lib/phys/units/load_units.rb in phys-units-0.9.9 vs lib/phys/units/load_units.rb in phys-units-1.0.0
- old
+ new
@@ -3,14 +3,13 @@
Phys::Unit.import_units <<EOL
#
# This file is the units database for use with GNU units, a units conversion
# program by Adrian Mariano adrianm@gnu.org
#
-# October 2012 Version 2.04
+# March 2017 Version 2.16
#
-# Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004, 2005, 2006
-# 2007, 2008, 2009, 2010, 2011, 2012
+# Copyright (C) 1996-2002, 2004-2017
# Free Software Foundation, Inc
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
@@ -28,11 +27,11 @@
#
############################################################################
#
# Improvements and corrections are welcome.
#
-# Fundamental constants in this file are the 2010 CODATA recommended values.
+# Fundamental constants in this file are the 2014 CODATA recommended values.
#
# Most units data was drawn from
# 1. NIST Special Publication 811, Guide for the
# Use of the International System of Units (SI).
# Barry N. Taylor. 1995
@@ -66,10 +65,13 @@
# Other Technical Requirements for Weighing and Measuring
# Devices. 2011
# 22. NIST Special Publication 447, Weights and Measures Standards
# of the the United States: a brief history. Lewis V. Judson.
# 1963; rev. 1976
+# 23. CRC Handbook of Chemistry and Physics, 96th edition
+# 24. Dictionary of Scientific Units, 6th ed. H.G. Jerrard and D.B.
+# McNeill. 1992
#
# Thanks to Jeff Conrad for assistance in ferreting out unit definitions.
#
###########################################################################
#
@@ -313,10 +315,21 @@
ninety 90
hundred 100
thousand 1000
million 1e6
+twoscore two score
+threescore three score
+fourscore four score
+fivescore five score
+sixscore six score
+sevenscore seven score
+eightscore eight score
+ninescore nine score
+tenscore ten score
+twelvescore twelve score
+
# These number terms were described by N. Chuquet and De la Roche in the 16th
# century as being successive powers of a million. These definitions are still
# used in most European countries. The current US definitions for these
# numbers arose in the 17th century and don't make nearly as much sense. These
# numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
@@ -421,11 +434,21 @@
septendecillion shortseptendecillion
octodecillion shortoctodecillion
novemdecillion shortnovemdecillion
vigintillion shortvigintillion
+#
+# Numbers used in India
+#
+lakh 1e5
+crore 1e7
+arab 1e9
+kharab 1e11
+neel 1e13
+padm 1e15
+shankh 1e17
#############################################################################
# #
# Derived units which can be reduced to the primitive units #
# #
@@ -612,11 +635,19 @@
cron 1e6 years
watch 4 hours # time a sentry stands watch or a ship's
# crew is on duty.
bell 1|8 watch # Bell would be sounded every 30 minutes.
+# French Revolutionary Time or Decimal Time. It was Proposed during
+# the French Revolution. A few clocks were made, but it never caught
+# on. In 1998 Swatch defined a time measurement called ".beat" and
+# sold some watches that displayed time in this unit.
+decimalhour 1|10 day
+decimalminute 1|100 decimalhour
+decimalsecond 1|100 decimalminute
+beat decimalminute # Swatch Internet Time
#
# angular measure
#
@@ -657,14 +688,15 @@
# 24 hours instead of 360 degrees.
#
# Some geometric formulas
#
-circlearea(r) units=[m;m^2] range=[0,] pi r^2 ; sqrt(circlearea/pi)
-spherevolume(r) units=[m;m^3] 4|3 pi r^3 ; cuberoot(spherevolume/4|3 pi)
-spherevol(r) units=[m;m^3] spherevolume(r) ; ~spherevolume(spherevol)
-square(x) range=[0,] x^2 ; sqrt(square)
+circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
+spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
+ cuberoot(spherevolume/4|3 pi)
+spherevol() spherevolume
+square(x) range=[0,) x^2 ; sqrt(square)
#
# Solid angle measure
#
@@ -707,11 +739,11 @@
# The pH scale is used to measure the concentration of hydronium (H3O+) ions in
# a solution. A neutral solution has a pH of 7 as a result of dissociated
# water molecules.
-pH(x) units=[;mol/liter] range=[0,] 10^(-x) mol/liter ; (-log(pH liters/mol))
+pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
#
# Temperature
#
@@ -732,12 +764,13 @@
# by the Celsius scale which is defined by subtracting 273.15 from the
# temperature in Kelvins. This definition differed slightly from the old
# centigrade definition, but the Kelvin scale depends on the triple point of
# water rather than a melting point, so it can be measured accurately.
-tempC(x) units=[;K] x K + stdtemp ; (tempC +(-stdtemp))/K
-tempcelsius(x) units=[;K] tempC(x); ~tempC(tempcelsius)
+tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
+ x K + stdtemp ; (tempC +(-stdtemp))/K
+tempcelsius() tempC
degcelsius K
degC K
# Fahrenheit defined his temperature scale by setting 0 to the coldest
# temperature he could produce in his lab with a salt water solution and by
@@ -749,12 +782,13 @@
# mixture is used without salt. Denote this position as 30. A
# third point, designated as 96, is obtained if the thermometer
# is placed in the mouth so as to acquire the heat of a healthy
# man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
-tempF(x) units=[;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
-tempfahrenheit(x) units=[;K] tempF(x) ; ~tempF(tempfahrenheit)
+tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
+ (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
+tempfahrenheit() tempF
degfahrenheit 5|9 degC
degF 5|9 degC
degreesrankine degF # The Rankine scale has the
@@ -762,12 +796,12 @@
degreerankine degF # is at absolute zero.
degR degrankine
tempR degrankine
temprankine degrankine
-tempreaumur(x) units=[;K] x degreaumur+stdtemp ; \
- (tempreaumur+(-stdtemp))/degreaumur
+tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \
+ x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
degreaumur 10|8 degC # The Reaumur scale was used in Europe and
# particularly in France. It is defined
# to be 0 at the freezing point of water
# and 80 at the boiling point. Reaumur
# apparently selected 80 because it is
@@ -835,85 +869,85 @@
c 2.99792458e8 m/s # speed of light in vacuum (exact)
light c
mu0 4 pi 1e-7 H/m # permeability of vacuum (exact)
epsilon0 1/mu0 c^2 # permittivity of vacuum (exact)
energy c^2 # convert mass to energy
-e 1.602176565e-19 C # electron charge
-h 4.135667516e-15 eV s # Planck constant
+e 1.6021766208e-19 C # electron charge
+h 4.135667662e-15 eV s # Planck constant
hbar h / 2 pi
spin hbar
-G 6.67384e-11 N m^2 / kg^2 # Newtonian gravitational constant
+G 6.67408e-11 N m^2 / kg^2 # Newtonian gravitational constant
# This is the NIST 2006 value.
# The relative uncertainty on this
# is 1e-4.
coulombconst 1/4 pi epsilon0 # listed as "k" sometimes
# Physico-chemical constants
-atomicmassunit 1.660538921e-27 kg # atomic mass unit (defined to be
+atomicmassunit 1.660539040e-27 kg # atomic mass unit (defined to be
u atomicmassunit # 1|12 of the mass of carbon 12)
amu atomicmassunit
amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of
# the 3 naturally occuring neutral
# isotopes of oxygen
amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral
# oxygen 16 atom
dalton u # Maybe this should be amu_chem?
avogadro grams/amu mol # size of a mole
N_A avogadro
-gasconstant 8.3144621 J / mol K # molar gas constant
+gasconstant k N_A # molar gas constant
R gasconstant
-boltzmann R / N_A # Boltzmann constant
+boltzmann 1.38064852e-23 J/K # Boltzmann constant
k boltzmann
kboltzmann boltzmann
molarvolume mol R stdtemp / atm # Volume occupied by one mole of an
# ideal gas at STP.
loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an
# ideal gas at STP. Loschmidt did
# work similar to Avogadro.
stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
sigma stefanboltzmann # blackbody at temperature T is
# given by sigma T^4.
-wiendisplacement 2.8977721e-3 m K # Wien's Displacement Law gives the
+wiendisplacement 2.8977729e-3 m K # Wien's Displacement Law gives the
# frequency at which the the Planck
# spectrum has maximum intensity.
# The relation is lambda T = b where
# lambda is wavelength, T is
# temperature and b is the Wien
# displacement. This relation is
# used to determine the temperature
# of stars.
-K_J 483597.870 GHz/V # Direct measurement of the volt is difficult. Until
- # recently, laboratories kept Weston cadmium cells as
+K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until
+K_J 483597.8525 GHz/V # recently, laboratories kept Weston cadmium cells as
# a reference, but they could drift. In 1987 the
# CGPM officially recommended the use of the
# Josephson effect as a laboratory representation of
# the volt. The Josephson effect occurs when two
# superconductors are separated by a thin insulating
# layer. A "supercurrent" flows across the insulator
# with a frequency that depends on the potential
# applied across the superconductors. This frequency
# can be very accurately measured. The Josephson
# constant K_J, which is equal to 2e/h, relates the
- # measured frequency to the potential. The value
- # given here is the officially specified value for
- # use beginning in 1990. The 2006 recommended value
- # of the constant is 483597.891 GHz/V.
-R_K 25812.8074434 ohm # Measurement of the ohm also presents difficulties.
- # The old approach involved maintaining resistances
+ # measured frequency to the potential. Two values
+ # given, the conventional (exact) value from 1990 and
+ # the current CODATA measured value.
+R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties.
