1# 2# This file is the units database for use with GNU units, a units conversion 3# program by Adrian Mariano adrianm@gnu.org 4# 5# October 2017 Version 2.19 6# 7# Copyright (C) 1996-2002, 2004-2017 8# Free Software Foundation, Inc 9# 10# This program is free software; you can redistribute it and/or modify 11# it under the terms of the GNU General Public License as published by 12# the Free Software Foundation; either version 3 of the License, or 13# (at your option) any later version. 14# 15# This program is distributed in the hope that it will be useful, 16# but WITHOUT ANY WARRANTY; without even the implied warranty of 17# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18# GNU General Public License for more details. 19# 20# You should have received a copy of the GNU General Public License 21# along with this program; if not, write to the Free Software 22# Foundation, Inc., 51 Franklin Street, Fifth Floor, 23# Boston, MA 02110-1301 USA 24# 25############################################################################ 26# 27# Improvements and corrections are welcome. 28# 29# Fundamental constants in this file are the 2014 CODATA recommended values. 30# 31# Most units data was drawn from 32# 1. NIST Special Publication 811, Guide for the 33# Use of the International System of Units (SI). 34# Barry N. Taylor. 1995 35# 2. CRC Handbook of Chemistry and Physics 70th edition 36# 3. Oxford English Dictionary 37# 4. Websters New Universal Unabridged Dictionary 38# 5. Units of Measure by Stephen Dresner 39# 6. A Dictionary of English Weights and Measures by Ronald Zupko 40# 7. British Weights and Measures by Ronald Zupko 41# 8. Realm of Measure by Isaac Asimov 42# 9. United States standards of weights and measures, their 43# creation and creators by Arthur H. Frazier. 44# 10. French weights and measures before the Revolution: a 45# dictionary of provincial and local units by Ronald Zupko 46# 11. Weights and Measures: their ancient origins and their 47# development in Great Britain up to AD 1855 by FG Skinner 48# 12. The World of Measurements by H. Arthur Klein 49# 13. For Good Measure by William Johnstone 50# 14. NTC's Encyclopedia of International Weights and Measures 51# by William Johnstone 52# 15. Sizes by John Lord 53# 16. Sizesaurus by Stephen Strauss 54# 17. CODATA Recommended Values of Physical Constants available at 55# http://physics.nist.gov/cuu/Constants/index.html 56# 18. How Many? A Dictionary of Units of Measurement. Available at 57# http://www.unc.edu/~rowlett/units/index.html 58# 19. Numericana. http://www.numericana.com 59# 20. UK history of measurement 60# http://www.ukmetrication.com/history.htm 61# 21. NIST Handbook 44, Specifications, Tolerances, and 62# Other Technical Requirements for Weighing and Measuring 63# Devices. 2011 64# 22. NIST Special Publication 447, Weights and Measures Standards 65# of the the United States: a brief history. Lewis V. Judson. 66# 1963; rev. 1976 67# 23. CRC Handbook of Chemistry and Physics, 96th edition 68# 24. Dictionary of Scientific Units, 6th ed. H.G. Jerrard and D.B. 69# McNeill. 1992 70# 71# Thanks to Jeff Conrad for assistance in ferreting out unit definitions. 72# 73########################################################################### 74# 75# If units you use are missing or defined incorrectly, please contact me. 76# If your country's local units are missing and you are willing to supply 77# them, please send me a list. 78# 79# I added shoe size information but I'm not convinced that it's correct. 80# If you know anything about shoe sizes please contact me. 81# 82########################################################################### 83 84########################################################################### 85# 86# Brief Philosophy of this file 87# 88# Most unit definitions are made in terms of integers or simple fractions of 89# other definitions. The typical exceptions are when converting between two 90# different unit systems, or the values of measured physical constants. In 91# this file definitions are given in the most natural and revealing way in 92# terms of integer factors. 93# 94# If you make changes be sure to run 'units --check' to check your work. 95# 96# The file is USA-centric, but there is some modest effort to support other 97# countries. This file is now coded in UTF-8. To support environments where 98# UTF-8 is not available, definitions that require this character set are 99# wrapped in !utf8 directives. 100# 101# When a unit name is used in different countries with the different meanings 102# the system should be as follows: 103# 104# Suppose countries ABC and XYZ both use the "foo". Then globally define 105# 106# ABCfoo <some value> 107# XYZfoo <different value> 108# 109# Then, using the !locale directive, define the "foo" appropriately for each of 110# the two countries with a definition like 111# 112# !locale ABC 113# foo ABCfoo 114# !endlocale 115# 116########################################################################### 117 118!locale en_US 119! set UNITS_ENGLISH US 120!endlocale 121 122!locale en_GB 123! set UNITS_ENGLISH GB 124!endlocale 125 126!set UNITS_ENGLISH US # Default setting for English units 127 128########################################################################### 129# # 130# Primitive units. Any unit defined to contain a '!' character is a # 131# primitive unit which will not be reduced any further. All units should # 132# reduce to primitive units. # 133# # 134########################################################################### 135 136# 137# SI units 138# 139 140kg ! # Mass of the international prototype 141kilogram kg 142 143s ! # Duration of 9192631770 periods of the radiation 144second s # corresponding to the transition between the two hyperfine 145 # levels of the ground state of the cesium-133 atom 146 147m ! # Length of the path traveled by light in a vacuum 148meter m # during 1|299792458 seconds. Originally meant to be 149 # 1e-7 of the length along a meridian from the equator 150 # to a pole. 151 152A ! # The current which produces a force of 2e-7 N/m between two 153ampere A # infinitely long wires that are 1 meter apart 154amp ampere 155 156cd ! # Luminous intensity in a given direction of a source which 157candela cd # emits monochromatic radiation at 540e12 Hz with radiant 158 # intensity 1|683 W/steradian. (This differs from radiant 159 # intensity (W/sr) in that it is adjusted for human 160 # perceptual dependence on wavelength. The frequency of 161 # 540e12 Hz (yellow) is where human perception is most 162 # efficient.) 163 164mol ! # The amount of substance of a system which contains as many 165mole mol # elementary entities as there are atoms in 0.012 kg of 166 # carbon 12. The elementary entities must be specified and 167 # may be atoms, molecules, ions, electrons, or other 168 # particles or groups of particles. It is understood that 169 # unbound atoms of carbon 12, at rest and in the ground 170 # state, are referred to. 171 172K ! # 1|273.16 of the thermodynamic temperature of the triple 173kelvin K # point of water 174 175# 176# The radian and steradian are defined as dimensionless primitive units. 177# The radian is equal to m/m and the steradian to m^2/m^2 so these units are 178# dimensionless. Retaining them as named units is useful because it allows 179# clarity in expressions and makes the meaning of unit definitions more clear. 180# These units will reduce to 1 in conversions but not for sums of units or for 181# arguments to functions. 182# 183 184radian !dimensionless # The angle subtended at the center of a circle by 185 # an arc equal in length to the radius of the 186 # circle 187sr !dimensionless # Solid angle which cuts off an area of the surface 188steradian sr # of the sphere equal to that of a square with 189 # sides of length equal to the radius of the 190 # sphere 191 192# 193# Some primitive non-SI units 194# 195 196US$ ! # The US dollar is chosen arbitrarily to be the primitive 197 # unit of money. 198 199bit ! # Basic unit of information (entropy). The entropy in bits 200 # of a random variable over a finite alphabet is defined 201 # to be the sum of -p(i)*log2(p(i)) over the alphabet where 202 # p(i) is the probability that the random variable takes 203 # on the value i. 204 205########################################################################### 206# # 207# Prefixes (longer names must come first) # 208# # 209########################################################################### 210 211yotta- 1e24 # Greek or Latin octo, "eight" 212zetta- 1e21 # Latin septem, "seven" 213exa- 1e18 # Greek hex, "six" 214peta- 1e15 # Greek pente, "five" 215tera- 1e12 # Greek teras, "monster" 216giga- 1e9 # Greek gigas, "giant" 217mega- 1e6 # Greek megas, "large" 218myria- 1e4 # Not an official SI prefix 219kilo- 1e3 # Greek chilioi, "thousand" 220hecto- 1e2 # Greek hekaton, "hundred" 221deca- 1e1 # Greek deka, "ten" 222deka- deca 223deci- 1e-1 # Latin decimus, "tenth" 224centi- 1e-2 # Latin centum, "hundred" 225milli- 1e-3 # Latin mille, "thousand" 226micro- 1e-6 # Latin micro or Greek mikros, "small" 227nano- 1e-9 # Latin nanus or Greek nanos, "dwarf" 228pico- 1e-12 # Spanish pico, "a bit" 229femto- 1e-15 # Danish-Norwegian femten, "fifteen" 230atto- 1e-18 # Danish-Norwegian atten, "eighteen" 231zepto- 1e-21 # Latin septem, "seven" 232yocto- 1e-24 # Greek or Latin octo, "eight" 233 234quarter- 1|4 235semi- 0.5 236demi- 0.5 237hemi- 0.5 238half- 0.5 239double- 2 240triple- 3 241treble- 3 242 243kibi- 2^10 # In response to the convention of illegally 244mebi- 2^20 # and confusingly using metric prefixes for 245gibi- 2^30 # powers of two, the International 246tebi- 2^40 # Electrotechnical Commission aproved these 247pebi- 2^50 # binary prefixes for use in 1998. If you 248exbi- 2^60 # want to refer to "megabytes" using the 249Ki- kibi # binary definition, use these prefixes. 250Mi- mebi 251Gi- gibi 252Ti- tebi 253Pi- pebi 254Ei- exbi 255 256Y- yotta 257Z- zetta 258E- exa 259P- peta 260T- tera 261G- giga 262M- mega 263k- kilo 264h- hecto 265da- deka 266d- deci 267c- centi 268m- milli 269u- micro # it should be a mu but u is easy to type 270n- nano 271p- pico 272f- femto 273a- atto 274z- zepto 275y- yocto 276 277# 278# Names of some numbers 279# 280 281one 1 282two 2 283double 2 284couple 2 285three 3 286triple 3 287four 4 288quadruple 4 289five 5 290quintuple 5 291six 6 292seven 7 293eight 8 294nine 9 295ten 10 296eleven 11 297twelve 12 298thirteen 13 299fourteen 14 300fifteen 15 301sixteen 16 302seventeen 17 303eighteen 18 304nineteen 19 305twenty 20 306thirty 30 307forty 40 308fifty 50 309sixty 60 310seventy 70 311eighty 80 312ninety 90 313hundred 100 314thousand 1000 315million 1e6 316 317twoscore two score 318threescore three score 319fourscore four score 320fivescore five score 321sixscore six score 322sevenscore seven score 323eightscore eight score 324ninescore nine score 325tenscore ten score 326twelvescore twelve score 327 328# These number terms were described by N. Chuquet and De la Roche in the 16th 329# century as being successive powers of a million. These definitions are still 330# used in most European countries. The current US definitions for these 331# numbers arose in the 17th century and don't make nearly as much sense. These 332# numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric 333# W. Weisstein. 334 335shortbillion 1e9 336shorttrillion 1e12 337shortquadrillion 1e15 338shortquintillion 1e18 339shortsextillion 1e21 340shortseptillion 1e24 341shortoctillion 1e27 342shortnonillion 1e30 343shortnoventillion shortnonillion 344shortdecillion 1e33 345shortundecillion 1e36 346shortduodecillion 1e39 347shorttredecillion 1e42 348shortquattuordecillion 1e45 349shortquindecillion 1e48 350shortsexdecillion 1e51 351shortseptendecillion 1e54 352shortoctodecillion 1e57 353shortnovemdecillion 1e60 354shortvigintillion 1e63 355 356centillion 1e303 357googol 1e100 358 359longbillion million^2 360longtrillion million^3 361longquadrillion million^4 362longquintillion million^5 363longsextillion million^6 364longseptillion million^7 365longoctillion million^8 366longnonillion million^9 367longnoventillion longnonillion 368longdecillion million^10 369longundecillion million^11 370longduodecillion million^12 371longtredecillion million^13 372longquattuordecillion million^14 373longquindecillion million^15 374longsexdecillion million^16 375longseptdecillion million^17 376longoctodecillion million^18 377longnovemdecillion million^19 378longvigintillion million^20 379 380# These numbers fill the gaps left by the long system above. 381 382milliard 1000 million 383billiard 1000 million^2 384trilliard 1000 million^3 385quadrilliard 1000 million^4 386quintilliard 1000 million^5 387sextilliard 1000 million^6 388septilliard 1000 million^7 389octilliard 1000 million^8 390nonilliard 1000 million^9 391noventilliard nonilliard 392decilliard 1000 million^10 393 394# For consistency 395 396longmilliard milliard 397longbilliard billiard 398longtrilliard trilliard 399longquadrilliard quadrilliard 400longquintilliard quintilliard 401longsextilliard sextilliard 402longseptilliard septilliard 403longoctilliard octilliard 404longnonilliard nonilliard 405longnoventilliard noventilliard 406longdecilliard decilliard 407 408# The long centillion would be 1e600. The googolplex is another 409# familiar large number equal to 10^googol. These numbers give overflows. 410 411# 412# The short system prevails in English speaking countries 413# 414 415billion shortbillion 416trillion shorttrillion 417quadrillion shortquadrillion 418quintillion shortquintillion 419sextillion shortsextillion 420septillion shortseptillion 421octillion shortoctillion 422nonillion shortnonillion 423noventillion shortnoventillion 424decillion shortdecillion 425undecillion shortundecillion 426duodecillion shortduodecillion 427tredecillion shorttredecillion 428quattuordecillion shortquattuordecillion 429quindecillion shortquindecillion 430sexdecillion shortsexdecillion 431septendecillion shortseptendecillion 432octodecillion shortoctodecillion 433novemdecillion shortnovemdecillion 434vigintillion shortvigintillion 435 436# 437# Numbers used in India 438# 439 440lakh 1e5 441crore 1e7 442arab 1e9 443kharab 1e11 444neel 1e13 445padm 1e15 446shankh 1e17 447 448############################################################################# 449# # 450# Derived units which can be reduced to the primitive units # 451# # 452############################################################################# 453 454 455 456# 457# Named SI derived units (officially accepted) 458# 459 460newton kg m / s^2 # force 461N newton 462pascal N/m^2 # pressure or stress 463Pa pascal 464joule N m # energy 465J joule 466watt J/s # power 467W watt 468coulomb A s # charge 469C coulomb 470volt W/A # potential difference 471V volt 472ohm V/A # electrical resistance 473siemens A/V # electrical conductance 474S siemens 475farad C/V # capacitance 476F farad 477weber V s # magnetic flux 478Wb weber 479henry Wb/A # inductance 480H henry 481tesla Wb/m^2 # magnetic flux density 482T tesla 483hertz /s # frequency 484Hz hertz 485 486# 487# Dimensions. These are here to help with dimensional analysis and 488# because they will appear in the list produced by hitting '?' at the 489# "You want:" prompt to tell the user the dimension of the unit. 490# 491 492LENGTH meter 493AREA LENGTH^2 494VOLUME LENGTH^3 495MASS kilogram 496CURRENT ampere 497AMOUNT mole 498ANGLE radian 499SOLID_ANGLE steradian 500MONEY US$ 501FORCE newton 502PRESSURE FORCE / AREA 503STRESS FORCE / AREA 504CHARGE coulomb 505CAPACITANCE farad 506RESISTANCE ohm 507CONDUCTANCE siemens 508INDUCTANCE henry 509FREQUENCY hertz 510VELOCITY LENGTH / TIME 511ACCELERATION VELOCITY / TIME 512DENSITY MASS / VOLUME 513LINEAR_DENSITY MASS / LENGTH 514VISCOSITY FORCE TIME / AREA 515KINEMATIC_VISCOSITY VISCOSITY / DENSITY 516 517 518# 519# units derived easily from SI units 520# 521 522gram millikg 523gm gram 524g gram 525tonne 1000 kg 526t tonne 527metricton tonne 528sthene tonne m / s^2 529funal sthene 530pieze sthene / m^2 531quintal 100 kg 532bar 1e5 Pa # About 1 atm 533b bar 534vac millibar 535micron micrometer # One millionth of a meter 536bicron picometer # One brbillionth of a meter 537cc cm^3 538are 100 m^2 539a are 540liter 1000 cc # The liter was defined in 1901 as the 541oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at 542L liter # the temperature of its maximum density 543l liter # under a pressure of 1 atm. This was 544 # supposed to be 1000 cubic cm, but it 545 # was discovered that the original 546 # measurement was off. In 1964, the 547 # liter was redefined to be exactly 1000 548 # cubic centimeters. 549mho siemens # Inverse of ohm, hence ohm spelled backward 550galvat ampere # Named after Luigi Galvani 551angstrom 1e-10 m # Convenient for describing molecular sizes 552xunit xunit_cu # Used for measuring x-ray wavelengths. 553siegbahn xunit # Originally defined to be 1|3029.45 of 554xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18 555xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly 556 # 1e-13 m, but was later found to be 557 # slightly off. Current usage is with 558 # reference to common x-ray lines, either 559 # the K-alpha 1 line of copper or the 560 # same line of molybdenum. 561angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965 562fermi 1e-15 m # Convenient for describing nuclear sizes 563 # Nuclear radius is from 1 to 10 fermis 564barn 1e-28 m^2 # Used to measure cross section for 565 # particle physics collision, said to 566 # have originated in the phrase "big as 567 # a barn". 568shed 1e-24 barn # Defined to be a smaller companion to the 569 # barn, but it's too small to be of 570 # much use. 571brewster micron^2/N # measures stress-optical coef 572diopter /m # measures reciprocal of lens focal length 573fresnel 1e12 Hz # occasionally used in spectroscopy 574shake 1e-8 sec 575svedberg 1e-13 s # Used for measuring the sedimentation 576 # coefficient for centrifuging. 577gamma microgram # Also used for 1e-9 tesla 578lambda microliter 579spat 1e12 m # Rarely used for astronomical measurements 580preece 1e13 ohm m # resistivity 581planck J s # action of one joule over one second 582sturgeon /henry # magnetic reluctance 583daraf 1/farad # elastance (farad spelled backwards) 584leo 10 m/s^2 585poiseuille N s / m^2 # viscosity 586mayer J/g K # specific heat 587mired / microK # reciprocal color temperature. The name 588 # abbreviates micro reciprocal degree. 589crocodile megavolt # used informally in UK physics labs 590metricounce 25 g 591mounce metricounce 592finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light 593 # with wavelength 296.7 nm. 594fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure 595 # the energy incident on the receiving 596 # body across a specified frequency 597 # bandwidth. [12] 598jansky fluxunit # K. G. Jansky identified radio waves coming 599Jy jansky # from outer space in 1931. 600flick W / cm^2 sr micrometer # Spectral radiance or irradiance 601pfu / cm^2 sr s # particle flux unit -- Used to measure 602 # rate at which particles are received by 603 # a spacecraft as particles per solid 604 # angle per detector area per second. [18] 605pyron cal_IT / cm^2 min # Measures heat flow from solar radiation, 606 # from Greek work "pyr" for fire. 607katal mol/sec # Measure of the amount of a catalyst. One 608kat katal # katal of catalyst enables the reaction 609 # to consume or produce on mol/sec. 610solarluminosity 382.8e24 W # A common yardstick for comparing the 611 # output of different stars. 612 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html 613# at mean earth-sun distance 614solarirradiance solarluminosity / (4 pi sundist^2) 615solarconstant solarirradiance 616TSI solarirradiance # total solar irradiance 617 618# 619# time 620# 621 622sec s 623minute 60 s 624min minute 625hour 60 min 626hr hour 627day 24 hr 628d day 629da day 630week 7 day 631wk week 632sennight 7 day 633fortnight 14 day 634blink 1e-5 day # Actual human blink takes 1|3 second 635ce 1e-2 day 636cron 1e6 years 637watch 4 hours # time a sentry stands watch or a ship's 638 # crew is on duty. 639bell 1|8 watch # Bell would be sounded every 30 minutes. 640 641# French Revolutionary Time or Decimal Time. It was Proposed during 642# the French Revolution. A few clocks were made, but it never caught 643# on. In 1998 Swatch defined a time measurement called ".beat" and 644# sold some watches that displayed time in this unit. 645 646decimalhour 1|10 day 647decimalminute 1|100 decimalhour 648decimalsecond 1|100 decimalminute 649beat decimalminute # Swatch Internet Time 650 651# 652# angular measure 653# 654 655circle 2 pi radian 656degree 1|360 circle 657deg degree 658arcdeg degree 659arcmin 1|60 degree 660arcminute arcmin 661' arcmin 662arcsec 1|60 arcmin 663arcsecond arcsec 664" arcsec 665'' " 666rightangle 90 degrees 667quadrant 1|4 circle 668quintant 1|5 circle 669sextant 1|6 circle 670 671sign 1|12 circle # Angular extent of one sign of the zodiac 672turn circle 673revolution turn 674rev turn 675pulsatance radian / sec 676gon 1|100 rightangle # measure of grade 677grade gon 678centesimalminute 1|100 grade 679centesimalsecond 1|100 centesimalminute 680milangle 1|6400 circle # Official NIST definition. 681 # Another choice is 1e-3 radian. 682pointangle 1|32 circle # Used for reporting compass readings 683centrad 0.01 radian # Used for angular deviation of light 684 # through a prism. 685mas milli arcsec # Used by astronomers 686seclongitude circle (seconds/day) # Astronomers measure longitude 687 # (which they call right ascension) in 688 # time units by dividing the equator into 689 # 24 hours instead of 360 degrees. 690# 691# Some geometric formulas 692# 693 694circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi) 695spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \ 696 cuberoot(spherevolume/4|3 pi) 697spherevol() spherevolume 698square(x) range=[0,) x^2 ; sqrt(square) 699 700# 701# Solid angle measure 702# 703 704sphere 4 pi sr 705squaredegree 1|180^2 pi^2 sr 706squareminute 1|60^2 squaredegree 707squaresecond 1|60^2 squareminute 708squarearcmin squareminute 709squarearcsec squaresecond 710sphericalrightangle 0.5 pi sr 711octant 0.5 pi sr 712 713# 714# Concentration measures 715# 716 717percent 0.01 718% percent 719mill 0.001 # Originally established by Congress in 1791 720 # as a unit of money equal to 0.001 dollars, 721 # it has come to refer to 0.001 in general. 722 # Used by some towns to set their property 723 # tax rate, and written with a symbol similar 724 # to the % symbol but with two 0's in the 725 # denominator. [18] 726proof 1|200 # Alcohol content measured by volume at 727 # 60 degrees Fahrenheit. This is a USA 728 # measure. In Europe proof=percent. 729ppm 1e-6 730partspermillion ppm 731ppb 1e-9 732partsperbillion ppb # USA billion 733ppt 1e-12 734partspertrillion ppt # USA trillion 735karat 1|24 # measure of gold purity 736caratgold karat 737gammil mg/l 738basispoint 0.01 % # Used in finance 739fine 1|1000 # Measure of gold purity 740 741# The pH scale is used to measure the concentration of hydronium (H3O+) ions in 742# a solution. A neutral solution has a pH of 7 as a result of dissociated 743# water molecules. 744 745pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol)) 746 747 748# 749# Temperature 750# 751# Two types of units are defined: units for converting temperature differences 752# and functions for converting absolute temperatures. Conversions for 753# differences start with "deg" and conversions for absolute temperature start 754# with "temp". 755# 756 757TEMPERATURE kelvin 758TEMPERATURE_DIFFERENCE kelvin 759 760# In 1741 Anders Celsius introduced a temperature scale with water boiling at 761# 0 degrees and freezing at 100 degrees at standard pressure. After his death 762# the fixed points were reversed and the scale was called the centigrade 763# scale. Due to the difficulty of accurately measuring the temperature of 764# melting ice at standard pressure, the centigrade scale was replaced in 1954 765# by the Celsius scale which is defined by subtracting 273.15 from the 766# temperature in Kelvins. This definition differed slightly from the old 767# centigrade definition, but the Kelvin scale depends on the triple point of 768# water rather than a melting point, so it can be measured accurately. 769 770tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \ 771 x K + stdtemp ; (tempC +(-stdtemp))/K 772tempcelsius() tempC 773degcelsius K 774degC K 775 776# Fahrenheit defined his temperature scale by setting 0 to the coldest 777# temperature he could produce in his lab with a salt water solution and by 778# setting 96 degrees to body heat. In Fahrenheit's words: 779# 780# Placing the thermometer in a mixture of sal ammoniac or sea 781# salt, ice, and water a point on the scale will be found which 782# is denoted as zero. A second point is obtained if the same 783# mixture is used without salt. Denote this position as 30. A 784# third point, designated as 96, is obtained if the thermometer 785# is placed in the mouth so as to acquire the heat of a healthy 786# man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724) 787 788tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \ 789 (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 790tempfahrenheit() tempF 791degfahrenheit 5|9 degC 792degF 5|9 degC 793 794 795degreesrankine degF # The Rankine scale has the 796degrankine degreesrankine # Fahrenheit degree, but its zero 797degreerankine degF # is at absolute zero. 798degR degrankine 799tempR degrankine 800temprankine degrankine 801 802tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \ 803 x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur 804degreaumur 10|8 degC # The Reaumur scale was used in Europe and 805 # particularly in France. It is defined 806 # to be 0 at the freezing point of water 807 # and 80 at the boiling point. Reaumur 808 # apparently selected 80 because it is 809 # divisible by many numbers. 810 811degK K # "Degrees Kelvin" is forbidden usage. 812tempK K # For consistency 813 814# Gas mark is implemented below but in a terribly ugly way. There is 815# a simple formula, but it requires a conditional which is not 816# presently supported. 817# 818# The formula to convert to degrees Fahrenheit is: 819# 820# 25 log2(gasmark) + k_f gasmark<=1 821# 25 (gasmark-1) + k_f gasmark>=1 822# 823# k_f = 275 824# 825gasmark[degR] \ 826 .0625 634.67 \ 827 .125 659.67 \ 828 .25 684.67 \ 829 .5 709.67 \ 830 1 734.67 \ 831 2 759.67 \ 832 3 784.67 \ 833 4 809.67 \ 834 5 834.67 \ 835 6 859.67 \ 836 7 884.67 \ 837 8 909.67 \ 838 9 934.67 \ 839 10 959.67 840 841# Units cannot handle wind chill or heat index because they are two variable 842# functions, but they are included here for your edification. Clearly these 843# equations are the result of a model fitting operation. 844# 845# wind chill index (WCI) a measurement of the combined cooling effect of low 846# air temperature and wind on the human body. The index was first defined 847# by the American Antarctic explorer Paul Siple in 1939. As currently used 848# by U.S. meteorologists, the wind chill index is computed from the 849# temperature T (in °F) and wind speed V (in mi/hr) using the formula: 850# WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4. 851# For very low wind speeds, below 4 mi/hr, the WCI is actually higher than 852# the air temperature, but for higher wind speeds it is lower than the air 853# temperature. 