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QUDT - Quantities, Units, Dimensions and Data Types Ontologies

March 18, 2014

Authors:
Ralph Hodgson, TopQuadrant, Inc.
Paul J. Keller, NASA AMES Research Center
Jack Hodges
Jack Spivak

Overview

The QUDT Ontologies, and derived XML Vocabularies, are being developed by TopQuadrant and NASA. Originally, they were developed for the NASA Exploration Initiatives Ontology Models (NExIOM) project, a Constellation Program initiative at the AMES Research Center (ARC). They now for the basis of the NASA QUDT Handbook to be published by NASA Headquarters.

Status

The current release of the QUDT ontologies is version 1.1 and may be downloaded from the QUDT Catalog, which can also be accessed from LinkedModel.org.

Release 2 of QUDT will be published incrementally. Currently the content, in the form of the NASA QUDT Handbook, is being reviewed by NASA.

A presentation on QUDT can be found at scribd.com/ralphtq.

Goals

The goals of QUDT are to provide:

  1. A standardized consistent vocabulary, focused on terminology used in science and engineering.
    1. The vocabulary in this standard consists of standardized terminology, definitions, identifiers, and information models.
    2. The intent is to use this vocabulary with a variety of encodings, formats, and data definitions, so it is defined independent of those forms.
    3. Some or all portions of this vocabulary will be of interest to various users and applications, depending on the use case and policy mandates.
    4. It is expected that a large set of existing corpus will not be changed, and so this standard serves as a critical “Rosetta Stone” to reference existing uses of quantities, units, dimensions, and types to a consistent base.
  2. A set of consistent coded identifiers, for human and machine use.
    1. In the same way that modern digital computers could not represent and process meaningful information without the use of standards such as ASCII and Unicode, this standard also introduces a similar coding scheme, for a like purpose.
    2. Assigning an explicit designator (e.g. ASCII uses a numerical value for each letter of the alphabet, numbers, and punctuation) to quantities, units, dimensions, and types is used to provide a robust, unequivocal method of identification of digital information by computer software and hardware.
    3. This definitional approach provides generalized usability for both humans and machines, avoiding problems with uncertainty and misinterpretation.
  3. A collection of foundational vocabularies that can serve a variety of applications. Some examples include:
    1. providing terminology and vocabulary definitions for Documents and Publications. Define consistent terminology for general Program and Project documentation, technical reports, conference papers, guides, drawings, technical specifications, engineering and process documentation, etc.
    2. defining software code documentation, pragmas and/or comments, and independent reference documentation. Referencing system and software variables and constants provides explicit, unambiguous definitions that can be used for data exchanges, semantic consistency, automated checking, software reuse, and more robust search and discovery.
    3. improving the quality of software interfaces, web services, and data exchanges. The model basis of this standard can be used by other software, or to build software, for a variety of purposes; model creation, validation, compilation and run-time checking, translation and transformation, data exchange definitions, etc.
    4. generating schema specifications and data definitions in other formalisms. Examples include database, data file (ex, XML) schema, software application data structures, code-lists, and other controlled vocabularies.
    5. enabling files, datasets, messages, communications and Data Exchange Packages to use consistent terms and constructs when defining elements of datasets and messages in a variety of forms and formats.
  4. A framework designed for extensibility and evolution, but model-based (instead of just a typical dictionary) and governed.
    1. The authors recognize that any given release will not have every possible quantity, unit, dimension, or type that a user may need.
    2. The framework has been designed to grow in a consistent manner.

QUDT Ontologies and Vocabularies

The QUDT Specification is more than a list of quantities, units, dimensions, data types, enumerations, and structures. In order to provide for interoperability and data exchange between information systems, the specification needs to be available in a machine processable form, with no ambiguities.

For these reasons, the QUDT approach to specifying quantities, units, dimensions, data types, enumerations, and other data structures is to use precise semantically grounded specifications in an ontology model with translation into machine-processable representations.

Ontologies provide the object-oriented strengths of encapsulation, inheritance, and polymorphism, strengths which are unavailable in other structured modeling approaches. The characteristics modeled in QUDT require a model-based approach because they are functionally dependent.

Modeling one without modeling its dependency on the other requires that the understanding of those dependencies be carried by the observer, which injects ambiguity into the modeling approach. These models (dimensions, coordinate systems, etc.), like everything else, are hierarchical, so using a language to model them which doesn't support inheritance imposes constraints on the models and their use which, again, results in ambiguity.