+R_K 25812.8074555 ohm # The old approach involved maintaining resistances
# that were subject to drift. The new standard is
# based on the Hall effect. When a current carrying
# ribbon is placed in a magnetic field, a potential
# difference develops across the ribbon. The ratio
# of the potential difference to the current is
# called the Hall resistance. Klaus von Klitzing
# discovered in 1980 that the Hall resistance varies
# in discrete jumps when the magnetic field is very
# large and the temperature very low. This enables
# accurate realization of the resistance h/e^2 in the
- # lab. The value given here is the officially
- # specified value for use beginning in 1990.
+ # lab. Two values given, the conventional (exact)
+ # value from 1990 and the current CODATA measured
+ # value.
# Various conventional values
gravity 9.80665 m/s^2 # std acceleration of gravity (exact)
force gravity # use to turn masses into forces
@@ -949,23 +983,23 @@
H2O50C 0.98807 force gram / cm^3
H2O100C 0.95838 force gram / cm^3
# Atomic constants
-Rinfinity 10973731.568527 /m # The wavelengths of a spectral series
+Rinfinity 10973731.568539 /m # The wavelengths of a spectral series
R_H 10967760 /m # can be expressed as
# 1/lambda = R (1/m^2 - 1/n^2).
# where R is a number that various
# slightly from element to element.
# For hydrogen, R_H is the value,
# and for heavy elements, the value
# approaches Rinfinity, which can be
# computed from
# m_e c alpha^2 / 2 h
- # with a loss of 5 digits
+ # with a loss of 4 digits
# of precision.
-alpha 7.2973525698e-3 # The fine structure constant was
+alpha 7.2973525664e-3 # The fine structure constant was
# introduced to explain fine
# structure visible in spectral
# lines. It can be computed from
# mu0 c e^2 / 2 h
# with a loss of 3 digits precision
@@ -974,42 +1008,42 @@
bohrradius alpha / 4 pi Rinfinity
prout 185.5 keV # nuclear binding energy equal to 1|12
# binding energy of the deuteron
# Planck constants
-planckmass 2.17644e-8 kg # sqrt(hbar c / G)
+planckmass 2.17651e-8 kg # sqrt(hbar c / G)
m_P planckmass
plancktime hbar / planckmass c^2
t_P plancktime
plancklength plancktime c
l_P plancklength
# Particle radius
electronradius (1/4 pi epsilon0) e^2 / electronmass c^2 # Classical
-deuteronchargeradius 2.1424e-15 m
-protonchargeradius 0.8775e-15
+deuteronchargeradius 2.1413e-15 m
+protonchargeradius 0.8751e-15 m
# Masses of elementary particles
-electronmass 5.4857990946e-4 u
+electronmass 5.48579909070e-4 u
m_e electronmass
-protonmass 1.007276466812 u
+protonmass 1.007276466879 u
m_p protonmass
-neutronmass 1.00866491600 u
+neutronmass 1.00866491588 u
m_n neutronmass
-muonmass 0.1134289267 u
+muonmass 0.1134289257 u
m_mu muonmass
-deuteronmass 2.013553212712 u
+deuteronmass 2.013553212745 u
m_d deuteronmass
-alphaparticlemass 4.001506179125 u
+alphaparticlemass 4.001506179127 u
m_alpha alphaparticlemass
taumass 1.90749 u
m_tau taumass
-tritonmass 3.0155007134 u
+tritonmass 3.01550071632 u
m_t tritonmass
-helionmass 3.0149322468 u
+helionmass 3.01493224673 u
m_h helionmass
# particle wavelengths: the compton wavelength of a particle is
@@ -1026,17 +1060,17 @@
bohrmagneton e hbar / 2 electronmass
mu_B bohrmagneton
nuclearmagneton e hbar / 2 protonmass
mu_N nuclearmagneton
-mu_mu -4.49044807e-26 J/T # Muon magnetic moment
-mu_p 1.410606743e-26 J/T # Proton magnetic moment
-mu_e -928.476430e-26 J/T # Electron magnetic moment
-mu_n -0.96623647e-26 # Neutron magnetic moment
-mu_d 0.433073489e-26 J/T # Deuteron magnetic moment
-mu_t 1.504609447e-26 J/T # Triton magnetic moment
-mu_h -1.074617486e-26 J/T # Helion magnetic moment
+mu_mu -4.49044826e-26 J/T # Muon magnetic moment
+mu_p 1.4106067873e-26 J/T # Proton magnetic moment
+mu_e -928.4764620e-26 J/T # Electron magnetic moment
+mu_n -0.96623650e-26 J/T # Neutron magnetic moment
+mu_d 0.4330735040e-26 J/T # Deuteron magnetic moment
+mu_t 1.504609503e-26 J/T # Triton magnetic moment
+mu_h -1.074617522e-26 J/T # Helion magnetic moment
#
# Units derived from physical constants
#
@@ -1044,14 +1078,15 @@
kgf kg force
technicalatmosphere kgf / cm^2
at technicalatmosphere
hyl kgf s^2 / m # Also gram-force s^2/m according to [15]
mmHg mm Hg
-torr mmHg # These units, both named after Evangelista
-tor Pa # Torricelli, should not be confused.
- # Acording to [15] the torr is actually
- # atm/760 which is slightly different.
+torr atm / 760 # The torr, named after Evangelista
+ # Torricelli, and is very close to the mm Hg
+tor Pa # Suggested in 1913 but seldom used [24].
+ # Eventually renamed the Pascal. Don't
+ # confuse the tor with the torr.
inHg inch Hg
inH2O inch water
mmH2O mm water
eV e V # Energy acquired by a particle with charge e
electronvolt eV # when it is accelerated through 1 V
@@ -1212,11 +1247,26 @@
# equal to N_A e and hence has units of
# C/mol.
kappline 6000 maxwell # Named by and for Gisbert Kapp
siemensunit 0.9534 ohm # Resistance of a meter long column of
# mercury with a 1 mm cross section.
+#
+# Printed circuit board units.
+#
+# http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm.
+#
+# Conductivity is often expressed as a percentage of IACS. A copper wire a
+# meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at
+# 20 deg C. Copper density is also standarized at that temperature.
+#
+copperconductivity 58 siemens m / mm^2 # A wire a meter long with
+IACS copperconductivity # a 1 mm^2 cross section
+copperdensity 8.89 g/cm^3 # The "ounce" measures the
+ouncecopper oz / ft^2 copperdensity # thickness of copper used
+ozcu ouncecopper # in circuitboard fabrication
+
#
# Photometric units
#
LUMINOUS_INTENSITY candela
@@ -1283,11 +1333,11 @@
# The bril is used to express "brilliance" of a source of light on a
# logarithmic scale to correspond to subjective perception. An increase of 1
# bril means doubling the luminance. A luminance of 1 lambert is defined to
# have a brilliance of 1 bril.
-bril(x) units=[;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100
+bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100
# Some luminance data from the IES Lighting Handbook, 8th ed, 1993
sunlum 1.6e9 cd/m^2 # at zenith
sunillum 100e3 lux # clear sky
@@ -1295,75 +1345,228 @@
sunlum_h 6e6 cd/m^2 # value at horizon
skylum 8000 cd/m^2 # average, clear sky
skylum_o 2000 cd/m^2 # average, overcast sky
moonlum 2500 cd/m^2
+#
# Photographic Exposure Value
+# This section by Jeff Conrad (jeff_conrad@msn.com)
#
-# The Additive Photographic EXposure (APEX) system proposed in ASA PH2.5-1960
-# was an attempt to simplify exposure determination for people who relied on
-# exposure tables rather than exposure meters. Shortly thereafter, nearly all
-# cameras incorporated exposure meters, so the APEX system never caught on,
-# but the concept of Exposure Value (EV) given by
+# The Additive system of Photographic EXposure (APEX) proposed in ASA
+# PH2.5-1960 was an attempt to simplify exposure determination for people who
+# relied on exposure tables rather than exposure meters. Shortly thereafter,
+# nearly all cameras incorporated exposure meters, so the APEX system never
+# caught on, but the concept of exposure value remains in use. Though given as
+# 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is
+# related to exposure parameters by
#
# A^2 LS ES
# 2^EV = --- = -- = --
-# T K C
+# t K C
#
# Where
# A = Relative aperture (f-number)
-# T = Shutter time in seconds
+# t = Exposure time in seconds
# L = Scene luminance in cd/m2
# E = Scene illuminance in lux
-# S = Arithmetic ISO film speed
+# S = Arithmetic ISO speed
# K = Reflected-light meter calibration constant
# C = Incident-light meter calibration constant
#
-# remains in use. Strictly speaking, an Exposure Value is a combination
-# of aperture and shutter time, but it's also commonly used to indicate
-# luminance (or illuminance). Conversion to luminance or illuminance
-# units depends on the ISO film speed and the meter calibration constant.
-# Common practice is to use an ISO film speed of 100 (because film speeds
-# are in even 1/3-step increments, the exact value is 64 * 2^(2|3)).
+# Strictly, an exposure value is a combination of aperture and exposure time,
+# but it's also commonly used to indicate luminance (or illuminance).
+# Conversion to luminance or illuminance units depends on the ISO speed and the
+# meter calibration constant. Common practice is to use an ISO speed of 100.
# Calibration constants vary among camera and meter manufacturers: Canon,
# Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while
-# Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and
-# Sekonic use a value of 250 for incident-light meters with flat
-# receptors.
+# Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use
+# a value of 250 for incident-light meters with flat receptors.
