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NAME

       units - unit conversion

SYNOPSIS

       package require Tcl  8.1

       package require units  ?2.1?

       ::units::convert value targetUnits

       ::units::reduce unitString

       ::units::new name baseUnits

_________________________________________________________________

DESCRIPTION

       This  library  provides a conversion facility from a variety of scientific and engineering
       shorthand notations into floating point numbers.  This allows  application  developers  to
       easily convert values with different units into uniformly scaled numbers.

       The  units  conversion facility is also able to convert between compatible units.  If, for
       example, a application is expecting a value in ohms (Resistance), and the  user  specifies
       units  of  milliwebers/femtocoulomb,  the conversion routine will handle it appropriately.
       An error will be generated if an incorrect conversion is attempted.

       Values are scaled from one set of units to another  by  dimensional  analysis.   Both  the
       value  units  and  the  target  units are reduced into primitive units and a scale factor.
       Units are checked for compatibility, and the scale factors are applied  by  multiplication
       and division.  This technique is extremely flexible and quite robust.

       New  units  and  new  unit  abbreviations  can  be  defined in terms of existing units and
       abbreviations.  It is also possible to define a new primitive  unit,  although  that  will
       probably  be  unnecessary.   New units will most commonly be defined to accommodate non-SI
       measurement systems, such as defining the unit inch as 2.54 cm.

COMMANDS

       ::units::convert value targetUnits
              Converts the value string into a floating point number,  scaled  to  the  specified
              targetUnits.   The  value  string  may  contain  a  number and units.  If units are
              specified, then they must be compatible with the targetUnits.   If  units  are  not
              specified for the value, then it will be scaled to the target units.  For example,
              % ::units::convert "2.3 miles" km
              3.7014912
              % ::units::convert 300m/s miles/hour
              671.080887616
              % ::units::convert "1.0 m kg/s^2" newton
              1.0
              % ::units::convert 1.0 millimeter
              1000.0

       ::units::reduce unitString
              Returns  a  unit  string consisting of a scale factor followed by a space separated
              list of sorted and reduced primitive units.  The reduced unit string may include  a
              forward-slash  (separated  from  the  surrounding  primitive  subunits  by  spaces)
              indicating that the remaining subunits are in the denominator.  Generates an  error
              if the unitString is invalid.
              % ::units::reduce pascal
              1000.0 gram / meter second second

       ::units::new name baseUnits
              Creates  a  new unit conversion with the specified name.  The new unit name must be
              only alphabetic (upper or lower case) letters.  The baseUnits string can consist of
              any  valid  units  conversion  string,  including  constant  factors, numerator and
              denominator parts, units with prefixes, and exponents.  The baseUnits  may  contain
              any  number  of  subunits,  but it must reduce to primitive units.  BaseUnits could
              also be the string -primitive to represent a new kind of quantity which  cannot  be
              derived  from  other  units.   But  you  probably would not do that unless you have
              discovered some kind of new universal property.
              % ::units::new furlong "220 yards"
              % ::units::new fortnight "14 days"
              % ::units::convert 100m/s furlongs/fortnight
              601288.475303

UNIT STRING FORMAT

       Value and unit string format is quite flexible.  It is possible to  define  virtually  any
       combination  of  units,  prefixes,  and  powers.  Valid unit strings must conform to these
       rules.

       •      A unit string consists of an  optional  scale  factor  followed  by  zero  or  more
              subunits.   The  scale factor must be a valid floating point number, and may or may
              not be separated from the subunits.  The scale factor could be negative.

       •      Subunits are separated form each other by one or more separator  characters,  which
              are  space  (" "), hyphen ("-"), asterisk ("*"), and forward-slash ("/").  Sure, go
              ahead and complain about using a minus sign ("-") to represent multiplication.   It
              just isn't sound mathematics, and, by rights, we should require everyone to use the
              asterisk ("*") to separate all units.  But the bottom line  is  that  complex  unit
              strings like m-kg/s^2 are pleasantly readable.

       •      The  forward-slash  seperator  ("/")  indicates  that following subunits are in the
              denominator.  There can be at most one forward-slash separator.

       •      Subunits can be floating point scale factors, but with the exception of the leading
              scale  factor,  they must be surrounded by valid separators.  Subunit scale factors
              cannot be negative. (Remember that the hyphen is a unit separator.)

       •      Subunits can be valid units or abbreviations.  They may include a prefix.  They may
              include  a plural suffix "s" or "es".  They may also include a power string denoted
              by a circumflex ("^"), followed by a  integer,  after  the  unit  name  (or  plural
              suffix,  if there is one).  Negative exponents are not allowed.  (Remember that the
              hyphen is a unit separator.)

