| Copyright | Copyright (C) 2006-2015 Bjorn Buckwalter |
|---|---|
| License | BSD3 |
| Maintainer | bjorn@buckwalter.se |
| Stability | Stable |
| Portability | GHC only |
| Safe Haskell | None |
| Language | Haskell2010 |
Numeric.Units.Dimensional.SIUnits
Contents
Description
Summary
This module defines the SI prefixes, the SI base units and the SI derived units. It also defines the units outside of the SI that are accepted for use with the SI. Any chapters, sections or tables referenced are from [1] unless otherwise specified.
References
- metre :: Num a => Unit Metric DLength a
- meter :: Num a => Unit Metric DLength a
- gram :: Fractional a => Unit Metric DMass a
- second :: Num a => Unit Metric DTime a
- ampere :: Num a => Unit Metric DElectricCurrent a
- kelvin :: Num a => Unit Metric DThermodynamicTemperature a
- mole :: Num a => Unit Metric DAmountOfSubstance a
- candela :: Num a => Unit Metric DLuminousIntensity a
- radian :: Num a => Unit Metric DPlaneAngle a
- steradian :: Num a => Unit Metric DSolidAngle a
- hertz :: Num a => Unit Metric DFrequency a
- newton :: Num a => Unit Metric DForce a
- pascal :: Num a => Unit Metric DPressure a
- joule :: Num a => Unit Metric DEnergy a
- watt :: Num a => Unit Metric DPower a
- coulomb :: Num a => Unit Metric DElectricCharge a
- volt :: Num a => Unit Metric DElectricPotential a
- farad :: Num a => Unit Metric DCapacitance a
- ohm :: Num a => Unit Metric DElectricResistance a
- siemens :: Num a => Unit Metric DElectricConductance a
- weber :: Num a => Unit Metric DMagneticFlux a
- tesla :: Num a => Unit Metric DMagneticFluxDensity a
- henry :: Num a => Unit Metric DInductance a
- lumen :: Num a => Unit Metric DLuminousFlux a
- lux :: Num a => Unit Metric DIlluminance a
- degreeCelsius :: Num a => Unit Metric DCelsiusTemperature a
- fromDegreeCelsiusAbsolute :: Floating a => a -> ThermodynamicTemperature a
- toDegreeCelsiusAbsolute :: Floating a => ThermodynamicTemperature a -> a
- becquerel :: Num a => Unit Metric DActivity a
- gray :: Num a => Unit Metric DAbsorbedDose a
- sievert :: Num a => Unit Metric DDoseEquivalent a
- katal :: Num a => Unit Metric DCatalyticActivity a
- minute :: Num a => Unit NonMetric DTime a
- hour :: Num a => Unit NonMetric DTime a
- day :: Num a => Unit NonMetric DTime a
- hectare :: Fractional a => Unit NonMetric DArea a
- litre :: Fractional a => Unit Metric DVolume a
- liter :: Fractional a => Unit Metric DVolume a
- tonne :: Num a => Unit Metric DMass a
- metricTon :: Num a => Unit Metric DMass a
- degree :: Floating a => Unit NonMetric DPlaneAngle a
- arcminute :: Floating a => Unit NonMetric DPlaneAngle a
- arcsecond :: Floating a => Unit NonMetric DPlaneAngle a
- degreeOfArc :: Floating a => Unit NonMetric DPlaneAngle a
- minuteOfArc :: Floating a => Unit NonMetric DPlaneAngle a
- secondOfArc :: Floating a => Unit NonMetric DPlaneAngle a
- astronomicalUnit :: Num a => Unit NonMetric DLength a
- deka :: Num a => Unit Metric d a -> Unit NonMetric d a
- deca :: Num a => Unit Metric d a -> Unit NonMetric d a
- hecto :: Num a => Unit Metric d a -> Unit NonMetric d a
- kilo :: Num a => Unit Metric d a -> Unit NonMetric d a
- mega :: Num a => Unit Metric d a -> Unit NonMetric d a
- giga :: Num a => Unit Metric d a -> Unit NonMetric d a
- tera :: Num a => Unit Metric d a -> Unit NonMetric d a
- peta :: Num a => Unit Metric d a -> Unit NonMetric d a
- exa :: Num a => Unit Metric d a -> Unit NonMetric d a
- zetta :: Num a => Unit Metric d a -> Unit NonMetric d a
- yotta :: Num a => Unit Metric d a -> Unit NonMetric d a
- deci :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- centi :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- milli :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- micro :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- nano :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- pico :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- femto :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- atto :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- zepto :: Fractional a => Unit Metric d a -> Unit NonMetric d a
- yocto :: Fractional a => Unit Metric d a -> Unit NonMetric d a
SI Base Units
These are the base units from section 4.1. To avoid a myriad of one-letter functions that would doubtlessly cause clashes and frustration in users' code we spell out all unit names in full, as we did for prefixes. We also elect to spell the unit names in singular form, as allowed by section 9.7 "Other spelling conventions".
We define the SI base units in the order of table 1.
SI Derived Units
From Table 3, SI derived units with special names and symbols, including the radian and steradian.
Celsius Temperature
A problematic area is units which increase proportionally to the base SI units but cross zero at a different point. An example would be degrees Celsius (see section 4.2.1.1). The author feels that it is appropriate to define a unit for use with relative quantities (taking only into account the proportionality) and complement the unit with functions for converting absolute values.
The function fromDegreeCelsiusAbsolute should be used in lieu of
"*~ degreeCelsius" when working with absolute temperatures. Similarily,
toDegreeCelsiusAbsolute should be used in lieu of "/~ degreeCelsius"
when working with absolute temperatures.
degreeCelsius :: Num a => Unit Metric DCelsiusTemperature a Source
fromDegreeCelsiusAbsolute :: Floating a => a -> ThermodynamicTemperature a Source
toDegreeCelsiusAbsolute :: Floating a => ThermodynamicTemperature a -> a Source
Units Admitted for Reasons of Safeguarding Human Health
The last units from Table 3 are SI derived units with special names and symbols admitted for reasons of safeguarding human health.
Units Accepted for Use with the SI
There are several units that are not strictly part of the SI but are either permanently or temporarily accepted for use with the SI. We define the permanently accepted ones in this module.
From Table 6, Units accepted for use with the SI.
We start with time which we grant exclusive rights to minute and
second.
Units of Plane Angle
Since minute and second are already in use for time we use
arcminute and arcsecond [2] for plane angle instead.
Alternate (longer) forms of the above. In particular degreeOfArc
can be used if there is a percieved need to disambiguate from e.g.
temperature.
degreeOfArc :: Floating a => Unit NonMetric DPlaneAngle a Source
minuteOfArc :: Floating a => Unit NonMetric DPlaneAngle a Source
secondOfArc :: Floating a => Unit NonMetric DPlaneAngle a Source
Units Formerly Defined By Experiment
We decline to provide here those units - listed in Table 7 - which, while accepted for use with the SI, have values which are determined experimentally. For versioning purposes, those units can be found in Numeric.Units.Dimensional.NonSI.
However, in 2012 the IAU redefined the astronomical unit as a conventional unit of length directly tied to the meter, with a length of exactly 149,597,870,700 m and the official abbreviation of au [3]. We therefore include it here.
SI Prefixes
Prefixes are used to form decimal multiples and submultiples of SI
Units as described in section 4.4. We will define the SI prefixes
in terms of the prefix function which applies a scale factor to a
unit.
By defining SI prefixes as functions applied to a Unit we satisfy
section 6.2.6 "Unacceptability of stand-alone prefixes".
We define all SI prefixes from Table 5. Multiples first.
Then the submultiples.