QUDT semantics are based on dimensional analysis expressed in the OWL Web Ontology Language (OWL). The dimensional approach relates each unit to a system of base units using numeric factors and a vector of exponents defined over a set of fundamental dimensions. In this way, the role of each base unit in the derived unit is precisely defined. A further relationship establishes the semantics of units and quantity kinds. By this means, QUDT supports reasoning over quantities as well as units.

All QUDT models may be translated into other representations for machine processing, or other programming language structures according to need.

An overview of the ontological structure of QUDT is provided below.

Ontology Class Structure

The diagram below, exported from TopBraid Composer, illustrates the main class structure of the QUDT ontology in OWL.

Quantities, Quantity Kinds, and Quantity Values

A Quantity is an observable property of an object, event or system that can be measured and quantified numerically. Quantities are differentiated by two attributes which together comprise the essential parameters needed to formalize the structure of quantities: kind and magnitude. The kind attribute of a quantity identifies the observable property quantified, e.g. length, force, frequency; the magnitude of the quantity expresses its relative size compared to other quantities of the same kind.

For example, the speed of light in a vacuum and the escape velocity of the Earth are both quantities of the kind speed but are of different magnitudes. The speed of light in a vacuum is greater than the escape velocity of the Earth. More generally, the speed of light in a vacuum is comparable to the escape velocity of the Earth. Thus, if two quantities are of the same kind, their magnitudes can be compared and ordered. However, the same is not true if the quantities are of different kinds. There is no intrinsic way to compare the magnitude of a quantity of mass with the magnitude of a quantity of length.

Quantities may arise from definition or convention, or they may be the result of one or a series of experiments and measurements. In the first case, the quantity is exact; in the second case, measurement uncertainty cannot be discounted so the expression of a quantity's magnitude must account for the parameters of uncertainty.

Quantity Kinds

A Quantity Kind is any observable property that can be measured and quantified numerically. Familiar examples include physical properties such as length, mass, time, force, energy, power, electric charge, etc. Less familiar examples include currency, interest rate, price to earning ratio, and information capacity.

Unit of Measure

A Unit of Measure or Unit is a particular quantity of a given kind that has been chosen as a scale for measuring other quantities of the same kind. For example, the Meter is a quantity of length that has been empirically defined by the BIPM. Any quantity of length can be expressed as a number multiplied by the unit meter.

More formally, the value of a quantity Q with respect to a unit (U) is expressed as the scalar multiple of a real number (n) and U:

Q = nU

Quantity Value

A quantity value expresses the magnitude and kind of a quantity and is given by the product of a numerical value n and a unit of measure U. The number multiplying the unit is referred to as the numerical value of the quantity expressed in that unit. Refer to NIST SP 811 section 7 for more on quantity values.

Numerical Quantity Value

The numerical value of a quantity is the numerical value without the unit of measure. For example, the value of Planck's constant in Joule-Seconds (J s) is approximately 6.62606896E-34, whereas the value in Erg-Seconds (erg s) is approximately 6.62606896E-27. The numerical value of a quantity n is a mere scaling factor for the unit U. It is the product of the two, n X U, that expresses the value (magnitude and quantity kind) of the unit.

Quantity Symbol

In the same way that a unit has a symbol, a quantity also has a symbol. For example a quantity of the (quantity) kind mass usually has the symbol m. Each quantity kind has a recommended symbol associated with it. For example, t for time, Q for charge, v for velocity, T for temperature, P for power and p for pressure. A quantity usually receives a symbol that consists of the symbol of its quantity kind and an optional subscript. Symbols for quantities should be chosen according to the international recommendations from ISO/IEC~80000, the IUPAP red book and the IUPAC green book.

The OWL model for the classes qudt:QuantityKind, qudt:Quantity, qudt:QuantityValue, qudt:Unit is shown below.

Systems of Quantities and Units

The art and science of defining, standardizing, and organizing quantity kinds and units is ancient and modern. Today, scientific boards and standards bodies maintain rigorous definitions for quantity kinds and units. The definitions of quantity kinds and their relationships are derived from physical laws and mathematical transformations. Units are defined by experimental observations, by the application of physical laws, as ratios of fundamental physical constants, or by reference. One significant advance in the modern treatment of metrology has been the use of logic and mathematics to organize quantity kinds and units into systems and to analyze the relationships between them.