+#
+# The values for in-camera meters apply only averaging, weighted-averaging, or
+# spot metering--the multi-segment metering incorporated in most current
+# cameras uses proprietary algorithms that evaluate many factors related to the
+# luminance distribution of what is being metered; they are not amenable to
+# simple conversions, and are usually not disclosed by the manufacturers.
-# This was stated in ASA PH2.5-1960, but it assumed APEX, which never
-# found widespread acceptance.
-
-#s100 64 * 2^(2|3) / lx s # exact speed for ISO 100 film
-
-# ISO speed standards (e.g., ISO 6:1993) do not discuss "exact" values;
-# this value assumes ISO 100 is exact.
-
-s100 100 / lx s # ISO 100 speed
+s100 100 / lx s # ISO 100 speed
iso100 s100
# Reflected-light meter calibration constant with ISO 100 speed
-k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic
-k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax
+k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic
+k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax
# Incident-light meter calibration constant with ISO 100 film
-c250 250 lx / lx s # flat-disc receptor
+c250 250 lx / lx s # flat-disc receptor
-# Exposure value to scene luminance with ISO 100 film
+# Exposure value to scene luminance with ISO 100 imaging media
# For Kenko (Minolta) or Pentax
-#ev100(x) units=[;cd/m^2] 2^x k1400 / s100; log2(ev100 s100 / k1400)
+#ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400)
# For Canon, Nikon, or Sekonic
-ev100(x) units=[;cd/m^2] 2^x k1250 / s100; log2(ev100 s100 / k1250)
+ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250)
+EV100() ev100
-# Exposure value to scene illuminance with ISO 100 film
+# Exposure value to scene illuminance with ISO 100 imaging media
-iv100(x) units=[1;lx] 2^x c250 / s100; log2(iv100 s100 / c250)
+iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250)
+# Other Photographic Exposure Conversions
#
+# As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities
+# related by
+#
+# Ev = Av + Tv = Bv + Sv
+#
+# where
+# Av = log2(A^2) Aperture value
+# Tv = log2(1/t) Time value
+# Sv = log2(N Sx) Speed value
+# Bv = log2(B S / K) Luminance ("brightness") value
+# Iv = log2(I S / C) Illuminance value
+#
+# and
+# A = Relative aperture (f-number)
+# t = Exposure time in seconds
+# Sx = Arithmetic ISO speed in 1/lux s
+# B = luminance in cd/m2
+# I = luminance in lux
+
+# The constant N derives from the arcane relationship between arithmetic
+# and logarithmic speed given in ASA PH2.5-1960. That relationship
+# apparently was not obvious--so much so that it was thought necessary
+# to explain it in PH2.12-1961. The constant has had several values
+# over the years, usually without explanation for the changes. Although
+# APEX had little impact on consumer cameras, it has seen a partial
+# resurrection in the Exif standards published by the Camera & Imaging
+# Products Association of Japan.
+
+#N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961,
+ # derived from ASA PH2.5-1960.
+#N_apex 0.30 lx s # rounded value in ASA PH2.5-1960,
+ # ASA PH2.12-1961, and ANSI PH2.7-1986
+#N_apex 0.3162 lx s # value in ANSI PH2.7-1973
+N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100
+K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961
+K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common
+C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in
+ # footcandles; flat sensor?)
+C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in
+ # footcandles; hemispherical sensor?)
+N_speed N_exif
+K_lum K_apex1971
+C_illum C_apex1961
+
+# Units for Photographic Exposure Variables
+#
+# Practical photography sometimes pays scant attention to units for exposure
+# variables. In particular, the "speed" of the imaging medium is treated as if
+# it were dimensionless when it should have units of reciprocal lux seconds;
+# this practice works only because "speed" is almost invariably given in
+# accordance with international standards (or similar ones used by camera
+# manufacturers)--so the assumed units are invariant. In calculating
+# logarithmic quantities--especially the time value Tv and the exposure value
+# EV--the units for exposure time ("shutter speed") are often ignored; this
+# practice works only because the units of exposure time are assumed to be in
+# seconds, and the missing units that make the argument to the logarithmic
+# function dimensionless are silently provided.
+#
+# In keeping with common practice, the definitions that follow treat "speeds"
+# as dimensionless, so ISO 100 speed is given simply as '100'. When
+# calculating the logarithmic APEX quantities Av and Tv, the definitions
+# provide the missing units, so the times can be given with any appropriate
+# units. For example, giving an exposure time of 1 minute as either '1 min' or
+# '60 s' will result in Tv of -5.9068906.
+#
+# Exposure Value from f-number and Exposure Time
+#
+# Because nonlinear unit conversions only accept a single quantity,
+# there is no direct conversion from f-number and exposure time to
+# exposure value EV. But the EV can be obtained from a combination of
+# Av and Tv. For example, the "sunny 16" rule states that correct
+# exposure for a sunlit scene can achieved by using f/16 and an exposure
+# time equal to the reciprocal of the ISO speed in seconds; this can be
+# calculated as
+#
+# ~Av(16) + ~Tv(1|100 s),
+#
+# which gives 14.643856. These conversions may be combined with the
+# ev100 conversion:
+#
+# ev100(~Av(16) + ~Tv(1|100 s))
+#
+# to yield the assumed average scene luminance of 3200 cd/m^2.
+
+# convert relative aperture (f-number) to aperture value
+Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av)
+# convert exposure time to time value
+Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv)
+# convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed;
+# make arithmetic speed dimensionless
+# 'Sv' conflicts with the symbol for sievert; you can uncomment this function
+# definition if you don't need that symbol
+#Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv)
+Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval)
+
+# convert luminance value Bv in ASA PH2.12-1961 to luminance
+Bv(x) units=[1;cd/m^2] range=(0,) \
+ 2^x K_lum N_speed ; log2(Bv / (K_lum N_speed))
+
+# convert illuminance value Iv in ASA PH2.12-1961 to illuminance
+Iv(x) units=[1;lx] range=(0,) \
+ 2^x C_illum N_speed ; log2(Iv / (C_illum N_speed))
+
+# convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in
+# ASA PH2.5-1960; make arithmetic speed dimensionless
+Sx(S) units=[1;1] domain=(0,) \
+ log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s)
+
+# convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed
+# for convenience, speed is treated here as if it were dimensionless
+Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg))
+Sdin() Sdeg
+
+# Numerical Aperture and f-Number of a Lens
+#
+# The numerical aperture (NA) is given by
+#
+# NA = n sin(theta)
+#
+# where n is the index of refraction of the medium and theta is half
+# of the angle subtended by the aperture stop from a point in the image
+# or object plane. For a lens in air, n = 1, and
+#
+# NA = 0.5 / f-number
+#
+# convert NA to f-number
+numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \
+ 0.5 / x ; 0.5 / numericalaperture
+NA() numericalaperture
+#
+# convert f-number to itself; restrict values to those possible
+fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber
+
+# Referenced Photographic Standards
+#
+# ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome,
+# Continuous-Tone) Speed of Photographic Negative Materials.
+# ASA PH2.12-1961. American Standard, General-Purpose Photographic
+# Exposure Meters (photoelectric type).
+# ANSI PH3.49-1971. American National Standard for general-purpose
+# photographic exposure meters (photoelectric type).
+# ANSI PH2.7-1973. American National Standard Photographic Exposure Guide.
+# ANSI PH2.7-1986. American National Standard for Photography --
+# Photographic Exposure Guide.
+# CIPA DC-008-2010. Exchangeable image file format for digital still
+# cameras: Exif Version 2.3
+# ISO 6:1993. International Standard, Photography -- Black-and-white
+# pictorial still camera negative film/process systems --
+# Determination of ISO Speed.
+
+
+#
# Astronomical time measurements
#
# Astronomical time measurement is a complicated matter. The length of the
# true day at a given place can be 21 seconds less than 24 hours or 30 seconds
# over 24 hours. The two main reasons for this are the varying speed of the
@@ -1946,11 +2149,10 @@
shot jigger # Sometimes 1 usfloz
eushot 25 ml # EU standard spirits measure
fifth 1|5 usgallon
winebottle 750 ml # US industry standard, 1979
winesplit 1|4 winebottle
-wineglass 4 usfloz
magnum 1.5 liter # Standardized in 1979, but given
# as 2 qt in some references
metrictenth 375 ml
metricfifth 750 ml
metricquart 1 liter
@@ -1969,11 +2171,49 @@
methuselah 4 magnum
salmanazar 6 magnum
balthazar 8 magnum
nebuchadnezzar 10 magnum
+# The wine glass doesn't seem to have an official standard, but the same value
+# is suggested by several organization.
+
+# https://www.rethinkingdrinking.niaaa.nih.gov/
+# http://www.rethinkyourdrinking.ca/what-is-a-standard-drink/
+# https://www.drinkaware.co.uk/
+# https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf
+# http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/content/drinksguide-cnt
+
+wineglass 150 mL # the size of a "typical" serving
+
+# A unit of alcohol is a specified mass of pure ethyl alcohol.
+# The term is used officially in the UK, but other countries use the same
+# concept but with different values. For example, the UK value of 8 g is
+# nominally the amount of alcohol that a typical adult can metabolize in
+# one hour. Values for several countries, converted to a volumetric basis:
+
+alcoholunitus 14 g / ethanoldensity
+alcoholunitca 13.6 g / ethanoldensity
+alcoholunituk 8 g / ethanoldensity
+alcoholunitau 10 g / ethanoldensity
+
+# Example: for 12% ABV (alcohol by volume)
+# alcoholunitus / 12% = 147.8 mL, close to the “standard” serving of 150 mL.
