PhysicalValues/en

Expecco supports values with units to represent physical values such as length, acceleration, area, volume, mass, temperature etc.

Physical values are useful for a nicer presentation of values (eg. in a report) and to convert between unit systems (eg. metric vs. imperial vs. US).

Physical values are implemented by the underlying Smalltalk system and can be used in JavaScript and Smalltalk elementary blocks. Similar public domain packages are available for Node and Python actions - these have to be installed with "rpm"or "pip".

Base Units

All base units are measured in their corresponding SI standard units and print with an appropriate scaling prefix.

For example, a mass, which has a base unit of kilogram ("kg") will print itself as "kg', 'mg', 'µg' etc. depending on its magnitude. Explicit converters can be used to enforce a particular unit printing (eg. if you insist on printing a mass in pounds, in grams, etc.). See examples below on how those converters affect the printout of a value.

Base units are:

s	second	    time
m	metre	    length
kg	kilogram    mass
A	ampere	    electric current
K	kelvin	    temperature
mol	mole	    amount of substance
cd	candela	    luminous intensity

Derived Units

Additional derived units are:

V      volt                voltage
Hz     hertz               frequency
m/s    meter per second    speed, velocity
m/s²   m/s per second      acceleration
m²     square meter        area
m³     cubic meter         volume
pa     pascal              pressure
w      watt                power
N      newton              force
J      joule               energy
Ω      ohm                 electric resistance
C      coulomb             electric charge
F      farad               electric capacitance

SI Prefix

Numbers can be scaled by an SI prefix message. For example, without si prefix:

1 gram -> '1 g'

whereas with a 'micro' prefix:

1 micro gram -> '1 µg'

and:

1 hecto liter -> '100 liter'

Possible scaling prefixes are:

yocto   1E-24   1 / 1000000000000000000000000 
zepto   1E-21   1 / 1000000000000000000000 
atto    1E-18   1 / 1000000000000000000
femto   1E-15   1 / 1000000000000000
pico    1E-12   1 / 1000000000000
nano    1E-9    1 / 1000000000
micro   1E-6    1 / 1000000
milli   1E-3    1 / 1000
centi   1E-2    1 / 100
deci    1E-1    1 / 10
deca    1E+1    10
hecto   1E+2    100
kilo    1E+3    1000
mega    1E+6    1000000
giga    1E+9    1000000000
tera    1E+12   1000000000000
peta    1E+15   1000000000000000
exa     1E+18   1000000000000000000
zetta   1E+21   1000000000000000000000
yotta   1E+24   1000000000000000000000000

Unit API

PhysicalValue instances can be created by sending the "amount:" message to a Unit.
For example:

Physics energy amount:100

generates an energy instance of 100 joule.

For the most common units, additional protocol is provided in the Number class (eg. "100 joules"). The additional protocol is described below.

When printed, physical values will scale and use an SI prefix as appropriate. Thus, by default, a value of 100 millimeter will print as "100 mm" instead of "0.1 m".

This print behavior can be changed by converting to an explicit unit via one of the "asXXX" messages listed below. However, the correct amount will be used in arithmetic operations. Thus, eg. when adding a meter with inches, the correct value will be generated, and the result will be presented in the same unit as the receiver (first operand). For example, "1 meter + 1 inch asInches" will print as meter, whereas "1 inch asInches + 1 meter" will print as inches.

Mass

Mass is measured in units of kilogram. The following operations return an instance of a mass (i.e. a value with a unit of "Mass"):

• number kiloGram
  Generates a mass-value of n kilograms. Same as n kilo gram.

• number gram
  Generates a mass-value of n grams.

• number milliGram
  Generates a mass-value of n milligrams. Same as n milli gram.

• number microGram
  Generates a mass-value of n micrograms. Same as n micro gram.

• number pounds
  Generates a mass-value of n pounds. A pound is 453.59237 gram.

Conversion

• aMass asGrams
  Returns the original mass but enforces explicit printing in grams (i.e. without any SI scaling prefix).

• aMass asMilliGrams
  Enforces explicit printing in milligrams ("mg").

• aMass asMicroGrams
  Enforces explicit printing in micrograms ("µg").

• aMass asKiloGrams
  Enforces explicit printing in kilograms ("kg").

• aMass asPounds
  Enforces explicit printing in pounds ("lb").

Length

Length is measured in meters.

• number meter
  Generates a length-value of n meters.

• number centiMeter
  Generates a length-value of n centimeters. Same as n centi meter.

• number milliMeter
  Generates a length-value of n millimeters. Same as n milli meter.

• number microMeter
  Generates a length-value of n micrometers. Same as n micro meter.