854# 855# heat index (HI or HX) a measure of the combined effect of heat and 856# humidity on the human body. U.S. meteorologists compute the index 857# from the temperature T (in °F) and the relative humidity H (as a 858# value from 0 to 1). 859# HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH 860# - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2 861# - 0.0199 T^2 H^2. 862 863# 864# Physical constants 865# 866 867# Basic constants 868 869pi 3.14159265358979323846 870c 2.99792458e8 m/s # speed of light in vacuum (exact) 871light c 872mu0 4 pi 1e-7 H/m # permeability of vacuum (exact) 873epsilon0 1/mu0 c^2 # permittivity of vacuum (exact) 874energy c^2 # convert mass to energy 875e 1.6021766208e-19 C # electron charge 876h 4.135667662e-15 eV s # Planck constant 877hbar h / 2 pi 878spin hbar 879G 6.67408e-11 N m^2 / kg^2 # Newtonian gravitational constant 880 # This is the NIST 2006 value. 881 # The relative uncertainty on this 882 # is 1e-4. 883coulombconst 1/4 pi epsilon0 # listed as "k" sometimes 884 885# Physico-chemical constants 886 887atomicmassunit 1.660539040e-27 kg # atomic mass unit (defined to be 888u atomicmassunit # 1|12 of the mass of carbon 12) 889amu atomicmassunit 890amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of 891 # the 3 naturally occuring neutral 892 # isotopes of oxygen 893amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral 894 # oxygen 16 atom 895dalton u # Maybe this should be amu_chem? 896avogadro grams/amu mol # size of a mole 897N_A avogadro 898gasconstant k N_A # molar gas constant 899R gasconstant 900boltzmann 1.38064852e-23 J/K # Boltzmann constant 901k boltzmann 902kboltzmann boltzmann 903molarvolume mol R stdtemp / atm # Volume occupied by one mole of an 904 # ideal gas at STP. 905loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an 906 # ideal gas at STP. Loschmidt did 907 # work similar to Avogadro. 908stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a 909sigma stefanboltzmann # blackbody at temperature T is 910 # given by sigma T^4. 911wiendisplacement 2.8977729e-3 m K # Wien's Displacement Law gives the 912 # frequency at which the the Planck 913 # spectrum has maximum intensity. 914 # The relation is lambda T = b where 915 # lambda is wavelength, T is 916 # temperature and b is the Wien 917 # displacement. This relation is 918 # used to determine the temperature 919 # of stars. 920K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until 921K_J 483597.8525 GHz/V # recently, laboratories kept Weston cadmium cells as 922 # a reference, but they could drift. In 1987 the 923 # CGPM officially recommended the use of the 924 # Josephson effect as a laboratory representation of 925 # the volt. The Josephson effect occurs when two 926 # superconductors are separated by a thin insulating 927 # layer. A "supercurrent" flows across the insulator 928 # with a frequency that depends on the potential 929 # applied across the superconductors. This frequency 930 # can be very accurately measured. The Josephson 931 # constant K_J, which is equal to 2e/h, relates the 932 # measured frequency to the potential. Two values 933 # given, the conventional (exact) value from 1990 and 934 # the current CODATA measured value. 935R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties. 936R_K 25812.8074555 ohm # The old approach involved maintaining resistances 937 # that were subject to drift. The new standard is 938 # based on the Hall effect. When a current carrying 939 # ribbon is placed in a magnetic field, a potential 940 # difference develops across the ribbon. The ratio 941 # of the potential difference to the current is 942 # called the Hall resistance. Klaus von Klitzing 943 # discovered in 1980 that the Hall resistance varies 944 # in discrete jumps when the magnetic field is very 945 # large and the temperature very low. This enables 946 # accurate realization of the resistance h/e^2 in the 947 # lab. Two values given, the conventional (exact) 948 # value from 1990 and the current CODATA measured 949 # value. 950 951# Various conventional values 952 953gravity 9.80665 m/s^2 # std acceleration of gravity (exact) 954force gravity # use to turn masses into forces 955atm 101325 Pa # Standard atmospheric pressure 956atmosphere atm 957Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact) 958water gram force/cm^3 # Standard weight of water (exact) 959waterdensity gram / cm^3 # Density of water 960H2O water 961wc water # water column 962mach 331.46 m/s # speed of sound in dry air at STP 963standardtemp 273.15 K # standard temperature 964stdtemp standardtemp 965normaltemp tempF(70) # for gas density, from NIST 966normtemp normaltemp # Handbook 44 967 968# Weight of mercury and water at different temperatures using the standard 969# force of gravity. 970 971Hg10C 13.5708 force gram / cm^3 # These units, when used to form 972Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate 973Hg23C 13.5386 force gram / cm^3 # because of considerations of the 974Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale. 975Hg40C 13.4973 force gram / cm^3 976Hg60F 13.5574 force gram / cm^3 977H2O0C 0.99987 force gram / cm^3 978H2O5C 0.99999 force gram / cm^3 979H2O10C 0.99973 force gram / cm^3 980H2O15C 0.99913 force gram / cm^3 981H2O18C 0.99862 force gram / cm^3 982H2O20C 0.99823 force gram / cm^3 983H2O25C 0.99707 force gram / cm^3 984H2O50C 0.98807 force gram / cm^3 985H2O100C 0.95838 force gram / cm^3 986 987# Atomic constants 988 989Rinfinity 10973731.568539 /m # The wavelengths of a spectral series 990R_H 10967760 /m # can be expressed as 991 # 1/lambda = R (1/m^2 - 1/n^2). 992 # where R is a number that various 993 # slightly from element to element. 994 # For hydrogen, R_H is the value, 995 # and for heavy elements, the value 996 # approaches Rinfinity, which can be 997 # computed from 998 # m_e c alpha^2 / 2 h 999 # with a loss of 4 digits 1000 # of precision. 1001alpha 7.2973525664e-3 # The fine structure constant was 1002 # introduced to explain fine 1003 # structure visible in spectral 1004 # lines. It can be computed from 1005 # mu0 c e^2 / 2 h 1006 # with a loss of 3 digits precision 1007 # and loss of precision in derived 1008 # values which use alpha. 1009bohrradius alpha / 4 pi Rinfinity 1010prout 185.5 keV # nuclear binding energy equal to 1|12 1011 # binding energy of the deuteron 1012# Planck constants 1013 1014planckmass 2.17651e-8 kg # sqrt(hbar c / G) 1015m_P planckmass 1016plancktime hbar / planckmass c^2 1017t_P plancktime 1018plancklength plancktime c 1019l_P plancklength 1020 1021# Particle radius 1022 1023electronradius (1/4 pi epsilon0) e^2 / electronmass c^2 # Classical 1024deuteronchargeradius 2.1413e-15 m 1025protonchargeradius 0.8751e-15 m 1026 1027# Masses of elementary particles 1028 1029electronmass 5.48579909070e-4 u 1030m_e electronmass 1031protonmass 1.007276466879 u 1032m_p protonmass 1033neutronmass 1.00866491588 u 1034m_n neutronmass 1035muonmass 0.1134289257 u 1036m_mu muonmass 1037deuteronmass 2.013553212745 u 1038m_d deuteronmass 1039alphaparticlemass 4.001506179127 u 1040m_alpha alphaparticlemass 1041taumass 1.90749 u 1042m_tau taumass 1043tritonmass 3.01550071632 u 1044m_t tritonmass 1045helionmass 3.01493224673 u 1046m_h helionmass 1047 1048 1049 1050# particle wavelengths: the compton wavelength of a particle is 1051# defined as h / m c where m is the mass of the particle. 1052 1053electronwavelength h / m_e c 1054lambda_C electronwavelength 1055protonwavelength h / m_p c 1056lambda_C,p protonwavelength 1057neutronwavelength h / m_n c 1058lambda_C,n neutronwavelength 1059 1060# Magnetic moments 1061 1062bohrmagneton e hbar / 2 electronmass 1063mu_B bohrmagneton 1064nuclearmagneton e hbar / 2 protonmass 1065mu_N nuclearmagneton 1066mu_mu -4.49044826e-26 J/T # Muon magnetic moment 1067mu_p 1.4106067873e-26 J/T # Proton magnetic moment 1068mu_e -928.4764620e-26 J/T # Electron magnetic moment 1069mu_n -0.96623650e-26 J/T # Neutron magnetic moment 1070mu_d 0.4330735040e-26 J/T # Deuteron magnetic moment 1071mu_t 1.504609503e-26 J/T # Triton magnetic moment 1072mu_h -1.074617522e-26 J/T # Helion magnetic moment 1073 1074 1075# 1076# Units derived from physical constants 1077# 1078 1079kgf kg force 1080technicalatmosphere kgf / cm^2 1081at technicalatmosphere 1082hyl kgf s^2 / m # Also gram-force s^2/m according to [15] 1083mmHg mm Hg 1084torr atm / 760 # The torr, named after Evangelista 1085 # Torricelli, and is very close to the mm Hg 1086tor Pa # Suggested in 1913 but seldom used [24]. 1087 # Eventually renamed the Pascal. Don't 1088 # confuse the tor with the torr. 1089inHg inch Hg 1090inH2O inch water 1091mmH2O mm water 1092eV e V # Energy acquired by a particle with charge e 1093electronvolt eV # when it is accelerated through 1 V 1094lightyear c julianyear # The 365.25 day year is specified in 1095ly lightyear # NIST publication 811 1096lightsecond c s 1097lightminute c min 1098parsec au / tan(arcsec) # Unit of length equal to distance 1099pc parsec # from the sun to a point having 1100 # heliocentric parallax of 1 1101 # arcsec (derived from parallax 1102 # second). A distant object with 1103 # paralax theta will be about 1104 # (arcsec/theta) parsecs from the 1105 # sun (using the approximation 1106 # that tan(theta) = theta). 1107rydberg h c Rinfinity # Rydberg energy 1108crith 0.089885 gram # The crith is the mass of one 1109 # liter of hydrogen at standard 1110 # temperature and pressure. 1111amagatvolume molarvolume 1112amagat mol/amagatvolume # Used to measure gas densities 1113lorentz bohrmagneton / h c # Used to measure the extent 1114 # that the frequency of light 1115 # is shifted by a magnetic field. 1116cminv h c / cm # Unit of energy used in infrared 1117invcm cminv # spectroscopy. 1118wavenumber cminv 1119kcal_mol kcal_th / mol N_A # kcal/mol is used as a unit of 1120 # energy by physical chemists. 1121# 1122# CGS system based on centimeter, gram and second 1123# 1124 1125dyne cm gram / s^2 # force 1126dyn dyne 1127erg cm dyne # energy 1128poise gram / cm s # viscosity, honors Jean Poiseuille 1129P poise 1130rhe /poise # reciprocal viscosity 1131stokes cm^2 / s # kinematic viscosity 1132St stokes 1133stoke stokes 1134lentor stokes # old name 1135Gal cm / s^2 # acceleration, used in geophysics 1136galileo Gal # for earth's gravitational field 1137 # (note that "gal" is for gallon 1138 # but "Gal" is the standard symbol 1139 # for the gal which is evidently a 1140 # shortened form of "galileo".) 1141barye dyne/cm^2 # pressure 1142barad barye # old name 1143kayser 1/cm # Proposed as a unit for wavenumber 1144balmer kayser # Even less common name than "kayser" 1145kine cm/s # velocity 1146bole g cm / s # momentum 1147pond gram force 1148glug gram force s^2 / cm # Mass which is accelerated at 1149 # 1 cm/s^2 by 1 gram force 1150darcy centipoise cm^2 / s atm # Measures permeability to fluid flow. 1151 1152 # One darcy is the permeability of a 1153 # medium that allows a flow of cc/s 1154 # of a liquid of centipoise viscosity 1155 # under a pressure gradient of 1156 # atm/cm. Named for H. Darcy. 1157 1158mobileohm cm / dyn s # mobile ohm, measure of mechanical 1159 # mobility 1160mechanicalohm dyn s / cm # mechanical resistance 1161acousticalohm dyn s / cm^5 # ratio of the sound pressure of 1162 # 1 dyn/cm^2 to a source of strength 1163 # 1 cm^3/s 1164ray acousticalohm 1165rayl dyn s / cm^3 # Specific acoustical resistance 1166eotvos 1e-9 Gal/cm # Change in gravitational acceleration 1167 # over horizontal distance 1168 1169# Electromagnetic units derived from the abampere 1170 1171abampere 10 A # Current which produces a force of 1172abamp abampere # 2 dyne/cm between two infinitely 1173aA abampere # long wires that are 1 cm apart 1174biot aA # alternative name for abamp 1175Bi biot 1176abcoulomb abamp sec 1177abcoul abcoulomb 1178abfarad abampere sec / abvolt 1179abhenry abvolt sec / abamp 1180abvolt dyne cm / abamp sec 1181abohm abvolt / abamp 1182abmho /abohm 1183gauss abvolt sec / cm^2 1184Gs gauss 1185maxwell abvolt sec # Also called the "line" 1186Mx maxwell 1187oersted gauss / mu0 1188Oe oersted 1189gilbert gauss cm / mu0 1190Gb gilbert 1191Gi gilbert 1192unitpole 4 pi maxwell 1193emu erg/gauss # "electro-magnetic unit", a measure of 1194 # magnetic moment, often used as emu/cm^3 1195 # to specify magnetic moment density. 1196 1197# Gaussian system: electromagnetic units derived from statampere. 1198# 1199# Note that the Gaussian units are often used in such a way that Coulomb's law 1200# has the form F= q1 * q2 / r^2. The constant 1|4*pi*epsilon0 is incorporated 1201# into the units. From this, we can get the relation force=charge^2/dist^2. 1202# This means that the simplification esu^2 = dyne cm^2 can be used to simplify 1203# units in the Gaussian system, with the curious result that capacitance can be 1204# measured in cm, resistance in sec/cm, and inductance in sec^2/cm. These 1205# units are given the names statfarad, statohm and stathenry below. 1206 1207statampere 10 A cm / s c 1208statamp statampere 1209statvolt dyne cm / statamp sec 1210statcoulomb statamp s 1211esu statcoulomb 1212statcoul statcoulomb 1213statfarad statamp sec / statvolt 1214cmcapacitance statfarad 1215stathenry statvolt sec / statamp 1216statohm statvolt / statamp 1217statmho /statohm 1218statmaxwell statvolt sec 1219franklin statcoulomb 1220debye 1e-18 statcoul cm # unit of electrical dipole moment 1221helmholtz debye/angstrom^2 # Dipole moment per area 1222jar 1000 statfarad # approx capacitance of Leyden jar 1223 1224# 1225# Some historical electromagnetic units 1226# 1227 1228intampere 0.999835 A # Defined as the current which in one 1229intamp intampere # second deposits .001118 gram of 1230 # silver from an aqueous solution of 1231 # silver nitrate. 1232intfarad 0.999505 F 1233intvolt 1.00033 V 1234intohm 1.000495 ohm # Defined as the resistance of a 1235 # uniform column of mercury containing 1236 # 14.4521 gram in a column 1.063 m 1237 # long and maintained at 0 degC. 1238daniell 1.042 V # Meant to be electromotive force of a 1239 # Daniell cell, but in error by .04 V 1240faraday N_A e mol # Charge that must flow to deposit or 1241faraday_phys 96521.9 C # liberate one gram equivalent of any 1242faraday_chem 96495.7 C # element. (The chemical and physical 1243 # values are off slightly from what is 1244 # obtained by multiplying by amu_chem 1245 # or amu_phys. These values are from 1246 # a 1991 NIST publication.) Note that 1247 # there is a Faraday constant which is 1248 # equal to N_A e and hence has units of 1249 # C/mol. 1250kappline 6000 maxwell # Named by and for Gisbert Kapp 1251siemensunit 0.9534 ohm # Resistance of a meter long column of 1252 # mercury with a 1 mm cross section. 1253# 1254# Printed circuit board units. 1255# 1256# http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm. 1257# 1258# Conductivity is often expressed as a percentage of IACS. A copper wire a 1259# meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at 1260# 20 deg C. Copper density is also standarized at that temperature. 1261# 1262 1263copperconductivity 58 siemens m / mm^2 # A wire a meter long with 1264IACS copperconductivity # a 1 mm^2 cross section 1265copperdensity 8.89 g/cm^3 # The "ounce" measures the 1266ouncecopper oz / ft^2 copperdensity # thickness of copper used 1267ozcu ouncecopper # in circuitboard fabrication 1268 1269# 1270# Photometric units 1271# 1272 1273LUMINOUS_INTENSITY candela 1274LUMINOUS_FLUX lumen 1275LUMINOUS_ENERGY talbot 1276ILLUMINANCE lux 1277EXITANCE lux 1278 1279candle 1.02 candela # Standard unit for luminous intensity 1280hefnerunit 0.9 candle # in use before candela 1281hefnercandle hefnerunit # 1282violle 20.17 cd # luminous intensity of 1 cm^2 of 1283 # platinum at its temperature of 1284 # solidification (2045 K) 1285 1286lumen cd sr # Luminous flux (luminous energy per 1287lm lumen # time unit) 1288 1289talbot lumen s # Luminous energy 1290lumberg talbot # References give these values for 1291lumerg talbot # lumerg and lumberg both. Note that 1292 # a paper from 1948 suggests that 1293 # lumerg should be 1e-7 talbots so 1294 # that lumergs/erg = talbots/joule. 1295 # lumerg = luminous erg 1296lux lm/m^2 # Illuminance or exitance (luminous 1297lx lux # flux incident on or coming from 1298phot lumen / cm^2 # a surface) 1299ph phot # 1300footcandle lumen/ft^2 # Illuminance from a 1 candela source 1301 # at a distance of one foot 1302metercandle lumen/m^2 # Illuminance from a 1 candela source 1303 # at a distance of one meter 1304 1305mcs metercandle s # luminous energy per area, used to 1306 # measure photographic exposure 1307 1308nox 1e-3 lux # These two units were proposed for 1309skot 1e-3 apostilb # measurements relating to dark adapted 1310 # eyes. 1311# Luminance measures 1312 1313LUMINANCE nit 1314 1315nit cd/m^2 # Luminance: the intensity per projected 1316stilb cd / cm^2 # area of an extended luminous source. 1317sb stilb # (nit is from latin nitere = to shine.) 1318 1319apostilb cd/pi m^2 1320asb apostilb 1321blondel apostilb # Named after a French scientist. 1322 1323# Equivalent luminance measures. These units are units which measure 1324# the luminance of a surface with a specified exitance which obeys 1325# Lambert's law. (Lambert's law specifies that luminous intensity of 1326# a perfectly diffuse luminous surface is proportional to the cosine 1327# of the angle at which you view the luminous surface.) 1328 1329equivalentlux cd / pi m^2 # luminance of a 1 lux surface 1330equivalentphot cd / pi cm^2 # luminance of a 1 phot surface 1331lambert cd / pi cm^2 1332footlambert cd / pi ft^2 1333 1334# The bril is used to express "brilliance" of a source of light on a 1335# logarithmic scale to correspond to subjective perception. An increase of 1 1336# bril means doubling the luminance. A luminance of 1 lambert is defined to 1337# have a brilliance of 1 bril. 1338 1339bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100 1340 1341# Some luminance data from the IES Lighting Handbook, 8th ed, 1993 1342 1343sunlum 1.6e9 cd/m^2 # at zenith 1344sunillum 100e3 lux # clear sky 1345sunillum_o 10e3 lux # overcast sky 1346sunlum_h 6e6 cd/m^2 # value at horizon 1347skylum 8000 cd/m^2 # average, clear sky 1348skylum_o 2000 cd/m^2 # average, overcast sky 1349moonlum 2500 cd/m^2 1350 1351# 1352# Photographic Exposure Value 1353# This section by Jeff Conrad (jeff_conrad@msn.com) 1354# 1355# The Additive system of Photographic EXposure (APEX) proposed in ASA 1356# PH2.5-1960 was an attempt to simplify exposure determination for people who 1357# relied on exposure tables rather than exposure meters. Shortly thereafter, 1358# nearly all cameras incorporated exposure meters, so the APEX system never 1359# caught on, but the concept of exposure value remains in use. Though given as 1360# 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is 1361# related to exposure parameters by 1362# 1363# A^2 LS ES 1364# 2^EV = --- = -- = -- 1365# t K C 1366# 1367# Where 1368# A = Relative aperture (f-number) 1369# t = Exposure time in seconds 1370# L = Scene luminance in cd/m2 1371# E = Scene illuminance in lux 1372# S = Arithmetic ISO speed 1373# K = Reflected-light meter calibration constant 1374# C = Incident-light meter calibration constant 1375# 1376# Strictly, an exposure value is a combination of aperture and exposure time, 1377# but it's also commonly used to indicate luminance (or illuminance). 1378# Conversion to luminance or illuminance units depends on the ISO speed and the 1379# meter calibration constant. Common practice is to use an ISO speed of 100. 1380# Calibration constants vary among camera and meter manufacturers: Canon, 1381# Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while 1382# Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use 1383# a value of 250 for incident-light meters with flat receptors. 1384# 1385# The values for in-camera meters apply only averaging, weighted-averaging, or 1386# spot metering--the multi-segment metering incorporated in most current 1387# cameras uses proprietary algorithms that evaluate many factors related to the 1388# luminance distribution of what is being metered; they are not amenable to 1389# simple conversions, and are usually not disclosed by the manufacturers. 1390 1391s100 100 / lx s # ISO 100 speed 1392iso100 s100 1393 1394# Reflected-light meter calibration constant with ISO 100 speed 1395 1396k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic 1397k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax 1398 1399# Incident-light meter calibration constant with ISO 100 film 1400 1401c250 250 lx / lx s # flat-disc receptor 1402 1403# Exposure value to scene luminance with ISO 100 imaging media 1404 1405# For Kenko (Minolta) or Pentax 1406#ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400) 1407# For Canon, Nikon, or Sekonic 1408ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250) 1409EV100() ev100 1410 1411# Exposure value to scene illuminance with ISO 100 imaging media 1412 1413iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250) 1414 1415# Other Photographic Exposure Conversions 1416# 1417# As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities 1418# related by 1419# 1420# Ev = Av + Tv = Bv + Sv 1421# 1422# where 1423# Av = log2(A^2) Aperture value 1424# Tv = log2(1/t) Time value 1425# Sv = log2(N Sx) Speed value 1426# Bv = log2(B S / K) Luminance ("brightness") value 1427# Iv = log2(I S / C) Illuminance value 1428# 1429# and 1430# A = Relative aperture (f-number) 1431# t = Exposure time in seconds 1432# Sx = Arithmetic ISO speed in 1/lux s 1433# B = luminance in cd/m2 1434# I = luminance in lux 1435 1436# The constant N derives from the arcane relationship between arithmetic 1437# and logarithmic speed given in ASA PH2.5-1960. That relationship 1438# apparently was not obvious--so much so that it was thought necessary 1439# to explain it in PH2.12-1961. The constant has had several values 1440# over the years, usually without explanation for the changes. Although 1441# APEX had little impact on consumer cameras, it has seen a partial 1442# resurrection in the Exif standards published by the Camera & Imaging 1443# Products Association of Japan. 1444 1445#N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961, 1446 # derived from ASA PH2.5-1960. 1447#N_apex 0.30 lx s # rounded value in ASA PH2.5-1960, 1448 # ASA PH2.12-1961, and ANSI PH2.7-1986 1449#N_apex 0.3162 lx s # value in ANSI PH2.7-1973 1450N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100 1451K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961 1452K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common 1453C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in 1454 # footcandles; flat sensor?) 1455C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in 1456 # footcandles; hemispherical sensor?) 1457N_speed N_exif 1458K_lum K_apex1971 1459C_illum C_apex1961 1460 1461# Units for Photographic Exposure Variables 1462# 1463# Practical photography sometimes pays scant attention to units for exposure 1464# variables. In particular, the "speed" of the imaging medium is treated as if 1465# it were dimensionless when it should have units of reciprocal lux seconds; 1466# this practice works only because "speed" is almost invariably given in 1467# accordance with international standards (or similar ones used by camera 1468# manufacturers)--so the assumed units are invariant. In calculating 1469# logarithmic quantities--especially the time value Tv and the exposure value 1470# EV--the units for exposure time ("shutter speed") are often ignored; this 1471# practice works only because the units of exposure time are assumed to be in 1472# seconds, and the missing units that make the argument to the logarithmic 1473# function dimensionless are silently provided. 1474# 1475# In keeping with common practice, the definitions that follow treat "speeds" 1476# as dimensionless, so ISO 100 speed is given simply as '100'. When 1477# calculating the logarithmic APEX quantities Av and Tv, the definitions 1478# provide the missing units, so the times can be given with any appropriate 1479# units. For example, giving an exposure time of 1 minute as either '1 min' or 1480# '60 s' will result in Tv of -5.9068906. 1481# 1482# Exposure Value from f-number and Exposure Time 1483# 1484# Because nonlinear unit conversions only accept a single quantity, 1485# there is no direct conversion from f-number and exposure time to 1486# exposure value EV. But the EV can be obtained from a combination of 1487# Av and Tv. For example, the "sunny 16" rule states that correct 1488# exposure for a sunlit scene can achieved by using f/16 and an exposure 1489# time equal to the reciprocal of the ISO speed in seconds; this can be 1490# calculated as 1491# 1492# ~Av(16) + ~Tv(1|100 s), 1493# 1494# which gives 14.643856. These conversions may be combined with the 1495# ev100 conversion: 1496# 1497# ev100(~Av(16) + ~Tv(1|100 s)) 1498# 1499# to yield the assumed average scene luminance of 3200 cd/m^2. 1500 1501# convert relative aperture (f-number) to aperture value 1502Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av) 1503# convert exposure time to time value 1504Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv) 1505# convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed; 1506# make arithmetic speed dimensionless 1507# 'Sv' conflicts with the symbol for sievert; you can uncomment this function 1508# definition if you don't need that symbol 1509#Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv) 1510Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval) 1511 1512# convert luminance value Bv in ASA PH2.12-1961 to luminance 1513Bv(x) units=[1;cd/m^2] range=(0,) \ 1514 2^x K_lum N_speed ; log2(Bv / (K_lum N_speed)) 1515 1516# convert illuminance value Iv in ASA PH2.12-1961 to illuminance 1517Iv(x) units=[1;lx] range=(0,) \ 1518 2^x C_illum N_speed ; log2(Iv / (C_illum N_speed)) 1519 1520# convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in 1521# ASA PH2.5-1960; make arithmetic speed dimensionless 1522Sx(S) units=[1;1] domain=(0,) \ 1523 log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s) 1524 1525# convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed 1526# for convenience, speed is treated here as if it were dimensionless 1527Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg)) 1528Sdin() Sdeg 1529 1530# Numerical Aperture and f-Number of a Lens 1531# 1532# The numerical aperture (NA) is given by 1533# 1534# NA = n sin(theta) 1535# 1536# where n is the index of refraction of the medium and theta is half 1537# of the angle subtended by the aperture stop from a point in the image 1538# or object plane. For a lens in air, n = 1, and 1539# 1540# NA = 0.5 / f-number 1541# 1542# convert NA to f-number 1543numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \ 1544 0.5 / x ; 0.5 / numericalaperture 1545NA() numericalaperture 1546# 1547# convert f-number to itself; restrict values to those possible 1548fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber 1549 1550# Referenced Photographic Standards 1551# 1552# ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome, 1553# Continuous-Tone) Speed of Photographic Negative Materials. 1554# ASA PH2.12-1961. American Standard, General-Purpose Photographic 1555# Exposure Meters (photoelectric type). 1556# ANSI PH3.49-1971. American National Standard for general-purpose 1557# photographic exposure meters (photoelectric type). 1558# ANSI PH2.7-1973. American National Standard Photographic Exposure Guide. 1559# ANSI PH2.7-1986. American National Standard for Photography -- 1560# Photographic Exposure Guide. 