+
+
+# Coffee
#
+# The recommended ratio of coffee to water. Values vary considerably;
+# one is from the Specialty Coffee Association of America
+# http://scaa.org/?page=resources&d=brewing-best-practices
+
+coffeeratio 55 g/L # ± 10%
+
+# other recommendations are more loose, e.g.,
+# http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee
+
+
+#
# Water is "hard" if it contains various minerals, expecially calcium
# carbonate.
#
clarkdegree grains/brgallon # Content by weigh of calcium carbonate
@@ -1998,17 +2238,17 @@
shoe_men0 8.25 inch
shoe_women0 (7+11|12) inch
shoe_boys0 (3+11|12) inch
shoe_girls0 (3+7|12) inch
-shoesize_men(n) units=[;inch] shoe_men0 + n shoesize_delta ; \
+shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \
(shoesize_men+(-shoe_men0))/shoesize_delta
-shoesize_women(n) units=[;inch] shoe_women0 + n shoesize_delta ; \
+shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \
(shoesize_women+(-shoe_women0))/shoesize_delta
-shoesize_boys(n) units=[;inch] shoe_boys0 + n shoesize_delta ; \
+shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \
(shoesize_boys+(-shoe_boys0))/shoesize_delta
-shoesize_girls(n) units=[;inch] shoe_girls0 + n shoesize_delta ; \
+shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \
(shoesize_girls+(-shoe_girls0))/shoesize_delta
# European shoe size. According to
# http://www.shoeline.com/footnotes/shoeterm.shtml
# shoe sizes in Europe are measured with Paris points which simply measure
@@ -2262,16 +2502,16 @@
# ending -ment is from the old English word
# for hand. [18]
smoot 5 ft + 7 in # Created as part of an MIT fraternity prank.
# In 1958 Oliver Smoot was used to measure
# the length of the Harvard Bridge, which was
- # marked off in smooth lengths. These
+ # marked off in Smoot lengths. These
# markings have been maintained on the bridge
# since then and repainted by subsequent
# incoming fraternity members. During a
- # bridge rennovation the new sidewalk was
- # scored every smooth rather than at the
+ # bridge renovation the new sidewalk was
+ # scored every Smoot rather than at the
# customary 6 ft spacing.
#
# Cooking measures
#
@@ -2425,10 +2665,15 @@
eggyolk 18.6 grams
eggvolume 3 ustablespoons + 1|2 ustsp
eggwhitevolume 2 ustablespoons
eggyolkvolume 3.5 ustsp
+# Alcohol density
+
+ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition
+alcoholdensity ethanoldensity
+
#
# Density measures. Density has traditionally been measured on a variety of
# bizarre nonlinear scales.
#
@@ -2555,22 +2800,22 @@
# 1 g/cm^3. An arbitrary constant appears in the definition. This value is
# equal to 145 in the US, but was according to [], the old scale used in
# Holland had a value of 144, and the new scale or Gerlach scale used 146.78.
baumeconst 145 # US value
-baume(d) units=[1;g/cm^3] domain=[0,] range=[1,] \
+baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \
(baumeconst/(baumeconst+-d)) g/cm^3 ; \
(baume+((-g)/cm^3)) baumeconst / baume
# It's not clear if this value was ever used with negative degrees.
-twaddell(x) units=[1;g/cm^3] domain=[-200,] range=[0,] \
+twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \
(1 + 0.005 x) g / cm^3 ; \
200 (twaddell / (g/cm^3) +- 1)
# The degree quevenne is a unit for measuring the density of milk.
# Similarly it's unclear if negative values were allowed here.
-quevenne(x) units=[1;g/cm^3] domain=[-1000,] range=[0,] \
+quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \
(1 + 0.001 x) g / cm^3 ; \
1000 (quevenne / (g/cm^3) +- 1)
# Degrees brix measures sugar concentration by weigh as a percentage, so a
# solution that is 3 degrees brix is 3% sugar by weight. This unit was named
@@ -2604,11 +2849,11 @@
# Density measure invented by the American Petroleum Institute. Lighter
# petroleum products are more valuable, and they get a higher API degree.
#
# The intervals of range and domain should be open rather than closed.
#
-apidegree(x) units=[1;g/cm^3] domain=[-131.5,] range=[0,] \
+apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \
141.5 g/cm^3 / (x+131.5) ; \
141.5 (g/cm^3) / apidegree + (-131.5)
#
# Units derived from imperial system
@@ -2620,10 +2865,13 @@
tondal longton ft / s^2 # and for a ton
pdl poundal
osi ounce force / inch^2 # used in aviation
psi pound force / inch^2
psia psi # absolute pressure
+ # Note that gauge pressure can be given
+ # using the gaugepressure() and
+ # psig() nonlinear unit definitions
tsi ton force / inch^2
reyn psi sec
slug lbf s^2 / ft
slugf slug force
slinch lbf s^2 / inch # Mass unit derived from inch second
@@ -2698,40 +2946,151 @@
#
ENERGY joule
WORK joule
-# Calories: energy to raise a gram of water one degree celsius
+# Calorie: approximate energy to raise a gram of water one degree celsius
-cal_IT 4.1868 J # International Table calorie
-cal_th 4.184 J # Thermochemical calorie
-cal_fifteen 4.18580 J # Energy to go from 14.5 to 15.5 degC
-cal_twenty 4.18190 J # Energy to go from 19.5 to 20.5 degC
-cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC
-calorie cal_IT
+calorie cal_th # Default is the thermochemical calorie
cal calorie
-calorie_IT cal_IT
-thermcalorie cal_th
-calorie_th thermcalorie
+calorie_th 4.184 J # Thermochemical calorie, defined in 1930
+thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to
+cal_th calorie_th # avoid difficulties associated with the
+ # uncertainty in the heat capacity of
+ # water. In 1948 the value of the joule
+ # was changed, so the thermochemical
+ # calorie was redefined to 4.184 J.
+ # This kept the energy measured by this
+ # unit the same.
+calorie_IT 4.1868 J # International (Steam) Table calorie,
+cal_IT calorie_IT # defined in 1929 as watt-hour/860 or
+ # equivalently 180|43 joules. At this
+ # time the international joule had a
+ # different value than the modern joule,
+ # and the values were different in the
+ # USA and in Europe. In 1956 at the
+ # Fifth International Conference on
+ # Properties of Steam the exact
+ # definition given here was adopted.
+calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC
+cal_15 calorie_15
+calorie_fifteen cal_15
+calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC
+cal_20 calorie_20
+calorie_twenty calorie_20
+cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC
Calorie kilocalorie # the food Calorie
-thermie 1e6 cal_fifteen # Heat required to raise the
+thermie 1e6 cal_15 # Heat required to raise the
# temperature of a tonne of
# water from 14.5 to 15.5 degC.
# btu definitions: energy to raise a pound of water 1 degF
-btu cal lb degF / gram K # international table BTU
+btu btu_IT # International Table BTU is the default
britishthermalunit btu
-btu_IT btu
+btu_IT cal_IT lb degF / gram K
btu_th cal_th lb degF / gram K
btu_mean cal_mean lb degF / gram K
quad quadrillion btu
ECtherm 1.05506e8 J # Exact definition, close to 1e5 btu
UStherm 1.054804e8 J # Exact definition
therm UStherm
+# Water latent heat from [23]
