units -
Convert and manipulate quantities with units
package require units ?1.0? units::convert value targetUnits units::reduce unitString units::new name baseUnits
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".
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.
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
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.
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
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) bacquerel 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 temperature. The units conversion routines can only scale values with multiplication and division, and the abbreviation "C" (which is the closest one could get to "degrees C" using the degrees symbol) is already used by Electric Potential.
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.
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.
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 9.144E-1 m year yd 3.1536E7 s
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.
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.