A system of quantity kinds is a set of one or more quantity kinds together with a set of zero or more algebraic equations that define relationships between quantity kinds in the set. In the physical sciences, the equations relating quantity kinds are typically physical laws and definitional relations, and constants of proportionality. Examples include Newton’s First Law of Motion, Coulomb’s Law, and the definition of velocity as the instantaneous change in position.

In almost all cases, the system identifies a subset of base quantity kinds. The base set is chosen so that all other quantity kinds of interest can be derived from the base quantity kinds and the algebraic equations.

A system of units is a set of units which are chosen as the reference scales for some set of quantity kinds together with the definitions of each unit. Units may be defined by experimental observation or by proportion to another unit not included in the system. If the unit system is explicitly associated with a quantity kind system, then the unit system must define at least one unit for each quantity kind.

Base and Derived Quantity Kinds

Many systems of quantity kinds identify a special subset of the included quantity kinds called the base quantity kinds. Base quantity kinds are typically chosen so that no base quantity kind can be expressed as an algebraic relation of one or more other base quantity kinds using only the constituent equations included in the system. A quantity kind that can be expressed as an algebraic relation of one or more base quantity kind is called a derived quantity kind. Thus, in any quantity kind system, the base set and derived set are disjoint.

Similarly, unit systems may distinguish between base units and derived units. A base unit is a unit of measurement for a base quantity, and a derived unit is a unit of measurement for a derived quantity. Unit systems define at least one base unit for each base quantity and at least one derived unit for each derived quantity.

Quantity Dimensions

Quantity kind systems that define base and derived sets have certain mathematical properties that permit quantity kinds to be manipulated symbolically. The construction goes as follows: Assign a distinct dimension symbol to each base quantity kind. For each derived quantity kind, take the formula that expresses it in terms of the base quantity kinds and replace every occurrence of a base quantity with its symbol. This is the dimension symbol for the derived quantity kind. In this way, every quantity kind maps to a dimension symbol of the form:

dim Q = (B1)d1(B2)d2…(Bn)dn

Here {B1,…,Bn} are the dimension symbols for the base quantities and {d1,…,dn} are rational numbers. Typically, the values of the di are between -3 and 3, however magnitudes as high as 7 are required to cover the range of quantity kinds currently defined. Using the multiplication identity for exponents AnAm = An+m one can show that the set of dimension symbols is homomorphic to an n-dimensional vector space over the rational numbers. Multiplication of quantity kinds corresponds to vector addition, division corresponds to vector subtraction, and inverting a quantity kind corresponds to computing the additive inverse of its dimension vector.

In some cases, distinct quantity kinds may have the same dimension symbol. This often occurs in cases where physical laws are discovered and formalized independently of each other, but reduce to the same base quantity kinds. A commonly quoted example is the dimensional equivalence of mechanical torque and energy. Both have the same dimensions (L2M1T-2) but are defined very differently.

One consequence of the equivalence is that the same units of measure are applicable to both. A salient difference between the two in this example is that torque is a pseudo-vector while energy is a scalar. However, this distinction (value type) is not accounted for in the quantity kind system formalism.

The OWL model of Dimensions is illustrated below.

Dimensionless Quantities and Units

Dimensionless Quantities, or quantities of dimension 1, are those for which all the exponents of the factors corresponding to the base quantities in its quantity dimension are zero. Counts, ratios and plane angles are examples of dimensionless quantities.

Allowed Units

Some unit systems identify units that are not defined within the system but are allowed to be used in combination with units that are defined within the system. Allowed units must be commensurable with some defined unit of the system, so that quantities expressed in the allowed unit may be converted to a defined unit. The SI System explicitly allows a number of non-SI units.

