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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 2018 Version 2.44 6 # 7 # Copyright (C) 1996-2002, 2004-2018 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 ########################################################################### 80 81 ########################################################################### 82 # 83 # Brief Philosophy of this file 84 # 85 # Most unit definitions are made in terms of integers or simple fractions of 86 # other definitions. The typical exceptions are when converting between two 87 # different unit systems, or the values of measured physical constants. In 88 # this file definitions are given in the most natural and revealing way in 89 # terms of integer factors. 90 # 91 # If you make changes be sure to run 'units --check' to check your work. 92 # 93 # The file is USA-centric, but there is some modest effort to support other 94 # countries. This file is now coded in UTF-8. To support environments where 95 # UTF-8 is not available, definitions that require this character set are 96 # wrapped in !utf8 directives. 97 # 98 # When a unit name is used in different countries with the different meanings 99 # the system should be as follows: 100 # 101 # Suppose countries ABC and XYZ both use the "foo". Then globally define 102 # 103 # ABCfoo <some value> 104 # XYZfoo <different value> 105 # 106 # Then, using the !locale directive, define the "foo" appropriately for each of 107 # the two countries with a definition like 108 # 109 # !locale ABC 110 # foo ABCfoo 111 # !endlocale 112 # 113 ########################################################################### 114 115 !locale en_US 116 ! set UNITS_ENGLISH US 117 !endlocale 118 119 !locale en_GB 120 ! set UNITS_ENGLISH GB 121 !endlocale 122 123 !set UNITS_ENGLISH US # Default setting for English units 124 125 !set UNITS_SYSTEM default # Set a default value 126 127 !varnot UNITS_SYSTEM si emu esu gaussian gauss default 128 !message Unknown unit system given with -u or UNITS_SYSTEM environment variable 129 !message Valid systems: si, emu, esu, gauss[ian] 130 !message Using SI 131 !prompt (SI) 132 !endvar 133 134 !var UNITS_SYSTEM si 135 !message SI units selected 136 !prompt (SI) 137 !endvar 138 139 ########################################################################### 140 # # 141 # Primitive units. Any unit defined to contain a '!' character is a # 142 # primitive unit which will not be reduced any further. All units should # 143 # reduce to primitive units. # 144 # # 145 ########################################################################### 146 147 # 148 # SI units 149 # 150 151 kg ! # Mass of the international prototype 152 kilogram kg 153 154 s ! # Duration of 9192631770 periods of the radiation 155 second s # corresponding to the transition between the two hyperfine 156 # levels of the ground state of the cesium-133 atom 157 158 m ! # Length of the path traveled by light in a vacuum 159 meter m # during 1|299792458 seconds. Originally meant to be 160 # 1e-7 of the length along a meridian from the equator 161 # to a pole. 162 163 A ! # The current which produces a force of 2e-7 N/m between two 164 ampere A # infinitely long wires that are 1 meter apart 165 amp ampere 166 167 cd ! # Luminous intensity in a given direction of a source which 168 candela cd # emits monochromatic radiation at 540e12 Hz with radiant 169 # intensity 1|683 W/steradian. (This differs from radiant 170 # intensity (W/sr) in that it is adjusted for human 171 # perceptual dependence on wavelength. The frequency of 172 # 540e12 Hz (yellow) is where human perception is most 173 # efficient.) 174 175 mol ! # The amount of substance of a system which contains as many 176 mole mol # elementary entities as there are atoms in 0.012 kg of 177 # carbon 12. The elementary entities must be specified and 178 # may be atoms, molecules, ions, electrons, or other 179 # particles or groups of particles. It is understood that 180 # unbound atoms of carbon 12, at rest and in the ground 181 # state, are referred to. 182 183 K ! # 1|273.16 of the thermodynamic temperature of the triple 184 kelvin K # point of water 185 186 # 187 # The radian and steradian are defined as dimensionless primitive units. 188 # The radian is equal to m/m and the steradian to m^2/m^2 so these units are 189 # dimensionless. Retaining them as named units is useful because it allows 190 # clarity in expressions and makes the meaning of unit definitions more clear. 191 # These units will reduce to 1 in conversions but not for sums of units or for 192 # arguments to functions. 193 # 194 195 radian !dimensionless # The angle subtended at the center of a circle by 196 # an arc equal in length to the radius of the 197 # circle 198 sr !dimensionless # Solid angle which cuts off an area of the surface 199 steradian sr # of the sphere equal to that of a square with 200 # sides of length equal to the radius of the 201 # sphere 202 203 # 204 # A primitive non-SI unit 205 # 206 207 bit ! # Basic unit of information (entropy). The entropy in bits 208 # of a random variable over a finite alphabet is defined 209 # to be the sum of -p(i)*log2(p(i)) over the alphabet where 210 # p(i) is the probability that the random variable takes 211 # on the value i. 212 213 # 214 # Currency: the primitive unit of currency is defined in currency.units. 215 # It is usually the US$ or the euro, but it is user selectable. 216 # 217 218 ########################################################################### 219 # # 220 # Prefixes (longer names must come first) # 221 # # 222 ########################################################################### 223 224 yotta- 1e24 # Greek or Latin octo, "eight" 225 zetta- 1e21 # Latin septem, "seven" 226 exa- 1e18 # Greek hex, "six" 227 peta- 1e15 # Greek pente, "five" 228 tera- 1e12 # Greek teras, "monster" 229 giga- 1e9 # Greek gigas, "giant" 230 mega- 1e6 # Greek megas, "large" 231 myria- 1e4 # Not an official SI prefix 232 kilo- 1e3 # Greek chilioi, "thousand" 233 hecto- 1e2 # Greek hekaton, "hundred" 234 deca- 1e1 # Greek deka, "ten" 235 deka- deca 236 deci- 1e-1 # Latin decimus, "tenth" 237 centi- 1e-2 # Latin centum, "hundred" 238 milli- 1e-3 # Latin mille, "thousand" 239 micro- 1e-6 # Latin micro or Greek mikros, "small" 240 nano- 1e-9 # Latin nanus or Greek nanos, "dwarf" 241 pico- 1e-12 # Spanish pico, "a bit" 242 femto- 1e-15 # Danish-Norwegian femten, "fifteen" 243 atto- 1e-18 # Danish-Norwegian atten, "eighteen" 244 zepto- 1e-21 # Latin septem, "seven" 245 yocto- 1e-24 # Greek or Latin octo, "eight" 246 247 quarter- 1|4 248 semi- 0.5 249 demi- 0.5 250 hemi- 0.5 251 half- 0.5 252 double- 2 253 triple- 3 254 treble- 3 255 256 kibi- 2^10 # In response to the convention of illegally 257 mebi- 2^20 # and confusingly using metric prefixes for 258 gibi- 2^30 # powers of two, the International 259 tebi- 2^40 # Electrotechnical Commission aproved these 260 pebi- 2^50 # binary prefixes for use in 1998. If you 261 exbi- 2^60 # want to refer to "megabytes" using the 262 Ki- kibi # binary definition, use these prefixes. 263 Mi- mebi 264 Gi- gibi 265 Ti- tebi 266 Pi- pebi 267 Ei- exbi 268 269 Y- yotta 270 Z- zetta 271 E- exa 272 P- peta 273 T- tera 274 G- giga 275 M- mega 276 k- kilo 277 h- hecto 278 da- deka 279 d- deci 280 c- centi 281 m- milli 282 u- micro # it should be a mu but u is easy to type 283 n- nano 284 p- pico 285 f- femto 286 a- atto 287 z- zepto 288 y- yocto 289 290 # 291 # Names of some numbers 292 # 293 294 one 1 295 two 2 296 double 2 297 couple 2 298 three 3 299 triple 3 300 four 4 301 quadruple 4 302 five 5 303 quintuple 5 304 six 6 305 seven 7 306 eight 8 307 nine 9 308 ten 10 309 eleven 11 310 twelve 12 311 thirteen 13 312 fourteen 14 313 fifteen 15 314 sixteen 16 315 seventeen 17 316 eighteen 18 317 nineteen 19 318 twenty 20 319 thirty 30 320 forty 40 321 fifty 50 322 sixty 60 323 seventy 70 324 eighty 80 325 ninety 90 326 hundred 100 327 thousand 1000 328 million 1e6 329 330 twoscore two score 331 threescore three score 332 fourscore four score 333 fivescore five score 334 sixscore six score 335 sevenscore seven score 336 eightscore eight score 337 ninescore nine score 338 tenscore ten score 339 twelvescore twelve score 340 341 # These number terms were described by N. Chuquet and De la Roche in the 16th 342 # century as being successive powers of a million. These definitions are still 343 # used in most European countries. The current US definitions for these 344 # numbers arose in the 17th century and don't make nearly as much sense. These 345 # numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric 346 # W. Weisstein. 347 348 shortbillion 1e9 349 shorttrillion 1e12 350 shortquadrillion 1e15 351 shortquintillion 1e18 352 shortsextillion 1e21 353 shortseptillion 1e24 354 shortoctillion 1e27 355 shortnonillion 1e30 356 shortnoventillion shortnonillion 357 shortdecillion 1e33 358 shortundecillion 1e36 359 shortduodecillion 1e39 360 shorttredecillion 1e42 361 shortquattuordecillion 1e45 362 shortquindecillion 1e48 363 shortsexdecillion 1e51 364 shortseptendecillion 1e54 365 shortoctodecillion 1e57 366 shortnovemdecillion 1e60 367 shortvigintillion 1e63 368 369 centillion 1e303 370 googol 1e100 371 372 longbillion million^2 373 longtrillion million^3 374 longquadrillion million^4 375 longquintillion million^5 376 longsextillion million^6 377 longseptillion million^7 378 longoctillion million^8 379 longnonillion million^9 380 longnoventillion longnonillion 381 longdecillion million^10 382 longundecillion million^11 383 longduodecillion million^12 384 longtredecillion million^13 385 longquattuordecillion million^14 386 longquindecillion million^15 387 longsexdecillion million^16 388 longseptdecillion million^17 389 longoctodecillion million^18 390 longnovemdecillion million^19 391 longvigintillion million^20 392 393 # These numbers fill the gaps left by the long system above. 394 395 milliard 1000 million 396 billiard 1000 million^2 397 trilliard 1000 million^3 398 quadrilliard 1000 million^4 399 quintilliard 1000 million^5 400 sextilliard 1000 million^6 401 septilliard 1000 million^7 402 octilliard 1000 million^8 403 nonilliard 1000 million^9 404 noventilliard nonilliard 405 decilliard 1000 million^10 406 407 # For consistency 408 409 longmilliard milliard 410 longbilliard billiard 411 longtrilliard trilliard 412 longquadrilliard quadrilliard 413 longquintilliard quintilliard 414 longsextilliard sextilliard 415 longseptilliard septilliard 416 longoctilliard octilliard 417 longnonilliard nonilliard 418 longnoventilliard noventilliard 419 longdecilliard decilliard 420 421 # The long centillion would be 1e600. The googolplex is another 422 # familiar large number equal to 10^googol. These numbers give overflows. 423 424 # 425 # The short system prevails in English speaking countries 426 # 427 428 billion shortbillion 429 trillion shorttrillion 430 quadrillion shortquadrillion 431 quintillion shortquintillion 432 sextillion shortsextillion 433 septillion shortseptillion 434 octillion shortoctillion 435 nonillion shortnonillion 436 noventillion shortnoventillion 437 decillion shortdecillion 438 undecillion shortundecillion 439 duodecillion shortduodecillion 440 tredecillion shorttredecillion 441 quattuordecillion shortquattuordecillion 442 quindecillion shortquindecillion 443 sexdecillion shortsexdecillion 444 septendecillion shortseptendecillion 445 octodecillion shortoctodecillion 446 novemdecillion shortnovemdecillion 447 vigintillion shortvigintillion 448 449 # 450 # Numbers used in India 451 # 452 453 lakh 1e5 454 crore 1e7 455 arab 1e9 456 kharab 1e11 457 neel 1e13 458 padm 1e15 459 shankh 1e17 460 461 ############################################################################# 462 # # 463 # Derived units which can be reduced to the primitive units # 464 # # 465 ############################################################################# 466 467 468 469 # 470 # Named SI derived units (officially accepted) 471 # 472 473 newton kg m / s^2 # force 474 N newton 475 pascal N/m^2 # pressure or stress 476 Pa pascal 477 joule N m # energy 478 J joule 479 watt J/s # power 480 W watt 481 coulomb A s # charge 482 C coulomb 483 volt W/A # potential difference 484 V volt 485 ohm V/A # electrical resistance 486 siemens A/V # electrical conductance 487 S siemens 488 farad C/V # capacitance 489 F farad 490 weber V s # magnetic flux 491 Wb weber 492 henry V s / A # inductance 493 H henry 494 tesla Wb/m^2 # magnetic flux density 495 T tesla 496 hertz /s # frequency 497 Hz hertz 498 499 # 500 # Dimensions. These are here to help with dimensional analysis and 501 # because they will appear in the list produced by hitting '?' at the 502 # "You want:" prompt to tell the user the dimension of the unit. 503 # 504 505 LENGTH meter 506 AREA LENGTH^2 507 VOLUME LENGTH^3 508 MASS kilogram 509 AMOUNT mole 510 ANGLE radian 511 SOLID_ANGLE steradian 512 MONEY US$ 513 FORCE newton 514 PRESSURE FORCE / AREA 515 STRESS FORCE / AREA 516 FREQUENCY hertz 517 VELOCITY LENGTH / TIME 518 ACCELERATION VELOCITY / TIME 519 DENSITY MASS / VOLUME 520 LINEAR_DENSITY MASS / LENGTH 521 VISCOSITY FORCE TIME / AREA 522 KINEMATIC_VISCOSITY VISCOSITY / DENSITY 523 CURRENT ampere 524 CHARGE coulomb 525 CAPACITANCE farad 526 RESISTANCE ohm 527 CONDUCTANCE siemens 528 INDUCTANCE henry 529 E_FIELD ELECTRIC_POTENTIAL / LENGTH 530 B_FIELD tesla 531 # The D and H fields are related to the E and B fields by factors of epsilon 532 # and mu respectively, so their units can be found by multiplying/dividing by 533 # the epsilon0 and mu0, but then it is necessary to remove the constant factors 534 # to get the correct scaling. Defining the units this way allows conversion to 535 # CGS units to work correctly. 536 D_FIELD E_FIELD epsilon0 (c/(m/s))^2 4 pi 1e-7 537 H_FIELD B_FIELD / mu0 * 4 pi 1e-7 538 ELECTRIC_DIPOLE_MOMENT C m 539 MAGNETIC_DIPOLE_MOMENT J / T 540 POLARIZATION ELECTRIC_DIPOLE_MOMENT / VOLUME 541 MAGNETIZATION MAGNETIC_DIPOLE_MOMENT / VOLUME 542 ELECTRIC_POTENTIAL volt 543 VOLTAGE ELECTRIC_POTENTIAL 544 E_FLUX E_FIELD AREA 545 D_FLUX D_FIELD AREA 546 B_FLUX B_FIELD AREA 547 H_FLUX H_FIELD AREA 548 549 # 550 # units derived easily from SI units 551 # 552 553 gram millikg 554 gm gram 555 g gram 556 tonne 1000 kg 557 t tonne 558 metricton tonne 559 sthene tonne m / s^2 560 funal sthene 561 pieze sthene / m^2 562 quintal 100 kg 563 bar 1e5 Pa # About 1 atm 564 b bar 565 vac millibar 566 micron micrometer # One millionth of a meter 567 bicron picometer # One brbillionth of a meter 568 cc cm^3 569 are 100 m^2 570 a are 571 liter 1000 cc # The liter was defined in 1901 as the 572 oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at 573 L liter # the temperature of its maximum density 574 l liter # under a pressure of 1 atm. This was 575 # supposed to be 1000 cubic cm, but it 576 # was discovered that the original 577 # measurement was off. In 1964, the 578 # liter was redefined to be exactly 1000 579 # cubic centimeters. 580 mho siemens # Inverse of ohm, hence ohm spelled backward 581 galvat ampere # Named after Luigi Galvani 582 angstrom 1e-10 m # Convenient for describing molecular sizes 583 xunit xunit_cu # Used for measuring x-ray wavelengths. 584 siegbahn xunit # Originally defined to be 1|3029.45 of 585 xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18 586 xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly 587 # 1e-13 m, but was later found to be 588 # slightly off. Current usage is with 589 # reference to common x-ray lines, either 590 # the K-alpha 1 line of copper or the 591 # same line of molybdenum. 592 angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965 593 fermi 1e-15 m # Convenient for describing nuclear sizes 594 # Nuclear radius is from 1 to 10 fermis 595 barn 1e-28 m^2 # Used to measure cross section for 596 # particle physics collision, said to 597 # have originated in the phrase "big as 598 # a barn". 599 shed 1e-24 barn # Defined to be a smaller companion to the 600 # barn, but it's too small to be of 601 # much use. 602 brewster micron^2/N # measures stress-optical coef 603 diopter /m # measures reciprocal of lens focal length 604 fresnel 1e12 Hz # occasionally used in spectroscopy 605 shake 1e-8 sec 606 svedberg 1e-13 s # Used for measuring the sedimentation 607 # coefficient for centrifuging. 608 gamma microgram # Also used for 1e-9 tesla 609 lambda microliter 610 spat 1e12 m # Rarely used for astronomical measurements 611 preece 1e13 ohm m # resistivity 612 planck J s # action of one joule over one second 613 sturgeon /henry # magnetic reluctance 614 daraf 1/farad # elastance (farad spelled backwards) 615 leo 10 m/s^2 616 poiseuille N s / m^2 # viscosity 617 mayer J/g K # specific heat 618 mired / microK # reciprocal color temperature. The name 619 # abbreviates micro reciprocal degree. 620 crocodile megavolt # used informally in UK physics labs 621 metricounce 25 g 622 mounce metricounce 623 finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light 624 # with wavelength 296.7 nm. 625 fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure 626 # the energy incident on the receiving 627 # body across a specified frequency 628 # bandwidth. [12] 629 jansky fluxunit # K. G. Jansky identified radio waves coming 630 Jy jansky # from outer space in 1931. 631 flick W / cm^2 sr micrometer # Spectral radiance or irradiance 632 pfu / cm^2 sr s # particle flux unit -- Used to measure 633 # rate at which particles are received by 634 # a spacecraft as particles per solid 635 # angle per detector area per second. [18] 636 pyron cal_IT / cm^2 min # Measures heat flow from solar radiation, 637 # from Greek work "pyr" for fire. 638 katal mol/sec # Measure of the amount of a catalyst. One 639 kat katal # katal of catalyst enables the reaction 640 # to consume or produce on mol/sec. 641 solarluminosity 382.8e24 W # A common yardstick for comparing the 642 # output of different stars. 643 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html 644 # at mean earth-sun distance 645 solarirradiance solarluminosity / (4 pi sundist^2) 646 solarconstant solarirradiance 647 TSI solarirradiance # total solar irradiance 648 649 # 650 # time 651 # 652 653 sec s 654 minute 60 s 655 min minute 656 hour 60 min 657 hr hour 658 day 24 hr 659 d day 660 da day 661 week 7 day 662 wk week 663 sennight 7 day 664 fortnight 14 day 665 blink 1e-5 day # Actual human blink takes 1|3 second 666 ce 1e-2 day 667 cron 1e6 years 668 watch 4 hours # time a sentry stands watch or a ship's 669 # crew is on duty. 670 bell 1|8 watch # Bell would be sounded every 30 minutes. 671 672 # French Revolutionary Time or Decimal Time. It was Proposed during 673 # the French Revolution. A few clocks were made, but it never caught 674 # on. In 1998 Swatch defined a time measurement called ".beat" and 675 # sold some watches that displayed time in this unit. 676 677 decimalhour 1|10 day 678 decimalminute 1|100 decimalhour 679 decimalsecond 1|100 decimalminute 680 beat decimalminute # Swatch Internet Time 681 682 # 683 # angular measure 684 # 685 686 circle 2 pi radian 687 degree 1|360 circle 688 deg degree 689 arcdeg degree 690 arcmin 1|60 degree 691 arcminute arcmin 692 ' arcmin 693 arcsec 1|60 arcmin 694 arcsecond arcsec 695 " arcsec 696 '' " 697 rightangle 90 degrees 698 quadrant 1|4 circle 699 quintant 1|5 circle 700 sextant 1|6 circle 701 702 sign 1|12 circle # Angular extent of one sign of the zodiac 703 turn circle 704 revolution turn 705 rev turn 706 pulsatance radian / sec 707 gon 1|100 rightangle # measure of grade 708 grade gon 709 centesimalminute 1|100 grade 710 centesimalsecond 1|100 centesimalminute 711 milangle 1|6400 circle # Official NIST definition. 712 # Another choice is 1e-3 radian. 713 pointangle 1|32 circle # Used for reporting compass readings 714 centrad 0.01 radian # Used for angular deviation of light 715 # through a prism. 716 mas milli arcsec # Used by astronomers 717 seclongitude circle (seconds/day) # Astronomers measure longitude 718 # (which they call right ascension) in 719 # time units by dividing the equator into 720 # 24 hours instead of 360 degrees. 721 # 722 # Some geometric formulas 723 # 724 725 circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi) 726 spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \ 727 cuberoot(spherevolume/4|3 pi) 728 spherevol() spherevolume 729 square(x) range=[0,) x^2 ; sqrt(square) 730 731 # 732 # Solid angle measure 733 # 734 735 sphere 4 pi sr 736 squaredegree 1|180^2 pi^2 sr 737 squareminute 1|60^2 squaredegree 738 squaresecond 1|60^2 squareminute 739 squarearcmin squareminute 740 squarearcsec squaresecond 741 sphericalrightangle 0.5 pi sr 742 octant 0.5 pi sr 743 744 # 745 # Concentration measures 746 # 747 748 percent 0.01 749 % percent 750 mill 0.001 # Originally established by Congress in 1791 751 # as a unit of money equal to 0.001 dollars, 752 # it has come to refer to 0.001 in general. 753 # Used by some towns to set their property 754 # tax rate, and written with a symbol similar 755 # to the % symbol but with two 0's in the 756 # denominator. [18] 757 proof 1|200 # Alcohol content measured by volume at 758 # 60 degrees Fahrenheit. This is a USA 759 # measure. In Europe proof=percent. 760 ppm 1e-6 761 partspermillion ppm 762 ppb 1e-9 763 partsperbillion ppb # USA billion 764 ppt 1e-12 765 partspertrillion ppt # USA trillion 766 karat 1|24 # measure of gold purity 767 caratgold karat 768 gammil mg/l 769 basispoint 0.01 % # Used in finance 770 fine 1|1000 # Measure of gold purity 771 772 # The pH scale is used to measure the concentration of hydronium (H3O+) ions in 773 # a solution. A neutral solution has a pH of 7 as a result of dissociated 774 # water molecules. 775 776 pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol)) 777 778 779 # 780 # Temperature 781 # 782 # Two types of units are defined: units for converting temperature differences 783 # and functions for converting absolute temperatures. Conversions for 784 # differences start with "deg" and conversions for absolute temperature start 785 # with "temp". 786 # 787 788 TEMPERATURE kelvin 789 TEMPERATURE_DIFFERENCE kelvin 790 791 # In 1741 Anders Celsius introduced a temperature scale with water boiling at 792 # 0 degrees and freezing at 100 degrees at standard pressure. After his death 793 # the fixed points were reversed and the scale was called the centigrade 794 # scale. Due to the difficulty of accurately measuring the temperature of 795 # melting ice at standard pressure, the centigrade scale was replaced in 1954 796 # by the Celsius scale which is defined by subtracting 273.15 from the 797 # temperature in Kelvins. This definition differed slightly from the old 798 # centigrade definition, but the Kelvin scale depends on the triple point of 799 # water rather than a melting point, so it can be measured accurately. 800 801 tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \ 802 x K + stdtemp ; (tempC +(-stdtemp))/K 803 tempcelsius() tempC 804 degcelsius K 805 degC K 806 807 # Fahrenheit defined his temperature scale by setting 0 to the coldest 808 # temperature he could produce in his lab with a salt water solution and by 809 # setting 96 degrees to body heat. In Fahrenheit's words: 810 # 811 # Placing the thermometer in a mixture of sal ammoniac or sea 812 # salt, ice, and water a point on the scale will be found which 813 # is denoted as zero. A second point is obtained if the same 814 # mixture is used without salt. Denote this position as 30. A 815 # third point, designated as 96, is obtained if the thermometer 816 # is placed in the mouth so as to acquire the heat of a healthy 817 # man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724) 818 819 tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \ 820 (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 821 tempfahrenheit() tempF 822 degfahrenheit 5|9 degC 823 degF 5|9 degC 824 825 826 degreesrankine degF # The Rankine scale has the 827 degrankine degreesrankine # Fahrenheit degree, but its zero 828 degreerankine degF # is at absolute zero. 829 degR degrankine 830 tempR degrankine 831 temprankine degrankine 832 833 tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \ 834 x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur 835 degreaumur 10|8 degC # The Reaumur scale was used in Europe and 836 # particularly in France. It is defined 837 # to be 0 at the freezing point of water 838 # and 80 at the boiling point. Reaumur 839 # apparently selected 80 because it is 840 # divisible by many numbers. 841 842 degK K # "Degrees Kelvin" is forbidden usage. 843 tempK K # For consistency 844 845 # Gas mark is implemented below but in a terribly ugly way. There is 846 # a simple formula, but it requires a conditional which is not 847 # presently supported. 848 # 849 # The formula to convert to degrees Fahrenheit is: 850 # 851 # 25 log2(gasmark) + k_f gasmark<=1 852 # 25 (gasmark-1) + k_f gasmark>=1 853 # 854 # k_f = 275 855 # 856 gasmark[degR] \ 857 .0625 634.67 \ 858 .125 659.67 \ 859 .25 684.67 \ 860 .5 709.67 \ 861 1 734.67 \ 862 2 759.67 \ 863 3 784.67 \ 864 4 809.67 \ 865 5 834.67 \ 866 6 859.67 \ 867 7 884.67 \ 868 8 909.67 \ 869 9 934.67 \ 870 10 959.67 871 872 # Units cannot handle wind chill or heat index because they are two variable 873 # functions, but they are included here for your edification. Clearly these 874 # equations are the result of a model fitting operation. 875 # 876 # wind chill index (WCI) a measurement of the combined cooling effect of low 877 # air temperature and wind on the human body. The index was first defined 878 # by the American Antarctic explorer Paul Siple in 1939. As currently used 879 # by U.S. meteorologists, the wind chill index is computed from the 880 # temperature T (in °F) and wind speed V (in mi/hr) using the formula: 881 # WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4. 882 # For very low wind speeds, below 4 mi/hr, the WCI is actually higher than 883 # the air temperature, but for higher wind speeds it is lower than the air 884 # temperature. 885 # 886 # heat index (HI or HX) a measure of the combined effect of heat and 887 # humidity on the human body. U.S. meteorologists compute the index 888 # from the temperature T (in °F) and the relative humidity H (as a 889 # value from 0 to 1). 890 # HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH 891 # - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2 892 # - 0.0199 T^2 H^2. 893 894 # 895 # Physical constants 896 # 897 898 # Basic constants 899 900 pi 3.14159265358979323846 901 c 2.99792458e8 m/s # speed of light in vacuum (exact) 902 light c 903 mu0 4 pi 1e-7 H/m # permeability of vacuum (exact) 904 epsilon0 1/mu0 c^2 # permittivity of vacuum (exact) 905 energy c^2 # convert mass to energy 906 e 1.6021766208e-19 C # electron charge 907 h 4.135667662e-15 eV s # Planck constant 908 hbar h / 2 pi 909 spin hbar 910 G 6.67408e-11 N m^2 / kg^2 # Newtonian gravitational constant 911 # This is the NIST 2006 value. 912 # The relative uncertainty on this 913 # is 1e-4. 914 coulombconst 1/4 pi epsilon0 # listed as "k" sometimes 915 916 # Physico-chemical constants 917 918 atomicmassunit 1.660539040e-27 kg # atomic mass unit (defined to be 919 u atomicmassunit # 1|12 of the mass of carbon 12) 920 amu atomicmassunit 921 amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of 922 # the 3 naturally occuring neutral 923 # isotopes of oxygen 924 amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral 925 # oxygen 16 atom 926 dalton u # Maybe this should be amu_chem? 927 avogadro grams/amu mol # size of a mole 928 N_A avogadro 929 gasconstant k N_A # molar gas constant 930 R gasconstant 931 boltzmann 1.38064852e-23 J/K # Boltzmann constant 932 k boltzmann 933 kboltzmann boltzmann 934 molarvolume mol R stdtemp / atm # Volume occupied by one mole of an 935 # ideal gas at STP. 936 loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an 937 # ideal gas at STP. Loschmidt did 938 # work similar to Avogadro. 939 stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a 940 sigma stefanboltzmann # blackbody at temperature T is 941 # given by sigma T^4. 942 wiendisplacement 2.8977729e-3 m K # Wien's Displacement Law gives the 943 # frequency at which the the Planck 944 # spectrum has maximum intensity. 945 # The relation is lambda T = b where 946 # lambda is wavelength, T is 947 # temperature and b is the Wien 948 # displacement. This relation is 949 # used to determine the temperature 950 # of stars. 