine) / 4 wood_mod_redpine 1.630e6 lbf/in^2 wood_mod_easternwhitepine 1.240e6 lbf/in^2 wood_mod_westernwhitepine 1.460e6 lbf/in^2 wood_mod_whitepine (wood_mod_easternwhitepine + \ wood_mod_westernwhitepine) / 2 wood_mod_douglasfir 1.765e6 lbf/in^2 wood_mod_blackspruce 1.523e6 lbf/in^2 wood_mod_englemannspruce 1.369e6 lbf/in^2 wood_mod_redspruce 1.560e6 lbf/in^2 wood_mod_sitkaspruce 1.600e6 lbf/in^2 wood_mod_whitespruce 1.315e6 lbf/in^2 wood_mod_spruce (wood_mod_blackspruce \ + wood_mod_englemannspruce \ + wood_mod_redspruce + wood_mod_sitkaspruce \ + wood_mod_whitespruce) / 5 # Other woods wood_mod_balsa 0.538e6 lbf/in^2 wood_mod_basswood 1.460e6 lbf/in^2 wood_mod_blackwood 2.603e6 lbf/in^2 # African, Dalbergia melanoxylon wood_mod_bubinga 2.670e6 lbf/in^2 wood_mod_cocobolo 2.712e6 lbf/in^2 wood_mod_ebony_gaboon 2.449e6 lbf/in^2 wood_mod_ebony_macassar 2.515e6 lbf/in^2 wood_mod_blackironwood 2.966e6 lbf/in^2 # Krugiodendron ferreum wood_mod_koa 1.503e6 lbf/in^2 wood_mod_lignumvitae 2.043e6 lbf/in^2 wood_mod_mahogany 1.458e6 lbf/in^2 # True (Honduran) mahogany, # Swietenia macrophylla wood_mod_rosewood_brazilian 2.020e6 lbf/in^2 wood_mod_rosewood_honduran 3.190e6 lbf/in^2 wood_mod_rosewood_indian 1.668e6 lbf/in^2 wood_mod_snakewood 3.364e6 lbf/in^2 wood_mod_teak 1.781e6 lbf/in^2 wood_mod_zebrawood 2.374e6 lbf/in^2 # # Area of countries and other regions. This is the "total area" which # includes land and water areas within international boundaries and # coastlines. Data from January, 2019. # # https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_area # https://www.cia.gov/library/publications/the-world-factbook) area_russia 17098246 km^2 area_antarctica 14000000 km^2 area_canada 9984670 km^2 area_china 9596961 km^2 area_unitedstates 9525067 km^2 # includes only the 50 states area_us area_unitedstates # and District of Columbia area_brazil 8515767 km^2 area_australia 7692024 km^2 area_europeanunion 4475757 km^2 area_eu area_europeanunion area_india 3287263 km^2 area_argentina 2780400 km^2 area_kazakhstan 2724900 km^2 area_algeria 2381741 km^2 area_drcongo 2344858 km^2 area_greenland 2166086 km^2 area_saudiarabia 2149690 km^2 area_mexico 1964375 km^2 area_indonesia 1910931 km^2 area_sudan 1861484 km^2 area_libya 1759540 km^2 area_iran 1648195 km^2 area_mongolia 1564110 km^2 area_peru 1285216 km^2 area_chad 1284000 km^2 area_niger 1267000 km^2 area_angola 1246700 km^2 area_mali 1240192 km^2 area_southafrica 1221037 km^2 area_colombia 1141748 km^2 area_ethiopia 1104300 km^2 area_bolivia 1098581 km^2 area_mauritania 1030700 km^2 area_egypt 1002450 km^2 area_tanzania 945087 km^2 area_nigeria 923768 km^2 area_venezuela 916445 km^2 area_pakistan 881912 km^2 area_namibia 825615 km^2 area_mozambique 801590 km^2 area_turkey 783562 km^2 area_chile 756102 km^2 area_zambia 752612 km^2 area_myanmar 676578 km^2 area_afghanistan 652230 km^2 area_southsudan 644329 km^2 area_france 640679 km^2 area_somalia 637657 km^2 area_centralafrica 622984 km^2 area_ukraine 603500 km^2 area_crimea 27000 km^2 # occupied by Russia; included in # (Encyclopedia Britannica) area_madagascar 587041 km^2 area_botswana 581730 km^2 area_kenya 580367 km^2 area_yemen 527968 km^2 area_thailand 513120 km^2 area_spain 505992 km^2 area_turkmenistan 488100 km^2 area_cameroon 475422 km^2 area_papuanewguinea 462840 km^2 area_sweden 450295 km^2 area_uzbekistan 447400 km^2 area_morocco 446550 km^2 area_iraq 438317 km^2 area_paraguay 406752 km^2 area_zimbabwe 390757 km^2 area_japan 377973 km^2 area_germany 357114 km^2 area_congorepublic 342000 km^2 area_finland 338424 km^2 area_vietnam 331212 km^2 area_malaysia 330803 km^2 area_norway 323802 km^2 area_ivorycoast 322463 km^2 area_poland 312696 km^2 area_oman 309500 km^2 area_italy 301339 km^2 area_philippines 300000 km^2 area_ecuador 276841 km^2 area_burkinafaso 274222 km^2 area_newzealand 270467 km^2 area_gabon 267668 km^2 area_westernsahara 266000 km^2 area_guinea 245857 km^2 area_uk 242495 km^2 area_uganda 241550 km^2 area_ghana 238533 km^2 area_romania 238397 km^2 area_laos 236800 km^2 area_guyana 214969 km^2 area_belarus 207600 km^2 area_kyrgyzstan 199951 km^2 area_senegal 196722 km^2 area_syria 185180 km^2 area_golanheights 1150 km^2 # occupied by Israel; included in # Syria (Encyclopedia Britannica) area_cambodia 181035 km^2 area_uruguay 176215 km^2 area_somaliland 176120 km^2 area_suriname 163820 km^2 area_tunisia 163610 km^2 area_bangladesh 147570 km^2 area_nepal 147181 km^2 area_tajikistan 143100 km^2 area_greece 131990 km^2 area_nicaragua 130373 km^2 area_northkorea 120540 km^2 area_malawi 118484 km^2 area_eritrea 117600 km^2 area_benin 114763 km^2 area_honduras 112492 km^2 area_liberia 111369 km^2 area_bulgaria 110879 km^2 area_cuba 109884 km^2 area_guatemala 108889 km^2 area_iceland 103000 km^2 area_southkorea 100210 km^2 area_hungary 93028 km^2 area_portugal 92090 km^2 area_jordan 89342 km^2 area_serbia 88361 km^2 area_azerbaijan 86600 km^2 area_austria 83871 km^2 area_uae 83600 km^2 area_czechrepublic 78865 km^2 area_panama 75417 km^2 area_sierraleone 71740 km^2 area_ireland 70273 km^2 area_georgia 69700 km^2 area_srilanka 65610 km^2 area_lithuania 65300 km^2 area_latvia 64559 km^2 area_togo 56785 km^2 area_croatia 56594 km^2 area_bosnia 51209 km^2 area_costarica 51100 km^2 area_slovakia 49037 km^2 area_dominicanrepublic 48671 km^2 area_estonia 45227 km^2 area_denmark 43094 km^2 area_netherlands 41850 km^2 area_switzerland 41284 km^2 area_bhutan 38394 km^2 area_taiwan 36193 km^2 area_guineabissau 36125 km^2 area_moldova 33846 km^2 area_gelgium 30528 km^2 area_lesotho 30355 km^2 area_armenia 29743 km^2 area_solomonislands 28896 km^2 area_albania 28748 km^2 area_equitorialguinea 28051 km^2 area_burundi 27834 km^2 area_haiti 27750 km^2 area_rwanda 26338 km^2 area_northmacedonia 25713 km^2 area_djibouti 23200 km^2 area_belize 22966 km^2 area_elsalvador 21041 km^2 area_israel 20770 km^2 area_slovenia 20273 km^2 area_fiji 18272 km^2 area_kuwait 17818 km^2 area_eswatini 17364 km^2 area_easttimor 14919 km^2 area_bahamas 13943 km^2 area_montenegro 13812 km^2 area_vanatu 12189 km^2 area_qatar 11586 km^2 area_gambia 11295 km^2 area_jamaica 10991 km^2 area_kosovo 10887 km^2 area_lebanon 10452 km^2 area_cyprus 9251 km^2 area_puertorico 9104 km^2 # United States territory; not included # in United States area area_westbank 5860 km^2 # (CIA World Factbook) area_hongkong 2755 km^2 area_luxembourg 2586 km^2 area_singapore 716 km^2 area_gazastrip 360 km^2 # (CIA World Factbook) area_liechtenstein 160 km^2 area_monaco 2.02 km^2 area_vaticancity 0.44 km^2 # # Area of the individual United States # # https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_area # area_alaska 1723337 km^2 area_texas 695662 km^2 area_california 423972 km^2 area_montana 380831 km^2 area_newmexico 314917 km^2 area_arizona 295234 km^2 area_nevada 286380 km^2 area_colorado 269601 km^2 area_oregon 254799 km^2 area_wyoming 253335 km^2 area_michigan 250487 km^2 area_minnesota 225163 km^2 area_utah 219882 km^2 area_idaho 216443 km^2 area_kansas 213100 km^2 area_nebraska 200330 km^2 area_southdakota 199729 km^2 area_washington 184661 km^2 area_northdakota 183108 km^2 area_oklahoma 181037 km^2 area_missouri 180540 km^2 area_florida 170312 km^2 area_wisconsin 169635 km^2 area_georgia_us 153910 km^2 area_illinois 149995 km^2 area_iowa 145746 km^2 area_newyork 141297 km^2 area_northcarolina 139391 km^2 area_arkansas 137732 km^2 area_alabama 135767 km^2 area_louisiana 135659 km^2 area_mississippi 125438 km^2 area_pennsylvania 119280 km^2 area_ohio 116098 km^2 area_virginia 110787 km^2 area_tennessee 109153 km^2 area_kentucky 104656 km^2 area_indiana 94326 km^2 area_maine 91633 km^2 area_southcarolina 82933 km^2 area_westvirginia 62756 km^2 area_maryland 32131 km^2 area_hawaii 28313 km^2 area_massachusetts 27336 km^2 area_vermont 24906 km^2 area_newhampshire 24214 km^2 area_newjersey 22591 km^2 area_connecticut 14357 km^2 area_delaware 6446 km^2 area_rhodeisland 4001 km^2 area_districtofcolumbia 177 km^2 # # Units derived from imperial system # ouncedal oz ft / s^2 # force which accelerates an ounce # at 1 ft/s^2 poundal lb ft / s^2 # same thing for a pound tondal longton ft / s^2 # and for a ton pdl poundal osi ounce force / inch^2 # used in aviation psi pound force / inch^2 psia psi # absolute pressure # Note that gauge pressure can be give n # using the gaugepressure() and # psig() nonlinear unit definitions tsi ton force / inch^2 reyn psi sec slug lbf s^2 / ft slugf slug force slinch lbf s^2 / inch # Mass unit derived from inch second slinchf slinch force # pound-force system. Used in space # applications where in/sec^2 was a # natural acceleration measure. geepound slug lbf lb force tonf ton force lbm lb kip 1000 lbf # from kilopound ksi kip / in^2 mil 0.001 inch thou 0.001 inch tenth 0.0001 inch # one tenth of one thousandth of an inch millionth 1e-6 inch # one millionth of an inch circularinch 1|4 pi in^2 # area of a one-inch diameter circle circleinch circularinch # A circle with diameter d inches has # an area of d^2 circularinches cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter # has volume d^2 h cylinder inches circularmil 1|4 pi mil^2 # area of one-mil diameter circle cmil circularmil cental 100 pound centner cental caliber 0.01 inch # for measuring bullets duty ft lbf celo ft / s^2 jerk ft / s^3 australiapoint 0.01 inch # The "point" is used to measure rainfall # in Australia sabin ft^2 # Measure of sound absorption equal to the # absorbing power of one square foot of # a perfectly absorbing material. The # sound absorptivity of an object is the # area times a dimensionless # absorptivity coefficient. standardgauge 4 ft + 8.5 in # Standard width between railroad track flag 5 ft^2 # Construction term referring to sidewalk. rollwallpaper 30 ft^2 # Area of roll of wall paper fillpower in^3 / ounce # Density of down at standard pressure. # The best down has 750-800 fillpower. pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA. buttonline 1|40 inch # The line was used in 19th century USA # to measure width of buttons. beespace 1|4 inch # Bees will fill any space that is smaller # than the bee space and leave open # spaces that are larger. The size of # the space varies with species. diamond 8|5 ft # Marking on US tape measures that is # useful to carpenters who wish to place # five studs in an 8 ft distance. Note # that the numbers appear in red every # 16 inches as well, giving six # divisions in 8 feet. retmaunit 1.75 in # Height of rack mountable equipment. U retmaunit # Equipment should be 1|32 inch narrower RU U # than its U measurement indicates to # allow for clearance, so 4U=(6+31|32)in # RETMA stands for the former name of # the standardizing organization, Radio # Electronics Television Manufacturers # Association. This organization is now # called the Electronic Industries # Alliance (EIA) and the rack standard # is specified in EIA RS-310-D. count per pound # For measuring the size of shrimp # # Other units of work, energy, power, etc # ENERGY joule WORK joule # Calorie: approximate energy to raise a gram of water one degree celsius calorie cal_th # Default is the thermochemical calorie cal calorie calorie_th 4.184 J # Thermochemical calorie, defined in 1930 thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to cal_th calorie_th # avoid difficulties associated with the # uncertainty in the heat capacity of # water. In 1948 the value of the joule # was changed, so the thermochemical # calorie was redefined to 4.184 J. # This kept the energy measured by this # unit the same. calorie_IT 4.1868 J # International (Steam) Table calorie, cal_IT calorie_IT # defined in 1929 as watt-hour/860 or # equivalently 180|43 joules. At this # time the international joule had a # different value than the modern joule, # and the values were different in the # USA and in Europe. In 1956 at the # Fifth International Conference on # Properties of Steam the exact # definition given here was adopted. calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC cal_15 calorie_15 calorie_fifteen cal_15 calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC cal_20 calorie_20 calorie_twenty calorie_20 calorie_4 4.204 J # Energy to go from 3.5 to 4.5 degC cal_4 calorie_4 calorie_four calorie_4 cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC Calorie kilocalorie # the food Calorie thermie 1e6 cal_15 # Heat required to raise the # temperature of a tonne of # water from 14.5 to 15.5 degC. # btu definitions: energy to raise a pound of water 1 degF btu btu_IT # International Table BTU is the default britishthermalunit btu btu_IT cal_IT lb degF / gram K btu_th cal_th lb degF / gram K btu_mean cal_mean lb degF / gram K btu_15 cal_15 