Example Quantity Kind and Unit Systems

This section contains tables of several of the quantity kind and unit systems that are currently defined in the ontology. The table columns are:

The SI System

SI Base and Derived Quantities and Units

Category

Quantity Kind

QName

Dimension Symbol

Unit

QName

Unit Symbol

Base

Dimensionless

quantity:Dimensionless

U

Unity

unit:Unity

U

Length

qunatity:Length

L

Meter

unit:Meter

m

Mass

quantity:Mass

M

Kilogram

unit:Kilogram

kg

Time

quantity:Time

T

Second

unit:SecondTime

s

Electric Current

quantity:ElectricCurrent

I

Ampere

unit:Ampere

A

Temperature

quantity:ThermodynamicTemperature

Θ

Kelvin

unit:Kelvin

K

Amount of Substance

quantity:AmountOfSubstance

N

Mole

unit:Mole

mol

Luminous Intensity

quantity:LuminousIntensity

J

Candela

unit:Candela

cd

Derived

Absorbed Dose

quantity:AbsorbedDose

L2T-2

Gray

unit:Gray

Gy

Absorbed Dose Rate

quantity:AbsorbedDoseRate

L2T-3

Gray per second

unit:GrayPerSecond

Gy/s

Activity

quantity:Activity

T-1

Becquerel

unit:Becquerel

Bq

Amount of Substance Per Unit Volume

quantity:AmountOfSubstancePerUnitVolume

L-3N1

Mole per cubic meter

unit:MolePerCubicMeter

mol/m^3

Amount of Substance per Unit Mass

quantity:AmountOfSubstancePerUnitMass

M-3N1

Mole per kilogram

unit:MolePerKilogram

mol/kg

Angular Acceleration

quantity:AngularAcceleration

U1T-2

Radian per second squared

unit:RadianPerSecondSquared

rad/s^2

Angular Mass

quantity:AngularMass

L2M1

Kilogram Meter Squared

unit:KilogramMeterSquared

kg-m^2

Angular Momentum

quantity:AngularMomentum

L2M1T-1

Joule Second

unit:JouleSecond

J s

Angular Velocity

quantity:AngularVelocity

U1T-1

Radian per second

unit:RadianPerSecond

rad/s

Area

quantity:Area

L2

Square meter

unit:SquareMeter

m^2

Area Angle

quantity:AreaAngle

U1L2

Square meter steradian

unit:SquareMeterSteradian

m^2-sr

Area Temperature

quantity:AreaTemperature

L2Θ1

Square meter kelvin

unit:SquareMeterKelvin

m^2-K

Area Thermal Expansion

quantity:AreaThermalExpansion

L2Θ-1

Square meter per kelvin

unit:SquareMeterPerKelvin

m^2/K

Capacitance

quantity:Capacitance

L-2M-1T4I2

Farad

unit:Farad

F

Catalytic Activity

quantity:CatalyticActivity

T-1N1

Katal

unit:Katal

kat

Coefficient of Heat Transfer

quantity:CoefficientOfHeatTransfer

M1T-3Θ-1

Watt per square meter kelvin

unit:WattPerSquareMeterKelvin

W/(m^2-K)