+
+water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C
+water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa
+
+# Specific heat capacities of various substances
+
+specificheat_water calorie / g K
+water_specificheat specificheat_water
+ # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html
+specificheat_aluminum 0.91 J/g K
+specificheat_antimony 0.21 J/g K
+specificheat_barium 0.20 J/g K
+specificheat_beryllium 1.83 J/g K
+specificheat_bismuth 0.13 J/g K
+specificheat_cadmium 0.23 J/g K
+specificheat_cesium 0.24 J/g K
+specificheat_chromium 0.46 J/g K
+specificheat_cobalt 0.42 J/g K
+specificheat_copper 0.39 J/g K
+specificheat_gallium 0.37 J/g K
+specificheat_germanium 0.32 J/g K
+specificheat_gold 0.13 J/g K
+specificheat_hafnium 0.14 J/g K
+specificheat_indium 0.24 J/g K
+specificheat_iridium 0.13 J/g K
+specificheat_iron 0.45 J/g K
+specificheat_lanthanum 0.195 J/g K
+specificheat_lead 0.13 J/g K
+specificheat_lithium 3.57 J/g K
+specificheat_lutetium 0.15 J/g K
+specificheat_magnesium 1.05 J/g K
+specificheat_manganese 0.48 J/g K
+specificheat_mercury 0.14 J/g K
+specificheat_molybdenum 0.25 J/g K
+specificheat_nickel 0.44 J/g K
+specificheat_osmium 0.13 J/g K
+specificheat_palladium 0.24 J/g K
+specificheat_platinum 0.13 J/g K
+specificheat_plutonum 0.13 J/g K
+specificheat_potassium 0.75 J/g K
+specificheat_rhenium 0.14 J/g K
+specificheat_rhodium 0.24 J/g K
+specificheat_rubidium 0.36 J/g K
+specificheat_ruthenium 0.24 J/g K
+specificheat_scandium 0.57 J/g K
+specificheat_selenium 0.32 J/g K
+specificheat_silicon 0.71 J/g K
+specificheat_silver 0.23 J/g K
+specificheat_sodium 1.21 J/g K
+specificheat_strontium 0.30 J/g K
+specificheat_tantalum 0.14 J/g K
+specificheat_thallium 0.13 J/g K
+specificheat_thorium 0.13 J/g K
+specificheat_tin 0.21 J/g K
+specificheat_titanium 0.54 J/g K
+specificheat_tungsten 0.13 J/g K
+specificheat_uranium 0.12 J/g K
+specificheat_vanadium 0.39 J/g K
+specificheat_yttrium 0.30 J/g K
+specificheat_zinc 0.39 J/g K
+specificheat_zirconium 0.27 J/g K
+specificheat_ethanol 2.3 J/g K
+specificheat_ammonia 4.6 J/g K
+specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit
+specificheat_gasoline 2.22 J/g K
+specificheat_iodine 2.15 J/g K
+specificheat_oliveoil 1.97 J/g K
+
+# en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
+specificheat_hydrogen 14.3 J/g K
+specificheat_helium 5.1932 J/g K
+specificheat_argon 0.5203 J/g K
+specificheat_tissue 3.5 J/g K
+specificheat_diamond 0.5091 J/g K
+specificheat_granite 0.79 J/g K
+specificheat_graphite 0.71 J/g K
+specificheat_ice 2.11 J/g K
+specificheat_asphalt 0.92 J/g K
+specificheat_brick 0.84 J/g K
+specificheat_concrete 0.88 J/g K
+specificheat_glass_silica 0.84 J/g K
+specificheat_glass_flint 0.503 J/g K
+specificheat_glass_pyrex 0.753 J/g K
+specificheat_gypsum 1.09 J/g K
+specificheat_marble 0.88 J/g K
+specificheat_sand 0.835 J/g K
+specificheat_soil 0.835 J/g K
+specificheat_wood 1.7 J/g K
+
+specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php
+
+
# Energy densities of various fuels
#
# Most of these fuels have varying compositions or qualities and hence their
# actual energy densities vary. These numbers are hence only approximate.
#
@@ -2794,10 +3153,18 @@
celsiusheatunit cal lb degC / gram K
chu celsiusheatunit
POWER watt
+# "Apparent" average power in an AC circuit, the product of rms voltage
+# and rms current, equal to the true power in watts when voltage and
+# current are in phase. In a DC circuit, always equal to the true power.
+
+VA volt ampere
+
+kWh kilowatt hour
+
# The horsepower is supposedly the power of one horse pulling. Obviously
# different people had different horses.
horsepower 550 foot pound force / sec # Invented by James Watt
mechanicalhorsepower horsepower
@@ -2858,49 +3225,49 @@
# Alexander Graham Bell. The bel proved inconveniently large so the decibel
# has become more common. The decibel is dimensionless since it reports a
# ratio, but it is used in various contexts to report a signal's power
# relative to some reference level.
-bel(x) units=[1;1] range=[0,] 10^(x); log(bel) # Basic bel definition
-decibel(x) units=[1;1] range=[0,] 10^(x/10); 10 log(decibel) # Basic decibel
-dB(x) units=[1;1] range=[0,] 10^(x/10); 10 log(dB) # Abbreviation
-dBW(x) units=[1;W] range=[0,] dB(x) W ; ~dB(dBW/W) # Reference = 1 W
-dBk(x) units=[1;W] range=[0,] dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW
-dBf(x) units=[1;W] range=[0,] dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW
-dBm(x) units=[1;W] range=[0,] dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW
-dBmW(x) units=[1;W] range=[0,] dBm(x) ; ~dBm(dBmW) # Reference = 1 mW
-dBJ(x) units=[1;J] range=[0,] dB(x) J; ~dB(dBJ/J) # Energy relative
+bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition
+decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel
+dB() decibel # Abbreviation
+dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W
+dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW
+dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW
+dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW
+dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW
+dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative
# to 1 joule. Used for power spectral
# density since W/Hz = J
# When used to measure amplitude, voltage, or current the signal is squared
# because power is proportional to the square of these measures. The root
# mean square (RMS) voltage is typically used with these units.
-dBV(x) units=[1;V] range=[0,] dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
-dBmV(x) units=[1;V] range=[0,] dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
-dBuV(x) units=[1;V] range=[0,] dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
+dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
+dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
+dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
# Reference = 1 microvolt
# Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load.
# Originally defined as dBv but changed to prevent confusion with dBV.
# The "u" is for unloaded.
-dBu(x) units=[1;V] range=[0,] dB(0.5 x) sqrt(mW 600 ohm) ; \
+dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \
~dB(dBu^2 / mW 600 ohm)
-dBv(x) units=[1;V] range=[0,] dBu(x) ; ~dBu(dBv) # Synonym for dBu
+dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu
# Measurements for sound in air, referenced to the threshold of human hearing
# Note that sound in other media typically uses 1 micropascal as a reference
# for sound pressure. Units dBA, dBB, dBC, refer to different frequency
# weightings meant to approximate the human ear's response.
-dBSPL(x) units=[1;Pa] range=[0,] dB(0.5 x) 20 microPa ; \
+dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \
~dB(dBSPL^2 / (20 microPa)^2) # pressure
-dBSIL(x) units=[1;W/m^2] range=[0,] dB(x) 1e-12 W/m^2; \
+dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \
~dB(dBSIL / (1e-12 W/m^2)) # intensity
-dBSWL(x) units=[1;W] range=[0,] dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
+dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
# Misc other measures
ENTROPY ENERGY / TEMPERATURE
@@ -2912,16 +3279,30 @@
# turn one ton of water to ice in
# a day. Ice is defined to have a
# latent heat of 144 btu/lb.
tonref tonrefrigeration
refrigeration tonref / ton
-frigorie 1000 cal_fifteen# Used in refrigeration engineering.
-tnt 1e9 cal_th / ton# So you can write tons-tnt. This
+frigorie 1000 cal_15 # Used in refrigeration engineering.
+tnt 1e9 cal_th / ton# So you can write tons tnt. This
# is a defined, not measured, value.
airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as
# pressure times air flow.
+# Nuclear weapon yields
+
+davycrocket 10 ton tnt # lightest US tactical nuclear weapon
+hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb
+nagasaki 21 kiloton tnt # Plutonium-239 fission bomb
+fatman nagasaki
+littleboy hiroshima
+ivyking 500 kiloton tnt # most powerful fission bomb
+castlebravo 15 megaton tnt # most powerful US test
+b53bomb 9 megaton tnt
+ # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/
+trinity 18 kiloton tnt # July 16, 1945
+gadget trinity
+
#
# Permeability: The permeability or permeance, n, of a substance determines
# how fast vapor flows through the substance. The formula W = n A dP
# holds where W is the rate of flow (in mass/time), n is the permeability,
# A is the area of the flow path, and dP is the vapor pressure difference.
@@ -2981,12 +3362,54 @@
Bpaper 11 inch 17 inch
Cpaper 17 inch 22 inch
Dpaper 22 inch 34 inch
Epaper 34 inch 44 inch
-pointthickness mil
+# Correspondence envelope sizes. #10 is the standard business
+# envelope in the USA.
+envelope6_25size 3.5 inch 6 inch
+envelope6_75size 3.625 inch 6.5 inch
+envelope7size 3.75 inch 6.75 inch
+envelope7_75size 3.875 inch 7.5 inch
+envelope8_625size 3.625 inch 8.625 inch
+envelope9size 3.875 inch 8.875 inch
+envelope10size 4.125 inch 9.5 inch
+envelope11size 4.5 inch 10.375 inch
+envelope12size 4.75 inch 11 inch
+envelope14size 5 inch 11.5 inch
+envelope16size 6 inch 12 inch
+
+# Announcement envelope sizes (no relation to metric paper sizes like A4)
+
+envelopeA1size 3.625 inch 5.125 inch # same as 4bar
+envelopeA2size 4.375 inch 5.75 inch
+envelopeA6size 4.75 inch 6.5 inch
+envelopeA7size 5.25 inch 7.25 inch
+envelopeA8size 5.5 inch 8.125 inch
+envelopeA9size 5.75 inch 8.75 inch
+envelopeA10size 6 inch 9.5 inch
+
+# Baronial envelopes
+
+envelope4bar 3.625 inch 5.125 inch # same as A1
+envelope5_5bar 4.375 inch 5.75 inch
+envelope6bar 4.75 inch 6.5 inch
+
+# Coin envelopes
+
+envelope1baby 2.25 inch 3.5 inch # same as #1 coin
+envelope00coin 1.6875 inch 2.75 inch
+envelope1coin 2.25 inch 3.5 inch
+envelope3coin 2.5 inch 4.25 inch
+envelope4coin 3 inch 4.5 inch
+envelope4_5coin 3 inch 4.875 inch
+envelope5coin 2.875 inch 5.25 inch
+envelope5_5coin 3.125 inch 5.5 inch
+envelope6coin 3.375 inch 6 inch
+envelope7coin 3.5 inch 6.5 inch
+
# The metric paper sizes are defined so that if a sheet is cut in half
# along the short direction, the result is two sheets which are
# similar to the original sheet. This means that for any metric size,
# the long side is close to sqrt(2) times the length of the short
# side. Each series of sizes is generated by repeated cuts in half,
@@ -3106,13 +3529,14 @@
# thickness of one sheet, typically in inches. Thickness is also reported in
# "points" where a point is 1|1000 inch. These conversions are supplied to
# convert these units roughly (using an approximate density) into the standard
# paper weight values.
+pointthickness 0.001 in
paperdensity 0.8 g/cm^3 # approximate--paper densities vary!
papercaliper in paperdensity
-paperpoint 0.001 in paperdensity
+paperpoint pointthickness paperdensity
#
# Printing
#
@@ -3221,14 +3645,16 @@
# to measure information and as a physical quantity.
#
INFORMATION bit
-nat ln(2) bits # Entropy measured base e
+nat (1/ln(2)) bits # Entropy measured base e
hartley log2(10) bits # Entropy of a uniformly
- # distributed random variable
+ban hartley # distributed random variable
# over 10 symbols.
+dit hartley # from Decimal digIT
+
#
# Computer
#
bps bit/sec # Sometimes the term "baud" is
@@ -3296,12 +3722,31 @@
# constant linear velocity (CLV) mode.
# Modern DVDs may vary the linear velocity
# as they go from the inside to the
# outside of the disc.
# See http://www.osta.org/technology/dvdqa/dvdqa4.htm
+#
+# The IP address space is divided into subnets. The number of hosts
+# in a subnet depends on the length of the subnet prefix. This is
+# often written as /N where N is the number of bits in the prefix.