1561# CIPA DC-008-2010. Exchangeable image file format for digital still 1562# cameras: Exif Version 2.3 1563# ISO 6:1993. International Standard, Photography -- Black-and-white 1564# pictorial still camera negative film/process systems -- 1565# Determination of ISO Speed. 1566 1567 1568# 1569# Astronomical time measurements 1570# 1571# Astronomical time measurement is a complicated matter. The length of the 1572# true day at a given place can be 21 seconds less than 24 hours or 30 seconds 1573# over 24 hours. The two main reasons for this are the varying speed of the 1574# earth in its elliptical orbit and the fact that the sun moves on the ecliptic 1575# instead of along the celestial equator. To devise a workable system for time 1576# measurement, Simon Newcomb (1835-1909) used a fictitious "mean sun". 1577# Consider a first fictitious sun traveling along the ecliptic at a constant 1578# speed and coinciding with the true sun at perigee and apogee. Then 1579# considering a second fictitious sun traveling along the celestial equator at 1580# a constant speed and coinciding with the first fictitious sun at the 1581# equinoxes. The second fictitious sun is the "mean sun". From this equations 1582# can be written out to determine the length of the mean day, and the tropical 1583# year. The length of the second was determined based on the tropical year 1584# from such a calculation and was officially used from 1960-1967 until atomic 1585# clocks replaced astronomical measurements for a standard of time. All of the 1586# values below give the mean time for the specified interval. 1587# 1588# See "Mathematical Astronomy Morsels" by Jean Meeus for more details 1589# and a description of how to compute the correction to mean time. 1590# 1591 1592TIME second 1593 1594anomalisticyear 365.2596 days # The time between successive 1595 # perihelion passages of the 1596 # earth. 1597siderealyear 365.256360417 day # The time for the earth to make 1598 # one revolution around the sun 1599 # relative to the stars. 1600tropicalyear 365.242198781 day # The time needed for the mean sun 1601 # as defined above to increase 1602 # its longitude by 360 degrees. 1603 # Most references defined the 1604 # tropical year as the interval 1605 # between vernal equinoxes, but 1606 # this is misleading. The length 1607 # of the season changes over time 1608 # because of the eccentricity of 1609 # the earth's orbit. The time 1610 # between vernal equinoxes is 1611 # approximately 365.24237 days 1612 # around the year 2000. See 1613 # "Mathematical Astronomy 1614 # Morsels" for more details. 1615eclipseyear 346.62 days # The line of nodes is the 1616 # intersection of the plane of 1617 # Earth's orbit around the sun 1618 # with the plane of the moon's 1619 # orbit around earth. Eclipses 1620 # can only occur when the moon 1621 # and sun are close to this 1622 # line. The line rotates and 1623 # appearances of the sun on the 1624 # line of nodes occur every 1625 # eclipse year. 1626saros 223 synodicmonth # The earth, moon and sun appear in 1627 # the same arrangement every 1628 # saros, so if an eclipse occurs, 1629 # then one saros later, a similar 1630 # eclipse will occur. (The saros 1631 # is close to 19 eclipse years.) 1632 # The eclipse will occur about 1633 # 120 degrees west of the 1634 # preceeding one because the 1635 # saros is not an even number of 1636 # days. After 3 saros, an 1637 # eclipse will occur at 1638 # approximately the same place. 1639siderealday 86164.09054 s # The sidereal day is the interval 1640siderealhour 1|24 siderealday # between two successive transits 1641siderealminute 1|60 siderealhour # of a star over the meridian, 1642siderealsecond 1|60 siderealminute # or the time required for the 1643 # earth to make one rotation 1644 # relative to the stars. The 1645 # more usual solar day is the 1646 # time required to make a 1647 # rotation relative to the sun. 1648 # Because the earth moves in its 1649 # orbit, it has to turn a bit 1650 # extra to face the sun again, 1651 # hence the solar day is slightly 1652 # longer. 1653anomalisticmonth 27.55454977 day # Time for the moon to travel from 1654 # perigee to perigee 1655nodicalmonth 27.2122199 day # The nodes are the points where 1656draconicmonth nodicalmonth # an orbit crosses the ecliptic. 1657draconiticmonth nodicalmonth # This is the time required to 1658 # travel from the ascending node 1659 # to the next ascending node. 1660siderealmonth 27.321661 day # Time required for the moon to 1661 # orbit the earth 1662lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds 1663 # Mean time between full moons. 1664synodicmonth lunarmonth # Full moons occur when the sun 1665lunation synodicmonth # and moon are on opposite sides 1666lune 1|30 lunation # of the earth. Since the earth 1667lunour 1|24 lune # moves around the sun, the moon 1668 # has to revolve a bit extra to 1669 # get into the full moon 1670 # configuration. 1671year tropicalyear 1672yr year 1673month 1|12 year 1674mo month 1675lustrum 5 years # The Lustrum was a Roman 1676 # purification ceremony that took 1677 # place every five years. 1678 # Classically educated Englishmen 1679 # used this term. 1680decade 10 years 1681century 100 years 1682millennium 1000 years 1683millennia millennium 1684solaryear year 1685lunaryear 12 lunarmonth 1686calendaryear 365 day 1687commonyear 365 day 1688leapyear 366 day 1689julianyear 365.25 day 1690gregorianyear 365.2425 day 1691islamicyear 354 day # A year of 12 lunar months. They 1692islamicleapyear 355 day # began counting on July 16, AD 622 1693 # when Muhammad emigrated to Medina 1694 # (the year of the Hegira). They need 1695 # 11 leap days in 30 years to stay in 1696 # sync with the lunar year which is a 1697 # bit longer than the 29.5 days of the 1698 # average month. The months do not 1699 # keep to the same seasons, but 1700 # regress through the seasons every 1701 # 32.5 years. 1702islamicmonth 1|12 islamicyear # They have 29 day and 30 day months. 1703 1704# The Hewbrew year is also based on lunar months, but synchronized to the solar 1705# calendar. The months vary irregularly between 29 and 30 days in length, and 1706# the years likewise vary. The regular year is 353, 354, or 355 days long. To 1707# keep up with the solar calendar, a leap month of 30 days is inserted every 1708# 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This 1709# gives leap years that last 383, 384, or 385 days. 1710 1711 1712# Sidereal days 1713 1714mercuryday 58.6462 day 1715venusday 243.01 day # retrograde 1716earthday siderealday 1717marsday 1.02595675 day 1718jupiterday 0.41354 day 1719saturnday 0.4375 day 1720uranusday 0.65 day # retrograde 1721neptuneday 0.768 day 1722plutoday 6.3867 day 1723 1724# Sidereal years from http://ssd.jpl.nasa.gov/phys_props_planets.html. Data 1725# was updated in May 2001 based on the 1992 Explanatory Supplement to the 1726# Astronomical Almanac and the mean longitude rates. Apparently the table of 1727# years in that reference is incorrect. 1728 1729mercuryyear 0.2408467 julianyear 1730venusyear 0.61519726 julianyear 1731earthyear siderealyear 1732marsyear 1.8808476 julianyear 1733jupiteryear 11.862615 julianyear 1734saturnyear 29.447498 julianyear 1735uranusyear 84.016846 julianyear 1736neptuneyear 164.79132 julianyear 1737plutoyear 247.92065 julianyear 1738 1739# Objects on the earth are charted relative to a perfect ellipsoid whose 1740# dimensions are specified by different organizations. The ellipsoid is 1741# specified by an equatorial radius and a flattening value which defines the 1742# polar radius. These values are the 1996 values given by the International 1743# Earth Rotation Service (IERS) whose reference documents can be found at 1744# http://maia.usno.navy.mil/ 1745 1746earthflattening 1|298.25642 1747earthradius_equatorial 6378136.49 m 1748earthradius_polar (-earthflattening+1) earthradius_equatorial 1749 1750landarea 148.847e6 km^2 1751oceanarea 361.254e6 km^2 1752 1753moonradius 1738 km # mean value 1754sunradius 6.96e8 m 1755 1756# Many astronomical values can be measured most accurately in a system of units 1757# using the astronomical unit and the mass of the sun as base units. The 1758# uncertainty in the gravitational constant makes conversion to SI units 1759# significantly less accurate. 1760 1761# The astronomical unit was defined to be the length of the of the semimajor 1762# axis of a massless object with the same year as the earth. With such a 1763# definition in force, and with the mass of the sun set equal to one, Kepler's 1764# third law can be used to solve for the value of the gravitational constant. 1765 1766# Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital 1767# period, a is the size of the semimajor axis, G is the gravitational constant 1768# and M is the mass. With M = 1 and T and a chosen for the earth's orbit, we 1769# find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called the Gaussian 1770# gravitational constant, apparently because Gauss originally did the 1771# calculations. However, when the original calculation was done, the value 1772# for the length of the earth's year was inaccurate. The value used is called 1773# the Gaussian year. Changing the astronomical unit to bring it into 1774# agreement with more accurate values for the year would have invalidated a 1775# lot of previous work, so instead the astronomical unit has been kept equal 1776# to this original value. This is accomplished by using a standard value for 1777# the Gaussian gravitational constant. This constant is called k. 1778# Many values below are from http://ssd.jpl.nasa.gov/?constants 1779 1780gauss_k 0.01720209895 # This beast has dimensions of 1781 # au^(3|2) / day and is exact. 1782gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian 1783 # gravitational constant. This is a 1784 # fictional year, and doesn't 1785 # correspond to any celestial event. 1786astronomicalunit 149597870700 m # IAU definition from 2012, exact 1787au astronomicalunit # ephemeris for the above described 1788 # astronomical unit. (See the NASA 1789 # site listed above.) 1790solarmass 1.9891e30 kg 1791sunmass solarmass 1792 1793 1794sundist 1.0000010178 au # mean earth-sun distance 1795moondist 3.844e8 m # mean earth-moon distance 1796sundist_near 1.471e11 m # earth-sun distance at perihelion 1797sundist_far 1.521e11 m # earth-sun distance at aphelion 1798moondist_min 3.564e8 m # approximate least distance at 1799 # perigee 1901-2300 1800moondist_max 4.067e8 m # approximate greatest distance at 1801 # apogee 1901-2300 1802 1803 1804# The following are masses for planetary systems, not just the planet itself. 1805# The comments give the uncertainty in the denominators. As noted above, 1806# masses are given relative to the solarmass because this is more accurate. 1807# The conversion to SI is uncertain because of uncertainty in G, the 1808# gravitational constant. 1809# 1810# Values are from http://ssd.jpl.nasa.gov/astro_constants.html 1811 1812mercurymass solarmass / 6023600 # 250 1813venusmass solarmass / 408523.71 # 0.06 1814earthmoonmass solarmass / 328900.56 # 0.02 1815marsmass solarmass / 3098708 # 9 1816jupitermass solarmass / 1047.3486 # 0.0008 1817saturnmass solarmass / 3497.898 # 0.018 1818uranusmass solarmass / 22902.98 # 0.03 1819neptunemass solarmass / 19412.24 # 0.04 1820plutomass solarmass / 1.35e8 # 0.07e8 1821 1822moonearthmassratio 0.012300034 # uncertainty 3e-9 1823earthmass earthmoonmass / ( 1 + moonearthmassratio) 1824moonmass moonearthmassratio earthmass 1825 1826# These are the old values for the planetary masses. They may give 1827# the masses of the planets alone. 1828 1829oldmercurymass 0.33022e24 kg 1830oldvenusmass 4.8690e24 kg 1831oldmarsmass 0.64191e24 kg 1832oldjupitermass 1898.8e24 kg 1833oldsaturnmass 568.5e24 kg 1834olduranusmass 86.625e24 kg 1835oldneptunemass 102.78e24 kg 1836oldplutomass 0.015e24 kg 1837 1838# Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in 1839# turn cites Global Earth Physics by CF Yoder, 1995. 1840 1841mercuryradius 2440 km 1842venusradius 6051.84 km 1843earthradius 6371.01 km 1844marsradius 3389.92 km 1845jupiterradius 69911 km 1846saturnradius 58232 km 1847uranusradius 25362 km 1848neptuneradius 24624 km 1849plutoradius 1151 km 1850 1851moongravity 1.62 m/s^2 1852 1853# The Hubble constant gives the speed at which distance galaxies are moving 1854# away from the earth according to v = H0*d, where H0 is the hubble constant 1855# and d is the distance to the galaxy. 1856 1857hubble 70 km/s/Mpc # approximate 1858H0 hubble 1859 1860# Parallax is the angular difference between the topocentric (on Earth's 1861# surface) and geocentric (at Earth's center) direction toward a celestial body 1862# when the body is at a given altitude. When the body is on the horizon, the 1863# parallax is the horizontal parallax; when the body is on the horizon and the 1864# observer is on the equator, the parallax is the equatorial horizontal 1865# parallax. When the body is at zenith, the parallax is zero. 1866 1867lunarparallax asin(earthradius_equatorial / moondist) # Moon equatorial 1868moonhp lunarparallax # horizontal parallax 1869 # at mean distance 1870 1871# Light from celestial objects is attenuated by passage through Earth's 1872# atmosphere. A body near the horizon passes through much more air than an 1873# object at zenith, and is consequently less bright. Air mass is the ratio of 1874# the length of the optical path at a given altitude (angle above the horizon) 1875# to the length at zenith. Air mass at zenith is by definition unity; at the 1876# horizon, air mass is approximately 38, though the latter value can vary 1877# considerably with atmospheric conditions. The general formula is # E = E0 1878# exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value 1879# seen by an observer, X is the air mass and c is the extinction coefficient. 1880# A common value for c in reasonably clear air is 0.21, but values can be 1881# considerably greater in urban areas. Apparent altitude is that perceived by 1882# an observer; it includes the effect of atmospheric refraction. There is no 1883# shortage of formulas for air mass 1884# (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to 1885# variations in local atmospheric conditions. The formula used here is simple 1886# and is in good agreement with rigorously calculated values under standard 1887# conditions. 1888# 1889# Extraterrestrial illuminance or luminance of an object at a given altitude 1890# determined with vmag() or SB_xxx() below can be multiplied by 1891# atm_transmission() or atm_transmissionz() to estimate the terrestrial value. 1892# 1893# Kasten and Young (1989) air mass formula. alt is apparent altitude 1894# Reference: 1895# Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables 1896# and Approximation Formula." Applied Optics. Vol. 28, 4735–4738. 1897# Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735. 1898 1899airmass(alt) units=[degree;1] domain=[0,90] noerror \ 1900 1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364) 1901 1902# zenith is apparent zenith angle (zenith = 90 deg - alt) 1903airmassz(zenith) units=[degree;1] domain=[0,90] noerror \ 1904 1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364) 1905 1906# For reasonably clear air at sea level; values may need adjustment for 1907# elevation and local atmospheric conditions 1908# for scotopic vision (510 nm), appropriate for the dark-adapted eye 1909# extinction_coeff 0.26 1910# for photopic vision, appropriate for observing brighter objects such 1911# as the full moon 1912extinction_coeff 0.21 1913 1914atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \ 1915 exp(-extinction_coeff airmass(alt)) 1916 1917# in terms of zenith angle (zenith = 90 deg - alt) 1918atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \ 1919 exp(-extinction_coeff airmassz(zenith)) 1920 1921# Moon and Sun data at mean distances 1922moonvmag -12.74 # Moon apparent visual magnitude at mean distance 1923sunvmag -26.74 # Sun apparent visual magnitude at mean distance 1924moonsd asin(moonradius / moondist) # Moon angular semidiameter at mean distance 1925sunsd asin(sunradius / sundist) # Sun angular semidiameter at mean distance 1926 1927# Visual magnitude of star or other celestial object. The system of stellar 1928# magnitudes, developed in ancient Greece, assigned magnitudes from 1 1929# (brightest) to 6 (faintest visible to the naked eye). In 1856, British 1930# astronomer Norman Pogson made the system precise, with a magnitude 1 object 1931# 100 times as bright as a magnitude 6 object, and each magnitude differing 1932# from the next by a constant ratio; the ratio, sometimes known as Pogson's 1933# ratio, is thus 100^0.2, or approximately 2.5119. The logarithm of 100^0.2 is 1934# 0.4, hence the common use of powers of 10 and base-10 logarithms. 1935# 1936# Reference: 1937# Allen, C.W. 1976. Astrophysical Quantities, 3rd ed. 1973, reprinted 1938# with corrections, 1976. London: Athlone. 1939# 1940# The function argument is the (dimensionless) visual magnitude; reference 1941# illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside 1942# Earth's atmosphere. Illuminance values can be adjusted to terrestrial values 1943# by multiplying by one of the atm_transmission functions above. 1944 1945# Illuminance from apparent visual magnitude 1946vmag(mag) units=[1;lx] domain=[,] range=(0,] \ 1947 2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx)) 1948 1949# Surface brightness of a celestial object of a given visual magnitude 1950# is a logarithmic measure of the luminance the object would have if its 1951# light were emitted by an object of specified solid angle; it is 1952# expressed in magnitudes per solid angle. Surface brightness can be 1953# obtained from the visual magnitude by 1954# S = m + 2.5 log(pi pi k a b), 1955# where k is the phase (fraction illuminated), a is the equatorial 1956# radius, and b is the polar radius. For 100% illumination (e.g., full 1957# moon), this is often simplified to 1958# S = m + 2.5 log(pi k s^2), 1959# where s is the object's angular semidiameter; the units of s determine 1960# the units of solid angle. The visual magnitude and semidiameter must 1961# be appropriate for the object's distance; for other than 100% 1962# illumination, the visual magnitude must be appropriate for the phase. 1963# Luminance values are for outside Earth's atmosphere; they can be 1964# adjusted to terrestrial values by multiplying by one of the atm_transmission 1965# functions above. 1966 1967# luminance from surface brightness in magnitudes per square degree 1968SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 1969 vmag(sb) / squaredegree ; \ 1970 ~vmag(SB_degree squaredegree) 1971 1972# luminance from surface brightness in magnitudes per square minute 1973SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 1974 vmag(sb) / squareminute ; \ 1975 ~vmag(SB_minute squareminute) 1976 1977# luminance from surface brightness in magnitudes per square second 1978SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 1979 vmag(sb) / squaresecond ; \ 1980 ~vmag(SB_second squaresecond) 1981 1982# luminance from surface brightness in magnitudes per steradian 1983SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 1984 vmag(sb) / sr ; \ 1985 ~vmag(SB_sr sr) 1986 1987SB() SB_second 1988SB_sec() SB_second 1989SB_min() SB_minute 1990SB_deg() SB_degree 1991 1992# The brightness of one tenth-magnitude star per square degree outside 1993# Earth's atmosphere; often used for night sky brightness. 1994S10 SB_degree(10) 1995 1996# Examples for magnitude and surface brightness functions 1997# Sun illuminance from visual magnitude 1998# You have: sunvmag 1999# You want: 2000# Definition: -26.74 = -26.74 2001# You have: vmag(sunvmag) 2002# You want: lx 2003# * 126134.45 2004# / 7.9280482e-06 2005# 2006# Moon surface brightness from visual magnitude and semidiameter at 100% 2007# illumination (full moon): 2008# You have: moonvmag 2009# You want: 2010# Definition: -12.74 = -12.74 2011# You have: moonsd 2012# You want: arcsec 2013# * 932.59484 2014# / 0.001072277 2015# You have: moonvmag + 2.5 log(pi 932.59484^2) 2016# You want: 2017# Definition: 3.3513397 2018# 2019# Similar example with specific data obtained from another source (JPL 2020# Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in 2021# arcseconds 2022# 2023# You have: -12.9 + 2.5 log(pi 2023.201|2^2) 2024# You want: 2025# Definition: 3.3679199 2026# You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2)) 2027# You want: 2028# Definition: 4858.6547 cd / m^2 2029# 2030# If surface brightness is provided by another source (e.g., Horizons), 2031# it can simply be used directly: 2032# You have: SB_second(3.3679199) 2033# You want: cd/m^2 2034# * 4858.6546 2035# / 0.0002058183 2036# The illuminance and luminance values are extraterrestrial (outside 2037# Earth's atmosphere). The values at Earth's surface are less than these 2038# because of atmospheric extinction. For example, in the last example 2039# above, if the Moon were at an altitude of 55 degrees, the terrestrial 2040# luminance could be calculated with 2041# You have: SB_second(3.3679199) 2042# You want: cd/m^2 2043# * 4858.6546 2044# / 0.0002058183 2045# You have: _ atm_transmission(55 deg) 2046# You want: cd/m^2 2047# * 3760.6356 2048# / 0.0002659125 2049# If desired, photographic exposure can be determined with EV100(), 2050# leading to acceptable combinations of aperture and exposure time. 2051# For the example above, but with the Moon at 10 degrees, 2052# You have: SB_second(3.3679199) atm_transmission(10 deg) 2053# You want: EV100 2054# 13.553962 2055 2056 2057 2058# 2059# The Hartree system of atomic units, derived from fundamental units 2060# of mass (of electron), action (planck's constant), charge, and 2061# the coulomb constant. 2062 2063# Fundamental units 2064 2065atomicmass electronmass 2066atomiccharge e 2067atomicaction hbar 2068 2069# derived units (Warning: accuracy is lost from deriving them this way) 2070 2071atomiclength bohrradius 2072atomictime hbar^3/coulombconst^2 atomicmass e^4 # Period of first 2073 # bohr orbit 2074atomicvelocity atomiclength / atomictime 2075atomicenergy hbar / atomictime 2076hartree atomicenergy 2077 2078# 2079# These thermal units treat entropy as charge, from [5] 2080# 2081 2082thermalcoulomb J/K # entropy 2083thermalampere W/K # entropy flow 2084thermalfarad J/K^2 2085thermalohm K^2/W # thermal resistance 2086fourier thermalohm 2087thermalhenry J K^2/W^2 # thermal inductance 2088thermalvolt K # thermal potential difference 2089 2090 2091# 2092# United States units 2093# 2094 2095# linear measure 2096 2097# The US Metric Law of 1866 legalized the metric system in the USA and 2098# defined the meter in terms of the British system with the exact 2099# 1 meter = 39.37 inches. On April 5, 1893 Thomas Corwin Mendenhall, 2100# Superintendent of Weights and Measures, decided, in what has become 2101# known as the "Mendenhall Order" that the meter and kilogram would be the 2102# fundamental standards in the USA. The definition from 1866 was turned 2103# around to give an exact definition of the yard as 3600|3937 meters This 2104# definition was used until July of 1959 when the definition was changed 2105# to bring the US and other English-speaking countries into agreement; the 2106# Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it 2107# was approximately halfway between the British and US values; it had the 2108# added advantage of making 1 inch = 25.4 mm (exactly). Since 1959, the 2109# "international" foot has been exactly 0.3048 meters. At the same time, 2110# it was decided that any data expressed in feet derived from geodetic 2111# surveys within the US would continue to use the old definition and call 2112# the old unit the "survey foot." The US continues to define the statute 2113# mile, furlong, chain, rod, link, and fathom in terms of the US survey 2114# foot. 2115# Sources: 2116# NIST Special Publication 447, Sects. 5, 7, and 8. 2117# NIST Handbook 44, 2011 ed., Appendix C. 2118# Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014. 2119 2120US 1200|3937 m/ft # These four values will convert 2121US- US # international measures to 2122survey- US # US Survey measures 2123geodetic- US 2124int 3937|1200 ft/m # Convert US Survey measures to 2125int- int # international measures 2126 2127inch 2.54 cm 2128in inch 2129foot 12 inch 2130feet foot 2131ft foot 2132yard 3 ft 2133yd yard 2134mile 5280 ft # The mile was enlarged from 5000 ft 2135 # to this number in order to make 2136 # it an even number of furlongs. 2137 # (The Roman mile is 5000 romanfeet.) 2138line 1|12 inch # Also defined as '.1 in' or as '1e-8 Wb' 2139rod 5.5 yard 2140perch rod 2141furlong 40 rod # From "furrow long" 2142statutemile mile 2143league 3 mile # Intended to be an an hour's walk 2144 2145# surveyor's measure 2146 2147surveyorschain 66 surveyft 2148surveychain surveyorschain 2149surveyorspole 1|4 surveyorschain 2150surveyorslink 1|100 surveyorschain 2151chain 66 ft 2152link 1|100 chain 2153ch chain 2154USacre 10 surveychain^2 2155intacre 10 chain^2 # Acre based on international ft 2156intacrefoot acre foot 2157USacrefoot USacre surveyfoot 2158acrefoot intacrefoot 2159acre intacre 2160section mile^2 2161township 36 section 2162homestead 160 acre # Area of land granted by the 1862 Homestead 2163 # Act of the United States Congress 2164gunterschain surveyorschain 2165 2166engineerschain 100 ft 2167engineerslink 1|100 engineerschain 2168ramsdenschain engineerschain 2169ramsdenslink engineerslink 2170 2171gurleychain 33 feet # Andrew Ellicott chain is the 2172gurleylink 1|50 gurleychain # same length 2173 2174wingchain 66 feet # Chain from 1664, introduced by 2175winglink 1|80 wingchain # Vincent Wing, also found in a 2176 # 33 foot length with 40 links. 2177# early US length standards 2178 2179# The US has had four standards for the yard: one by Troughton of London 2180# (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent 2181# with the definition of the meter in the metric joint resolution of 2182# Congress in 1866, but defining the yard in terms of the meter; and the 2183# international yard (1959), which standardized definitions for Australia, 2184# Canada, New Zealand, South Africa, the UK, and the US. 2185# Sources: Pat Naughtin (2009), Which Inch?, www.metricationmatters.com; 2186# Lewis E. Barbrow and Lewis V. Judson (1976). NBS Special Publication 2187# 447, Weights and Measures Standards of the United States: A Brief 2188# History. 2189 2190troughtonyard 914.42190 mm 2191bronzeyard11 914.39980 mm 2192mendenhallyard surveyyard 2193internationalyard yard 2194 2195# nautical measure 2196 2197fathom 6 ft # Originally defined as the distance from 2198 # fingertip to fingertip with arms fully 2199 # extended. 2200nauticalmile 1852 m # Supposed to be one minute of latitude at 2201 # the equator. That value is about 1855 m. 2202 # Early estimates of the earth's circumference 2203 # were a bit off. The value of 1852 m was 2204 # made the international standard in 1929. 2205 # The US did not accept this value until 2206 # 1954. The UK switched in 1970. 2207 2208cable 1|10 nauticalmile 2209intcable cable # international cable 2210cablelength cable 2211UScable 100 USfathom 2212navycablelength 720 USft # used for depth in water 2213marineleague 3 nauticalmile 2214geographicalmile brnauticalmile 2215knot nauticalmile / hr 2216click km # US military slang 2217klick click 2218 2219# Avoirdupois weight 2220 2221pound 0.45359237 kg # The one normally used 2222lb pound # From the latin libra 2223grain 1|7000 pound # The grain is the same in all three 2224 # weight systems. It was originally 2225 # defined as the weight of a barley 2226 # corn taken from the middle of the 2227 # ear. 2228ounce 1|16 pound 2229oz ounce 2230dram 1|16 ounce 2231dr dram 2232ushundredweight 100 pounds 2233cwt hundredweight 2234shorthundredweight ushundredweight 2235uston shortton 2236shortton 2000 lb 2237quarterweight 1|4 uston 2238shortquarterweight 1|4 shortton 2239shortquarter shortquarterweight 2240 2241# Troy Weight. In 1828 the troy pound was made the first United States 2242# standard weight. It was to be used to regulate coinage. 