lb degF / gram K btu_ISO 1055.06 J # Exact, rounded ISO definition based # on the IT calorie quad quadrillion btu ECtherm 1e5 btu_ISO # Exact definition UStherm 1.054804e8 J # Exact definition, therm UStherm # Water latent heat from [23] water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa # Specific heat capacities of various substances specificheat_water calorie / g K water_specificheat specificheat_water # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html specificheat_aluminum 0.91 J/g K specificheat_antimony 0.21 J/g K specificheat_barium 0.20 J/g K specificheat_beryllium 1.83 J/g K specificheat_bismuth 0.13 J/g K specificheat_cadmium 0.23 J/g K specificheat_cesium 0.24 J/g K specificheat_chromium 0.46 J/g K specificheat_cobalt 0.42 J/g K specificheat_copper 0.39 J/g K specificheat_gallium 0.37 J/g K specificheat_germanium 0.32 J/g K specificheat_gold 0.13 J/g K specificheat_hafnium 0.14 J/g K specificheat_indium 0.24 J/g K specificheat_iridium 0.13 J/g K specificheat_iron 0.45 J/g K specificheat_lanthanum 0.195 J/g K specificheat_lead 0.13 J/g K specificheat_lithium 3.57 J/g K specificheat_lutetium 0.15 J/g K specificheat_magnesium 1.05 J/g K specificheat_manganese 0.48 J/g K specificheat_mercury 0.14 J/g K specificheat_molybdenum 0.25 J/g K specificheat_nickel 0.44 J/g K specificheat_osmium 0.13 J/g K specificheat_palladium 0.24 J/g K specificheat_platinum 0.13 J/g K specificheat_plutonum 0.13 J/g K specificheat_potassium 0.75 J/g K specificheat_rhenium 0.14 J/g K specificheat_rhodium 0.24 J/g K specificheat_rubidium 0.36 J/g K specificheat_ruthenium 0.24 J/g K specificheat_scandium 0.57 J/g K specificheat_selenium 0.32 J/g K specificheat_silicon 0.71 J/g K specificheat_silver 0.23 J/g K specificheat_sodium 1.21 J/g K specificheat_strontium 0.30 J/g K specificheat_tantalum 0.14 J/g K specificheat_thallium 0.13 J/g K specificheat_thorium 0.13 J/g K specificheat_tin 0.21 J/g K specificheat_titanium 0.54 J/g K specificheat_tungsten 0.13 J/g K specificheat_uranium 0.12 J/g K specificheat_vanadium 0.39 J/g K specificheat_yttrium 0.30 J/g K specificheat_zinc 0.39 J/g K specificheat_zirconium 0.27 J/g K specificheat_ethanol 2.3 J/g K specificheat_ammonia 4.6 J/g K specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit specificheat_gasoline 2.22 J/g K specificheat_iodine 2.15 J/g K specificheat_oliveoil 1.97 J/g K # en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities specificheat_hydrogen 14.3 J/g K specificheat_helium 5.1932 J/g K specificheat_argon 0.5203 J/g K specificheat_tissue 3.5 J/g K specificheat_diamond 0.5091 J/g K specificheat_granite 0.79 J/g K specificheat_graphite 0.71 J/g K specificheat_ice 2.11 J/g K specificheat_asphalt 0.92 J/g K specificheat_brick 0.84 J/g K specificheat_concrete 0.88 J/g K specificheat_glass_silica 0.84 J/g K specificheat_glass_flint 0.503 J/g K specificheat_glass_pyrex 0.753 J/g K specificheat_gypsum 1.09 J/g K specificheat_marble 0.88 J/g K specificheat_sand 0.835 J/g K specificheat_soil 0.835 J/g K specificheat_wood 1.7 J/g K specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php # Energy densities of various fuels # # Most of these fuels have varying compositions or qualities and hence their # actual energy densities vary. These numbers are hence only approximate. # # E1. http://bioenergy.ornl.gov/papers/misc/energy_conv.html # E2. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm # E3. http://www.ior.com.au/ecflist.html tonoil 1e10 cal_IT # Ton oil equivalent. A conventional # value for the energy released by toe tonoil # burning one metric ton of oil. [18,E2] # Note that energy per mass of petroleum # products is fairly constant. # Variations in volumetric energy # density result from variations in the # density (kg/m^3) of different fuels. # This definition is given by the # IEA/OECD. toncoal 7e9 cal_IT # Energy in metric ton coal from [18]. # This is a nominal value which # is close to the heat content # of coal used in the 1950's barreloil 5.8 Mbtu # Conventional value for barrel of crude # oil [E2]. Actual range is 5.6 - 6.3. naturalgas_HHV 1027 btu/ft3 # Energy content of natural gas. HHV naturalgas_LHV 930 btu/ft3 # is for Higher Heating Value and naturalgas naturalgas_HHV # includes energy from condensation # combustion products. LHV is for Lower # Heating Value and excludes these. # American publications typically report # HHV whereas European ones report LHV. charcoal 30 GJ/tonne woodenergy_dry 20 GJ/tonne # HHV, a cord weights about a tonne woodenergy_airdry 15 GJ/tonne # 20% moisture content coal_bituminous 27 GJ / tonne coal_lignite 15 GJ / tonne coal_US 22 GJ / uston # Average for US coal (short ton), 1995 ethanol_HHV 84000 btu/usgallon ethanol_LHV 75700 btu/usgallon diesel 130500 btu/usgallon gasoline_LHV 115000 btu/usgallon gasoline_HHV 125000 btu/usgallon gasoline gasoline_HHV heating 37.3 MJ/liter fueloil 39.7 MJ/liter # low sulphur propane 93.3 MJ/m^3 butane 124 MJ/m^3 # These values give total energy from uranium fission. Actual efficiency # of nuclear power plants is around 30%-40%. Note also that some reactors # use enriched uranium around 3% U-235. Uranium during processing or use # may be in a compound of uranium oxide or uranium hexafluoride, in which # case the energy density would be lower depending on how much uranium is # in the compound. uranium_pure 200 MeV avogadro / (235.0439299 g/mol) # Pure U-235 uranium_natural 0.7% uranium_pure # Natural uranium: 0.7% U-235 # Celsius heat unit: energy to raise a pound of water 1 degC celsiusheatunit cal lb degC / gram K chu celsiusheatunit POWER watt # "Apparent" average power in an AC circuit, the product of rms voltage # and rms current, equal to the true power in watts when voltage and # current are in phase. In a DC circuit, always equal to the true power. VA volt ampere kWh kilowatt hour # The horsepower is supposedly the power of one horse pulling. Obviously # different people had different horses. horsepower 550 foot pound force / sec # Invented by James Watt mechanicalhorsepower horsepower hp horsepower metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in electrichorsepower 746 W # Germany boilerhorsepower 9809.50 W waterhorsepower 746.043 W brhorsepower 745.70 W donkeypower 250 W chevalvapeur metrichorsepower # # Heat Transfer # # Thermal conductivity, K, measures the rate of heat transfer across # a material. The heat transfered is # Q = K dT A t / L # where dT is the temperature difference across the material, A is the # cross sectional area, t is the time, and L is the length (thickness). # Thermal conductivity is a material property. THERMAL_CONDUCTIVITY POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH) THERMAL_RESISTIVITY 1/THERMAL_CONDUCTIVITY # Thermal conductance is the rate at which heat flows across a given # object, so the area and thickness have been fixed. It depends on # the size of the object and is hence not a material property. THERMAL_CONDUCTANCE POWER / TEMPERATURE_DIFFERENCE THERMAL_RESISTANCE 1/THERMAL_CONDUCTANCE # Thermal admittance is the rate of heat flow per area across an # object whose thickness has been fixed. Its reciprocal, thermal # insulation, is used to for measuring the heat transfer per area # of sheets of insulation or cloth that are of specified thickness. THERMAL_ADMITTANCE THERMAL_CONDUCTIVITY / LENGTH THERMAL_INSULANCE THERMAL_RESISTIVITY LENGTH THERMAL_INSULATION THERMAL_RESISTIVITY LENGTH Rvalue degF ft^2 hr / btu Uvalue 1/Rvalue europeanUvalue watt / m^2 K RSI degC m^2 / W clo 0.155 degC m^2 / W # Supposed to be the insulance # required to keep a resting person # comfortable indoors. The value # given is from NIST and the CRC, # but [5] gives a slightly different # value of 0.875 ft^2 degF hr / btu. tog 0.1 degC m^2 / W # Also used for clothing. # The bel was defined by engineers of Bell Laboratories to describe the # reduction in audio level over a length of one mile. It was originally # called the transmission unit (TU) but was renamed around 1923 to honor # Alexander Graham Bell. The bel proved inconveniently large so the decibel # has become more common. The decibel is dimensionless since it reports a # ratio, but it is used in various contexts to report a signal's power # relative to some reference level. bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel dB() decibel # Abbreviation dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative # to 1 joule. Used for power spectral # density since W/Hz = J # When used to measure amplitude, voltage, or current the signal is squared # because power is proportional to the square of these measures. The root # mean square (RMS) voltage is typically used with these units. dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2) # Reference = 1 microvolt # Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load. # Originally defined as dBv but changed to prevent confusion with dBV. # The "u" is for unloaded. dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \ ~dB(dBu^2 / mW 600 ohm) dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu # Measurements for sound in air, referenced to the threshold of human hearing # Note that sound in other media typically uses 1 micropascal as a reference # for sound pressure. Units dBA, dBB, dBC, refer to different frequency # weightings meant to approximate the human ear's response. dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \ ~dB(dBSPL^2 / (20 microPa)^2) # pressure dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \ ~dB(dBSIL / (1e-12 W/m^2)) # intensity dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W) # Misc other measures ENTROPY ENERGY / TEMPERATURE clausius 1e3 cal/K # A unit of physical entropy langley thermcalorie/cm^2 # Used in radiation theory poncelet 100 kg force m / s tonrefrigeration uston 144 btu / lb day # One ton refrigeration is # the rate of heat extraction required # turn one ton of water to ice in # a day. Ice is defined to have a # latent heat of 144 btu/lb. tonref tonrefrigeration refrigeration tonref / ton frigorie 1000 cal_15 # Used in refrigeration engineering. tnt 1e9 cal_th / ton# So you can write tons tnt. This # is a defined, not measured, value. airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as # pressure times air flow. # Nuclear weapon yields davycrocket 10 ton tnt # lightest US tactical nuclear weapon hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb nagasaki 21 kiloton tnt # Plutonium-239 fission bomb fatman nagasaki littleboy hiroshima ivyking 500 kiloton tnt # most powerful fission bomb castlebravo 15 megaton tnt # most powerful US test tsarbomba 50 megaton tnt # most powerful test ever: USSR, # 30 October 1961 b53bomb 9 megaton tnt # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/ trinity 18 kiloton tnt # July 16, 1945 gadget trinity # # Permeability: The permeability or permeance, n, of a substance determines # how fast vapor flows through the substance. The formula W = n A dP # holds where W is the rate of flow (in mass/time), n is the permeability, # A is the area of the flow path, and dP is the vapor pressure difference. # perm_0C grain / hr ft^2 inHg perm_zero perm_0C perm_0 perm_0C perm perm_0C perm_23C grain / hr ft^2 in Hg23C perm_twentythree perm_23C # # Counting measures # pair 2 brace 2 nest 3 # often used for items like bowls that # nest together hattrick 3 # Used in sports, especially cricket and ice # hockey to report the number of goals. dicker 10 dozen 12 bakersdozen 13 score 20 flock 40 timer 40 shock 60 toncount 100 # Used in sports in the UK longhundred 120 # From a germanic counting system gross 144 greatgross 12 gross tithe 1|10 # From Anglo-Saxon word for tenth # Paper counting measure shortquire 24 quire 25 shortream 480 ream 500 perfectream 516 bundle 2 reams bale 5 bundles # # Paper measures # # USA paper sizes lettersize 8.5 inch 11 inch legalsize 8.5 inch 14 inch ledgersize 11 inch 17 inch executivesize 7.25 inch 10.5 inch Apaper 8.5 inch 11 inch Bpaper 11 inch 17 inch Cpaper 17 inch 22 inch Dpaper 22 inch 34 inch Epaper 34 inch 44 inch # Correspondence envelope sizes. #10 is the standard business # envelope in the USA. envelope6_25size 3.5 inch 6 inch envelope6_75size 3.625 inch 6.5 inch envelope7size 3.75 inch 6.75 inch envelope7_75size 3.875 inch 7.5 inch envelope8_625size 3.625 inch 8.625 inch envelope9size 3.875 inch 8.875 inch envelope10size 4.125 inch 9.5 inch envelope11size 4.5 inch 10.375 inch envelope12size 4.75 inch 11 inch envelope14size 5 inch 11.5 inch envelope16size 6 inch 12 inch # Announcement envelope sizes (no relation to metric paper sizes like A4) envelopeA1size 3.625 inch 5.125 inch # same as 4bar envelopeA2size 4.375 inch 5.75 inch envelopeA6size 4.75 inch 6.5 inch