951 K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until 952 K_J 483597.8525 GHz/V # recently, laboratories kept Weston cadmium cells as 953 # a reference, but they could drift. In 1987 the 954 # CGPM officially recommended the use of the 955 # Josephson effect as a laboratory representation of 956 # the volt. The Josephson effect occurs when two 957 # superconductors are separated by a thin insulating 958 # layer. A "supercurrent" flows across the insulator 959 # with a frequency that depends on the potential 960 # applied across the superconductors. This frequency 961 # can be very accurately measured. The Josephson 962 # constant K_J, which is equal to 2e/h, relates the 963 # measured frequency to the potential. Two values 964 # given, the conventional (exact) value from 1990 and 965 # the current CODATA measured value. 966 R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties. 967 R_K 25812.8074555 ohm # The old approach involved maintaining resistances 968 # that were subject to drift. The new standard is 969 # based on the Hall effect. When a current carrying 970 # ribbon is placed in a magnetic field, a potential 971 # difference develops across the ribbon. The ratio 972 # of the potential difference to the current is 973 # called the Hall resistance. Klaus von Klitzing 974 # discovered in 1980 that the Hall resistance varies 975 # in discrete jumps when the magnetic field is very 976 # large and the temperature very low. This enables 977 # accurate realization of the resistance h/e^2 in the 978 # lab. Two values given, the conventional (exact) 979 # value from 1990 and the current CODATA measured 980 # value. 981 982 # Various conventional values 983 984 gravity 9.80665 m/s^2 # std acceleration of gravity (exact) 985 force gravity # use to turn masses into forces 986 atm 101325 Pa # Standard atmospheric pressure 987 atmosphere atm 988 Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact) 989 water gram force/cm^3 # Standard weight of water (exact) 990 waterdensity gram / cm^3 # Density of water 991 H2O water 992 wc water # water column 993 mach 331.46 m/s # speed of sound in dry air at STP 994 standardtemp 273.15 K # standard temperature 995 stdtemp standardtemp 996 normaltemp tempF(70) # for gas density, from NIST 997 normtemp normaltemp # Handbook 44 998 999 # Weight of mercury and water at different temperatures using the standard 1000 # force of gravity. 1001 1002 Hg10C 13.5708 force gram / cm^3 # These units, when used to form 1003 Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate 1004 Hg23C 13.5386 force gram / cm^3 # because of considerations of the 1005 Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale. 1006 Hg40C 13.4973 force gram / cm^3 1007 Hg60F 13.5574 force gram / cm^3 1008 H2O0C 0.99987 force gram / cm^3 1009 H2O5C 0.99999 force gram / cm^3 1010 H2O10C 0.99973 force gram / cm^3 1011 H2O15C 0.99913 force gram / cm^3 1012 H2O18C 0.99862 force gram / cm^3 1013 H2O20C 0.99823 force gram / cm^3 1014 H2O25C 0.99707 force gram / cm^3 1015 H2O50C 0.98807 force gram / cm^3 1016 H2O100C 0.95838 force gram / cm^3 1017 1018 # Atomic constants 1019 1020 Rinfinity 10973731.568539 /m # The wavelengths of a spectral series 1021 R_H 10967760 /m # can be expressed as 1022 # 1/lambda = R (1/m^2 - 1/n^2). 1023 # where R is a number that various 1024 # slightly from element to element. 1025 # For hydrogen, R_H is the value, 1026 # and for heavy elements, the value 1027 # approaches Rinfinity, which can be 1028 # computed from 1029 # m_e c alpha^2 / 2 h 1030 # with a loss of 4 digits 1031 # of precision. 1032 alpha 7.2973525664e-3 # The fine structure constant was 1033 # introduced to explain fine 1034 # structure visible in spectral 1035 # lines. It can be computed from 1036 # mu0 c e^2 / 2 h 1037 # with a loss of 3 digits precision 1038 # and loss of precision in derived 1039 # values which use alpha. 1040 bohrradius alpha / 4 pi Rinfinity 1041 prout 185.5 keV # nuclear binding energy equal to 1|12 1042 # binding energy of the deuteron 1043 # Planck constants 1044 1045 planckmass 2.17651e-8 kg # sqrt(hbar c / G) 1046 m_P planckmass 1047 plancktime hbar / planckmass c^2 1048 t_P plancktime 1049 plancklength plancktime c 1050 l_P plancklength 1051 1052 # Particle radius 1053 1054 electronradius coulombconst e^2 / electronmass c^2 # Classical 1055 deuteronchargeradius 2.1413e-15 m 1056 protonchargeradius 0.8751e-15 m 1057 1058 # Masses of elementary particles 1059 1060 electronmass 5.48579909070e-4 u 1061 m_e electronmass 1062 protonmass 1.007276466879 u 1063 m_p protonmass 1064 neutronmass 1.00866491588 u 1065 m_n neutronmass 1066 muonmass 0.1134289257 u 1067 m_mu muonmass 1068 deuteronmass 2.013553212745 u 1069 m_d deuteronmass 1070 alphaparticlemass 4.001506179127 u 1071 m_alpha alphaparticlemass 1072 taumass 1.90749 u 1073 m_tau taumass 1074 tritonmass 3.01550071632 u 1075 m_t tritonmass 1076 helionmass 3.01493224673 u 1077 m_h helionmass 1078 1079 1080 1081 # particle wavelengths: the compton wavelength of a particle is 1082 # defined as h / m c where m is the mass of the particle. 1083 1084 electronwavelength h / m_e c 1085 lambda_C electronwavelength 1086 protonwavelength h / m_p c 1087 lambda_C,p protonwavelength 1088 neutronwavelength h / m_n c 1089 lambda_C,n neutronwavelength 1090 1091 # Magnetic moments 1092 1093 bohrmagneton e hbar / 2 electronmass 1094 mu_B bohrmagneton 1095 nuclearmagneton e hbar / 2 protonmass 1096 mu_N nuclearmagneton 1097 mu_mu -4.49044826e-26 J/T # Muon magnetic moment 1098 mu_p 1.4106067873e-26 J/T # Proton magnetic moment 1099 mu_e -928.4764620e-26 J/T # Electron magnetic moment 1100 mu_n -0.96623650e-26 J/T # Neutron magnetic moment 1101 mu_d 0.4330735040e-26 J/T # Deuteron magnetic moment 1102 mu_t 1.504609503e-26 J/T # Triton magnetic moment 1103 mu_h -1.074617522e-26 J/T # Helion magnetic moment 1104 1105 1106 # 1107 # Units derived from physical constants 1108 # 1109 1110 kgf kg force 1111 technicalatmosphere kgf / cm^2 1112 at technicalatmosphere 1113 hyl kgf s^2 / m # Also gram-force s^2/m according to [15] 1114 mmHg mm Hg 1115 torr atm / 760 # The torr, named after Evangelista 1116 # Torricelli, and is very close to the mm Hg 1117 tor Pa # Suggested in 1913 but seldom used [24]. 1118 # Eventually renamed the Pascal. Don't 1119 # confuse the tor with the torr. 1120 inHg inch Hg 1121 inH2O inch water 1122 mmH2O mm water 1123 eV e V # Energy acquired by a particle with charge e 1124 electronvolt eV # when it is accelerated through 1 V 1125 lightyear c julianyear # The 365.25 day year is specified in 1126 ly lightyear # NIST publication 811 1127 lightsecond c s 1128 lightminute c min 1129 parsec au / tan(arcsec) # Unit of length equal to distance 1130 pc parsec # from the sun to a point having 1131 # heliocentric parallax of 1 1132 # arcsec (derived from parallax 1133 # second). A distant object with 1134 # paralax theta will be about 1135 # (arcsec/theta) parsecs from the 1136 # sun (using the approximation 1137 # that tan(theta) = theta). 1138 rydberg h c Rinfinity # Rydberg energy 1139 crith 0.089885 gram # The crith is the mass of one 1140 # liter of hydrogen at standard 1141 # temperature and pressure. 1142 amagatvolume molarvolume 1143 amagat mol/amagatvolume # Used to measure gas densities 1144 lorentz bohrmagneton / h c # Used to measure the extent 1145 # that the frequency of light 1146 # is shifted by a magnetic field. 1147 cminv h c / cm # Unit of energy used in infrared 1148 invcm cminv # spectroscopy. 1149 wavenumber cminv 1150 kcal_mol kcal_th / mol N_A # kcal/mol is used as a unit of 1151 # energy by physical chemists. 1152 # 1153 # CGS system based on centimeter, gram and second 1154 # 1155 1156 dyne cm gram / s^2 # force 1157 dyn dyne 1158 erg cm dyne # energy 1159 poise gram / cm s # viscosity, honors Jean Poiseuille 1160 P poise 1161 rhe /poise # reciprocal viscosity 1162 stokes cm^2 / s # kinematic viscosity 1163 St stokes 1164 stoke stokes 1165 lentor stokes # old name 1166 Gal cm / s^2 # acceleration, used in geophysics 1167 galileo Gal # for earth's gravitational field 1168 # (note that "gal" is for gallon 1169 # but "Gal" is the standard symbol 1170 # for the gal which is evidently a 1171 # shortened form of "galileo".) 1172 barye dyne/cm^2 # pressure 1173 barad barye # old name 1174 kayser 1/cm # Proposed as a unit for wavenumber 1175 balmer kayser # Even less common name than "kayser" 1176 kine cm/s # velocity 1177 bole g cm / s # momentum 1178 pond gram force 1179 glug gram force s^2 / cm # Mass which is accelerated at 1180 # 1 cm/s^2 by 1 gram force 1181 darcy centipoise cm^2 / s atm # Measures permeability to fluid flow. 1182 # One darcy is the permeability of a 1183 # medium that allows a flow of cc/s 1184 # of a liquid of centipoise viscosity 1185 # under a pressure gradient of 1186 # atm/cm. Named for H. Darcy. 1187 mobileohm cm / dyn s # mobile ohm, measure of mechanical 1188 # mobility 1189 mechanicalohm dyn s / cm # mechanical resistance 1190 acousticalohm dyn s / cm^5 # ratio of the sound pressure of 1191 # 1 dyn/cm^2 to a source of strength 1192 # 1 cm^3/s 1193 ray acousticalohm 1194 rayl dyn s / cm^3 # Specific acoustical resistance 1195 eotvos 1e-9 Gal/cm # Change in gravitational acceleration 1196 # over horizontal distance 1197 # 1198 # Electromagnetic CGS Units 1199 # 1200 # For measuring electromagnetic quantities in SI, we introduce the new base 1201 # dimension of current, define the ampere to measure current, and derive the 1202 # other electromagnetic units from the ampere. With the CGS units one approach 1203 # is to use the basic equations of electromagnetism to define units that 1204 # eliminate constants from those equations. Coulombs law has the form 1205 # 1206 # F = k_C q1 q2 / r^2 1207 # 1208 # where k_C is the coulomb constant equal to 1|4 pi epsilon0 in SI units. 1209 # Ampere's force law takes the form 1210 # 1211 # dF/dl = 2 k_A I1 I2 / r 1212 # 1213 # where k_A is the ampere constant. In the CGS system we force either k_C or 1214 # k_A to 1 which then defines either a unit for charge or a unit for current. 1215 # The other unit then becomes a derived unit. When k_C is 1 the ESU system 1216 # results. When k_A is 1 the EMU system results. Note that these parameters 1217 # are not independent of each other: Maxwell's equations indicate that 1218 # 1219 # k_C / k_A = c^2 1220 # 1221 # where c is the speed of light. 1222 # 1223 # One more choice is needed to define a complete system. Using Coulomb's law 1224 # we define the electric field as the force per unit charge 1225 # 1226 # E = k_C 1 / r^2. 1227 # 1228 # But what about the magnetic field? It is derived from Ampere's law but we 1229 # have the option of adding a proportionality constant, k_B, that may have 1230 # dimensions: 1231 # 1232 # B = 2 k_A k_B I / r 1233 # 1234 # We can choose k_B = 1, which is done in the SI, ESU and EMU systems. But if 1235 # instead we give k_B units of length/time then the magnetic field has 1236 # the same units as the electric field. This choice leads to the Gaussian 1237 # system. 1238 # 1239 # The relations above are used to determine the dimensions, but the units are 1240 # derived from the base units of CGS, not directly from those formulas. We 1241 # will use the notation [unit] to refer to the dimension of the unit in 1242 # brackets. This same process gives rise to the SI units such as the tesla, 1243 # which is defined by 1244 # 1245 # B = 2 1246 # 1247 # References: 1248 # 1249 # Classical Electrodynamics by John David Jackson, 3rd edition. 1250 # Cardarelli, Francois. 1999. Scientific Unit Conversion. 2nd ed. Trans. 1251 # M.J. Shields. London: Springer-Verlag. ISBN 1-85233-043-0 1252 # 1253 # 1254 # All of these systems result in electromagnetic units that involve the square 1255 # roots of the centimeter and gram. This requires a change in the primitive 1256 # units. 1257 # 1258 1259 !var UNITS_SYSTEM esu emu gaussian gauss 1260 sqrt_cm ! 1261 sqrt_centimeter sqrt_cm 1262 +m 100 sqrt_cm^2 1263 sqrt_g ! 1264 sqrt_gram sqrt_g 1265 +kg kilo sqrt_g^2 1266 !endvar 1267 1268 # Electrostatic CGS (ESU) 1269 # 1270 # This system uses the statcoulomb as the fundamental unit of charge, with 1271 # derived units that parallel the conventional terminology but use the stat- 1272 # prefix. The statcoulomb is designed by setting k_C=1, which means 1273 # 1274 # dyne = statcoulomb^2 / cm^2. 1275 # 1276 # The statcoulomb is also called the franklin or esu. 1277 # 1278 # The ESU system was specified by a committee report in 1873 and rarely used. 1279 1280 statcoulomb 10 coulomb cm / s c # Charge such that two charges 1281 esu statcoulomb # of 1 statC separated by 1 cm 1282 statcoul statcoulomb # exert a force of 1 dyne 1283 statC statcoulomb 1284 stC statcoulomb 1285 franklin statcoulomb 1286 Fr franklin 1287 1288 !var UNITS_SYSTEM esu 1289 !message CGS-ESU units selected 1290 !prompt (ESU) 1291 +statcoulomb sqrt(dyne) cm 1292 +A 0.1 statamp c/(cm/s) 1293 +mu0 1/c^2 1294 +coulombconst 1 1295 !endvar 1296 1297 statampere statcoulomb / s 1298 statamp statampere 1299 statA statampere 1300 stA statampere 1301 statvolt dyne cm / statamp sec 1302 statV statvolt 1303 stV statvolt 1304 statfarad statamp sec / statvolt 1305 statF statfarad 1306 stF statfarad 1307 cmcapacitance statfarad 1308 stathenry statvolt sec / statamp 1309 statH stathenry 1310 stH stathenry 1311 statohm statvolt / statamp 1312 stohm statohm 1313 statmho /statohm 1314 stmho statmho 1315 statweber statvolt sec 1316 statWb statweber 1317 stWb statweber 1318 stattesla statWb/cm^2 # Defined by analogy with SI; rarely 1319 statT stattesla # if ever used 1320 stT stattesla 1321 debye 1e-10 statC angstrom # unit of electrical dipole moment 1322 helmholtz debye/angstrom^2 # Dipole moment per area 1323 jar 1000 statfarad # approx capacitance of Leyden jar 1324 1325 # Electromagnetic CGS (EMU) 1326 # 1327 # The abampere is the fundamental unit of this system, with the derived units 1328 # using the ab- prefix. The dimensions of the abampere are defined by assuming 1329 # that k_A=1, which 1330 # 1331 # [dyne / cm] = [2 abampere^2 / cm] 1332 # 1333 # where the brackets indicate taking the dimension of the unit in base units 1334 # and discarding any constant factors. This results in the definition from 1335 # base CGS units of: 1336 # 1337 # abampere = sqrt(dyne). 1338 # 1339 # The abampere is also called the biot. The magnetic field unit (the gauss) 1340 # follows from the assumption that k_B=1, which means 1341 # 1342 # B = 2 I / r, 1343 # 1344 # and hence the dimensions of the gauss are given by 1345 # 1346 # [gauss] = [2 abampere / cm] 1347 # 1348 # or rewriting in terms of the base units 1349 # 1350 # gauss = abampere / cm. 1351 # 1352 # The definition given below is different because it is in a form that 1353 # gives a valid reduction for SI and ESU and still gives the correct 1354 # result in EMU. (It can be derived from Faraday's law.) 1355 # 1356 # The EMU system was developed by Gauss and Weber and formalized as a system in 1357 # a committee report by the British Association for the Advancement of Science 1358 # in 1873. 1359 1360 abampere 10 A # Current which produces a force of 1361 abamp abampere # 2 dyne/cm between two infinitely 1362 aA abampere # long wires that are 1 cm apart 1363 abA abampere 1364 biot abampere 1365 Bi biot 1366 1367 !var UNITS_SYSTEM emu 1368 !message CGS-EMU units selected 1369 !prompt (EMU) 1370 +abampere sqrt(dyne) 1371 +A 0.1 abamp 1372 +mu0 1 1373 +coulombconst c^2 1374 !endvar 1375 1376 abcoulomb abamp sec 1377 abcoul abcoulomb 1378 abC abcoulomb 1379 abfarad abampere sec / abvolt 1380 abF abfarad 1381 abhenry abvolt sec / abamp 1382 abH abhenry 1383 abvolt dyne cm / abamp sec 1384 abV abvolt 1385 abohm abvolt / abamp 1386 abmho /abohm 1387 gauss abvolt sec / cm^2 # The magnetic field 2 cm from a wire 1388 Gs gauss # carrying a current of 1 abampere 1389 maxwell gauss cm^2 # Also called the "line" 1390 Mx maxwell 1391 oersted gauss / mu0 # From the relation H = B / mu 1392 Oe oersted 1393 gilbert gauss cm / mu0 1394 Gb gilbert 1395 Gi gilbert 1396 unitpole 4 pi maxwell # unit magnetic pole 1397 emu erg/gauss # "electro-magnetic unit", a measure of 1398 # magnetic moment, often used as emu/cm^3 1399 # to specify magnetic moment density. 1400 1401 # Electromagnetic CGS (Gaussian) 1402 # 1403 # The Gaussian system uses the statcoulomb and statamp from the ESU system 1404 # derived by setting k_C=1, but it defines the magnetic field unit differently 1405 # by taking k_B=c instead of k_B=1. As noted above, k_C and k_A are not 1406 # independent. With k_C=1 we must have k_A=c^-2. This results in the magnetic 1407 # field unit, the gauss, having dimensions give by: 1408 # 1409 # [gauss] = [2 (c^-2) c statamp / cm] = [statamp / c cm] 1410 # 1411 # We then define the gauss using base CGS units to obtain 1412 # 1413 # gauss = statamp / ((cm/s) cm) = statcoulomb / cm^2. 1414 # 1415 # Note that this definition happens to give the same result as the definition 1416 # for the EMU system, so the definitions of the gauss are consistent. 1417 # 1418 # This definition gives the same dimensions for the E and B fields and was also 1419 # known as the "symmetric system". This system was proposed by Hertz in 1888. 1420 1421 !var UNITS_SYSTEM gaussian gauss 1422 !message CGS-Gaussian units selected 1423 !prompt (Gaussian) 1424 +statcoulomb sqrt(dyne) cm 1425 +A 0.1 statamp c/(cm/s) 1426 +mu0 1 1427 +epsilon0 1 1428 +coulombconst 1 # The gauss is the B field produced 1429 +gauss statcoulomb / cm^2 # 1 cm from a wire carrying a current 1430 +weber 1e8 maxwell # of 0.5*(c/(cm/s)) stA = 1.5e10 stA 1431 +bohrmagneton e hbar / 2 electronmass c 1432 +nuclearmagneton e hbar / 2 protonmass c 1433 !endvar 1434 1435 # 1436 # Some historical electromagnetic units 1437 # 1438 1439 intampere 0.999835 A # Defined as the current which in one 1440 intamp intampere # second deposits .001118 gram of 1441 # silver from an aqueous solution of 1442 # silver nitrate. 1443 intfarad 0.999505 F 1444 intvolt 1.00033 V 1445 intohm 1.000495 ohm # Defined as the resistance of a 1446 # uniform column of mercury containing 1447 # 14.4521 gram in a column 1.063 m 1448 # long and maintained at 0 degC. 1449 daniell 1.042 V # Meant to be electromotive force of a 1450 # Daniell cell, but in error by .04 V 1451 faraday N_A e mol # Charge that must flow to deposit or 1452 faraday_phys 96521.9 C # liberate one gram equivalent of any 1453 faraday_chem 96495.7 C # element. (The chemical and physical 1454 # values are off slightly from what is 1455 # obtained by multiplying by amu_chem 1456 # or amu_phys. These values are from 1457 # a 1991 NIST publication.) Note that 1458 # there is a Faraday constant which is 1459 # equal to N_A e and hence has units of 1460 # C/mol. 1461 kappline 6000 maxwell # Named by and for Gisbert Kapp 1462 siemensunit 0.9534 ohm # Resistance of a meter long column of 1463 # mercury with a 1 mm cross section. 1464 # 1465 # Printed circuit board units. 1466 # 1467 # http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm. 1468 # 1469 # Conductivity is often expressed as a percentage of IACS. A copper wire a 1470 # meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at 1471 # 20 deg C. Copper density is also standarized at that temperature. 1472 # 1473 1474 copperconductivity 58 siemens m / mm^2 # A wire a meter long with 1475 IACS copperconductivity # a 1 mm^2 cross section 1476 copperdensity 8.89 g/cm^3 # The "ounce" measures the 1477 ouncecopper oz / ft^2 copperdensity # thickness of copper used 1478 ozcu ouncecopper # in circuitboard fabrication 1479 1480 # 1481 # Photometric units 1482 # 1483 1484 LUMINOUS_INTENSITY candela 1485 LUMINOUS_FLUX lumen 1486 LUMINOUS_ENERGY talbot 1487 ILLUMINANCE lux 1488 EXITANCE lux 1489 1490 candle 1.02 candela # Standard unit for luminous intensity 1491 hefnerunit 0.9 candle # in use before candela 1492 hefnercandle hefnerunit # 1493 violle 20.17 cd # luminous intensity of 1 cm^2 of 1494 # platinum at its temperature of 1495 # solidification (2045 K) 1496 1497 lumen cd sr # Luminous flux (luminous energy per 1498 lm lumen # time unit) 1499 1500 talbot lumen s # Luminous energy 1501 lumberg talbot # References give these values for 1502 lumerg talbot # lumerg and lumberg both. Note that 1503 # a paper from 1948 suggests that 1504 # lumerg should be 1e-7 talbots so 1505 # that lumergs/erg = talbots/joule. 1506 # lumerg = luminous erg 1507 lux lm/m^2 # Illuminance or exitance (luminous 1508 lx lux # flux incident on or coming from 1509 phot lumen / cm^2 # a surface) 1510 ph phot # 1511 footcandle lumen/ft^2 # Illuminance from a 1 candela source 1512 # at a distance of one foot 1513 metercandle lumen/m^2 # Illuminance from a 1 candela source 1514 # at a distance of one meter 1515 1516 mcs metercandle s # luminous energy per area, used to 1517 # measure photographic exposure 1518 1519 nox 1e-3 lux # These two units were proposed for 1520 skot 1e-3 apostilb # measurements relating to dark adapted 1521 # eyes. 1522 # Luminance measures 1523 1524 LUMINANCE nit 1525 1526 nit cd/m^2 # Luminance: the intensity per projected 1527 stilb cd / cm^2 # area of an extended luminous source. 1528 sb stilb # (nit is from latin nitere = to shine.) 1529 1530 apostilb cd/pi m^2 1531 asb apostilb 1532 blondel apostilb # Named after a French scientist. 1533 1534 # Equivalent luminance measures. These units are units which measure 1535 # the luminance of a surface with a specified exitance which obeys 1536 # Lambert's law. (Lambert's law specifies that luminous intensity of 1537 # a perfectly diffuse luminous surface is proportional to the cosine 1538 # of the angle at which you view the luminous surface.) 1539 1540 equivalentlux cd / pi m^2 # luminance of a 1 lux surface 1541 equivalentphot cd / pi cm^2 # luminance of a 1 phot surface 1542 lambert cd / pi cm^2 1543 footlambert cd / pi ft^2 1544 1545 # The bril is used to express "brilliance" of a source of light on a 1546 # logarithmic scale to correspond to subjective perception. An increase of 1 1547 # bril means doubling the luminance. A luminance of 1 lambert is defined to 1548 # have a brilliance of 1 bril. 1549 1550 bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100 1551 1552 # Some luminance data from the IES Lighting Handbook, 8th ed, 1993 1553 1554 sunlum 1.6e9 cd/m^2 # at zenith 1555 sunillum 100e3 lux # clear sky 1556 sunillum_o 10e3 lux # overcast sky 1557 sunlum_h 6e6 cd/m^2 # value at horizon 1558 skylum 8000 cd/m^2 # average, clear sky 1559 skylum_o 2000 cd/m^2 # average, overcast sky 1560 moonlum 2500 cd/m^2 1561 1562 # 1563 # Photographic Exposure Value 1564 # This section by Jeff Conrad (jeff_conrad@msn.com) 1565 # 1566 # The Additive system of Photographic EXposure (APEX) proposed in ASA 1567 # PH2.5-1960 was an attempt to simplify exposure determination for people who 1568 # relied on exposure tables rather than exposure meters. Shortly thereafter, 1569 # nearly all cameras incorporated exposure meters, so the APEX system never 1570 # caught on, but the concept of exposure value remains in use. Though given as 1571 # 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is 1572 # related to exposure parameters by 1573 # 1574 # A^2 LS ES 1575 # 2^EV = --- = -- = -- 1576 # t K C 1577 # 1578 # Where 1579 # A = Relative aperture (f-number) 1580 # t = Exposure time in seconds 1581 # L = Scene luminance in cd/m2 1582 # E = Scene illuminance in lux 1583 # S = Arithmetic ISO speed 1584 # K = Reflected-light meter calibration constant 1585 # C = Incident-light meter calibration constant 1586 # 1587 # Strictly, an exposure value is a combination of aperture and exposure time, 1588 # but it's also commonly used to indicate luminance (or illuminance). 1589 # Conversion to luminance or illuminance units depends on the ISO speed and the 1590 # meter calibration constant. Common practice is to use an ISO speed of 100. 1591 # Calibration constants vary among camera and meter manufacturers: Canon, 1592 # Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while 1593 # Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use 1594 # a value of 250 for incident-light meters with flat receptors. 1595 # 1596 # The values for in-camera meters apply only averaging, weighted-averaging, or 1597 # spot metering--the multi-segment metering incorporated in most current 1598 # cameras uses proprietary algorithms that evaluate many factors related to the 1599 # luminance distribution of what is being metered; they are not amenable to 1600 # simple conversions, and are usually not disclosed by the manufacturers. 1601 1602 s100 100 / lx s # ISO 100 speed 1603 iso100 s100 1604 1605 # Reflected-light meter calibration constant with ISO 100 speed 1606 1607 k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic 1608 k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax 1609 1610 # Incident-light meter calibration constant with ISO 100 film 1611 1612 c250 250 lx / lx s # flat-disc receptor 1613 1614 # Exposure value to scene luminance with ISO 100 imaging media 1615 1616 # For Kenko (Minolta) or Pentax 1617 #ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400) 1618 # For Canon, Nikon, or Sekonic 1619 ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250) 1620 EV100() ev100 1621 1622 # Exposure value to scene illuminance with ISO 100 imaging media 1623 1624 iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250) 1625 1626 # Other Photographic Exposure Conversions 1627 # 1628 # As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities 1629 # related by 1630 # 1631 # Ev = Av + Tv = Bv + Sv 1632 # 1633 # where 1634 # Av = log2(A^2) Aperture value 1635 # Tv = log2(1/t) Time value 1636 # Sv = log2(N Sx) Speed value 1637 # Bv = log2(B S / K) Luminance ("brightness") value 1638 # Iv = log2(I S / C) Illuminance value 1639 # 1640 # and 1641 # A = Relative aperture (f-number) 1642 # t = Exposure time in seconds 1643 # Sx = Arithmetic ISO speed in 1/lux s 1644 # B = luminance in cd/m2 1645 # I = luminance in lux 1646 1647 # The constant N derives from the arcane relationship between arithmetic 1648 # and logarithmic speed given in ASA PH2.5-1960. That relationship 1649 # apparently was not obvious--so much so that it was thought necessary 1650 # to explain it in PH2.12-1961. The constant has had several values 1651 # over the years, usually without explanation for the changes. Although 1652 # APEX had little impact on consumer cameras, it has seen a partial 1653 # resurrection in the Exif standards published by the Camera & Imaging 1654 # Products Association of Japan. 1655 1656 #N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961, 1657 # derived from ASA PH2.5-1960. 1658 #N_apex 0.30 lx s # rounded value in ASA PH2.5-1960, 1659 # ASA PH2.12-1961, and ANSI PH2.7-1986 1660 #N_apex 0.3162 lx s # value in ANSI PH2.7-1973 1661 N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100 1662 K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961 1663 K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common 1664 C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in 1665 # footcandles; flat sensor?) 1666 C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in 1667 # footcandles; hemispherical sensor?) 1668 N_speed N_exif 1669 K_lum K_apex1971 1670 C_illum C_apex1961 1671 1672 # Units for Photographic Exposure Variables 1673 # 1674 # Practical photography sometimes pays scant attention to units for exposure 1675 # variables. In particular, the "speed" of the imaging medium is treated as if 1676 # it were dimensionless when it should have units of reciprocal lux seconds; 1677 # this practice works only because "speed" is almost invariably given in 1678 # accordance with international standards (or similar ones used by camera 1679 # manufacturers)--so the assumed units are invariant. In calculating 1680 # logarithmic quantities--especially the time value Tv and the exposure value 1681 # EV--the units for exposure time ("shutter speed") are often ignored; this 1682 # practice works only because the units of exposure time are assumed to be in 1683 # seconds, and the missing units that make the argument to the logarithmic 1684 # function dimensionless are silently provided. 1685 # 1686 # In keeping with common practice, the definitions that follow treat "speeds" 1687 # as dimensionless, so ISO 100 speed is given simply as '100'. When 1688 # calculating the logarithmic APEX quantities Av and Tv, the definitions 1689 # provide the missing units, so the times can be given with any appropriate 1690 # units. For example, giving an exposure time of 1 minute as either '1 min' or 1691 # '60 s' will result in Tv of -5.9068906. 1692 # 1693 # Exposure Value from f-number and Exposure Time 1694 # 1695 # Because nonlinear unit conversions only accept a single quantity, 1696 # there is no direct conversion from f-number and exposure time to 1697 # exposure value EV. But the EV can be obtained from a combination of 1698 # Av and Tv. For example, the "sunny 16" rule states that correct 1699 # exposure for a sunlit scene can achieved by using f/16 and an exposure 1700 # time equal to the reciprocal of the ISO speed in seconds; this can be 1701 # calculated as 1702 # 1703 # ~Av(16) + ~Tv(1|100 s), 1704 # 1705 # which gives 14.643856. These conversions may be combined with the 1706 # ev100 conversion: 1707 # 1708 # ev100(~Av(16) + ~Tv(1|100 s)) 1709 # 1710 # to yield the assumed average scene luminance of 3200 cd/m^2. 