   EXAMPLE VALID UNIT STRINGS
              Unit String              Reduced Unit String
              ------------------------------------------------------------
              meter                    1.0 meter
              kilometer                1000.0 meter
              km                       1000.0 meter
              km/s                     1000.0 meter / second
              /microsecond             1000000.0 / second
              /us                      1000000.0 / second
              kg-m/s^2                 1000.0 gram meter / second second
              30second                 30.0 second
              30 second                30.0 second
              30 seconds               30.0 second
              200*meter/20.5*second    9.75609756098 meter / second

SI UNITS

       The standard SI units are predefined according to NIST Special Publication 330.   Standard
       units  for both SI Base Units (Table 1) and SI Derived Units with Special Names (Tables 3a
       and 3b) are included here for reference.  Each standard unit  name  and  abbreviation  are
       included in this package.

   SI BASE UNITS
              Quantity                Unit Name    Abbr.
              ---------------------------------------------
              Length                  meter        m
              Mass                    kilogram     kg
              Time                    second       s
              Current                 ampere       A
              Temperature             kelvin       K
              Amount                  mole         mol
              Luminous Intensity      candela      cd

   SI DERIVED UNITS WITH SPECIAL NAMES
              Quantity                Unit Name    Abbr.   Units     Base Units
              --------------------------------------------------------------------
              plane angle             radian      rad     m/m       m/m
              solid angle             steradian   sr      m^2/m^2   m^2/m^2
              frequency               hertz       Hz                /s
              force                   newton      N                 m-kg/s^2
              pressure                pascal      Pa      N/m^2     kg/m-s^2
              energy, work            joule       J       N-m       m^2-kg/s^2
              power, radiant flux     watt        W       J/s       m^2-kg/s^3
              electric charge         coulomb     C                 s-A
              electric potential      volt        V       W/A       m^2-kg/s^3-A
              capacitance             farad       F       C/V       s^4-A^2/m^2-kg
              electric resistance     ohm                 V/A       m^2-kg/s^3-A^2
              electric conductance    siemens     S       A/V       s^3-A^2/m^2-kg
              magnetic flux           weber       Wb      V-s       m^2-kg/s^2-A
              magnetic flux density   tesla       T       Wb/m^2    kg/s^2-A
              inductance              henry       H       Wb/A      m^2-kg/s^2-A^2
              luminous flux           lumen       lm                cd-sr
              illuminance             lux         lx      lm/m^2    cd-sr/m^2
              activity (of a
              radionuclide)           becquerel   Bq                /s
              absorbed dose           gray        Gy      J/kg      m^2/s^2
              dose equivalent         sievert     Sv      J/kg      m^2/s^2

       Note that the SI unit kilograms is actually implemented as grams because 1e-6 kilogram = 1
       milligram, not 1 microkilogram.  The abbreviation for Electric Resistance (ohms), which is
       the omega character, is not supported.

       Also  note  that  there  is  no  support  for Celsius or Farenheit temperature.  The units
       conversion routines can only scale values with multiplication and division, so it  is  not
       possible  to  convert from thermodynamic temperature (kelvins) to absolute degrees Celsius
       or Farenheit.  Conversion of thermodynamic quantities, such as thermal expansion (per unit
       temperature), however, are easy to add to the units library.

       SI  Units  can  have  a  multiple  or sub-multiple prefix.  The prefix or its abbreviation
       should appear before the unit, without spaces.  Compound prefixes are not allowed,  and  a
       prefix  should  never  be  used  alone.   These prefixes are defined in Table 5 of Special
       Publication 330.

   SI PREFIXES
              Prefix Name     Abbr.   Factor
              ---------------------------------------
              yotta           Y       1e24
              zetta           Z       1e21
              exa             E       1e18
              peta            P       1e15
              tera            T       1e12
              giga            G       1e9
              mega            M       1e6
              kilo            k       1e3
              hecto           h       1e2
              deka            da      1e1
              deca                    1e1
              deci            d       1e-1
              centi           c       1e-2
              milli           m       1e-3
              micro           u       1e-6
              nano            n       1e-9
              pico            p       1e-12
              femto           f       1e-15
              atto            a       1e-18
              zepto           z       1e-21
              yocto           y       1e-24

       Note that we define the same prefix with  both  the  USA  ("deka")  and  non-USA  ("deca")
       spellings.   Also  note  that we take the liberty of allowing "micro" to be typed as a "u"
       instead of the Greek character mu.