envelopeA7size 5.25 inch 7.25 inch envelopeA8size 5.5 inch 8.125 inch envelopeA9size 5.75 inch 8.75 inch envelopeA10size 6 inch 9.5 inch # Baronial envelopes envelope4bar 3.625 inch 5.125 inch # same as A1 envelope5_5bar 4.375 inch 5.75 inch envelope6bar 4.75 inch 6.5 inch # Coin envelopes envelope1baby 2.25 inch 3.5 inch # same as #1 coin envelope00coin 1.6875 inch 2.75 inch envelope1coin 2.25 inch 3.5 inch envelope3coin 2.5 inch 4.25 inch envelope4coin 3 inch 4.5 inch envelope4_5coin 3 inch 4.875 inch envelope5coin 2.875 inch 5.25 inch envelope5_5coin 3.125 inch 5.5 inch envelope6coin 3.375 inch 6 inch envelope7coin 3.5 inch 6.5 inch # The metric paper sizes are defined so that if a sheet is cut in half # along the short direction, the result is two sheets which are # similar to the original sheet. This means that for any metric size, # the long side is close to sqrt(2) times the length of the short # side. Each series of sizes is generated by repeated cuts in half, # with the values rounded down to the nearest millimeter. A0paper 841 mm 1189 mm # The basic size in the A series A1paper 594 mm 841 mm # is defined to have an area of A2paper 420 mm 594 mm # one square meter. A3paper 297 mm 420 mm A4paper 210 mm 297 mm A5paper 148 mm 210 mm A6paper 105 mm 148 mm A7paper 74 mm 105 mm A8paper 52 mm 74 mm A9paper 37 mm 52 mm A10paper 26 mm 37 mm B0paper 1000 mm 1414 mm # The basic B size has an area B1paper 707 mm 1000 mm # of sqrt(2) square meters. B2paper 500 mm 707 mm B3paper 353 mm 500 mm B4paper 250 mm 353 mm B5paper 176 mm 250 mm B6paper 125 mm 176 mm B7paper 88 mm 125 mm B8paper 62 mm 88 mm B9paper 44 mm 62 mm B10paper 31 mm 44 mm C0paper 917 mm 1297 mm # The basic C size has an area C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters. C2paper 458 mm 648 mm C3paper 324 mm 458 mm # Intended for envelope sizes C4paper 229 mm 324 mm C5paper 162 mm 229 mm C6paper 114 mm 162 mm C7paper 81 mm 114 mm C8paper 57 mm 81 mm C9paper 40 mm 57 mm C10paper 28 mm 40 mm # gsm (Grams per Square Meter), a sane, metric paper weight measure gsm grams / meter^2 # In the USA, a collection of crazy historical paper measures are used. Paper # is measured as a weight of a ream of that particular type of paper. This is # sometimes called the "substance" or "basis" (as in "substance 20" paper). # The standard sheet size or "basis size" varies depending on the type of # paper. As a result, 20 pound bond paper and 50 pound text paper are actually # about the same weight. The different sheet sizes were historically the most # convenient for printing or folding in the different applications. These # different basis weights are standards maintained by American Society for # Testing Materials (ASTM) and the American Forest and Paper Association # (AF&PA). poundbookpaper lb / 25 inch 38 inch ream lbbook poundbookpaper poundtextpaper poundbookpaper lbtext poundtextpaper poundoffsetpaper poundbookpaper # For offset printing lboffset poundoffsetpaper poundbiblepaper poundbookpaper # Designed to be lightweight, thin, lbbible poundbiblepaper # strong and opaque. poundtagpaper lb / 24 inch 36 inch ream lbtag poundtagpaper poundbagpaper poundtagpaper lbbag poundbagpaper poundnewsprintpaper poundtagpaper lbnewsprint poundnewsprintpaper poundposterpaper poundtagpaper lbposter poundposterpaper poundtissuepaper poundtagpaper lbtissue poundtissuepaper poundwrappingpaper poundtagpaper lbwrapping poundwrappingpaper poundwaxingpaper poundtagpaper lbwaxing poundwaxingpaper poundglassinepaper poundtagpaper lbglassine poundglassinepaper poundcoverpaper lb / 20 inch 26 inch ream lbcover poundcoverpaper poundindexpaper lb / 25.5 inch 30.5 inch ream lbindex poundindexpaper poundindexbristolpaper poundindexpaper lbindexbristol poundindexpaper poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and lbbond poundbondpaper # durable for repeated poundwritingpaper poundbondpaper # filing, and it resists lbwriting poundwritingpaper # ink penetration. poundledgerpaper poundbondpaper lbledger poundledgerpaper poundcopypaper poundbondpaper lbcopy poundcopypaper poundblottingpaper lb / 19 inch 24 inch ream lbblotting poundblottingpaper poundblankspaper lb / 22 inch 28 inch ream lbblanks poundblankspaper poundpostcardpaper lb / 22.5 inch 28.5 inch ream lbpostcard poundpostcardpaper poundweddingbristol poundpostcardpaper lbweddingbristol poundweddingbristol poundbristolpaper poundweddingbristol lbbristol poundbristolpaper poundboxboard lb / 1000 ft^2 lbboxboard poundboxboard poundpaperboard poundboxboard lbpaperboard poundpaperboard # When paper is marked in units of M, it means the weight of 1000 sheets of the # given size of paper. To convert this to paper weight, divide by the size of # the paper in question. paperM lb / 1000 # In addition paper weight is reported in "caliper" which is simply the # thickness of one sheet, typically in inches. Thickness is also reported in # "points" where a point is 1|1000 inch. These conversions are supplied to # convert these units roughly (using an approximate density) into the standard # paper weight values. pointthickness 0.001 in paperdensity 0.8 g/cm^3 # approximate--paper densities vary! papercaliper in paperdensity paperpoint pointthickness paperdensity # # Printing # fournierpoint 0.1648 inch / 12 # First definition of the printers # point made by Pierre Fournier who # defined it in 1737 as 1|12 of a # cicero which was 0.1648 inches. olddidotpoint 1|72 frenchinch # François Ambroise Didot, one of # a family of printers, changed # Fournier's definition around 1770 # to fit to the French units then in # use. bertholdpoint 1|2660 m # H. Berthold tried to create a # metric version of the didot point # in 1878. INpoint 0.4 mm # This point was created by a # group directed by Fermin Didot in # 1881 and is associated with the # imprimerie nationale. It doesn't # seem to have been used much. germandidotpoint 0.376065 mm # Exact definition appears in DIN # 16507, a German standards document # of 1954. Adopted more broadly in # 1966 by ??? metricpoint 3|8 mm # Proposed in 1977 by Eurograf oldpoint 1|72.27 inch # The American point was invented printerspoint oldpoint # by Nelson Hawks in 1879 and texpoint oldpoint # dominates USA publishing. # It was standardized by the American # Typefounders Association at the # value of 0.013837 inches exactly. # Knuth uses the approximation given # here (which is very close). The # comp.fonts FAQ claims that this # value is supposed to be 1|12 of a # pica where 83 picas is equal to 35 # cm. But this value differs from # the standard. texscaledpoint 1|65536 texpoint # The TeX typesetting system uses texsp texscaledpoint # this for all computations. computerpoint 1|72 inch # The American point was rounded point computerpoint computerpica 12 computerpoint # to an even 1|72 inch by computer postscriptpoint computerpoint # people at some point. pspoint postscriptpoint twip 1|20 point # TWentieth of an Imperial Point Q 1|4 mm # Used in Japanese phototypesetting # Q is for quarter frenchprinterspoint olddidotpoint didotpoint germandidotpoint # This seems to be the dominant value europeanpoint didotpoint # for the point used in Europe cicero 12 didotpoint stick 2 inches # Type sizes excelsior 3 oldpoint brilliant 3.5 oldpoint diamondtype 4 oldpoint pearl 5 oldpoint agate 5.5 oldpoint # Originally agate type was 14 lines per # inch, giving a value of 1|14 in. ruby agate # British nonpareil 6 oldpoint mignonette 6.5 oldpoint emerald mignonette # British minion 7 oldpoint brevier 8 oldpoint bourgeois 9 oldpoint longprimer 10 oldpoint smallpica 11 oldpoint pica 12 oldpoint english 14 oldpoint columbian 16 oldpoint greatprimer 18 oldpoint paragon 20 oldpoint meridian 44 oldpoint canon 48 oldpoint # German type sizes nonplusultra 2 didotpoint brillant 3 didotpoint diamant 4 didotpoint perl 5 didotpoint nonpareille 6 didotpoint kolonel 7 didotpoint petit 8 didotpoint borgis 9 didotpoint korpus 10 didotpoint corpus korpus garamond korpus mittel 14 didotpoint tertia 16 didotpoint text 18 didotpoint kleine_kanon 32 didotpoint kanon 36 didotpoint grobe_kanon 42 didotpoint missal 48 didotpoint kleine_sabon 72 didotpoint grobe_sabon 84 didotpoint # # Information theory units. Note that the name "entropy" is used both # to measure information and as a physical quantity. # INFORMATION bit nat (1/ln(2)) bits # Entropy measured base e hartley log2(10) bits # Entropy of a uniformly ban hartley # distributed random variable # over 10 symbols. dit hartley # from Decimal digIT # # Computer # bps bit/sec # Sometimes the term "baud" is # incorrectly used to refer to # bits per second. Baud refers # to symbols per second. Modern # modems transmit several bits # per symbol. byte 8 bit # Not all machines had 8 bit B byte # bytes, but these days most of # them do. But beware: for # transmission over modems, a # few extra bits are used so # there are actually 10 bits per # byte. octet 8 bits # The octet is always 8 bits nybble 4 bits # Half of a byte. Sometimes # equal to different lengths # such as 3 bits. nibble nybble nyp 2 bits # Donald Knuth asks in an exercise # for a name for a 2 bit # quantity and gives the "nyp" # as a solution due to Gregor # Purdy. Not in common use. meg megabyte # Some people consider these # units along with the kilobyte gig gigabyte # to be defined according to # powers of 2 with the kilobyte # equal to 2^10 bytes, the # megabyte equal to 2^20 bytes and # the gigabyte equal to 2^30 bytes # but these usages are forbidden # by SI. Binary prefixes have # been defined by IEC to replace # the SI prefixes. Use them to # get the binary values: KiB, MiB, # and GiB. jiffy 0.01 sec # This is defined in the Jargon File jiffies jiffy # (http://www.jargon.org) as being the # duration of a clock tick for measuring # wall-clock time. Supposedly the value # used to be 1|60 sec or 1|50 sec # depending on the frequency of AC power, # but then 1|100 sec became more common. # On linux systems, this term is used and # for the Intel based chips, it does have # the value of .01 sec. The Jargon File # also lists two other definitions: # millisecond, and the time taken for # light to travel one foot. cdaudiospeed 44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2 # samples of sixteen bits each. cdromspeed 75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read # each second with 2048 bytes per sector. # Audio CDs do not have sectors, but # people sometimes divide the bit rate by # 75 and claim a sector length of 2352. # Data CDs have a lower rate due to # increased error correction overhead. # There is a rarely used mode (mode2) with # 2336 bytes per sector that has fewer # error correction bits than mode1. dvdspeed 1385 kB/s # This is the "1x" speed of a DVD using # constant linear velocity (CLV) mode. # Modern DVDs may vary the linear velocity # as they go from the inside to the # outside of the disc. # See http://www.osta.org/technology/dvdqa/dvdqa4.htm # # The IP address space is divided into subnets. The number of hosts # in a subnet depends on the length of the subnet prefix. This is # often written as /N where N is the number of bits in the prefix. # # https://en.wikipedia.org/wiki/Subnetwork # # These definitions gives the number of hosts for a subnet whose # prefix has the specified length in bits. # ipv4subnetsize(prefix_len) units=[1;1] domain=[0,32] range=[1,4294967296] \ 2^(32-prefix_len) ; 32-log2(ipv4subnetsize) ipv4classA ipv4subnetsize(8) ipv4classB ipv4subnetsize(16) ipv4classC ipv4subnetsize(24) ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \ range=[1,340282366920938463463374607431768211456] \ 2^(128-prefix_len) ; 128-log2(ipv6subnetsize) # # Musical measures. Musical intervals expressed as ratios. Multiply # two intervals together to get the sum of the interval. The function # musicalcent can be used to convert ratios to cents. # # Perfect intervals octave 2 majorsecond musicalfifth^2 / octave majorthird 5|4 minorthird 6|5 musicalfourth 4|3 musicalfifth 3|2 majorsixth musicalfourth majorthird minorsixth musicalfourth minorthird majorseventh musicalfifth majorthird minorseventh musicalfifth minorthird pythagoreanthird majorsecond musicalfifth^2 / octave syntoniccomma pythagoreanthird / majorthird pythagoreancomma musicalfifth^12 / octave^7 # Equal tempered definitions semitone octave^(1|12) musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \ 100 log(musicalcent)/log(semitone) # # Musical note lengths. # wholenote ! MUSICAL_NOTE_LENGTH wholenote halfnote 1|2 wholenote quarternote 1|4 wholenote eighthnote 1|8 wholenote sixteenthnote 1|16 wholenote thirtysecondnote 1|32 wholenote sixtyfourthnote 1|64 wholenote dotted 3|2 doubledotted 7|4 breve doublewholenote semibreve wholenote