1711 1712 # convert relative aperture (f-number) to aperture value 1713 Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av) 1714 # convert exposure time to time value 1715 Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv) 1716 # convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed; 1717 # make arithmetic speed dimensionless 1718 # 'Sv' conflicts with the symbol for sievert; you can uncomment this function 1719 # definition if you don't need that symbol 1720 #Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv) 1721 Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval) 1722 1723 # convert luminance value Bv in ASA PH2.12-1961 to luminance 1724 Bv(x) units=[1;cd/m^2] range=(0,) \ 1725 2^x K_lum N_speed ; log2(Bv / (K_lum N_speed)) 1726 1727 # convert illuminance value Iv in ASA PH2.12-1961 to illuminance 1728 Iv(x) units=[1;lx] range=(0,) \ 1729 2^x C_illum N_speed ; log2(Iv / (C_illum N_speed)) 1730 1731 # convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in 1732 # ASA PH2.5-1960; make arithmetic speed dimensionless 1733 Sx(S) units=[1;1] domain=(0,) \ 1734 log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s) 1735 1736 # convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed 1737 # for convenience, speed is treated here as if it were dimensionless 1738 Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg)) 1739 Sdin() Sdeg 1740 1741 # Numerical Aperture and f-Number of a Lens 1742 # 1743 # The numerical aperture (NA) is given by 1744 # 1745 # NA = n sin(theta) 1746 # 1747 # where n is the index of refraction of the medium and theta is half 1748 # of the angle subtended by the aperture stop from a point in the image 1749 # or object plane. For a lens in air, n = 1, and 1750 # 1751 # NA = 0.5 / f-number 1752 # 1753 # convert NA to f-number 1754 numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \ 1755 0.5 / x ; 0.5 / numericalaperture 1756 NA() numericalaperture 1757 # 1758 # convert f-number to itself; restrict values to those possible 1759 fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber 1760 1761 # Referenced Photographic Standards 1762 # 1763 # ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome, 1764 # Continuous-Tone) Speed of Photographic Negative Materials. 1765 # ASA PH2.12-1961. American Standard, General-Purpose Photographic 1766 # Exposure Meters (photoelectric type). 1767 # ANSI PH3.49-1971. American National Standard for general-purpose 1768 # photographic exposure meters (photoelectric type). 1769 # ANSI PH2.7-1973. American National Standard Photographic Exposure Guide. 1770 # ANSI PH2.7-1986. American National Standard for Photography -- 1771 # Photographic Exposure Guide. 1772 # CIPA DC-008-2010. Exchangeable image file format for digital still 1773 # cameras: Exif Version 2.3 1774 # ISO 6:1993. International Standard, Photography -- Black-and-white 1775 # pictorial still camera negative film/process systems -- 1776 # Determination of ISO Speed. 1777 1778 1779 # 1780 # Astronomical time measurements 1781 # 1782 # Astronomical time measurement is a complicated matter. The length of the 1783 # true day at a given place can be 21 seconds less than 24 hours or 30 seconds 1784 # over 24 hours. The two main reasons for this are the varying speed of the 1785 # earth in its elliptical orbit and the fact that the sun moves on the ecliptic 1786 # instead of along the celestial equator. To devise a workable system for time 1787 # measurement, Simon Newcomb (1835-1909) used a fictitious "mean sun". 1788 # Consider a first fictitious sun traveling along the ecliptic at a constant 1789 # speed and coinciding with the true sun at perigee and apogee. Then 1790 # considering a second fictitious sun traveling along the celestial equator at 1791 # a constant speed and coinciding with the first fictitious sun at the 1792 # equinoxes. The second fictitious sun is the "mean sun". From this equations 1793 # can be written out to determine the length of the mean day, and the tropical 1794 # year. The length of the second was determined based on the tropical year 1795 # from such a calculation and was officially used from 1960-1967 until atomic 1796 # clocks replaced astronomical measurements for a standard of time. All of the 1797 # values below give the mean time for the specified interval. 1798 # 1799 # See "Mathematical Astronomy Morsels" by Jean Meeus for more details 1800 # and a description of how to compute the correction to mean time. 1801 # 1802 1803 TIME second 1804 1805 anomalisticyear 365.2596 days # The time between successive 1806 # perihelion passages of the 1807 # earth. 1808 siderealyear 365.256360417 day # The time for the earth to make 1809 # one revolution around the sun 1810 # relative to the stars. 1811 tropicalyear 365.242198781 day # The time needed for the mean sun 1812 # as defined above to increase 1813 # its longitude by 360 degrees. 1814 # Most references defined the 1815 # tropical year as the interval 1816 # between vernal equinoxes, but 1817 # this is misleading. The length 1818 # of the season changes over time 1819 # because of the eccentricity of 1820 # the earth's orbit. The time 1821 # between vernal equinoxes is 1822 # approximately 365.24237 days 1823 # around the year 2000. See 1824 # "Mathematical Astronomy 1825 # Morsels" for more details. 1826 eclipseyear 346.62 days # The line of nodes is the 1827 # intersection of the plane of 1828 # Earth's orbit around the sun 1829 # with the plane of the moon's 1830 # orbit around earth. Eclipses 1831 # can only occur when the moon 1832 # and sun are close to this 1833 # line. The line rotates and 1834 # appearances of the sun on the 1835 # line of nodes occur every 1836 # eclipse year. 1837 saros 223 synodicmonth # The earth, moon and sun appear in 1838 # the same arrangement every 1839 # saros, so if an eclipse occurs, 1840 # then one saros later, a similar 1841 # eclipse will occur. (The saros 1842 # is close to 19 eclipse years.) 1843 # The eclipse will occur about 1844 # 120 degrees west of the 1845 # preceeding one because the 1846 # saros is not an even number of 1847 # days. After 3 saros, an 1848 # eclipse will occur at 1849 # approximately the same place. 1850 siderealday 86164.09054 s # The sidereal day is the interval 1851 siderealhour 1|24 siderealday # between two successive transits 1852 siderealminute 1|60 siderealhour # of a star over the meridian, 1853 siderealsecond 1|60 siderealminute # or the time required for the 1854 # earth to make one rotation 1855 # relative to the stars. The 1856 # more usual solar day is the 1857 # time required to make a 1858 # rotation relative to the sun. 1859 # Because the earth moves in its 1860 # orbit, it has to turn a bit 1861 # extra to face the sun again, 1862 # hence the solar day is slightly 1863 # longer. 1864 anomalisticmonth 27.55454977 day # Time for the moon to travel from 1865 # perigee to perigee 1866 nodicalmonth 27.2122199 day # The nodes are the points where 1867 draconicmonth nodicalmonth # an orbit crosses the ecliptic. 1868 draconiticmonth nodicalmonth # This is the time required to 1869 # travel from the ascending node 1870 # to the next ascending node. 1871 siderealmonth 27.321661 day # Time required for the moon to 1872 # orbit the earth 1873 lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds 1874 # Mean time between full moons. 1875 synodicmonth lunarmonth # Full moons occur when the sun 1876 lunation synodicmonth # and moon are on opposite sides 1877 lune 1|30 lunation # of the earth. Since the earth 1878 lunour 1|24 lune # moves around the sun, the moon 1879 # has to revolve a bit extra to 1880 # get into the full moon 1881 # configuration. 1882 year tropicalyear 1883 yr year 1884 month 1|12 year 1885 mo month 1886 lustrum 5 years # The Lustrum was a Roman 1887 # purification ceremony that took 1888 # place every five years. 1889 # Classically educated Englishmen 1890 # used this term. 1891 decade 10 years 1892 century 100 years 1893 millennium 1000 years 1894 millennia millennium 1895 solaryear year 1896 lunaryear 12 lunarmonth 1897 calendaryear 365 day 1898 commonyear 365 day 1899 leapyear 366 day 1900 julianyear 365.25 day 1901 gregorianyear 365.2425 day 1902 islamicyear 354 day # A year of 12 lunar months. They 1903 islamicleapyear 355 day # began counting on July 16, AD 622 1904 # when Muhammad emigrated to Medina 1905 # (the year of the Hegira). They need 1906 # 11 leap days in 30 years to stay in 1907 # sync with the lunar year which is a 1908 # bit longer than the 29.5 days of the 1909 # average month. The months do not 1910 # keep to the same seasons, but 1911 # regress through the seasons every 1912 # 32.5 years. 1913 islamicmonth 1|12 islamicyear # They have 29 day and 30 day months. 1914 1915 # The Hewbrew year is also based on lunar months, but synchronized to the solar 1916 # calendar. The months vary irregularly between 29 and 30 days in length, and 1917 # the years likewise vary. The regular year is 353, 354, or 355 days long. To 1918 # keep up with the solar calendar, a leap month of 30 days is inserted every 1919 # 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This 1920 # gives leap years that last 383, 384, or 385 days. 1921 1922 1923 # Sidereal days 1924 1925 mercuryday 58.6462 day 1926 venusday 243.01 day # retrograde 1927 earthday siderealday 1928 marsday 1.02595675 day 1929 jupiterday 0.41354 day 1930 saturnday 0.4375 day 1931 uranusday 0.65 day # retrograde 1932 neptuneday 0.768 day 1933 plutoday 6.3867 day 1934 1935 # Sidereal years from http://ssd.jpl.nasa.gov/phys_props_planets.html. Data 1936 # was updated in May 2001 based on the 1992 Explanatory Supplement to the 1937 # Astronomical Almanac and the mean longitude rates. Apparently the table of 1938 # years in that reference is incorrect. 1939 1940 mercuryyear 0.2408467 julianyear 1941 venusyear 0.61519726 julianyear 1942 earthyear siderealyear 1943 marsyear 1.8808476 julianyear 1944 jupiteryear 11.862615 julianyear 1945 saturnyear 29.447498 julianyear 1946 uranusyear 84.016846 julianyear 1947 neptuneyear 164.79132 julianyear 1948 plutoyear 247.92065 julianyear 1949 1950 # Objects on the earth are charted relative to a perfect ellipsoid whose 1951 # dimensions are specified by different organizations. The ellipsoid is 1952 # specified by an equatorial radius and a flattening value which defines the 1953 # polar radius. These values are the 1996 values given by the International 1954 # Earth Rotation Service (IERS) whose reference documents can be found at 1955 # http://maia.usno.navy.mil/ 1956 1957 earthflattening 1|298.25642 1958 earthradius_equatorial 6378136.49 m 1959 earthradius_polar (-earthflattening+1) earthradius_equatorial 1960 1961 landarea 148.847e6 km^2 1962 oceanarea 361.254e6 km^2 1963 1964 moonradius 1738 km # mean value 1965 sunradius 6.96e8 m 1966 1967 # Many astronomical values can be measured most accurately in a system of units 1968 # using the astronomical unit and the mass of the sun as base units. The 1969 # uncertainty in the gravitational constant makes conversion to SI units 1970 # significantly less accurate. 1971 1972 # The astronomical unit was defined to be the length of the of the semimajor 1973 # axis of a massless object with the same year as the earth. With such a 1974 # definition in force, and with the mass of the sun set equal to one, Kepler's 1975 # third law can be used to solve for the value of the gravitational constant. 1976 1977 # Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital 1978 # period, a is the size of the semimajor axis, G is the gravitational constant 1979 # and M is the mass. With M = 1 and T and a chosen for the earth's orbit, we 1980 # find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called the Gaussian 1981 # gravitational constant, apparently because Gauss originally did the 1982 # calculations. However, when the original calculation was done, the value 1983 # for the length of the earth's year was inaccurate. The value used is called 1984 # the Gaussian year. Changing the astronomical unit to bring it into 1985 # agreement with more accurate values for the year would have invalidated a 1986 # lot of previous work, so instead the astronomical unit has been kept equal 1987 # to this original value. This is accomplished by using a standard value for 1988 # the Gaussian gravitational constant. This constant is called k. 1989 # Many values below are from http://ssd.jpl.nasa.gov/?constants 1990 1991 gauss_k 0.01720209895 # This beast has dimensions of 1992 # au^(3|2) / day and is exact. 1993 gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian 1994 # gravitational constant. This is a 1995 # fictional year, and doesn't 1996 # correspond to any celestial event. 1997 astronomicalunit 149597870700 m # IAU definition from 2012, exact 1998 au astronomicalunit # ephemeris for the above described 1999 # astronomical unit. (See the NASA 2000 # site listed above.) 2001 solarmass 1.9891e30 kg 2002 sunmass solarmass 2003 2004 2005 sundist 1.0000010178 au # mean earth-sun distance 2006 moondist 3.844e8 m # mean earth-moon distance 2007 sundist_near 1.471e11 m # earth-sun distance at perihelion 2008 sundist_far 1.521e11 m # earth-sun distance at aphelion 2009 moondist_min 3.564e8 m # approximate least distance at 2010 # perigee 1901-2300 2011 moondist_max 4.067e8 m # approximate greatest distance at 2012 # apogee 1901-2300 2013 2014 2015 # The following are masses for planetary systems, not just the planet itself. 2016 # The comments give the uncertainty in the denominators. As noted above, 2017 # masses are given relative to the solarmass because this is more accurate. 2018 # The conversion to SI is uncertain because of uncertainty in G, the 2019 # gravitational constant. 2020 # 2021 # Values are from http://ssd.jpl.nasa.gov/astro_constants.html 2022 2023 mercurymass solarmass / 6023600 # 250 2024 venusmass solarmass / 408523.71 # 0.06 2025 earthmoonmass solarmass / 328900.56 # 0.02 2026 marsmass solarmass / 3098708 # 9 2027 jupitermass solarmass / 1047.3486 # 0.0008 2028 saturnmass solarmass / 3497.898 # 0.018 2029 uranusmass solarmass / 22902.98 # 0.03 2030 neptunemass solarmass / 19412.24 # 0.04 2031 plutomass solarmass / 1.35e8 # 0.07e8 2032 2033 moonearthmassratio 0.012300034 # uncertainty 3e-9 2034 earthmass earthmoonmass / ( 1 + moonearthmassratio) 2035 moonmass moonearthmassratio earthmass 2036 2037 # These are the old values for the planetary masses. They may give 2038 # the masses of the planets alone. 2039 2040 oldmercurymass 0.33022e24 kg 2041 oldvenusmass 4.8690e24 kg 2042 oldmarsmass 0.64191e24 kg 2043 oldjupitermass 1898.8e24 kg 2044 oldsaturnmass 568.5e24 kg 2045 olduranusmass 86.625e24 kg 2046 oldneptunemass 102.78e24 kg 2047 oldplutomass 0.015e24 kg 2048 2049 # Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in 2050 # turn cites Global Earth Physics by CF Yoder, 1995. 2051 2052 mercuryradius 2440 km 2053 venusradius 6051.84 km 2054 earthradius 6371.01 km 2055 marsradius 3389.92 km 2056 jupiterradius 69911 km 2057 saturnradius 58232 km 2058 uranusradius 25362 km 2059 neptuneradius 24624 km 2060 plutoradius 1151 km 2061 2062 moongravity 1.62 m/s^2 2063 2064 # The Hubble constant gives the speed at which distance galaxies are moving 2065 # away from the earth according to v = H0*d, where H0 is the hubble constant 2066 # and d is the distance to the galaxy. 2067 2068 hubble 70 km/s/Mpc # approximate 2069 H0 hubble 2070 2071 # Parallax is the angular difference between the topocentric (on Earth's 2072 # surface) and geocentric (at Earth's center) direction toward a celestial body 2073 # when the body is at a given altitude. When the body is on the horizon, the 2074 # parallax is the horizontal parallax; when the body is on the horizon and the 2075 # observer is on the equator, the parallax is the equatorial horizontal 2076 # parallax. When the body is at zenith, the parallax is zero. 2077 2078 lunarparallax asin(earthradius_equatorial / moondist) # Moon equatorial 2079 moonhp lunarparallax # horizontal parallax 2080 # at mean distance 2081 2082 # Light from celestial objects is attenuated by passage through Earth's 2083 # atmosphere. A body near the horizon passes through much more air than an 2084 # object at zenith, and is consequently less bright. Air mass is the ratio of 2085 # the length of the optical path at a given altitude (angle above the horizon) 2086 # to the length at zenith. Air mass at zenith is by definition unity; at the 2087 # horizon, air mass is approximately 38, though the latter value can vary 2088 # considerably with atmospheric conditions. The general formula is # E = E0 2089 # exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value 2090 # seen by an observer, X is the air mass and c is the extinction coefficient. 2091 # A common value for c in reasonably clear air is 0.21, but values can be 2092 # considerably greater in urban areas. Apparent altitude is that perceived by 2093 # an observer; it includes the effect of atmospheric refraction. There is no 2094 # shortage of formulas for air mass 2095 # (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to 2096 # variations in local atmospheric conditions. The formula used here is simple 2097 # and is in good agreement with rigorously calculated values under standard 2098 # conditions. 2099 # 2100 # Extraterrestrial illuminance or luminance of an object at a given altitude 2101 # determined with vmag() or SB_xxx() below can be multiplied by 2102 # atm_transmission() or atm_transmissionz() to estimate the terrestrial value. 2103 # 2104 # Kasten and Young (1989) air mass formula. alt is apparent altitude 2105 # Reference: 2106 # Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables 2107 # and Approximation Formula." Applied Optics. Vol. 28, 4735–4738. 2108 # Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735. 2109 2110 airmass(alt) units=[degree;1] domain=[0,90] noerror \ 2111 1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364) 2112 2113 # zenith is apparent zenith angle (zenith = 90 deg - alt) 2114 airmassz(zenith) units=[degree;1] domain=[0,90] noerror \ 2115 1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364) 2116 2117 # For reasonably clear air at sea level; values may need adjustment for 2118 # elevation and local atmospheric conditions 2119 # for scotopic vision (510 nm), appropriate for the dark-adapted eye 2120 # extinction_coeff 0.26 2121 # for photopic vision, appropriate for observing brighter objects such 2122 # as the full moon 2123 extinction_coeff 0.21 2124 2125 atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \ 2126 exp(-extinction_coeff airmass(alt)) 2127 2128 # in terms of zenith angle (zenith = 90 deg - alt) 2129 atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \ 2130 exp(-extinction_coeff airmassz(zenith)) 2131 2132 # Moon and Sun data at mean distances 2133 moonvmag -12.74 # Moon apparent visual magnitude at mean distance 2134 sunvmag -26.74 # Sun apparent visual magnitude at mean distance 2135 moonsd asin(moonradius / moondist) # Moon angular semidiameter at mean distance 2136 sunsd asin(sunradius / sundist) # Sun angular semidiameter at mean distance 2137 2138 # Visual magnitude of star or other celestial object. The system of stellar 2139 # magnitudes, developed in ancient Greece, assigned magnitudes from 1 2140 # (brightest) to 6 (faintest visible to the naked eye). In 1856, British 2141 # astronomer Norman Pogson made the system precise, with a magnitude 1 object 2142 # 100 times as bright as a magnitude 6 object, and each magnitude differing 2143 # from the next by a constant ratio; the ratio, sometimes known as Pogson's 2144 # ratio, is thus 100^0.2, or approximately 2.5119. The logarithm of 100^0.2 is 2145 # 0.4, hence the common use of powers of 10 and base-10 logarithms. 2146 # 2147 # Reference: 2148 # Allen, C.W. 1976. Astrophysical Quantities, 3rd ed. 1973, reprinted 2149 # with corrections, 1976. London: Athlone. 2150 # 2151 # The function argument is the (dimensionless) visual magnitude; reference 2152 # illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside 2153 # Earth's atmosphere. Illuminance values can be adjusted to terrestrial values 2154 # by multiplying by one of the atm_transmission functions above. 2155 2156 # Illuminance from apparent visual magnitude 2157 vmag(mag) units=[1;lx] domain=[,] range=(0,] \ 2158 2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx)) 2159 2160 # Surface brightness of a celestial object of a given visual magnitude 2161 # is a logarithmic measure of the luminance the object would have if its 2162 # light were emitted by an object of specified solid angle; it is 2163 # expressed in magnitudes per solid angle. Surface brightness can be 2164 # obtained from the visual magnitude by 2165 # S = m + 2.5 log(pi pi k a b), 2166 # where k is the phase (fraction illuminated), a is the equatorial 2167 # radius, and b is the polar radius. For 100% illumination (e.g., full 2168 # moon), this is often simplified to 2169 # S = m + 2.5 log(pi k s^2), 2170 # where s is the object's angular semidiameter; the units of s determine 2171 # the units of solid angle. The visual magnitude and semidiameter must 2172 # be appropriate for the object's distance; for other than 100% 2173 # illumination, the visual magnitude must be appropriate for the phase. 2174 # Luminance values are for outside Earth's atmosphere; they can be 2175 # adjusted to terrestrial values by multiplying by one of the atm_transmission 2176 # functions above. 2177 2178 # luminance from surface brightness in magnitudes per square degree 2179 SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 2180 vmag(sb) / squaredegree ; \ 2181 ~vmag(SB_degree squaredegree) 2182 2183 # luminance from surface brightness in magnitudes per square minute 2184 SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 2185 vmag(sb) / squareminute ; \ 2186 ~vmag(SB_minute squareminute) 2187 2188 # luminance from surface brightness in magnitudes per square second 2189 SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 2190 vmag(sb) / squaresecond ; \ 2191 ~vmag(SB_second squaresecond) 2192 2193 # luminance from surface brightness in magnitudes per steradian 2194 SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \ 2195 vmag(sb) / sr ; \ 2196 ~vmag(SB_sr sr) 2197 2198 SB() SB_second 2199 SB_sec() SB_second 2200 SB_min() SB_minute 2201 SB_deg() SB_degree 2202 2203 # The brightness of one tenth-magnitude star per square degree outside 2204 # Earth's atmosphere; often used for night sky brightness. 2205 S10 SB_degree(10) 2206 2207 # Examples for magnitude and surface brightness functions 2208 # Sun illuminance from visual magnitude 2209 # You have: sunvmag 2210 # You want: 2211 # Definition: -26.74 = -26.74 2212 # You have: vmag(sunvmag) 2213 # You want: lx 2214 # * 126134.45 2215 # / 7.9280482e-06 2216 # 2217 # Moon surface brightness from visual magnitude and semidiameter at 100% 2218 # illumination (full moon): 2219 # You have: moonvmag 2220 # You want: 2221 # Definition: -12.74 = -12.74 2222 # You have: moonsd 2223 # You want: arcsec 2224 # * 932.59484 2225 # / 0.001072277 2226 # You have: moonvmag + 2.5 log(pi 932.59484^2) 2227 # You want: 2228 # Definition: 3.3513397 2229 # 2230 # Similar example with specific data obtained from another source (JPL 2231 # Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in 2232 # arcseconds 2233 # 2234 # You have: -12.9 + 2.5 log(pi 2023.201|2^2) 2235 # You want: 2236 # Definition: 3.3679199 2237 # You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2)) 2238 # You want: 2239 # Definition: 4858.6547 cd / m^2 2240 # 2241 # If surface brightness is provided by another source (e.g., Horizons), 2242 # it can simply be used directly: 2243 # You have: SB_second(3.3679199) 2244 # You want: cd/m^2 2245 # * 4858.6546 2246 # / 0.0002058183 2247 # The illuminance and luminance values are extraterrestrial (outside 2248 # Earth's atmosphere). The values at Earth's surface are less than these 2249 # because of atmospheric extinction. For example, in the last example 2250 # above, if the Moon were at an altitude of 55 degrees, the terrestrial 2251 # luminance could be calculated with 2252 # You have: SB_second(3.3679199) 2253 # You want: cd/m^2 2254 # * 4858.6546 2255 # / 0.0002058183 2256 # You have: _ atm_transmission(55 deg) 2257 # You want: cd/m^2 2258 # * 3760.6356 2259 # / 0.0002659125 2260 # If desired, photographic exposure can be determined with EV100(), 2261 # leading to acceptable combinations of aperture and exposure time. 2262 # For the example above, but with the Moon at 10 degrees, 2263 # You have: SB_second(3.3679199) atm_transmission(10 deg) 2264 # You want: EV100 2265 # 13.553962 2266 2267 2268 2269 # 2270 # The Hartree system of atomic units, derived from fundamental units 2271 # of mass (of electron), action (planck's constant), charge, and 2272 # the coulomb constant. 2273 2274 # Fundamental units 2275 2276 atomicmass electronmass 2277 atomiccharge e 2278 atomicaction hbar 2279 2280 # derived units (Warning: accuracy is lost from deriving them this way) 2281 2282 atomiclength bohrradius 2283 atomictime hbar^3/coulombconst^2 atomicmass e^4 # Period of first 2284 # bohr orbit 2285 atomicvelocity atomiclength / atomictime 2286 atomicenergy hbar / atomictime 2287 hartree atomicenergy 2288 2289 # 2290 # These thermal units treat entropy as charge, from [5] 2291 # 2292 2293 thermalcoulomb J/K # entropy 2294 thermalampere W/K # entropy flow 2295 thermalfarad J/K^2 2296 thermalohm K^2/W # thermal resistance 2297 fourier thermalohm 2298 thermalhenry J K^2/W^2 # thermal inductance 2299 thermalvolt K # thermal potential difference 2300 2301 2302 # 2303 # United States units 2304 # 2305 2306 # linear measure 2307 2308 # The US Metric Law of 1866 legalized the metric system in the USA and 2309 # defined the meter in terms of the British system with the exact 2310 # 1 meter = 39.37 inches. On April 5, 1893 Thomas Corwin Mendenhall, 2311 # Superintendent of Weights and Measures, decided, in what has become 2312 # known as the "Mendenhall Order" that the meter and kilogram would be the 2313 # fundamental standards in the USA. The definition from 1866 was turned 2314 # around to give an exact definition of the yard as 3600|3937 meters This 2315 # definition was used until July of 1959 when the definition was changed 2316 # to bring the US and other English-speaking countries into agreement; the 2317 # Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it 2318 # was approximately halfway between the British and US values; it had the 2319 # added advantage of making 1 inch = 25.4 mm (exactly). Since 1959, the 2320 # "international" foot has been exactly 0.3048 meters. At the same time, 2321 # it was decided that any data expressed in feet derived from geodetic 2322 # surveys within the US would continue to use the old definition and call 2323 # the old unit the "survey foot." The US continues to define the statute 2324 # mile, furlong, chain, rod, link, and fathom in terms of the US survey 2325 # foot. 2326 # Sources: 2327 # NIST Special Publication 447, Sects. 5, 7, and 8. 2328 # NIST Handbook 44, 2011 ed., Appendix C. 2329 # Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014. 2330 2331 US 1200|3937 m/ft # These four values will convert 2332 US- US # international measures to 2333 survey- US # US Survey measures 2334 geodetic- US 2335 int 3937|1200 ft/m # Convert US Survey measures to 2336 int- int # international measures 2337 2338 inch 2.54 cm 2339 in inch 2340 foot 12 inch 2341 feet foot 2342 ft foot 2343 yard 3 ft 2344 yd yard 2345 mile 5280 ft # The mile was enlarged from 5000 ft 2346 # to this number in order to make 2347 # it an even number of furlongs. 2348 # (The Roman mile is 5000 romanfeet.) 2349 line 1|12 inch # Also defined as '.1 in' or as '1e-8 Wb' 2350 rod 5.5 yard 2351 perch rod 2352 furlong 40 rod # From "furrow long" 2353 statutemile mile 2354 league 3 mile # Intended to be an an hour's walk 2355 2356 # surveyor's measure 2357 2358 surveyorschain 66 surveyft 2359 surveychain surveyorschain 2360 surveyorspole 1|4 surveyorschain 2361 surveyorslink 1|100 surveyorschain 2362 chain 66 ft 2363 link 1|100 chain 2364 ch chain 2365 USacre 10 surveychain^2 2366 intacre 10 chain^2 # Acre based on international ft 2367 intacrefoot acre foot 2368 USacrefoot USacre surveyfoot 2369 acrefoot intacrefoot 2370 acre intacre 2371 section mile^2 2372 township 36 section 2373 homestead 160 acre # Area of land granted by the 1862 Homestead 2374 # Act of the United States Congress 2375 gunterschain surveyorschain 2376 2377 engineerschain 100 ft 2378 engineerslink 1|100 engineerschain 2379 ramsdenschain engineerschain 2380 ramsdenslink engineerslink 2381 2382 gurleychain 33 feet # Andrew Ellicott chain is the 2383 gurleylink 1|50 gurleychain # same length 2384 2385 wingchain 66 feet # Chain from 1664, introduced by 2386 winglink 1|80 wingchain # Vincent Wing, also found in a 2387 # 33 foot length with 40 links. 