+#
+# https://en.wikipedia.org/wiki/Subnetwork
+#
+# These definitions gives the number of hosts for a subnet whose
+# prefix has the specified length in bits.
+#
+ipv4subnetsize(prefix_len) units=[1;1] domain=[0,32] range=[1,4294967296] \
+ 2^(32-prefix_len) ; 32-log2(ipv4subnetsize)
+#ipv4classA ipv4subnetsize(8)
+#ipv4classB ipv4subnetsize(16)
+#ipv4classC ipv4subnetsize(24)
+ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \
+ range=[1,340282366920938463463374607431768211456] \
+ 2^(128-prefix_len) ; 128-log2(ipv6subnetsize)
+
#
# Musical measures. Musical intervals expressed as ratios. Multiply
# two intervals together to get the sum of the interval. The function
# musicalcent can be used to convert ratios to cents.
#
@@ -3324,11 +3769,11 @@
pythagoreancomma musicalfifth^12 / octave^7
# Equal tempered definitions
semitone octave^(1|12)
-musicalcent(x) units=[1;1] range=[0,] semitone^(x/100) ; \
+musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \
100 log(musicalcent)/log(semitone)
#
# Musical note lengths.
#
@@ -3423,10 +3868,11 @@
# misc medical measure
#
frenchcathetersize 1|3 mm # measure used for the outer diameter
# of a catheter
+charriere frenchcathetersize
#
# fixup units for times when prefix handling doesn't do the job
#
@@ -3443,23 +3889,127 @@
# Note that US$ is the primitive unit so other currencies are
# generally given in US$.
#
unitedstatesdollar US$
+usdollar US$
$ dollar
+#mark germanymark
+#bolivar venezuelabolivar
+#venezuelanbolivarfuerte venezuelabolivar
+#bolivarfuerte bolivar # The currency was revalued by
+#oldbolivar 1|1000 bolivar # a factor of 1000.
+#peseta spainpeseta
+#rand southafricarand
+#escudo portugalescudo
+#guilder netherlandsguilder
+#hollandguilder netherlandsguilder
+#peso mexicopeso
+#yen japanyen
+#lira italylira
+#rupee indiarupee
+#drachma greecedrachma
+#franc francefranc
+#markka finlandmarkka
+#britainpound unitedkingdompound
+#greatbritainpound unitedkingdompound
+#unitedkingdompound ukpound
+#poundsterling britainpound
+#yuan chinayuan
+# Some European currencies have permanent fixed exchange rates with
+# the Euro. These rates were taken from the EC's web site:
+# http://ec.europa.eu/economy_finance/euro/adoption/conversion/index_en.htm
+
+#austriaschilling 1|13.7603 euro
+#belgiumfranc 1|40.3399 euro
+#estoniakroon 1|15.6466 euro # Equal to 1|8 germanymark
+#finlandmarkka 1|5.94573 euro
+#francefranc 1|6.55957 euro
+#germanymark 1|1.95583 euro
+#greecedrachma 1|340.75 euro
+#irelandpunt 1|0.787564 euro
+#italylira 1|1936.27 euro
+#luxembourgfranc 1|40.3399 euro
+#netherlandsguilder 1|2.20371 euro
+#portugalescudo 1|200.482 euro
+#spainpeseta 1|166.386 euro
+#cypruspound 1|0.585274 euro
+#maltalira 1|0.429300 euro
+#sloveniatolar 1|239.640 euro
+#slovakiakoruna 1|30.1260 euro
+
+#UKP GBP # Not an ISO code, but looks like one, and
+# # sometimes used on usenet.
+#VEB 1|1000 VEF # old venezuelan bolivar
+
+!include currency.units
+
+# Money on the gold standard, used in the late 19th century and early
+# 20th century.
+
+#olddollargold 23.22 grains goldprice # Used until 1934
+#newdollargold 96|7 grains goldprice # After Jan 31, 1934
+#dollargold newdollargold
+#poundgold 113 grains goldprice
+#goldounce goldprice troyounce
+#silverounce silverprice troyounce
+#platinumounce platinumprice troyounce
+#XAU goldounce
+#XPT platinumounce
+#XAG silverounce
+
# Nominal masses of US coins. Note that dimes, quarters and half dollars
# have weight proportional to value. Before 1965 it was $40 / kg.
USpennyweight 2.5 grams # Since 1982, 48 grains before
USnickelweight 5 grams
USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965
USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965
UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971
USdollarmass 8.1 grams
+# British currency
+#quid britainpound # Slang names
+#fiver 5 quid
+#tenner 10 quid
+#monkey 500 quid
+#brgrand 1000 quid
+#bob shilling
+
+#shilling 1|20 britainpound # Before decimalisation, there
+#oldpence 1|12 shilling # were 20 shillings to a pound,
+#farthing 1|4 oldpence # each of twelve old pence
+#guinea 21 shilling # Still used in horse racing
+#crown 5 shilling
+#florin 2 shilling
+#groat 4 oldpence
+#tanner 6 oldpence
+#brpenny 0.01 britainpound
+#pence brpenny
+#tuppence 2 pence
+#tuppenny tuppence
+#ha'penny halfbrpenny
+#hapenny ha'penny
+#oldpenny oldpence
+#oldtuppence 2 oldpence
+#oldtuppenny oldtuppence
+#threepence 3 oldpence # threepence never refers to new money
+#threepenny threepence
+#oldthreepence threepence
+#oldthreepenny threepence
+#oldhalfpenny halfoldpenny
+#oldha'penny oldhalfpenny
+#oldhapenny oldha'penny
+#brpony 25 britainpound
+
+# Canadian currency
+
+#loony 1 canadadollar # This coin depicts a loon
+#toony 2 canadadollar
+
#
# Units used for measuring volume of wood
#
cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood
@@ -3505,10 +4055,15 @@
wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard
# deal it's called a "whole deal"!
splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal.
+# Used for shellac mixing rate
+
+poundcut pound / gallon
+lbcut poundcut
+
#
# Gas and Liquid flow units
#
FLUID_FLOW VOLUME / TIME
@@ -3579,11 +4134,156 @@
scfm atm ft^3/min
slpm atm liter/min
slph atm liter/hour
lusec liter micron Hg / s # Used in vacuum science
+# US Standard Atmosphere (1976)
+# Atmospheric temperature and pressure vs. geometric height above sea level
+# This definition covers only the troposphere (the lowest atmospheric
+# layer, up to 11 km), and assumes the layer is polytropic.
+# A polytropic process is one for which PV^k = const, where P is the
+# pressure, V is the volume, and k is the polytropic exponent. The
+# polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article
+# https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse
+# the definitions of "exponent" and "index." The functions below assume
+# the following parameters:
+
+# temperature lapse rate, -dT/dz, in troposphere
+
+lapserate 6.5 K/km # US Std Atm (1976)
+
+# air molecular weight, including constituent mol wt, given
+# in Table 3, p. 3
+
+air_1976 78.084 % 28.0134 \
+ + 20.9476 % 31.9988 \
+ + 9340 ppm 39.948 \
+ + 314 ppm 44.00995 \
+ + 18.18 ppm 20.183 \
+ + 5.24 ppm 4.0026 \
+ + 2 ppm 16.04303 \
+ + 1.14 ppm 83.80 \
+ + 0.55 ppm 2.01594 \
+ + 0.087 ppm 131.30
+
+# universal gas constant
+R_1976 8.31432e3 N m/(kmol K)
+
+# polytropic index n
+polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1
+
+# If desired, redefine using current values for air mol wt and R
+
+polyndx polyndx_1976
+# polyndx air (kg/kmol) gravity/(R lapserate) - 1
+
+# for comparison with various references
+
+polyexpnt (polyndx + 1) / polyndx
+
+# The model assumes the following reference values:
+# sea-level temperature and pressure
+
+stdatmT0 288.15 K
+stdatmP0 atm
+
+# "effective radius" for relation of geometric to geopotential height,
+# at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no
+# relation to actual radius
+
+earthradUSAtm 6356766 m
+
+# Temperature vs. geopotential height h
+# Assumes 15 degC at sea level
+# Based on approx 45 deg latitude
+# Lower limits of domain and upper limits of range are those of the
+# tables in US Standard Atmosphere (NASA 1976)
+
+stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \
+ stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate
+
+# Temperature vs. geometric height z; based on approx 45 deg latitude
+stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \
+ stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT))
+
+# Pressure vs. geopotential height h
+# Assumes 15 degC and 101325 Pa at sea level
+# Based on approx 45 deg latitude
+# Lower limits of domain and upper limits of range are those of the
+# tables in US Standard Atmosphere (NASA 1976)
+
+stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
+ atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \
+ (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1))))
+
+# Pressure vs. geometric height z; based on approx 45 deg latitude
+stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
+ stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP))
+
+# Geopotential height from geometric height
+# Based on approx 45 deg latitude
+# Lower limits of domain and range are somewhat arbitrary; they
+# correspond to the limits in the US Std Atm tables
+
+geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \
+ (earthradUSAtm z) / (earthradUSAtm + z) ; \
+ (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht))
+
+# The standard value for the sea-level acceleration due to gravity is
+# 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949)
+# R_eff = 2 g_phi / denom
+# g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2)
+# or
+# g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2)
+# denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?)