minimnote halfnote crotchet quarternote quaver eighthnote semiquaver sixteenthnote demisemiquaver thirtysecondnote hemidemisemiquaver sixtyfourthnote semidemisemiquaver hemidemisemiquaver # # yarn and cloth measures # # yarn linear density woolyarnrun 1600 yard/pound # 1600 yds of "number 1 yarn" weighs # a pound. yarncut 300 yard/pound # Less common system used in # Pennsylvania for wool yarn cottonyarncount 840 yard/pound linenyarncount 300 yard/pound # Also used for hemp and ramie worstedyarncount 1680 ft/pound metricyarncount meter/gram denier 1|9 tex # used for silk and rayon manchesteryarnnumber drams/1000 yards # old system used for silk pli lb/in typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound asbestoscut 100 yd/lb # used for glass and asbestos yarn tex gram / km # rational metric yarn measure, meant drex 0.1 tex # to be used for any kind of yarn poumar lb / 1e6 yard # yarn and cloth length skeincotton 80*54 inch # 80 turns of thread on a reel with a # 54 in circumference (varies for other # kinds of thread) cottonbolt 120 ft # cloth measurement woolbolt 210 ft bolt cottonbolt heer 600 yards cut 300 yards # used for wet-spun linen yarn lea 300 yards sailmakersyard 28.5 in sailmakersounce oz / sailmakersyard 36 inch silkmomme momme / 25 yards 1.49 inch # Traditional silk weight silkmm silkmomme # But it is also defined as # lb/100 yd 45 inch. The two # definitions are slightly different # and neither one seems likely to be # the true source definition. # # drug dosage # mcg microgram # Frequently used for vitamins iudiptheria 62.8 microgram # IU is for international unit iupenicillin 0.6 microgram iuinsulin 41.67 microgram drop 1|20 ml # The drop was an old "unit" that was # replaced by the minim. But I was # told by a pharmacist that in his # profession, the conversion of 20 # drops per ml is actually used. bloodunit 450 ml # For whole blood. For blood # components, a blood unit is the # quanity of the component found in a # blood unit of whole blood. The # human body contains about 12 blood # units of whole blood. # # misc medical measure # frenchcathetersize 1|3 mm # measure used for the outer diameter # of a catheter charriere frenchcathetersize # # fixup units for times when prefix handling doesn't do the job # hectare hectoare megohm megaohm kilohm kiloohm microhm microohm megalerg megaerg # 'L' added to make it pronounceable [18]. # # Money # # Note that US$ is the primitive unit so other currencies are # generally given in US$. # unitedstatesdollar US$ usdollar US$ $ dollar mark germanymark #bolivar venezuelabolivar # Not all databases are #venezuelabolivarfuerte 1e-5 bolivar # supplying these #bolivarfuerte 1e-5 bolivar # The currency was revalued #oldbolivar 1|1000 bolivarfuerte # twice peseta spainpeseta rand southafricarand escudo portugalescudo guilder netherlandsguilder hollandguilder netherlandsguilder peso mexicopeso yen japanyen lira italylira rupee indiarupee drachma greecedrachma franc francefranc markka finlandmarkka britainpound unitedkingdompound greatbritainpound unitedkingdompound unitedkingdompound ukpound poundsterling britainpound yuan chinayuan # Unicode Currency Names !utf8 icelandkróna icelandkrona polandzłoty polandzloty tongapa’anga tongapa'anga #venezuelabolívar venezuelabolivar vietnamđồng vietnamdong mongoliatögrög mongoliatugrik sãotomé&príncipedobra saotome&principedobra !endutf8 UKP GBP # Not an ISO code, but looks like one, and # sometimes used on usenet. !include currency.units # Money on the gold standard, used in the late 19th century and early # 20th century. olddollargold 23.22 grains goldprice # Used until 1934 newdollargold 96|7 grains goldprice # After Jan 31, 1934 dollargold newdollargold poundgold 113 grains goldprice # British pound # Precious metals goldounce goldprice troyounce silverounce silverprice troyounce platinumounce platinumprice troyounce XAU goldounce XPT platinumounce XAG silverounce # Nominal masses of US coins. Note that dimes, quarters and half dollars # have weight proportional to value. Before 1965 it was $40 / kg. USpennyweight 2.5 grams # Since 1982, 48 grains before USnickelweight 5 grams USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965 USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965 UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971 USdollarweight 8.1 grams # Weight of Susan B. Anthony and # Sacagawea dollar coins # British currency quid britainpound # Slang names fiver 5 quid tenner 10 quid monkey 500 quid brgrand 1000 quid bob shilling shilling 1|20 britainpound # Before decimalisation, there oldpence 1|12 shilling # were 20 shillings to a pound, farthing 1|4 oldpence # each of twelve old pence guinea 21 shilling # Still used in horse racing crown 5 shilling florin 2 shilling groat 4 oldpence tanner 6 oldpence brpenny 0.01 britainpound pence brpenny tuppence 2 pence tuppenny tuppence ha'penny halfbrpenny hapenny ha'penny oldpenny oldpence oldtuppence 2 oldpence oldtuppenny oldtuppence threepence 3 oldpence # threepence never refers to new money threepenny threepence oldthreepence threepence oldthreepenny threepence oldhalfpenny halfoldpenny oldha'penny oldhalfpenny oldhapenny oldha'penny brpony 25 britainpound # Canadian currency loony 1 canadadollar # This coin depicts a loon toony 2 canadadollar # Cryptocurrency satoshi 1e-8 bitcoin XBT bitcoin # nonstandard code # # Units used for measuring volume of wood # cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood facecord 1|2 cord cordfoot 1|8 cord # One foot long section of a cord cordfeet cordfoot housecord 1|3 cord # Used to sell firewood for residences, # often confusingly called a "cord" boardfoot ft^2 inch # Usually 1 inch thick wood boardfeet boardfoot fbm boardfoot # feet board measure stack 4 yard^3 # British, used for firewood and coal [18] rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly # sometimes called a face cord, but this # value is equal to 1|3 cord. Name # comes from an old Norse word for a # stack of wood. stere m^3 timberfoot ft^3 # Used for measuring solid blocks of wood standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or # Pittsburg standard. Apparently the # term is short for "standard hundred" # which was meant to refer to 100 pieces # of wood (deals). However, this # particular standard is equal to 120 # deals which are 12 ft by 11 in by 1.5 # inches (not the standard deal). hoppusfoot (4/pi) ft^3 # Volume calculation suggested in 1736 hoppusboardfoot 1|12 hoppusfoot # forestry manual by Edward Hoppus, for hoppuston 50 hoppusfoot # estimating the usable volume of a log. # It results from computing the volume # of a cylindrical log of length, L, and # girth (circumference), G, by V=L(G/4)^2 . # The hoppus ton is apparently still in # use for shipments from Southeast Asia. # In Britain, the deal is apparently any piece of wood over 6 feet long, over # 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece # of wood less than 7 inches wide is called a "batten". This unit is now used # exclusively for fir and pine. deal 12 ft 11 in 2.5 in # The standard North American deal [OED] wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard # deal it's called a "whole deal"! splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal. # Used for shellac mixing rate poundcut pound / gallon lbcut poundcut # # Gas and Liquid flow units # FLUID_FLOW VOLUME / TIME # Some obvious volumetric gas flow units (cu is short for cubic) cumec m^3/s cusec ft^3/s # Conventional abbreviations for fluid flow units gph gal/hr gpm gal/min mgd megagal/day cfs ft^3/s cfh ft^3/hour cfm ft^3/min lpm liter/min lfm ft/min # Used to report air flow produced by fans. # Multiply by cross sectional area to get a # flow in cfm. pru mmHg / (ml/min) # peripheral resistance unit, used in # medicine to assess blood flow in # the capillaries. # Miner's inch: This is an old historic unit used in the Western United # States. It is generally defined as the rate of flow through a one square # inch hole at a specified depth such as 4 inches. In the late 19th century, # volume of water was sometimes measured in the "24 hour inch". Values for the # miner's inch were fixed by state statues. (This information is from a web # site operated by the Nevada Division of Water Planning: The Water Words # Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.) minersinchAZ 1.5 ft^3/min minersinchCA 1.5 ft^3/min minersinchMT 1.5 ft^3/min minersinchNV 1.5 ft^3/min minersinchOR 1.5 ft^3/min minersinchID 1.2 ft^3/min minersinchKS 1.2 ft^3/min minersinchNE 1.2 ft^3/min minersinchNM 1.2 ft^3/min minersinchND 1.2 ft^3/min minersinchSD 1.2 ft^3/min minersinchUT 1.2 ft^3/min minersinchCO 1 ft^3/sec / 38.4 # 38.4 miner's inches = 1 ft^3/sec minersinchBC 1.68 ft^3/min # British Columbia # Oceanographic flow sverdrup 1e6 m^3 / sec # Used to express flow of ocean # currents. Named after Norwegian # oceanographer H. Sverdrup. # In vacuum science and some other applications, gas flow is measured # as the product of volumetric flow and pressure. This is useful # because it makes it easy to compare with the flow at standard # pressure (one atmosphere). It also directly relates to the number # of gas molecules per unit time, and hence to the mass flow if the # molecular mass is known. GAS_FLOW PRESSURE FLUID_FLOW sccm atm cc/min # 's' is for "standard" to indicate sccs atm cc/sec # flow at standard pressure scfh atm ft^3/hour # scfm atm ft^3/min slpm atm liter/min slph atm liter/hour lusec liter micron Hg / s # Used in vacuum science # US Standard Atmosphere (1976) # Atmospheric temperature and pressure vs. geometric height above sea level # This definition covers only the troposphere (the lowest atmospheric # layer, up to 11 km), and assumes the layer is polytropic. # A polytropic process is one for which PV^k = const, where P is the # pressure, V is the volume, and k is the polytropic exponent. The # polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article # https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse # the definitions of "exponent" and "index." The functions below assume # the following parameters: # temperature lapse rate, -dT/dz, in troposphere lapserate 6.5 K/km # US Std Atm (1976) # air molecular weight, including constituent mol wt, given # in Table 3, p. 3 air_1976 78.084 % 28.0134 \ + 20.9476 % 31.9988 \ + 9340 ppm 39.948 \ + 314 ppm 44.00995 \ + 18.18 ppm 20.183 \ + 5.24 ppm 4.0026 \ + 2 ppm 16.04303 \ + 1.14 ppm 83.80 \ + 0.55 ppm 2.01594 \ + 0.087 ppm 131.30 # universal gas constant R_1976 8.31432e3 N m/(kmol K) # polytropic index n polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1 # If desired, redefine using current values for air mol wt and R polyndx polyndx_1976 # polyndx air (kg/kmol) gravity/(R lapserate) - 1 # for comparison with various references polyexpnt (polyndx + 1) / polyndx # The model assumes the following reference values: # sea-level temperature and pressure stdatmT0 288.15 K stdatmP0 atm # "effective radius" for relation of geometric to geopotential height, # at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no # relation to actual radius earthradUSAtm 6356766 m # Temperature vs. geopotential height h # Assumes 15 degC at sea level # Based on approx 45 deg latitude # Lower limits of domain and upper limits of range are those of the # tables in US Standard Atmosphere (NASA 1976) stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \ stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate # Temperature vs. geometric height z; based on approx 45 deg latitude stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \ stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT)) # Pressure vs. geopotential height h # Assumes 15 degC and 101325 Pa at sea level # Based on approx 45 deg latitude # Lower limits of domain and upper limits of range are those of the # tables in US Standard Atmosphere (NASA 1976) stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \ atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \ (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1)))) # Pressure vs. geometric height z; based on approx 45 deg latitude stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \ stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP)) # Geopotential height from geometric height # Based on approx 45 deg latitude # Lower limits of domain and range are somewhat arbitrary; they # correspond to the limits in the US Std Atm tables geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \ (earthradUSAtm z) / (earthradUSAtm + z) ; \ (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht)) # The standard value for the sea-level acceleration due to gravity is # 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949) # R_eff = 2 g_phi / denom # g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) # or # g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) # denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?) # There is no inverse function; the standard value applies at a latitude # of about 45.543 deg g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \ 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2 # effective Earth radius for relation of geometric height to # geopotential height, as function of latitude (Harrison 1949) earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \ m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \ (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat)) # References # Harrison, L.P. 1949. Relation Between Geopotential and Geometric # Height. In Smithsonian Meteorological Tables. List, Robert J., ed. # 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution. # NASA. US National Aeronautics and Space Administration. 