2243 2244troypound 5760 grain 2245troyounce 1|12 troypound 2246ozt troyounce 2247pennyweight 1|20 troyounce # Abbreviated "d" in reference to a 2248dwt pennyweight # Frankish coin called the "denier" 2249 # minted in the late 700's. There 2250 # were 240 deniers to the pound. 2251assayton mg ton / troyounce # mg / assayton = troyounce / ton 2252usassayton mg uston / troyounce 2253brassayton mg brton / troyounce 2254fineounce troyounce # A troy ounce of 99.5% pure gold 2255 2256# Some other jewelers units 2257 2258metriccarat 0.2 gram # Defined in 1907 2259metricgrain 50 mg 2260carat metriccarat 2261ct carat 2262jewelerspoint 1|100 carat 2263silversmithpoint 1|4000 inch 2264momme 3.75 grams # Traditional Japanese unit based 2265 # on the chinese mace. It is used for 2266 # pearls in modern times and also for 2267 # silk density. The definition here 2268 # was adopted in 1891. 2269# Apothecaries' weight 2270 2271appound troypound 2272apounce troyounce 2273apdram 1|8 apounce 2274apscruple 1|3 apdram 2275 2276# Liquid measure 2277 2278usgallon 231 in^3 # US liquid measure is derived from 2279gal gallon # the British wine gallon of 1707. 2280quart 1|4 gallon # See the "winegallon" entry below 2281pint 1|2 quart # more historical information. 2282gill 1|4 pint 2283usquart 1|4 usgallon 2284uspint 1|2 usquart 2285usgill 1|4 uspint 2286usfluidounce 1|16 uspint 2287fluiddram 1|8 usfloz 2288minimvolume 1|60 fluiddram 2289qt quart 2290pt pint 2291floz fluidounce 2292usfloz usfluidounce 2293fldr fluiddram 2294liquidbarrel 31.5 usgallon 2295usbeerbarrel 2 beerkegs 2296beerkeg 15.5 usgallon # Various among brewers 2297ponykeg 1|2 beerkeg 2298winekeg 12 usgallon 2299petroleumbarrel 42 usgallon # Originated in Pennsylvania oil 2300barrel petroleumbarrel # fields, from the winetierce 2301bbl barrel 2302ushogshead 2 liquidbarrel 2303usfirkin 9 usgallon 2304 2305# Dry measures: The Winchester Bushel was defined by William III in 1702 and 2306# legally adopted in the US in 1836. 2307 2308usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5 2309bu bushel # inch diameter (rounded) 2310peck 1|4 bushel 2311uspeck 1|4 usbushel 2312brpeck 1|4 brbushel 2313pk peck 2314drygallon 1|2 uspeck 2315dryquart 1|4 drygallon 2316drypint 1|2 dryquart 2317drybarrel 7056 in^3 # Used in US for fruits, vegetables, 2318 # and other dry commodities except for 2319 # cranberries. 2320cranberrybarrel 5826 in^3 # US cranberry barrel 2321heapedbushel 1.278 usbushel# The following explanation for this 2322 # value was provided by Wendy Krieger 2323 # <os2fan2@yahoo.com> based on 2324 # guesswork. The cylindrical vessel is 2325 # 18.5 inches in diameter and 1|2 inch 2326 # thick. A heaped bushel includes the 2327 # contents of this cylinder plus a heap 2328 # on top. The heap is a cone 19.5 2329 # inches in diameter and 6 inches 2330 # high. With these values, the volume 2331 # of the bushel is 684.5 pi in^3 and 2332 # the heap occupies 190.125 pi in^3. 2333 # Therefore, the heaped bushel is 2334 # 874.625|684.5 bushels. This value is 2335 # approximately 1.2777575 and it rounds 2336 # to the value listed for the size of 2337 # the heaped bushel. Sometimes the 2338 # heaped bushel is reported as 1.25 2339 # bushels. This same explanation gives 2340 # that value if the heap is taken to 2341 # have an 18.5 inch diameter. 2342 2343# Grain measures. The bushel as it is used by farmers in the USA is actually 2344# a measure of mass which varies for different commodities. Canada uses the 2345# same bushel masses for most commodities, but not for oats. 2346 2347wheatbushel 60 lb 2348soybeanbushel 60 lb 2349cornbushel 56 lb 2350ryebushel 56 lb 2351barleybushel 48 lb 2352oatbushel 32 lb 2353ricebushel 45 lb 2354canada_oatbushel 34 lb 2355 2356# Wine and Spirits measure 2357 2358ponyvolume 1 usfloz 2359jigger 1.5 usfloz # Can vary between 1 and 2 usfloz 2360shot jigger # Sometimes 1 usfloz 2361eushot 25 ml # EU standard spirits measure 2362fifth 1|5 usgallon 2363winebottle 750 ml # US industry standard, 1979 2364winesplit 1|4 winebottle 2365magnum 1.5 liter # Standardized in 1979, but given 2366 # as 2 qt in some references 2367metrictenth 375 ml 2368metricfifth 750 ml 2369metricquart 1 liter 2370 2371# Old British bottle size 2372 2373reputedquart 1|6 brgallon 2374reputedpint 1|2 reputedquart 2375brwinebottle reputedquart # Very close to 1|5 winegallon 2376 2377# French champagne bottle sizes 2378 2379split 200 ml 2380jeroboam 2 magnum 2381rehoboam 3 magnum 2382methuselah 4 magnum 2383salmanazar 6 magnum 2384balthazar 8 magnum 2385nebuchadnezzar 10 magnum 2386 2387# The wine glass doesn't seem to have an official standard, but the same value 2388# is suggested by several organization. 2389 2390# https://www.rethinkingdrinking.niaaa.nih.gov/ 2391# http://www.rethinkyourdrinking.ca/what-is-a-standard-drink/ 2392# https://www.drinkaware.co.uk/ 2393# https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf 2394# http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/content/drinksguide-cnt 2395 2396wineglass 150 mL # the size of a "typical" serving 2397 2398# A unit of alcohol is a specified mass of pure ethyl alcohol. 2399# The term is used officially in the UK, but other countries use the same 2400# concept but with different values. For example, the UK value of 8 g is 2401# nominally the amount of alcohol that a typical adult can metabolize in 2402# one hour. Values for several countries, converted to a volumetric basis: 2403 2404alcoholunitus 14 g / ethanoldensity 2405alcoholunitca 13.6 g / ethanoldensity 2406alcoholunituk 8 g / ethanoldensity 2407alcoholunitau 10 g / ethanoldensity 2408 2409# Example: for 12% ABV (alcohol by volume) 2410# alcoholunitus / 12% = 147.8 mL, close to the “standard” serving of 150 mL. 2411 2412 2413# Coffee 2414# 2415# The recommended ratio of coffee to water. Values vary considerably; 2416# one is from the Specialty Coffee Association of America 2417# http://scaa.org/?page=resources&d=brewing-best-practices 2418 2419coffeeratio 55 g/L # ± 10% 2420 2421# other recommendations are more loose, e.g., 2422# http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee 2423 2424 2425# 2426# Water is "hard" if it contains various minerals, expecially calcium 2427# carbonate. 2428# 2429 2430clarkdegree grains/brgallon # Content by weigh of calcium carbonate 2431gpg grains/usgallon # Divide by water's density to convert to 2432 # a dimensionless concentration measure 2433# 2434# Shoe measures 2435# 2436 2437shoeiron 1|48 inch # Used to measure leather in soles 2438shoeounce 1|64 inch # Used to measure non-sole shoe leather 2439 2440# USA shoe sizes. These express the length of the shoe or the length 2441# of the "last", the form that the shoe is made on. But note that 2442# this only captures the length. It appears that widths change 1/4 2443# inch for each letter within the same size, and if you change the 2444# length by half a size then the width changes between 1/8 inch and 2445# 1/4 inch. But this may not be standard. If you know better, please 2446# contact me. 2447 2448shoesize_delta 1|3 inch # USA shoe sizes differ by this amount 2449shoe_men0 8.25 inch 2450shoe_women0 (7+11|12) inch 2451shoe_boys0 (3+11|12) inch 2452shoe_girls0 (3+7|12) inch 2453 2454shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \ 2455 (shoesize_men+(-shoe_men0))/shoesize_delta 2456shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \ 2457 (shoesize_women+(-shoe_women0))/shoesize_delta 2458shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \ 2459 (shoesize_boys+(-shoe_boys0))/shoesize_delta 2460shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \ 2461 (shoesize_girls+(-shoe_girls0))/shoesize_delta 2462 2463# European shoe size. According to 2464# http://www.shoeline.com/footnotes/shoeterm.shtml 2465# shoe sizes in Europe are measured with Paris points which simply measure 2466# the length of the shoe. 2467 2468europeshoesize 2|3 cm 2469 2470# 2471# USA slang units 2472# 2473 2474buck US$ 2475fin 5 US$ 2476sawbuck 10 US$ 2477usgrand 1000 US$ 2478greenback US$ 2479key kg # usually of marijuana, 60's 2480lid 1 oz # Another 60's weed unit 2481footballfield usfootballfield 2482usfootballfield 100 yards 2483canadafootballfield 110 yards # And 65 yards wide 2484marathon 26 miles + 385 yards 2485 2486# 2487# British 2488# 2489 2490# The length measure in the UK was defined by a bronze bar manufactured in 2491# 1844. Various conversions were sanctioned for convenience at different 2492# times, which makes conversions before 1963 a confusing matter. Apparently 2493# previous conversions were never explicitly revoked. Four different 2494# conversion factors appear below. Multiply them times an imperial length 2495# units as desired. The Weights and Measures Act of 1963 switched the UK away 2496# from their bronze standard and onto a definition of the yard in terms of the 2497# meter. This happened after an international agreement in 1959 to align the 2498# world's measurement systems. 2499 2500UK UKlength_SJJ 2501UK- UK 2502british- UK 2503 2504UKlength_B 0.9143992 meter / yard # Benoit found the yard to be 2505 # 0.9143992 m at a weights and 2506 # measures conference around 2507 # 1896. Legally sanctioned 2508 # in 1898. 2509UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and 2510 # Johnson found the yard to be 2511 # 0.91439841 meters. 2512 # Used starting in the 1930's. 2513UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio 2514 # for the meter and inch. This 2515 # value was used as the legal 2516 # conversion ratio when the 2517 # metric system was legalized 2518 # for contract in 1864. 2519UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter 2520 # to be 1.09362311 yards. This 2521 # conversion was legalized 2522 # around 1878. 2523brnauticalmile 6080 ft # Used until 1970 when the UK 2524brknot brnauticalmile / hr # switched to the international 2525brcable 1|10 brnauticalmile # nautical mile. 2526admiraltymile brnauticalmile 2527admiraltyknot brknot 2528admiraltycable brcable 2529seamile 6000 ft 2530shackle 15 fathoms # Adopted 1949 by British navy 2531 2532# British Imperial weight is mostly the same as US weight. A few extra 2533# units are added here. 2534 2535clove 7 lb 2536stone 14 lb 2537tod 28 lb 2538brquarterweight 1|4 brhundredweight 2539brhundredweight 8 stone 2540longhundredweight brhundredweight 2541longton 20 brhundredweight 2542brton longton 2543 2544# British Imperial volume measures 2545 2546brminim 1|60 brdram 2547brscruple 1|3 brdram 2548fluidscruple brscruple 2549brdram 1|8 brfloz 2550brfluidounce 1|20 brpint 2551brfloz brfluidounce 2552brgill 1|4 brpint 2553brpint 1|2 brquart 2554brquart 1|4 brgallon 2555brgallon 4.54609 l # The British Imperial gallon was 2556 # defined in 1824 to be the volume of 2557 # water which weighed 10 pounds at 62 2558 # deg F with a pressure of 30 inHg. 2559 # It was also defined as 277.274 in^3, 2560 # Which is slightly in error. In 2561 # 1963 it was defined to be the volume 2562 # occupied by 10 pounds of distilled 2563 # water of density 0.998859 g/ml weighed 2564 # in air of density 0.001217 g/ml 2565 # against weights of density 8.136 g/ml. 2566 # This gives a value of approximately 2567 # 4.5459645 liters, but the old liter 2568 # was in force at this time. In 1976 2569 # the definition was changed to exactly 2570 # 4.54609 liters using the new 2571 # definition of the liter (1 dm^3). 2572brbarrel 36 brgallon # Used for beer 2573brbushel 8 brgallon 2574brheapedbushel 1.278 brbushel 2575brquarter 8 brbushel 2576brchaldron 36 brbushel 2577 2578# Obscure British volume measures. These units are generally traditional 2579# measures whose definitions have fluctuated over the years. Often they 2580# depended on the quantity being measured. They are given here in terms of 2581# British Imperial measures. For example, the puncheon may have historically 2582# been defined relative to the wine gallon or beer gallon or ale gallon 2583# rather than the British Imperial gallon. 2584 2585bag 4 brbushel 2586bucket 4 brgallon 2587kilderkin 2 brfirkin 2588last 40 brbushel 2589noggin brgill 2590pottle 0.5 brgallon 2591pin 4.5 brgallon 2592puncheon 72 brgallon 2593seam 8 brbushel 2594coomb 4 brbushel 2595boll 6 brbushel 2596firlot 1|4 boll 2597brfirkin 9 brgallon # Used for ale and beer 2598cran 37.5 brgallon # measures herring, about 750 fish 2599brwinehogshead 52.5 brgallon # This value is approximately equal 2600brhogshead brwinehogshead # to the old wine hogshead of 63 2601 # wine gallons. This adjustment 2602 # is listed in the OED and in 2603 # "The Weights and Measures of 2604 # England" by R. D. Connor 2605brbeerhogshead 54 brgallon 2606brbeerbutt 2 brbeerhogshead 2607registerton 100 ft^3 # Used for internal capacity of ships 2608shippington 40 ft^3 # Used for ship's cargo freight or timber 2609brshippington 42 ft^3 # 2610freightton shippington # Both register ton and shipping ton derive 2611 # from the "tun cask" of wine. 2612displacementton 35 ft^3 # Approximate volume of a longton weight of 2613 # sea water. Measures water displaced by 2614 # ships. 2615waterton 224 brgallon 2616strike 70.5 l # 16th century unit, sometimes 2617 # defined as .5, 2, or 4 bushels 2618 # depending on the location. It 2619 # probably doesn't make a lot of 2620 # sense to define in terms of imperial 2621 # bushels. Zupko gives a value of 2622 # 2 Winchester grain bushels or about 2623 # 70.5 liters. 2624amber 4 brbushel# Used for dry and liquid capacity [18] 2625 2626# British volume measures with "imperial" 2627 2628imperialminim brminim 2629imperialscruple brscruple 2630imperialdram brdram 2631imperialfluidounce brfluidounce 2632imperialfloz brfloz 2633imperialgill brgill 2634imperialpint brpint 2635imperialquart brquart 2636imperialgallon brgallon 2637imperialbarrel brbarrel 2638imperialbushel brbushel 2639imperialheapedbushel brheapedbushel 2640imperialquarter brquarter 2641imperialchaldron brchaldron 2642imperialwinehogshead brwinehogshead 2643imperialhogshead brhogshead 2644imperialbeerhogshead brbeerhogshead 2645imperialbeerbutt brbeerbutt 2646imperialfirkin brfirkin 2647 2648# obscure British lengths 2649 2650barleycorn 1|3 UKinch # Given in Realm of Measure as the 2651 # difference between successive shoe sizes 2652nail 1|16 UKyard # Originally the width of the thumbnail, 2653 # or 1|16 ft. This took on the general 2654 # meaning of 1|16 and settled on the 2655 # nail of a yard or 1|16 yards as its 2656 # final value. [12] 2657pole 16.5 UKft # This was 15 Saxon feet, the Saxon 2658rope 20 UKft # foot (aka northern foot) being longer 2659englishell 45 UKinch 2660flemishell 27 UKinch 2661ell englishell # supposed to be measure from elbow to 2662 # fingertips 2663span 9 UKinch # supposed to be distance from thumb 2664 # to pinky with full hand extension 2665goad 4.5 UKft # used for cloth, possibly named after the 2666 # stick used for prodding animals. 2667 2668# misc obscure British units 2669 2670hide 120 acre # English unit of land area dating to the 7th 2671 # century, originally the amount of land 2672 # that a single plowman could cultivate, 2673 # which varied from 60-180 acres regionally. 2674 # Standardized at Normon conquest. 2675virgate 1|4 hide 2676nook 1|2 virgate 2677rood furlong rod # Area of a strip a rod by a furlong 2678englishcarat troyounce/151.5 # Originally intended to be 4 grain 2679 # but this value ended up being 2680 # used in the London diamond market 2681mancus 2 oz 2682mast 2.5 lb 2683nailkeg 100 lbs 2684basebox 31360 in^2 # Used in metal plating 2685 2686# alternate spellings 2687 2688metre meter 2689gramme gram 2690litre liter 2691dioptre diopter 2692aluminium aluminum 2693sulphur sulfur 2694 2695# 2696# Units derived the human body (may not be very accurate) 2697# 2698 2699geometricpace 5 ft # distance between points where the same 2700 # foot hits the ground 2701pace 2.5 ft # distance between points where alternate 2702 # feet touch the ground 2703USmilitarypace 30 in # United States official military pace 2704USdoubletimepace 36 in # United States official doubletime pace 2705fingerbreadth 7|8 in # The finger is defined as either the width 2706fingerlength 4.5 in # or length of the finger 2707finger fingerbreadth 2708palmwidth hand # The palm is a unit defined as either the width 2709palmlength 8 in # or the length of the hand 2710hand 4 inch # width of hand 2711shaftment 6 inch # Distance from tip of outstretched thumb to the 2712 # opposite side of the palm of the hand. The 2713 # ending -ment is from the old English word 2714 # for hand. [18] 2715smoot 5 ft + 7 in # Created as part of an MIT fraternity prank. 2716 # In 1958 Oliver Smoot was used to measure 2717 # the length of the Harvard Bridge, which was 2718 # marked off in Smoot lengths. These 2719 # markings have been maintained on the bridge 2720 # since then and repainted by subsequent 2721 # incoming fraternity members. During a 2722 # bridge renovation the new sidewalk was 2723 # scored every Smoot rather than at the 2724 # customary 6 ft spacing. 2725# 2726# Cooking measures 2727# 2728 2729# Common abbreviations 2730 2731tbl tablespoon 2732tbsp tablespoon 2733tblsp tablespoon 2734Tb tablespoon 2735tsp teaspoon 2736saltspoon 1|4 tsp 2737 2738# US measures 2739 2740uscup 8 usfloz 2741ustablespoon 1|16 uscup 2742usteaspoon 1|3 ustablespoon 2743ustbl ustablespoon 2744ustbsp ustablespoon 2745ustblsp ustablespoon 2746ustsp usteaspoon 2747metriccup 250 ml 2748stickbutter 1|4 lb # Butter in the USA is sold in one 2749 # pound packages that contain four 2750 # individually wrapped pieces. The 2751 # pieces are marked into tablespoons, 2752 # making it possible to measure out 2753 # butter by volume by slicing the 2754 # butter. 2755 2756legalcup 240 ml # The cup used on nutrition labeling 2757legaltablespoon 1|16 legalcup 2758legaltbsp legaltablespoon 2759 2760# Scoop size. Ice cream scoops in the US are marked with numbers 2761# indicating the number of scoops requird to fill a US quart. 2762 2763scoop(n) units=[1;cup] domain=[4,100] range=[0.04,1] \ 2764 32 usfloz / n ; 32 usfloz / scoop 2765 2766 2767# US can sizes. 2768 2769number1can 10 usfloz 2770number2can 19 usfloz 2771number2.5can 3.5 uscups 2772number3can 4 uscups 2773number5can 7 uscups 2774number10can 105 usfloz 2775 2776# British measures 2777 2778brcup 1|2 brpint 2779brteacup 1|3 brpint 2780brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml 2781brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon 2782brdessertspoon 2 brteaspoon 2783dessertspoon brdessertspoon 2784dsp dessertspoon 2785brtsp brteaspoon 2786brtbl brtablespoon 2787brtbsp brtablespoon 2788brtblsp brtablespoon 2789 2790# Australian 2791 2792australiatablespoon 20 ml 2793austbl australiatablespoon 2794austbsp australiatablespoon 2795austblsp australiatablespoon 2796australiateaspoon 1|4 australiatablespoon 2797austsp australiateaspoon 2798 2799# Italian 2800 2801etto 100 g # Used for buying items like meat and 2802etti etto # cheese. 2803 2804# Chinese 2805 2806catty 0.5 kg 2807oldcatty 4|3 lbs # Before metric conversion. 2808tael 1|16 oldcatty # Should the tael be defined both ways? 2809mace 0.1 tael 2810oldpicul 100 oldcatty 2811picul 100 catty # Chinese usage 2812 2813# Indian 2814 2815seer 14400 grain # British Colonial standard 2816ser seer 2817maund 40 seer 2818pakistanseer 1 kg 2819pakistanmaund 40 pakistanseer 2820chittak 1|16 seer 2821tola 1|5 chittak 2822ollock 1|4 liter # Is this right? 2823 2824# Japanese 2825 2826japancup 200 ml 2827 2828# densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum 2829# so you can convert '2 cups sugar' to grams, for example, or in the other 2830# direction grams could be converted to 'cup flour_scooped'. 2831 2832butter 8 oz/uscup 2833butter_clarified 6.8 oz/uscup 2834cocoa_butter 9 oz/uscup 2835shortening 6.75 oz/uscup # vegetable shortening 2836oil 7.5 oz/uscup 2837cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the 2838cakeflour_spooned 4 oz/uscup # measuring method. "Scooped", or 2839cakeflour_scooped 4.5 oz/uscup # "dip and sweep" refers to dipping a 2840flour_sifted 4 oz/uscup # measure into a bin, and then sweeping 2841flour_spooned 4.25 oz/uscup # the excess off the top. "Spooned" 2842flour_scooped 5 oz/uscup # means to lightly spoon into a measure 2843breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means 2844breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a 2845breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top. 2846cornstarch 120 grams/uscup 2847dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa 2848dutchcocoa_spooned 92 g/uscup 2849dutchcocoa_scooped 95 g/uscup 2850cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa 2851cocoa_spooned 82 g/uscup 2852cocoa_scooped 95 g/uscup 2853heavycream 232 g/uscup 2854milk 242 g/uscup 2855sourcream 242 g/uscup 2856molasses 11.25 oz/uscup 2857cornsyrup 11.5 oz/uscup 2858honey 11.75 oz/uscup 2859sugar 200 g/uscup 2860powdered_sugar 4 oz/uscup 2861brownsugar_light 217 g/uscup # packed 2862brownsugar_dark 239 g/uscup 2863 2864baking_powder 4.6 grams / ustsp 2865salt 6 g / ustsp 2866koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt 2867koshersalt_morton 4.8 g / ustsp # Morton kosher salt 2868 # Values are from the nutrition info 2869 # on the packages 2870 2871 2872# Egg weights and volumes for a USA large egg 2873 2874egg 50 grams # without shell 2875eggwhite 30 grams 2876eggyolk 18.6 grams 2877eggvolume 3 ustablespoons + 1|2 ustsp 2878eggwhitevolume 2 ustablespoons 2879eggyolkvolume 3.5 ustsp 2880 2881# Alcohol density 2882 2883ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition 2884alcoholdensity ethanoldensity 2885 2886# 2887# Density measures. Density has traditionally been measured on a variety of 2888# bizarre nonlinear scales. 2889# 2890 2891# Density of a sugar syrup is frequently measured in candy making procedures. 2892# In the USA the boiling point of the syrup is measured. Some recipes instead 2893# specify the density using degrees Baume. Conversion between degrees Baume 2894# and the boiling point measure has proved elusive. This table appeared in one 2895# text, and provides a fragmentary relationship to the concentration. 2896# 2897# temp(C) conc (%) 2898# 100 30 2899# 101 40 2900# 102 50 2901# 103 60 2902# 106 70 2903# 112 80 2904# 123 90 2905# 140 95 2906# 151 97 2907# 160 98.2 2908# 166 99.5 2909# 171 99.6 2910# 2911# The best source identified to date came from "Boiling point elevation of 2912# technical sugarcane solutions and its use in automatic pan boiling" by 2913# Michael Saska. International Sugar Journal, 2002, 104, 1247, pp 500-507. 2914# 2915# But I'm using equation (3) which is credited to Starzak and Peacock, 2916# "Water activity coefficient in aqueous solutions of sucrose--A comprehensive 2917# data analyzis. Zuckerindustrie, 122, 380-387. (I couldn't find this 2918# document.) 2919# 2920# Note that the range of validity is uncertain, but answers are in agreement 2921# with the above table all the way to 99.6. 2922# 2923# The original equation has a parameter for the boiling point of water, which 2924# of course varies with altitude. It also includes various other model 2925# parameters. The input is the molar concentration of sucrose in the solution, 2926# (moles sucrose) / (total moles). 2927# 2928# Bsp 3797.06 degC 2929# Csp 226.28 degC 2930# QQ -17638 J/mol 2931# asp -1.0038 2932# bsp -0.24653 2933# tbw 100 degC # boiling point of water 2934# sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \ 2935# /(tbw+stdtemp)) / (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp) 2936# 2937# To convert mass concentration (brix) to molar concentration 2938# 2939# sc(x) (x / 342.3) / (( x/342.3) + (100-x)/18.02); \ 2940# 100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1) 2941# 2942# Here is a simplfied version of this equation where the temperature of boiling 2943# water has been fixed at 100 degrees Celcius and the argument is now the 2944# concentration (brix). 2945# 2946# sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \ 2947# / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K 2948# 2949# 2950# The formula is not invertible, so to implement it in units we unfortunately 2951# must turn it into a table. 2952 2953# This table gives the boiling point elevation as a function of the sugar syrup 2954# concentration expressed as a percentage. 2955 2956sugar_conc_bpe[K] \ 2957 0 0.0000 5 0.0788 10 0.1690 15 0.2729 20 0.3936 25 0.5351 \ 295830 0.7027 35 0.9036 40 1.1475 42 1.2599 44 1.3825 46 1.5165 \ 295948 1.6634 50 1.8249 52 2.0031 54 2.2005 56 2.4200 58 2.6651 \ 296060 2.9400 61 3.0902 62 3.2499 63 3.4198 64 3.6010 65 3.7944 \ 296166 4.0012 67 4.2227 68 4.4603 69 4.7156 70 4.9905 71 5.2870 \ 296272 5.6075 73 5.9546 74 6.3316 75 6.7417 76 7.1892 77 7.6786 \ 296378.0 8.2155 79.0 8.8061 80.0 9.4578 80.5 9.8092 81.0 10.1793 \ 296481.5 10.5693 82.0 10.9807 82.5 11.4152 83.0 11.8743 83.5 12.3601 \ 296584.0 12.8744 84.5 13.4197 85.0 13.9982 85.5 14.6128 86.0 15.2663 \ 296686.5 15.9620 87.0 16.7033 87.5 17.4943 88.0 18.3391 88.5 19.2424 \ 296789.0 20.2092 89.5 21.2452 90.0 22.3564 90.5 23.5493 91.0 24.8309 \ 296891.5 26.2086 92.0 27.6903 92.5 29.2839 93.0 30.9972 93.5 32.8374 \ 296994.0 34.8104 94.5 36.9195 95.0 39.1636 95.5 41.5348 96.0 44.0142 \ 297096.5 46.5668 97.0 49.1350 97.5 51.6347 98.0 53.9681 98.1 54.4091 \ 297198.2 54.8423 98.3 55.2692 98.4 55.6928 98.5 56.1174 98.6 56.5497 \ 297298.7 56.9999 98.8 57.4828 98.9 58.0206 99.0 58.6455 99.1 59.4062 \ 297399.2 60.3763 99.3 61.6706 99.4 63.4751 99.5 66.1062 99.6 70.1448 \ 297499.7 76.7867 2975 2976# Using the brix table we can use this to produce a mapping from boiling point 2977# to density which makes all of the units interconvertible. Because the brix 2978# table stops at 95 this approach works up to a boiling point elevation of 39 K 2979# or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy 2980# making. The "hard crack" stage continues up to 310 F. 2981 2982# Boiling point elevation 2983sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \ 2984 brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe)) 2985# Absolute boiling point (produces an absolute temperature) 2986sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \ 2987 range=[0.99717,1.5144619] \ 2988 brix(~sugar_conc_bpe(T-tempC(100))) ;\ 2989 sugar_conc_bpe(~brix(sugar_bp))+tempC(100) 2990 2991# In practice dealing with the absolute temperature is annoying because it is 2992# not possible to convert to a nested function, so you're stuck retyping the 2993# absolute temperature in Kelvins to convert to celsius or Fahrenheit. To 2994# prevent this we supply definitions that build in the temperature conversion 2995# and produce results in the Fahrenheit and Celcius scales. So using these 2996# measures, to convert 46 degrees Baume to a Fahrenheit boiling point: 2997# 2998# You have: baume(45) 2999# You want: sugar_bpF 3000# 239.05647 3001# 3002sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\ 3003 brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\ 3004 ~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100)) 3005sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\ 3006 brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\ 3007 ~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100)) 3008 3009# Degrees Baume is used in European recipes to specify the density of a sugar 3010# syrup. An entirely different definition is used for densities below 3011# 1 g/cm^3. An arbitrary constant appears in the definition. This value is 3012# equal to 145 in the US, but was according to [], the old scale used in 3013# Holland had a value of 144, and the new scale or Gerlach scale used 146.78. 