2388 # early US length standards 2389 2390 # The US has had four standards for the yard: one by Troughton of London 2391 # (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent 2392 # with the definition of the meter in the metric joint resolution of 2393 # Congress in 1866, but defining the yard in terms of the meter; and the 2394 # international yard (1959), which standardized definitions for Australia, 2395 # Canada, New Zealand, South Africa, the UK, and the US. 2396 # Sources: Pat Naughtin (2009), Which Inch?, www.metricationmatters.com; 2397 # Lewis E. Barbrow and Lewis V. Judson (1976). NBS Special Publication 2398 # 447, Weights and Measures Standards of the United States: A Brief 2399 # History. 2400 2401 troughtonyard 914.42190 mm 2402 bronzeyard11 914.39980 mm 2403 mendenhallyard surveyyard 2404 internationalyard yard 2405 2406 # nautical measure 2407 2408 fathom 6 ft # Originally defined as the distance from 2409 # fingertip to fingertip with arms fully 2410 # extended. 2411 nauticalmile 1852 m # Supposed to be one minute of latitude at 2412 # the equator. That value is about 1855 m. 2413 # Early estimates of the earth's circumference 2414 # were a bit off. The value of 1852 m was 2415 # made the international standard in 1929. 2416 # The US did not accept this value until 2417 # 1954. The UK switched in 1970. 2418 2419 cable 1|10 nauticalmile 2420 intcable cable # international cable 2421 cablelength cable 2422 UScable 100 USfathom 2423 navycablelength 720 USft # used for depth in water 2424 marineleague 3 nauticalmile 2425 geographicalmile brnauticalmile 2426 knot nauticalmile / hr 2427 click km # US military slang 2428 klick click 2429 2430 # Avoirdupois weight 2431 2432 pound 0.45359237 kg # The one normally used 2433 lb pound # From the latin libra 2434 grain 1|7000 pound # The grain is the same in all three 2435 # weight systems. It was originally 2436 # defined as the weight of a barley 2437 # corn taken from the middle of the 2438 # ear. 2439 ounce 1|16 pound 2440 oz ounce 2441 dram 1|16 ounce 2442 dr dram 2443 ushundredweight 100 pounds 2444 cwt hundredweight 2445 shorthundredweight ushundredweight 2446 uston shortton 2447 shortton 2000 lb 2448 quarterweight 1|4 uston 2449 shortquarterweight 1|4 shortton 2450 shortquarter shortquarterweight 2451 2452 # Troy Weight. In 1828 the troy pound was made the first United States 2453 # standard weight. It was to be used to regulate coinage. 2454 2455 troypound 5760 grain 2456 troyounce 1|12 troypound 2457 ozt troyounce 2458 pennyweight 1|20 troyounce # Abbreviated "d" in reference to a 2459 dwt pennyweight # Frankish coin called the "denier" 2460 # minted in the late 700's. There 2461 # were 240 deniers to the pound. 2462 assayton mg ton / troyounce # mg / assayton = troyounce / ton 2463 usassayton mg uston / troyounce 2464 brassayton mg brton / troyounce 2465 fineounce troyounce # A troy ounce of 99.5% pure gold 2466 2467 # Some other jewelers units 2468 2469 metriccarat 0.2 gram # Defined in 1907 2470 metricgrain 50 mg 2471 carat metriccarat 2472 ct carat 2473 jewelerspoint 1|100 carat 2474 silversmithpoint 1|4000 inch 2475 momme 3.75 grams # Traditional Japanese unit based 2476 # on the chinese mace. It is used for 2477 # pearls in modern times and also for 2478 # silk density. The definition here 2479 # was adopted in 1891. 2480 # Apothecaries' weight 2481 2482 appound troypound 2483 apounce troyounce 2484 apdram 1|8 apounce 2485 apscruple 1|3 apdram 2486 2487 # Liquid measure 2488 2489 usgallon 231 in^3 # US liquid measure is derived from 2490 gal gallon # the British wine gallon of 1707. 2491 quart 1|4 gallon # See the "winegallon" entry below 2492 pint 1|2 quart # more historical information. 2493 gill 1|4 pint 2494 usquart 1|4 usgallon 2495 uspint 1|2 usquart 2496 usgill 1|4 uspint 2497 usfluidounce 1|16 uspint 2498 fluiddram 1|8 usfloz 2499 minimvolume 1|60 fluiddram 2500 qt quart 2501 pt pint 2502 floz fluidounce 2503 usfloz usfluidounce 2504 fldr fluiddram 2505 liquidbarrel 31.5 usgallon 2506 usbeerbarrel 2 beerkegs 2507 beerkeg 15.5 usgallon # Various among brewers 2508 ponykeg 1|2 beerkeg 2509 winekeg 12 usgallon 2510 petroleumbarrel 42 usgallon # Originated in Pennsylvania oil 2511 barrel petroleumbarrel # fields, from the winetierce 2512 bbl barrel 2513 ushogshead 2 liquidbarrel 2514 usfirkin 9 usgallon 2515 2516 # Dry measures: The Winchester Bushel was defined by William III in 1702 and 2517 # legally adopted in the US in 1836. 2518 2519 usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5 2520 bu bushel # inch diameter (rounded) 2521 peck 1|4 bushel 2522 uspeck 1|4 usbushel 2523 brpeck 1|4 brbushel 2524 pk peck 2525 drygallon 1|2 uspeck 2526 dryquart 1|4 drygallon 2527 drypint 1|2 dryquart 2528 drybarrel 7056 in^3 # Used in US for fruits, vegetables, 2529 # and other dry commodities except for 2530 # cranberries. 2531 cranberrybarrel 5826 in^3 # US cranberry barrel 2532 heapedbushel 1.278 usbushel# The following explanation for this 2533 # value was provided by Wendy Krieger 2534 # <os2fan2@yahoo.com> based on 2535 # guesswork. The cylindrical vessel is 2536 # 18.5 inches in diameter and 1|2 inch 2537 # thick. A heaped bushel includes the 2538 # contents of this cylinder plus a heap 2539 # on top. The heap is a cone 19.5 2540 # inches in diameter and 6 inches 2541 # high. With these values, the volume 2542 # of the bushel is 684.5 pi in^3 and 2543 # the heap occupies 190.125 pi in^3. 2544 # Therefore, the heaped bushel is 2545 # 874.625|684.5 bushels. This value is 2546 # approximately 1.2777575 and it rounds 2547 # to the value listed for the size of 2548 # the heaped bushel. Sometimes the 2549 # heaped bushel is reported as 1.25 2550 # bushels. This same explanation gives 2551 # that value if the heap is taken to 2552 # have an 18.5 inch diameter. 2553 2554 # Grain measures. The bushel as it is used by farmers in the USA is actually 2555 # a measure of mass which varies for different commodities. Canada uses the 2556 # same bushel masses for most commodities, but not for oats. 2557 2558 wheatbushel 60 lb 2559 soybeanbushel 60 lb 2560 cornbushel 56 lb 2561 ryebushel 56 lb 2562 barleybushel 48 lb 2563 oatbushel 32 lb 2564 ricebushel 45 lb 2565 canada_oatbushel 34 lb 2566 2567 # Wine and Spirits measure 2568 2569 ponyvolume 1 usfloz 2570 jigger 1.5 usfloz # Can vary between 1 and 2 usfloz 2571 shot jigger # Sometimes 1 usfloz 2572 eushot 25 ml # EU standard spirits measure 2573 fifth 1|5 usgallon 2574 winebottle 750 ml # US industry standard, 1979 2575 winesplit 1|4 winebottle 2576 magnum 1.5 liter # Standardized in 1979, but given 2577 # as 2 qt in some references 2578 metrictenth 375 ml 2579 metricfifth 750 ml 2580 metricquart 1 liter 2581 2582 # Old British bottle size 2583 2584 reputedquart 1|6 brgallon 2585 reputedpint 1|2 reputedquart 2586 brwinebottle reputedquart # Very close to 1|5 winegallon 2587 2588 # French champagne bottle sizes 2589 2590 split 200 ml 2591 jeroboam 2 magnum 2592 rehoboam 3 magnum 2593 methuselah 4 magnum 2594 imperialbottle 4 magnum 2595 salmanazar 6 magnum 2596 balthazar 8 magnum 2597 nebuchadnezzar 10 magnum 2598 solomon 12 magnum 2599 melchior 12 magnum 2600 sovereign 17.5 magnum 2601 primat 18 magnum 2602 goliath 18 magnum 2603 melchizedek 20 magnum 2604 midas 20 magnum 2605 2606 # The wine glass doesn't seem to have an official standard, but the same value 2607 # is suggested by several organization. 2608 2609 # https://www.rethinkingdrinking.niaaa.nih.gov/ 2610 # http://www.rethinkyourdrinking.ca/what-is-a-standard-drink/ 2611 # https://www.drinkaware.co.uk/ 2612 # https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf 2613 # http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/content/drinksguide-cnt 2614 2615 wineglass 150 mL # the size of a "typical" serving 2616 2617 # A unit of alcohol is a specified mass of pure ethyl alcohol. 2618 # The term is used officially in the UK, but other countries use the same 2619 # concept but with different values. For example, the UK value of 8 g is 2620 # nominally the amount of alcohol that a typical adult can metabolize in 2621 # one hour. Values for several countries, converted to a volumetric basis: 2622 2623 alcoholunitus 14 g / ethanoldensity 2624 alcoholunitca 13.6 g / ethanoldensity 2625 alcoholunituk 8 g / ethanoldensity 2626 alcoholunitau 10 g / ethanoldensity 2627 2628 # Example: for 12% ABV (alcohol by volume) 2629 # alcoholunitus / 12% = 147.8 mL, close to the “standard” serving of 150 mL. 2630 2631 2632 # Coffee 2633 # 2634 # The recommended ratio of coffee to water. Values vary considerably; 2635 # one is from the Specialty Coffee Association of America 2636 # http://scaa.org/?page=resources&d=brewing-best-practices 2637 2638 coffeeratio 55 g/L # ± 10% 2639 2640 # other recommendations are more loose, e.g., 2641 # http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee 2642 2643 2644 # 2645 # Water is "hard" if it contains various minerals, expecially calcium 2646 # carbonate. 2647 # 2648 2649 clarkdegree grains/brgallon # Content by weigh of calcium carbonate 2650 gpg grains/usgallon # Divide by water's density to convert to 2651 # a dimensionless concentration measure 2652 # 2653 # Shoe measures 2654 # 2655 2656 shoeiron 1|48 inch # Used to measure leather in soles 2657 shoeounce 1|64 inch # Used to measure non-sole shoe leather 2658 2659 # USA shoe sizes. These express the length of the shoe or the length 2660 # of the "last", the form that the shoe is made on. But note that 2661 # this only captures the length. It appears that widths change 1/4 2662 # inch for each letter within the same size, and if you change the 2663 # length by half a size then the width changes between 1/8 inch and 2664 # 1/4 inch. But this may not be standard. If you know better, please 2665 # contact me. 2666 2667 shoesize_delta 1|3 inch # USA shoe sizes differ by this amount 2668 shoe_men0 8.25 inch 2669 shoe_women0 (7+11|12) inch 2670 shoe_boys0 (3+11|12) inch 2671 shoe_girls0 (3+7|12) inch 2672 2673 shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \ 2674 (shoesize_men+(-shoe_men0))/shoesize_delta 2675 shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \ 2676 (shoesize_women+(-shoe_women0))/shoesize_delta 2677 shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \ 2678 (shoesize_boys+(-shoe_boys0))/shoesize_delta 2679 shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \ 2680 (shoesize_girls+(-shoe_girls0))/shoesize_delta 2681 2682 # European shoe size. According to 2683 # http://www.shoeline.com/footnotes/shoeterm.shtml 2684 # shoe sizes in Europe are measured with Paris points which simply measure 2685 # the length of the shoe. 2686 2687 europeshoesize 2|3 cm 2688 2689 # 2690 # USA slang units 2691 # 2692 2693 buck US$ 2694 fin 5 US$ 2695 sawbuck 10 US$ 2696 usgrand 1000 US$ 2697 greenback US$ 2698 key kg # usually of marijuana, 60's 2699 lid 1 oz # Another 60's weed unit 2700 footballfield usfootballfield 2701 usfootballfield 100 yards 2702 canadafootballfield 110 yards # And 65 yards wide 2703 marathon 26 miles + 385 yards 2704 2705 # 2706 # British 2707 # 2708 2709 # The length measure in the UK was defined by a bronze bar manufactured in 2710 # 1844. Various conversions were sanctioned for convenience at different 2711 # times, which makes conversions before 1963 a confusing matter. Apparently 2712 # previous conversions were never explicitly revoked. Four different 2713 # conversion factors appear below. Multiply them times an imperial length 2714 # units as desired. The Weights and Measures Act of 1963 switched the UK away 2715 # from their bronze standard and onto a definition of the yard in terms of the 2716 # meter. This happened after an international agreement in 1959 to align the 2717 # world's measurement systems. 2718 2719 UK UKlength_SJJ 2720 UK- UK 2721 british- UK 2722 2723 UKlength_B 0.9143992 meter / yard # Benoit found the yard to be 2724 # 0.9143992 m at a weights and 2725 # measures conference around 2726 # 1896. Legally sanctioned 2727 # in 1898. 2728 UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and 2729 # Johnson found the yard to be 2730 # 0.91439841 meters. 2731 # Used starting in the 1930's. 2732 UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio 2733 # for the meter and inch. This 2734 # value was used as the legal 2735 # conversion ratio when the 2736 # metric system was legalized 2737 # for contract in 1864. 2738 UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter 2739 # to be 1.09362311 yards. This 2740 # conversion was legalized 2741 # around 1878. 2742 brnauticalmile 6080 ft # Used until 1970 when the UK 2743 brknot brnauticalmile / hr # switched to the international 2744 brcable 1|10 brnauticalmile # nautical mile. 2745 admiraltymile brnauticalmile 2746 admiraltyknot brknot 2747 admiraltycable brcable 2748 seamile 6000 ft 2749 shackle 15 fathoms # Adopted 1949 by British navy 2750 2751 # British Imperial weight is mostly the same as US weight. A few extra 2752 # units are added here. 2753 2754 clove 7 lb 2755 stone 14 lb 2756 tod 28 lb 2757 brquarterweight 1|4 brhundredweight 2758 brhundredweight 8 stone 2759 longhundredweight brhundredweight 2760 longton 20 brhundredweight 2761 brton longton 2762 2763 # British Imperial volume measures 2764 2765 brminim 1|60 brdram 2766 brscruple 1|3 brdram 2767 fluidscruple brscruple 2768 brdram 1|8 brfloz 2769 brfluidounce 1|20 brpint 2770 brfloz brfluidounce 2771 brgill 1|4 brpint 2772 brpint 1|2 brquart 2773 brquart 1|4 brgallon 2774 brgallon 4.54609 l # The British Imperial gallon was 2775 # defined in 1824 to be the volume of 2776 # water which weighed 10 pounds at 62 2777 # deg F with a pressure of 30 inHg. 2778 # It was also defined as 277.274 in^3, 2779 # Which is slightly in error. In 2780 # 1963 it was defined to be the volume 2781 # occupied by 10 pounds of distilled 2782 # water of density 0.998859 g/ml weighed 2783 # in air of density 0.001217 g/ml 2784 # against weights of density 8.136 g/ml. 2785 # This gives a value of approximately 2786 # 4.5459645 liters, but the old liter 2787 # was in force at this time. In 1976 2788 # the definition was changed to exactly 2789 # 4.54609 liters using the new 2790 # definition of the liter (1 dm^3). 2791 brbarrel 36 brgallon # Used for beer 2792 brbushel 8 brgallon 2793 brheapedbushel 1.278 brbushel 2794 brquarter 8 brbushel 2795 brchaldron 36 brbushel 2796 2797 # Obscure British volume measures. These units are generally traditional 2798 # measures whose definitions have fluctuated over the years. Often they 2799 # depended on the quantity being measured. They are given here in terms of 2800 # British Imperial measures. For example, the puncheon may have historically 2801 # been defined relative to the wine gallon or beer gallon or ale gallon 2802 # rather than the British Imperial gallon. 2803 2804 bag 4 brbushel 2805 bucket 4 brgallon 2806 kilderkin 2 brfirkin 2807 last 40 brbushel 2808 noggin brgill 2809 pottle 0.5 brgallon 2810 pin 4.5 brgallon 2811 puncheon 72 brgallon 2812 seam 8 brbushel 2813 coomb 4 brbushel 2814 boll 6 brbushel 2815 firlot 1|4 boll 2816 brfirkin 9 brgallon # Used for ale and beer 2817 cran 37.5 brgallon # measures herring, about 750 fish 2818 brwinehogshead 52.5 brgallon # This value is approximately equal 2819 brhogshead brwinehogshead # to the old wine hogshead of 63 2820 # wine gallons. This adjustment 2821 # is listed in the OED and in 2822 # "The Weights and Measures of 2823 # England" by R. D. Connor 2824 brbeerhogshead 54 brgallon 2825 brbeerbutt 2 brbeerhogshead 2826 registerton 100 ft^3 # Used for internal capacity of ships 2827 shippington 40 ft^3 # Used for ship's cargo freight or timber 2828 brshippington 42 ft^3 # 2829 freightton shippington # Both register ton and shipping ton derive 2830 # from the "tun cask" of wine. 2831 displacementton 35 ft^3 # Approximate volume of a longton weight of 2832 # sea water. Measures water displaced by 2833 # ships. 2834 waterton 224 brgallon 2835 strike 70.5 l # 16th century unit, sometimes 2836 # defined as .5, 2, or 4 bushels 2837 # depending on the location. It 2838 # probably doesn't make a lot of 2839 # sense to define in terms of imperial 2840 # bushels. Zupko gives a value of 2841 # 2 Winchester grain bushels or about 2842 # 70.5 liters. 2843 amber 4 brbushel# Used for dry and liquid capacity [18] 2844 2845 # British volume measures with "imperial" 2846 2847 imperialminim brminim 2848 imperialscruple brscruple 2849 imperialdram brdram 2850 imperialfluidounce brfluidounce 2851 imperialfloz brfloz 2852 imperialgill brgill 2853 imperialpint brpint 2854 imperialquart brquart 2855 imperialgallon brgallon 2856 imperialbarrel brbarrel 2857 imperialbushel brbushel 2858 imperialheapedbushel brheapedbushel 2859 imperialquarter brquarter 2860 imperialchaldron brchaldron 2861 imperialwinehogshead brwinehogshead 2862 imperialhogshead brhogshead 2863 imperialbeerhogshead brbeerhogshead 2864 imperialbeerbutt brbeerbutt 2865 imperialfirkin brfirkin 2866 2867 # obscure British lengths 2868 2869 barleycorn 1|3 UKinch # Given in Realm of Measure as the 2870 # difference between successive shoe sizes 2871 nail 1|16 UKyard # Originally the width of the thumbnail, 2872 # or 1|16 ft. This took on the general 2873 # meaning of 1|16 and settled on the 2874 # nail of a yard or 1|16 yards as its 2875 # final value. [12] 2876 pole 16.5 UKft # This was 15 Saxon feet, the Saxon 2877 rope 20 UKft # foot (aka northern foot) being longer 2878 englishell 45 UKinch 2879 flemishell 27 UKinch 2880 ell englishell # supposed to be measure from elbow to 2881 # fingertips 2882 span 9 UKinch # supposed to be distance from thumb 2883 # to pinky with full hand extension 2884 goad 4.5 UKft # used for cloth, possibly named after the 2885 # stick used for prodding animals. 2886 2887 # misc obscure British units 2888 2889 hide 120 acre # English unit of land area dating to the 7th 2890 # century, originally the amount of land 2891 # that a single plowman could cultivate, 2892 # which varied from 60-180 acres regionally. 2893 # Standardized at Normon conquest. 2894 virgate 1|4 hide 2895 nook 1|2 virgate 2896 rood furlong rod # Area of a strip a rod by a furlong 2897 englishcarat troyounce/151.5 # Originally intended to be 4 grain 2898 # but this value ended up being 2899 # used in the London diamond market 2900 mancus 2 oz 2901 mast 2.5 lb 2902 nailkeg 100 lbs 2903 basebox 31360 in^2 # Used in metal plating 2904 2905 # alternate spellings 2906 2907 metre meter 2908 gramme gram 2909 litre liter 2910 dioptre diopter 2911 aluminium aluminum 2912 sulphur sulfur 2913 2914 # 2915 # Units derived the human body (may not be very accurate) 2916 # 2917 2918 geometricpace 5 ft # distance between points where the same 2919 # foot hits the ground 2920 pace 2.5 ft # distance between points where alternate 2921 # feet touch the ground 2922 USmilitarypace 30 in # United States official military pace 2923 USdoubletimepace 36 in # United States official doubletime pace 2924 fingerbreadth 7|8 in # The finger is defined as either the width 2925 fingerlength 4.5 in # or length of the finger 2926 finger fingerbreadth 2927 palmwidth hand # The palm is a unit defined as either the width 2928 palmlength 8 in # or the length of the hand 2929 hand 4 inch # width of hand 2930 shaftment 6 inch # Distance from tip of outstretched thumb to the 2931 # opposite side of the palm of the hand. The 2932 # ending -ment is from the old English word 2933 # for hand. [18] 2934 smoot 5 ft + 7 in # Created as part of an MIT fraternity prank. 2935 # In 1958 Oliver Smoot was used to measure 2936 # the length of the Harvard Bridge, which was 2937 # marked off in Smoot lengths. These 2938 # markings have been maintained on the bridge 2939 # since then and repainted by subsequent 2940 # incoming fraternity members. During a 2941 # bridge renovation the new sidewalk was 2942 # scored every Smoot rather than at the 2943 # customary 6 ft spacing. 2944 # 2945 # Cooking measures 2946 # 2947 2948 # Common abbreviations 2949 2950 tbl tablespoon 2951 tbsp tablespoon 2952 tblsp tablespoon 2953 Tb tablespoon 2954 tsp teaspoon 2955 saltspoon 1|4 tsp 2956 2957 # US measures 2958 2959 uscup 8 usfloz 2960 ustablespoon 1|16 uscup 2961 usteaspoon 1|3 ustablespoon 2962 ustbl ustablespoon 2963 ustbsp ustablespoon 2964 ustblsp ustablespoon 2965 ustsp usteaspoon 2966 metriccup 250 ml 2967 stickbutter 1|4 lb # Butter in the USA is sold in one 2968 # pound packages that contain four 2969 # individually wrapped pieces. The 2970 # pieces are marked into tablespoons, 2971 # making it possible to measure out 2972 # butter by volume by slicing the 2973 # butter. 2974 2975 legalcup 240 ml # The cup used on nutrition labeling 2976 legaltablespoon 1|16 legalcup 2977 legaltbsp legaltablespoon 2978 2979 # Scoop size. Ice cream scoops in the US are marked with numbers 2980 # indicating the number of scoops requird to fill a US quart. 2981 2982 scoop(n) units=[1;cup] domain=[4,100] range=[0.04,1] \ 2983 32 usfloz / n ; 32 usfloz / scoop 2984 2985 2986 # US can sizes. 2987 2988 number1can 10 usfloz 2989 number2can 19 usfloz 2990 number2.5can 3.5 uscups 2991 number3can 4 uscups 2992 number5can 7 uscups 2993 number10can 105 usfloz 2994 2995 # British measures 2996 2997 brcup 1|2 brpint 2998 brteacup 1|3 brpint 2999 brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml 3000 brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon 3001 brdessertspoon 2 brteaspoon 3002 dessertspoon brdessertspoon 3003 dsp dessertspoon 3004 brtsp brteaspoon 3005 brtbl brtablespoon 3006 brtbsp brtablespoon 3007 brtblsp brtablespoon 3008 3009 # Australian 3010 3011 australiatablespoon 20 ml 3012 austbl australiatablespoon 3013 austbsp australiatablespoon 3014 austblsp australiatablespoon 3015 australiateaspoon 1|4 australiatablespoon 3016 austsp australiateaspoon 3017 3018 # Italian 3019 3020 etto 100 g # Used for buying items like meat and 3021 etti etto # cheese. 3022 3023 # Chinese 3024 3025 catty 0.5 kg 3026 oldcatty 4|3 lbs # Before metric conversion. 3027 tael 1|16 oldcatty # Should the tael be defined both ways? 3028 mace 0.1 tael 3029 oldpicul 100 oldcatty 3030 picul 100 catty # Chinese usage 3031 3032 # Indian 3033 3034 seer 14400 grain # British Colonial standard 3035 ser seer 3036 maund 40 seer 3037 pakistanseer 1 kg 3038 pakistanmaund 40 pakistanseer 3039 chittak 1|16 seer 3040 tola 1|5 chittak 3041 ollock 1|4 liter # Is this right? 3042 3043 # Japanese 3044 3045 japancup 200 ml 3046 3047 # densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum 3048 # so you can convert '2 cups sugar' to grams, for example, or in the other 3049 # direction grams could be converted to 'cup flour_scooped'. 3050 3051 butter 8 oz/uscup 3052 butter_clarified 6.8 oz/uscup 3053 cocoa_butter 9 oz/uscup 3054 shortening 6.75 oz/uscup # vegetable shortening 3055 oil 7.5 oz/uscup 3056 cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the 3057 cakeflour_spooned 4 oz/uscup # measuring method. "Scooped", or 3058 cakeflour_scooped 4.5 oz/uscup # "dip and sweep" refers to dipping a 3059 flour_sifted 4 oz/uscup # measure into a bin, and then sweeping 3060 flour_spooned 4.25 oz/uscup # the excess off the top. "Spooned" 3061 flour_scooped 5 oz/uscup # means to lightly spoon into a measure 3062 breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means 3063 breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a 3064 breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top. 3065 cornstarch 120 grams/uscup 3066 dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa 3067 dutchcocoa_spooned 92 g/uscup 3068 dutchcocoa_scooped 95 g/uscup 3069 cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa 3070 cocoa_spooned 82 g/uscup 3071 cocoa_scooped 95 g/uscup 3072 heavycream 232 g/uscup 3073 milk 242 g/uscup 3074 sourcream 242 g/uscup 3075 molasses 11.25 oz/uscup 3076 cornsyrup 11.5 oz/uscup 3077 honey 11.75 oz/uscup 3078 sugar 200 g/uscup 3079 powdered_sugar 4 oz/uscup 3080 brownsugar_light 217 g/uscup # packed 3081 brownsugar_dark 239 g/uscup 3082 3083 baking_powder 4.6 grams / ustsp 3084 salt 6 g / ustsp 3085 koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt 3086 koshersalt_morton 4.8 g / ustsp # Morton kosher salt 3087 # Values are from the nutrition info 3088 # on the packages 3089 3090 3091 # Egg weights and volumes for a USA large egg 3092 3093 egg 50 grams # without shell 3094 eggwhite 30 grams 3095 eggyolk 18.6 grams 3096 eggvolume 3 ustablespoons + 1|2 ustsp 3097 eggwhitevolume 2 ustablespoons 3098 eggyolkvolume 3.5 ustsp 3099 3100 # Alcohol density 3101 3102 ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition 3103 alcoholdensity ethanoldensity 3104 3105 # 3106 # Density measures. Density has traditionally been measured on a variety of 3107 # bizarre nonlinear scales. 3108 # 3109 3110 # Density of a sugar syrup is frequently measured in candy making procedures. 3111 # In the USA the boiling point of the syrup is measured. Some recipes instead 3112 # specify the density using degrees Baume. Conversion between degrees Baume 3113 # and the boiling point measure has proved elusive. This table appeared in one 3114 # text, and provides a fragmentary relationship to the concentration. 3115 # 3116 # temp(C) conc (%) 3117 # 100 30 3118 # 101 40 3119 # 102 50 3120 # 103 60 3121 # 106 70 3122 # 112 80 3123 # 123 90 3124 # 140 95 3125 # 151 97 3126 # 160 98.2 3127 # 166 99.5 3128 # 171 99.6 3129 # 3130 # The best source identified to date came from "Boiling point elevation of 3131 # technical sugarcane solutions and its use in automatic pan boiling" by 3132 # Michael Saska. International Sugar Journal, 2002, 104, 1247, pp 500-507. 3133 # 3134 # But I'm using equation (3) which is credited to Starzak and Peacock, 3135 # "Water activity coefficient in aqueous solutions of sucrose--A comprehensive 3136 # data analyzis. Zuckerindustrie, 122, 380-387. (I couldn't find this 3137 # document.) 3138 # 3139 # Note that the range of validity is uncertain, but answers are in agreement 3140 # with the above table all the way to 99.6. 3141 # 3142 # The original equation has a parameter for the boiling point of water, which 3143 # of course varies with altitude. It also includes various other model 3144 # parameters. The input is the molar concentration of sucrose in the solution, 3145 # (moles sucrose) / (total moles). 3146 # 3147 # Bsp 3797.06 degC 3148 # Csp 226.28 degC 3149 # QQ -17638 J/mol 3150 # asp -1.0038 3151 # bsp -0.24653 3152 # tbw 100 degC # boiling point of water 3153 # sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \ 3154 # /(tbw+stdtemp)) / (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp) 3155 # 3156 # To convert mass concentration (brix) to molar concentration 3157 # 3158 # sc(x) (x / 342.3) / (( x/342.3) + (100-x)/18.02); \ 3159 # 100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1) 3160 # 3161 # Here is a simplfied version of this equation where the temperature of boiling 3162 # water has been fixed at 100 degrees Celcius and the argument is now the 3163 # concentration (brix). 3164 # 3165 # sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \ 3166 # / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K 3167 # 3168 # 3169 # The formula is not invertible, so to implement it in units we unfortunately 3170 # must turn it into a table. 3171 3172 # This table gives the boiling point elevation as a function of the sugar syrup 3173 # concentration expressed as a percentage. 