Density

quantity:Density

L-3M1

Kilogram per cubic meter

unit:KilogramPerCubicMeter

kg/m^3

Dose Equivalent

quantity:DoseEquivalent

L2T-2

Sievert

unit:Sievert

Sv

Dynamic Viscosity

quantity:DynamicViscosity

L-1M1T-1

Pascal second

unit:PascalSecond

Pa-s

Electric Charge

quantity:ElectricCharge

T1I1

Coulomb

unit:Coulomb

C

Electric Charge Line Density

quantity:ElectricChargeLineDensity

L-1T1I1

Coulomb per meter

unit:CoulombPerMeter

C/m

Electric Charge Volume Density

quantity:ElectricChargeVolumeDensity

L-3T1I1

Coulomb per cubic meter

unit:CoulombPerCubicMeter

C/m^3

Electric Charge per Amount of Substance

quantity:ElectricChargePerAmountOfSubstance

T1I1N-1

Coulomb per mole

unit:CoulombPerMole

C/mol

Electric Current Density

quantity:ElectricCurrentDensity

L-2I1

Ampere per square meter

unit:AmperePerSquareMeter

A/m^2

Electric Current per Angle

quantity:CurrentPerAngle

U-1I1

Ampere per radian

unit:AmperePerRadian

A/rad

Electric Dipole Moment

quantity:ElectricDipoleMoment

L1T1I1

Coulomb meter

unit:CoulombMeter

C-m

Electric Field Strength

quantity:ElectricFieldStrength

L1M1T-3I-1

Volt per Meter

unit:VoltPerMeter

V/m

Electric Flux Density

quantity:ElectricFluxDensity

L-2T1I1

Coulomb per Square Meter

unit:CoulombPerSquareMeter

C/m^2

Electrical Conductivity

quantity:ElectricalConductivity

L-2M-1T3I2

Siemens

unit:Siemens

S

Electromotive Force

quantity:ElectromotiveForce

L2M1T-3I-1

Volt

unit:Volt

V

Energy Density

quantity:EnergyDensity

L-1M1T-2

Joule per cubic meter

unit:JoulePerCubicMeter

J/m^3

Energy and Work

quantity:EnergyAndWork

L2M1T-2

Joule

unit:Joule

J

Energy per Unit Area

quantity:EnergyPerUnitArea

M1T-2

Joule per square meter

unit:JoulePerSquareMeter

J/m^2

Exposure

quantity:Exposure

M-1T1I1

Coulomb per kilogram

unit:CoulombPerKilogram

C/kg

Force

quantity:Force

L1M1T-2

Newton

unit:Newton

N

Force per Electric Charge

quantity:ForcePerElectricCharge

L1M1T-3I-1

Newton per coulomb

unit:NewtonPerCoulomb

N/C

Force per Unit Length

quantity:ForcePerUnitLength

M1T-2

Newton per meter

unit:NewtonPerMeter

N/m

Frequency

quantity:Frequency

T-1

Hertz

unit:Hertz

Hz

Inverse second time

quantity:InverseSecondTime

s^-1

Gravitational Attraction

quantity:GravitationalAttraction

L3M-1T-2

Cubic meter per kilogram second squared

unit:CubicMeterPerKilogramSecondSquared

m^3/(kg-s^2)

Heat Capacity and Entropy

quantity:HeatCapacityAndEntropy

L2M1T-2Θ-1

Joule per kelvin

unit:JoulePerKelvin

J/K

Heat Flow Rate

quantity:HeatFlowRate

L2M1T-3

Watt

unit:Watt

W

Heat Flow Rate per Unit Area

quantity:HeatFlowRatePerUnitArea

M1T-3

Watt per square meter

unit:WattPerSquareMeter

W/m^2

Illuminance

quantity:Illuminance

U1L-2J1

Lux

unit:Lux

lx

Inductance

quantity:Inductance

L2M1T-2I-2

Henry

unit:Henry

H

Inverse Amount of Substance

quantity:InverseAmountOfSubstance

N-1

Per mole

unit:PerMole

mol^(-1)