       Many non-SI units are commonly  used  in  applications.   Appendix  B.8  of  NIST  Special
       Publication  811  lists many non-SI conversion factors.  It is not possible to include all
       possible unit definitions in this package.   In  some  cases,  many  different  conversion
       factors  exist  for  a  given  unit, depending on the context. (The appendix lists over 40
       conversions for British thermal units!)  Application specific conversions  can  always  be
       added  using  the new command, but some well known and often used conversions are included
       in this package.

   NON-SI UNITS
              Unit Name            Abbr.    Base Units
              --------------------------------------------------
              angstrom                      1.0E-10 m
              astronomicalUnit     AU       1.495979E11 m
              atmosphere                    1.01325E5 Pa
              bar                           1.0E5 Pa
              calorie                       4.1868 J
              curie                         3.7E10 Bq
              day                           8.64E4 s
              degree                        1.745329E-2 rad
              erg                           1.0E-7 J
              faraday                       9.648531 C
              fermi                         1.0E-15 m
              foot                 ft       3.048E-1 m
              gauss                         1.0E-4 T
              gilbert                       7.957747E-1 A
              grain                gr       6.479891E-5 kg
              hectare              ha       1.0E4 m^2
              hour                 h        3.6E3 s
              inch                 in       2.54E-2 m
              lightYear                     9.46073E15 m
              liter                L        1.0E-3 m^3
              maxwell              Mx       1.0E-8 Wb
              mho                           1.0 S
              micron                        1.0E-6 m
              mil                           2.54E-5 m
              mile                 mi       1.609344E3 m
              minute               min      6.0E1 s
              parsec               pc       3.085E16 m
              pica                          4.233333E-3 m
              pound                lb       4.535924E-1 kg
              revolution                    6.283185 rad
              revolutionPerMinute  rpm      1.047198E-1 rad/s
              yard                 yd       9.144E-1 m
              year                          3.1536E7 s

   QUANTITIES AND DERIVED UNITS WITH SPECIAL NAMES
       This units conversion package is limited specifically to unit reduction,  comparison,  and
       scaling.   This  package  does  not  consider any of the quantity names for either base or
       derived units.  A similar implementation or an extension in  a  typed  or  object-oriented
       language  might  introduce  user defined types for the quantities.  Quantity type checking
       could be used, for example, to ensure that all length values properly reduced  to  meters,
       or that all velocity values properly reduced to meters/second.

       A  C  implementation  of  this  package  has  been created to work in conjunction with the
       Simplified Wrapper Interface Generator  (http://www.swig.org/).   That  package  (units.i)
       exploits  SWIG's  typemap  system  to  automatically  convert script quantity strings into
       floating point quantities.  Function arguments are  specified  as  quantity  types  (e.g.,
       typedef float Length), and target units (expected by the C application code) are specified
       in an associative array.  Default units are also defined for each quantity type,  and  are
       applied to any unit-less quantity strings.

       A  units system enhanced with quantity type checking might benefit from inclusion of other
       derived types which are expressed in terms of special units, as illustrated in Table 2  of
       NIST  Publication 330.  The quantity area, for example, could be defined as units properly
       reducing to meter^2, although the utility  of  defining  a  unit  named  square  meter  is
       arguable.

REFERENCES

       The  unit  names, abbreviations, and conversion values are derived from those published by
       the United States Department of Commerce Technology Administration, National Institute  of
       Standards  and Technology (NIST) in NIST Special Publication 330: The International System
       of Units (SI) and NIST Special Publication 811: Guide for the  Use  of  the  International
       System of Units (SI).  Both of these publications are available (as of December 2000) from
       http://physics.nist.gov/cuu/Reference/contents.html

       The ideas behind implementation of this package is based in part on code written  in  1993
       by  Adrian  Mariano  which performed dimensional analysis of unit strings using fixed size
       tables of C structs.  After going missing in the late 1990's, Adrian's code has reappeared
       in the GNU Units program at http://www.gnu.org/software/units/

AUTHORS

       Robert W. Techentin

BUGS, IDEAS, FEEDBACK

       This  document,  and  the  package  it  describes, will undoubtedly contain bugs and other
       problems.   Please  report  such  in  the  category  units  of  the  Tcllib  SF   Trackers
       [http://sourceforge.net/tracker/?group_id=12883].    Please  also  report  any  ideas  for
       enhancements you may have for either package and/or documentation.

KEYWORDS

       angle, constants, conversion, distance, radians, unit

COPYRIGHT

       Copyright (c) 2000-2005 Mayo Foundation