3174 3175 sugar_conc_bpe[K] \ 3176 0 0.0000 5 0.0788 10 0.1690 15 0.2729 20 0.3936 25 0.5351 \ 3177 30 0.7027 35 0.9036 40 1.1475 42 1.2599 44 1.3825 46 1.5165 \ 3178 48 1.6634 50 1.8249 52 2.0031 54 2.2005 56 2.4200 58 2.6651 \ 3179 60 2.9400 61 3.0902 62 3.2499 63 3.4198 64 3.6010 65 3.7944 \ 3180 66 4.0012 67 4.2227 68 4.4603 69 4.7156 70 4.9905 71 5.2870 \ 3181 72 5.6075 73 5.9546 74 6.3316 75 6.7417 76 7.1892 77 7.6786 \ 3182 78.0 8.2155 79.0 8.8061 80.0 9.4578 80.5 9.8092 81.0 10.1793 \ 3183 81.5 10.5693 82.0 10.9807 82.5 11.4152 83.0 11.8743 83.5 12.3601 \ 3184 84.0 12.8744 84.5 13.4197 85.0 13.9982 85.5 14.6128 86.0 15.2663 \ 3185 86.5 15.9620 87.0 16.7033 87.5 17.4943 88.0 18.3391 88.5 19.2424 \ 3186 89.0 20.2092 89.5 21.2452 90.0 22.3564 90.5 23.5493 91.0 24.8309 \ 3187 91.5 26.2086 92.0 27.6903 92.5 29.2839 93.0 30.9972 93.5 32.8374 \ 3188 94.0 34.8104 94.5 36.9195 95.0 39.1636 95.5 41.5348 96.0 44.0142 \ 3189 96.5 46.5668 97.0 49.1350 97.5 51.6347 98.0 53.9681 98.1 54.4091 \ 3190 98.2 54.8423 98.3 55.2692 98.4 55.6928 98.5 56.1174 98.6 56.5497 \ 3191 98.7 56.9999 98.8 57.4828 98.9 58.0206 99.0 58.6455 99.1 59.4062 \ 3192 99.2 60.3763 99.3 61.6706 99.4 63.4751 99.5 66.1062 99.6 70.1448 \ 3193 99.7 76.7867 3194 3195 # Using the brix table we can use this to produce a mapping from boiling point 3196 # to density which makes all of the units interconvertible. Because the brix 3197 # table stops at 95 this approach works up to a boiling point elevation of 39 K 3198 # or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy 3199 # making. The "hard crack" stage continues up to 310 F. 3200 3201 # Boiling point elevation 3202 sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \ 3203 brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe)) 3204 # Absolute boiling point (produces an absolute temperature) 3205 sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \ 3206 range=[0.99717,1.5144619] \ 3207 brix(~sugar_conc_bpe(T-tempC(100))) ;\ 3208 sugar_conc_bpe(~brix(sugar_bp))+tempC(100) 3209 3210 # In practice dealing with the absolute temperature is annoying because it is 3211 # not possible to convert to a nested function, so you're stuck retyping the 3212 # absolute temperature in Kelvins to convert to celsius or Fahrenheit. To 3213 # prevent this we supply definitions that build in the temperature conversion 3214 # and produce results in the Fahrenheit and Celcius scales. So using these 3215 # measures, to convert 46 degrees Baume to a Fahrenheit boiling point: 3216 # 3217 # You have: baume(45) 3218 # You want: sugar_bpF 3219 # 239.05647 3220 # 3221 sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\ 3222 brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\ 3223 ~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100)) 3224 sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\ 3225 brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\ 3226 ~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100)) 3227 3228 # Degrees Baume is used in European recipes to specify the density of a sugar 3229 # syrup. An entirely different definition is used for densities below 3230 # 1 g/cm^3. An arbitrary constant appears in the definition. This value is 3231 # equal to 145 in the US, but was according to [], the old scale used in 3232 # Holland had a value of 144, and the new scale or Gerlach scale used 146.78. 3233 3234 baumeconst 145 # US value 3235 baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \ 3236 (baumeconst/(baumeconst+-d)) g/cm^3 ; \ 3237 (baume+((-g)/cm^3)) baumeconst / baume 3238 3239 # It's not clear if this value was ever used with negative degrees. 3240 twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \ 3241 (1 + 0.005 x) g / cm^3 ; \ 3242 200 (twaddell / (g/cm^3) +- 1) 3243 3244 # The degree quevenne is a unit for measuring the density of milk. 3245 # Similarly it's unclear if negative values were allowed here. 3246 quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \ 3247 (1 + 0.001 x) g / cm^3 ; \ 3248 1000 (quevenne / (g/cm^3) +- 1) 3249 3250 # Degrees brix measures sugar concentration by weigh as a percentage, so a 3251 # solution that is 3 degrees brix is 3% sugar by weight. This unit was named 3252 # after Adolf Brix who invented a hydrometer that read this percentage 3253 # directly. This data is from Table 114 of NIST Circular 440, "Polarimetry, 3254 # Saccharimetry and the Sugars". It gives apparent specific gravity at 20 3255 # degrees Celsius of various sugar concentrations. As rendered below this 3256 # data is converted to apparent density at 20 degrees Celsius using the 3257 # density figure for water given in the same NIST reference. They use the 3258 # word "apparent" to refer to measurements being made in air with brass 3259 # weights rather than vacuum. 3260 3261 brix[0.99717g/cm^3]\ 3262 0 1.00000 1 1.00390 2 1.00780 3 1.01173 4 1.01569 5 1.01968 \ 3263 6 1.02369 7 1.02773 8 1.03180 9 1.03590 10 1.04003 11 1.04418 \ 3264 12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \ 3265 18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \ 3266 24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \ 3267 30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \ 3268 36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \ 3269 42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \ 3270 48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \ 3271 54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \ 3272 60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \ 3273 66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \ 3274 72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \ 3275 78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \ 3276 84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \ 3277 90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876 3278 3279 # Density measure invented by the American Petroleum Institute. Lighter 3280 # petroleum products are more valuable, and they get a higher API degree. 3281 # 3282 # The intervals of range and domain should be open rather than closed. 3283 # 3284 apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \ 3285 141.5 g/cm^3 / (x+131.5) ; \ 3286 141.5 (g/cm^3) / apidegree + (-131.5) 3287 3288 # 3289 # Units derived from imperial system 3290 # 3291 3292 ouncedal oz ft / s^2 # force which accelerates an ounce 3293 # at 1 ft/s^2 3294 poundal lb ft / s^2 # same thing for a pound 3295 tondal longton ft / s^2 # and for a ton 3296 pdl poundal 3297 osi ounce force / inch^2 # used in aviation 3298 psi pound force / inch^2 3299 psia psi # absolute pressure 3300 # Note that gauge pressure can be given 3301 # using the gaugepressure() and 3302 # psig() nonlinear unit definitions 3303 tsi ton force / inch^2 3304 reyn psi sec 3305 slug lbf s^2 / ft 3306 slugf slug force 3307 slinch lbf s^2 / inch # Mass unit derived from inch second 3308 slinchf slinch force # pound-force system. Used in space 3309 # applications where in/sec^2 was a 3310 # natural acceleration measure. 3311 geepound slug 3312 lbf lb force 3313 tonf ton force 3314 lbm lb 3315 kip 1000 lbf # from kilopound 3316 ksi kip / in^2 3317 mil 0.001 inch 3318 thou 0.001 inch 3319 tenth 0.0001 inch # one tenth of one thousandth of an inch 3320 millionth 1e-6 inch # one millionth of an inch 3321 circularinch 1|4 pi in^2 # area of a one-inch diameter circle 3322 circleinch circularinch # A circle with diameter d inches has 3323 # an area of d^2 circularinches 3324 cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter 3325 # has volume d^2 h cylinder inches 3326 circularmil 1|4 pi mil^2 # area of one-mil diameter circle 3327 cmil circularmil 3328 3329 cental 100 pound 3330 centner cental 3331 caliber 0.01 inch # for measuring bullets 3332 duty ft lbf 3333 celo ft / s^2 3334 jerk ft / s^3 3335 australiapoint 0.01 inch # The "point" is used to measure rainfall 3336 # in Australia 3337 sabin ft^2 # Measure of sound absorption equal to the 3338 # absorbing power of one square foot of 3339 # a perfectly absorbing material. The 3340 # sound absorptivity of an object is the 3341 # area times a dimensionless 3342 # absorptivity coefficient. 3343 standardgauge 4 ft + 8.5 in # Standard width between railroad track 3344 flag 5 ft^2 # Construction term referring to sidewalk. 3345 rollwallpaper 30 ft^2 # Area of roll of wall paper 3346 fillpower in^3 / ounce # Density of down at standard pressure. 3347 # The best down has 750-800 fillpower. 3348 pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA. 3349 buttonline 1|40 inch # The line was used in 19th century USA 3350 # to measure width of buttons. 3351 beespace 1|4 inch # Bees will fill any space that is smaller 3352 # than the bee space and leave open 3353 # spaces that are larger. The size of 3354 # the space varies with species. 3355 diamond 8|5 ft # Marking on US tape measures that is 3356 # useful to carpenters who wish to place 3357 # five studs in an 8 ft distance. Note 3358 # that the numbers appear in red every 3359 # 16 inches as well, giving six 3360 # divisions in 8 feet. 3361 retmaunit 1.75 in # Height of rack mountable equipment. 3362 U retmaunit # Equipment should be 1|32 inch narrower 3363 RU U # than its U measurement indicates to 3364 # allow for clearance, so 4U=(6+31|32)in 3365 # RETMA stands for the former name of 3366 # the standardizing organization, Radio 3367 # Electronics Television Manufacturers 3368 # Association. This organization is now 3369 # called the Electronic Industries 3370 # Alliance (EIA) and the rack standard 3371 # is specified in EIA RS-310-D. 3372 count per pound # For measuring the size of shrimp 3373 3374 # 3375 # Other units of work, energy, power, etc 3376 # 3377 3378 ENERGY joule 3379 WORK joule 3380 3381 # Calorie: approximate energy to raise a gram of water one degree celsius 3382 3383 calorie cal_th # Default is the thermochemical calorie 3384 cal calorie 3385 calorie_th 4.184 J # Thermochemical calorie, defined in 1930 3386 thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to 3387 cal_th calorie_th # avoid difficulties associated with the 3388 # uncertainty in the heat capacity of 3389 # water. In 1948 the value of the joule 3390 # was changed, so the thermochemical 3391 # calorie was redefined to 4.184 J. 3392 # This kept the energy measured by this 3393 # unit the same. 3394 calorie_IT 4.1868 J # International (Steam) Table calorie, 3395 cal_IT calorie_IT # defined in 1929 as watt-hour/860 or 3396 # equivalently 180|43 joules. At this 3397 # time the international joule had a 3398 # different value than the modern joule, 3399 # and the values were different in the 3400 # USA and in Europe. In 1956 at the 3401 # Fifth International Conference on 3402 # Properties of Steam the exact 3403 # definition given here was adopted. 3404 calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC 3405 cal_15 calorie_15 3406 calorie_fifteen cal_15 3407 calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC 3408 cal_20 calorie_20 3409 calorie_twenty calorie_20 3410 calorie_4 4.204 J # Energy to go from 3.5 to 4.5 degC 3411 cal_4 calorie_4 3412 calorie_four calorie_4 3413 cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC 3414 Calorie kilocalorie # the food Calorie 3415 thermie 1e6 cal_15 # Heat required to raise the 3416 # temperature of a tonne of 3417 # water from 14.5 to 15.5 degC. 3418 3419 # btu definitions: energy to raise a pound of water 1 degF 3420 3421 btu btu_IT # International Table BTU is the default 3422 britishthermalunit btu 3423 btu_IT cal_IT lb degF / gram K 3424 btu_th cal_th lb degF / gram K 3425 btu_mean cal_mean lb degF / gram K 3426 btu_15 cal_15 lb degF / gram K 3427 btu_ISO 1055.06 J # Exact, rounded ISO definition based 3428 # on the IT calorie 3429 quad quadrillion btu 3430 3431 ECtherm 1e5 btu_ISO # Exact definition 3432 UStherm 1.054804e8 J # Exact definition, 3433 therm UStherm 3434 3435 # Water latent heat from [23] 3436 3437 water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C 3438 water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa 3439 3440 # Specific heat capacities of various substances 3441 3442 specificheat_water calorie / g K 3443 water_specificheat specificheat_water 3444 # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html 3445 specificheat_aluminum 0.91 J/g K 3446 specificheat_antimony 0.21 J/g K 3447 specificheat_barium 0.20 J/g K 3448 specificheat_beryllium 1.83 J/g K 3449 specificheat_bismuth 0.13 J/g K 3450 specificheat_cadmium 0.23 J/g K 3451 specificheat_cesium 0.24 J/g K 3452 specificheat_chromium 0.46 J/g K 3453 specificheat_cobalt 0.42 J/g K 3454 specificheat_copper 0.39 J/g K 3455 specificheat_gallium 0.37 J/g K 3456 specificheat_germanium 0.32 J/g K 3457 specificheat_gold 0.13 J/g K 3458 specificheat_hafnium 0.14 J/g K 3459 specificheat_indium 0.24 J/g K 3460 specificheat_iridium 0.13 J/g K 3461 specificheat_iron 0.45 J/g K 3462 specificheat_lanthanum 0.195 J/g K 3463 specificheat_lead 0.13 J/g K 3464 specificheat_lithium 3.57 J/g K 3465 specificheat_lutetium 0.15 J/g K 3466 specificheat_magnesium 1.05 J/g K 3467 specificheat_manganese 0.48 J/g K 3468 specificheat_mercury 0.14 J/g K 3469 specificheat_molybdenum 0.25 J/g K 3470 specificheat_nickel 0.44 J/g K 3471 specificheat_osmium 0.13 J/g K 3472 specificheat_palladium 0.24 J/g K 3473 specificheat_platinum 0.13 J/g K 3474 specificheat_plutonum 0.13 J/g K 3475 specificheat_potassium 0.75 J/g K 3476 specificheat_rhenium 0.14 J/g K 3477 specificheat_rhodium 0.24 J/g K 3478 specificheat_rubidium 0.36 J/g K 3479 specificheat_ruthenium 0.24 J/g K 3480 specificheat_scandium 0.57 J/g K 3481 specificheat_selenium 0.32 J/g K 3482 specificheat_silicon 0.71 J/g K 3483 specificheat_silver 0.23 J/g K 3484 specificheat_sodium 1.21 J/g K 3485 specificheat_strontium 0.30 J/g K 3486 specificheat_tantalum 0.14 J/g K 3487 specificheat_thallium 0.13 J/g K 3488 specificheat_thorium 0.13 J/g K 3489 specificheat_tin 0.21 J/g K 3490 specificheat_titanium 0.54 J/g K 3491 specificheat_tungsten 0.13 J/g K 3492 specificheat_uranium 0.12 J/g K 3493 specificheat_vanadium 0.39 J/g K 3494 specificheat_yttrium 0.30 J/g K 3495 specificheat_zinc 0.39 J/g K 3496 specificheat_zirconium 0.27 J/g K 3497 specificheat_ethanol 2.3 J/g K 3498 specificheat_ammonia 4.6 J/g K 3499 specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit 3500 specificheat_gasoline 2.22 J/g K 3501 specificheat_iodine 2.15 J/g K 3502 specificheat_oliveoil 1.97 J/g K 3503 3504 # en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities 3505 specificheat_hydrogen 14.3 J/g K 3506 specificheat_helium 5.1932 J/g K 3507 specificheat_argon 0.5203 J/g K 3508 specificheat_tissue 3.5 J/g K 3509 specificheat_diamond 0.5091 J/g K 3510 specificheat_granite 0.79 J/g K 3511 specificheat_graphite 0.71 J/g K 3512 specificheat_ice 2.11 J/g K 3513 specificheat_asphalt 0.92 J/g K 3514 specificheat_brick 0.84 J/g K 3515 specificheat_concrete 0.88 J/g K 3516 specificheat_glass_silica 0.84 J/g K 3517 specificheat_glass_flint 0.503 J/g K 3518 specificheat_glass_pyrex 0.753 J/g K 3519 specificheat_gypsum 1.09 J/g K 3520 specificheat_marble 0.88 J/g K 3521 specificheat_sand 0.835 J/g K 3522 specificheat_soil 0.835 J/g K 3523 specificheat_wood 1.7 J/g K 3524 3525 specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php 3526 3527 3528 # Energy densities of various fuels 3529 # 3530 # Most of these fuels have varying compositions or qualities and hence their 3531 # actual energy densities vary. These numbers are hence only approximate. 3532 # 3533 # E1. http://bioenergy.ornl.gov/papers/misc/energy_conv.html 3534 # E2. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm 3535 # E3. http://www.ior.com.au/ecflist.html 3536 3537 tonoil 1e10 cal_IT # Ton oil equivalent. A conventional 3538 # value for the energy released by 3539 toe tonoil # burning one metric ton of oil. [18,E2] 3540 # Note that energy per mass of petroleum 3541 # products is fairly constant. 3542 # Variations in volumetric energy 3543 # density result from variations in the 3544 # density (kg/m^3) of different fuels. 3545 # This definition is given by the 3546 # IEA/OECD. 3547 toncoal 7e9 cal_IT # Energy in metric ton coal from [18]. 3548 # This is a nominal value which 3549 # is close to the heat content 3550 # of coal used in the 1950's 3551 barreloil 5.8 Mbtu # Conventional value for barrel of crude 3552 # oil [E2]. Actual range is 5.6 - 6.3. 3553 naturalgas_HHV 1027 btu/ft3 # Energy content of natural gas. HHV 3554 naturalgas_LHV 930 btu/ft3 # is for Higher Heating Value and 3555 naturalgas naturalgas_HHV # includes energy from condensation 3556 # combustion products. LHV is for Lower 3557 # Heating Value and excludes these. 3558 # American publications typically report 3559 # HHV whereas European ones report LHV. 3560 charcoal 30 GJ/tonne 3561 woodenergy_dry 20 GJ/tonne # HHV, a cord weights about a tonne 3562 woodenergy_airdry 15 GJ/tonne # 20% moisture content 3563 coal_bituminous 27 GJ / tonne 3564 coal_lignite 15 GJ / tonne 3565 coal_US 22 GJ / uston # Average for US coal (short ton), 1995 3566 ethanol_HHV 84000 btu/usgallon 3567 ethanol_LHV 75700 btu/usgallon 3568 diesel 130500 btu/usgallon 3569 gasoline_LHV 115000 btu/usgallon 3570 gasoline_HHV 125000 btu/usgallon 3571 gasoline gasoline_HHV 3572 heating 37.3 MJ/liter 3573 fueloil 39.7 MJ/liter # low sulphur 3574 propane 93.3 MJ/m^3 3575 butane 124 MJ/m^3 3576 3577 # These values give total energy from uranium fission. Actual efficiency 3578 # of nuclear power plants is around 30%-40%. Note also that some reactors 3579 # use enriched uranium around 3% U-235. Uranium during processing or use 3580 # may be in a compound of uranium oxide or uranium hexafluoride, in which 3581 # case the energy density would be lower depending on how much uranium is 3582 # in the compound. 3583 3584 uranium_pure 200 MeV avogadro / (235.0439299 g/mol) # Pure U-235 3585 uranium_natural 0.7% uranium_pure # Natural uranium: 0.7% U-235 3586 3587 # Celsius heat unit: energy to raise a pound of water 1 degC 3588 3589 celsiusheatunit cal lb degC / gram K 3590 chu celsiusheatunit 3591 3592 POWER watt 3593 3594 # "Apparent" average power in an AC circuit, the product of rms voltage 3595 # and rms current, equal to the true power in watts when voltage and 3596 # current are in phase. In a DC circuit, always equal to the true power. 3597 3598 VA volt ampere 3599 3600 kWh kilowatt hour 3601 3602 # The horsepower is supposedly the power of one horse pulling. Obviously 3603 # different people had different horses. 3604 3605 horsepower 550 foot pound force / sec # Invented by James Watt 3606 mechanicalhorsepower horsepower 3607 hp horsepower 3608 metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in 3609 electrichorsepower 746 W # Germany 3610 boilerhorsepower 9809.50 W 3611 waterhorsepower 746.043 W 3612 brhorsepower 745.70 W 3613 donkeypower 250 W 3614 chevalvapeur metrichorsepower 3615 3616 # 3617 # Heat Transfer 3618 # 3619 # Thermal conductivity, K, measures the rate of heat transfer across 3620 # a material. The heat transfered is 3621 # Q = K dT A t / L 3622 # where dT is the temperature difference across the material, A is the 3623 # cross sectional area, t is the time, and L is the length (thickness). 3624 # Thermal conductivity is a material property. 3625 3626 THERMAL_CONDUCTIVITY POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH) 3627 THERMAL_RESISTIVITY 1/THERMAL_CONDUCTIVITY 3628 3629 # Thermal conductance is the rate at which heat flows across a given 3630 # object, so the area and thickness have been fixed. It depends on 3631 # the size of the object and is hence not a material property. 3632 3633 THERMAL_CONDUCTANCE POWER / TEMPERATURE_DIFFERENCE 3634 THERMAL_RESISTANCE 1/THERMAL_CONDUCTANCE 3635 3636 # Thermal admittance is the rate of heat flow per area across an 3637 # object whose thickness has been fixed. Its reciprocal, thermal 3638 # insulation, is used to for measuring the heat transfer per area 3639 # of sheets of insulation or cloth that are of specified thickness. 3640 3641 THERMAL_ADMITTANCE THERMAL_CONDUCTIVITY / LENGTH 3642 THERMAL_INSULANCE THERMAL_RESISTIVITY LENGTH 3643 THERMAL_INSULATION THERMAL_RESISTIVITY LENGTH 3644 3645 Rvalue degF ft^2 hr / btu 3646 Uvalue 1/Rvalue 3647 europeanUvalue watt / m^2 K 3648 RSI degC m^2 / W 3649 clo 0.155 degC m^2 / W # Supposed to be the insulance 3650 # required to keep a resting person 3651 # comfortable indoors. The value 3652 # given is from NIST and the CRC, 3653 # but [5] gives a slightly different 3654 # value of 0.875 ft^2 degF hr / btu. 3655 tog 0.1 degC m^2 / W # Also used for clothing. 3656 3657 3658 # The bel was defined by engineers of Bell Laboratories to describe the 3659 # reduction in audio level over a length of one mile. It was originally 3660 # called the transmission unit (TU) but was renamed around 1923 to honor 3661 # Alexander Graham Bell. The bel proved inconveniently large so the decibel 3662 # has become more common. The decibel is dimensionless since it reports a 3663 # ratio, but it is used in various contexts to report a signal's power 3664 # relative to some reference level. 3665 3666 bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition 3667 decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel 3668 dB() decibel # Abbreviation 3669 dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W 3670 dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW 3671 dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW 3672 dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW 3673 dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW 3674 dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative 3675 # to 1 joule. Used for power spectral 3676 # density since W/Hz = J 3677 3678 # When used to measure amplitude, voltage, or current the signal is squared 3679 # because power is proportional to the square of these measures. The root 3680 # mean square (RMS) voltage is typically used with these units. 3681 3682 dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V 3683 dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV 3684 dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2) 3685 # Reference = 1 microvolt 3686 3687 # Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load. 3688 # Originally defined as dBv but changed to prevent confusion with dBV. 3689 # The "u" is for unloaded. 3690 dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \ 3691 ~dB(dBu^2 / mW 600 ohm) 3692 dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu 3693 3694 3695 # Measurements for sound in air, referenced to the threshold of human hearing 3696 # Note that sound in other media typically uses 1 micropascal as a reference 3697 # for sound pressure. Units dBA, dBB, dBC, refer to different frequency 3698 # weightings meant to approximate the human ear's response. 3699 3700 dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \ 3701 ~dB(dBSPL^2 / (20 microPa)^2) # pressure 3702 dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \ 3703 ~dB(dBSIL / (1e-12 W/m^2)) # intensity 3704 dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W) 3705 3706 3707 # Misc other measures 3708 3709 ENTROPY ENERGY / TEMPERATURE 3710 clausius 1e3 cal/K # A unit of physical entropy 3711 langley thermcalorie/cm^2 # Used in radiation theory 3712 poncelet 100 kg force m / s 3713 tonrefrigeration uston 144 btu / lb day # One ton refrigeration is 3714 # the rate of heat extraction required 3715 # turn one ton of water to ice in 3716 # a day. Ice is defined to have a 3717 # latent heat of 144 btu/lb. 3718 tonref tonrefrigeration 3719 refrigeration tonref / ton 3720 frigorie 1000 cal_15 # Used in refrigeration engineering. 3721 tnt 1e9 cal_th / ton# So you can write tons tnt. This 3722 # is a defined, not measured, value. 3723 airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as 3724 # pressure times air flow. 3725 3726 # Nuclear weapon yields 3727 3728 davycrocket 10 ton tnt # lightest US tactical nuclear weapon 3729 hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb 3730 nagasaki 21 kiloton tnt # Plutonium-239 fission bomb 3731 fatman nagasaki 3732 littleboy hiroshima 3733 ivyking 500 kiloton tnt # most powerful fission bomb 3734 castlebravo 15 megaton tnt # most powerful US test 3735 b53bomb 9 megaton tnt 3736 # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/ 3737 trinity 18 kiloton tnt # July 16, 1945 3738 gadget trinity 3739 3740 # 3741 # Permeability: The permeability or permeance, n, of a substance determines 3742 # how fast vapor flows through the substance. The formula W = n A dP 3743 # holds where W is the rate of flow (in mass/time), n is the permeability, 3744 # A is the area of the flow path, and dP is the vapor pressure difference. 3745 # 3746 3747 perm_0C grain / hr ft^2 inHg 3748 perm_zero perm_0C 3749 perm_0 perm_0C 3750 perm perm_0C 3751 perm_23C grain / hr ft^2 in Hg23C 3752 perm_twentythree perm_23C 3753 3754 # 3755 # Counting measures 3756 # 3757 3758 pair 2 3759 brace 2 3760 nest 3 # often used for items like bowls that 3761 # nest together 3762 hattrick 3 # Used in sports, especially cricket and ice 3763 # hockey to report the number of goals. 3764 dicker 10 3765 dozen 12 3766 bakersdozen 13 3767 score 20 3768 flock 40 3769 timer 40 3770 shock 60 3771 toncount 100 # Used in sports in the UK 3772 longhundred 120 # From a germanic counting system 3773 gross 144 3774 greatgross 12 gross 3775 tithe 1|10 # From Anglo-Saxon word for tenth 3776 3777 # Paper counting measure 3778 3779 shortquire 24 3780 quire 25 3781 shortream 480 3782 ream 500 3783 perfectream 516 3784 bundle 2 reams 3785 bale 5 bundles 3786 3787 # 3788 # Paper measures 3789 # 3790 3791 # USA paper sizes 3792 3793 lettersize 8.5 inch 11 inch 3794 legalsize 8.5 inch 14 inch 3795 ledgersize 11 inch 17 inch 3796 executivesize 7.25 inch 10.5 inch 3797 Apaper 8.5 inch 11 inch 3798 Bpaper 11 inch 17 inch 3799 Cpaper 17 inch 22 inch 3800 Dpaper 22 inch 34 inch 3801 Epaper 34 inch 44 inch 3802 3803 # Correspondence envelope sizes. #10 is the standard business 3804 # envelope in the USA. 3805 3806 envelope6_25size 3.5 inch 6 inch 3807 envelope6_75size 3.625 inch 6.5 inch 3808 envelope7size 3.75 inch 6.75 inch 3809 envelope7_75size 3.875 inch 7.5 inch 3810 envelope8_625size 3.625 inch 8.625 inch 3811 envelope9size 3.875 inch 8.875 inch 3812 envelope10size 4.125 inch 9.5 inch 3813 envelope11size 4.5 inch 10.375 inch 3814 envelope12size 4.75 inch 11 inch 3815 envelope14size 5 inch 11.5 inch 3816 envelope16size 6 inch 12 inch 3817 3818 # Announcement envelope sizes (no relation to metric paper sizes like A4) 3819 3820 envelopeA1size 3.625 inch 5.125 inch # same as 4bar 3821 envelopeA2size 4.375 inch 5.75 inch 3822 envelopeA6size 4.75 inch 6.5 inch 3823 envelopeA7size 5.25 inch 7.25 inch 3824 envelopeA8size 5.5 inch 8.125 inch 3825 envelopeA9size 5.75 inch 8.75 inch 3826 envelopeA10size 6 inch 9.5 inch 3827 3828 # Baronial envelopes 3829 3830 envelope4bar 3.625 inch 5.125 inch # same as A1 3831 envelope5_5bar 4.375 inch 5.75 inch 3832 envelope6bar 4.75 inch 6.5 inch 3833 3834 # Coin envelopes 3835 3836 envelope1baby 2.25 inch 3.5 inch # same as #1 coin 3837 envelope00coin 1.6875 inch 2.75 inch 3838 envelope1coin 2.25 inch 3.5 inch 3839 envelope3coin 2.5 inch 4.25 inch 3840 envelope4coin 3 inch 4.5 inch 3841 envelope4_5coin 3 inch 4.875 inch 3842 envelope5coin 2.875 inch 5.25 inch 3843 envelope5_5coin 3.125 inch 5.5 inch 3844 envelope6coin 3.375 inch 6 inch 3845 envelope7coin 3.5 inch 6.5 inch 3846 3847 # The metric paper sizes are defined so that if a sheet is cut in half 3848 # along the short direction, the result is two sheets which are 3849 # similar to the original sheet. This means that for any metric size, 3850 # the long side is close to sqrt(2) times the length of the short 3851 # side. Each series of sizes is generated by repeated cuts in half, 3852 # with the values rounded down to the nearest millimeter. 3853 3854 A0paper 841 mm 1189 mm # The basic size in the A series 3855 A1paper 594 mm 841 mm # is defined to have an area of 3856 A2paper 420 mm 594 mm # one square meter. 3857 A3paper 297 mm 420 mm 3858 A4paper 210 mm 297 mm 3859 A5paper 148 mm 210 mm 3860 A6paper 105 mm 148 mm 3861 A7paper 74 mm 105 mm 3862 A8paper 52 mm 74 mm 3863 A9paper 37 mm 52 mm 3864 A10paper 26 mm 37 mm 3865 3866 B0paper 1000 mm 1414 mm # The basic B size has an area 3867 B1paper 707 mm 1000 mm # of sqrt(2) square meters. 3868 B2paper 500 mm 707 mm 3869 B3paper 353 mm 500 mm 3870 B4paper 250 mm 353 mm 3871 B5paper 176 mm 250 mm 3872 B6paper 125 mm 176 mm 3873 B7paper 88 mm 125 mm 3874 B8paper 62 mm 88 mm 3875 B9paper 44 mm 62 mm 3876 B10paper 31 mm 44 mm 3877 3878 C0paper 917 mm 1297 mm # The basic C size has an area 3879 C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters. 3880 C2paper 458 mm 648 mm 3881 C3paper 324 mm 458 mm # Intended for envelope sizes 3882 C4paper 229 mm 324 mm 3883 C5paper 162 mm 229 mm 3884 C6paper 114 mm 162 mm 3885 C7paper 81 mm 114 mm 3886 C8paper 57 mm 81 mm 3887 C9paper 40 mm 57 mm 3888 C10paper 28 mm 40 mm 3889 3890 # gsm (Grams per Square Meter), a sane, metric paper weight measure 3891 3892 gsm grams / meter^2 3893 3894 # In the USA, a collection of crazy historical paper measures are used. Paper 3895 # is measured as a weight of a ream of that particular type of paper. This is 3896 # sometimes called the "substance" or "basis" (as in "substance 20" paper). 3897 # The standard sheet size or "basis size" varies depending on the type of 3898 # paper. As a result, 20 pound bond paper and 50 pound text paper are actually 3899 # about the same weight. The different sheet sizes were historically the most 3900 # convenient for printing or folding in the different applications. These 3901 # different basis weights are standards maintained by American Society for 3902 # Testing Materials (ASTM) and the American Forest and Paper Association 3903 # (AF&PA). 