Inverse Permittivity

quantity:InversePermittivity

L3M1T-4I-2

Meter per farad

unit:MeterPerFarad

m/F

Kinematic Viscosity

quantity:KinematicViscosity

L2T-1

Square meter per second

unit:SquareMeterPerSecond

m^2/sec

Length Mass

quantity:LengthMass

L1M1

Meter kilogram

unit:MeterKilogram

m-kg

Length Temperature

quantity:LengthTemperature

L1Θ1

Meter kelvin

unit:MeterKelvin

m-K

Linear Acceleration

quantity:LinearAcceleration

L1T-2

Meter per second squared

unit:MeterPerSecondSquared

m/s^2

Linear Momentum

quantity:LinearMomentum

L1M1T-1

Kilogram Meter Per Second

unit:KilogramMeterPerSecond

kg-m/s

Linear Thermal Expansion

quantity:LinearThermalExpansion

L1Θ-1

Meter per kelvin

unit:MeterPerKelvin

m/K

Linear Velocity

quantity:LinearVelocity

L1T-1

Meter per second

unit:MeterPerSecond

m/s

Luminance

quantity:Luminance

L-2J1

Candela per square meter

unit:CandelaPerSquareMeter

cd/m^2

Luminous Flux

quantity:LuminousFlux

U1J1

Lumen

unit:Lumen

lm

Magnetic Dipole Moment

quantity:MagneticDipoleMoment

L2I1

Joule per Tesla

unit:JoulePerTesla

J/T

Magnetic Field Strength

quantity:MagneticFieldStrength

L-1I1

Ampere Turn per Meter

unit:AmpereTurnPerMeter

At/m

Ampere per meter

quantity:AmperePerMeter

A/m

Magnetic Flux

quantity:MagneticFlux

L2M1T-2I-1

Weber

unit:Weber

Wb

Magnetic Flux Density

quantity:MagneticFluxDensity

M1T-2I-1

Tesla

unit:Tesla

T

Magnetomotive Force

quantity:MagnetomotiveForce

U1I1

Ampere Turn

unit:AmpereTurn

At

Mass Temperature

quantity:MassTemperature

M1Θ1

Kilogram kelvin

unit:KilogramKelvin

kg-K

Mass per Time

quantity:MassPerUnitTime

M1T-1

Kilogram per second

unit:KilogramPerSecond

kg/s

Mass per Unit Area

quantity:MassPerUnitArea

L-2M1

Kilogram per square meter

unit:KilogramPerSquareMeter

kg/m^2

Mass per Unit Length

quantity:MassPerUnitLength

L-1M1

Kilogram per meter

unit:KilogramPerMeter

kg/m

Molar Energy

quantity:MolarEnergy

L2M1T-2N-1

Joule per mole

unit:JoulePerMole

J/mol

Molar Heat Capacity

quantity:MolarHeatCapacity

L2M1T-2Θ-1N-1

Joule per mole kelvin

unit:JoulePerMoleKelvin

J/(mol-K)

Permeability

quantity:Permeability

L1M1T-2I-2

Henry per meter

unit:HenryPerMeter

H/m

Permittivity

quantity:Permittivity

L-3M-1T4I2

Farad per meter

unit:FaradPerMeter

F/m

Plane Angle

quantity:PlaneAngle

U1

Radian

unit:Radian

rad

Power

quantity:Power

L2M1T-3

Watt

unit:Watt

W

Power per Angle

quantity:PowerPerAngle

U-1L2M1T-3

Watt per steradian

unit:WattPerSteradian

W/sr

Power per Area Angle

quantity:PowerPerAreaAngle

U-1M1T-3

Watt per square meter steradian

unit:WattPerSquareMeterSteradian

W/(m^2-sr)

Power per Unit Area

quantity:PowerPerUnitArea

M1T-3

Watt per square meter

unit:WattPerSquareMeter

W/m^2

Pressure or Stress

quantity:PressureOrStress

L-1M1T-2

Pascal

unit:Pascal

Pa

Resistance

quantity:Resistance

L2M1T-3I-2

Ohm

unit:Ohm

Ohm

Solid Angle

quantity:SolidAngle

U1

Steradian

unit:Steradian

sr

Specific Energy

quantity:SpecificEnergy

L2T-2

Joule per kilogram

unit:JoulePerKilogram

J/kg

Specific Heat Capacity

quantity:SpecificHeatCapacity

L2T-2Θ-1

Joule per kilogram kelvin

unit:JoulePerKilogramKelvin

J/(kg-K)

Specific Heat Pressure

quantity:SpecificHeatPressure

L3M-1Θ-1

Joule per kilogram kelvin per pascal

unit:JoulePerKilogramKelvinPerPascal

J/(km-K-Pa)

Specific Heat Volume

quantity:SpecificHeatVolume

L-1T-2Θ-1

Joule per kilogram kelvin per cubic meter

unit:JoulePerKilogramKelvinPerCubicMeter

J/(kg-K-m^3)

Temperature Amount of Substance

quantity:TemperatureAmountOfSubstance

Θ1N1

Mole kelvin

unit:MoleKelvin

mol-K

Thermal Conductivity

quantity:ThermalConductivity

L1M1T-3Θ-1

Watt per meter kelvin

unit:WattPerMeterKelvin

W/(m*K)

Thermal Diffusivity

quantity:ThermalDiffusivity

L2T-1

Square meter per second

unit:SquareMeterPerSecond

m^2/sec

Thermal Insulance

quantity:ThermalInsulance

M-1T3Θ1

Square meter Kelvin per watt

unit:SquareMeterKelvinPerWatt

(K^2)m/W

Thermal Resistance

quantity:ThermalResistance

L-2M-1T3Θ1

Kelvin per watt

unit:KelvinPerWatt

K/W

Thermal Resistivity

quantity:ThermalResistivity

L-1M-1T3Θ1

Meter Kelvin per watt

unit:MeterKelvinPerWatt

K-m/W

Thrust to Mass Ratio

quantity:ThrustToMassRatio

L1T-2

Newton per kilogram

unit:NewtonPerKilogram

N/kg

Time Squared

quantity:TimeSquared

T2

Second time squared

unit:SecondTimeSquared

s^2

Torque

quantity:BendingMomentOrTorque

L2M1T-2

Newton meter

unit:NewtonMeter

N-m

Volume

quantity:Volume

L3

Cubic Meter

unit:CubicMeter

m^3

Volume Thermal Expansion

quantity:VolumeThermalExpansion

L3Θ-1

Cubic meter per kelvin

unit:CubicMeterPerKelvin

m^3/K

Volume per Unit Time

quantity:VolumePerUnitTime

L3T-1

Cubic meter per second

unit:CubicMeterPerSecond

m^3/s

Volumetric heat capacity

quantity:VolumetricHeatCapacity

L-1M1T-2Θ-1

Joule per cubic meter kelvin

unit:JoulePerCubicMeterKelvin

J/(m^3 K)