+# There is no inverse function; the standard value applies at a latitude
+# of about 45.543 deg
+
+g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \
+ 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2
+
+# effective Earth radius for relation of geometric height to
+# geopotential height, as function of latitude (Harrison 1949)
+
+earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \
+ m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \
+ (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat))
+
+# References
+# Harrison, L.P. 1949. Relation Between Geopotential and Geometric
+# Height. In Smithsonian Meteorological Tables. List, Robert J., ed.
+# 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution.
+# NASA. US National Aeronautics and Space Administration. 1976.
+# US Standard Atmosphere 1976. Washington, DC: US Government Printing Office.
+
+# Gauge pressure functions
#
+# Gauge pressure is measured relative to atmospheric pressure. In the English
+# system, where pressure is often given in pounds per square inch, gauge
+# pressure is often indicated by 'psig' to distinguish it from absolute
+# pressure, often indicated by 'psia'. At the standard atmospheric pressure
+# of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696
+# psia; an automobile tire inflated to 31 psig has an absolute pressure of
+# 45.696 psia.
+#
+# With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5
+# bar)); with psig(), the units are taken as psi, so the example above of tire
+# pressure could be given as psig(31).
+#
+# If the normal elevation is significantly different from sea level, change
+# Patm appropriately, and adjust the lower domain limit on the gaugepressure
+# definition.
+
+Patm atm
+
+gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \
+ x + Patm ; gaugepressure+(-Patm)
+
+psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \
+ gaugepressure(x psi) ; ~gaugepressure(psig) / psi
+
+#
# Wire Gauge
#
# This area is a nightmare with huge charts of wire gauge diameters
# that usually have no clear origin. There are at least 5 competing wire gauge
# systems to add to the confusion. The use of wire gauge is related to the
@@ -3617,12 +4317,13 @@
#
# In addition to being used to measure wire thickness, this gauge is used to
# measure the thickness of sheets of aluminum, copper, and most metals other
# than steel, iron and zinc.
-wiregauge(g) units=[;m] range=[0,] \
+wiregauge(g) units=[1;m] range=(0,) \
1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92)
+awg() wiregauge
# Next we have the SWG, the Imperial or British Standard Wire Gauge. This one
# is piecewise linear. It was used for aluminum sheets.
brwiregauge[in] \
@@ -3702,17 +4403,118 @@
24 0.125 \
27 0.5 \
28 1
#
+# Imperial drill bit sizes are reported in inches or in a numerical or
+# letter gauge.
+#
+
+drillgauge[in] \
+ 1 0.2280 \
+ 2 0.2210 \
+ 3 0.2130 \
+ 4 0.2090 \
+ 5 0.2055 \
+ 6 0.2040 \
+ 7 0.2010 \
+ 8 0.1990 \
+ 9 0.1960 \
+ 10 0.1935 \
+ 11 0.1910 \
+ 12 0.1890 \
+ 13 0.1850 \
+ 14 0.1820 \
+ 15 0.1800 \
+ 16 0.1770 \
+ 17 0.1730 \
+ 18 0.1695 \
+ 19 0.1660 \
+ 20 0.1610 \
+ 22 0.1570 \
+ 23 0.1540 \
+ 24 0.1520 \
+ 25 0.1495 \
+ 26 0.1470 \
+ 27 0.1440 \
+ 28 0.1405 \
+ 29 0.1360 \
+ 30 0.1285 \
+ 31 0.1200 \
+ 32 0.1160 \
+ 33 0.1130 \
+ 34 0.1110 \
+ 35 0.1100 \
+ 36 0.1065 \
+ 38 0.1015 \
+ 39 0.0995 \
+ 40 0.0980 \
+ 41 0.0960 \
+ 42 0.0935 \
+ 43 0.0890 \
+ 44 0.0860 \
+ 45 0.0820 \
+ 46 0.0810 \
+ 48 0.0760 \
+ 51 0.0670 \
+ 52 0.0635 \
+ 53 0.0595 \
+ 54 0.0550 \
+ 55 0.0520 \
+ 56 0.0465 \
+ 57 0.0430 \
+ 65 0.0350 \
+ 66 0.0330 \
+ 68 0.0310 \
+ 69 0.0292 \
+ 70 0.0280 \
+ 71 0.0260 \
+ 73 0.0240 \
+ 74 0.0225 \
+ 75 0.0210 \
+ 76 0.0200 \
+ 78 0.0160 \
+ 79 0.0145 \
+ 80 0.0135 \
+ 88 0.0095 \
+ 104 0.0031
+
+drillA 0.234 in
+drillB 0.238 in
+drillC 0.242 in
+drillD 0.246 in
+drillE 0.250 in
+drillF 0.257 in
+drillG 0.261 in
+drillH 0.266 in
+drillI 0.272 in
+drillJ 0.277 in
+drillK 0.281 in
+drillL 0.290 in
+drillM 0.295 in
+drillN 0.302 in
+drillO 0.316 in
+drillP 0.323 in
+drillQ 0.332 in
+drillR 0.339 in
+drillS 0.348 in
+drillT 0.358 in
+drillU 0.368 in
+drillV 0.377 in
+drillW 0.386 in
+drillX 0.397 in
+drillY 0.404 in
+drillZ 0.413 in
+
+#
# Screw sizes
#
# In the USA, screw diameters are reported using a gauge number.
# Metric screws are reported as Mxx where xx is the diameter in mm.
#
-screwgauge(g) units=[;m] range=[0,] \
+screwgauge(g) units=[1;m] range=[0,) \
(.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013
#
# Abrasive grit size
#
@@ -3874,12 +4676,11 @@
600 10.55 \
800 7.65 \
1000 5.8 \
1200 3.8
-grit_ansibonded(x) units=[1;micron] domain=[4,1200] range=[3.8,4890] \
- ansibonded(x); ~ansibonded(grit_ansibonded)
+grit_ansibonded() ansibonded
# Like the bonded grit, the coated macrogrits below 240 are taken from the
# FEPA F table. Data above this is from the UAMA site. Note that the coated
# and bonded standards are evidently the same from 240 up to 600 grit, but
# starting at 800 grit, the coated standard diverges. The data from UAMA show
@@ -3888,11 +4689,11 @@
# smaller particle size variation.
#
# Because of this non-monotonicity from 600 grit to 800 grit this definition
# produces a warning about the lack of a unique inverse.
-ansicoated[micron] \
+ansicoated[micron] noerror \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
@@ -3931,12 +4732,11 @@
3000 4 \
4000 3 \
6000 2 \
8000 1.2
-grit_ansicoated(x) units=[1;micron] domain=[4,8000] range=[1.2,4890] \
- ansicoated(x); ~ansicoated(grit_ansicoated)
+grit_ansicoated() ansicoated
#
# Is this correct? This is the JIS Japanese standard used on waterstones
#
@@ -4029,10 +4829,177 @@
hardblackarkansas 6 micron
hardwhitearkansas 11 micron
washita 35 micron
#
+# Mesh systems for measuring particle sizes by sifting through a wire
+# mesh or sieve
+#
+
+# The Tyler system and US Sieve system are based on four steps for
+# each factor of 2 change in the size, so each size is 2^1|4 different
+# from the adjacent sizes. Unfortunately, the mesh numbers are
+# arbitrary, so the sizes cannot be expressed with a functional form.
+# Various references round the values differently. The mesh numbers
+# are supposed to correspond to the number of holes per inch, but this
+# correspondence is only approximate because it doesn't include the
+# wire size of the mesh.
+
+# The Tyler Mesh system was apparently introduced by the WS Tyler
+# company, but it appears that they no longer use it. They follow the
+# ASTM E11 standard.
+
+meshtyler[micron] \
+ 2.5 8000 \
+ 3 6727 \
+ 3.5 5657 \
+ 4 4757 \
+ 5 4000 \
+ 6 3364 \
+ 7 2828 \
+ 8 2378 \
+ 9 2000 \
+ 10 1682 \
+ 12 1414 \
+ 14 1189 \
+ 16 1000 \
+ 20 841 \
+ 24 707 \
+ 28 595 \
+ 32 500 \
+ 35 420 \
+ 42 354 \
+ 48 297 \
+ 60 250 \
+ 65 210 \
+ 80 177 \
+ 100 149 \
+ 115 125 \
+ 150 105 \
+ 170 88 \
+ 200 74 \
+ 250 63 \
+ 270 53 \
+ 325 44 \
+ 400 37
+
+# US Sieve size, ASTM E11
+#
+# The WS Tyler company prints the list from ASTM E11 in their catalog,
+# http://wstyler.com/wp-content/uploads/2015/11/Product-Catalog-2.pdf
+
+sieve[micron] \
+ 3.5 5600 \
+ 4 4750 \
+ 5 4000 \
+ 6 3350 \
+ 7 2800 \
+ 8 2360 \
+ 10 2000 \
+ 12 1700 \
+ 14 1400 \
+ 16 1180 \
+ 18 1000 \
+ 20 850 \
+ 25 710 \
+ 30 600 \
+ 35 500 \
+ 40 425 \
+ 45 355 \
+ 50 300 \
+ 60 250 \
+ 70 212 \
+ 80 180 \
+ 100 150 \
+ 120 125 \
+ 140 106 \
+ 170 90 \
+ 200 75 \
+ 230 63 \
+ 270 53 \
+ 325 45 \
+ 400 38 \
+ 450 32 \
+ 500 25 \
+ 625 20 # These last two values are not in the standard series
+ # but were included in the ASTM standard because they
+meshUS() sieve # were in common usage.