3904 3905 poundbookpaper lb / 25 inch 38 inch ream 3906 lbbook poundbookpaper 3907 poundtextpaper poundbookpaper 3908 lbtext poundtextpaper 3909 poundoffsetpaper poundbookpaper # For offset printing 3910 lboffset poundoffsetpaper 3911 poundbiblepaper poundbookpaper # Designed to be lightweight, thin, 3912 lbbible poundbiblepaper # strong and opaque. 3913 poundtagpaper lb / 24 inch 36 inch ream 3914 lbtag poundtagpaper 3915 poundbagpaper poundtagpaper 3916 lbbag poundbagpaper 3917 poundnewsprintpaper poundtagpaper 3918 lbnewsprint poundnewsprintpaper 3919 poundposterpaper poundtagpaper 3920 lbposter poundposterpaper 3921 poundtissuepaper poundtagpaper 3922 lbtissue poundtissuepaper 3923 poundwrappingpaper poundtagpaper 3924 lbwrapping poundwrappingpaper 3925 poundwaxingpaper poundtagpaper 3926 lbwaxing poundwaxingpaper 3927 poundglassinepaper poundtagpaper 3928 lbglassine poundglassinepaper 3929 poundcoverpaper lb / 20 inch 26 inch ream 3930 lbcover poundcoverpaper 3931 poundindexpaper lb / 25.5 inch 30.5 inch ream 3932 lbindex poundindexpaper 3933 poundindexbristolpaper poundindexpaper 3934 lbindexbristol poundindexpaper 3935 poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and 3936 lbbond poundbondpaper # durable for repeated 3937 poundwritingpaper poundbondpaper # filing, and it resists 3938 lbwriting poundwritingpaper # ink penetration. 3939 poundledgerpaper poundbondpaper 3940 lbledger poundledgerpaper 3941 poundcopypaper poundbondpaper 3942 lbcopy poundcopypaper 3943 poundblottingpaper lb / 19 inch 24 inch ream 3944 lbblotting poundblottingpaper 3945 poundblankspaper lb / 22 inch 28 inch ream 3946 lbblanks poundblankspaper 3947 poundpostcardpaper lb / 22.5 inch 28.5 inch ream 3948 lbpostcard poundpostcardpaper 3949 poundweddingbristol poundpostcardpaper 3950 lbweddingbristol poundweddingbristol 3951 poundbristolpaper poundweddingbristol 3952 lbbristol poundbristolpaper 3953 poundboxboard lb / 1000 ft^2 3954 lbboxboard poundboxboard 3955 poundpaperboard poundboxboard 3956 lbpaperboard poundpaperboard 3957 3958 # When paper is marked in units of M, it means the weight of 1000 sheets of the 3959 # given size of paper. To convert this to paper weight, divide by the size of 3960 # the paper in question. 3961 3962 paperM lb / 1000 3963 3964 # In addition paper weight is reported in "caliper" which is simply the 3965 # thickness of one sheet, typically in inches. Thickness is also reported in 3966 # "points" where a point is 1|1000 inch. These conversions are supplied to 3967 # convert these units roughly (using an approximate density) into the standard 3968 # paper weight values. 3969 3970 pointthickness 0.001 in 3971 paperdensity 0.8 g/cm^3 # approximate--paper densities vary! 3972 papercaliper in paperdensity 3973 paperpoint pointthickness paperdensity 3974 3975 # 3976 # Printing 3977 # 3978 3979 fournierpoint 0.1648 inch / 12 # First definition of the printers 3980 # point made by Pierre Fournier who 3981 # defined it in 1737 as 1|12 of a 3982 # cicero which was 0.1648 inches. 3983 olddidotpoint 1|72 frenchinch # François Ambroise Didot, one of 3984 # a family of printers, changed 3985 # Fournier's definition around 1770 3986 # to fit to the French units then in 3987 # use. 3988 bertholdpoint 1|2660 m # H. Berthold tried to create a 3989 # metric version of the didot point 3990 # in 1878. 3991 INpoint 0.4 mm # This point was created by a 3992 # group directed by Fermin Didot in 3993 # 1881 and is associated with the 3994 # imprimerie nationale. It doesn't 3995 # seem to have been used much. 3996 germandidotpoint 0.376065 mm # Exact definition appears in DIN 3997 # 16507, a German standards document 3998 # of 1954. Adopted more broadly in 3999 # 1966 by ??? 4000 metricpoint 3|8 mm # Proposed in 1977 by Eurograf 4001 oldpoint 1|72.27 inch # The American point was invented 4002 printerspoint oldpoint # by Nelson Hawks in 1879 and 4003 texpoint oldpoint # dominates USA publishing. 4004 # It was standardized by the American 4005 # Typefounders Association at the 4006 # value of 0.013837 inches exactly. 4007 # Knuth uses the approximation given 4008 # here (which is very close). The 4009 # comp.fonts FAQ claims that this 4010 # value is supposed to be 1|12 of a 4011 # pica where 83 picas is equal to 35 4012 # cm. But this value differs from 4013 # the standard. 4014 texscaledpoint 1|65536 texpoint # The TeX typesetting system uses 4015 texsp texscaledpoint # this for all computations. 4016 computerpoint 1|72 inch # The American point was rounded 4017 point computerpoint 4018 computerpica 12 computerpoint # to an even 1|72 inch by computer 4019 postscriptpoint computerpoint # people at some point. 4020 pspoint postscriptpoint 4021 twip 1|20 point # TWentieth of an Imperial Point 4022 Q 1|4 mm # Used in Japanese phototypesetting 4023 # Q is for quarter 4024 frenchprinterspoint olddidotpoint 4025 didotpoint germandidotpoint # This seems to be the dominant value 4026 europeanpoint didotpoint # for the point used in Europe 4027 cicero 12 didotpoint 4028 4029 stick 2 inches 4030 4031 # Type sizes 4032 4033 excelsior 3 oldpoint 4034 brilliant 3.5 oldpoint 4035 diamondtype 4 oldpoint 4036 pearl 5 oldpoint 4037 agate 5.5 oldpoint # Originally agate type was 14 lines per 4038 # inch, giving a value of 1|14 in. 4039 ruby agate # British 4040 nonpareil 6 oldpoint 4041 mignonette 6.5 oldpoint 4042 emerald mignonette # British 4043 minion 7 oldpoint 4044 brevier 8 oldpoint 4045 bourgeois 9 oldpoint 4046 longprimer 10 oldpoint 4047 smallpica 11 oldpoint 4048 pica 12 oldpoint 4049 english 14 oldpoint 4050 columbian 16 oldpoint 4051 greatprimer 18 oldpoint 4052 paragon 20 oldpoint 4053 meridian 44 oldpoint 4054 canon 48 oldpoint 4055 4056 # German type sizes 4057 4058 nonplusultra 2 didotpoint 4059 brillant 3 didotpoint 4060 diamant 4 didotpoint 4061 perl 5 didotpoint 4062 nonpareille 6 didotpoint 4063 kolonel 7 didotpoint 4064 petit 8 didotpoint 4065 borgis 9 didotpoint 4066 korpus 10 didotpoint 4067 corpus korpus 4068 garamond korpus 4069 mittel 14 didotpoint 4070 tertia 16 didotpoint 4071 text 18 didotpoint 4072 kleine_kanon 32 didotpoint 4073 kanon 36 didotpoint 4074 grobe_kanon 42 didotpoint 4075 missal 48 didotpoint 4076 kleine_sabon 72 didotpoint 4077 grobe_sabon 84 didotpoint 4078 4079 # 4080 # Information theory units. Note that the name "entropy" is used both 4081 # to measure information and as a physical quantity. 4082 # 4083 4084 INFORMATION bit 4085 4086 nat (1/ln(2)) bits # Entropy measured base e 4087 hartley log2(10) bits # Entropy of a uniformly 4088 ban hartley # distributed random variable 4089 # over 10 symbols. 4090 dit hartley # from Decimal digIT 4091 4092 # 4093 # Computer 4094 # 4095 4096 bps bit/sec # Sometimes the term "baud" is 4097 # incorrectly used to refer to 4098 # bits per second. Baud refers 4099 # to symbols per second. Modern 4100 # modems transmit several bits 4101 # per symbol. 4102 byte 8 bit # Not all machines had 8 bit 4103 B byte # bytes, but these days most of 4104 # them do. But beware: for 4105 # transmission over modems, a 4106 # few extra bits are used so 4107 # there are actually 10 bits per 4108 # byte. 4109 octet 8 bits # The octet is always 8 bits 4110 nybble 4 bits # Half of a byte. Sometimes 4111 # equal to different lengths 4112 # such as 3 bits. 4113 nibble nybble 4114 nyp 2 bits # Donald Knuth asks in an exercise 4115 # for a name for a 2 bit 4116 # quantity and gives the "nyp" 4117 # as a solution due to Gregor 4118 # Purdy. Not in common use. 4119 meg megabyte # Some people consider these 4120 # units along with the kilobyte 4121 gig gigabyte # to be defined according to 4122 # powers of 2 with the kilobyte 4123 # equal to 2^10 bytes, the 4124 # megabyte equal to 2^20 bytes and 4125 # the gigabyte equal to 2^30 bytes 4126 # but these usages are forbidden 4127 # by SI. Binary prefixes have 4128 # been defined by IEC to replace 4129 # the SI prefixes. Use them to 4130 # get the binary values: KiB, MiB, 4131 # and GiB. 4132 jiffy 0.01 sec # This is defined in the Jargon File 4133 jiffies jiffy # (http://www.jargon.org) as being the 4134 # duration of a clock tick for measuring 4135 # wall-clock time. Supposedly the value 4136 # used to be 1|60 sec or 1|50 sec 4137 # depending on the frequency of AC power, 4138 # but then 1|100 sec became more common. 4139 # On linux systems, this term is used and 4140 # for the Intel based chips, it does have 4141 # the value of .01 sec. The Jargon File 4142 # also lists two other definitions: 4143 # millisecond, and the time taken for 4144 # light to travel one foot. 4145 cdaudiospeed 44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2 4146 # samples of sixteen bits each. 4147 cdromspeed 75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read 4148 # each second with 2048 bytes per sector. 4149 # Audio CDs do not have sectors, but 4150 # people sometimes divide the bit rate by 4151 # 75 and claim a sector length of 2352. 4152 # Data CDs have a lower rate due to 4153 # increased error correction overhead. 4154 # There is a rarely used mode (mode2) with 4155 # 2336 bytes per sector that has fewer 4156 # error correction bits than mode1. 4157 dvdspeed 1385 kB/s # This is the "1x" speed of a DVD using 4158 # constant linear velocity (CLV) mode. 4159 # Modern DVDs may vary the linear velocity 4160 # as they go from the inside to the 4161 # outside of the disc. 4162 # See http://www.osta.org/technology/dvdqa/dvdqa4.htm 4163 # 4164 # The IP address space is divided into subnets. The number of hosts 4165 # in a subnet depends on the length of the subnet prefix. This is 4166 # often written as /N where N is the number of bits in the prefix. 4167 # 4168 # https://en.wikipedia.org/wiki/Subnetwork 4169 # 4170 # These definitions gives the number of hosts for a subnet whose 4171 # prefix has the specified length in bits. 4172 # 4173 4174 ipv4subnetsize(prefix_len) units=[1;1] domain=[0,32] range=[1,4294967296] \ 4175 2^(32-prefix_len) ; 32-log2(ipv4subnetsize) 4176 ipv4classA ipv4subnetsize(8) 4177 ipv4classB ipv4subnetsize(16) 4178 ipv4classC ipv4subnetsize(24) 4179 4180 ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \ 4181 range=[1,340282366920938463463374607431768211456] \ 4182 2^(128-prefix_len) ; 128-log2(ipv6subnetsize) 4183 4184 # 4185 # Musical measures. Musical intervals expressed as ratios. Multiply 4186 # two intervals together to get the sum of the interval. The function 4187 # musicalcent can be used to convert ratios to cents. 4188 # 4189 4190 # Perfect intervals 4191 4192 octave 2 4193 majorsecond musicalfifth^2 / octave 4194 majorthird 5|4 4195 minorthird 6|5 4196 musicalfourth 4|3 4197 musicalfifth 3|2 4198 majorsixth musicalfourth majorthird 4199 minorsixth musicalfourth minorthird 4200 majorseventh musicalfifth majorthird 4201 minorseventh musicalfifth minorthird 4202 4203 pythagoreanthird majorsecond musicalfifth^2 / octave 4204 syntoniccomma pythagoreanthird / majorthird 4205 pythagoreancomma musicalfifth^12 / octave^7 4206 4207 # Equal tempered definitions 4208 4209 semitone octave^(1|12) 4210 musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \ 4211 100 log(musicalcent)/log(semitone) 4212 4213 # 4214 # Musical note lengths. 4215 # 4216 4217 wholenote ! 4218 MUSICAL_NOTE_LENGTH wholenote 4219 halfnote 1|2 wholenote 4220 quarternote 1|4 wholenote 4221 eighthnote 1|8 wholenote 4222 sixteenthnote 1|16 wholenote 4223 thirtysecondnote 1|32 wholenote 4224 sixtyfourthnote 1|64 wholenote 4225 dotted 3|2 4226 doubledotted 7|4 4227 breve doublewholenote 4228 semibreve wholenote 4229 minimnote halfnote 4230 crotchet quarternote 4231 quaver eighthnote 4232 semiquaver sixteenthnote 4233 demisemiquaver thirtysecondnote 4234 hemidemisemiquaver sixtyfourthnote 4235 semidemisemiquaver hemidemisemiquaver 4236 4237 # 4238 # yarn and cloth measures 4239 # 4240 4241 # yarn linear density 4242 4243 woolyarnrun 1600 yard/pound # 1600 yds of "number 1 yarn" weighs 4244 # a pound. 4245 yarncut 300 yard/pound # Less common system used in 4246 # Pennsylvania for wool yarn 4247 cottonyarncount 840 yard/pound 4248 linenyarncount 300 yard/pound # Also used for hemp and ramie 4249 worstedyarncount 1680 ft/pound 4250 metricyarncount meter/gram 4251 denier 1|9 tex # used for silk and rayon 4252 manchesteryarnnumber drams/1000 yards # old system used for silk 4253 pli lb/in 4254 typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound 4255 asbestoscut 100 yd/lb # used for glass and asbestos yarn 4256 4257 tex gram / km # rational metric yarn measure, meant 4258 drex 0.1 tex # to be used for any kind of yarn 4259 poumar lb / 1e6 yard 4260 4261 # yarn and cloth length 4262 4263 skeincotton 80*54 inch # 80 turns of thread on a reel with a 4264 # 54 in circumference (varies for other 4265 # kinds of thread) 4266 cottonbolt 120 ft # cloth measurement 4267 woolbolt 210 ft 4268 bolt cottonbolt 4269 heer 600 yards 4270 cut 300 yards # used for wet-spun linen yarn 4271 lea 300 yards 4272 4273 sailmakersyard 28.5 in 4274 sailmakersounce oz / sailmakersyard 36 inch 4275 4276 silkmomme momme / 25 yards 1.49 inch # Traditional silk weight 4277 silkmm silkmomme # But it is also defined as 4278 # lb/100 yd 45 inch. The two 4279 # definitions are slightly different 4280 # and neither one seems likely to be 4281 # the true source definition. 4282 4283 # 4284 # drug dosage 4285 # 4286 4287 mcg microgram # Frequently used for vitamins 4288 iudiptheria 62.8 microgram # IU is for international unit 4289 iupenicillin 0.6 microgram 4290 iuinsulin 41.67 microgram 4291 drop 1|20 ml # The drop was an old "unit" that was 4292 # replaced by the minim. But I was 4293 # told by a pharmacist that in his 4294 # profession, the conversion of 20 4295 # drops per ml is actually used. 4296 bloodunit 450 ml # For whole blood. For blood 4297 # components, a blood unit is the 4298 # quanity of the component found in a 4299 # blood unit of whole blood. The 4300 # human body contains about 12 blood 4301 # units of whole blood. 4302 4303 # 4304 # misc medical measure 4305 # 4306 4307 frenchcathetersize 1|3 mm # measure used for the outer diameter 4308 # of a catheter 4309 charriere frenchcathetersize 4310 4311 4312 # 4313 # fixup units for times when prefix handling doesn't do the job 4314 # 4315 4316 hectare hectoare 4317 megohm megaohm 4318 kilohm kiloohm 4319 microhm microohm 4320 megalerg megaerg # 'L' added to make it pronounceable [18]. 4321 4322 # 4323 # Money 4324 # 4325 # Note that US$ is the primitive unit so other currencies are 4326 # generally given in US$. 4327 # 4328 4329 unitedstatesdollar US$ 4330 usdollar US$ 4331 $ dollar 4332 mark germanymark 4333 #bolivar venezuelabolivar # Not all databases are 4334 #venezuelabolivarfuerte 1e-5 bolivar # supplying these 4335 #bolivarfuerte 1e-5 bolivar # The currency was revalued 4336 #oldbolivar 1|1000 bolivarfuerte # twice 4337 peseta spainpeseta 4338 rand southafricarand 4339 escudo portugalescudo 4340 guilder netherlandsguilder 4341 hollandguilder netherlandsguilder 4342 peso mexicopeso 4343 yen japanyen 4344 lira italylira 4345 rupee indiarupee 4346 drachma greecedrachma 4347 franc francefranc 4348 markka finlandmarkka 4349 britainpound unitedkingdompound 4350 greatbritainpound unitedkingdompound 4351 unitedkingdompound ukpound 4352 poundsterling britainpound 4353 yuan chinayuan 4354 4355 # Unicode Currency Names 4356 4357 !utf8 4358 icelandkróna icelandkrona 4359 polandzłoty polandzloty 4360 tongapa’anga tongapa'anga 4361 #venezuelabolívar venezuelabolivar 4362 vietnamđồng vietnamdong 4363 mongoliatögrög mongoliatugrik 4364 sãotomé&príncipedobra saotome&principedobra 4365 !endutf8 4366 4367 UKP GBP # Not an ISO code, but looks like one, and 4368 # sometimes used on usenet. 4369 4370 !include currency.units 4371 4372 # Money on the gold standard, used in the late 19th century and early 4373 # 20th century. 4374 4375 olddollargold 23.22 grains goldprice # Used until 1934 4376 newdollargold 96|7 grains goldprice # After Jan 31, 1934 4377 dollargold newdollargold 4378 poundgold 113 grains goldprice # British pound 4379 4380 # Precious metals 4381 4382 goldounce goldprice troyounce 4383 silverounce silverprice troyounce 4384 platinumounce platinumprice troyounce 4385 XAU goldounce 4386 XPT platinumounce 4387 XAG silverounce 4388 4389 # Nominal masses of US coins. Note that dimes, quarters and half dollars 4390 # have weight proportional to value. Before 1965 it was $40 / kg. 4391 4392 USpennyweight 2.5 grams # Since 1982, 48 grains before 4393 USnickelweight 5 grams 4394 USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965 4395 USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965 4396 UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971 4397 USdollarweight 8.1 grams # Weight of Susan B. Anthony and 4398 # Sacagawea dollar coins 4399 4400 # British currency 4401 4402 quid britainpound # Slang names 4403 fiver 5 quid 4404 tenner 10 quid 4405 monkey 500 quid 4406 brgrand 1000 quid 4407 bob shilling 4408 4409 shilling 1|20 britainpound # Before decimalisation, there 4410 oldpence 1|12 shilling # were 20 shillings to a pound, 4411 farthing 1|4 oldpence # each of twelve old pence 4412 guinea 21 shilling # Still used in horse racing 4413 crown 5 shilling 4414 florin 2 shilling 4415 groat 4 oldpence 4416 tanner 6 oldpence 4417 brpenny 0.01 britainpound 4418 pence brpenny 4419 tuppence 2 pence 4420 tuppenny tuppence 4421 ha'penny halfbrpenny 4422 hapenny ha'penny 4423 oldpenny oldpence 4424 oldtuppence 2 oldpence 4425 oldtuppenny oldtuppence 4426 threepence 3 oldpence # threepence never refers to new money 4427 threepenny threepence 4428 oldthreepence threepence 4429 oldthreepenny threepence 4430 oldhalfpenny halfoldpenny 4431 oldha'penny oldhalfpenny 4432 oldhapenny oldha'penny 4433 brpony 25 britainpound 4434 4435 # Canadian currency 4436 4437 loony 1 canadadollar # This coin depicts a loon 4438 toony 2 canadadollar 4439 4440 # Cryptocurrency 4441 4442 satoshi 1e-8 bitcoin 4443 XBT bitcoin # nonstandard code 4444 4445 # 4446 # Units used for measuring volume of wood 4447 # 4448 4449 cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood 4450 facecord 1|2 cord 4451 cordfoot 1|8 cord # One foot long section of a cord 4452 cordfeet cordfoot 4453 housecord 1|3 cord # Used to sell firewood for residences, 4454 # often confusingly called a "cord" 4455 boardfoot ft^2 inch # Usually 1 inch thick wood 4456 boardfeet boardfoot 4457 fbm boardfoot # feet board measure 4458 stack 4 yard^3 # British, used for firewood and coal [18] 4459 rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly 4460 # sometimes called a face cord, but this 4461 # value is equal to 1|3 cord. Name 4462 # comes from an old Norse word for a 4463 # stack of wood. 4464 stere m^3 4465 timberfoot ft^3 # Used for measuring solid blocks of wood 4466 standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or 4467 # Pittsburg standard. Apparently the 4468 # term is short for "standard hundred" 4469 # which was meant to refer to 100 pieces 4470 # of wood (deals). However, this 4471 # particular standard is equal to 120 4472 # deals which are 12 ft by 11 in by 1.5 4473 # inches (not the standard deal). 4474 hoppusfoot (4/pi) ft^3 # Volume calculation suggested in 1736 4475 hoppusboardfoot 1|12 hoppusfoot # forestry manual by Edward Hoppus, for 4476 hoppuston 50 hoppusfoot # estimating the usable volume of a log. 4477 # It results from computing the volume 4478 # of a cylindrical log of length, L, and 4479 # girth (circumference), G, by V=L(G/4)^2. 4480 # The hoppus ton is apparently still in 4481 # use for shipments from Southeast Asia. 4482 4483 # In Britain, the deal is apparently any piece of wood over 6 feet long, over 4484 # 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece 4485 # of wood less than 7 inches wide is called a "batten". This unit is now used 4486 # exclusively for fir and pine. 4487 4488 deal 12 ft 11 in 2.5 in # The standard North American deal [OED] 4489 wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard 4490 # deal it's called a "whole deal"! 4491 splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal. 4492 4493 4494 # Used for shellac mixing rate 4495 4496 poundcut pound / gallon 4497 lbcut poundcut 4498 4499 # 4500 # Gas and Liquid flow units 4501 # 4502 4503 FLUID_FLOW VOLUME / TIME 4504 4505 # Some obvious volumetric gas flow units (cu is short for cubic) 4506 4507 cumec m^3/s 4508 cusec ft^3/s 4509 4510 # Conventional abbreviations for fluid flow units 4511 4512 gph gal/hr 4513 gpm gal/min 4514 mgd megagal/day 4515 cfs ft^3/s 4516 cfh ft^3/hour 4517 cfm ft^3/min 4518 lpm liter/min 4519 lfm ft/min # Used to report air flow produced by fans. 4520 # Multiply by cross sectional area to get a 4521 # flow in cfm. 4522 4523 pru mmHg / (ml/min) # peripheral resistance unit, used in 4524 # medicine to assess blood flow in 4525 # the capillaries. 4526 4527 # Miner's inch: This is an old historic unit used in the Western United 4528 # States. It is generally defined as the rate of flow through a one square 4529 # inch hole at a specified depth such as 4 inches. In the late 19th century, 4530 # volume of water was sometimes measured in the "24 hour inch". Values for the 4531 # miner's inch were fixed by state statues. (This information is from a web 4532 # site operated by the Nevada Division of Water Planning: The Water Words 4533 # Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.) 4534 4535 minersinchAZ 1.5 ft^3/min 4536 minersinchCA 1.5 ft^3/min 4537 minersinchMT 1.5 ft^3/min 4538 minersinchNV 1.5 ft^3/min 4539 minersinchOR 1.5 ft^3/min 4540 minersinchID 1.2 ft^3/min 4541 minersinchKS 1.2 ft^3/min 4542 minersinchNE 1.2 ft^3/min 4543 minersinchNM 1.2 ft^3/min 4544 minersinchND 1.2 ft^3/min 4545 minersinchSD 1.2 ft^3/min 4546 minersinchUT 1.2 ft^3/min 4547 minersinchCO 1 ft^3/sec / 38.4 # 38.4 miner's inches = 1 ft^3/sec 4548 minersinchBC 1.68 ft^3/min # British Columbia 4549 4550 # Oceanographic flow 4551 4552 sverdrup 1e6 m^3 / sec # Used to express flow of ocean 4553 # currents. Named after Norwegian 4554 # oceanographer H. Sverdrup. 4555 4556 # In vacuum science and some other applications, gas flow is measured 4557 # as the product of volumetric flow and pressure. This is useful 4558 # because it makes it easy to compare with the flow at standard 4559 # pressure (one atmosphere). It also directly relates to the number 4560 # of gas molecules per unit time, and hence to the mass flow if the 4561 # molecular mass is known. 4562 4563 GAS_FLOW PRESSURE FLUID_FLOW 4564 4565 sccm atm cc/min # 's' is for "standard" to indicate 4566 sccs atm cc/sec # flow at standard pressure 4567 scfh atm ft^3/hour # 4568 scfm atm ft^3/min 4569 slpm atm liter/min 4570 slph atm liter/hour 4571 lusec liter micron Hg / s # Used in vacuum science 4572 4573 # US Standard Atmosphere (1976) 4574 # Atmospheric temperature and pressure vs. geometric height above sea level 4575 # This definition covers only the troposphere (the lowest atmospheric 4576 # layer, up to 11 km), and assumes the layer is polytropic. 4577 # A polytropic process is one for which PV^k = const, where P is the 4578 # pressure, V is the volume, and k is the polytropic exponent. The 4579 # polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article 4580 # https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse 4581 # the definitions of "exponent" and "index." The functions below assume 4582 # the following parameters: 4583 4584 # temperature lapse rate, -dT/dz, in troposphere 4585 4586 lapserate 6.5 K/km # US Std Atm (1976) 4587 4588 # air molecular weight, including constituent mol wt, given 4589 # in Table 3, p. 3 4590 4591 air_1976 78.084 % 28.0134 \ 4592 + 20.9476 % 31.9988 \ 4593 + 9340 ppm 39.948 \ 4594 + 314 ppm 44.00995 \ 4595 + 18.18 ppm 20.183 \ 4596 + 5.24 ppm 4.0026 \ 4597 + 2 ppm 16.04303 \ 4598 + 1.14 ppm 83.80 \ 4599 + 0.55 ppm 2.01594 \ 4600 + 0.087 ppm 131.30 4601 4602 # universal gas constant 4603 R_1976 8.31432e3 N m/(kmol K) 4604 4605 # polytropic index n 4606 polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1 4607 4608 # If desired, redefine using current values for air mol wt and R 4609 4610 polyndx polyndx_1976 4611 # polyndx air (kg/kmol) gravity/(R lapserate) - 1 4612 4613 # for comparison with various references 4614 4615 polyexpnt (polyndx + 1) / polyndx 4616 4617 # The model assumes the following reference values: 4618 # sea-level temperature and pressure 4619 4620 stdatmT0 288.15 K 4621 stdatmP0 atm 4622 4623 # "effective radius" for relation of geometric to geopotential height, 4624 # at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no 4625 # relation to actual radius 4626 4627 earthradUSAtm 6356766 m 4628 4629 # Temperature vs. geopotential height h 4630 # Assumes 15 degC at sea level 4631 # Based on approx 45 deg latitude 4632 # Lower limits of domain and upper limits of range are those of the 4633 # tables in US Standard Atmosphere (NASA 1976) 4634 4635 stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \ 4636 stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate 4637 4638 # Temperature vs. geometric height z; based on approx 45 deg latitude 4639 stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \ 4640 stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT)) 4641 4642 # Pressure vs. geopotential height h 4643 # Assumes 15 degC and 101325 Pa at sea level 4644 # Based on approx 45 deg latitude 4645 # Lower limits of domain and upper limits of range are those of the 4646 # tables in US Standard Atmosphere (NASA 1976) 4647 4648 stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \ 4649 atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \ 4650 (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1)))) 4651 4652 # Pressure vs. geometric height z; based on approx 45 deg latitude 4653 stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \ 4654 stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP)) 4655 4656 # Geopotential height from geometric height 4657 # Based on approx 45 deg latitude 4658 # Lower limits of domain and range are somewhat arbitrary; they 4659 # correspond to the limits in the US Std Atm tables 4660 4661 geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \ 4662 (earthradUSAtm z) / (earthradUSAtm + z) ; \ 4663 (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht)) 4664 4665 # The standard value for the sea-level acceleration due to gravity is 4666 # 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949) 4667 # R_eff = 2 g_phi / denom 4668 # g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) 4669 # or 4670 # g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) 4671 # denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?) 4672 # There is no inverse function; the standard value applies at a latitude 4673 # of about 45.543 deg 4674 4675 g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \ 4676 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2 4677 4678 # effective Earth radius for relation of geometric height to 4679 # geopotential height, as function of latitude (Harrison 1949) 4680 4681 earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \ 4682 m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \ 4683 (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat)) 4684 4685 # References 4686 # Harrison, L.P. 1949. Relation Between Geopotential and Geometric 4687 # Height. In Smithsonian Meteorological Tables. List, Robert J., ed. 4688 # 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution. 4689 # NASA. US National Aeronautics and Space Administration. 1976. 4690 # US Standard Atmosphere 1976. Washington, DC: US Government Printing Office. 4691 4692 # Gauge pressure functions 4693 # 4694 # Gauge pressure is measured relative to atmospheric pressure. In the English 4695 # system, where pressure is often given in pounds per square inch, gauge 4696 # pressure is often indicated by 'psig' to distinguish it from absolute 4697 # pressure, often indicated by 'psia'. At the standard atmospheric pressure 4698 # of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696 4699 # psia; an automobile tire inflated to 31 psig has an absolute pressure of 4700 # 45.696 psia. 4701 # 4702 # With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5 4703 # bar)); with psig(), the units are taken as psi, so the example above of tire 4704 # pressure could be given as psig(31). 4705 # 4706 # If the normal elevation is significantly different from sea level, change 4707 # Patm appropriately, and adjust the lower domain limit on the gaugepressure 4708 # definition. 