3014 3015baumeconst 145 # US value 3016baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \ 3017 (baumeconst/(baumeconst+-d)) g/cm^3 ; \ 3018 (baume+((-g)/cm^3)) baumeconst / baume 3019 3020# It's not clear if this value was ever used with negative degrees. 3021twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \ 3022 (1 + 0.005 x) g / cm^3 ; \ 3023 200 (twaddell / (g/cm^3) +- 1) 3024 3025# The degree quevenne is a unit for measuring the density of milk. 3026# Similarly it's unclear if negative values were allowed here. 3027quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \ 3028 (1 + 0.001 x) g / cm^3 ; \ 3029 1000 (quevenne / (g/cm^3) +- 1) 3030 3031# Degrees brix measures sugar concentration by weigh as a percentage, so a 3032# solution that is 3 degrees brix is 3% sugar by weight. This unit was named 3033# after Adolf Brix who invented a hydrometer that read this percentage 3034# directly. This data is from Table 114 of NIST Circular 440, "Polarimetry, 3035# Saccharimetry and the Sugars". It gives apparent specific gravity at 20 3036# degrees Celsius of various sugar concentrations. As rendered below this 3037# data is converted to apparent density at 20 degrees Celsius using the 3038# density figure for water given in the same NIST reference. They use the 3039# word "apparent" to refer to measurements being made in air with brass 3040# weights rather than vacuum. 3041 3042brix[0.99717g/cm^3]\ 3043 0 1.00000 1 1.00390 2 1.00780 3 1.01173 4 1.01569 5 1.01968 \ 3044 6 1.02369 7 1.02773 8 1.03180 9 1.03590 10 1.04003 11 1.04418 \ 3045 12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \ 3046 18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \ 3047 24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \ 3048 30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \ 3049 36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \ 3050 42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \ 3051 48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \ 3052 54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \ 3053 60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \ 3054 66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \ 3055 72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \ 3056 78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \ 3057 84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \ 3058 90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876 3059 3060# Density measure invented by the American Petroleum Institute. Lighter 3061# petroleum products are more valuable, and they get a higher API degree. 3062# 3063# The intervals of range and domain should be open rather than closed. 3064# 3065apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \ 3066 141.5 g/cm^3 / (x+131.5) ; \ 3067 141.5 (g/cm^3) / apidegree + (-131.5) 3068 3069# 3070# Units derived from imperial system 3071# 3072 3073ouncedal oz ft / s^2 # force which accelerates an ounce 3074 # at 1 ft/s^2 3075poundal lb ft / s^2 # same thing for a pound 3076tondal longton ft / s^2 # and for a ton 3077pdl poundal 3078osi ounce force / inch^2 # used in aviation 3079psi pound force / inch^2 3080psia psi # absolute pressure 3081 # Note that gauge pressure can be given 3082 # using the gaugepressure() and 3083 # psig() nonlinear unit definitions 3084tsi ton force / inch^2 3085reyn psi sec 3086slug lbf s^2 / ft 3087slugf slug force 3088slinch lbf s^2 / inch # Mass unit derived from inch second 3089slinchf slinch force # pound-force system. Used in space 3090 # applications where in/sec^2 was a 3091 # natural acceleration measure. 3092geepound slug 3093lbf lb force 3094tonf ton force 3095lbm lb 3096kip 1000 lbf # from kilopound 3097ksi kip / in^2 3098mil 0.001 inch 3099thou 0.001 inch 3100tenth 0.0001 inch # one tenth of one thousandth of an inch 3101millionth 1e-6 inch # one millionth of an inch 3102circularinch 1|4 pi in^2 # area of a one-inch diameter circle 3103circleinch circularinch # A circle with diameter d inches has 3104 # an area of d^2 circularinches 3105cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter 3106 # has volume d^2 h cylinder inches 3107circularmil 1|4 pi mil^2 # area of one-mil diameter circle 3108cmil circularmil 3109 3110cental 100 pound 3111centner cental 3112caliber 0.01 inch # for measuring bullets 3113duty ft lbf 3114celo ft / s^2 3115jerk ft / s^3 3116australiapoint 0.01 inch # The "point" is used to measure rainfall 3117 # in Australia 3118sabin ft^2 # Measure of sound absorption equal to the 3119 # absorbing power of one square foot of 3120 # a perfectly absorbing material. The 3121 # sound absorptivity of an object is the 3122 # area times a dimensionless 3123 # absorptivity coefficient. 3124standardgauge 4 ft + 8.5 in # Standard width between railroad track 3125flag 5 ft^2 # Construction term referring to sidewalk. 3126rollwallpaper 30 ft^2 # Area of roll of wall paper 3127fillpower in^3 / ounce # Density of down at standard pressure. 3128 # The best down has 750-800 fillpower. 3129pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA. 3130buttonline 1|40 inch # The line was used in 19th century USA 3131 # to measure width of buttons. 3132beespace 1|4 inch # Bees will fill any space that is smaller 3133 # than the bee space and leave open 3134 # spaces that are larger. The size of 3135 # the space varies with species. 3136diamond 8|5 ft # Marking on US tape measures that is 3137 # useful to carpenters who wish to place 3138 # five studs in an 8 ft distance. Note 3139 # that the numbers appear in red every 3140 # 16 inches as well, giving six 3141 # divisions in 8 feet. 3142retmaunit 1.75 in # Height of rack mountable equipment. 3143U retmaunit # Equipment should be 1|32 inch narrower 3144RU U # than its U measurement indicates to 3145 # allow for clearance, so 4U=(6+31|32)in 3146 # RETMA stands for the former name of 3147 # the standardizing organization, Radio 3148 # Electronics Television Manufacturers 3149 # Association. This organization is now 3150 # called the Electronic Industries 3151 # Alliance (EIA) and the rack standard 3152 # is specified in EIA RS-310-D. 3153count per pound # For measuring the size of shrimp 3154 3155# 3156# Other units of work, energy, power, etc 3157# 3158 3159ENERGY joule 3160WORK joule 3161 3162# Calorie: approximate energy to raise a gram of water one degree celsius 3163 3164calorie cal_th # Default is the thermochemical calorie 3165cal calorie 3166calorie_th 4.184 J # Thermochemical calorie, defined in 1930 3167thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to 3168cal_th calorie_th # avoid difficulties associated with the 3169 # uncertainty in the heat capacity of 3170 # water. In 1948 the value of the joule 3171 # was changed, so the thermochemical 3172 # calorie was redefined to 4.184 J. 3173 # This kept the energy measured by this 3174 # unit the same. 3175calorie_IT 4.1868 J # International (Steam) Table calorie, 3176cal_IT calorie_IT # defined in 1929 as watt-hour/860 or 3177 # equivalently 180|43 joules. At this 3178 # time the international joule had a 3179 # different value than the modern joule, 3180 # and the values were different in the 3181 # USA and in Europe. In 1956 at the 3182 # Fifth International Conference on 3183 # Properties of Steam the exact 3184 # definition given here was adopted. 3185calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC 3186cal_15 calorie_15 3187calorie_fifteen cal_15 3188calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC 3189cal_20 calorie_20 3190calorie_twenty calorie_20 3191cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC 3192Calorie kilocalorie # the food Calorie 3193thermie 1e6 cal_15 # Heat required to raise the 3194 # temperature of a tonne of 3195 # water from 14.5 to 15.5 degC. 3196 3197# btu definitions: energy to raise a pound of water 1 degF 3198 3199btu btu_IT # International Table BTU is the default 3200britishthermalunit btu 3201btu_IT cal_IT lb degF / gram K 3202btu_th cal_th lb degF / gram K 3203btu_mean cal_mean lb degF / gram K 3204quad quadrillion btu 3205 3206ECtherm 1.05506e8 J # Exact definition, close to 1e5 btu 3207UStherm 1.054804e8 J # Exact definition 3208therm UStherm 3209 3210# Water latent heat from [23] 3211 3212water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C 3213water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa 3214 3215# Specific heat capacities of various substances 3216 3217specificheat_water calorie / g K 3218water_specificheat specificheat_water 3219 # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html 3220specificheat_aluminum 0.91 J/g K 3221specificheat_antimony 0.21 J/g K 3222specificheat_barium 0.20 J/g K 3223specificheat_beryllium 1.83 J/g K 3224specificheat_bismuth 0.13 J/g K 3225specificheat_cadmium 0.23 J/g K 3226specificheat_cesium 0.24 J/g K 3227specificheat_chromium 0.46 J/g K 3228specificheat_cobalt 0.42 J/g K 3229specificheat_copper 0.39 J/g K 3230specificheat_gallium 0.37 J/g K 3231specificheat_germanium 0.32 J/g K 3232specificheat_gold 0.13 J/g K 3233specificheat_hafnium 0.14 J/g K 3234specificheat_indium 0.24 J/g K 3235specificheat_iridium 0.13 J/g K 3236specificheat_iron 0.45 J/g K 3237specificheat_lanthanum 0.195 J/g K 3238specificheat_lead 0.13 J/g K 3239specificheat_lithium 3.57 J/g K 3240specificheat_lutetium 0.15 J/g K 3241specificheat_magnesium 1.05 J/g K 3242specificheat_manganese 0.48 J/g K 3243specificheat_mercury 0.14 J/g K 3244specificheat_molybdenum 0.25 J/g K 3245specificheat_nickel 0.44 J/g K 3246specificheat_osmium 0.13 J/g K 3247specificheat_palladium 0.24 J/g K 3248specificheat_platinum 0.13 J/g K 3249specificheat_plutonum 0.13 J/g K 3250specificheat_potassium 0.75 J/g K 3251specificheat_rhenium 0.14 J/g K 3252specificheat_rhodium 0.24 J/g K 3253specificheat_rubidium 0.36 J/g K 3254specificheat_ruthenium 0.24 J/g K 3255specificheat_scandium 0.57 J/g K 3256specificheat_selenium 0.32 J/g K 3257specificheat_silicon 0.71 J/g K 3258specificheat_silver 0.23 J/g K 3259specificheat_sodium 1.21 J/g K 3260specificheat_strontium 0.30 J/g K 3261specificheat_tantalum 0.14 J/g K 3262specificheat_thallium 0.13 J/g K 3263specificheat_thorium 0.13 J/g K 3264specificheat_tin 0.21 J/g K 3265specificheat_titanium 0.54 J/g K 3266specificheat_tungsten 0.13 J/g K 3267specificheat_uranium 0.12 J/g K 3268specificheat_vanadium 0.39 J/g K 3269specificheat_yttrium 0.30 J/g K 3270specificheat_zinc 0.39 J/g K 3271specificheat_zirconium 0.27 J/g K 3272specificheat_ethanol 2.3 J/g K 3273specificheat_ammonia 4.6 J/g K 3274specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit 3275specificheat_gasoline 2.22 J/g K 3276specificheat_iodine 2.15 J/g K 3277specificheat_oliveoil 1.97 J/g K 3278 3279# en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities 3280specificheat_hydrogen 14.3 J/g K 3281specificheat_helium 5.1932 J/g K 3282specificheat_argon 0.5203 J/g K 3283specificheat_tissue 3.5 J/g K 3284specificheat_diamond 0.5091 J/g K 3285specificheat_granite 0.79 J/g K 3286specificheat_graphite 0.71 J/g K 3287specificheat_ice 2.11 J/g K 3288specificheat_asphalt 0.92 J/g K 3289specificheat_brick 0.84 J/g K 3290specificheat_concrete 0.88 J/g K 3291specificheat_glass_silica 0.84 J/g K 3292specificheat_glass_flint 0.503 J/g K 3293specificheat_glass_pyrex 0.753 J/g K 3294specificheat_gypsum 1.09 J/g K 3295specificheat_marble 0.88 J/g K 3296specificheat_sand 0.835 J/g K 3297specificheat_soil 0.835 J/g K 3298specificheat_wood 1.7 J/g K 3299 3300specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php 3301 3302 3303# Energy densities of various fuels 3304# 3305# Most of these fuels have varying compositions or qualities and hence their 3306# actual energy densities vary. These numbers are hence only approximate. 3307# 3308# E1. http://bioenergy.ornl.gov/papers/misc/energy_conv.html 3309# E2. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm 3310# E3. http://www.ior.com.au/ecflist.html 3311 3312tonoil 1e10 cal_IT # Ton oil equivalent. A conventional 3313 # value for the energy released by 3314toe tonoil # burning one metric ton of oil. [18,E2] 3315 # Note that energy per mass of petroleum 3316 # products is fairly constant. 3317 # Variations in volumetric energy 3318 # density result from variations in the 3319 # density (kg/m^3) of different fuels. 3320 # This definition is given by the 3321 # IEA/OECD. 3322toncoal 7e9 cal_IT # Energy in metric ton coal from [18]. 3323 # This is a nominal value which 3324 # is close to the heat content 3325 # of coal used in the 1950's 3326barreloil 5.8 Mbtu # Conventional value for barrel of crude 3327 # oil [E2]. Actual range is 5.6 - 6.3. 3328naturalgas_HHV 1027 btu/ft3 # Energy content of natural gas. HHV 3329naturalgas_LHV 930 btu/ft3 # is for Higher Heating Value and 3330naturalgas naturalgas_HHV # includes energy from condensation 3331 # combustion products. LHV is for Lower 3332 # Heating Value and excludes these. 3333 # American publications typically report 3334 # HHV whereas European ones report LHV. 3335charcoal 30 GJ/tonne 3336woodenergy_dry 20 GJ/tonne # HHV, a cord weights about a tonne 3337woodenergy_airdry 15 GJ/tonne # 20% moisture content 3338coal_bituminous 27 GJ / tonne 3339coal_lignite 15 GJ / tonne 3340coal_US 22 GJ / uston # Average for US coal (short ton), 1995 3341ethanol_HHV 84000 btu/usgallon 3342ethanol_LHV 75700 btu/usgallon 3343diesel 130500 btu/usgallon 3344gasoline_LHV 115000 btu/usgallon 3345gasoline_HHV 125000 btu/usgallon 3346gasoline gasoline_HHV 3347heating 37.3 MJ/liter 3348fueloil 39.7 MJ/liter # low sulphur 3349propane 93.3 MJ/m^3 3350butane 124 MJ/m^3 3351 3352# These values give total energy from uranium fission. Actual efficiency 3353# of nuclear power plants is around 30%-40%. Note also that some reactors 3354# use enriched uranium around 3% U-235. Uranium during processing or use 3355# may be in a compound of uranium oxide or uranium hexafluoride, in which 3356# case the energy density would be lower depending on how much uranium is 3357# in the compound. 3358 3359uranium_pure 200 MeV avogadro / (235.0439299 g/mol) # Pure U-235 3360uranium_natural 0.7% uranium_pure # Natural uranium: 0.7% U-235 3361 3362# Celsius heat unit: energy to raise a pound of water 1 degC 3363 3364celsiusheatunit cal lb degC / gram K 3365chu celsiusheatunit 3366 3367POWER watt 3368 3369# "Apparent" average power in an AC circuit, the product of rms voltage 3370# and rms current, equal to the true power in watts when voltage and 3371# current are in phase. In a DC circuit, always equal to the true power. 3372 3373VA volt ampere 3374 3375kWh kilowatt hour 3376 3377# The horsepower is supposedly the power of one horse pulling. Obviously 3378# different people had different horses. 3379 3380horsepower 550 foot pound force / sec # Invented by James Watt 3381mechanicalhorsepower horsepower 3382hp horsepower 3383metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in 3384electrichorsepower 746 W # Germany 3385boilerhorsepower 9809.50 W 3386waterhorsepower 746.043 W 3387brhorsepower 745.70 W 3388donkeypower 250 W 3389chevalvapeur metrichorsepower 3390 3391# 3392# Heat Transfer 3393# 3394# Thermal conductivity, K, measures the rate of heat transfer across 3395# a material. The heat transfered is 3396# Q = K dT A t / L 3397# where dT is the temperature difference across the material, A is the 3398# cross sectional area, t is the time, and L is the length (thickness). 3399# Thermal conductivity is a material property. 3400 3401THERMAL_CONDUCTIVITY POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH) 3402THERMAL_RESISTIVITY 1/THERMAL_CONDUCTIVITY 3403 3404# Thermal conductance is the rate at which heat flows across a given 3405# object, so the area and thickness have been fixed. It depends on 3406# the size of the object and is hence not a material property. 3407 3408THERMAL_CONDUCTANCE POWER / TEMPERATURE_DIFFERENCE 3409THERMAL_RESISTANCE 1/THERMAL_CONDUCTANCE 3410 3411# Thermal admittance is the rate of heat flow per area across an 3412# object whose thickness has been fixed. Its reciprocal, thermal 3413# insulation, is used to for measuring the heat transfer per area 3414# of sheets of insulation or cloth that are of specified thickness. 3415 3416THERMAL_ADMITTANCE THERMAL_CONDUCTIVITY / LENGTH 3417THERMAL_INSULANCE THERMAL_RESISTIVITY LENGTH 3418THERMAL_INSULATION THERMAL_RESISTIVITY LENGTH 3419 3420Rvalue degF ft^2 hr / btu 3421Uvalue 1/Rvalue 3422europeanUvalue watt / m^2 K 3423RSI degC m^2 / W 3424clo 0.155 degC m^2 / W # Supposed to be the insulance 3425 # required to keep a resting person 3426 # comfortable indoors. The value 3427 # given is from NIST and the CRC, 3428 # but [5] gives a slightly different 3429 # value of 0.875 ft^2 degF hr / btu. 3430tog 0.1 degC m^2 / W # Also used for clothing. 3431 3432 3433# The bel was defined by engineers of Bell Laboratories to describe the 3434# reduction in audio level over a length of one mile. It was originally 3435# called the transmission unit (TU) but was renamed around 1923 to honor 3436# Alexander Graham Bell. The bel proved inconveniently large so the decibel 3437# has become more common. The decibel is dimensionless since it reports a 3438# ratio, but it is used in various contexts to report a signal's power 3439# relative to some reference level. 3440 3441bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition 3442decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel 3443dB() decibel # Abbreviation 3444dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W 3445dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW 3446dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW 3447dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW 3448dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW 3449dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative 3450 # to 1 joule. Used for power spectral 3451 # density since W/Hz = J 3452 3453# When used to measure amplitude, voltage, or current the signal is squared 3454# because power is proportional to the square of these measures. The root 3455# mean square (RMS) voltage is typically used with these units. 3456 3457dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V 3458dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV 3459dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2) 3460 # Reference = 1 microvolt 3461 3462# Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load. 3463# Originally defined as dBv but changed to prevent confusion with dBV. 3464# The "u" is for unloaded. 3465dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \ 3466 ~dB(dBu^2 / mW 600 ohm) 3467dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu 3468 3469 3470# Measurements for sound in air, referenced to the threshold of human hearing 3471# Note that sound in other media typically uses 1 micropascal as a reference 3472# for sound pressure. Units dBA, dBB, dBC, refer to different frequency 3473# weightings meant to approximate the human ear's response. 3474 3475dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \ 3476 ~dB(dBSPL^2 / (20 microPa)^2) # pressure 3477dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \ 3478 ~dB(dBSIL / (1e-12 W/m^2)) # intensity 3479dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W) 3480 3481 3482# Misc other measures 3483 3484ENTROPY ENERGY / TEMPERATURE 3485clausius 1e3 cal/K # A unit of physical entropy 3486langley thermcalorie/cm^2 # Used in radiation theory 3487poncelet 100 kg force m / s 3488tonrefrigeration uston 144 btu / lb day # One ton refrigeration is 3489 # the rate of heat extraction required 3490 # turn one ton of water to ice in 3491 # a day. Ice is defined to have a 3492 # latent heat of 144 btu/lb. 3493tonref tonrefrigeration 3494refrigeration tonref / ton 3495frigorie 1000 cal_15 # Used in refrigeration engineering. 3496tnt 1e9 cal_th / ton# So you can write tons tnt. This 3497 # is a defined, not measured, value. 3498airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as 3499 # pressure times air flow. 3500 3501# Nuclear weapon yields 3502 3503davycrocket 10 ton tnt # lightest US tactical nuclear weapon 3504hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb 3505nagasaki 21 kiloton tnt # Plutonium-239 fission bomb 3506fatman nagasaki 3507littleboy hiroshima 3508ivyking 500 kiloton tnt # most powerful fission bomb 3509castlebravo 15 megaton tnt # most powerful US test 3510b53bomb 9 megaton tnt 3511 # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/ 3512trinity 18 kiloton tnt # July 16, 1945 3513gadget trinity 3514 3515# 3516# Permeability: The permeability or permeance, n, of a substance determines 3517# how fast vapor flows through the substance. The formula W = n A dP 3518# holds where W is the rate of flow (in mass/time), n is the permeability, 3519# A is the area of the flow path, and dP is the vapor pressure difference. 3520# 3521 3522perm_0C grain / hr ft^2 inHg 3523perm_zero perm_0C 3524perm_0 perm_0C 3525perm perm_0C 3526perm_23C grain / hr ft^2 in Hg23C 3527perm_twentythree perm_23C 3528 3529# 3530# Counting measures 3531# 3532 3533pair 2 3534brace 2 3535nest 3 # often used for items like bowls that 3536 # nest together 3537hattrick 3 # Used in sports, especially cricket and ice 3538 # hockey to report the number of goals. 3539dicker 10 3540dozen 12 3541bakersdozen 13 3542score 20 3543flock 40 3544timer 40 3545shock 60 3546toncount 100 # Used in sports in the UK 3547longhundred 120 # From a germanic counting system 3548gross 144 3549greatgross 12 gross 3550tithe 1|10 # From Anglo-Saxon word for tenth 3551 3552# Paper counting measure 3553 3554shortquire 24 3555quire 25 3556shortream 480 3557ream 500 3558perfectream 516 3559bundle 2 reams 3560bale 5 bundles 3561 3562# 3563# Paper measures 3564# 3565 3566# USA paper sizes 3567 3568lettersize 8.5 inch 11 inch 3569legalsize 8.5 inch 14 inch 3570ledgersize 11 inch 17 inch 3571executivesize 7.25 inch 10.5 inch 3572Apaper 8.5 inch 11 inch 3573Bpaper 11 inch 17 inch 3574Cpaper 17 inch 22 inch 3575Dpaper 22 inch 34 inch 3576Epaper 34 inch 44 inch 3577 3578# Correspondence envelope sizes. #10 is the standard business 3579# envelope in the USA. 3580 3581envelope6_25size 3.5 inch 6 inch 3582envelope6_75size 3.625 inch 6.5 inch 3583envelope7size 3.75 inch 6.75 inch 3584envelope7_75size 3.875 inch 7.5 inch 3585envelope8_625size 3.625 inch 8.625 inch 3586envelope9size 3.875 inch 8.875 inch 3587envelope10size 4.125 inch 9.5 inch 3588envelope11size 4.5 inch 10.375 inch 3589envelope12size 4.75 inch 11 inch 3590envelope14size 5 inch 11.5 inch 3591envelope16size 6 inch 12 inch 3592 3593# Announcement envelope sizes (no relation to metric paper sizes like A4) 3594 3595envelopeA1size 3.625 inch 5.125 inch # same as 4bar 3596envelopeA2size 4.375 inch 5.75 inch 3597envelopeA6size 4.75 inch 6.5 inch 3598envelopeA7size 5.25 inch 7.25 inch 3599envelopeA8size 5.5 inch 8.125 inch 3600envelopeA9size 5.75 inch 8.75 inch 3601envelopeA10size 6 inch 9.5 inch 3602 3603# Baronial envelopes 3604 3605envelope4bar 3.625 inch 5.125 inch # same as A1 3606envelope5_5bar 4.375 inch 5.75 inch 3607envelope6bar 4.75 inch 6.5 inch 3608 3609# Coin envelopes 3610 3611envelope1baby 2.25 inch 3.5 inch # same as #1 coin 3612envelope00coin 1.6875 inch 2.75 inch 3613envelope1coin 2.25 inch 3.5 inch 3614envelope3coin 2.5 inch 4.25 inch 3615envelope4coin 3 inch 4.5 inch 3616envelope4_5coin 3 inch 4.875 inch 3617envelope5coin 2.875 inch 5.25 inch 3618envelope5_5coin 3.125 inch 5.5 inch 3619envelope6coin 3.375 inch 6 inch 3620envelope7coin 3.5 inch 6.5 inch 3621 3622# The metric paper sizes are defined so that if a sheet is cut in half 3623# along the short direction, the result is two sheets which are 3624# similar to the original sheet. This means that for any metric size, 3625# the long side is close to sqrt(2) times the length of the short 3626# side. Each series of sizes is generated by repeated cuts in half, 3627# with the values rounded down to the nearest millimeter. 3628 3629A0paper 841 mm 1189 mm # The basic size in the A series 3630A1paper 594 mm 841 mm # is defined to have an area of 3631A2paper 420 mm 594 mm # one square meter. 3632A3paper 297 mm 420 mm 3633A4paper 210 mm 297 mm 3634A5paper 148 mm 210 mm 3635A6paper 105 mm 148 mm 3636A7paper 74 mm 105 mm 3637A8paper 52 mm 74 mm 3638A9paper 37 mm 52 mm 3639A10paper 26 mm 37 mm 3640 3641B0paper 1000 mm 1414 mm # The basic B size has an area 3642B1paper 707 mm 1000 mm # of sqrt(2) square meters. 3643B2paper 500 mm 707 mm 3644B3paper 353 mm 500 mm 3645B4paper 250 mm 353 mm 3646B5paper 176 mm 250 mm 3647B6paper 125 mm 176 mm 3648B7paper 88 mm 125 mm 3649B8paper 62 mm 88 mm 3650B9paper 44 mm 62 mm 3651B10paper 31 mm 44 mm 3652 3653C0paper 917 mm 1297 mm # The basic C size has an area 3654C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters. 3655C2paper 458 mm 648 mm 3656C3paper 324 mm 458 mm # Intended for envelope sizes 3657C4paper 229 mm 324 mm 3658C5paper 162 mm 229 mm 3659C6paper 114 mm 162 mm 3660C7paper 81 mm 114 mm 3661C8paper 57 mm 81 mm 3662C9paper 40 mm 57 mm 3663C10paper 28 mm 40 mm 3664 3665# gsm (Grams per Square Meter), a sane, metric paper weight measure 3666 3667gsm grams / meter^2 3668 3669# In the USA, a collection of crazy historical paper measures are used. Paper 3670# is measured as a weight of a ream of that particular type of paper. This is 3671# sometimes called the "substance" or "basis" (as in "substance 20" paper). 3672# The standard sheet size or "basis size" varies depending on the type of 3673# paper. As a result, 20 pound bond paper and 50 pound text paper are actually 3674# about the same weight. The different sheet sizes were historically the most 3675# convenient for printing or folding in the different applications. These 3676# different basis weights are standards maintained by American Society for 3677# Testing Materials (ASTM) and the American Forest and Paper Association 3678# (AF&PA). 3679 3680poundbookpaper lb / 25 inch 38 inch ream 3681lbbook poundbookpaper 3682poundtextpaper poundbookpaper 3683lbtext poundtextpaper 3684poundoffsetpaper poundbookpaper # For offset printing 3685lboffset poundoffsetpaper 3686poundbiblepaper poundbookpaper # Designed to be lightweight, thin, 3687lbbible poundbiblepaper # strong and opaque. 3688poundtagpaper lb / 24 inch 36 inch ream 3689lbtag poundtagpaper 3690poundbagpaper poundtagpaper 3691lbbag poundbagpaper 3692poundnewsprintpaper poundtagpaper 3693lbnewsprint poundnewsprintpaper 3694poundposterpaper poundtagpaper 3695lbposter poundposterpaper 3696poundtissuepaper poundtagpaper 3697lbtissue poundtissuepaper 3698poundwrappingpaper poundtagpaper 3699lbwrapping poundwrappingpaper 3700poundwaxingpaper poundtagpaper 3701lbwaxing poundwaxingpaper 3702poundglassinepaper poundtagpaper 3703lbglassine poundglassinepaper 3704poundcoverpaper lb / 20 inch 26 inch ream 3705lbcover poundcoverpaper 3706poundindexpaper lb / 25.5 inch 30.5 inch ream 3707lbindex poundindexpaper 3708poundindexbristolpaper poundindexpaper 3709lbindexbristol poundindexpaper 3710poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and 3711lbbond poundbondpaper # durable for repeated 3712poundwritingpaper poundbondpaper # filing, and it resists 3713lbwriting poundwritingpaper # ink penetration. 