The CGS System

CGS Base and Derived Quantity Kinds and Units

Category

Quantity Kind

QName

Dimension Symbol

Unit

QName

Unit Symbol

Base

Dimensionless

quantity:Dimensionless

U

Unity

unit:Unity

U

Length

quantity:Length

L

Centimeter

unit:Centimeter

cm

Mass

quantity:Mass

M

Gram

unit:Gram

g

Time

quantity:Time

T

Second

unit:SecondTime

s

Derived

Angular Momentum

quantity:AngularMomentum

L2M1T-1

Erg second

unit:ErgSecond

erg s

Area

quantity:Area

L2

Square centimeter

unit:SquareCentimeter

cm^2

Dynamic Viscosity

quantity:DynamicViscosity

L-1M1T-1

Poise

unit:Poise

P

Energy Density

quantity:EnergyDensity

L-1M1T-2

Erg per cubic centimeter

unit:ErgPerCubicCentimeter

erg/cm^3

Energy and Work

quantity:EnergyAndWork

L2M1T-2

Erg

unit:Erg

erg

Force

quantity:Force

L1M1T-2

Dyne

unit:Dyne

dyn

Frequency

quantity:Frequency

T-1

Inverse second time

unit:InverseSecondTime

s^-1

Linear Acceleration

quantity:LinearAcceleration

L1T-2

Centimeter per second squared

unit:CentimeterPerSecondSquared

cm/s^2

Linear Velocity

quantity:LinearVelocity

L1T-1

Centimeter per second

unit:CentimeterPerSecond

cm/s

Power

quantity:Power

L2M1T-3

Erg per second

unit:ErgPerSecond

erg/s

Power per Unit Area

quantity:PowerPerUnitArea

M1T-3

Erg per square centimeter second

unit:ErgPerSquareCentimeterSecond

erg/(cm^2-s)

Pressure or Stress

quantity:PressureOrStress

L-1M1T-2

Dyne per square centimeter

unit:DynePerSquareCentimeter

dyn/cm^2

Time Area

quantity:TimeArea

L2T1

Square centimeter second

unit:SquareCentimeterSecond

cm^2-s

Torque

quantity:BendingMomentOrTorque

L2M1T-2

Dyne centimeter

unit:DyneCentimeter

dyn-cm

Volume

quantity:Volume

L3

Cubic Centimeter

unit:CubicCentimeter

cm^3



CGS Units for Electricity and Magnetism

There are two different approaches to defining electric and magnetic quantities using the base CGS mechanical quantities of length, mass and time. The Electromagnetic Unit (EMU) approach derives electric charge from Coulomb’s Law, while the Electrostatic Unit (ESU) approach derives electric charge from Ampere’s Law.

EMU Derived Units

Coulomb’s Law states that the force exerted between two charged particles, q1 and q2, is inversely proportional to the square of their distance, r.

F=k(q1q2)/r2

Retaining only the terms of the quantity kinds involved (force, electric charge, distance), this equation can be rearranged to express electric charge as length multiplied by the square root of force. The CGS Electromagnetic Unit is called the Abcoulomb. The table below contains the dimension symbols and corresponding units of other electricity and magnetism quantity kinds in terms of the base CGS quantity kinds and the definition of electric charge above.

