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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