3714poundledgerpaper poundbondpaper 3715lbledger poundledgerpaper 3716poundcopypaper poundbondpaper 3717lbcopy poundcopypaper 3718poundblottingpaper lb / 19 inch 24 inch ream 3719lbblotting poundblottingpaper 3720poundblankspaper lb / 22 inch 28 inch ream 3721lbblanks poundblankspaper 3722poundpostcardpaper lb / 22.5 inch 28.5 inch ream 3723lbpostcard poundpostcardpaper 3724poundweddingbristol poundpostcardpaper 3725lbweddingbristol poundweddingbristol 3726poundbristolpaper poundweddingbristol 3727lbbristol poundbristolpaper 3728poundboxboard lb / 1000 ft^2 3729lbboxboard poundboxboard 3730poundpaperboard poundboxboard 3731lbpaperboard poundpaperboard 3732 3733# When paper is marked in units of M, it means the weight of 1000 sheets of the 3734# given size of paper. To convert this to paper weight, divide by the size of 3735# the paper in question. 3736 3737paperM lb / 1000 3738 3739# In addition paper weight is reported in "caliper" which is simply the 3740# thickness of one sheet, typically in inches. Thickness is also reported in 3741# "points" where a point is 1|1000 inch. These conversions are supplied to 3742# convert these units roughly (using an approximate density) into the standard 3743# paper weight values. 3744 3745pointthickness 0.001 in 3746paperdensity 0.8 g/cm^3 # approximate--paper densities vary! 3747papercaliper in paperdensity 3748paperpoint pointthickness paperdensity 3749 3750# 3751# Printing 3752# 3753 3754fournierpoint 0.1648 inch / 12 # First definition of the printers 3755 # point made by Pierre Fournier who 3756 # defined it in 1737 as 1|12 of a 3757 # cicero which was 0.1648 inches. 3758olddidotpoint 1|72 frenchinch # François Ambroise Didot, one of 3759 # a family of printers, changed 3760 # Fournier's definition around 1770 3761 # to fit to the French units then in 3762 # use. 3763bertholdpoint 1|2660 m # H. Berthold tried to create a 3764 # metric version of the didot point 3765 # in 1878. 3766INpoint 0.4 mm # This point was created by a 3767 # group directed by Fermin Didot in 3768 # 1881 and is associated with the 3769 # imprimerie nationale. It doesn't 3770 # seem to have been used much. 3771germandidotpoint 0.376065 mm # Exact definition appears in DIN 3772 # 16507, a German standards document 3773 # of 1954. Adopted more broadly in 3774 # 1966 by ??? 3775metricpoint 3|8 mm # Proposed in 1977 by Eurograf 3776oldpoint 1|72.27 inch # The American point was invented 3777printerspoint oldpoint # by Nelson Hawks in 1879 and 3778texpoint oldpoint # dominates USA publishing. 3779 # It was standardized by the American 3780 # Typefounders Association at the 3781 # value of 0.013837 inches exactly. 3782 # Knuth uses the approximation given 3783 # here (which is very close). The 3784 # comp.fonts FAQ claims that this 3785 # value is supposed to be 1|12 of a 3786 # pica where 83 picas is equal to 35 3787 # cm. But this value differs from 3788 # the standard. 3789texscaledpoint 1|65536 texpoint # The TeX typesetting system uses 3790texsp texscaledpoint # this for all computations. 3791computerpoint 1|72 inch # The American point was rounded 3792point computerpoint 3793computerpica 12 computerpoint # to an even 1|72 inch by computer 3794postscriptpoint computerpoint # people at some point. 3795pspoint postscriptpoint 3796twip 1|20 point # TWentieth of an Imperial Point 3797Q 1|4 mm # Used in Japanese phototypesetting 3798 # Q is for quarter 3799frenchprinterspoint olddidotpoint 3800didotpoint germandidotpoint # This seems to be the dominant value 3801europeanpoint didotpoint # for the point used in Europe 3802cicero 12 didotpoint 3803 3804stick 2 inches 3805 3806# Type sizes 3807 3808excelsior 3 oldpoint 3809brilliant 3.5 oldpoint 3810diamondtype 4 oldpoint 3811pearl 5 oldpoint 3812agate 5.5 oldpoint # Originally agate type was 14 lines per 3813 # inch, giving a value of 1|14 in. 3814ruby agate # British 3815nonpareil 6 oldpoint 3816mignonette 6.5 oldpoint 3817emerald mignonette # British 3818minion 7 oldpoint 3819brevier 8 oldpoint 3820bourgeois 9 oldpoint 3821longprimer 10 oldpoint 3822smallpica 11 oldpoint 3823pica 12 oldpoint 3824english 14 oldpoint 3825columbian 16 oldpoint 3826greatprimer 18 oldpoint 3827paragon 20 oldpoint 3828meridian 44 oldpoint 3829canon 48 oldpoint 3830 3831# German type sizes 3832 3833nonplusultra 2 didotpoint 3834brillant 3 didotpoint 3835diamant 4 didotpoint 3836perl 5 didotpoint 3837nonpareille 6 didotpoint 3838kolonel 7 didotpoint 3839petit 8 didotpoint 3840borgis 9 didotpoint 3841korpus 10 didotpoint 3842corpus korpus 3843garamond korpus 3844mittel 14 didotpoint 3845tertia 16 didotpoint 3846text 18 didotpoint 3847kleine_kanon 32 didotpoint 3848kanon 36 didotpoint 3849grobe_kanon 42 didotpoint 3850missal 48 didotpoint 3851kleine_sabon 72 didotpoint 3852grobe_sabon 84 didotpoint 3853 3854# 3855# Information theory units. Note that the name "entropy" is used both 3856# to measure information and as a physical quantity. 3857# 3858 3859INFORMATION bit 3860 3861nat (1/ln(2)) bits # Entropy measured base e 3862hartley log2(10) bits # Entropy of a uniformly 3863ban hartley # distributed random variable 3864 # over 10 symbols. 3865dit hartley # from Decimal digIT 3866 3867# 3868# Computer 3869# 3870 3871bps bit/sec # Sometimes the term "baud" is 3872 # incorrectly used to refer to 3873 # bits per second. Baud refers 3874 # to symbols per second. Modern 3875 # modems transmit several bits 3876 # per symbol. 3877byte 8 bit # Not all machines had 8 bit 3878B byte # bytes, but these days most of 3879 # them do. But beware: for 3880 # transmission over modems, a 3881 # few extra bits are used so 3882 # there are actually 10 bits per 3883 # byte. 3884octet 8 bits # The octet is always 8 bits 3885nybble 4 bits # Half of a byte. Sometimes 3886 # equal to different lengths 3887 # such as 3 bits. 3888nibble nybble 3889nyp 2 bits # Donald Knuth asks in an exercise 3890 # for a name for a 2 bit 3891 # quantity and gives the "nyp" 3892 # as a solution due to Gregor 3893 # Purdy. Not in common use. 3894meg megabyte # Some people consider these 3895 # units along with the kilobyte 3896gig gigabyte # to be defined according to 3897 # powers of 2 with the kilobyte 3898 # equal to 2^10 bytes, the 3899 # megabyte equal to 2^20 bytes and 3900 # the gigabyte equal to 2^30 bytes 3901 # but these usages are forbidden 3902 # by SI. Binary prefixes have 3903 # been defined by IEC to replace 3904 # the SI prefixes. Use them to 3905 # get the binary values: KiB, MiB, 3906 # and GiB. 3907jiffy 0.01 sec # This is defined in the Jargon File 3908jiffies jiffy # (http://www.jargon.org) as being the 3909 # duration of a clock tick for measuring 3910 # wall-clock time. Supposedly the value 3911 # used to be 1|60 sec or 1|50 sec 3912 # depending on the frequency of AC power, 3913 # but then 1|100 sec became more common. 3914 # On linux systems, this term is used and 3915 # for the Intel based chips, it does have 3916 # the value of .01 sec. The Jargon File 3917 # also lists two other definitions: 3918 # millisecond, and the time taken for 3919 # light to travel one foot. 3920cdaudiospeed 44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2 3921 # samples of sixteen bits each. 3922cdromspeed 75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read 3923 # each second with 2048 bytes per sector. 3924 # Audio CDs do not have sectors, but 3925 # people sometimes divide the bit rate by 3926 # 75 and claim a sector length of 2352. 3927 # Data CDs have a lower rate due to 3928 # increased error correction overhead. 3929 # There is a rarely used mode (mode2) with 3930 # 2336 bytes per sector that has fewer 3931 # error correction bits than mode1. 3932dvdspeed 1385 kB/s # This is the "1x" speed of a DVD using 3933 # constant linear velocity (CLV) mode. 3934 # Modern DVDs may vary the linear velocity 3935 # as they go from the inside to the 3936 # outside of the disc. 3937 # See http://www.osta.org/technology/dvdqa/dvdqa4.htm 3938# 3939# The IP address space is divided into subnets. The number of hosts 3940# in a subnet depends on the length of the subnet prefix. This is 3941# often written as /N where N is the number of bits in the prefix. 3942# 3943# https://en.wikipedia.org/wiki/Subnetwork 3944# 3945# These definitions gives the number of hosts for a subnet whose 3946# prefix has the specified length in bits. 3947# 3948 3949ipv4subnetsize(prefix_len) units=[1;1] domain=[0,32] range=[1,4294967296] \ 3950 2^(32-prefix_len) ; 32-log2(ipv4subnetsize) 3951ipv4classA ipv4subnetsize(8) 3952ipv4classB ipv4subnetsize(16) 3953ipv4classC ipv4subnetsize(24) 3954 3955ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \ 3956 range=[1,340282366920938463463374607431768211456] \ 3957 2^(128-prefix_len) ; 128-log2(ipv6subnetsize) 3958 3959# 3960# Musical measures. Musical intervals expressed as ratios. Multiply 3961# two intervals together to get the sum of the interval. The function 3962# musicalcent can be used to convert ratios to cents. 3963# 3964 3965# Perfect intervals 3966 3967octave 2 3968majorsecond musicalfifth^2 / octave 3969majorthird 5|4 3970minorthird 6|5 3971musicalfourth 4|3 3972musicalfifth 3|2 3973majorsixth musicalfourth majorthird 3974minorsixth musicalfourth minorthird 3975majorseventh musicalfifth majorthird 3976minorseventh musicalfifth minorthird 3977 3978pythagoreanthird majorsecond musicalfifth^2 / octave 3979syntoniccomma pythagoreanthird / majorthird 3980pythagoreancomma musicalfifth^12 / octave^7 3981 3982# Equal tempered definitions 3983 3984semitone octave^(1|12) 3985musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \ 3986 100 log(musicalcent)/log(semitone) 3987 3988# 3989# Musical note lengths. 3990# 3991 3992wholenote ! 3993MUSICAL_NOTE_LENGTH wholenote 3994halfnote 1|2 wholenote 3995quarternote 1|4 wholenote 3996eighthnote 1|8 wholenote 3997sixteenthnote 1|16 wholenote 3998thirtysecondnote 1|32 wholenote 3999sixtyfourthnote 1|64 wholenote 4000dotted 3|2 4001doubledotted 7|4 4002breve doublewholenote 4003semibreve wholenote 4004minimnote halfnote 4005crotchet quarternote 4006quaver eighthnote 4007semiquaver sixteenthnote 4008demisemiquaver thirtysecondnote 4009hemidemisemiquaver sixtyfourthnote 4010semidemisemiquaver hemidemisemiquaver 4011 4012# 4013# yarn and cloth measures 4014# 4015 4016# yarn linear density 4017 4018woolyarnrun 1600 yard/pound # 1600 yds of "number 1 yarn" weighs 4019 # a pound. 4020yarncut 300 yard/pound # Less common system used in 4021 # Pennsylvania for wool yarn 4022cottonyarncount 840 yard/pound 4023linenyarncount 300 yard/pound # Also used for hemp and ramie 4024worstedyarncount 1680 ft/pound 4025metricyarncount meter/gram 4026denier 1|9 tex # used for silk and rayon 4027manchesteryarnnumber drams/1000 yards # old system used for silk 4028pli lb/in 4029typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound 4030asbestoscut 100 yd/lb # used for glass and asbestos yarn 4031 4032tex gram / km # rational metric yarn measure, meant 4033drex 0.1 tex # to be used for any kind of yarn 4034poumar lb / 1e6 yard 4035 4036# yarn and cloth length 4037 4038skeincotton 80*54 inch # 80 turns of thread on a reel with a 4039 # 54 in circumference (varies for other 4040 # kinds of thread) 4041cottonbolt 120 ft # cloth measurement 4042woolbolt 210 ft 4043bolt cottonbolt 4044heer 600 yards 4045cut 300 yards # used for wet-spun linen yarn 4046lea 300 yards 4047 4048sailmakersyard 28.5 in 4049sailmakersounce oz / sailmakersyard 36 inch 4050 4051silkmomme momme / 25 yards 1.49 inch # Traditional silk weight 4052silkmm silkmomme # But it is also defined as 4053 # lb/100 yd 45 inch. The two 4054 # definitions are slightly different 4055 # and neither one seems likely to be 4056 # the true source definition. 4057 4058# 4059# drug dosage 4060# 4061 4062mcg microgram # Frequently used for vitamins 4063iudiptheria 62.8 microgram # IU is for international unit 4064iupenicillin 0.6 microgram 4065iuinsulin 41.67 microgram 4066drop 1|20 ml # The drop was an old "unit" that was 4067 # replaced by the minim. But I was 4068 # told by a pharmacist that in his 4069 # profession, the conversion of 20 4070 # drops per ml is actually used. 4071bloodunit 450 ml # For whole blood. For blood 4072 # components, a blood unit is the 4073 # quanity of the component found in a 4074 # blood unit of whole blood. The 4075 # human body contains about 12 blood 4076 # units of whole blood. 4077 4078# 4079# misc medical measure 4080# 4081 4082frenchcathetersize 1|3 mm # measure used for the outer diameter 4083 # of a catheter 4084charriere frenchcathetersize 4085 4086 4087# 4088# fixup units for times when prefix handling doesn't do the job 4089# 4090 4091hectare hectoare 4092megohm megaohm 4093kilohm kiloohm 4094microhm microohm 4095megalerg megaerg # 'L' added to make it pronounceable [18]. 4096 4097# 4098# Money 4099# 4100# Note that US$ is the primitive unit so other currencies are 4101# generally given in US$. 4102# 4103 4104usdollar US$ 4105$ dollar 4106mark germanymark 4107bolivar venezuelabolivar 4108venezuelanbolivarfuerte venezuelabolivar 4109bolivarfuerte bolivar # The currency was revalued by 4110oldbolivar 1|1000 bolivar # a factor of 1000. 4111peseta spainpeseta 4112rand southafricarand 4113escudo portugalescudo 4114guilder netherlandsguilder 4115hollandguilder netherlandsguilder 4116peso mexicopeso 4117yen japanyen 4118lira italylira 4119rupee indiarupee 4120drachma greecedrachma 4121franc francefranc 4122markka finlandmarkka 4123britainpound unitedkingdompound 4124greatbritainpound unitedkingdompound 4125unitedkingdompound ukpound 4126poundsterling britainpound 4127yuan chinayuan 4128 4129# Unicode Currency Names 4130 4131!utf8 4132icelandkróna icelandkrona 4133polandzłoty polandzloty 4134tongapa’anga tongapa'anga 4135venezuelabolívar venezuelabolivar 4136vietnamđồng vietnamdong 4137mongoliatögrög mongoliatugrik 4138sãotomé&príncipedobra saotome&principedobra 4139!endutf8 4140 4141UKP GBP # Not an ISO code, but looks like one, and 4142 # sometimes used on usenet. 4143 4144!include currency.units 4145 4146# Money on the gold standard, used in the late 19th century and early 4147# 20th century. 4148 4149olddollargold 23.22 grains goldprice # Used until 1934 4150newdollargold 96|7 grains goldprice # After Jan 31, 1934 4151dollargold newdollargold 4152poundgold 113 grains goldprice # British pound 4153 4154# Precious metals 4155 4156goldounce goldprice troyounce 4157silverounce silverprice troyounce 4158platinumounce platinumprice troyounce 4159XAU goldounce 4160XPT platinumounce 4161XAG silverounce 4162 4163# Nominal masses of US coins. Note that dimes, quarters and half dollars 4164# have weight proportional to value. Before 1965 it was $40 / kg. 4165 4166USpennyweight 2.5 grams # Since 1982, 48 grains before 4167USnickelweight 5 grams 4168USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965 4169USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965 4170UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971 4171USdollarweight 8.1 grams # Weight of Susan B. Anthony and 4172 # Sacagawea dollar coins 4173 4174# British currency 4175 4176quid britainpound # Slang names 4177fiver 5 quid 4178tenner 10 quid 4179monkey 500 quid 4180brgrand 1000 quid 4181bob shilling 4182 4183shilling 1|20 britainpound # Before decimalisation, there 4184oldpence 1|12 shilling # were 20 shillings to a pound, 4185farthing 1|4 oldpence # each of twelve old pence 4186guinea 21 shilling # Still used in horse racing 4187crown 5 shilling 4188florin 2 shilling 4189groat 4 oldpence 4190tanner 6 oldpence 4191brpenny 0.01 britainpound 4192pence brpenny 4193tuppence 2 pence 4194tuppenny tuppence 4195ha'penny halfbrpenny 4196hapenny ha'penny 4197oldpenny oldpence 4198oldtuppence 2 oldpence 4199oldtuppenny oldtuppence 4200threepence 3 oldpence # threepence never refers to new money 4201threepenny threepence 4202oldthreepence threepence 4203oldthreepenny threepence 4204oldhalfpenny halfoldpenny 4205oldha'penny oldhalfpenny 4206oldhapenny oldha'penny 4207brpony 25 britainpound 4208 4209# Canadian currency 4210 4211loony 1 canadadollar # This coin depicts a loon 4212toony 2 canadadollar 4213 4214# Cryptocurrency 4215 4216satoshi 1e-8 bitcoin 4217XBT bitcoin # nonstandard code 4218 4219# 4220# Units used for measuring volume of wood 4221# 4222 4223cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood 4224facecord 1|2 cord 4225cordfoot 1|8 cord # One foot long section of a cord 4226cordfeet cordfoot 4227housecord 1|3 cord # Used to sell firewood for residences, 4228 # often confusingly called a "cord" 4229boardfoot ft^2 inch # Usually 1 inch thick wood 4230boardfeet boardfoot 4231fbm boardfoot # feet board measure 4232stack 4 yard^3 # British, used for firewood and coal [18] 4233rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly 4234 # sometimes called a face cord, but this 4235 # value is equal to 1|3 cord. Name 4236 # comes from an old Norse word for a 4237 # stack of wood. 4238stere m^3 4239timberfoot ft^3 # Used for measuring solid blocks of wood 4240standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or 4241 # Pittsburg standard. Apparently the 4242 # term is short for "standard hundred" 4243 # which was meant to refer to 100 pieces 4244 # of wood (deals). However, this 4245 # particular standard is equal to 120 4246 # deals which are 12 ft by 11 in by 1.5 4247 # inches (not the standard deal). 4248hoppusfoot (4/pi) ft^3 # Volume calculation suggested in 1736 4249hoppusboardfoot 1|12 hoppusfoot # forestry manual by Edward Hoppus, for 4250hoppuston 50 hoppusfoot # estimating the usable volume of a log. 4251 # It results from computing the volume 4252 # of a cylindrical log of length, L, and 4253 # girth (circumference), G, by V=L(G/4)^2. 4254 # The hoppus ton is apparently still in 4255 # use for shipments from Southeast Asia. 4256 4257# In Britain, the deal is apparently any piece of wood over 6 feet long, over 4258# 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece 4259# of wood less than 7 inches wide is called a "batten". This unit is now used 4260# exclusively for fir and pine. 4261 4262deal 12 ft 11 in 2.5 in # The standard North American deal [OED] 4263wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard 4264 # deal it's called a "whole deal"! 4265splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal. 4266 4267 4268# Used for shellac mixing rate 4269 4270poundcut pound / gallon 4271lbcut poundcut 4272 4273# 4274# Gas and Liquid flow units 4275# 4276 4277FLUID_FLOW VOLUME / TIME 4278 4279# Some obvious volumetric gas flow units (cu is short for cubic) 4280 4281cumec m^3/s 4282cusec ft^3/s 4283 4284# Conventional abbreviations for fluid flow units 4285 4286gph gal/hr 4287gpm gal/min 4288mgd megagal/day 4289cfs ft^3/s 4290cfh ft^3/hour 4291cfm ft^3/min 4292lpm liter/min 4293lfm ft/min # Used to report air flow produced by fans. 4294 # Multiply by cross sectional area to get a 4295 # flow in cfm. 4296 4297pru mmHg / (ml/min) # peripheral resistance unit, used in 4298 # medicine to assess blood flow in 4299 # the capillaries. 4300 4301# Miner's inch: This is an old historic unit used in the Western United 4302# States. It is generally defined as the rate of flow through a one square 4303# inch hole at a specified depth such as 4 inches. In the late 19th century, 4304# volume of water was sometimes measured in the "24 hour inch". Values for the 4305# miner's inch were fixed by state statues. (This information is from a web 4306# site operated by the Nevada Division of Water Planning: The Water Words 4307# Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.) 4308 4309minersinchAZ 1.5 ft^3/min 4310minersinchCA 1.5 ft^3/min 4311minersinchMT 1.5 ft^3/min 4312minersinchNV 1.5 ft^3/min 4313minersinchOR 1.5 ft^3/min 4314minersinchID 1.2 ft^3/min 4315minersinchKS 1.2 ft^3/min 4316minersinchNE 1.2 ft^3/min 4317minersinchNM 1.2 ft^3/min 4318minersinchND 1.2 ft^3/min 4319minersinchSD 1.2 ft^3/min 4320minersinchUT 1.2 ft^3/min 4321minersinchCO 1 ft^3/sec / 38.4 # 38.4 miner's inches = 1 ft^3/sec 4322minersinchBC 1.68 ft^3/min # British Columbia 4323 4324# Oceanographic flow 4325 4326sverdrup 1e6 m^3 / sec # Used to express flow of ocean 4327 # currents. Named after Norwegian 4328 # oceanographer H. Sverdrup. 4329 4330# In vacuum science and some other applications, gas flow is measured 4331# as the product of volumetric flow and pressure. This is useful 4332# because it makes it easy to compare with the flow at standard 4333# pressure (one atmosphere). It also directly relates to the number 4334# of gas molecules per unit time, and hence to the mass flow if the 4335# molecular mass is known. 4336 4337GAS_FLOW PRESSURE FLUID_FLOW 4338 4339sccm atm cc/min # 's' is for "standard" to indicate 4340sccs atm cc/sec # flow at standard pressure 4341scfh atm ft^3/hour # 4342scfm atm ft^3/min 4343slpm atm liter/min 4344slph atm liter/hour 4345lusec liter micron Hg / s # Used in vacuum science 4346 4347# US Standard Atmosphere (1976) 4348# Atmospheric temperature and pressure vs. geometric height above sea level 4349# This definition covers only the troposphere (the lowest atmospheric 4350# layer, up to 11 km), and assumes the layer is polytropic. 4351# A polytropic process is one for which PV^k = const, where P is the 4352# pressure, V is the volume, and k is the polytropic exponent. The 4353# polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article 4354# https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse 4355# the definitions of "exponent" and "index." The functions below assume 4356# the following parameters: 4357 4358# temperature lapse rate, -dT/dz, in troposphere 4359 4360lapserate 6.5 K/km # US Std Atm (1976) 4361 4362# air molecular weight, including constituent mol wt, given 4363# in Table 3, p. 3 4364 4365air_1976 78.084 % 28.0134 \ 4366 + 20.9476 % 31.9988 \ 4367 + 9340 ppm 39.948 \ 4368 + 314 ppm 44.00995 \ 4369 + 18.18 ppm 20.183 \ 4370 + 5.24 ppm 4.0026 \ 4371 + 2 ppm 16.04303 \ 4372 + 1.14 ppm 83.80 \ 4373 + 0.55 ppm 2.01594 \ 4374 + 0.087 ppm 131.30 4375 4376# universal gas constant 4377R_1976 8.31432e3 N m/(kmol K) 4378 4379# polytropic index n 4380polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1 4381 4382# If desired, redefine using current values for air mol wt and R 4383 4384polyndx polyndx_1976 4385# polyndx air (kg/kmol) gravity/(R lapserate) - 1 4386 4387# for comparison with various references 4388 4389polyexpnt (polyndx + 1) / polyndx 4390 4391# The model assumes the following reference values: 4392# sea-level temperature and pressure 4393 4394stdatmT0 288.15 K 4395stdatmP0 atm 4396 4397# "effective radius" for relation of geometric to geopotential height, 4398# at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no 4399# relation to actual radius 4400 4401earthradUSAtm 6356766 m 4402 4403# Temperature vs. geopotential height h 4404# Assumes 15 degC at sea level 4405# Based on approx 45 deg latitude 4406# Lower limits of domain and upper limits of range are those of the 4407# tables in US Standard Atmosphere (NASA 1976) 4408 4409stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \ 4410 stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate 4411 4412# Temperature vs. geometric height z; based on approx 45 deg latitude 4413stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \ 4414 stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT)) 4415 4416# Pressure vs. geopotential height h 4417# Assumes 15 degC and 101325 Pa at sea level 4418# Based on approx 45 deg latitude 4419# Lower limits of domain and upper limits of range are those of the 4420# tables in US Standard Atmosphere (NASA 1976) 4421 4422stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \ 4423 atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \ 4424 (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1)))) 4425 4426# Pressure vs. geometric height z; based on approx 45 deg latitude 4427stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \ 4428 stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP)) 4429 4430# Geopotential height from geometric height 4431# Based on approx 45 deg latitude 4432# Lower limits of domain and range are somewhat arbitrary; they 4433# correspond to the limits in the US Std Atm tables 4434 4435geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \ 4436 (earthradUSAtm z) / (earthradUSAtm + z) ; \ 4437 (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht)) 4438 4439# The standard value for the sea-level acceleration due to gravity is 4440# 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949) 4441# R_eff = 2 g_phi / denom 4442# g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) 4443# or 4444# g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) 4445# denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?) 4446# There is no inverse function; the standard value applies at a latitude 4447# of about 45.543 deg 4448 4449g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \ 4450 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2 4451 4452# effective Earth radius for relation of geometric height to 4453# geopotential height, as function of latitude (Harrison 1949) 4454 4455earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \ 4456 m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \ 4457 (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat)) 4458 4459# References 4460# Harrison, L.P. 1949. Relation Between Geopotential and Geometric 4461# Height. In Smithsonian Meteorological Tables. List, Robert J., ed. 4462# 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution. 4463# NASA. US National Aeronautics and Space Administration. 1976. 4464# US Standard Atmosphere 1976. Washington, DC: US Government Printing Office. 4465 4466# Gauge pressure functions 4467# 4468# Gauge pressure is measured relative to atmospheric pressure. In the English 4469# system, where pressure is often given in pounds per square inch, gauge 4470# pressure is often indicated by 'psig' to distinguish it from absolute 4471# pressure, often indicated by 'psia'. At the standard atmospheric pressure 4472# of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696 4473# psia; an automobile tire inflated to 31 psig has an absolute pressure of 4474# 45.696 psia. 4475# 4476# With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5 4477# bar)); with psig(), the units are taken as psi, so the example above of tire 4478# pressure could be given as psig(31). 4479# 4480# If the normal elevation is significantly different from sea level, change 4481# Patm appropriately, and adjust the lower domain limit on the gaugepressure 4482# definition. 4483 4484Patm atm 4485 4486gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \ 4487 x + Patm ; gaugepressure+(-Patm) 4488 4489psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \ 4490 gaugepressure(x psi) ; ~gaugepressure(psig) / psi 4491 4492 4493# Pressure for underwater diving 4494 4495seawater 0.1 bar / meter 4496msw meter seawater 4497fsw foot seawater 4498 4499# 4500# Wire Gauge 4501# 4502# This area is a nightmare with huge charts of wire gauge diameters 4503# that usually have no clear origin. There are at least 5 competing wire gauge 4504# systems to add to the confusion. The use of wire gauge is related to the 4505# manufacturing method: a metal rod is heated and drawn through a hole. The 4506# size change can't be too big. To get smaller wires, the process is repeated 4507# with a series of smaller holes. Generally larger gauges mean smaller wires. 4508# The gauges often have values such as "00" and "000" which are larger sizes 4509# than simply "0" gauge. In the tables that appear below, these gauges must be 4510# specified as negative numbers (e.g. "00" is -1, "000" is -2, etc). 