1976. # US Standard Atmosphere 1976. Washington, DC: US Government Printing Office. # Gauge pressure functions # # Gauge pressure is measured relative to atmospheric pressure. In the English # system, where pressure is often given in pounds per square inch, gauge # pressure is often indicated by 'psig' to distinguish it from absolute # pressure, often indicated by 'psia'. At the standard atmospheric pressure # of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696 # psia; an automobile tire inflated to 31 psig has an absolute pressure of # 45.696 psia. # # With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5 # bar)); with psig(), the units are taken as psi, so the example above of tire # pressure could be given as psig(31). # # If the normal elevation is significantly different from sea level, change # Patm appropriately, and adjust the lower domain limit on the gaugepressure # definition. Patm atm gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \ x + Patm ; gaugepressure+(-Patm) psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \ gaugepressure(x psi) ; ~gaugepressure(psig) / psi # Pressure for underwater diving seawater 0.1 bar / meter msw meter seawater fsw foot seawater # # Wire Gauge # # This area is a nightmare with huge charts of wire gauge diameters # that usually have no clear origin. There are at least 5 competing wire gauge # systems to add to the confusion. The use of wire gauge is related to the # manufacturing method: a metal rod is heated and drawn through a hole. The # size change can't be too big. To get smaller wires, the process is repeated # with a series of smaller holes. Generally larger gauges mean smaller wires. # The gauges often have values such as "00" and "000" which are larger sizes # than simply "0" gauge. In the tables that appear below, these gauges must be # specified as negative numbers (e.g. "00" is -1, "000" is -2, etc). # Alternatively, you can use the following units: # g00 (-1) g000 (-2) g0000 (-3) g00000 (-4) g000000 (-5) g0000000 (-6) # American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most # important gauge. ASTM B-258 specifies that this gauge is based on geometric # interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36 # which is 0.005 inches exactly. Therefore, the diameter in inches of a wire # is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close # to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the # repeated zero values, use negative numbers in the formula. The same document # also specifies rounding rules which seem to be ignored by makers of tables. # Gauges up to 44 are to be specified with up to 4 significant figures, but no # closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the # nearest 0.00001 inch. # # In addition to being used to measure wire thickness, this gauge is used to # measure the thickness of sheets of aluminum, copper, and most metals other # than steel, iron and zinc. wiregauge(g) units=[1;m] range=(0,) \ 1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92) awg() wiregauge # Next we have the SWG, the Imperial or British Standard Wire Gauge. This one # is piecewise linear. It was used for aluminum sheets. brwiregauge[in] \ -6 0.5 \ -5 0.464 \ -3 0.4 \ -2 0.372 \ 3 0.252 \ 6 0.192 \ 10 0.128 \ 14 0.08 \ 19 0.04 \ 23 0.024 \ 26 0.018 \ 28 0.0148 \ 30 0.0124 \ 39 0.0052 \ 49 0.0012 \ 50 0.001 # The following is from the Appendix to ASTM B 258 # # For example, in U.S. gage, the standard for sheet metal is based on the # weight of the metal, not on the thickness. 16-gage is listed as # approximately .0625 inch thick and 40 ounces per square foot (the original # standard was based on wrought iron at .2778 pounds per cubic inch; steel # has almost entirely superseded wrought iron for sheet use, at .2833 pounds # per cubic inch). Smaller numbers refer to greater thickness. There is no # formula for converting gage to thickness or weight. # # It's rather unclear from the passage above whether the plate gauge values are # therefore wrong if steel is being used. Reference [15] states that steel is # in fact measured using this gauge (under the name Manufacturers' Standard # Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel. # But this doesn't seem to be the correct density of steel (.2833 lb/in3 is # closer). # # This gauge was established in 1893 for purposes of taxation. # Old plate gauge for iron plategauge[(oz/ft^2)/(480*lb/ft^3)] \ -5 300 \ 1 180 \ 14 50 \ 16 40 \ 17 36 \ 20 24 \ 26 12 \ 31 7 \ 36 4.5 \ 38 4 # Manufacturers Standard Gage stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \ -5 300 \ 1 180 \ 14 50 \ 16 40 \ 17 36 \ 20 24 \ 26 12 \ 31 7 \ 36 4.5 \ 38 4 # A special gauge is used for zinc sheet metal. Notice that larger gauges # indicate thicker sheets. zincgauge[in] \ 1 0.002 \ 10 0.02 \ 15 0.04 \ 19 0.06 \ 23 0.1 \ 24 0.125 \ 27 0.5 \ 28 1 # # Imperial drill bit sizes are reported in inches or in a numerical or # letter gauge. # drillgauge[in] \ 1 0.2280 \ 2 0.2210 \ 3 0.2130 \ 4 0.2090 \ 5 0.2055 \ 6 0.2040 \ 7 0.2010 \ 8 0.1990 \ 9 0.1960 \ 10 0.1935 \ 11 0.1910 \ 12 0.1890 \ 13 0.1850 \ 14 0.1820 \ 15 0.1800 \ 16 0.1770 \ 17 0.1730 \ 18 0.1695 \ 19 0.1660 \ 20 0.1610 \ 22 0.1570 \ 23 0.1540 \ 24 0.1520 \ 25 0.1495 \ 26 0.1470 \ 27 0.1440 \ 28 0.1405 \ 29 0.1360 \ 30 0.1285 \ 31 0.1200 \ 32 0.1160 \ 33 0.1130 \ 34 0.1110 \ 35 0.1100 \ 36 0.1065 \ 38 0.1015 \ 39 0.0995 \ 40 0.0980 \ 41 0.0960 \ 42 0.0935 \ 43 0.0890 \ 44 0.0860 \ 45 0.0820 \ 46 0.0810 \ 48 0.0760 \ 51 0.0670 \ 52 0.0635 \ 53 0.0595 \ 54 0.0550 \ 55 0.0520 \ 56 0.0465 \ 57 0.0430 \ 65 0.0350 \ 66 0.0330 \ 68 0.0310 \ 69 0.0292 \ 70 0.0280 \ 71 0.0260 \ 73 0.0240 \ 74 0.0225 \ 75 0.0210 \ 76 0.0200 \ 78 0.0160 \ 79 0.0145 \ 80 0.0135 \ 88 0.0095 \ 104 0.0031 drillA 0.234 in drillB 0.238 in drillC 0.242 in drillD 0.246 in drillE 0.250 in drillF 0.257 in drillG 0.261 in drillH 0.266 in drillI 0.272 in drillJ 0.277 in drillK 0.281 in drillL 0.290 in drillM 0.295 in drillN 0.302 in drillO 0.316 in drillP 0.323 in drillQ 0.332 in drillR 0.339 in drillS 0.348 in drillT 0.358 in drillU 0.368 in drillV 0.377 in drillW 0.386 in drillX 0.397 in drillY 0.404 in drillZ 0.413 in # # Screw sizes # # In the USA, screw diameters for both wood screws and machine screws # are reported using a gauge number. Metric machine screws are # reported as Mxx where xx is the diameter in mm. # screwgauge(g) units=[1;m] range=[0,) \ (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013 # # Abrasive grit size # # Standards governing abrasive grit sizes are complicated, specifying # fractions of particles that are passed or retained by different mesh # sizes. As a result, it is not possible to make precise comparisons # of different grit standards. The tables below allow the # determination of rough equivlants by using median particle size. # # Standards in the USA are determined by the Unified Abrasives # Manufacturers' Association (UAMA), which resulted from the merger of # several previous organizations. One of the old organizations was # CAMI (Coated Abrasives Manufacturers' Institute). # # UAMA has a web page with plots showing abrasive particle ranges for # various different grits and comparisons between standards. # # http://www.uama.org/Abrasives101/101Standards.html # # Abrasives are grouped into "bonded" abrasives for use with grinding # wheels and "coated" abrasives for sandpapers and abrasive films. # The industry uses different grit standards for these two # categories. # # Another division is between "macrogrits", grits below 240 and # "microgrits", which are above 240. Standards differ, as do methods # for determining particle size. In the USA, ANSI B74.12 is the # standard governing macrogrits. ANSI B74.10 covers bonded microgrit # abrasives, and ANSI B74.18 covers coated microgrit abrasives. It # appears that the coated standard is identical to the bonded standard # for grits up through 600 but then diverges significantly. # # European grit sizes are determined by the Federation of European # Producers of Abrasives. http://www.fepa-abrasives.org # # They give two standards, the "F" grit for bonded abrasives and the # "P" grit for coated abrasives. This data is taken directly from # their web page. # FEPA P grit for coated abrasives is commonly seen on sandpaper in # the USA where the paper will be marked P600, for example. FEPA P # grits are said to be more tightly constrained than comparable ANSI # grits so that the particles are more uniform in size and hence give # a better finish. grit_P[micron] \ 12 1815 \ 16 1324 \ 20 1000 \ 24 764 \ 30 642 \ 36 538 \ 40 425 \ 50 336 \ 60 269 \ 80 201 \ 100 162 \ 120 125 \ 150 100 \ 180 82 \ 220 68 \ 240 58.5 \ 280 52.2 \ 320 46.2 \ 360 40.5 \ 400 35 \ 500 30.2 \ 600 25.8 \ 800 21.8 \ 1000 18.3 \ 1200 15.3 \ 1500 12.6 \ 2000 10.3 \ 2500 8.4 # The F grit is the European standard for bonded abrasives such as # grinding wheels grit_F[micron] \ 4 4890 \ 5 4125 \ 6 3460 \ 7 2900 \ 8 2460 \ 10 2085 \ 12 1765 \ 14 1470 \ 16 1230 \ 20 1040 \ 22 885 \ 24 745 \ 30 625 \ 36 525 \ 40 438 \ 46 370 \ 54 310 \ 60 260 \ 70 218 \ 80 185 \ 90 154 \ 100 129 \ 120 109 \ 150 82 \ 180 69 \ 220 58 \ 230 53 \ 240 44.5 \ 280 36.5 \ 320 29.2 \ 360 22.8 \ 400 17.3 \ 500 12.8 \ 600 9.3 \ 800 6.5 \ 1000 4.5 \ 1200 3 \ 1500 2.0 \ 2000 1.2 # According to the UAMA web page, the ANSI bonded and ANSI coated standards # are identical to FEPA F in the macrogrit range (under 240 grit), so these # values are taken from the FEPA F table. The values for 240 and above are # from the UAMA web site and represent the average of the "d50" range # endpoints listed there. ansibonded[micron] \ 4 4890 \ 5 4125 \ 6 3460 \ 7 2900 \ 8 2460 \ 10 2085 \ 12 1765 \ 14 1470 \ 16 1230 \ 20 1040 \ 22 885 \ 24 745 \ 30 625 \ 36 525 \ 40 438 \ 46 370 \ 54 310 \ 60 260 \ 70 218 \ 80 185 \ 90 154 \ 100 129 \ 120 109 \ 150 82 \ 180 69 \ 220 58 \ 240 50 \ 280 39.5 \ 320 29.5 \ 360 23 \ 400 18.25 \ 500 13.9 \ 600 10.55 \ 800 7.65 \ 1000 5.8 \ 1200 3.8 grit_ansibonded() ansibonded # Like the bonded grit, the coated macrogrits below 240 are taken from the # FEPA F table. Data above this is from the UAMA site. Note that the coated # and bonded standards are evidently the same from 240 up to 600 grit, but # starting at 800 grit, the coated standard diverges. The data from UAMA show # that 800 grit coated has an average size slightly larger than the average # size of 600 grit coated/bonded. However, the 800 grit has a significantly # smaller particle size variation. # # Because of this non-monotonicity from 600 grit to 800 grit this definition # produces a warning about the lack of a unique inverse. ansicoated[micron] noerror \ 4 4890 \ 5 4125 \ 6 3460 \ 7 2900 \ 8 2460 \ 10 2085 \ 12 1765 \ 14 1470 \ 16 1230 \ 20 1040 \ 22 885 \ 24 745 \ 30 625 \ 36 525 \ 40 438 \ 46 370 \ 54 310 \ 60 260 \ 70 218 \ 80 185 \ 90 154 \ 100 129 \ 120 109 \ 150 82 \ 180 69 \ 220 58 \ 240 50 \ 280 39.5 \ 320 29.5 \ 360 23 \ 400 18.25 \ 500 13.9 \ 600 10.55 \ 800 11.5 \ 1000 9.5 \ 2000 7.2 \ 2500 5.5 \ 3000 4 \ 4000 3 \ 6000 2 \ 8000 1.2 grit_ansicoated() ansicoated # # Is this correct? This is the JIS Japanese standard used on waterstones # jisgrit[micron] \ 150 75 \ 180 63 \ 220 53 \ 280 48 \ 320 40 \ 360 35 \ 400 30 \ 600 20 \ 700 17 \ 800 14 \ 1000 11.5 \ 1200 9.5 \ 1500 8 \ 2000 6.7 \ 2500 5.5 \ 3000 4 \ 4000 3 \ 6000 2 \ 8000 1.2 # The "Finishing Scale" marked with an A (e.g. A75). This information # is from the web page of the sand paper manufacturer Klingspor # http://www.klingspor.com/gritgradingsystems.htm # # I have no information about what this scale is used for. grit_A[micron]\ 16 15.3 \ 25 21.8 \ 30 23.6 \ 35 25.75 \ 45 35 \ 60 46.2 \ 65 53.5 \ 75 58.5 \ 90 65 \ 110 78 \ 130 93 \ 160 127 \ 200 156 # # Grits for DMT brand diamond sharpening stones from # http://dmtsharp.com/products/colorcode.htm # dmtxxcoarse 120 micron # 120 mesh dmtsilver dmtxxcoarse dmtxx dmtxxcoarse dmtxcoarse 60 micron # 220 mesh dmtx dmtxcoarse dmtblack dmtxcoarse dmtcoarse 45 micron # 325 mesh dmtc dmtcoarse dmtblue dmtcoarse dmtfine 25 micron # 600 mesh dmtred dmtfine dmtf dmtfine dmtefine 9 micron # 1200 mesh dmte dmtefine dmtgreen dmtefine dmtceramic 7 micron # 2200 mesh dmtcer dmtceramic dmtwhite dmtceramic dmteefine 3 micron # 8000 mesh dmttan dmteefine dmtee dmteefine # # The following values come from a page in the Norton Stones catalog, # available at their web page, http://www.nortonstones.com. # hardtranslucentarkansas 6 micron # Natural novaculite (silicon quartz) softarkansas 22 micron # stones extrafineindia 22 micron # India stones are Norton's manufactured fineindia 35 micron # aluminum oxide product mediumindia 53.5 micron coarseindia 97 micron finecrystolon 45 micron # Crystolon stones are Norton's mediumcrystalon 78 micron # manufactured silicon carbide product coarsecrystalon 127 micron # The following are not from the Norton catalog hardblackarkansas 6 micron hardwhitearkansas 11 micron washita 35 micron # # Mesh systems for measuring particle sizes by sifting through a wire # mesh or sieve # # The Tyler system and US Sieve system are based on four steps for # each factor of 2 change in the size, so each size is 2^1|4 different # from the adjacent sizes. Unfortunately, the mesh numbers are # arbitrary, so the sizes cannot be expressed with a functional form. # Various references round the values differently. The mesh numbers # are supposed to correspond to the number of holes per inch, but this # correspondence is only approximate because it doesn't include the # wire size of the mesh. # The Tyler Mesh system was apparently introduced by the WS Tyler # company, but it appears that they no longer use it. They follow the # ASTM E11 standard. meshtyler[micron] \ 2.5 8000 \ 3 6727 \ 3.5 5657 \ 4 4757 \ 5 4000 \ 6 3364 \ 7 2828 \ 8 2378 \ 9 2000 \ 10 1682 \ 12 1414 \ 14 1189 \ 16 1000 \ 20 841 \ 24 707 \ 28 595 \ 32 500 \ 35 420 \ 42 354 \ 48 297 \ 60 250 \ 65 210 \ 80 177 \ 100 149 \ 115 125 \ 150 105 \ 170 88 \ 200 74 \ 250 63 \ 270 53 \ 325 44 \ 400 37 # US Sieve size, ASTM E11 # # The WS Tyler company prints the list from ASTM E11 in their catalog, # http://wstyler.com/wp-content/uploads/2015/11/Product-Catalog-2.pdf sieve[micron] \ 3.5 5600 \ 4 4750 \ 5 4000 \ 6 3350 \ 7 2800 \ 8 2360 \ 10 2000 \ 12 1700 \ 14 1400 \ 16 1180 \ 18 1000 \ 20 850 \ 25 710 \ 30 600 \ 35 500 \ 40 425 \ 45 355 \ 50 300 \ 60 250 \ 70 212 \ 80 180 \ 100 150 \ 120 125 \ 140 106 \ 170 90 \ 200 75 \ 230 63 \ 270 53 \ 325 45 \ 400 38 \ 450 32 \ 500 25 \ 625 20 # These last two values are not in the standard series # but were included in the ASTM standard because they meshUS() sieve # were in common usage. # British Mesh size, BS 410: 1986 # This system appears to correspond to the Tyler and US system, but # with different mesh numbers. # # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf # meshbritish[micron] \ 3 5657 \ 3.5 4757 \ 4 4000 \ 5 3364 \ 6 2828 \ 7 2378 \ 8 2000 \ 10 1682 \ 12 1414 \ 14 1189 \ 16 1000 \ 18 841 \ 22 707 \ 25 595 \ 30 500 \ 36 420 \ 44 354 \ 52 297 \ 60 250 \ 72 210 \ 85 177 \ 100 149 \ 120 125 \ 150 105 \ 170 88 \ 200 74 \ 240 63 \ 300 53 \ 350 44 \ 400 37 # French system, AFNOR NFX11-501: 1970 # The system appears to be based on size doubling every 3 mesh # numbers, though the values have been agressively rounded. # It's not clear if the unrounded values would be considered # incorrect, so this is given as a table rather than a function. # Functional form: # meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron # # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf meshtamis[micron] \ 17 40 \ 18 50 \ 19 63 \ 20 80 \ 21 100 \ 22 125 \ 23 160 \ 24 200 \ 25 250 \ 26 315 \ 27 400 \ 28 500 \ 29 630 \ 30 800 \ 31 1000 \ 32 1250 \ 33 1600 \ 34 2000 \ 35 2500 \ 36 3150 \ 37 4000 \ 38 5000 # # Ring size. All ring sizes are given as the circumference of the ring. # # USA ring sizes. Several slightly different definitions seem to be in # circulation. According to [15], the interior diameter of size n ring in # inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The # size 2 ring is inconsistently 0.538in and no 2.5 size is listed. # # However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the # diameter and list no special case for size 2. (Or alternatively they are # 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One # reference claimed that the original system was that each size was 1|10 inch # circumference, but that source doesn't have an explanation for the modern # system which is somewhat different. ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \ (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018 # Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes # specified alphabetically and based on the ring inside diameter in steps of # 1|64 inch. This system was replaced in 1987 by British Standard 6820 which # specifies sizes based on circumference. Each size is 1.25 mm different from # the preceding size. The baseline is size C which is 40 mm circumference. # The new sizes are close to the old ones. Sometimes it's necessary to go # beyond size Z to Z+1, Z+2, etc. sizeAring 37.50 mm sizeBring 38.75 mm sizeCring 40.00 mm sizeDring 41.25 mm sizeEring 42.50 mm sizeFring 43.75 mm sizeGring 45.00 mm sizeHring 46.25 mm sizeIring 47.50 mm sizeJring 48.75 mm sizeKring 50.00 mm sizeLring 51.25 mm sizeMring 52.50 mm sizeNring 53.75 mm sizeOring 55.00 mm sizePring 56.25 mm sizeQring 57.50 mm sizeRring 58.75 mm sizeSring 60.00 mm sizeTring 61.25 mm sizeUring 62.50 mm sizeVring 63.75 mm sizeWring 65.00 mm sizeXring 66.25 mm sizeYring 67.50 mm sizeZring 68.75 mm # Japanese sizes start with size 1 at a 13mm inside diameter and each size is # 1|3 mm larger in diameter than the previous one. They are multiplied by pi # to give circumference. jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \ (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38) # The European ring sizes are the length of the circumference in mm minus 40. euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40) # # Abbreviations # mph mile/hr mpg mile/gal kph km/hr fL footlambert fpm ft/min fps ft/s rpm rev/min rps rev/sec mi mile smi mile nmi nauticalmile mbh 1e3 btu/hour mcm 1e3 circularmil ipy inch/year # used for corrosion rates ccf 100 ft^3 # used for selling water [18] Mcf 1000 ft^3 # not million cubic feet [18] kp kilopond kpm kp meter Wh W hour hph hp hour plf lb / foot # pounds per linear foot # # Compatibility units with Unix version # pa Pa ev eV hg Hg oe Oe mh mH rd rod pf pF gr grain nt N hz Hz hd hogshead dry drygallon/gallon nmile nauticalmile beV GeV bev beV coul C # # Radioactivity units # becquerel /s # Activity of radioactive source Bq becquerel # curie 3.7e10 Bq # Defined in 1910 as the radioactivity Ci curie # emitted by the amount of radon that is # in equilibrium with 1 gram of radium. rutherford 1e6 Bq # RADIATION_DOSE gray gray J/kg # Absorbed dose of radiation Gy gray # rad 1e-2 Gy # From Radiation Absorbed Dose rep 8.38 mGy # Roentgen Equivalent Physical, the amount # of radiation which , absorbed in the # body, would liberate the same amount # of energy as 1 roentgen of X rays # would, or 97 ergs. sievert J/kg # Dose equivalent: dosage that has the Sv sievert # same effect on human tissues as 200 rem 1e-2 Sv # keV X-rays. Different types of # radiation are weighted by the # Relative Biological Effectiveness # (RBE). # # Radiation type RBE # X-ray, gamma ray 1 # beta rays, > 1 MeV 1 # beta rays, < 1 MeV 1.08 # neutrons, < 1 MeV 4-5 # neutrons, 1-10 MeV 10 # protons, 1 MeV 8.5 # protons, .1 MeV 10 # alpha, 5 MeV 15 # alpha, 1 MeV 20 # # The energies are the kinetic energy # of the particles. Slower particles # interact more, so they are more # effective ionizers, and hence have # higher RBE values. # # rem stands for Roentgen Equivalent # Mammal banana_dose 0.1e-6 sievert # Informal measure of the dose due to # eating one average sized banana roentgen 2.58e-4 C / kg # Ionizing radiation that produces # 1 statcoulomb of charge in 1 cc of # dry air at stp. rontgen roentgen # Sometimes it appears spelled this way sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one # hour at a distance of 1 cm from a # point source of 1 mg of radium # enclosed in platinum .5 mm thick. eman 1e-7 Ci/m^3 # radioactive concentration mache 3.7e-7 Ci/m^3 # # Atomic weights. The atomic weight of an element is the ratio of the mass of # a mole of the element to 1|12 of a mole of Carbon 12. The Standard Atomic # Weights apply to the elements as they occur naturally on earth. Elements # which do not occur naturally or which occur with wide isotopic variability do # not have Standard Atomic Weights. For these elements, the atomic weight is # based on the longest lived isotope, as marked in the comments. In some # cases, the comment for these entries also gives a number which is an atomic # weight for a different isotope that may be of more interest than the longest # lived isotope. # actinium 227.0278 aluminum 26.981539 americium 243.0614 # Longest lived. 241.06 antimony 121.760 argon 39.948 arsenic 74.92159 astatine 209.9871 # Longest lived barium 137.327 berkelium 247.0703 # Longest lived. 249.08 beryllium 9.012182 bismuth 208.98037 boron 10.811 bromine 79.904 cadmium 112.411 calcium 40.078 californium 251.0796 # Longest lived. 252.08 carbon 12.011 cerium 140.115 cesium 132.90543 chlorine 35.4527 chromium 51.9961 cobalt 58.93320 copper 63.546 curium 247.0703 deuterium 2.0141017778 dysprosium 162.50 einsteinium 252.083 # Longest lived erbium 167.26 europium 151.965 fermium 257.0951 # Longest lived fluorine 18.9984032 francium 223.0197 # Longest lived gadolinium 157.25 gallium 69.723 germanium 72.61 gold 196.96654 hafnium 178.49 helium 4.002602 holmium 164.93032 hydrogen 1.00794 indium 114.818 iodine 126.90447 iridium 192.217 iron 55.845 krypton 83.80 lanthanum 138.9055 lawrencium 262.11 # Longest lived lead 207.2 lithium 6.941 lutetium 174.967 magnesium 24.3050 manganese 54.93805 mendelevium 258.10 # Longest lived mercury 200.59 molybdenum 95.94 neodymium 144.24 neon 20.1797 neptunium 237.0482 nickel 58.6934 niobium 92.90638 nitrogen 14.00674 nobelium 259.1009 # Longest lived osmium 190.23 oxygen 15.9994 palladium 106.42 phosphorus 30.973762 platinum 195.08 plutonium 244.0642 # Longest lived. 239.05 polonium 208.9824 # Longest lived. 209.98 potassium 39.0983 praseodymium 140.90765 promethium 144.9127 # Longest lived. 146.92 protactinium 231.03588 radium 226.0254 radon 222.0176 # Longest lived rhenium 186.207 rhodium 102.90550 rubidium 85.4678 ruthenium 101.07 samarium 150.36 scandium 44.955910 selenium 78.96 silicon 28.0855 silver 107.8682 sodium 22.989768 strontium 87.62 sulfur 32.066 tantalum 180.9479 technetium 97.9072 # Longest lived. 