• number nanoMeter
  Generates a length-value of n nanometers. Same as n nano meter.

• number kiloMeter
  Generates a length-value of n kilometers. Same as n kilo meter.

• number inch
  Generates a length-value of n inches. An inch is 25.4 mm.

• number feet
  Generates a length-value of n feet. A foot is 0.3048 m.

• number landMiles
  Generates a length-value of n landMiles. A landMile is 5280 feet or 1609.344 m.

• number nauticalMiles
  Generates a length-value of n nauticalMiles. A nauticalMile is 1852 m.

• number astronomicalUnits
  Generates a length-value of n astronomical units. An au is 149597870.7 km.

• number lightSeconds
  Generates a length-value of n lightseconds. An ls is 299792.458 km.

• number lightYears
  Generates a length-value of n lightyears. An ly is 9460730472580.8 km.

• number angstrom
  Generates a length-value of n angstroms. 1 Å = 0,1 = 10E−10 m.

Conversion

• aLength asMeters
  Returns the original length but enforces explicit printing in meters (i.e. prevents scaling prefix when printed).

• aLength asMilliMeters
  Enforces explicit printing in millimeters ("mm").

• aLength asMicroMeters
  Enforces explicit printing in micrometers ("µm").

• aLength asNanoMeters
  Enforces explicit printing in nanometers ("nm").

• aLength asKiloMeters
  Enforces explicit printing in kilometers ("km").

• aLength asInches
  Enforces explicit printing in inches ("in").

• aLength asFeet
  Enforces explicit printing in feet ("ft").

• aLength asYards
  Enforces explicit printing in yards ("yd").

• aLength asFeetAndInches
  Enforces explicit printing in feet and inches (inches rounded to 4 digits).

• aLength asLightYears
  Enforces explicit printing in lightyears ("ly").

Temperature

• number kelvin
  Generates an temperature-value of n Kelvin.

• number degreesCelcius
  Generates an temperature-value of n degrees Celsius.

• number degreesFahrenheit
  Generates an temperature-value of n degrees Fahrenheit.

• number rankine
  Generates an temperature-value of n degrees Rankine.

Conversion

• aTemperature asFahrenheit
  Returns the original temperature but enforces explicit printing in Fahrenheit.

• aTemperature asCelsius
  Enforces explicit printing in degrees celsius.

Frequency

• number hertz
  Generates an frequency-value of n hertz.

• number kiloHertz
  Generates an frequency-value of n kilohertz. Same as n kilo hertz.

• number megaHertz
  Generates an frequency-value of n megahertz. Same as n mega hertz.

• number gigaHertz
  Generates an frequency-value of n gigahertz. Same as n giga hertz.

Conversion

• aFrequency asKiloHertz
  Returns the original frequency but enforces explicit printing in kilohertz ("kHz").

• aFrequency asMegaHertz
  Enforces explicit printing in megahertz ("mHz").

• aFrequency asGigaHertz
  Enforces explicit printing in gigahertz ("gHz").

Energy

• number joule
  Generates an energy-value of n joule.

• number kiloJoule
  Generates an energy-value of n kilojoule. Same as n kilo joule .

• number megaJoule
  Generates an energy-value of n megajoule. Same as n mega joule .

• number wattHours
  Generates an energy-value of n wattHours. Same as n watt * 1 hours.

• number kiloWattHours
  Generates an energy-value of n kiloWattHours. Same as n kilo wattHours and also the same as n kilo watt * 1 hours.

• number megaWattHours
  Generates an energy-value of n megaWattHours. Same as n mega wattHours and also the same as n mega watt * 1 hours.

• number electronVolts
  Generates an energy-value of n electronVolts.

• number btu
  Generates an energy-value of n BTUs (british thermal units).

• number calories
  Generates an energy-value of n calories.

• number kiloCalories
  Generates an energy-value of n kcal.

Converting

• energy asElectronVolts
  Present as electronVolts

• energy asKiloWattHours
  Present as kiloWattHours

• energy asMegaWattHours
  Present as megaWattHours

• energy asGigaWattHours
  Present as gigaWattHours

• energy asBTUs
  Present as BTUs (British Thermal Units)

• energy asCalories
  Present as calories

• energy asKiloCalories
  Present as kilo calories

Power

• number watt
  Generates a power-value of n watt.

• number kiloWatt
  Generates a power-value of n kiloWatt. Same as n kilo watt .

• number megaWatt
  Generates a power-value of n megaWatt. Same as n mega watt .

• number gigaWatt
  Generates a power-value of n gigaWatt. Same as n giga watt .

Converting

• power asKiloWattHours
  Presents itself as kWh

• power asMegaWattHours
  Presents itself as mWh

• area asGigaWattHours
  Presents itself as gWh

Force

• number newton
  Generates a force-value of n newton.