4511# Alternatively, you can use the following units: 4512# 4513 4514g00 (-1) 4515g000 (-2) 4516g0000 (-3) 4517g00000 (-4) 4518g000000 (-5) 4519g0000000 (-6) 4520 4521# American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most 4522# important gauge. ASTM B-258 specifies that this gauge is based on geometric 4523# interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36 4524# which is 0.005 inches exactly. Therefore, the diameter in inches of a wire 4525# is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close 4526# to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the 4527# repeated zero values, use negative numbers in the formula. The same document 4528# also specifies rounding rules which seem to be ignored by makers of tables. 4529# Gauges up to 44 are to be specified with up to 4 significant figures, but no 4530# closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the 4531# nearest 0.00001 inch. 4532# 4533# In addition to being used to measure wire thickness, this gauge is used to 4534# measure the thickness of sheets of aluminum, copper, and most metals other 4535# than steel, iron and zinc. 4536 4537wiregauge(g) units=[1;m] range=(0,) \ 4538 1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92) 4539awg() wiregauge 4540 4541# Next we have the SWG, the Imperial or British Standard Wire Gauge. This one 4542# is piecewise linear. It was used for aluminum sheets. 4543 4544brwiregauge[in] \ 4545 -6 0.5 \ 4546 -5 0.464 \ 4547 -3 0.4 \ 4548 -2 0.372 \ 4549 3 0.252 \ 4550 6 0.192 \ 4551 10 0.128 \ 4552 14 0.08 \ 4553 19 0.04 \ 4554 23 0.024 \ 4555 26 0.018 \ 4556 28 0.0148 \ 4557 30 0.0124 \ 4558 39 0.0052 \ 4559 49 0.0012 \ 4560 50 0.001 4561 4562# The following is from the Appendix to ASTM B 258 4563# 4564# For example, in U.S. gage, the standard for sheet metal is based on the 4565# weight of the metal, not on the thickness. 16-gage is listed as 4566# approximately .0625 inch thick and 40 ounces per square foot (the original 4567# standard was based on wrought iron at .2778 pounds per cubic inch; steel 4568# has almost entirely superseded wrought iron for sheet use, at .2833 pounds 4569# per cubic inch). Smaller numbers refer to greater thickness. There is no 4570# formula for converting gage to thickness or weight. 4571# 4572# It's rather unclear from the passage above whether the plate gauge values are 4573# therefore wrong if steel is being used. Reference [15] states that steel is 4574# in fact measured using this gauge (under the name Manufacturers' Standard 4575# Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel. 4576# But this doesn't seem to be the correct density of steel (.2833 lb/in3 is 4577# closer). 4578# 4579# This gauge was established in 1893 for purposes of taxation. 4580 4581# Old plate gauge for iron 4582 4583plategauge[(oz/ft^2)/(480*lb/ft^3)] \ 4584 -5 300 \ 4585 1 180 \ 4586 14 50 \ 4587 16 40 \ 4588 17 36 \ 4589 20 24 \ 4590 26 12 \ 4591 31 7 \ 4592 36 4.5 \ 4593 38 4 4594 4595# Manufacturers Standard Gage 4596 4597stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \ 4598 -5 300 \ 4599 1 180 \ 4600 14 50 \ 4601 16 40 \ 4602 17 36 \ 4603 20 24 \ 4604 26 12 \ 4605 31 7 \ 4606 36 4.5 \ 4607 38 4 4608 4609# A special gauge is used for zinc sheet metal. Notice that larger gauges 4610# indicate thicker sheets. 4611 4612zincgauge[in] \ 4613 1 0.002 \ 4614 10 0.02 \ 4615 15 0.04 \ 4616 19 0.06 \ 4617 23 0.1 \ 4618 24 0.125 \ 4619 27 0.5 \ 4620 28 1 4621 4622# 4623# Imperial drill bit sizes are reported in inches or in a numerical or 4624# letter gauge. 4625# 4626 4627drillgauge[in] \ 4628 1 0.2280 \ 4629 2 0.2210 \ 4630 3 0.2130 \ 4631 4 0.2090 \ 4632 5 0.2055 \ 4633 6 0.2040 \ 4634 7 0.2010 \ 4635 8 0.1990 \ 4636 9 0.1960 \ 4637 10 0.1935 \ 4638 11 0.1910 \ 4639 12 0.1890 \ 4640 13 0.1850 \ 4641 14 0.1820 \ 4642 15 0.1800 \ 4643 16 0.1770 \ 4644 17 0.1730 \ 4645 18 0.1695 \ 4646 19 0.1660 \ 4647 20 0.1610 \ 4648 22 0.1570 \ 4649 23 0.1540 \ 4650 24 0.1520 \ 4651 25 0.1495 \ 4652 26 0.1470 \ 4653 27 0.1440 \ 4654 28 0.1405 \ 4655 29 0.1360 \ 4656 30 0.1285 \ 4657 31 0.1200 \ 4658 32 0.1160 \ 4659 33 0.1130 \ 4660 34 0.1110 \ 4661 35 0.1100 \ 4662 36 0.1065 \ 4663 38 0.1015 \ 4664 39 0.0995 \ 4665 40 0.0980 \ 4666 41 0.0960 \ 4667 42 0.0935 \ 4668 43 0.0890 \ 4669 44 0.0860 \ 4670 45 0.0820 \ 4671 46 0.0810 \ 4672 48 0.0760 \ 4673 51 0.0670 \ 4674 52 0.0635 \ 4675 53 0.0595 \ 4676 54 0.0550 \ 4677 55 0.0520 \ 4678 56 0.0465 \ 4679 57 0.0430 \ 4680 65 0.0350 \ 4681 66 0.0330 \ 4682 68 0.0310 \ 4683 69 0.0292 \ 4684 70 0.0280 \ 4685 71 0.0260 \ 4686 73 0.0240 \ 4687 74 0.0225 \ 4688 75 0.0210 \ 4689 76 0.0200 \ 4690 78 0.0160 \ 4691 79 0.0145 \ 4692 80 0.0135 \ 4693 88 0.0095 \ 4694 104 0.0031 4695 4696drillA 0.234 in 4697drillB 0.238 in 4698drillC 0.242 in 4699drillD 0.246 in 4700drillE 0.250 in 4701drillF 0.257 in 4702drillG 0.261 in 4703drillH 0.266 in 4704drillI 0.272 in 4705drillJ 0.277 in 4706drillK 0.281 in 4707drillL 0.290 in 4708drillM 0.295 in 4709drillN 0.302 in 4710drillO 0.316 in 4711drillP 0.323 in 4712drillQ 0.332 in 4713drillR 0.339 in 4714drillS 0.348 in 4715drillT 0.358 in 4716drillU 0.368 in 4717drillV 0.377 in 4718drillW 0.386 in 4719drillX 0.397 in 4720drillY 0.404 in 4721drillZ 0.413 in 4722 4723# 4724# Screw sizes 4725# 4726# In the USA, screw diameters for both wood screws and machine screws 4727# are reported using a gauge number. Metric machine screws are 4728# reported as Mxx where xx is the diameter in mm. 4729# 4730 4731screwgauge(g) units=[1;m] range=[0,) \ 4732 (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013 4733 4734# 4735# Abrasive grit size 4736# 4737# Standards governing abrasive grit sizes are complicated, specifying 4738# fractions of particles that are passed or retained by different mesh 4739# sizes. As a result, it is not possible to make precise comparisons 4740# of different grit standards. The tables below allow the 4741# determination of rough equivlants by using median particle size. 4742# 4743# Standards in the USA are determined by the Unified Abrasives 4744# Manufacturers' Association (UAMA), which resulted from the merger of 4745# several previous organizations. One of the old organizations was 4746# CAMI (Coated Abrasives Manufacturers' Institute). 4747# 4748# UAMA has a web page with plots showing abrasive particle ranges for 4749# various different grits and comparisons between standards. 4750# 4751# http://www.uama.org/Abrasives101/101Standards.html 4752# 4753# Abrasives are grouped into "bonded" abrasives for use with grinding 4754# wheels and "coated" abrasives for sandpapers and abrasive films. 4755# The industry uses different grit standards for these two 4756# categories. 4757# 4758# Another division is between "macrogrits", grits below 240 and 4759# "microgrits", which are above 240. Standards differ, as do methods 4760# for determining particle size. In the USA, ANSI B74.12 is the 4761# standard governing macrogrits. ANSI B74.10 covers bonded microgrit 4762# abrasives, and ANSI B74.18 covers coated microgrit abrasives. It 4763# appears that the coated standard is identical to the bonded standard 4764# for grits up through 600 but then diverges significantly. 4765# 4766# European grit sizes are determined by the Federation of European 4767# Producers of Abrasives. http://www.fepa-abrasives.org 4768# 4769# They give two standards, the "F" grit for bonded abrasives and the 4770# "P" grit for coated abrasives. This data is taken directly from 4771# their web page. 4772 4773# FEPA P grit for coated abrasives is commonly seen on sandpaper in 4774# the USA where the paper will be marked P600, for example. FEPA P 4775# grits are said to be more tightly constrained than comparable ANSI 4776# grits so that the particles are more uniform in size and hence give 4777# a better finish. 4778 4779grit_P[micron] \ 4780 12 1815 \ 4781 16 1324 \ 4782 20 1000 \ 4783 24 764 \ 4784 30 642 \ 4785 36 538 \ 4786 40 425 \ 4787 50 336 \ 4788 60 269 \ 4789 80 201 \ 4790 100 162 \ 4791 120 125 \ 4792 150 100 \ 4793 180 82 \ 4794 220 68 \ 4795 240 58.5 \ 4796 280 52.2 \ 4797 320 46.2 \ 4798 360 40.5 \ 4799 400 35 \ 4800 500 30.2 \ 4801 600 25.8 \ 4802 800 21.8 \ 4803 1000 18.3 \ 4804 1200 15.3 \ 4805 1500 12.6 \ 4806 2000 10.3 \ 4807 2500 8.4 4808 4809# The F grit is the European standard for bonded abrasives such as 4810# grinding wheels 4811 4812grit_F[micron] \ 4813 4 4890 \ 4814 5 4125 \ 4815 6 3460 \ 4816 7 2900 \ 4817 8 2460 \ 4818 10 2085 \ 4819 12 1765 \ 4820 14 1470 \ 4821 16 1230 \ 4822 20 1040 \ 4823 22 885 \ 4824 24 745 \ 4825 30 625 \ 4826 36 525 \ 4827 40 438 \ 4828 46 370 \ 4829 54 310 \ 4830 60 260 \ 4831 70 218 \ 4832 80 185 \ 4833 90 154 \ 4834 100 129 \ 4835 120 109 \ 4836 150 82 \ 4837 180 69 \ 4838 220 58 \ 4839 230 53 \ 4840 240 44.5 \ 4841 280 36.5 \ 4842 320 29.2 \ 4843 360 22.8 \ 4844 400 17.3 \ 4845 500 12.8 \ 4846 600 9.3 \ 4847 800 6.5 \ 4848 1000 4.5 \ 4849 1200 3 \ 4850 1500 2.0 \ 4851 2000 1.2 4852 4853# According to the UAMA web page, the ANSI bonded and ANSI coated standards 4854# are identical to FEPA F in the macrogrit range (under 240 grit), so these 4855# values are taken from the FEPA F table. The values for 240 and above are 4856# from the UAMA web site and represent the average of the "d50" range 4857# endpoints listed there. 4858 4859ansibonded[micron] \ 4860 4 4890 \ 4861 5 4125 \ 4862 6 3460 \ 4863 7 2900 \ 4864 8 2460 \ 4865 10 2085 \ 4866 12 1765 \ 4867 14 1470 \ 4868 16 1230 \ 4869 20 1040 \ 4870 22 885 \ 4871 24 745 \ 4872 30 625 \ 4873 36 525 \ 4874 40 438 \ 4875 46 370 \ 4876 54 310 \ 4877 60 260 \ 4878 70 218 \ 4879 80 185 \ 4880 90 154 \ 4881 100 129 \ 4882 120 109 \ 4883 150 82 \ 4884 180 69 \ 4885 220 58 \ 4886 240 50 \ 4887 280 39.5 \ 4888 320 29.5 \ 4889 360 23 \ 4890 400 18.25 \ 4891 500 13.9 \ 4892 600 10.55 \ 4893 800 7.65 \ 4894 1000 5.8 \ 4895 1200 3.8 4896 4897grit_ansibonded() ansibonded 4898 4899# Like the bonded grit, the coated macrogrits below 240 are taken from the 4900# FEPA F table. Data above this is from the UAMA site. Note that the coated 4901# and bonded standards are evidently the same from 240 up to 600 grit, but 4902# starting at 800 grit, the coated standard diverges. The data from UAMA show 4903# that 800 grit coated has an average size slightly larger than the average 4904# size of 600 grit coated/bonded. However, the 800 grit has a significantly 4905# smaller particle size variation. 4906# 4907# Because of this non-monotonicity from 600 grit to 800 grit this definition 4908# produces a warning about the lack of a unique inverse. 4909 4910ansicoated[micron] noerror \ 4911 4 4890 \ 4912 5 4125 \ 4913 6 3460 \ 4914 7 2900 \ 4915 8 2460 \ 4916 10 2085 \ 4917 12 1765 \ 4918 14 1470 \ 4919 16 1230 \ 4920 20 1040 \ 4921 22 885 \ 4922 24 745 \ 4923 30 625 \ 4924 36 525 \ 4925 40 438 \ 4926 46 370 \ 4927 54 310 \ 4928 60 260 \ 4929 70 218 \ 4930 80 185 \ 4931 90 154 \ 4932 100 129 \ 4933 120 109 \ 4934 150 82 \ 4935 180 69 \ 4936 220 58 \ 4937 240 50 \ 4938 280 39.5 \ 4939 320 29.5 \ 4940 360 23 \ 4941 400 18.25 \ 4942 500 13.9 \ 4943 600 10.55 \ 4944 800 11.5 \ 4945 1000 9.5 \ 4946 2000 7.2 \ 4947 2500 5.5 \ 4948 3000 4 \ 4949 4000 3 \ 4950 6000 2 \ 4951 8000 1.2 4952 4953grit_ansicoated() ansicoated 4954 4955 4956# 4957# Is this correct? This is the JIS Japanese standard used on waterstones 4958# 4959jisgrit[micron] \ 4960 150 75 \ 4961 180 63 \ 4962 220 53 \ 4963 280 48 \ 4964 320 40 \ 4965 360 35 \ 4966 400 30 \ 4967 600 20 \ 4968 700 17 \ 4969 800 14 \ 4970 1000 11.5 \ 4971 1200 9.5 \ 4972 1500 8 \ 4973 2000 6.7 \ 4974 2500 5.5 \ 4975 3000 4 \ 4976 4000 3 \ 4977 6000 2 \ 4978 8000 1.2 4979 4980# The "Finishing Scale" marked with an A (e.g. A75). This information 4981# is from the web page of the sand paper manufacturer Klingspor 4982# http://www.klingspor.com/gritgradingsystems.htm 4983# 4984# I have no information about what this scale is used for. 4985 4986grit_A[micron]\ 4987 16 15.3 \ 4988 25 21.8 \ 4989 30 23.6 \ 4990 35 25.75 \ 4991 45 35 \ 4992 60 46.2 \ 4993 65 53.5 \ 4994 75 58.5 \ 4995 90 65 \ 4996 110 78 \ 4997 130 93 \ 4998 160 127 \ 4999 200 156 5000# 5001# Grits for DMT brand diamond sharpening stones from 5002# http://dmtsharp.com/products/colorcode.htm 5003# 5004 5005dmtxxcoarse 120 micron # 120 mesh 5006dmtsilver dmtxxcoarse 5007dmtxx dmtxxcoarse 5008dmtxcoarse 60 micron # 220 mesh 5009dmtx dmtxcoarse 5010dmtblack dmtxcoarse 5011dmtcoarse 45 micron # 325 mesh 5012dmtc dmtcoarse 5013dmtblue dmtcoarse 5014dmtfine 25 micron # 600 mesh 5015dmtred dmtfine 5016dmtf dmtfine 5017dmtefine 9 micron # 1200 mesh 5018dmte dmtefine 5019dmtgreen dmtefine 5020dmtceramic 7 micron # 2200 mesh 5021dmtcer dmtceramic 5022dmtwhite dmtceramic 5023dmteefine 3 micron # 8000 mesh 5024dmttan dmteefine 5025dmtee dmteefine 5026 5027# 5028# The following values come from a page in the Norton Stones catalog, 5029# available at their web page, http://www.nortonstones.com. 5030# 5031 5032hardtranslucentarkansas 6 micron # Natural novaculite (silicon quartz) 5033softarkansas 22 micron # stones 5034 5035extrafineindia 22 micron # India stones are Norton's manufactured 5036fineindia 35 micron # aluminum oxide product 5037mediumindia 53.5 micron 5038coarseindia 97 micron 5039 5040finecrystolon 45 micron # Crystolon stones are Norton's 5041mediumcrystalon 78 micron # manufactured silicon carbide product 5042coarsecrystalon 127 micron 5043 5044# The following are not from the Norton catalog 5045hardblackarkansas 6 micron 5046hardwhitearkansas 11 micron 5047washita 35 micron 5048 5049# 5050# Mesh systems for measuring particle sizes by sifting through a wire 5051# mesh or sieve 5052# 5053 5054# The Tyler system and US Sieve system are based on four steps for 5055# each factor of 2 change in the size, so each size is 2^1|4 different 5056# from the adjacent sizes. Unfortunately, the mesh numbers are 5057# arbitrary, so the sizes cannot be expressed with a functional form. 5058# Various references round the values differently. The mesh numbers 5059# are supposed to correspond to the number of holes per inch, but this 5060# correspondence is only approximate because it doesn't include the 5061# wire size of the mesh. 5062 5063# The Tyler Mesh system was apparently introduced by the WS Tyler 5064# company, but it appears that they no longer use it. They follow the 5065# ASTM E11 standard. 5066 5067meshtyler[micron] \ 5068 2.5 8000 \ 5069 3 6727 \ 5070 3.5 5657 \ 5071 4 4757 \ 5072 5 4000 \ 5073 6 3364 \ 5074 7 2828 \ 5075 8 2378 \ 5076 9 2000 \ 5077 10 1682 \ 5078 12 1414 \ 5079 14 1189 \ 5080 16 1000 \ 5081 20 841 \ 5082 24 707 \ 5083 28 595 \ 5084 32 500 \ 5085 35 420 \ 5086 42 354 \ 5087 48 297 \ 5088 60 250 \ 5089 65 210 \ 5090 80 177 \ 5091 100 149 \ 5092 115 125 \ 5093 150 105 \ 5094 170 88 \ 5095 200 74 \ 5096 250 63 \ 5097 270 53 \ 5098 325 44 \ 5099 400 37 5100 5101# US Sieve size, ASTM E11 5102# 5103# The WS Tyler company prints the list from ASTM E11 in their catalog, 5104# http://wstyler.com/wp-content/uploads/2015/11/Product-Catalog-2.pdf 5105 5106sieve[micron] \ 5107 3.5 5600 \ 5108 4 4750 \ 5109 5 4000 \ 5110 6 3350 \ 5111 7 2800 \ 5112 8 2360 \ 5113 10 2000 \ 5114 12 1700 \ 5115 14 1400 \ 5116 16 1180 \ 5117 18 1000 \ 5118 20 850 \ 5119 25 710 \ 5120 30 600 \ 5121 35 500 \ 5122 40 425 \ 5123 45 355 \ 5124 50 300 \ 5125 60 250 \ 5126 70 212 \ 5127 80 180 \ 5128 100 150 \ 5129 120 125 \ 5130 140 106 \ 5131 170 90 \ 5132 200 75 \ 5133 230 63 \ 5134 270 53 \ 5135 325 45 \ 5136 400 38 \ 5137 450 32 \ 5138 500 25 \ 5139 625 20 # These last two values are not in the standard series 5140 # but were included in the ASTM standard because they 5141meshUS() sieve # were in common usage. 5142 5143# British Mesh size, BS 410: 1986 5144# This system appears to correspond to the Tyler and US system, but 5145# with different mesh numbers. 5146# 5147# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf 5148# 5149 5150meshbritish[micron] \ 5151 3 5657 \ 5152 3.5 4757 \ 5153 4 4000 \ 5154 5 3364 \ 5155 6 2828 \ 5156 7 2378 \ 5157 8 2000 \ 5158 10 1682 \ 5159 12 1414 \ 5160 14 1189 \ 5161 16 1000 \ 5162 18 841 \ 5163 22 707 \ 5164 25 595 \ 5165 30 500 \ 5166 36 420 \ 5167 44 354 \ 5168 52 297 \ 5169 60 250 \ 5170 72 210 \ 5171 85 177 \ 5172 100 149 \ 5173 120 125 \ 5174 150 105 \ 5175 170 88 \ 5176 200 74 \ 5177 240 63 \ 5178 300 53 \ 5179 350 44 \ 5180 400 37 5181 5182# French system, AFNOR NFX11-501: 1970 5183# The system appears to be based on size doubling every 3 mesh 5184# numbers, though the values have been agressively rounded. 5185# It's not clear if the unrounded values would be considered 5186# incorrect, so this is given as a table rather than a function. 5187# Functional form: 5188# meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron 5189# 5190# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf 5191 5192meshtamis[micron] \ 5193 17 40 \ 5194 18 50 \ 5195 19 63 \ 5196 20 80 \ 5197 21 100 \ 5198 22 125 \ 5199 23 160 \ 5200 24 200 \ 5201 25 250 \ 5202 26 315 \ 5203 27 400 \ 5204 28 500 \ 5205 29 630 \ 5206 30 800 \ 5207 31 1000 \ 5208 32 1250 \ 5209 33 1600 \ 5210 34 2000 \ 5211 35 2500 \ 5212 36 3150 \ 5213 37 4000 \ 5214 38 5000 5215 5216# 5217# Ring size. All ring sizes are given as the circumference of the ring. 5218# 5219 5220# USA ring sizes. Several slightly different definitions seem to be in 5221# circulation. According to [15], the interior diameter of size n ring in 5222# inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The 5223# size 2 ring is inconsistently 0.538in and no 2.5 size is listed. 5224# 5225# However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the 5226# diameter and list no special case for size 2. (Or alternatively they are 5227# 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One 5228# reference claimed that the original system was that each size was 1|10 inch 5229# circumference, but that source doesn't have an explanation for the modern 5230# system which is somewhat different. 5231 5232ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \ 5233 (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018 5234 5235# Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes 5236# specified alphabetically and based on the ring inside diameter in steps of 5237# 1|64 inch. This system was replaced in 1987 by British Standard 6820 which 5238# specifies sizes based on circumference. Each size is 1.25 mm different from 5239# the preceding size. The baseline is size C which is 40 mm circumference. 5240# The new sizes are close to the old ones. Sometimes it's necessary to go 5241# beyond size Z to Z+1, Z+2, etc. 5242 5243sizeAring 37.50 mm 5244sizeBring 38.75 mm 5245sizeCring 40.00 mm 5246sizeDring 41.25 mm 5247sizeEring 42.50 mm 5248sizeFring 43.75 mm 5249sizeGring 45.00 mm 5250sizeHring 46.25 mm 5251sizeIring 47.50 mm 5252sizeJring 48.75 mm 5253sizeKring 50.00 mm 5254sizeLring 51.25 mm 5255sizeMring 52.50 mm 5256sizeNring 53.75 mm 5257sizeOring 55.00 mm 5258sizePring 56.25 mm 5259sizeQring 57.50 mm 5260sizeRring 58.75 mm 5261sizeSring 60.00 mm 5262sizeTring 61.25 mm 5263sizeUring 62.50 mm 5264sizeVring 63.75 mm 5265sizeWring 65.00 mm 5266sizeXring 66.25 mm 5267sizeYring 67.50 mm 5268sizeZring 68.75 mm 5269 5270# Japanese sizes start with size 1 at a 13mm inside diameter and each size is 5271# 1|3 mm larger in diameter than the previous one. They are multiplied by pi 5272# to give circumference. 5273 5274jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \ 5275 (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38) 5276 5277# The European ring sizes are the length of the circumference in mm minus 40. 5278 5279euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40) 5280 5281# 5282# Abbreviations 5283# 5284 5285mph mile/hr 5286mpg mile/gal 5287kph km/hr 5288fL footlambert 5289fpm ft/min 5290fps ft/s 5291rpm rev/min 5292rps rev/sec 5293mi mile 5294smi mile 5295nmi nauticalmile 5296mbh 1e3 btu/hour 5297mcm 1e3 circularmil 5298ipy inch/year # used for corrosion rates 5299ccf 100 ft^3 # used for selling water [18] 5300Mcf 1000 ft^3 # not million cubic feet [18] 5301kp kilopond 5302kpm kp meter 5303Wh W hour 5304hph hp hour 5305plf lb / foot # pounds per linear foot 5306 5307# 5308# Compatibility units with unix version 5309# 5310 5311pa Pa 5312ev eV 5313hg Hg 5314oe Oe 5315mh mH 5316rd rod 5317pf pF 5318gr grain 5319nt N 5320hz Hz 5321hd hogshead 5322dry drygallon/gallon 5323nmile nauticalmile 5324beV GeV 5325bev beV 5326coul C 5327 5328# 5329# Radioactivity units 5330# 5331 5332becquerel /s # Activity of radioactive source 5333Bq becquerel # 5334curie 3.7e10 Bq # Defined in 1910 as the radioactivity 5335Ci curie # emitted by the amount of radon that is 5336 # in equilibrium with 1 gram of radium. 5337rutherford 1e6 Bq # 5338 5339RADIATION_DOSE gray 5340gray J/kg # Absorbed dose of radiation 5341Gy gray # 5342rad 1e-2 Gy # From Radiation Absorbed Dose 5343rep 8.38 mGy # Roentgen Equivalent Physical, the amount 5344 # of radiation which , absorbed in the 5345 # body, would liberate the same amount 5346 # of energy as 1 roentgen of X rays 5347 # would, or 97 ergs. 5348 5349sievert J/kg # Dose equivalent: dosage that has the 5350Sv sievert # same effect on human tissues as 200 5351rem 1e-2 Sv # keV X-rays. Different types of 5352 # radiation are weighted by the 5353 # Relative Biological Effectiveness 5354 # (RBE). 5355 # 5356 # Radiation type RBE 5357 # X-ray, gamma ray 1 5358 # beta rays, > 1 MeV 1 5359 # beta rays, < 1 MeV 1.08 5360 # neutrons, < 1 MeV 4-5 5361 # neutrons, 1-10 MeV 10 5362 # protons, 1 MeV 8.5 5363 # protons, .1 MeV 10 5364 # alpha, 5 MeV 15 5365 # alpha, 1 MeV 20 5366 # 5367 # The energies are the kinetic energy 5368 # of the particles. Slower particles 5369 # interact more, so they are more 5370 # effective ionizers, and hence have 5371 # higher RBE values. 5372 # 5373 # rem stands for Roentgen Equivalent 5374 # Mammal 5375banana_dose 0.1e-6 sievert # Informal measure of the dose due to 5376 # eating one average sized banana 5377roentgen 2.58e-4 C / kg # Ionizing radiation that produces 5378 # 1 statcoulomb of charge in 1 cc of 5379 # dry air at stp. 5380rontgen roentgen # Sometimes it appears spelled this way 5381sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one 5382 # hour at a distance of 1 cm from a 5383 # point source of 1 mg of radium 5384 # enclosed in platinum .5 mm thick. 5385 5386eman 1e-7 Ci/m^3 # radioactive concentration 5387mache 3.7e-7 Ci/m^3 5388 5389# 5390# Atomic weights. The atomic weight of an element is the ratio of the mass of 5391# a mole of the element to 1|12 of a mole of Carbon 12. The Standard Atomic 5392# Weights apply to the elements as they occur naturally on earth. Elements 5393# which do not occur naturally or which occur with wide isotopic variability do 5394# not have Standard Atomic Weights. For these elements, the atomic weight is 5395# based on the longest lived isotope, as marked in the comments. In some 5396# cases, the comment for these entries also gives a number which is an atomic 5397# weight for a different isotope that may be of more interest than the longest 5398# lived isotope. 5399# 5400 5401actinium 227.0278 5402aluminum 26.981539 5403americium 243.0614 # Longest lived. 241.06 5404antimony 121.760 5405argon 39.948 5406arsenic 74.92159 5407astatine 209.9871 # Longest lived 5408barium 137.327 5409berkelium 247.0703 # Longest lived. 249.08 5410beryllium 9.012182 5411bismuth 208.98037 5412boron 10.811 5413bromine 79.904 5414cadmium 112.411 5415calcium 40.078 5416californium 251.0796 # Longest lived. 252.08 5417carbon 12.011 5418cerium 140.115 5419cesium 132.90543 5420chlorine 35.4527 5421chromium 51.9961 5422cobalt 58.93320 5423copper 63.546 5424curium 247.0703 5425deuterium 2.0141017778 5426dysprosium 162.50 5427einsteinium 252.083 # Longest lived 5428erbium 167.26 5429europium 151.965 5430fermium 257.0951 # Longest lived 5431fluorine 18.9984032 5432francium 223.0197 # Longest lived 5433gadolinium 157.25 5434gallium 69.723 5435germanium 72.61 5436gold 196.96654 5437hafnium 178.49 5438helium 4.002602 5439holmium 164.93032 5440hydrogen 1.00794 5441indium 114.818 5442iodine 126.90447 5443iridium 192.217 5444iron 55.845 5445krypton 83.80 5446lanthanum 138.9055 5447lawrencium 262.11 # Longest lived 5448lead 207.2 5449lithium 6.941 5450lutetium 174.967 5451magnesium 24.3050 5452manganese 54.93805 5453mendelevium 258.10 # Longest lived 5454mercury 200.59 5455molybdenum 95.94 5456neodymium 144.24 5457neon 20.1797 5458neptunium 237.0482 5459nickel 58.6934 5460niobium 92.90638 5461nitrogen 14.00674 5462nobelium 259.1009 # Longest lived 5463osmium 190.23 5464oxygen 15.9994 5465palladium 106.42 5466phosphorus 30.973762 5467platinum 195.08 5468plutonium 244.0642 # Longest lived. 239.05 5469polonium 208.9824 # Longest lived. 209.98 5470potassium 39.0983 5471praseodymium 140.90765 5472promethium 144.9127 # Longest lived. 146.92 5473protactinium 231.03588 5474radium 226.0254 5475radon 222.0176 # Longest lived 5476rhenium 186.207 5477rhodium 102.90550 5478rubidium 85.4678 5479ruthenium 101.07 5480samarium 150.36 5481scandium 44.955910 5482selenium 78.96 5483silicon 28.0855 5484silver 107.8682 5485sodium 22.989768 5486strontium 87.62 5487sulfur 32.066 5488tantalum 180.9479 5489technetium 97.9072 # Longest lived. 98.906 5490tellurium 127.60 5491terbium 158.92534 5492thallium 204.3833 5493thorium 232.0381 5494thullium 168.93421 5495tin 118.710 5496titanium 47.867 5497tungsten 183.84 5498uranium 238.0289 5499vanadium 50.9415 5500xenon 131.29 5501ytterbium 173.04 5502yttrium 88.90585 5503zinc 65.39 5504zirconium 91.224 5505 5506# Average molecular weight of air 5507# 5508# The atmospheric composition listed is from NASA Earth Fact Sheet (accessed 5509# 28 August 2015) 5510# http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html 5511# Numbers do not add up to exactly 100% due to roundoff and uncertainty Water 5512# is highly variable, typically makes up about 1% 5513 5514air 78.08% nitrogen 2 \ 5515 + 20.95% oxygen 2 \ 5516 + 9340 ppm argon \ 5517 + 400 ppm (carbon + oxygen 2) \ 5518 + 18.18 ppm neon \ 5519 + 5.24 ppm helium \ 5520 + 1.7 ppm (carbon + 4 hydrogen) \ 5521 + 1.14 ppm krypton \ 5522 + 0.55 ppm hydrogen 2 5523# 5524# population units 5525# 5526 5527people 1 5528person people 5529death people 5530capita people 5531percapita per capita 5532 5533# TGM dozen based unit system listed on the "dozenal" forum 5534# http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are 5535# proposed as an allegedly more rational alternative to the SI system. 5536 5537Tim 12^-4 hour # Time 5538Grafut gravity Tim^2 # Length based on gravity 5539Surf Grafut^2 # area 5540Volm Grafut^3 # volume 5541Vlos Grafut/Tim # speed 5542Denz Maz/Volm # density 5543Mag Maz gravity # force 5544Maz Volm kg / oldliter # mass based on water 5545 5546Tm Tim # Abbreviations 5547Gf Grafut 5548Sf Surf 5549Vm Volm 5550Vl Vlos 5551Mz Maz 5552Dz Denz 5553 5554# Dozen based unit prefixes 5555 5556Zena- 12 5557Duna- 12^2 5558Trina- 12^3 5559Quedra- 12^4 5560Quena- 12^5 5561Hesa- 12^6 5562Seva- 12^7 5563Aka- 12^8 5564Neena- 12^9 5565Dexa- 12^10 5566Lefa- 12^11 5567Zennila- 12^12 5568 5569Zeni- 12^-1 5570Duni- 12^-2 5571Trini- 12^-3 5572Quedri- 12^-4 5573Queni- 12^-5 5574Hesi- 12^-6 5575Sevi- 12^-7 5576Aki- 12^-8 5577Neeni- 12^-9 5578Dexi- 12^-10 5579Lefi- 12^-11 5580Zennili- 12^-12 5581 5582# 5583# Traditional Japanese units (shakkanhou) 5584# 5585# The traditional system of weights and measures is called shakkanhou from the 5586# shaku and the ken. Japan accepted SI units in 1891 and legalized conversions 5587# to the traditional system. In 1909 the inch-pound system was also legalized, 5588# so Japan had three legally approved systems. A change to the metric system 5589# started in 1921 but there was a lot of resistance. The Measurement Law of 5590# October 1999 prohibits sales in anything but SI units. However, the old 5591# units still live on in construction and as the basis for paper sizes of books 5592# and tools used for handicrafts. 