98.906 tellurium 127.60 terbium 158.92534 thallium 204.3833 thorium 232.0381 thullium 168.93421 tin 118.710 titanium 47.867 tungsten 183.84 uranium 238.0289 vanadium 50.9415 xenon 131.29 ytterbium 173.04 yttrium 88.90585 zinc 65.39 zirconium 91.224 # Average molecular weight of air # # The atmospheric composition listed is from NASA Earth Fact Sheet (accessed # 28 August 2015) # http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html # Numbers do not add up to exactly 100% due to roundoff and uncertainty Water # is highly variable, typically makes up about 1% air 78.08% nitrogen 2 \ + 20.95% oxygen 2 \ + 9340 ppm argon \ + 400 ppm (carbon + oxygen 2) \ + 18.18 ppm neon \ + 5.24 ppm helium \ + 1.7 ppm (carbon + 4 hydrogen) \ + 1.14 ppm krypton \ + 0.55 ppm hydrogen 2 # # population units # people 1 person people death people capita people percapita per capita # TGM dozen based unit system listed on the "dozenal" forum # http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are # proposed as an allegedly more rational alternative to the SI system. Tim 12^-4 hour # Time Grafut gravity Tim^2 # Length based on gravity Surf Grafut^2 # area Volm Grafut^3 # volume Vlos Grafut/Tim # speed Denz Maz/Volm # density Mag Maz gravity # force Maz Volm kg / oldliter # mass based on water Tm Tim # Abbreviations Gf Grafut Sf Surf Vm Volm Vl Vlos Mz Maz Dz Denz # Dozen based unit prefixes Zena- 12 Duna- 12^2 Trina- 12^3 Quedra- 12^4 Quena- 12^5 Hesa- 12^6 Seva- 12^7 Aka- 12^8 Neena- 12^9 Dexa- 12^10 Lefa- 12^11 Zennila- 12^12 Zeni- 12^-1 Duni- 12^-2 Trini- 12^-3 Quedri- 12^-4 Queni- 12^-5 Hesi- 12^-6 Sevi- 12^-7 Aki- 12^-8 Neeni- 12^-9 Dexi- 12^-10 Lefi- 12^-11 Zennili- 12^-12 # # Traditional Japanese units (shakkanhou) # # The traditional system of weights and measures is called shakkanhou from the # shaku and the ken. Japan accepted SI units in 1891 and legalized conversions # to the traditional system. In 1909 the inch-pound system was also legalized, # so Japan had three legally approved systems. A change to the metric system # started in 1921 but there was a lot of resistance. The Measurement Law of # October 1999 prohibits sales in anything but SI units. However, the old # units still live on in construction and as the basis for paper sizes of books # and tools used for handicrafts. # # Note that units below use the Hepburn romanization system. Some other # systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho". # # # http://hiramatu-hifuka.com/onyak/onyindx.html # Japanese Proportions. These are still in everyday use. They also # get used as units to represent the proportion of the standard unit. wari_proportion 1|10 wari wari_proportion bu_proportion 1|100 # The character bu can also be read fun or bun # but usually "bu" is used for units. rin_proportion 1|1000 mou_proportion 1|10000 # Japanese Length Measures # # The length system is called kanejaku or # square and originated in China. It was # adopted as Japan's official measure in 701 # by the Taiho Code. This system is still in # common use in architecture and clothing. shaku 1|3.3 m mou 1|10000 shaku rin 1|1000 shaku bu_distance 1|100 shaku sun 1|10 shaku jou_distance 10 shaku jou jou_distance kanejakusun sun # Alias to emphasize architectural name kanejaku shaku kanejakujou jou # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement taichi shaku # http://zh.wikipedia.org/wiki/台尺 taicun sun # http://zh.wikipedia.org/wiki/台制 !utf8 台尺 taichi # via Hanyu Pinyin romanizations 台寸 taicun !endutf8 # In context of clothing, shaku is different from architecture # http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html kujirajaku 10|8 shaku kujirajakusun 1|10 kujirajaku kujirajakubu 1|100 kujirajaku kujirajakujou 10 kujirajaku tan_distance 3 kujirajakujou ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6 # http://www.homarewood.co.jp/syakusun.htm # mostly unused chou_distance 60 ken chou chou_distance ri 36 chou # Japanese Area Measures # Tsubo is still used for land size, though the others are more # recognized by their homonyms in the other measurements. gou_area 1|10 tsubo tsubo 36 shaku^2 # Size of two tatami = ken^2 ?? se 30 tsubo tan_area 10 se chou_area 10 tan_area # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement ping tsubo # http://zh.wikipedia.org/wiki/坪 jia 2934 ping # http://zh.wikipedia.org/wiki/甲_(单位) fen 1|10 jia # http://zh.wikipedia.org/wiki/分 fen_area 1|10 jia # Protection against future collisions !utf8 坪 ping # via Hanyu Pinyin romanizations 甲 jia 分 fen 分地 fen_area # Protection against future collisions !endutf8 # Japanese architecture is based on a "standard" size of tatami mat. # Room sizes today are given in number of tatami, and this number # determines the spacing between colums and hence sizes of sliding # doors and paper screens. However, every region has its own slightly # different tatami size. Edoma, used in and around Tokyo and # Hokkaido, is becoming a nationwide standard. Kyouma is used around # Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya. # Note that the tatami all have the aspect ratio 2:1 so that the mats # can tile the room with some of them turned 90 degrees. # # http://www.moon2.net/tatami/infotatami/structure.html edoma (5.8*2.9) shaku^2 kyouma (6.3*3.15) shaku^2 chuukyouma (6*3) shaku^2 jou_area edoma tatami jou_area # Japanese Volume Measures # The "shou" is still used for such things as alcohol and seasonings. # Large quantities of paint are still purchased in terms of "to". shaku_volume 1|10 gou_volume gou_volume 1|10 shou gou gou_volume shou (4.9*4.9*2.7) sun^3 # The character shou which is # the same as masu refers to a # rectangular wooden cup used to # measure liquids and cereal. # Sake is sometimes served in a masu # Note that it happens to be # EXACTLY 7^4/11^3 liters. to 10 shou koku 10 to # No longer used; historically a measure of rice # Japanese Weight Measures # # http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html # Not really used anymore. rin_weight 1|10 bu_weight bu_weight 1|10 monme fun 1|10 monme monme momme kin 160 monme kan 1000 monme kwan kan # This was the old pronounciation of the unit. # The old spelling persisted a few centuries # longer and was not changed until around # 1950. # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement # says: "Volume measure in Taiwan is largely metric". taijin kin # http://zh.wikipedia.org/wiki/台斤 tailiang 10 monme # http://zh.wikipedia.org/wiki/台斤 taiqian monme # http://zh.wikipedia.org/wiki/台制 !utf8 台斤 taijin # via Hanyu Pinyin romanizations 台兩 tailiang 台錢 taiqian !endutf8 # # Australian unit # australiasquare (10 ft)^2 # Used for house area # # A few German units as currently in use. # zentner 50 kg doppelzentner 2 zentner pfund 500 g # The klafter, which was used in central Europe, was derived from the span of # outstretched arms. # # https://en.wikipedia.org/wiki/Obsolete_Austrian_units_of_measurement # https://www.llv.li/files/abi/klafter-m2-en.pdf austriaklafter 1.89648384 m # Exact definition, 23 July 1871 austriafoot 1|6 austriaklafter prussiaklafter 1.88 m prussiafoot 1|6 prussiaklafter bavariaklafter 1.751155 m bavariafoot 1|6 bavariaklafter hesseklafter 2.5 m hessefoot 1|6 hesseklafter switzerlandklafter metricklafter switzerlandfoot 1|6 switzerlandklafter swissklafter switzerlandklafter swissfoot 1|6 swissklafter metricklafter 1.8 m austriayoke 8 austriaklafter * 200 austriaklafter liechtensteinsquareklafter 3.596652 m^2 # Used until 2017 to measure land area liechtensteinklafter sqrt(liechtensteinsquareklafter) # The klafter was also used to measure volume of wood, generally being a stack # of wood one klafter wide, one klafter long, with logs 3 feet (half a klafter) # in length prussiawoodklafter 0.5 prussiaklafter^3 austriawoodklafter 0.5 austriaklafter^3 festmeter m^3 # modern measure of wood, solid cube raummeter 0.7 festmeter # Air space between the logs, stacked schuettraummeter 0.65 raummeter # A cubic meter volume of split and cut schüttraummeter schuettraummeter# firewood in a loose, unordered # pile, not stacked. This is called # "tipped". # # Swedish (Sweden) pre-metric units of 1739. # The metric system was adopted in 1878. # https://sv.wikipedia.org/wiki/Verkm%C3%A5tt # verklinje 2.0618125 mm verktum 12 verklinje kvarter 6 verktum fot 2 kvarter aln 2 fot famn 3 aln # # Some traditional Russian measures # # If you would like to help expand this section and understand # cyrillic transliteration, let me know. These measures are meant to # reflect common usage, e.g. in translated literature. # dessiatine 2400 sazhen^2 # Land measure dessjatine dessiatine funt 409.51718 grams # similar to pound zolotnik 1|96 funt # used for precious metal measure pood 40 funt # common in agricultural measure arshin (2 + 1|3) feet sazhen 3 arshin # analogous to fathom verst 500 sazhen # of similar use to mile versta verst borderverst 1000 sazhen russianmile 7 verst # # Old French distance measures, from French Weights and Measures # Before the Revolution by Zupko # frenchfoot 144|443.296 m # pied de roi, the standard of Paris. pied frenchfoot # Half of the hashimicubit, frenchfeet frenchfoot # instituted by Charlemagne. frenchinch 1|12 frenchfoot # This exact definition comes from frenchthumb frenchinch # a law passed on 10 Dec 1799 which pouce frenchthumb # fixed the meter at # 3 frenchfeet + 11.296 lignes. frenchline 1|12 frenchinch # This is supposed to be the size ligne frenchline # of the average barleycorn frenchpoint 1|12 frenchline toise 6 frenchfeet arpent 180^2 pied^2 # The arpent is 100 square perches, # but the perche seems to vary a lot # and can be 18 feet, 20 feet, or 22 # feet. This measure was described # as being in common use in Canada in # 1934 (Websters 2nd). The value # given here is the Paris standard # arpent. frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence # smaller than the British grain. frenchpound 9216 frenchgrain # # Before the Imperial Weights and Measures Act of 1824, various different # weights and measures were in use in different places. # # Scots linear measure scotsinch 1.00540054 UKinch scotslink 1|100 scotschain scotsfoot 12 scotsinch scotsfeet scotsfoot scotsell 37 scotsinch scotsfall 6 scotsell scotschain 4 scotsfall scotsfurlong 10 scotschain scotsmile 8 scotsfurlong # Scots area measure scotsrood 40 scotsfall^2 scotsacre 4 scotsrood # Irish linear measure irishinch UKinch irishpalm 3 irishinch irishspan 3 irishpalm irishfoot 12 irishinch irishfeet irishfoot irishcubit 18 irishinch irishyard 3 irishfeet irishpace 5 irishfeet irishfathom 6 irishfeet irishpole 7 irishyard # Only these values irishperch irishpole # are different from irishchain 4 irishperch # the British Imperial irishlink 1|100 irishchain # or English values for irishfurlong 10 irishchain # these lengths. irishmile 8 irishfurlong # # Irish area measure irishrood 40 irishpole^2 irishacre 4 irishrood # English wine capacity measures (Winchester measures) winepint 1|2 winequart winequart 1|4 winegallon winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon, # it was legalized in 1707 by Queen Anne, and # given the definition of 231 cubic inches. It # had been in use for a while as 8 pounds of wine # using a merchant's pound, but the definition of # the merchant's pound had become uncertain. A # pound of 15 tower ounces (6750 grains) had been # common, but then a pound of 15 troy ounces # (7200 grains) gained popularity. Because of # the switch in the value of the merchants pound, # the size of the wine gallon was uncertain in # the market, hence the official act in 1707. # The act allowed that a six inch tall cylinder # with a 7 inch diameter was a lawful wine # gallon. (This comes out to 230.9 in^3.) # Note also that in Britain a legal conversion # was established to the 1824 Imperial gallon # then taken as 277.274 in^3 so that the wine # gallon was 0.8331 imperial gallons. This is # 231.1 cubic inches (using the international # inch). winerundlet 18 winegallon winebarrel 31.5 winegallon winetierce 42 winegallon winehogshead 2 winebarrel winepuncheon 2 winetierce winebutt 2 winehogshead winepipe winebutt winetun 2 winebutt # English beer and ale measures used 1803-1824 and used for beer before 1688 beerpint 1|2 beerquart beerquart 1|4 beergallon beergallon 282 UKinch^3 beerbarrel 36 beergallon beerhogshead 1.5 beerbarrel # English ale measures used from 1688-1803 for both ale and beer alepint 1|2 alequart alequart 1|4 alegallon alegallon beergallon alebarrel 34 alegallon alehogshead 1.5 alebarrel # Scots capacity measure scotsgill 1|4 mutchkin mutchkin 1|2 choppin choppin 1|2 scotspint scotspint 1|2 scotsquart scotsquart 1|4 scotsgallon scotsgallon 827.232 UKinch^3 scotsbarrel 8 scotsgallon jug scotspint # Scots dry capacity measure scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt scotswheatlippies scotswheatlippy scotswheatpeck 4 scotswheatlippy scotswheatfirlot 4 scotswheatpeck scotswheatboll 4 scotswheatfirlot scotswheatchalder 16 scotswheatboll scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt scotsoatlippies scotsoatlippy scotsoatpeck 4 scotsoatlippy scotsoatfirlot 4 scotsoatpeck scotsoatboll 4 scotsoatfirlot scotsoatchalder 16 scotsoatboll # Scots Tron weight trondrop 1|16 tronounce tronounce 1|20 tronpound tronpound 9520 grain tronstone 16 tronpound # Irish liquid capacity measure irishnoggin 1|4 irishpint irishpint 1|2 irishquart irishquart 1|2 irishpottle irishpottle 1|2 irishgallon irishgallon 217.6 UKinch^3 irishrundlet 18 irishgallon irishbarrel 31.5 irishgallon irishtierce 42 irishgallon irishhogshead 2 irishbarrel irishpuncheon 2 irishtierce irishpipe 2 irishhogshead irishtun 2 irishpipe # Irish dry capacity measure irishpeck 2 irishgallon irishbushel 4 irishpeck irishstrike 2 irishbushel irishdrybarrel 2 irishstrike irishquarter 2 irishbarrel # English Tower weights, abolished in 1528 towerpound 5400 grain towerounce 1|12 towerpound towerpennyweight 1|20 towerounce towergrain 1|32 towerpennyweight # English Mercantile weights, used since the late 12th century mercpound 6750 grain mercounce 1|15 mercpound mercpennyweight 1|20 mercounce # English weights for lead leadstone 12.5 lb fotmal 70 lb leadwey 14 leadstone fothers 12 leadwey # English Hay measure newhaytruss 60 lb # New and old here seem to refer to "new" newhayload 36 newhaytruss # hay and "old" hay rather than a