Area

• number squareMeter
  Generates an area-value of n square meters.

• number hectare
  Generates an area-value of n hectares. Same as n hecto are .

• number are
  Generates an area-value of n ares. 1 are being 10 m².

• number squareFeet
  Generates an area-value of n square feet. 1 sq ft being 0.0929 m².

• number acres
  Generates an area-value of n acres. 1 acre being 4046.856 m².

Converting

• area asSquareFeet
  Presents itself as square feet

• area asHectare
  Presents itself as hectare

• area asAcres
  Presents itself as acres

Volume

• number cubicMeter
  Generates an volume-value of n cubic meters (1000 l).

• number liter
  Generates an volume-value of n liters.

• number milliLiter
  Generates a volume-value of n milliliters. Same as n milli liter.

• number hectoLiter
  Generates a volume-value of n hectoliters. Same as n hecto liter.

• number barrel
  Generates a volume of n barrels (oil volume measurement).

• number flozGB
  Generates a volume of n imperial fluid ounces (0.02841 liter).

• number flozUS
  Generates a volume of n US fluid ounces (0.02957 liter).

• number pintGB
  Generates a volume of n imperial pints (568.26125 ml).

• number pintUS
  Generates a volume of n US pints (473.176473 ml).

• number quartGB
  Generates a volume of n imperial quarts (1.1365 liter).

• number quartUS
  Generates a volume of n US quarts (946.353 ml).

• number gallonGB
  Generates a volume of n imperial gallons (4.5461 liter).

• number gallonUS
  Generates a volume of n US gallons (3.7854 liter).

Converting

• volume asCubicMeters
  Presents itself as cubic meters

• volume asFlozGB
  Presents itself as imperial fluid ounces

• volume asFlozUS
  Presents itself as US fluid ounces

• volume asGallonsGB
  Presents itself as imperial gallons

• volume asGallonsUS
  Presents itself as US gallons

• volume asHectoLiters
  Presents itself as hectoliters

• volume asMilliLiters
  Presents itself as milliliters

Velocity (Speed)

• number meterPerSecond
  Generates a velocity of n meters per second.

• number kiloMeterPerHour
  Generates a velocity of n km per hour.

• number milesPerHour
  Generates a velocity of n mph.

• number knots
  Generates a velocity of n nautical miles per hour.

Converting

• volume asKiloMetersPerHour
  Presents itself as km/h

• volume asMilesPerHour
  Presents itself as mph

Acceleration

• number metersPerSecondPerSecond
  Generates an acceleration of n m/s².

Mass Density

This is a derived unit, which is generated when dividing a mass by a volume; eg:

10 kiloGram / 1 liter 

gives

'10000 kg / m³'

Arithmetic

Arithmetic on physical values will generate an appropriate physical value. Eg, when multiplying a velocity by a time, you will get a distances, or when dividing a distance by a time, you will get a velocity.

Acceleration

speed = acceleration * time

1 meterPerSecondPerSecond * 10 seconds -> 10 m/s
 
(1 meterPerSecondPerSecond distanceAfter:1 hours) -> 6480.0 km

Mass

force = mass * acceleration

1 kg * 1 meterPerSecondPerSecond -> 1 N

Examples

Smalltalk code + printed representation.

1 kiloGram + 10.0 gram -> '1.01 kg' 
10 gram -> '10 g'
10 gram asKiloGrams -> '0.01 kg'
10 gram asMilliGrams -> '10000 mg'

1 microGram -> '1 µg'
1 micro gram -> '1 µg'

1 pound -> '453.59237 g'
1 pound asKiloGrams -> '0.45359237 kg'
1 pound asPounds -> '1.0 lb' 
1 kiloGram asPounds -> '2.20462262184878 lb'

10 kiloMeters asMeters -> '10000 m'
1 micro inch -> '25.4 nm'
1.80 meter asFeetAndInches -> '5′10.866″'
1 yards -> '0.9144 m'

0 degreesCelsius -> '273.16 K'
0 degreesCelsius asFahrenheit -> '32.018 °F'
40 degreesFahrenheit -> '277.59 K'
60 degreesFahrenheit asCelsius -> '15.556 °C'
40 degreesFahrenheit asKelvin -> '277.59 K'
10 kelvin -> '10 K'
100 rankine -> '55.556 K'

1 joule asElectronVolts -> '6.24150912550149E+18 eV'
10 electronVolts -> 1.6021766208E-18 J
1000 joule asKiloWattHours -> '0.000278 kWh'
1000.0 kiloJoule asKiloWattHours -> 0.2778 kWh

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