5593# 5594# Note that units below use the Hepburn romanization system. Some other 5595# systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho". 5596# 5597# 5598# http://hiramatu-hifuka.com/onyak/onyindx.html 5599 5600# Japanese Proportions. These are still in everyday use. They also 5601# get used as units to represent the proportion of the standard unit. 5602 5603wari_proportion 1|10 5604wari wari_proportion 5605bu_proportion 1|100 # The character bu can also be read fun or bun 5606 # but usually "bu" is used for units. 5607rin_proportion 1|1000 5608mou_proportion 1|10000 5609 5610 5611# Japanese Length Measures 5612# 5613# The length system is called kanejaku or 5614# square and originated in China. It was 5615# adopted as Japan's official measure in 701 5616# by the Taiho Code. This system is still in 5617# common use in architecture and clothing. 5618 5619shaku 1|3.3 m 5620mou 1|10000 shaku 5621rin 1|1000 shaku 5622bu_distance 1|100 shaku 5623sun 1|10 shaku 5624jou_distance 10 shaku 5625jou jou_distance 5626 5627kanejakusun sun # Alias to emphasize architectural name 5628kanejaku shaku 5629kanejakujou jou 5630 5631# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement 5632taichi shaku # http://zh.wikipedia.org/wiki/台尺 5633taicun sun # http://zh.wikipedia.org/wiki/台制 5634!utf8 5635台尺 taichi # via Hanyu Pinyin romanizations 5636台寸 taicun 5637!endutf8 5638 5639# In context of clothing, shaku is different from architecture 5640# http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html 5641 5642kujirajaku 10|8 shaku 5643kujirajakusun 1|10 kujirajaku 5644kujirajakubu 1|100 kujirajaku 5645kujirajakujou 10 kujirajaku 5646tan_distance 3 kujirajakujou 5647 5648ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6 5649 # http://www.homarewood.co.jp/syakusun.htm 5650 5651# mostly unused 5652chou_distance 60 ken 5653chou chou_distance 5654ri 36 chou 5655 5656# Japanese Area Measures 5657 5658# Tsubo is still used for land size, though the others are more 5659# recognized by their homonyms in the other measurements. 5660 5661gou_area 1|10 tsubo 5662tsubo 36 shaku^2 # Size of two tatami = ken^2 ?? 5663se 30 tsubo 5664tan_area 10 se 5665chou_area 10 tan_area 5666 5667# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement 5668ping tsubo # http://zh.wikipedia.org/wiki/坪 5669jia 2934 ping # http://zh.wikipedia.org/wiki/甲_(单位) 5670fen 1|10 jia # http://zh.wikipedia.org/wiki/分 5671fen_area 1|10 jia # Protection against future collisions 5672!utf8 5673坪 ping # via Hanyu Pinyin romanizations 5674甲 jia 5675分 fen 5676分地 fen_area # Protection against future collisions 5677!endutf8 5678 5679# Japanese architecture is based on a "standard" size of tatami mat. 5680# Room sizes today are given in number of tatami, and this number 5681# determines the spacing between colums and hence sizes of sliding 5682# doors and paper screens. However, every region has its own slightly 5683# different tatami size. Edoma, used in and around Tokyo and 5684# Hokkaido, is becoming a nationwide standard. Kyouma is used around 5685# Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya. 5686# Note that the tatami all have the aspect ratio 2:1 so that the mats 5687# can tile the room with some of them turned 90 degrees. 5688# 5689# http://www.moon2.net/tatami/infotatami/structure.html 5690 5691edoma (5.8*2.9) shaku^2 5692kyouma (6.3*3.15) shaku^2 5693chuukyouma (6*3) shaku^2 5694jou_area edoma 5695tatami jou_area 5696 5697# Japanese Volume Measures 5698 5699# The "shou" is still used for such things as alcohol and seasonings. 5700# Large quantities of paint are still purchased in terms of "to". 5701 5702shaku_volume 1|10 gou_volume 5703gou_volume 1|10 shou 5704gou gou_volume 5705shou (4.9*4.9*2.7) sun^3 # The character shou which is 5706 # the same as masu refers to a 5707 # rectangular wooden cup used to 5708 # measure liquids and cereal. 5709 # Sake is sometimes served in a masu 5710 # Note that it happens to be 5711 # EXACTLY 7^4/11^3 liters. 5712to 10 shou 5713koku 10 to # No longer used; historically a measure of rice 5714 5715# Japanese Weight Measures 5716# 5717# http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html 5718 5719# Not really used anymore. 5720 5721rin_weight 1|10 bu_weight 5722bu_weight 1|10 monme 5723fun 1|10 monme 5724monme momme 5725kin 160 monme 5726kan 1000 monme 5727kwan kan # This was the old pronounciation of the unit. 5728 # The old spelling persisted a few centuries 5729 # longer and was not changed until around 5730 # 1950. 5731 5732# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement 5733# says: "Volume measure in Taiwan is largely metric". 5734taijin kin # http://zh.wikipedia.org/wiki/台斤 5735tailiang 10 monme # http://zh.wikipedia.org/wiki/台斤 5736taiqian monme # http://zh.wikipedia.org/wiki/台制 5737!utf8 5738台斤 taijin # via Hanyu Pinyin romanizations 5739台兩 tailiang 5740台錢 taiqian 5741!endutf8 5742 5743# 5744# Australian unit 5745# 5746 5747australiasquare (10 ft)^2 # Used for house area 5748 5749 5750# 5751# A few German units as currently in use. 5752# 5753 5754zentner 50 kg 5755doppelzentner 2 zentner 5756pfund 500 g 5757 5758# 5759# Swedish (Sweden) pre-metric units of 1739. 5760# The metric system was adopted in 1878. 5761# https://sv.wikipedia.org/wiki/Verkm%C3%A5tt 5762# 5763 5764verklinje 2.0618125 mm 5765verktum 12 verklinje 5766kvarter 6 verktum 5767fot 2 kvarter 5768aln 2 fot 5769famn 3 aln 5770 5771# 5772# Some traditional Russian measures 5773# 5774# If you would like to help expand this section and understand 5775# cyrillic transliteration, let me know. These measures are meant to 5776# reflect common usage, e.g. in translated literature. 5777# 5778 5779dessiatine 2400 sazhen^2 # Land measure 5780dessjatine dessiatine 5781 5782funt 409.51718 grams # similar to pound 5783zolotnik 1|96 funt # used for precious metal measure 5784pood 40 funt # common in agricultural measure 5785 5786arshin (2 + 1|3) feet 5787sazhen 3 arshin # analogous to fathom 5788verst 500 sazhen # of similar use to mile 5789versta verst 5790borderverst 1000 sazhen 5791russianmile 7 verst 5792 5793 5794 5795 5796# 5797# Old French distance measures, from French Weights and Measures 5798# Before the Revolution by Zupko 5799# 5800 5801frenchfoot 144|443.296 m # pied de roi, the standard of Paris. 5802pied frenchfoot # Half of the hashimicubit, 5803frenchfeet frenchfoot # instituted by Charlemagne. 5804frenchinch 1|12 frenchfoot # This exact definition comes from 5805frenchthumb frenchinch # a law passed on 10 Dec 1799 which 5806pouce frenchthumb # fixed the meter at 5807 # 3 frenchfeet + 11.296 lignes. 5808frenchline 1|12 frenchinch # This is supposed to be the size 5809ligne frenchline # of the average barleycorn 5810frenchpoint 1|12 frenchline 5811toise 6 frenchfeet 5812arpent 180^2 pied^2 # The arpent is 100 square perches, 5813 # but the perche seems to vary a lot 5814 # and can be 18 feet, 20 feet, or 22 5815 # feet. This measure was described 5816 # as being in common use in Canada in 5817 # 1934 (Websters 2nd). The value 5818 # given here is the Paris standard 5819 # arpent. 5820frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence 5821 # smaller than the British grain. 5822frenchpound 9216 frenchgrain 5823 5824# 5825# Before the Imperial Weights and Measures Act of 1824, various different 5826# weights and measures were in use in different places. 5827# 5828 5829# Scots linear measure 5830 5831scotsinch 1.00540054 UKinch 5832scotslink 1|100 scotschain 5833scotsfoot 12 scotsinch 5834scotsfeet scotsfoot 5835scotsell 37 scotsinch 5836scotsfall 6 scotsell 5837scotschain 4 scotsfall 5838scotsfurlong 10 scotschain 5839scotsmile 8 scotsfurlong 5840 5841# Scots area measure 5842 5843scotsrood 40 scotsfall^2 5844scotsacre 4 scotsrood 5845 5846# Irish linear measure 5847 5848irishinch UKinch 5849irishpalm 3 irishinch 5850irishspan 3 irishpalm 5851irishfoot 12 irishinch 5852irishfeet irishfoot 5853irishcubit 18 irishinch 5854irishyard 3 irishfeet 5855irishpace 5 irishfeet 5856irishfathom 6 irishfeet 5857irishpole 7 irishyard # Only these values 5858irishperch irishpole # are different from 5859irishchain 4 irishperch # the British Imperial 5860irishlink 1|100 irishchain # or English values for 5861irishfurlong 10 irishchain # these lengths. 5862irishmile 8 irishfurlong # 5863 5864# Irish area measure 5865 5866irishrood 40 irishpole^2 5867irishacre 4 irishrood 5868 5869# English wine capacity measures (Winchester measures) 5870 5871winepint 1|2 winequart 5872winequart 1|4 winegallon 5873winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon, 5874 # it was legalized in 1707 by Queen Anne, and 5875 # given the definition of 231 cubic inches. It 5876 # had been in use for a while as 8 pounds of wine 5877 # using a merchant's pound, but the definition of 5878 # the merchant's pound had become uncertain. A 5879 # pound of 15 tower ounces (6750 grains) had been 5880 # common, but then a pound of 15 troy ounces 5881 # (7200 grains) gained popularity. Because of 5882 # the switch in the value of the merchants pound, 5883 # the size of the wine gallon was uncertain in 5884 # the market, hence the official act in 1707. 5885 # The act allowed that a six inch tall cylinder 5886 # with a 7 inch diameter was a lawful wine 5887 # gallon. (This comes out to 230.9 in^3.) 5888 # Note also that in Britain a legal conversion 5889 # was established to the 1824 Imperial gallon 5890 # then taken as 277.274 in^3 so that the wine 5891 # gallon was 0.8331 imperial gallons. This is 5892 # 231.1 cubic inches (using the international 5893 # inch). 5894winerundlet 18 winegallon 5895winebarrel 31.5 winegallon 5896winetierce 42 winegallon 5897winehogshead 2 winebarrel 5898winepuncheon 2 winetierce 5899winebutt 2 winehogshead 5900winepipe winebutt 5901winetun 2 winebutt 5902 5903# English beer and ale measures used 1803-1824 and used for beer before 1688 5904 5905beerpint 1|2 beerquart 5906beerquart 1|4 beergallon 5907beergallon 282 UKinch^3 5908beerbarrel 36 beergallon 5909beerhogshead 1.5 beerbarrel 5910 5911# English ale measures used from 1688-1803 for both ale and beer 5912 5913alepint 1|2 alequart 5914alequart 1|4 alegallon 5915alegallon beergallon 5916alebarrel 34 alegallon 5917alehogshead 1.5 alebarrel 5918 5919# Scots capacity measure 5920 5921scotsgill 1|4 mutchkin 5922mutchkin 1|2 choppin 5923choppin 1|2 scotspint 5924scotspint 1|2 scotsquart 5925scotsquart 1|4 scotsgallon 5926scotsgallon 827.232 UKinch^3 5927scotsbarrel 8 scotsgallon 5928jug scotspint 5929 5930# Scots dry capacity measure 5931 5932scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt 5933scotswheatlippies scotswheatlippy 5934scotswheatpeck 4 scotswheatlippy 5935scotswheatfirlot 4 scotswheatpeck 5936scotswheatboll 4 scotswheatfirlot 5937scotswheatchalder 16 scotswheatboll 5938 5939scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt 5940scotsoatlippies scotsoatlippy 5941scotsoatpeck 4 scotsoatlippy 5942scotsoatfirlot 4 scotsoatpeck 5943scotsoatboll 4 scotsoatfirlot 5944scotsoatchalder 16 scotsoatboll 5945 5946# Scots Tron weight 5947 5948trondrop 1|16 tronounce 5949tronounce 1|20 tronpound 5950tronpound 9520 grain 5951tronstone 16 tronpound 5952 5953# Irish liquid capacity measure 5954 5955irishnoggin 1|4 irishpint 5956irishpint 1|2 irishquart 5957irishquart 1|2 irishpottle 5958irishpottle 1|2 irishgallon 5959irishgallon 217.6 UKinch^3 5960irishrundlet 18 irishgallon 5961irishbarrel 31.5 irishgallon 5962irishtierce 42 irishgallon 5963irishhogshead 2 irishbarrel 5964irishpuncheon 2 irishtierce 5965irishpipe 2 irishhogshead 5966irishtun 2 irishpipe 5967 5968# Irish dry capacity measure 5969 5970irishpeck 2 irishgallon 5971irishbushel 4 irishpeck 5972irishstrike 2 irishbushel 5973irishdrybarrel 2 irishstrike 5974irishquarter 2 irishbarrel 5975 5976# English Tower weights, abolished in 1528 5977 5978towerpound 5400 grain 5979towerounce 1|12 towerpound 5980towerpennyweight 1|20 towerounce 5981towergrain 1|32 towerpennyweight 5982 5983# English Mercantile weights, used since the late 12th century 5984 5985mercpound 6750 grain 5986mercounce 1|15 mercpound 5987mercpennyweight 1|20 mercounce 5988 5989# English weights for lead 5990 5991leadstone 12.5 lb 5992fotmal 70 lb 5993leadwey 14 leadstone 5994fothers 12 leadwey 5995 5996# English Hay measure 5997 5998newhaytruss 60 lb # New and old here seem to refer to "new" 5999newhayload 36 newhaytruss # hay and "old" hay rather than a new unit 6000oldhaytruss 56 lb # and an old unit. 6001oldhayload 36 oldhaytruss 6002 6003# English wool measure 6004 6005woolclove 7 lb 6006woolstone 2 woolclove 6007wooltod 2 woolstone 6008woolwey 13 woolstone 6009woolsack 2 woolwey 6010woolsarpler 2 woolsack 6011woollast 6 woolsarpler 6012 6013# 6014# Ancient history units: There tends to be uncertainty in the definitions 6015# of the units in this section 6016# These units are from [11] 6017 6018# Roman measure. The Romans had a well defined distance measure, but their 6019# measures of weight were poor. They adopted local weights in different 6020# regions without distinguishing among them so that there are half a dozen 6021# different Roman "standard" weight systems. 6022 6023romanfoot 296 mm # There is some uncertainty in this definition 6024romanfeet romanfoot # from which all the other units are derived. 6025pes romanfoot # This value appears in numerous sources. In "The 6026pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm. 6027romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the 6028romandigit 1|16 romanfoot # same names as the subdivisions of the pound, 6029romanpalm 1|4 romanfoot # but we can't have the names for different 6030romancubit 18 romaninch # units. 6031romanpace 5 romanfeet # Roman double pace (basic military unit) 6032passus romanpace 6033romanperch 10 romanfeet 6034stade 125 romanpaces 6035stadia stade 6036stadium stade 6037romanmile 8 stadia # 1000 paces 6038romanleague 1.5 romanmile 6039schoenus 4 romanmile 6040 6041# Other values for the Roman foot (from Dilke) 6042 6043earlyromanfoot 29.73 cm 6044pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC 6045lateromanfoot 29.42 cm 6046 6047# Roman areas 6048 6049actuslength 120 romanfeet # length of a Roman furrow 6050actus 120*4 romanfeet^2 # area of the furrow 6051squareactus 120^2 romanfeet^2 # actus quadratus 6052acnua squareactus 6053iugerum 2 squareactus 6054iugera iugerum 6055jugerum iugerum 6056jugera iugerum 6057heredium 2 iugera # heritable plot 6058heredia heredium 6059centuria 100 heredia 6060centurium centuria 6061 6062# Roman volumes 6063 6064sextarius 35.4 in^3 # Basic unit of Roman volume. As always, 6065sextarii sextarius # there is uncertainty. Six large Roman 6066 # measures survive with volumes ranging from 6067 # 34.4 in^3 to 39.55 in^3. Three of them 6068 # cluster around the size given here. 6069 # 6070 # But the values for this unit vary wildly 6071 # in other sources. One reference gives 0.547 6072 # liters, but then says the amphora is a 6073 # cubic Roman foot. This gives a value for the 6074 # sextarius of 0.540 liters. And the 6075 # encyclopedia Brittanica lists 0.53 liters for 6076 # this unit. Both [7] and [11], which were 6077 # written by scholars of weights and measures, 6078 # give the value of 35.4 cubic inches. 6079cochlearia 1|48 sextarius 6080cyathi 1|12 sextarius 6081acetabula 1|8 sextarius 6082quartaria 1|4 sextarius 6083quartarius quartaria 6084heminae 1|2 sextarius 6085hemina heminae 6086cheonix 1.5 sextarii 6087 6088# Dry volume measures (usually) 6089 6090semodius 8 sextarius 6091semodii semodius 6092modius 16 sextarius 6093modii modius 6094 6095# Liquid volume measures (usually) 6096 6097congius 12 heminae 6098congii congius 6099amphora 8 congii 6100amphorae amphora # Also a dry volume measure 6101culleus 20 amphorae 6102quadrantal amphora 6103 6104# Roman weights 6105 6106libra 5052 grain # The Roman pound varied significantly 6107librae libra # from 4210 grains to 5232 grains. Most of 6108romanpound libra # the standards were obtained from the weight 6109uncia 1|12 libra # of particular coins. The one given here is 6110unciae uncia # based on the Gold Aureus of Augustus which 6111romanounce uncia # was in use from BC 27 to AD 296. 6112deunx 11 uncia 6113dextans 10 uncia 6114dodrans 9 uncia 6115bes 8 uncia 6116seprunx 7 uncia 6117semis 6 uncia 6118quincunx 5 uncia 6119triens 4 uncia 6120quadrans 3 uncia 6121sextans 2 uncia 6122sescuncia 1.5 uncia 6123semuncia 1|2 uncia 6124siscilius 1|4 uncia 6125sextula 1|6 uncia 6126semisextula 1|12 uncia 6127scriptulum 1|24 uncia 6128scrupula scriptulum 6129romanobol 1|2 scrupula 6130 6131romanaspound 4210 grain # Old pound based on bronze coinage, the 6132 # earliest money of Rome BC 338 to BC 268. 6133 6134# Egyptian length measure 6135 6136egyptianroyalcubit 20.63 in # plus or minus .2 in 6137egyptianpalm 1|7 egyptianroyalcubit 6138egyptiandigit 1|4 egyptianpalm 6139egyptianshortcubit 6 egyptianpalm 6140 6141doubleremen 29.16 in # Length of the diagonal of a square with 6142remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit. 6143 # This is divided into 40 digits which are 6144 # not the same size as the digits based on 6145 # the royal cubit. 6146 6147# Greek length measures 6148 6149greekfoot 12.45 in # Listed as being derived from the 6150greekfeet greekfoot # Egyptian Royal cubit in [11]. It is 6151greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit. 6152pous greekfoot 6153podes greekfoot 6154orguia 6 greekfoot 6155greekfathom orguia 6156stadion 100 orguia 6157akaina 10 greekfeet 6158plethron 10 akaina 6159greekfinger 1|16 greekfoot 6160homericcubit 20 greekfingers # Elbow to end of knuckles. 6161shortgreekcubit 18 greekfingers # Elbow to start of fingers. 6162 6163ionicfoot 296 mm 6164doricfoot 326 mm 6165 6166olympiccubit 25 remendigit # These olympic measures were not as 6167olympicfoot 2|3 olympiccubit # common as the other greek measures. 6168olympicfinger 1|16 olympicfoot # They were used in agriculture. 6169olympicfeet olympicfoot 6170olympicdakylos olympicfinger 6171olympicpalm 1|4 olympicfoot 6172olympicpalestra olympicpalm 6173olympicspithame 3|4 foot 6174olympicspan olympicspithame 6175olympicbema 2.5 olympicfeet 6176olympicpace olympicbema 6177olympicorguia 6 olympicfeet 6178olympicfathom olympicorguia 6179olympiccord 60 olympicfeet 6180olympicamma olympiccord 6181olympicplethron 100 olympicfeet 6182olympicstadion 600 olympicfeet 6183 6184# Greek capacity measure 6185 6186greekkotyle 270 ml # This approximate value is obtained 6187xestes 2 greekkotyle # from two earthenware vessels that 6188khous 12 greekkotyle # were reconstructed from fragments. 6189metretes 12 khous # The kotyle is a day's corn ration 6190choinix 4 greekkotyle # for one man. 6191hekteos 8 choinix 6192medimnos 6 hekteos 6193 6194# Greek weight. Two weight standards were used, an Aegina standard based 6195# on the Beqa shekel and an Athens (attic) standard. 6196 6197aeginastater 192 grain # Varies up to 199 grain 6198aeginadrachmae 1|2 aeginastater 6199aeginaobol 1|6 aeginadrachmae 6200aeginamina 50 aeginastaters 6201aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot 6202 # of water (whichever foot was in use) 6203 6204atticstater 135 grain # Varies 134-138 grain 6205atticdrachmae 1|2 atticstater 6206atticobol 1|6 atticdrachmae 6207atticmina 50 atticstaters 6208attictalent 60 atticmina # Supposedly the mass of a cubic foot 6209 # of water (whichever foot was in use) 6210 6211# "Northern" cubit and foot. This was used by the pre-Aryan civilization in 6212# the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China, 6213# central and Western Europe until modern times when it was displaced by 6214# the metric system. 6215 6216northerncubit 26.6 in # plus/minus .2 in 6217northernfoot 1|2 northerncubit 6218 6219sumeriancubit 495 mm 6220kus sumeriancubit 6221sumerianfoot 2|3 sumeriancubit 6222 6223assyriancubit 21.6 in 6224assyrianfoot 1|2 assyriancubit 6225assyrianpalm 1|3 assyrianfoot 6226assyriansusi 1|20 assyrianpalm 6227susi assyriansusi 6228persianroyalcubit 7 assyrianpalm 6229 6230 6231# Arabic measures. The arabic standards were meticulously kept. Glass weights 6232# accurate to .2 grains were made during AD 714-900. 6233 6234hashimicubit 25.56 in # Standard of linear measure used 6235 # in Persian dominions of the Arabic 6236 # empire 7-8th cent. Is equal to two 6237 # French feet. 6238 6239blackcubit 21.28 in 6240arabicfeet 1|2 blackcubit 6241arabicfoot arabicfeet 6242arabicinch 1|12 arabicfoot 6243arabicmile 4000 blackcubit 6244 6245silverdirhem 45 grain # The weights were derived from these two 6246tradedirhem 48 grain # units with two identically named systems 6247 # used for silver and used for trade purposes 6248 6249silverkirat 1|16 silverdirhem 6250silverwukiyeh 10 silverdirhem 6251silverrotl 12 silverwukiyeh 6252arabicsilverpound silverrotl 6253 6254tradekirat 1|16 tradedirhem 6255tradewukiyeh 10 tradedirhem 6256traderotl 12 tradewukiyeh 6257arabictradepound traderotl 6258 6259# Miscellaneous ancient units 6260 6261parasang 3.5 mile # Persian unit of length usually thought 6262 # to be between 3 and 3.5 miles 6263biblicalcubit 21.8 in 6264hebrewcubit 17.58 in 6265li 10|27.8 mile # Chinese unit of length 6266 # 100 li is considered a day's march 6267liang 11|3 oz # Chinese weight unit 6268 6269 6270# Medieval time units. According to the OED, these appear in Du Cange 6271# by Papias. 6272 6273timepoint 1|5 hour # also given as 1|4 6274timeminute 1|10 hour 6275timeostent 1|60 hour 6276timeounce 1|8 timeostent 6277timeatom 1|47 timeounce 6278 6279# Given in [15], these subdivisions of the grain were supposedly used 6280# by jewelers. The mite may have been used but the blanc could not 6281# have been accurately measured. 6282 6283mite 1|20 grain 6284droit 1|24 mite 6285periot 1|20 droit 6286blanc 1|24 periot 6287 6288# 6289# Localization 6290# 6291 6292!var UNITS_ENGLISH US 6293hundredweight ushundredweight 6294ton uston 6295scruple apscruple 6296fluidounce usfluidounce 6297gallon usgallon 6298bushel usbushel 6299quarter quarterweight 6300cup uscup 6301tablespoon ustablespoon 6302teaspoon usteaspoon 6303dollar US$ 6304cent $ 0.01 6305penny cent 6306minim minimvolume 6307pony ponyvolume 6308grand usgrand 6309firkin usfirkin 6310hogshead ushogshead 6311!endvar 6312 6313!var UNITS_ENGLISH GB 6314hundredweight brhundredweight 6315ton brton 6316scruple brscruple 6317fluidounce brfluidounce 6318gallon brgallon 6319bushel brbushel 6320quarter brquarter 6321chaldron brchaldron 6322cup brcup 6323teacup brteacup 6324tablespoon brtablespoon 6325teaspoon brteaspoon 6326dollar US$ 6327cent $ 0.01 6328penny brpenny 6329minim minimnote 6330pony brpony 6331grand brgrand 6332firkin brfirkin 6333hogshead brhogshead 6334!endvar 6335 6336!varnot UNITS_ENGLISH GB US 6337!message Unknown value for environment variable UNITS_ENGLISH. Should be GB or US. 6338!endvar 6339 6340 6341!utf8 6342⅛- 1|8 6343¼- 1|4 6344⅜- 3|8 6345½- 1|2 6346⅝- 5|8 6347¾- 3|4 6348⅞- 7|8 6349⅙- 1|6 6350⅓- 1|3 6351⅔- 2|3 6352⅚- 5|6 6353⅕- 1|5 6354⅖- 2|5 6355⅗- 3|5 6356⅘- 4|5 6357# U+2150- 1|7 For some reason these characters are getting 6358# U+2151- 1|9 flagged as invalid UTF8. 6359# U+2152- 1|10 6360ℯ exp(1) # U+212F, base of natural log 6361µ- micro # micro sign U+00B5 6362μ- micro # small mu U+03BC 6363ångström angstrom 6364Å angstrom # angstrom symbol U+212B 6365Å angstrom # A with ring U+00C5 6366röntgen roentgen 6367°C degC 6368°F degF 6369°K K # °K is incorrect notation 6370°R degR 6371° degree 6372℃ degC 6373℉ degF 6374K K # Kelvin symbol, U+212A 6375ℓ liter # unofficial abbreviation used in some places 6376Ω ohm # Ohm symbol U+2126 6377Ω ohm # Greek capital omega U+03A9 6378℧ mho 6379ʒ dram # U+0292 6380℈ scruple 6381℥ ounce 6382℔ lb 6383ℎ h 6384ℏ hbar 6385‰ 1|1000 6386‱ 1|10000 6387′ ' # U+2032 6388″ " # U+2033 6389 6390# 6391# Unicode currency symbols 6392# 6393 6394¢ cent 6395£ britainpound 6396¥ japanyen 6397€ euro 6398₩ southkoreawon 6399₪ israelnewshekel 6400₤ lira 6401₺ turkeylira 6402₨ rupee # unofficial legacy rupee sign 6403₹ indiarupee # official rupee sign 6404؋ afghanafghani 6405฿ thailandbaht 6406₡ elsalvadorcolon # Also costaricacolon 6407₣ francefranc 6408₦ nigerianaira 6409₧ spainpeseta 6410₫ vietnamdong 6411₭ laokip 6412₮ mongoliatugrik 6413₯ greecedrachma 6414₱ philippinepeso 6415₲ paraguayguarani 6416₴ ukrainehryvnia 6417₵ ghanacedi 6418₸ kazakhstantenge 6419₼ azerbaijanmanat 6420₽ russiaruble 6421₾ georgialari 6422﷼ iranrial 6423﹩ $ 6424￠ ¢ 6425￡ £ 6426￥ ¥ 6427￦ ₩ 6428 6429# 6430# Square unicode symbols starting at U+3371 6431# 6432 6433㍱ hPa 6434㍲ da 6435㍳ au 6436㍴ bar 6437# ㍵ oV??? 6438㍶ pc 6439#㍷ dm invalid on Mac 6440#㍸ dm^2 invalid on Mac 6441#㍹ dm^3 invalid on Mac 6442㎀ pA 6443㎁ nA 6444㎂ µA 6445㎃ mA 6446㎄ kA 6447㎅ kB 6448㎆ MB 6449㎇ GB 6450㎈ cal 6451㎉ kcal 6452㎊ pF 6453㎋ nF 6454㎌ µF 6455㎍ µg 6456㎎ mg 6457㎏ kg 6458㎐ Hz 6459㎑ kHz 6460㎒ MHz 6461㎓ GHz 6462㎔ THz 6463㎕ µL 6464㎖ mL 6465㎗ dL 6466㎘ kL 6467㎙ fm 6468㎚ nm 6469㎛ µm 6470㎜ mm 6471㎝ cm 6472㎞ km 6473㎟ mm^2 6474㎠ cm^2 6475㎡ m^2 6476㎢ km^2 6477㎣ mm^3 6478㎤ cm^3 6479㎥ m^3 6480㎦ km^3 6481㎧ m/s 6482㎨ m/s^2 6483㎩ Pa 6484㎪ kPa 6485㎫ MPa 6486㎬ GPa 6487㎭ rad 6488㎮ rad/s 6489㎯ rad/s^2 6490㎰ ps 6491㎱ ns 6492㎲ µs 6493㎳ ms 6494㎴ pV 6495㎵ nV 6496㎶ µV 6497㎷ mV 6498㎸ kV 6499㎹ MV 6500㎺ pW 6501㎻ nW 6502㎼ µW 6503㎽ mW 6504㎾ kW 6505㎿ MW 6506㏀ kΩ 6507㏁ MΩ 6508㏃ Bq 6509㏄ cc 6510㏅ cd 6511㏆ C/kg 6512㏈() dB 6513㏉ Gy 6514㏊ ha 6515# ㏋ HP?? 6516㏌ in 6517# ㏍ KK?? 6518# ㏎ KM??? 6519㏏ kt 6520㏐ lm 6521# ㏑ ln 6522# ㏒ log 6523㏓ lx 6524㏔ mb 6525㏕ mil 6526㏖ mol 6527㏗() pH 6528㏙ ppm 6529# ㏚ PR??? 6530㏛ sr 6531㏜ Sv 6532㏝ Wb 6533#㏞ V/m Invalid on Mac 6534#㏟ A/m Invalid on Mac 6535#㏿ gal Invalid on Mac 6536 6537!endutf8 6538 6539############################################################################ 6540# 6541# Unit list aliases 6542# 6543# These provide a shorthand for conversions to unit lists. 6544# 6545############################################################################ 6546 6547!unitlist hms hr;min;sec 6548!unitlist time year;day;hr;min;sec 6549!unitlist dms deg;arcmin;arcsec 6550!unitlist ftin ft;in;1|8 in 6551!unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in 6552!unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\ 6553 tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp 6554 6555############################################################################ 6556# 6557# The following units were in the unix units database but do not appear in 6558# this file: 6559# 6560# wey used for cheese, salt and other goods. Measured mass or 6561# waymass volume depending on what was measured and where the measuring 6562# took place. A wey of cheese ranged from 200 to 324 pounds. 6563# 6564# sack No precise definition 6565# 6566# spindle The length depends on the type of yarn 6567# 6568# block Defined variously on different computer systems 6569# 6570# erlang A unit of telephone traffic defined variously. 6571# Omitted because there are no other units for this 6572# dimension. Is this true? What about CCS = 1/36 erlang? 6573# Erlang is supposed to be dimensionless. One erlang means 6574# a single channel occupied for one hour. 6575# 6576############################################################################ 6577 6578