4709 4710 Patm atm 4711 4712 gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \ 4713 x + Patm ; gaugepressure+(-Patm) 4714 4715 psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \ 4716 gaugepressure(x psi) ; ~gaugepressure(psig) / psi 4717 4718 4719 # Pressure for underwater diving 4720 4721 seawater 0.1 bar / meter 4722 msw meter seawater 4723 fsw foot seawater 4724 4725 # 4726 # Wire Gauge 4727 # 4728 # This area is a nightmare with huge charts of wire gauge diameters 4729 # that usually have no clear origin. There are at least 5 competing wire gauge 4730 # systems to add to the confusion. The use of wire gauge is related to the 4731 # manufacturing method: a metal rod is heated and drawn through a hole. The 4732 # size change can't be too big. To get smaller wires, the process is repeated 4733 # with a series of smaller holes. Generally larger gauges mean smaller wires. 4734 # The gauges often have values such as "00" and "000" which are larger sizes 4735 # than simply "0" gauge. In the tables that appear below, these gauges must be 4736 # specified as negative numbers (e.g. "00" is -1, "000" is -2, etc). 4737 # Alternatively, you can use the following units: 4738 # 4739 4740 g00 (-1) 4741 g000 (-2) 4742 g0000 (-3) 4743 g00000 (-4) 4744 g000000 (-5) 4745 g0000000 (-6) 4746 4747 # American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most 4748 # important gauge. ASTM B-258 specifies that this gauge is based on geometric 4749 # interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36 4750 # which is 0.005 inches exactly. Therefore, the diameter in inches of a wire 4751 # is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close 4752 # to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the 4753 # repeated zero values, use negative numbers in the formula. The same document 4754 # also specifies rounding rules which seem to be ignored by makers of tables. 4755 # Gauges up to 44 are to be specified with up to 4 significant figures, but no 4756 # closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the 4757 # nearest 0.00001 inch. 4758 # 4759 # In addition to being used to measure wire thickness, this gauge is used to 4760 # measure the thickness of sheets of aluminum, copper, and most metals other 4761 # than steel, iron and zinc. 4762 4763 wiregauge(g) units=[1;m] range=(0,) \ 4764 1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92) 4765 awg() wiregauge 4766 4767 # Next we have the SWG, the Imperial or British Standard Wire Gauge. This one 4768 # is piecewise linear. It was used for aluminum sheets. 4769 4770 brwiregauge[in] \ 4771 -6 0.5 \ 4772 -5 0.464 \ 4773 -3 0.4 \ 4774 -2 0.372 \ 4775 3 0.252 \ 4776 6 0.192 \ 4777 10 0.128 \ 4778 14 0.08 \ 4779 19 0.04 \ 4780 23 0.024 \ 4781 26 0.018 \ 4782 28 0.0148 \ 4783 30 0.0124 \ 4784 39 0.0052 \ 4785 49 0.0012 \ 4786 50 0.001 4787 4788 # The following is from the Appendix to ASTM B 258 4789 # 4790 # For example, in U.S. gage, the standard for sheet metal is based on the 4791 # weight of the metal, not on the thickness. 16-gage is listed as 4792 # approximately .0625 inch thick and 40 ounces per square foot (the original 4793 # standard was based on wrought iron at .2778 pounds per cubic inch; steel 4794 # has almost entirely superseded wrought iron for sheet use, at .2833 pounds 4795 # per cubic inch). Smaller numbers refer to greater thickness. There is no 4796 # formula for converting gage to thickness or weight. 4797 # 4798 # It's rather unclear from the passage above whether the plate gauge values are 4799 # therefore wrong if steel is being used. Reference [15] states that steel is 4800 # in fact measured using this gauge (under the name Manufacturers' Standard 4801 # Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel. 4802 # But this doesn't seem to be the correct density of steel (.2833 lb/in3 is 4803 # closer). 4804 # 4805 # This gauge was established in 1893 for purposes of taxation. 4806 4807 # Old plate gauge for iron 4808 4809 plategauge[(oz/ft^2)/(480*lb/ft^3)] \ 4810 -5 300 \ 4811 1 180 \ 4812 14 50 \ 4813 16 40 \ 4814 17 36 \ 4815 20 24 \ 4816 26 12 \ 4817 31 7 \ 4818 36 4.5 \ 4819 38 4 4820 4821 # Manufacturers Standard Gage 4822 4823 stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \ 4824 -5 300 \ 4825 1 180 \ 4826 14 50 \ 4827 16 40 \ 4828 17 36 \ 4829 20 24 \ 4830 26 12 \ 4831 31 7 \ 4832 36 4.5 \ 4833 38 4 4834 4835 # A special gauge is used for zinc sheet metal. Notice that larger gauges 4836 # indicate thicker sheets. 4837 4838 zincgauge[in] \ 4839 1 0.002 \ 4840 10 0.02 \ 4841 15 0.04 \ 4842 19 0.06 \ 4843 23 0.1 \ 4844 24 0.125 \ 4845 27 0.5 \ 4846 28 1 4847 4848 # 4849 # Imperial drill bit sizes are reported in inches or in a numerical or 4850 # letter gauge. 4851 # 4852 4853 drillgauge[in] \ 4854 1 0.2280 \ 4855 2 0.2210 \ 4856 3 0.2130 \ 4857 4 0.2090 \ 4858 5 0.2055 \ 4859 6 0.2040 \ 4860 7 0.2010 \ 4861 8 0.1990 \ 4862 9 0.1960 \ 4863 10 0.1935 \ 4864 11 0.1910 \ 4865 12 0.1890 \ 4866 13 0.1850 \ 4867 14 0.1820 \ 4868 15 0.1800 \ 4869 16 0.1770 \ 4870 17 0.1730 \ 4871 18 0.1695 \ 4872 19 0.1660 \ 4873 20 0.1610 \ 4874 22 0.1570 \ 4875 23 0.1540 \ 4876 24 0.1520 \ 4877 25 0.1495 \ 4878 26 0.1470 \ 4879 27 0.1440 \ 4880 28 0.1405 \ 4881 29 0.1360 \ 4882 30 0.1285 \ 4883 31 0.1200 \ 4884 32 0.1160 \ 4885 33 0.1130 \ 4886 34 0.1110 \ 4887 35 0.1100 \ 4888 36 0.1065 \ 4889 38 0.1015 \ 4890 39 0.0995 \ 4891 40 0.0980 \ 4892 41 0.0960 \ 4893 42 0.0935 \ 4894 43 0.0890 \ 4895 44 0.0860 \ 4896 45 0.0820 \ 4897 46 0.0810 \ 4898 48 0.0760 \ 4899 51 0.0670 \ 4900 52 0.0635 \ 4901 53 0.0595 \ 4902 54 0.0550 \ 4903 55 0.0520 \ 4904 56 0.0465 \ 4905 57 0.0430 \ 4906 65 0.0350 \ 4907 66 0.0330 \ 4908 68 0.0310 \ 4909 69 0.0292 \ 4910 70 0.0280 \ 4911 71 0.0260 \ 4912 73 0.0240 \ 4913 74 0.0225 \ 4914 75 0.0210 \ 4915 76 0.0200 \ 4916 78 0.0160 \ 4917 79 0.0145 \ 4918 80 0.0135 \ 4919 88 0.0095 \ 4920 104 0.0031 4921 4922 drillA 0.234 in 4923 drillB 0.238 in 4924 drillC 0.242 in 4925 drillD 0.246 in 4926 drillE 0.250 in 4927 drillF 0.257 in 4928 drillG 0.261 in 4929 drillH 0.266 in 4930 drillI 0.272 in 4931 drillJ 0.277 in 4932 drillK 0.281 in 4933 drillL 0.290 in 4934 drillM 0.295 in 4935 drillN 0.302 in 4936 drillO 0.316 in 4937 drillP 0.323 in 4938 drillQ 0.332 in 4939 drillR 0.339 in 4940 drillS 0.348 in 4941 drillT 0.358 in 4942 drillU 0.368 in 4943 drillV 0.377 in 4944 drillW 0.386 in 4945 drillX 0.397 in 4946 drillY 0.404 in 4947 drillZ 0.413 in 4948 4949 # 4950 # Screw sizes 4951 # 4952 # In the USA, screw diameters for both wood screws and machine screws 4953 # are reported using a gauge number. Metric machine screws are 4954 # reported as Mxx where xx is the diameter in mm. 4955 # 4956 4957 screwgauge(g) units=[1;m] range=[0,) \ 4958 (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013 4959 4960 # 4961 # Abrasive grit size 4962 # 4963 # Standards governing abrasive grit sizes are complicated, specifying 4964 # fractions of particles that are passed or retained by different mesh 4965 # sizes. As a result, it is not possible to make precise comparisons 4966 # of different grit standards. The tables below allow the 4967 # determination of rough equivlants by using median particle size. 4968 # 4969 # Standards in the USA are determined by the Unified Abrasives 4970 # Manufacturers' Association (UAMA), which resulted from the merger of 4971 # several previous organizations. One of the old organizations was 4972 # CAMI (Coated Abrasives Manufacturers' Institute). 4973 # 4974 # UAMA has a web page with plots showing abrasive particle ranges for 4975 # various different grits and comparisons between standards. 4976 # 4977 # http://www.uama.org/Abrasives101/101Standards.html 4978 # 4979 # Abrasives are grouped into "bonded" abrasives for use with grinding 4980 # wheels and "coated" abrasives for sandpapers and abrasive films. 4981 # The industry uses different grit standards for these two 4982 # categories. 4983 # 4984 # Another division is between "macrogrits", grits below 240 and 4985 # "microgrits", which are above 240. Standards differ, as do methods 4986 # for determining particle size. In the USA, ANSI B74.12 is the 4987 # standard governing macrogrits. ANSI B74.10 covers bonded microgrit 4988 # abrasives, and ANSI B74.18 covers coated microgrit abrasives. It 4989 # appears that the coated standard is identical to the bonded standard 4990 # for grits up through 600 but then diverges significantly. 4991 # 4992 # European grit sizes are determined by the Federation of European 4993 # Producers of Abrasives. http://www.fepa-abrasives.org 4994 # 4995 # They give two standards, the "F" grit for bonded abrasives and the 4996 # "P" grit for coated abrasives. This data is taken directly from 4997 # their web page. 4998 4999 # FEPA P grit for coated abrasives is commonly seen on sandpaper in 5000 # the USA where the paper will be marked P600, for example. FEPA P 5001 # grits are said to be more tightly constrained than comparable ANSI 5002 # grits so that the particles are more uniform in size and hence give 5003 # a better finish. 5004 5005 grit_P[micron] \ 5006 12 1815 \ 5007 16 1324 \ 5008 20 1000 \ 5009 24 764 \ 5010 30 642 \ 5011 36 538 \ 5012 40 425 \ 5013 50 336 \ 5014 60 269 \ 5015 80 201 \ 5016 100 162 \ 5017 120 125 \ 5018 150 100 \ 5019 180 82 \ 5020 220 68 \ 5021 240 58.5 \ 5022 280 52.2 \ 5023 320 46.2 \ 5024 360 40.5 \ 5025 400 35 \ 5026 500 30.2 \ 5027 600 25.8 \ 5028 800 21.8 \ 5029 1000 18.3 \ 5030 1200 15.3 \ 5031 1500 12.6 \ 5032 2000 10.3 \ 5033 2500 8.4 5034 5035 # The F grit is the European standard for bonded abrasives such as 5036 # grinding wheels 5037 5038 grit_F[micron] \ 5039 4 4890 \ 5040 5 4125 \ 5041 6 3460 \ 5042 7 2900 \ 5043 8 2460 \ 5044 10 2085 \ 5045 12 1765 \ 5046 14 1470 \ 5047 16 1230 \ 5048 20 1040 \ 5049 22 885 \ 5050 24 745 \ 5051 30 625 \ 5052 36 525 \ 5053 40 438 \ 5054 46 370 \ 5055 54 310 \ 5056 60 260 \ 5057 70 218 \ 5058 80 185 \ 5059 90 154 \ 5060 100 129 \ 5061 120 109 \ 5062 150 82 \ 5063 180 69 \ 5064 220 58 \ 5065 230 53 \ 5066 240 44.5 \ 5067 280 36.5 \ 5068 320 29.2 \ 5069 360 22.8 \ 5070 400 17.3 \ 5071 500 12.8 \ 5072 600 9.3 \ 5073 800 6.5 \ 5074 1000 4.5 \ 5075 1200 3 \ 5076 1500 2.0 \ 5077 2000 1.2 5078 5079 # According to the UAMA web page, the ANSI bonded and ANSI coated standards 5080 # are identical to FEPA F in the macrogrit range (under 240 grit), so these 5081 # values are taken from the FEPA F table. The values for 240 and above are 5082 # from the UAMA web site and represent the average of the "d50" range 5083 # endpoints listed there. 5084 5085 ansibonded[micron] \ 5086 4 4890 \ 5087 5 4125 \ 5088 6 3460 \ 5089 7 2900 \ 5090 8 2460 \ 5091 10 2085 \ 5092 12 1765 \ 5093 14 1470 \ 5094 16 1230 \ 5095 20 1040 \ 5096 22 885 \ 5097 24 745 \ 5098 30 625 \ 5099 36 525 \ 5100 40 438 \ 5101 46 370 \ 5102 54 310 \ 5103 60 260 \ 5104 70 218 \ 5105 80 185 \ 5106 90 154 \ 5107 100 129 \ 5108 120 109 \ 5109 150 82 \ 5110 180 69 \ 5111 220 58 \ 5112 240 50 \ 5113 280 39.5 \ 5114 320 29.5 \ 5115 360 23 \ 5116 400 18.25 \ 5117 500 13.9 \ 5118 600 10.55 \ 5119 800 7.65 \ 5120 1000 5.8 \ 5121 1200 3.8 5122 5123 grit_ansibonded() ansibonded 5124 5125 # Like the bonded grit, the coated macrogrits below 240 are taken from the 5126 # FEPA F table. Data above this is from the UAMA site. Note that the coated 5127 # and bonded standards are evidently the same from 240 up to 600 grit, but 5128 # starting at 800 grit, the coated standard diverges. The data from UAMA show 5129 # that 800 grit coated has an average size slightly larger than the average 5130 # size of 600 grit coated/bonded. However, the 800 grit has a significantly 5131 # smaller particle size variation. 5132 # 5133 # Because of this non-monotonicity from 600 grit to 800 grit this definition 5134 # produces a warning about the lack of a unique inverse. 5135 5136 ansicoated[micron] noerror \ 5137 4 4890 \ 5138 5 4125 \ 5139 6 3460 \ 5140 7 2900 \ 5141 8 2460 \ 5142 10 2085 \ 5143 12 1765 \ 5144 14 1470 \ 5145 16 1230 \ 5146 20 1040 \ 5147 22 885 \ 5148 24 745 \ 5149 30 625 \ 5150 36 525 \ 5151 40 438 \ 5152 46 370 \ 5153 54 310 \ 5154 60 260 \ 5155 70 218 \ 5156 80 185 \ 5157 90 154 \ 5158 100 129 \ 5159 120 109 \ 5160 150 82 \ 5161 180 69 \ 5162 220 58 \ 5163 240 50 \ 5164 280 39.5 \ 5165 320 29.5 \ 5166 360 23 \ 5167 400 18.25 \ 5168 500 13.9 \ 5169 600 10.55 \ 5170 800 11.5 \ 5171 1000 9.5 \ 5172 2000 7.2 \ 5173 2500 5.5 \ 5174 3000 4 \ 5175 4000 3 \ 5176 6000 2 \ 5177 8000 1.2 5178 5179 grit_ansicoated() ansicoated 5180 5181 5182 # 5183 # Is this correct? This is the JIS Japanese standard used on waterstones 5184 # 5185 jisgrit[micron] \ 5186 150 75 \ 5187 180 63 \ 5188 220 53 \ 5189 280 48 \ 5190 320 40 \ 5191 360 35 \ 5192 400 30 \ 5193 600 20 \ 5194 700 17 \ 5195 800 14 \ 5196 1000 11.5 \ 5197 1200 9.5 \ 5198 1500 8 \ 5199 2000 6.7 \ 5200 2500 5.5 \ 5201 3000 4 \ 5202 4000 3 \ 5203 6000 2 \ 5204 8000 1.2 5205 5206 # The "Finishing Scale" marked with an A (e.g. A75). This information 5207 # is from the web page of the sand paper manufacturer Klingspor 5208 # http://www.klingspor.com/gritgradingsystems.htm 5209 # 5210 # I have no information about what this scale is used for. 5211 5212 grit_A[micron]\ 5213 16 15.3 \ 5214 25 21.8 \ 5215 30 23.6 \ 5216 35 25.75 \ 5217 45 35 \ 5218 60 46.2 \ 5219 65 53.5 \ 5220 75 58.5 \ 5221 90 65 \ 5222 110 78 \ 5223 130 93 \ 5224 160 127 \ 5225 200 156 5226 # 5227 # Grits for DMT brand diamond sharpening stones from 5228 # http://dmtsharp.com/products/colorcode.htm 5229 # 5230 5231 dmtxxcoarse 120 micron # 120 mesh 5232 dmtsilver dmtxxcoarse 5233 dmtxx dmtxxcoarse 5234 dmtxcoarse 60 micron # 220 mesh 5235 dmtx dmtxcoarse 5236 dmtblack dmtxcoarse 5237 dmtcoarse 45 micron # 325 mesh 5238 dmtc dmtcoarse 5239 dmtblue dmtcoarse 5240 dmtfine 25 micron # 600 mesh 5241 dmtred dmtfine 5242 dmtf dmtfine 5243 dmtefine 9 micron # 1200 mesh 5244 dmte dmtefine 5245 dmtgreen dmtefine 5246 dmtceramic 7 micron # 2200 mesh 5247 dmtcer dmtceramic 5248 dmtwhite dmtceramic 5249 dmteefine 3 micron # 8000 mesh 5250 dmttan dmteefine 5251 dmtee dmteefine 5252 5253 # 5254 # The following values come from a page in the Norton Stones catalog, 5255 # available at their web page, http://www.nortonstones.com. 5256 # 5257 5258 hardtranslucentarkansas 6 micron # Natural novaculite (silicon quartz) 5259 softarkansas 22 micron # stones 5260 5261 extrafineindia 22 micron # India stones are Norton's manufactured 5262 fineindia 35 micron # aluminum oxide product 5263 mediumindia 53.5 micron 5264 coarseindia 97 micron 5265 5266 finecrystolon 45 micron # Crystolon stones are Norton's 5267 mediumcrystalon 78 micron # manufactured silicon carbide product 5268 coarsecrystalon 127 micron 5269 5270 # The following are not from the Norton catalog 5271 hardblackarkansas 6 micron 5272 hardwhitearkansas 11 micron 5273 washita 35 micron 5274 5275 # 5276 # Mesh systems for measuring particle sizes by sifting through a wire 5277 # mesh or sieve 5278 # 5279 5280 # The Tyler system and US Sieve system are based on four steps for 5281 # each factor of 2 change in the size, so each size is 2^1|4 different 5282 # from the adjacent sizes. Unfortunately, the mesh numbers are 5283 # arbitrary, so the sizes cannot be expressed with a functional form. 5284 # Various references round the values differently. The mesh numbers 5285 # are supposed to correspond to the number of holes per inch, but this 5286 # correspondence is only approximate because it doesn't include the 5287 # wire size of the mesh. 5288 5289 # The Tyler Mesh system was apparently introduced by the WS Tyler 5290 # company, but it appears that they no longer use it. They follow the 5291 # ASTM E11 standard. 5292 5293 meshtyler[micron] \ 5294 2.5 8000 \ 5295 3 6727 \ 5296 3.5 5657 \ 5297 4 4757 \ 5298 5 4000 \ 5299 6 3364 \ 5300 7 2828 \ 5301 8 2378 \ 5302 9 2000 \ 5303 10 1682 \ 5304 12 1414 \ 5305 14 1189 \ 5306 16 1000 \ 5307 20 841 \ 5308 24 707 \ 5309 28 595 \ 5310 32 500 \ 5311 35 420 \ 5312 42 354 \ 5313 48 297 \ 5314 60 250 \ 5315 65 210 \ 5316 80 177 \ 5317 100 149 \ 5318 115 125 \ 5319 150 105 \ 5320 170 88 \ 5321 200 74 \ 5322 250 63 \ 5323 270 53 \ 5324 325 44 \ 5325 400 37 5326 5327 # US Sieve size, ASTM E11 5328 # 5329 # The WS Tyler company prints the list from ASTM E11 in their catalog, 5330 # http://wstyler.com/wp-content/uploads/2015/11/Product-Catalog-2.pdf 5331 5332 sieve[micron] \ 5333 3.5 5600 \ 5334 4 4750 \ 5335 5 4000 \ 5336 6 3350 \ 5337 7 2800 \ 5338 8 2360 \ 5339 10 2000 \ 5340 12 1700 \ 5341 14 1400 \ 5342 16 1180 \ 5343 18 1000 \ 5344 20 850 \ 5345 25 710 \ 5346 30 600 \ 5347 35 500 \ 5348 40 425 \ 5349 45 355 \ 5350 50 300 \ 5351 60 250 \ 5352 70 212 \ 5353 80 180 \ 5354 100 150 \ 5355 120 125 \ 5356 140 106 \ 5357 170 90 \ 5358 200 75 \ 5359 230 63 \ 5360 270 53 \ 5361 325 45 \ 5362 400 38 \ 5363 450 32 \ 5364 500 25 \ 5365 625 20 # These last two values are not in the standard series 5366 # but were included in the ASTM standard because they 5367 meshUS() sieve # were in common usage. 5368 5369 # British Mesh size, BS 410: 1986 5370 # This system appears to correspond to the Tyler and US system, but 5371 # with different mesh numbers. 5372 # 5373 # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf 5374 # 5375 5376 meshbritish[micron] \ 5377 3 5657 \ 5378 3.5 4757 \ 5379 4 4000 \ 5380 5 3364 \ 5381 6 2828 \ 5382 7 2378 \ 5383 8 2000 \ 5384 10 1682 \ 5385 12 1414 \ 5386 14 1189 \ 5387 16 1000 \ 5388 18 841 \ 5389 22 707 \ 5390 25 595 \ 5391 30 500 \ 5392 36 420 \ 5393 44 354 \ 5394 52 297 \ 5395 60 250 \ 5396 72 210 \ 5397 85 177 \ 5398 100 149 \ 5399 120 125 \ 5400 150 105 \ 5401 170 88 \ 5402 200 74 \ 5403 240 63 \ 5404 300 53 \ 5405 350 44 \ 5406 400 37 5407 5408 # French system, AFNOR NFX11-501: 1970 5409 # The system appears to be based on size doubling every 3 mesh 5410 # numbers, though the values have been agressively rounded. 5411 # It's not clear if the unrounded values would be considered 5412 # incorrect, so this is given as a table rather than a function. 5413 # Functional form: 5414 # meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron 5415 # 5416 # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf 5417 5418 meshtamis[micron] \ 5419 17 40 \ 5420 18 50 \ 5421 19 63 \ 5422 20 80 \ 5423 21 100 \ 5424 22 125 \ 5425 23 160 \ 5426 24 200 \ 5427 25 250 \ 5428 26 315 \ 5429 27 400 \ 5430 28 500 \ 5431 29 630 \ 5432 30 800 \ 5433 31 1000 \ 5434 32 1250 \ 5435 33 1600 \ 5436 34 2000 \ 5437 35 2500 \ 5438 36 3150 \ 5439 37 4000 \ 5440 38 5000 5441 5442 # 5443 # Ring size. All ring sizes are given as the circumference of the ring. 5444 # 5445 5446 # USA ring sizes. Several slightly different definitions seem to be in 5447 # circulation. According to [15], the interior diameter of size n ring in 5448 # inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The 5449 # size 2 ring is inconsistently 0.538in and no 2.5 size is listed. 5450 # 5451 # However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the 5452 # diameter and list no special case for size 2. (Or alternatively they are 5453 # 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One 5454 # reference claimed that the original system was that each size was 1|10 inch 5455 # circumference, but that source doesn't have an explanation for the modern 5456 # system which is somewhat different. 5457 5458 ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \ 5459 (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018 5460 5461 # Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes 5462 # specified alphabetically and based on the ring inside diameter in steps of 5463 # 1|64 inch. This system was replaced in 1987 by British Standard 6820 which 5464 # specifies sizes based on circumference. Each size is 1.25 mm different from 5465 # the preceding size. The baseline is size C which is 40 mm circumference. 5466 # The new sizes are close to the old ones. Sometimes it's necessary to go 5467 # beyond size Z to Z+1, Z+2, etc. 5468 5469 sizeAring 37.50 mm 5470 sizeBring 38.75 mm 5471 sizeCring 40.00 mm 5472 sizeDring 41.25 mm 5473 sizeEring 42.50 mm 5474 sizeFring 43.75 mm 5475 sizeGring 45.00 mm 5476 sizeHring 46.25 mm 5477 sizeIring 47.50 mm 5478 sizeJring 48.75 mm 5479 sizeKring 50.00 mm 5480 sizeLring 51.25 mm 5481 sizeMring 52.50 mm 5482 sizeNring 53.75 mm 5483 sizeOring 55.00 mm 5484 sizePring 56.25 mm 5485 sizeQring 57.50 mm 5486 sizeRring 58.75 mm 5487 sizeSring 60.00 mm 5488 sizeTring 61.25 mm 5489 sizeUring 62.50 mm 5490 sizeVring 63.75 mm 5491 sizeWring 65.00 mm 5492 sizeXring 66.25 mm 5493 sizeYring 67.50 mm 5494 sizeZring 68.75 mm 5495 5496 # Japanese sizes start with size 1 at a 13mm inside diameter and each size is 5497 # 1|3 mm larger in diameter than the previous one. They are multiplied by pi 5498 # to give circumference. 5499 5500 jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \ 5501 (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38) 5502 5503 # The European ring sizes are the length of the circumference in mm minus 40. 5504 5505 euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40) 5506 5507 # 5508 # Abbreviations 5509 # 5510 5511 mph mile/hr 5512 mpg mile/gal 5513 kph km/hr 5514 fL footlambert 5515 fpm ft/min 5516 fps ft/s 5517 rpm rev/min 5518 rps rev/sec 5519 mi mile 5520 smi mile 5521 nmi nauticalmile 5522 mbh 1e3 btu/hour 5523 mcm 1e3 circularmil 5524 ipy inch/year # used for corrosion rates 5525 ccf 100 ft^3 # used for selling water [18] 5526 Mcf 1000 ft^3 # not million cubic feet [18] 5527 kp kilopond 5528 kpm kp meter 5529 Wh W hour 5530 hph hp hour 5531 plf lb / foot # pounds per linear foot 5532 5533 # 5534 # Compatibility units with unix version 5535 # 5536 5537 pa Pa 5538 ev eV 5539 hg Hg 5540 oe Oe 5541 mh mH 5542 rd rod 5543 pf pF 5544 gr grain 5545 nt N 5546 hz Hz 5547 hd hogshead 5548 dry drygallon/gallon 5549 nmile nauticalmile 5550 beV GeV 5551 bev beV 5552 coul C 5553 5554 # 5555 # Radioactivity units 5556 # 5557 5558 becquerel /s # Activity of radioactive source 5559 Bq becquerel # 5560 curie 3.7e10 Bq # Defined in 1910 as the radioactivity 5561 Ci curie # emitted by the amount of radon that is 5562 # in equilibrium with 1 gram of radium. 5563 rutherford 1e6 Bq # 5564 5565 RADIATION_DOSE gray 5566 gray J/kg # Absorbed dose of radiation 5567 Gy gray # 5568 rad 1e-2 Gy # From Radiation Absorbed Dose 5569 rep 8.38 mGy # Roentgen Equivalent Physical, the amount 5570 # of radiation which , absorbed in the 5571 # body, would liberate the same amount 5572 # of energy as 1 roentgen of X rays 5573 # would, or 97 ergs. 5574 5575 sievert J/kg # Dose equivalent: dosage that has the 5576 Sv sievert # same effect on human tissues as 200 5577 rem 1e-2 Sv # keV X-rays. Different types of 5578 # radiation are weighted by the 5579 # Relative Biological Effectiveness 5580 # (RBE). 5581 # 5582 # Radiation type RBE 5583 # X-ray, gamma ray 1 5584 # beta rays, > 1 MeV 1 5585 # beta rays, < 1 MeV 1.08 5586 # neutrons, < 1 MeV 4-5 5587 # neutrons, 1-10 MeV 10 5588 # protons, 1 MeV 8.5 5589 # protons, .1 MeV 10 5590 # alpha, 5 MeV 15 5591 # alpha, 1 MeV 20 5592 # 5593 # The energies are the kinetic energy 5594 # of the particles. Slower particles 5595 # interact more, so they are more 5596 # effective ionizers, and hence have 5597 # higher RBE values. 5598 # 5599 # rem stands for Roentgen Equivalent 5600 # Mammal 5601 banana_dose 0.1e-6 sievert # Informal measure of the dose due to 5602 # eating one average sized banana 5603 roentgen 2.58e-4 C / kg # Ionizing radiation that produces 5604 # 1 statcoulomb of charge in 1 cc of 5605 # dry air at stp. 5606 rontgen roentgen # Sometimes it appears spelled this way 5607 sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one 5608 # hour at a distance of 1 cm from a 5609 # point source of 1 mg of radium 5610 # enclosed in platinum .5 mm thick. 5611 5612 eman 1e-7 Ci/m^3 # radioactive concentration 5613 mache 3.7e-7 Ci/m^3 5614 5615 # 5616 # Atomic weights. The atomic weight of an element is the ratio of the mass of 5617 # a mole of the element to 1|12 of a mole of Carbon 12. The Standard Atomic 5618 # Weights apply to the elements as they occur naturally on earth. Elements 5619 # which do not occur naturally or which occur with wide isotopic variability do 5620 # not have Standard Atomic Weights. For these elements, the atomic weight is 5621 # based on the longest lived isotope, as marked in the comments. In some 5622 # cases, the comment for these entries also gives a number which is an atomic 5623 # weight for a different isotope that may be of more interest than the longest 5624 # lived isotope. 5625 # 5626 5627 actinium 227.0278 5628 aluminum 26.981539 5629 americium 243.0614 # Longest lived. 241.06 5630 antimony 121.760 5631 argon 39.948 5632 arsenic 74.92159 5633 astatine 209.9871 # Longest lived 5634 barium 137.327 5635 berkelium 247.0703 # Longest lived. 249.08 5636 beryllium 9.012182 5637 bismuth 208.98037 5638 boron 10.811 5639 bromine 79.904 5640 cadmium 112.411 5641 calcium 40.078 5642 californium 251.0796 # Longest lived. 252.08 5643 carbon 12.011 5644 cerium 140.115 5645 cesium 132.90543 5646 chlorine 35.4527 5647 chromium 51.9961 5648 cobalt 58.93320 5649 copper 63.546 5650 curium 247.0703 5651 deuterium 2.0141017778 5652 dysprosium 162.50 5653 einsteinium 252.083 # Longest lived 5654 erbium 167.26 5655 europium 151.965 5656 fermium 257.0951 # Longest lived 5657 fluorine 18.9984032 5658 francium 223.0197 # Longest lived 5659 gadolinium 157.25 5660 gallium 69.723 5661 germanium 72.61 5662 gold 196.96654 5663 hafnium 178.49 5664 helium 4.002602 5665 holmium 164.93032 5666 hydrogen 1.00794 5667 indium 114.818 5668 iodine 126.90447 5669 iridium 192.217 5670 iron 55.845 5671 krypton 83.80 5672 lanthanum 138.9055 5673 lawrencium 262.11 # Longest lived 5674 lead 207.2 5675 lithium 6.941 5676 lutetium 174.967 5677 magnesium 24.3050 5678 manganese 54.93805 5679 mendelevium 258.10 # Longest lived 5680 mercury 200.59 5681 molybdenum 95.94 5682 neodymium 144.24 5683 neon 20.1797 5684 neptunium 237.0482 5685 nickel 58.6934 5686 niobium 92.90638 5687 nitrogen 14.00674 5688 nobelium 259.1009 # Longest lived 5689 osmium 190.23 5690 oxygen 15.9994 5691 palladium 106.42 5692 phosphorus 30.973762 5693 platinum 195.08 5694 plutonium 244.0642 # Longest lived. 239.05 5695 polonium 208.9824 # Longest lived. 209.98 5696 potassium 39.0983 5697 praseodymium 140.90765 5698 promethium 144.9127 # Longest lived. 146.92 5699 protactinium 231.03588 5700 radium 226.0254 5701 radon 222.0176 # Longest lived 5702 rhenium 186.207 5703 rhodium 102.90550 5704 rubidium 85.4678 5705 ruthenium 101.07 5706 samarium 150.36 5707 scandium 44.955910 5708 selenium 78.96 5709 silicon 28.0855 5710 silver 107.8682 5711 sodium 22.989768 5712 strontium 87.62 5713 sulfur 32.066 5714 tantalum 180.9479 5715 technetium 97.9072 # Longest lived. 98.906 5716 tellurium 127.60 5717 terbium 158.92534 5718 thallium 204.3833 5719 thorium 232.0381 5720 thullium 168.93421 5721 tin 118.710 5722 titanium 47.867 5723 tungsten 183.84 5724 uranium 238.0289 5725 vanadium 50.9415 5726 xenon 131.29 5727 ytterbium 173.04 5728 yttrium 88.90585 5729 zinc 65.39 5730 zirconium 91.224 5731 5732 # Average molecular weight of air 5733 # 5734 # The atmospheric composition listed is from NASA Earth Fact Sheet (accessed 5735 # 28 August 2015) 5736 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html 5737 # Numbers do not add up to exactly 100% due to roundoff and uncertainty Water 5738 # is highly variable, typically makes up about 1% 5739 5740 air 78.08% nitrogen 2 \ 5741 + 20.95% oxygen 2 \ 5742 + 9340 ppm argon \ 5743 + 400 ppm (carbon + oxygen 2) \ 5744 + 18.18 ppm neon \ 5745 + 5.24 ppm helium \ 5746 + 1.7 ppm (carbon + 4 hydrogen) \ 5747 + 1.14 ppm krypton \ 5748 + 0.55 ppm hydrogen 2 5749 # 5750 # population units 5751 # 5752 5753 people 1 5754 person people 5755 death people 5756 capita people 5757 percapita per capita 5758 5759 # TGM dozen based unit system listed on the "dozenal" forum 5760 # http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are 5761 # proposed as an allegedly more rational alternative to the SI system. 5762 5763 Tim 12^-4 hour # Time 5764 Grafut gravity Tim^2 # Length based on gravity 5765 Surf Grafut^2 # area 5766 Volm Grafut^3 # volume 5767 Vlos Grafut/Tim # speed 5768 Denz Maz/Volm # density 5769 Mag Maz gravity # force 5770 Maz Volm kg / oldliter # mass based on water 5771 5772 Tm Tim # Abbreviations 5773 Gf Grafut 5774 Sf Surf 5775 Vm Volm 5776 Vl Vlos 5777 Mz Maz 5778 Dz Denz 5779 5780 # Dozen based unit prefixes 5781 5782 Zena- 12 5783 Duna- 12^2 5784 Trina- 12^3 5785 Quedra- 12^4 5786 Quena- 12^5 5787 Hesa- 12^6 5788 Seva- 12^7 5789 Aka- 12^8 5790 Neena- 12^9 5791 Dexa- 12^10 5792 Lefa- 12^11 5793 Zennila- 12^12 5794 5795 Zeni- 12^-1 5796 Duni- 12^-2 5797 Trini- 12^-3 5798 Quedri- 12^-4 5799 Queni- 12^-5 5800 Hesi- 12^-6 5801 Sevi- 12^-7 5802 Aki- 12^-8 5803 Neeni- 12^-9 5804 Dexi- 12^-10 5805 Lefi- 12^-11 5806 Zennili- 12^-12 5807 5808 # 5809 # Traditional Japanese units (shakkanhou) 5810 # 5811 # The traditional system of weights and measures is called shakkanhou from the 5812 # shaku and the ken. Japan accepted SI units in 1891 and legalized conversions 5813 # to the traditional system. In 1909 the inch-pound system was also legalized, 5814 # so Japan had three legally approved systems. A change to the metric system 5815 # started in 1921 but there was a lot of resistance. The Measurement Law of 5816 # October 1999 prohibits sales in anything but SI units. However, the old 5817 # units still live on in construction and as the basis for paper sizes of books 5818 # and tools used for handicrafts. 