new unit oldhaytruss 56 lb # and an old unit. oldhayload 36 oldhaytruss # English wool measure woolclove 7 lb woolstone 2 woolclove wooltod 2 woolstone woolwey 13 woolstone woolsack 2 woolwey woolsarpler 2 woolsack woollast 6 woolsarpler # # Ancient history units: There tends to be uncertainty in the definitions # of the units in this section # These units are from [11] # Roman measure. The Romans had a well defined distance measure, but their # measures of weight were poor. They adopted local weights in different # regions without distinguishing among them so that there are half a dozen # different Roman "standard" weight systems. romanfoot 296 mm # There is some uncertainty in this definition romanfeet romanfoot # from which all the other units are derived. pes romanfoot # This value appears in numerous sources. In "The pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm. romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the romandigit 1|16 romanfoot # same names as the subdivisions of the pound, romanpalm 1|4 romanfoot # but we can't have the names for different romancubit 18 romaninch # units. romanpace 5 romanfeet # Roman double pace (basic military unit) passus romanpace romanperch 10 romanfeet stade 125 romanpaces stadia stade stadium stade romanmile 8 stadia # 1000 paces romanleague 1.5 romanmile schoenus 4 romanmile # Other values for the Roman foot (from Dilke) earlyromanfoot 29.73 cm pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC lateromanfoot 29.42 cm # Roman areas actuslength 120 romanfeet # length of a Roman furrow actus 120*4 romanfeet^2 # area of the furrow squareactus 120^2 romanfeet^2 # actus quadratus acnua squareactus iugerum 2 squareactus iugera iugerum jugerum iugerum jugera iugerum heredium 2 iugera # heritable plot heredia heredium centuria 100 heredia centurium centuria # Roman volumes sextarius 35.4 in^3 # Basic unit of Roman volume. As always, sextarii sextarius # there is uncertainty. Six large Roman # measures survive with volumes ranging from # 34.4 in^3 to 39.55 in^3. Three of them # cluster around the size given here. # # But the values for this unit vary wildly # in other sources. One reference gives 0.547 # liters, but then says the amphora is a # cubic Roman foot. This gives a value for the # sextarius of 0.540 liters. And the # encyclopedia Britannica lists 0.53 liters for # this unit. Both [7] and [11], which were # written by scholars of weights and measures, # give the value of 35.4 cubic inches. cochlearia 1|48 sextarius cyathi 1|12 sextarius acetabula 1|8 sextarius quartaria 1|4 sextarius quartarius quartaria heminae 1|2 sextarius hemina heminae cheonix 1.5 sextarii # Dry volume measures (usually) semodius 8 sextarius semodii semodius modius 16 sextarius modii modius # Liquid volume measures (usually) congius 12 heminae congii congius amphora 8 congii amphorae amphora # Also a dry volume measure culleus 20 amphorae quadrantal amphora # Roman weights libra 5052 grain # The Roman pound varied significantly librae libra # from 4210 grains to 5232 grains. Most of romanpound libra # the standards were obtained from the weight uncia 1|12 libra # of particular coins. The one given here is unciae uncia # based on the Gold Aureus of Augustus which romanounce uncia # was in use from BC 27 to AD 296. deunx 11 uncia dextans 10 uncia dodrans 9 uncia bes 8 uncia seprunx 7 uncia semis 6 uncia quincunx 5 uncia triens 4 uncia quadrans 3 uncia sextans 2 uncia sescuncia 1.5 uncia semuncia 1|2 uncia siscilius 1|4 uncia sextula 1|6 uncia semisextula 1|12 uncia scriptulum 1|24 uncia scrupula scriptulum romanobol 1|2 scrupula romanaspound 4210 grain # Old pound based on bronze coinage, the # earliest money of Rome BC 338 to BC 268. # Egyptian length measure egyptianroyalcubit 20.63 in # plus or minus .2 in egyptianpalm 1|7 egyptianroyalcubit egyptiandigit 1|4 egyptianpalm egyptianshortcubit 6 egyptianpalm doubleremen 29.16 in # Length of the diagonal of a square with remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit. # This is divided into 40 digits which are # not the same size as the digits based on # the royal cubit. # Greek length measures greekfoot 12.45 in # Listed as being derived from the greekfeet greekfoot # Egyptian Royal cubit in [11]. It is greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit. pous greekfoot podes greekfoot orguia 6 greekfoot greekfathom orguia stadion 100 orguia akaina 10 greekfeet plethron 10 akaina greekfinger 1|16 greekfoot homericcubit 20 greekfingers # Elbow to end of knuckles. shortgreekcubit 18 greekfingers # Elbow to start of fingers. ionicfoot 296 mm doricfoot 326 mm olympiccubit 25 remendigit # These olympic measures were not as olympicfoot 2|3 olympiccubit # common as the other greek measures. olympicfinger 1|16 olympicfoot # They were used in agriculture. olympicfeet olympicfoot olympicdakylos olympicfinger olympicpalm 1|4 olympicfoot olympicpalestra olympicpalm olympicspithame 3|4 foot olympicspan olympicspithame olympicbema 2.5 olympicfeet olympicpace olympicbema olympicorguia 6 olympicfeet olympicfathom olympicorguia olympiccord 60 olympicfeet olympicamma olympiccord olympicplethron 100 olympicfeet olympicstadion 600 olympicfeet # Greek capacity measure greekkotyle 270 ml # This approximate value is obtained xestes 2 greekkotyle # from two earthenware vessels that khous 12 greekkotyle # were reconstructed from fragments. metretes 12 khous # The kotyle is a day's corn ration choinix 4 greekkotyle # for one man. hekteos 8 choinix medimnos 6 hekteos # Greek weight. Two weight standards were used, an Aegina standard based # on the Beqa shekel and an Athens (attic) standard. aeginastater 192 grain # Varies up to 199 grain aeginadrachmae 1|2 aeginastater aeginaobol 1|6 aeginadrachmae aeginamina 50 aeginastaters aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot # of water (whichever foot was in use) atticstater 135 grain # Varies 134-138 grain atticdrachmae 1|2 atticstater atticobol 1|6 atticdrachmae atticmina 50 atticstaters attictalent 60 atticmina # Supposedly the mass of a cubic foot # of water (whichever foot was in use) # "Northern" cubit and foot. This was used by the pre-Aryan civilization in # the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China, # central and Western Europe until modern times when it was displaced by # the metric system. northerncubit 26.6 in # plus/minus .2 in northernfoot 1|2 northerncubit sumeriancubit 495 mm kus sumeriancubit sumerianfoot 2|3 sumeriancubit assyriancubit 21.6 in assyrianfoot 1|2 assyriancubit assyrianpalm 1|3 assyrianfoot assyriansusi 1|20 assyrianpalm susi assyriansusi persianroyalcubit 7 assyrianpalm # Arabic measures. The arabic standards were meticulously kept. Glass weights # accurate to .2 grains were made during AD 714-900. hashimicubit 25.56 in # Standard of linear measure used # in Persian dominions of the Arabic # empire 7-8th cent. Is equal to two # French feet. blackcubit 21.28 in arabicfeet 1|2 blackcubit arabicfoot arabicfeet arabicinch 1|12 arabicfoot arabicmile 4000 blackcubit silverdirhem 45 grain # The weights were derived from these two tradedirhem 48 grain # units with two identically named systems # used for silver and used for trade purposes silverkirat 1|16 silverdirhem silverwukiyeh 10 silverdirhem silverrotl 12 silverwukiyeh arabicsilverpound silverrotl tradekirat 1|16 tradedirhem tradewukiyeh 10 tradedirhem traderotl 12 tradewukiyeh arabictradepound traderotl # Miscellaneous ancient units parasang 3.5 mile # Persian unit of length usually thought # to be between 3 and 3.5 miles biblicalcubit 21.8 in hebrewcubit 17.58 in li 10|27.8 mile # Chinese unit of length # 100 li is considered a day's march liang 11|3 oz # Chinese weight unit # Medieval time units. According to the OED, these appear in Du Cange # by Papias. timepoint 1|5 hour # also given as 1|4 timeminute 1|10 hour timeostent 1|60 hour timeounce 1|8 timeostent timeatom 1|47 timeounce # Given in [15], these subdivisions of the grain were supposedly used # by jewelers. The mite may have been used but the blanc could not # have been accurately measured. mite 1|20 grain droit 1|24 mite periot 1|20 droit blanc 1|24 periot # # Localization # !var UNITS_ENGLISH US hundredweight ushundredweight ton uston scruple apscruple fluidounce usfluidounce gallon usgallon bushel usbushel quarter quarterweight cup uscup tablespoon ustablespoon teaspoon usteaspoon dollar US$ cent $ 0.01 penny cent minim minimvolume pony ponyvolume grand usgrand firkin usfirkin hogshead ushogshead !endvar !var UNITS_ENGLISH GB hundredweight brhundredweight ton brton scruple brscruple fluidounce brfluidounce gallon brgallon bushel brbushel quarter brquarter chaldron brchaldron cup brcup teacup brteacup tablespoon brtablespoon teaspoon brteaspoon dollar US$ cent $ 0.01 penny brpenny minim minimnote pony brpony grand brgrand firkin brfirkin hogshead brhogshead !endvar !varnot UNITS_ENGLISH GB US !message Unknown value for environment variable UNITS_ENGLISH. Should be GB or US. !endvar !utf8 ⅛- 1|8 ¼- 1|4 ⅜- 3|8 ½- 1|2 ⅝- 5|8 ¾- 3|4 ⅞- 7|8 ⅙- 1|6 ⅓- 1|3 ⅔- 2|3 ⅚- 5|6 ⅕- 1|5 ⅖- 2|5 ⅗- 3|5 ⅘- 4|5 # U+2150- 1|7 For some reason these characters are getting # U+2151- 1|9 flagged as invalid UTF8. # U+2152- 1|10 #⅐- 1|7 # fails under MacOS #⅑- 1|9 # fails under MacOS #⅒- 1|10 # fails under MacOS ℯ exp(1) # U+212F, base of natural log µ- micro # micro sign U+00B5 μ- micro # small mu U+03BC ångström angstrom Å angstrom # angstrom symbol U+212B Å angstrom # A with ring U+00C5 röntgen roentgen °C degC °F degF °K K # °K is incorrect notation °R degR ° degree ℃ degC ℉ degF K K # Kelvin symbol, U+212A ℓ liter # unofficial abbreviation used in some places Ω ohm # Ohm symbol U+2126 Ω ohm # Greek capital omega U+03A9 ℧ mho ʒ dram # U+0292 ℈ scruple ℥ ounce ℔ lb ℎ h ℏ hbar ‰ 1|1000 ‱ 1|10000 ′ ' # U+2032 ″ " # U+2033 # # Unicode currency symbols # ¢ cent £ britainpound ¥ japanyen € euro ₩ southkoreawon ₪ israelnewshekel ₤ lira # ₺ turkeylira # fails under MacOS ₨ rupee # unofficial legacy rupee sign # ₹ indiarupee # official rupee sign # MacOS fail #؋ afghanafghani # fails under MacOS ฿ thailandbaht ₡ elsalvadorcolon # Also costaricacolon ₣ francefranc ₦ nigerianaira ₧ spainpeseta ₫ vietnamdong ₭ laokip ₮ mongoliatugrik ₯ greecedrachma ₱ philippinepeso # ₲ paraguayguarani # fails under MacOS #₴ ukrainehryvnia # fails under MacOS #₵ ghanacedi # fails under MacOS #₸ kazakhstantenge # fails under MacOS #₼ azerbaijanmanat # fails under MacOS #₽ russiaruble # fails under MacOS #₾ georgialari # fails under MacOS ﷼ iranrial ﹩ $ ￠ ¢ ￡ £ ￥ ¥ ￦ ₩ # # Square Unicode symbols starting at U+3371 # ㍱ hPa ㍲ da ㍳ au ㍴ bar # ㍵ oV??? ㍶ pc #㍷ dm invalid on Mac #㍸ dm^2 invalid on Mac #㍹ dm^3 invalid on Mac ㎀ pA ㎁ nA ㎂ µA ㎃ mA ㎄ kA ㎅ kB ㎆ MB ㎇ GB ㎈ cal ㎉ kcal ㎊ pF ㎋ nF ㎌ µF ㎍ µg ㎎ mg ㎏ kg ㎐ Hz ㎑ kHz ㎒ MHz ㎓ GHz ㎔ THz ㎕ µL ㎖ mL ㎗ dL ㎘ kL ㎙ fm ㎚ nm ㎛ µm ㎜ mm ㎝ cm ㎞ km ㎟ mm^2 ㎠ cm^2 ㎡ m^2 ㎢ km^2 ㎣ mm^3 ㎤ cm^3 ㎥ m^3 ㎦ km^3 ㎧ m/s ㎨ m/s^2 ㎩ Pa ㎪ kPa ㎫ MPa ㎬ GPa ㎭ rad ㎮ rad/s ㎯ rad/s^2 ㎰ ps ㎱ ns ㎲ µs ㎳ ms ㎴ pV ㎵ nV ㎶ µV ㎷ mV ㎸ kV ㎹ MV ㎺ pW ㎻ nW ㎼ µW ㎽ mW ㎾ kW ㎿ MW ㏀ kΩ ㏁ MΩ ㏃ Bq ㏄ cc ㏅ cd ㏆ C/kg ㏈() dB ㏉ Gy ㏊ ha # ㏋ HP?? ㏌ in # ㏍ KK?? # ㏎ KM??? ㏏ kt ㏐ lm # ㏑ ln # ㏒ log ㏓ lx ㏔ mb ㏕ mil ㏖ mol ㏗() pH ㏙ ppm # ㏚ PR??? ㏛ sr ㏜ Sv ㏝ Wb #㏞ V/m Invalid on Mac #㏟ A/m Invalid on Mac #㏿ gal Invalid on Mac !endutf8 ############################################################################ # # Unit list aliases # # These provide a shorthand for conversions to unit lists. # ############################################################################ !unitlist hms hr;min;sec !unitlist time year;day;hr;min;sec !unitlist dms deg;arcmin;arcsec !unitlist ftin ft;in;1|8 in !unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in !unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\ tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp ############################################################################ # # The following units were in the Unix units database but do not appear in # this file: # # wey used for cheese, salt and other goods. Measured mass or # waymass volume depending on what was measured and where the measuring # took place. A wey of cheese ranged from 200 to 324 pounds. # # sack No precise definition # # spindle The length depends on the type of yarn # # block Defined variously on different computer systems # # erlang A unit of telephone traffic defined variously. # Omitted because there are no other units for this # dimension. Is this true? What about CCS = 1/36 erlang? # Erlang is supposed to be dimensionless. One erlang means # a single channel occupied for one hour. # ############################################################################