+
+# British Mesh size, BS 410: 1986
+# This system appears to correspond to the Tyler and US system, but
+# with different mesh numbers.
+#
+# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
+#
+
+meshbritish[micron] \
+ 3 5657 \
+ 3.5 4757 \
+ 4 4000 \
+ 5 3364 \
+ 6 2828 \
+ 7 2378 \
+ 8 2000 \
+ 10 1682 \
+ 12 1414 \
+ 14 1189 \
+ 16 1000 \
+ 18 841 \
+ 22 707 \
+ 25 595 \
+ 30 500 \
+ 36 420 \
+ 44 354 \
+ 52 297 \
+ 60 250 \
+ 72 210 \
+ 85 177 \
+ 100 149 \
+ 120 125 \
+ 150 105 \
+ 170 88 \
+ 200 74 \
+ 240 63 \
+ 300 53 \
+ 350 44 \
+ 400 37
+
+# French system, AFNOR NFX11-501: 1970
+# The system appears to be based on size doubling every 3 mesh
+# numbers, though the values have been agressively rounded.
+# It's not clear if the unrounded values would be considered
+# incorrect, so this is given as a table rather than a function.
+# Functional form:
+# meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron
+#
+# http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
+
+meshtamis[micron] \
+ 17 40 \
+ 18 50 \
+ 19 63 \
+ 20 80 \
+ 21 100 \
+ 22 125 \
+ 23 160 \
+ 24 200 \
+ 25 250 \
+ 26 315 \
+ 27 400 \
+ 28 500 \
+ 29 630 \
+ 30 800 \
+ 31 1000 \
+ 32 1250 \
+ 33 1600 \
+ 34 2000 \
+ 35 2500 \
+ 36 3150 \
+ 37 4000 \
+ 38 5000
+
+#
# Ring size. All ring sizes are given as the circumference of the ring.
#
# USA ring sizes. Several slightly different definitions seem to be in
# circulation. According to [15], the interior diameter of size n ring in
@@ -4044,11 +5011,11 @@
# 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One
# reference claimed that the original system was that each size was 1|10 inch
# circumference, but that source doesn't have an explanation for the modern
# system which is somewhat different.
-ringsize(n) units=[;in] domain=[2,] range=[1.6252,] \
+ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \
(1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018
# Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
# specified alphabetically and based on the ring inside diameter in steps of
# 1|64 inch. This system was replaced in 1987 by British Standard 6820 which
@@ -4086,16 +5053,16 @@
# Japanese sizes start with size 1 at a 13mm inside diameter and each size is
# 1|3 mm larger in diameter than the previous one. They are multiplied by pi
# to give circumference.
-jpringsize(n) units=[;mm] domain=[1,] range=[0.040840704,] \
+jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \
(38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)
# The European ring sizes are the length of the circumference in mm minus 40.
-euringsize(n) units=[;mm] (n+40) mm ; euringsize/mm + (-40)
+euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40)
#
# Abbreviations
#
@@ -4187,11 +5154,12 @@
# effective ionizers, and hence have
# higher RBE values.
#
# rem stands for Roentgen Equivalent
# Mammal
-
+banana_dose 0.1e-6 sievert # Informal measure of the dose due to
+ # eating one average sized banana
roentgen 2.58e-4 C / kg # Ionizing radiation that produces
# 1 statcoulomb of charge in 1 cc of
# dry air at stp.
rontgen roentgen # Sometimes it appears spelled this way
sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one
@@ -4236,10 +5204,11 @@
chlorine 35.4527
chromium 51.9961
cobalt 58.93320
copper 63.546
curium 247.0703
+deuterium 2.0141017778
dysprosium 162.50
einsteinium 252.083 # Longest lived
erbium 167.26
europium 151.965
fermium 257.0951 # Longest lived
@@ -4316,37 +5285,86 @@
ytterbium 173.04
yttrium 88.90585
zinc 65.39
zirconium 91.224
-# from NASA Earth Fact Sheet (accessed 4 November 2011)
+# Average molecular weight of air
+#
+# The atmospheric composition listed is from NASA Earth Fact Sheet (accessed
+# 28 August 2015)
# http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
-# Atmospheric composition:
-# Nitrogen (N2) 78.08%
-# Oxygen (O2) 20.95%
-# Argon (Ar) 9340 ppm
-# Carbon Dioxide (CO2) 380 ppm
-# Neon (Ne) 18.18 ppm
-# Helium (He) 5.24 ppm
-# Methane (CH4) 1.7 ppm
-# Krypton (Kr) 1.14 ppm
-# Hydrogen (H2) 0.55 ppm
+# Numbers do not add up to exactly 100% due to roundoff and uncertainty Water
+# is highly variable, typically makes up about 1%
-air 28.967
-
-
+air 78.08% nitrogen 2 \
+ + 20.95% oxygen 2 \
+ + 9340 ppm argon \
+ + 400 ppm (carbon + oxygen 2) \
+ + 18.18 ppm neon \
+ + 5.24 ppm helium \
+ + 1.7 ppm (carbon + 4 hydrogen) \
+ + 1.14 ppm krypton \
+ + 0.55 ppm hydrogen 2
#
# population units
#
people 1
person people
death people
capita people
percapita per capita
+# TGM dozen based unit system listed on the "dozenal" forum
+# http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are
+# proposed as an allegedly more rational alternative to the SI system.
+Tim 12^-4 hour # Time
+Grafut gravity Tim^2 # Length based on gravity
+Surf Grafut^2 # area
+Volm Grafut^3 # volume
+Vlos Grafut/Tim # speed
+Denz Maz/Volm # density
+Mag Maz gravity # force
+Maz Volm kg / oldliter # mass based on water
+
+Tm Tim # Abbreviations
+Gf Grafut
+Sf Surf
+Vm Volm
+Vl Vlos
+Mz Maz
+Dz Denz
+
+# Dozen based unit prefixes
+
+Zena- 12
+Duna- 12^2
+Trina- 12^3
+Quedra- 12^4
+Quena- 12^5
+Hesa- 12^6
+Seva- 12^7
+Aka- 12^8
+Neena- 12^9
+Dexa- 12^10
+Lefa- 12^11
+Zennila- 12^12
+
+Zeni- 12^-1
+Duni- 12^-2
+Trini- 12^-3
+Quedri- 12^-4
+Queni- 12^-5
+Hesi- 12^-6
+Sevi- 12^-7
+Aki- 12^-8
+Neeni- 12^-9
+Dexi- 12^-10
+Lefi- 12^-11
+Zennili- 12^-12
+
#
# Traditional Japanese units (shakkanhou)
#
# The traditional system of weights and measures is called shakkanhou from the
# shaku and the ken. Japan accepted SI units in 1891 and legalized conversions
@@ -5126,10 +6144,17 @@
℃ degC
℉ degF
K K # Kelvin symbol, U+212A
ℓ liter # unofficial abbreviation used in some places
¢ cent
+#£ britainpound
+#¥ japanyen
+#€ euro
+#₩ southkoreawon
+#₪ israelnewshekel
+#₤ lira
+#₨ rupee
Ω ohm # Ohm symbol U+2126
Ω ohm # Greek capital omega U+03A9
℧ mho
ʒ dram # U+0292
@@ -5137,13 +6162,13 @@
℥ ounce
℔ lb
ℎ h
ℏ hbar
‰ 1|1000
-‱ 1|10000
-′ ' # U+2032 '
-″ " # U+2033 "
+‱ 1|10000
+′ ' # U+2032
+″ " # U+2033
#
# Square unicode symbols starting at U+3371
#
@@ -5151,13 +6176,13 @@
㍲ da
㍳ au
㍴ bar
# ㍵ oV???
㍶ pc
-㍷ dm
-㍸ dm^2
-㍹ dm^3
+#㍷ dm invalid on Mac
+#㍸ dm^2 invalid on Mac
+#㍹ dm^3 invalid on Mac
㎀ pA
㎁ nA
㎂ µA
㎃ mA
㎄ kA
@@ -5224,11 +6249,11 @@
㏁ MΩ
㏃ Bq
㏄ cc
㏅ cd
㏆ C/kg
-㏈(x) units=[1;1] range=[0,] dB(x); ~dB(㏈)
+㏈() dB
㏉ Gy
㏊ ha
# ㏋ HP??
㏌ in
# ㏍ KK??
@@ -5239,19 +6264,19 @@
# ㏒ log
㏓ lx
㏔ mb
㏕ mil
㏖ mol
-㏗(x) units=[;mol/liter] range=[0,] pH(x); ~pH(㏗)
+㏗() pH
㏙ ppm
# ㏚ PR???
㏛ sr
㏜ Sv
㏝ Wb
-㏞ V/m
-㏟ A/m
-㏿ gal
+#㏞ V/m Invalid on Mac
+#㏟ A/m Invalid on Mac
+#㏿ gal Invalid on Mac
!endutf8
############################################################################
#
@@ -5263,9 +6288,10 @@
!unitlist hms hr;min;sec
!unitlist time year;day;hr;min;sec
!unitlist dms deg;arcmin;arcsec
!unitlist ftin ft;in;1|8 in
+!unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in
!unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
############################################################################
#