5819 # 5820 # Note that units below use the Hepburn romanization system. Some other 5821 # systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho". 5822 # 5823 # 5824 # http://hiramatu-hifuka.com/onyak/onyindx.html 5825 5826 # Japanese Proportions. These are still in everyday use. They also 5827 # get used as units to represent the proportion of the standard unit. 5828 5829 wari_proportion 1|10 5830 wari wari_proportion 5831 bu_proportion 1|100 # The character bu can also be read fun or bun 5832 # but usually "bu" is used for units. 5833 rin_proportion 1|1000 5834 mou_proportion 1|10000 5835 5836 5837 # Japanese Length Measures 5838 # 5839 # The length system is called kanejaku or 5840 # square and originated in China. It was 5841 # adopted as Japan's official measure in 701 5842 # by the Taiho Code. This system is still in 5843 # common use in architecture and clothing. 5844 5845 shaku 1|3.3 m 5846 mou 1|10000 shaku 5847 rin 1|1000 shaku 5848 bu_distance 1|100 shaku 5849 sun 1|10 shaku 5850 jou_distance 10 shaku 5851 jou jou_distance 5852 5853 kanejakusun sun # Alias to emphasize architectural name 5854 kanejaku shaku 5855 kanejakujou jou 5856 5857 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement 5858 taichi shaku # http://zh.wikipedia.org/wiki/台尺 5859 taicun sun # http://zh.wikipedia.org/wiki/台制 5860 !utf8 5861 台尺 taichi # via Hanyu Pinyin romanizations 5862 台寸 taicun 5863 !endutf8 5864 5865 # In context of clothing, shaku is different from architecture 5866 # http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html 5867 5868 kujirajaku 10|8 shaku 5869 kujirajakusun 1|10 kujirajaku 5870 kujirajakubu 1|100 kujirajaku 5871 kujirajakujou 10 kujirajaku 5872 tan_distance 3 kujirajakujou 5873 5874 ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6 5875 # http://www.homarewood.co.jp/syakusun.htm 5876 5877 # mostly unused 5878 chou_distance 60 ken 5879 chou chou_distance 5880 ri 36 chou 5881 5882 # Japanese Area Measures 5883 5884 # Tsubo is still used for land size, though the others are more 5885 # recognized by their homonyms in the other measurements. 5886 5887 gou_area 1|10 tsubo 5888 tsubo 36 shaku^2 # Size of two tatami = ken^2 ?? 5889 se 30 tsubo 5890 tan_area 10 se 5891 chou_area 10 tan_area 5892 5893 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement 5894 ping tsubo # http://zh.wikipedia.org/wiki/坪 5895 jia 2934 ping # http://zh.wikipedia.org/wiki/甲_(单位) 5896 fen 1|10 jia # http://zh.wikipedia.org/wiki/分 5897 fen_area 1|10 jia # Protection against future collisions 5898 !utf8 5899 坪 ping # via Hanyu Pinyin romanizations 5900 甲 jia 5901 分 fen 5902 分地 fen_area # Protection against future collisions 5903 !endutf8 5904 5905 # Japanese architecture is based on a "standard" size of tatami mat. 5906 # Room sizes today are given in number of tatami, and this number 5907 # determines the spacing between colums and hence sizes of sliding 5908 # doors and paper screens. However, every region has its own slightly 5909 # different tatami size. Edoma, used in and around Tokyo and 5910 # Hokkaido, is becoming a nationwide standard. Kyouma is used around 5911 # Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya. 5912 # Note that the tatami all have the aspect ratio 2:1 so that the mats 5913 # can tile the room with some of them turned 90 degrees. 5914 # 5915 # http://www.moon2.net/tatami/infotatami/structure.html 5916 5917 edoma (5.8*2.9) shaku^2 5918 kyouma (6.3*3.15) shaku^2 5919 chuukyouma (6*3) shaku^2 5920 jou_area edoma 5921 tatami jou_area 5922 5923 # Japanese Volume Measures 5924 5925 # The "shou" is still used for such things as alcohol and seasonings. 5926 # Large quantities of paint are still purchased in terms of "to". 5927 5928 shaku_volume 1|10 gou_volume 5929 gou_volume 1|10 shou 5930 gou gou_volume 5931 shou (4.9*4.9*2.7) sun^3 # The character shou which is 5932 # the same as masu refers to a 5933 # rectangular wooden cup used to 5934 # measure liquids and cereal. 5935 # Sake is sometimes served in a masu 5936 # Note that it happens to be 5937 # EXACTLY 7^4/11^3 liters. 5938 to 10 shou 5939 koku 10 to # No longer used; historically a measure of rice 5940 5941 # Japanese Weight Measures 5942 # 5943 # http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html 5944 5945 # Not really used anymore. 5946 5947 rin_weight 1|10 bu_weight 5948 bu_weight 1|10 monme 5949 fun 1|10 monme 5950 monme momme 5951 kin 160 monme 5952 kan 1000 monme 5953 kwan kan # This was the old pronounciation of the unit. 5954 # The old spelling persisted a few centuries 5955 # longer and was not changed until around 5956 # 1950. 5957 5958 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement 5959 # says: "Volume measure in Taiwan is largely metric". 5960 taijin kin # http://zh.wikipedia.org/wiki/台斤 5961 tailiang 10 monme # http://zh.wikipedia.org/wiki/台斤 5962 taiqian monme # http://zh.wikipedia.org/wiki/台制 5963 !utf8 5964 台斤 taijin # via Hanyu Pinyin romanizations 5965 台兩 tailiang 5966 台錢 taiqian 5967 !endutf8 5968 5969 # 5970 # Australian unit 5971 # 5972 5973 australiasquare (10 ft)^2 # Used for house area 5974 5975 5976 # 5977 # A few German units as currently in use. 5978 # 5979 5980 zentner 50 kg 5981 doppelzentner 2 zentner 5982 pfund 500 g 5983 5984 # 5985 # Swedish (Sweden) pre-metric units of 1739. 5986 # The metric system was adopted in 1878. 5987 # https://sv.wikipedia.org/wiki/Verkm%C3%A5tt 5988 # 5989 5990 verklinje 2.0618125 mm 5991 verktum 12 verklinje 5992 kvarter 6 verktum 5993 fot 2 kvarter 5994 aln 2 fot 5995 famn 3 aln 5996 5997 # 5998 # Some traditional Russian measures 5999 # 6000 # If you would like to help expand this section and understand 6001 # cyrillic transliteration, let me know. These measures are meant to 6002 # reflect common usage, e.g. in translated literature. 6003 # 6004 6005 dessiatine 2400 sazhen^2 # Land measure 6006 dessjatine dessiatine 6007 6008 funt 409.51718 grams # similar to pound 6009 zolotnik 1|96 funt # used for precious metal measure 6010 pood 40 funt # common in agricultural measure 6011 6012 arshin (2 + 1|3) feet 6013 sazhen 3 arshin # analogous to fathom 6014 verst 500 sazhen # of similar use to mile 6015 versta verst 6016 borderverst 1000 sazhen 6017 russianmile 7 verst 6018 6019 6020 6021 6022 # 6023 # Old French distance measures, from French Weights and Measures 6024 # Before the Revolution by Zupko 6025 # 6026 6027 frenchfoot 144|443.296 m # pied de roi, the standard of Paris. 6028 pied frenchfoot # Half of the hashimicubit, 6029 frenchfeet frenchfoot # instituted by Charlemagne. 6030 frenchinch 1|12 frenchfoot # This exact definition comes from 6031 frenchthumb frenchinch # a law passed on 10 Dec 1799 which 6032 pouce frenchthumb # fixed the meter at 6033 # 3 frenchfeet + 11.296 lignes. 6034 frenchline 1|12 frenchinch # This is supposed to be the size 6035 ligne frenchline # of the average barleycorn 6036 frenchpoint 1|12 frenchline 6037 toise 6 frenchfeet 6038 arpent 180^2 pied^2 # The arpent is 100 square perches, 6039 # but the perche seems to vary a lot 6040 # and can be 18 feet, 20 feet, or 22 6041 # feet. This measure was described 6042 # as being in common use in Canada in 6043 # 1934 (Websters 2nd). The value 6044 # given here is the Paris standard 6045 # arpent. 6046 frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence 6047 # smaller than the British grain. 6048 frenchpound 9216 frenchgrain 6049 6050 # 6051 # Before the Imperial Weights and Measures Act of 1824, various different 6052 # weights and measures were in use in different places. 6053 # 6054 6055 # Scots linear measure 6056 6057 scotsinch 1.00540054 UKinch 6058 scotslink 1|100 scotschain 6059 scotsfoot 12 scotsinch 6060 scotsfeet scotsfoot 6061 scotsell 37 scotsinch 6062 scotsfall 6 scotsell 6063 scotschain 4 scotsfall 6064 scotsfurlong 10 scotschain 6065 scotsmile 8 scotsfurlong 6066 6067 # Scots area measure 6068 6069 scotsrood 40 scotsfall^2 6070 scotsacre 4 scotsrood 6071 6072 # Irish linear measure 6073 6074 irishinch UKinch 6075 irishpalm 3 irishinch 6076 irishspan 3 irishpalm 6077 irishfoot 12 irishinch 6078 irishfeet irishfoot 6079 irishcubit 18 irishinch 6080 irishyard 3 irishfeet 6081 irishpace 5 irishfeet 6082 irishfathom 6 irishfeet 6083 irishpole 7 irishyard # Only these values 6084 irishperch irishpole # are different from 6085 irishchain 4 irishperch # the British Imperial 6086 irishlink 1|100 irishchain # or English values for 6087 irishfurlong 10 irishchain # these lengths. 6088 irishmile 8 irishfurlong # 6089 6090 # Irish area measure 6091 6092 irishrood 40 irishpole^2 6093 irishacre 4 irishrood 6094 6095 # English wine capacity measures (Winchester measures) 6096 6097 winepint 1|2 winequart 6098 winequart 1|4 winegallon 6099 winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon, 6100 # it was legalized in 1707 by Queen Anne, and 6101 # given the definition of 231 cubic inches. It 6102 # had been in use for a while as 8 pounds of wine 6103 # using a merchant's pound, but the definition of 6104 # the merchant's pound had become uncertain. A 6105 # pound of 15 tower ounces (6750 grains) had been 6106 # common, but then a pound of 15 troy ounces 6107 # (7200 grains) gained popularity. Because of 6108 # the switch in the value of the merchants pound, 6109 # the size of the wine gallon was uncertain in 6110 # the market, hence the official act in 1707. 6111 # The act allowed that a six inch tall cylinder 6112 # with a 7 inch diameter was a lawful wine 6113 # gallon. (This comes out to 230.9 in^3.) 6114 # Note also that in Britain a legal conversion 6115 # was established to the 1824 Imperial gallon 6116 # then taken as 277.274 in^3 so that the wine 6117 # gallon was 0.8331 imperial gallons. This is 6118 # 231.1 cubic inches (using the international 6119 # inch). 6120 winerundlet 18 winegallon 6121 winebarrel 31.5 winegallon 6122 winetierce 42 winegallon 6123 winehogshead 2 winebarrel 6124 winepuncheon 2 winetierce 6125 winebutt 2 winehogshead 6126 winepipe winebutt 6127 winetun 2 winebutt 6128 6129 # English beer and ale measures used 1803-1824 and used for beer before 1688 6130 6131 beerpint 1|2 beerquart 6132 beerquart 1|4 beergallon 6133 beergallon 282 UKinch^3 6134 beerbarrel 36 beergallon 6135 beerhogshead 1.5 beerbarrel 6136 6137 # English ale measures used from 1688-1803 for both ale and beer 6138 6139 alepint 1|2 alequart 6140 alequart 1|4 alegallon 6141 alegallon beergallon 6142 alebarrel 34 alegallon 6143 alehogshead 1.5 alebarrel 6144 6145 # Scots capacity measure 6146 6147 scotsgill 1|4 mutchkin 6148 mutchkin 1|2 choppin 6149 choppin 1|2 scotspint 6150 scotspint 1|2 scotsquart 6151 scotsquart 1|4 scotsgallon 6152 scotsgallon 827.232 UKinch^3 6153 scotsbarrel 8 scotsgallon 6154 jug scotspint 6155 6156 # Scots dry capacity measure 6157 6158 scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt 6159 scotswheatlippies scotswheatlippy 6160 scotswheatpeck 4 scotswheatlippy 6161 scotswheatfirlot 4 scotswheatpeck 6162 scotswheatboll 4 scotswheatfirlot 6163 scotswheatchalder 16 scotswheatboll 6164 6165 scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt 6166 scotsoatlippies scotsoatlippy 6167 scotsoatpeck 4 scotsoatlippy 6168 scotsoatfirlot 4 scotsoatpeck 6169 scotsoatboll 4 scotsoatfirlot 6170 scotsoatchalder 16 scotsoatboll 6171 6172 # Scots Tron weight 6173 6174 trondrop 1|16 tronounce 6175 tronounce 1|20 tronpound 6176 tronpound 9520 grain 6177 tronstone 16 tronpound 6178 6179 # Irish liquid capacity measure 6180 6181 irishnoggin 1|4 irishpint 6182 irishpint 1|2 irishquart 6183 irishquart 1|2 irishpottle 6184 irishpottle 1|2 irishgallon 6185 irishgallon 217.6 UKinch^3 6186 irishrundlet 18 irishgallon 6187 irishbarrel 31.5 irishgallon 6188 irishtierce 42 irishgallon 6189 irishhogshead 2 irishbarrel 6190 irishpuncheon 2 irishtierce 6191 irishpipe 2 irishhogshead 6192 irishtun 2 irishpipe 6193 6194 # Irish dry capacity measure 6195 6196 irishpeck 2 irishgallon 6197 irishbushel 4 irishpeck 6198 irishstrike 2 irishbushel 6199 irishdrybarrel 2 irishstrike 6200 irishquarter 2 irishbarrel 6201 6202 # English Tower weights, abolished in 1528 6203 6204 towerpound 5400 grain 6205 towerounce 1|12 towerpound 6206 towerpennyweight 1|20 towerounce 6207 towergrain 1|32 towerpennyweight 6208 6209 # English Mercantile weights, used since the late 12th century 6210 6211 mercpound 6750 grain 6212 mercounce 1|15 mercpound 6213 mercpennyweight 1|20 mercounce 6214 6215 # English weights for lead 6216 6217 leadstone 12.5 lb 6218 fotmal 70 lb 6219 leadwey 14 leadstone 6220 fothers 12 leadwey 6221 6222 # English Hay measure 6223 6224 newhaytruss 60 lb # New and old here seem to refer to "new" 6225 newhayload 36 newhaytruss # hay and "old" hay rather than a new unit 6226 oldhaytruss 56 lb # and an old unit. 6227 oldhayload 36 oldhaytruss 6228 6229 # English wool measure 6230 6231 woolclove 7 lb 6232 woolstone 2 woolclove 6233 wooltod 2 woolstone 6234 woolwey 13 woolstone 6235 woolsack 2 woolwey 6236 woolsarpler 2 woolsack 6237 woollast 6 woolsarpler 6238 6239 # 6240 # Ancient history units: There tends to be uncertainty in the definitions 6241 # of the units in this section 6242 # These units are from [11] 6243 6244 # Roman measure. The Romans had a well defined distance measure, but their 6245 # measures of weight were poor. They adopted local weights in different 6246 # regions without distinguishing among them so that there are half a dozen 6247 # different Roman "standard" weight systems. 6248 6249 romanfoot 296 mm # There is some uncertainty in this definition 6250 romanfeet romanfoot # from which all the other units are derived. 6251 pes romanfoot # This value appears in numerous sources. In "The 6252 pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm. 6253 romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the 6254 romandigit 1|16 romanfoot # same names as the subdivisions of the pound, 6255 romanpalm 1|4 romanfoot # but we can't have the names for different 6256 romancubit 18 romaninch # units. 6257 romanpace 5 romanfeet # Roman double pace (basic military unit) 6258 passus romanpace 6259 romanperch 10 romanfeet 6260 stade 125 romanpaces 6261 stadia stade 6262 stadium stade 6263 romanmile 8 stadia # 1000 paces 6264 romanleague 1.5 romanmile 6265 schoenus 4 romanmile 6266 6267 # Other values for the Roman foot (from Dilke) 6268 6269 earlyromanfoot 29.73 cm 6270 pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC 6271 lateromanfoot 29.42 cm 6272 6273 # Roman areas 6274 6275 actuslength 120 romanfeet # length of a Roman furrow 6276 actus 120*4 romanfeet^2 # area of the furrow 6277 squareactus 120^2 romanfeet^2 # actus quadratus 6278 acnua squareactus 6279 iugerum 2 squareactus 6280 iugera iugerum 6281 jugerum iugerum 6282 jugera iugerum 6283 heredium 2 iugera # heritable plot 6284 heredia heredium 6285 centuria 100 heredia 6286 centurium centuria 6287 6288 # Roman volumes 6289 6290 sextarius 35.4 in^3 # Basic unit of Roman volume. As always, 6291 sextarii sextarius # there is uncertainty. Six large Roman 6292 # measures survive with volumes ranging from 6293 # 34.4 in^3 to 39.55 in^3. Three of them 6294 # cluster around the size given here. 6295 # 6296 # But the values for this unit vary wildly 6297 # in other sources. One reference gives 0.547 6298 # liters, but then says the amphora is a 6299 # cubic Roman foot. This gives a value for the 6300 # sextarius of 0.540 liters. And the 6301 # encyclopedia Brittanica lists 0.53 liters for 6302 # this unit. Both [7] and [11], which were 6303 # written by scholars of weights and measures, 6304 # give the value of 35.4 cubic inches. 6305 cochlearia 1|48 sextarius 6306 cyathi 1|12 sextarius 6307 acetabula 1|8 sextarius 6308 quartaria 1|4 sextarius 6309 quartarius quartaria 6310 heminae 1|2 sextarius 6311 hemina heminae 6312 cheonix 1.5 sextarii 6313 6314 # Dry volume measures (usually) 6315 6316 semodius 8 sextarius 6317 semodii semodius 6318 modius 16 sextarius 6319 modii modius 6320 6321 # Liquid volume measures (usually) 6322 6323 congius 12 heminae 6324 congii congius 6325 amphora 8 congii 6326 amphorae amphora # Also a dry volume measure 6327 culleus 20 amphorae 6328 quadrantal amphora 6329 6330 # Roman weights 6331 6332 libra 5052 grain # The Roman pound varied significantly 6333 librae libra # from 4210 grains to 5232 grains. Most of 6334 romanpound libra # the standards were obtained from the weight 6335 uncia 1|12 libra # of particular coins. The one given here is 6336 unciae uncia # based on the Gold Aureus of Augustus which 6337 romanounce uncia # was in use from BC 27 to AD 296. 6338 deunx 11 uncia 6339 dextans 10 uncia 6340 dodrans 9 uncia 6341 bes 8 uncia 6342 seprunx 7 uncia 6343 semis 6 uncia 6344 quincunx 5 uncia 6345 triens 4 uncia 6346 quadrans 3 uncia 6347 sextans 2 uncia 6348 sescuncia 1.5 uncia 6349 semuncia 1|2 uncia 6350 siscilius 1|4 uncia 6351 sextula 1|6 uncia 6352 semisextula 1|12 uncia 6353 scriptulum 1|24 uncia 6354 scrupula scriptulum 6355 romanobol 1|2 scrupula 6356 6357 romanaspound 4210 grain # Old pound based on bronze coinage, the 6358 # earliest money of Rome BC 338 to BC 268. 6359 6360 # Egyptian length measure 6361 6362 egyptianroyalcubit 20.63 in # plus or minus .2 in 6363 egyptianpalm 1|7 egyptianroyalcubit 6364 egyptiandigit 1|4 egyptianpalm 6365 egyptianshortcubit 6 egyptianpalm 6366 6367 doubleremen 29.16 in # Length of the diagonal of a square with 6368 remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit. 6369 # This is divided into 40 digits which are 6370 # not the same size as the digits based on 6371 # the royal cubit. 6372 6373 # Greek length measures 6374 6375 greekfoot 12.45 in # Listed as being derived from the 6376 greekfeet greekfoot # Egyptian Royal cubit in [11]. It is 6377 greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit. 6378 pous greekfoot 6379 podes greekfoot 6380 orguia 6 greekfoot 6381 greekfathom orguia 6382 stadion 100 orguia 6383 akaina 10 greekfeet 6384 plethron 10 akaina 6385 greekfinger 1|16 greekfoot 6386 homericcubit 20 greekfingers # Elbow to end of knuckles. 6387 shortgreekcubit 18 greekfingers # Elbow to start of fingers. 6388 6389 ionicfoot 296 mm 6390 doricfoot 326 mm 6391 6392 olympiccubit 25 remendigit # These olympic measures were not as 6393 olympicfoot 2|3 olympiccubit # common as the other greek measures. 6394 olympicfinger 1|16 olympicfoot # They were used in agriculture. 6395 olympicfeet olympicfoot 6396 olympicdakylos olympicfinger 6397 olympicpalm 1|4 olympicfoot 6398 olympicpalestra olympicpalm 6399 olympicspithame 3|4 foot 6400 olympicspan olympicspithame 6401 olympicbema 2.5 olympicfeet 6402 olympicpace olympicbema 6403 olympicorguia 6 olympicfeet 6404 olympicfathom olympicorguia 6405 olympiccord 60 olympicfeet 6406 olympicamma olympiccord 6407 olympicplethron 100 olympicfeet 6408 olympicstadion 600 olympicfeet 6409 6410 # Greek capacity measure 6411 6412 greekkotyle 270 ml # This approximate value is obtained 6413 xestes 2 greekkotyle # from two earthenware vessels that 6414 khous 12 greekkotyle # were reconstructed from fragments. 6415 metretes 12 khous # The kotyle is a day's corn ration 6416 choinix 4 greekkotyle # for one man. 6417 hekteos 8 choinix 6418 medimnos 6 hekteos 6419 6420 # Greek weight. Two weight standards were used, an Aegina standard based 6421 # on the Beqa shekel and an Athens (attic) standard. 6422 6423 aeginastater 192 grain # Varies up to 199 grain 6424 aeginadrachmae 1|2 aeginastater 6425 aeginaobol 1|6 aeginadrachmae 6426 aeginamina 50 aeginastaters 6427 aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot 6428 # of water (whichever foot was in use) 6429 6430 atticstater 135 grain # Varies 134-138 grain 6431 atticdrachmae 1|2 atticstater 6432 atticobol 1|6 atticdrachmae 6433 atticmina 50 atticstaters 6434 attictalent 60 atticmina # Supposedly the mass of a cubic foot 6435 # of water (whichever foot was in use) 6436 6437 # "Northern" cubit and foot. This was used by the pre-Aryan civilization in 6438 # the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China, 6439 # central and Western Europe until modern times when it was displaced by 6440 # the metric system. 6441 6442 northerncubit 26.6 in # plus/minus .2 in 6443 northernfoot 1|2 northerncubit 6444 6445 sumeriancubit 495 mm 6446 kus sumeriancubit 6447 sumerianfoot 2|3 sumeriancubit 6448 6449 assyriancubit 21.6 in 6450 assyrianfoot 1|2 assyriancubit 6451 assyrianpalm 1|3 assyrianfoot 6452 assyriansusi 1|20 assyrianpalm 6453 susi assyriansusi 6454 persianroyalcubit 7 assyrianpalm 6455 6456 6457 # Arabic measures. The arabic standards were meticulously kept. Glass weights 6458 # accurate to .2 grains were made during AD 714-900. 6459 6460 hashimicubit 25.56 in # Standard of linear measure used 6461 # in Persian dominions of the Arabic 6462 # empire 7-8th cent. Is equal to two 6463 # French feet. 6464 6465 blackcubit 21.28 in 6466 arabicfeet 1|2 blackcubit 6467 arabicfoot arabicfeet 6468 arabicinch 1|12 arabicfoot 6469 arabicmile 4000 blackcubit 6470 6471 silverdirhem 45 grain # The weights were derived from these two 6472 tradedirhem 48 grain # units with two identically named systems 6473 # used for silver and used for trade purposes 6474 6475 silverkirat 1|16 silverdirhem 6476 silverwukiyeh 10 silverdirhem 6477 silverrotl 12 silverwukiyeh 6478 arabicsilverpound silverrotl 6479 6480 tradekirat 1|16 tradedirhem 6481 tradewukiyeh 10 tradedirhem 6482 traderotl 12 tradewukiyeh 6483 arabictradepound traderotl 6484 6485 # Miscellaneous ancient units 6486 6487 parasang 3.5 mile # Persian unit of length usually thought 6488 # to be between 3 and 3.5 miles 6489 biblicalcubit 21.8 in 6490 hebrewcubit 17.58 in 6491 li 10|27.8 mile # Chinese unit of length 6492 # 100 li is considered a day's march 6493 liang 11|3 oz # Chinese weight unit 6494 6495 6496 # Medieval time units. According to the OED, these appear in Du Cange 6497 # by Papias. 6498 6499 timepoint 1|5 hour # also given as 1|4 6500 timeminute 1|10 hour 6501 timeostent 1|60 hour 6502 timeounce 1|8 timeostent 6503 timeatom 1|47 timeounce 6504 6505 # Given in [15], these subdivisions of the grain were supposedly used 6506 # by jewelers. The mite may have been used but the blanc could not 6507 # have been accurately measured. 6508 6509 mite 1|20 grain 6510 droit 1|24 mite 6511 periot 1|20 droit 6512 blanc 1|24 periot 6513 6514 # 6515 # Localization 6516 # 6517 6518 !var UNITS_ENGLISH US 6519 hundredweight ushundredweight 6520 ton uston 6521 scruple apscruple 6522 fluidounce usfluidounce 6523 gallon usgallon 6524 bushel usbushel 6525 quarter quarterweight 6526 cup uscup 6527 tablespoon ustablespoon 6528 teaspoon usteaspoon 6529 dollar US$ 6530 cent $ 0.01 6531 penny cent 6532 minim minimvolume 6533 pony ponyvolume 6534 grand usgrand 6535 firkin usfirkin 6536 hogshead ushogshead 6537 !endvar 6538 6539 !var UNITS_ENGLISH GB 6540 hundredweight brhundredweight 6541 ton brton 6542 scruple brscruple 6543 fluidounce brfluidounce 6544 gallon brgallon 6545 bushel brbushel 6546 quarter brquarter 6547 chaldron brchaldron 6548 cup brcup 6549 teacup brteacup 6550 tablespoon brtablespoon 6551 teaspoon brteaspoon 6552 dollar US$ 6553 cent $ 0.01 6554 penny brpenny 6555 minim minimnote 6556 pony brpony 6557 grand brgrand 6558 firkin brfirkin 6559 hogshead brhogshead 6560 !endvar 6561 6562 !varnot UNITS_ENGLISH GB US 6563 !message Unknown value for environment variable UNITS_ENGLISH. Should be GB or US. 6564 !endvar 6565 6566 6567 !utf8 6568 ⅛- 1|8 6569 ¼- 1|4 6570 ⅜- 3|8 6571 ½- 1|2 6572 ⅝- 5|8 6573 ¾- 3|4 6574 ⅞- 7|8 6575 ⅙- 1|6 6576 ⅓- 1|3 6577 ⅔- 2|3 6578 ⅚- 5|6 6579 ⅕- 1|5 6580 ⅖- 2|5 6581 ⅗- 3|5 6582 ⅘- 4|5 6583 # U+2150- 1|7 For some reason these characters are getting 6584 # U+2151- 1|9 flagged as invalid UTF8. 6585 # U+2152- 1|10 6586 #⅐- 1|7 # fails under MacOS 6587 #⅑- 1|9 # fails under MacOS 6588 #⅒- 1|10 # fails under MacOS 6589 ℯ exp(1) # U+212F, base of natural log 6590 µ- micro # micro sign U+00B5 6591 μ- micro # small mu U+03BC 6592 ångström angstrom 6593 Å angstrom # angstrom symbol U+212B 6594 Å angstrom # A with ring U+00C5 6595 röntgen roentgen 6596 °C degC 6597 °F degF 6598 °K K # °K is incorrect notation 6599 °R degR 6600 ° degree 6601 ℃ degC 6602 ℉ degF 6603 K K # Kelvin symbol, U+212A 6604 ℓ liter # unofficial abbreviation used in some places 6605 Ω ohm # Ohm symbol U+2126 6606 Ω ohm # Greek capital omega U+03A9 6607 ℧ mho 6608 ʒ dram # U+0292 6609 ℈ scruple 6610 ℥ ounce 6611 ℔ lb 6612 ℎ h 6613 ℏ hbar 6614 ‰ 1|1000 6615 ‱ 1|10000 6616 ′ ' # U+2032 6617 ″ " # U+2033 6618 6619 # 6620 # Unicode currency symbols 6621 # 6622 6623 ¢ cent 6624 £ britainpound 6625 ¥ japanyen 6626 € euro 6627 ₩ southkoreawon 6628 ₪ israelnewshekel 6629 ₤ lira 6630 # ₺ turkeylira # fails under MacOS 6631 ₨ rupee # unofficial legacy rupee sign 6632 # ₹ indiarupee # official rupee sign # MacOS fail 6633 #؋ afghanafghani # fails under MacOS 6634 ฿ thailandbaht 6635 ₡ elsalvadorcolon # Also costaricacolon 6636 ₣ francefranc 6637 ₦ nigerianaira 6638 ₧ spainpeseta 6639 ₫ vietnamdong 6640 ₭ laokip 6641 ₮ mongoliatugrik 6642 ₯ greecedrachma 6643 ₱ philippinepeso 6644 # ₲ paraguayguarani # fails under MacOS 6645 #₴ ukrainehryvnia # fails under MacOS 6646 #₵ ghanacedi # fails under MacOS 6647 #₸ kazakhstantenge # fails under MacOS 6648 #₼ azerbaijanmanat # fails under MacOS 6649 #₽ russiaruble # fails under MacOS 6650 #₾ georgialari # fails under MacOS 6651 ﷼ iranrial 6652 ﹩ $ 6653 ￠ ¢ 6654 ￡ £ 6655 ￥ ¥ 6656 ￦ ₩ 6657 6658 # 6659 # Square unicode symbols starting at U+3371 6660 # 6661 6662 ㍱ hPa 6663 ㍲ da 6664 ㍳ au 6665 ㍴ bar 6666 # ㍵ oV??? 6667 ㍶ pc 6668 #㍷ dm invalid on Mac 6669 #㍸ dm^2 invalid on Mac 6670 #㍹ dm^3 invalid on Mac 6671 ㎀ pA 6672 ㎁ nA 6673 ㎂ µA 6674 ㎃ mA 6675 ㎄ kA 6676 ㎅ kB 6677 ㎆ MB 6678 ㎇ GB 6679 ㎈ cal 6680 ㎉ kcal 6681 ㎊ pF 6682 ㎋ nF 6683 ㎌ µF 6684 ㎍ µg 6685 ㎎ mg 6686 ㎏ kg 6687 ㎐ Hz 6688 ㎑ kHz 6689 ㎒ MHz 6690 ㎓ GHz 6691 ㎔ THz 6692 ㎕ µL 6693 ㎖ mL 6694 ㎗ dL 6695 ㎘ kL 6696 ㎙ fm 6697 ㎚ nm 6698 ㎛ µm 6699 ㎜ mm 6700 ㎝ cm 6701 ㎞ km 6702 ㎟ mm^2 6703 ㎠ cm^2 6704 ㎡ m^2 6705 ㎢ km^2 6706 ㎣ mm^3 6707 ㎤ cm^3 6708 ㎥ m^3 6709 ㎦ km^3 6710 ㎧ m/s 6711 ㎨ m/s^2 6712 ㎩ Pa 6713 ㎪ kPa 6714 ㎫ MPa 6715 ㎬ GPa 6716 ㎭ rad 6717 ㎮ rad/s 6718 ㎯ rad/s^2 6719 ㎰ ps 6720 ㎱ ns 6721 ㎲ µs 6722 ㎳ ms 6723 ㎴ pV 6724 ㎵ nV 6725 ㎶ µV 6726 ㎷ mV 6727 ㎸ kV 6728 ㎹ MV 6729 ㎺ pW 6730 ㎻ nW 6731 ㎼ µW 6732 ㎽ mW 6733 ㎾ kW 6734 ㎿ MW 6735 ㏀ kΩ 6736 ㏁ MΩ 6737 ㏃ Bq 6738 ㏄ cc 6739 ㏅ cd 6740 ㏆ C/kg 6741 ㏈() dB 6742 ㏉ Gy 6743 ㏊ ha 6744 # ㏋ HP?? 6745 ㏌ in 6746 # ㏍ KK?? 6747 # ㏎ KM??? 6748 ㏏ kt 6749 ㏐ lm 6750 # ㏑ ln 6751 # ㏒ log 6752 ㏓ lx 6753 ㏔ mb 6754 ㏕ mil 6755 ㏖ mol 6756 ㏗() pH 6757 ㏙ ppm 6758 # ㏚ PR??? 6759 ㏛ sr 6760 ㏜ Sv 6761 ㏝ Wb 6762 #㏞ V/m Invalid on Mac 6763 #㏟ A/m Invalid on Mac 6764 #㏿ gal Invalid on Mac 6765 6766 !endutf8 6767 6768 ############################################################################ 6769 # 6770 # Unit list aliases 6771 # 6772 # These provide a shorthand for conversions to unit lists. 6773 # 6774 ############################################################################ 6775 6776 !unitlist hms hr;min;sec 6777 !unitlist time year;day;hr;min;sec 6778 !unitlist dms deg;arcmin;arcsec 6779 !unitlist ftin ft;in;1|8 in 6780 !unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in 6781 !unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\ 6782 tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp 6783 6784 ############################################################################ 6785 # 6786 # The following units were in the unix units database but do not appear in 6787 # this file: 6788 # 6789 # wey used for cheese, salt and other goods. Measured mass or 6790 # waymass volume depending on what was measured and where the measuring 6791 # took place. A wey of cheese ranged from 200 to 324 pounds. 6792 # 6793 # sack No precise definition 6794 # 6795 # spindle The length depends on the type of yarn 6796 # 6797 # block Defined variously on different computer systems 6798 # 6799 # erlang A unit of telephone traffic defined variously. 6800 # Omitted because there are no other units for this 6801 # dimension. Is this true? What about CCS = 1/36 erlang? 6802 # Erlang is supposed to be dimensionless. One erlang means 6803 # a single channel occupied for one hour. 6804 # 6805 ############################################################################ 6806