CGS EMU Derived Units for Electricity and Magnetism

Quantity Kind

QName

Dimension Symbol

Unit

QName

Unit Symbol

Capacitance

quantity:Capacitance

L-1T2

Abfarad

unit:Abfarad

abF

Electric Charge

quantity:ElectricCharge

L0.5M0.5

Abcoulomb

unit:Abcoulomb

abC

Electric Current

quantity:ElectricCurrent

L0.5M0.5T-1

Abampere

unit:Abampere

abA

Electric Field Strength

quantity:ElectricFieldStrength

L0.5M0.5T-2

Abvolt per Centimeter

unit:AbvoltPerCentimeter

abV/cm

Electric Flux Density

quantity:ElectricFluxDensity

L-1.5M0.5

Abcoulomb per square centimeter

unit:AbcoulombPerSquareCentimeter

abC/cm^2

Electrical Conductivity

quantity:ElectricalConductivity

L-1T1

Absiemen

unit:Absiemen

aS

Electromotive Force

quantity:ElectromotiveForce

L1.5M0.5T-2

Abvolt

unit:Abvolt

abV

Inductance

quantity:Inductance

L1

Abhenry

unit:Abhenry

abH

Magnetic Field Strength

quantity:MagneticFieldStrength

L-0.5M0.5T-1

Abtesla

unit:Abtesla

abT

Magnetic Flux

quantity:MagneticFlux

L1.5M0.5T-1

Abvolt Second

unit:AbvoltSecond

abV-s

Magnetic Flux Density

quantity:MagneticFluxDensity

L-0.5M0.5T-1

Abtesla

unit:Abtesla

abT

Magnetomotive Force

quantity:MagnetomotiveForce

L0.5M0.5T-1

Gilbert

unit:Gilbert

Gi

Permeability

quantity:Permeability

U1

Relative permeability

unit:RelativePermeability

μ r

Permittivity

quantity:Permittivity

L-2T2

Abfarad per centimeter

unit:AbfaradPerCentimeter

abF/cm

Resistance

quantity:Resistance

L1T-1

Abohm

unit:Abohm

abOhm

ESU Derived Units

Ampere’s Law of Magnetic Induction states that the force per unit length exerted between two infinite parallel wires at a distince, d, and carrying electric currents I1 and I2 is proportional to their product divided by the distance between them. I.e.

dF/dl = k(I1I2/d)

Retaining only the terms of the quantity kinds involved (force, electric current, distance), this equation can be rearranged to express electric current as the square root of force. The CGS Electrostatic Unit of electric current is called the Statampere. The table below contains the dimension symbols and corresponding units of other electricity and magnetism quantity kinds in terms of the base CGS quantity kinds and the definition of electric current above.

CGS ESU Derived Units for Electricity and Magnetism

Quantity Kind

QName

Dimension Symbol

Unit

QName

Unit Symbol

Capacitance

quantity:Capacitance

L1

Statfarad

unit:Statfarad

statF

Electric Charge

quantity:ElectricCharge

L1.5M0.5T-1

Statcoulomb

unit:Statcoulomb

statC

Electric Current

quantity:ElectricCurrent

L1.5M0.5T-2

Statampere

unit:Statampere

statA

Electric Field Strength

quantity:ElectricFieldStrength

L-0.5M0.5T-1

Statvolt per centimeter

unit:StatvoltPerCentimeter

statV/cm

Electric Flux Density

quantity:ElectricFluxDensity

L-0.5M0.5T-1

Statcoulomb per square centimeter

unit:StatcoulombPerSquareCentimeter

statC/cm^2

Electromotive Force

quantity:ElectromotiveForce

L0.5M0.5T-1

Statvolt

unit:Statvolt

statV

Inductance

quantity:Inductance

L-1T2

Stathenry

unit:Stathenry

statH

Magnetic Field Strength

quantity:MagneticFieldStrength

L0.5M0.5T-2

Oersted

unit:Oersted

Oe

Magnetic Flux

quantity:MagneticFlux

L0.5M0.5

Maxwell

unit:Maxwell

Mx

Magnetic Flux Density

quantity:MagneticFluxDensity

L-1.5M0.5

Gauss

unit:Gauss

G

Magnetomotive Force

quantity:MagnetomotiveForce

L1.5M0.5T-2

Oersted centimeter

unit:OerstedCentimeter

Oe-cm

Permeability

quantity:Permeability

L-2T2

Stathenry per centimeter

unit:StathenryPerCentimeter

statH/cm

Permittivity

quantity:Permittivity

U1

Relative permittivity

unit:RelativePermittivity

ε r

Resistance

quantity:Resistance

L-1T1

Statohm

unit:Statohm

statOhm

Glossary

NExIOM
NASA Exploration Intiatives Ontology Models
TBD
To Be Done
TBR
To Be Revised

Acknowledgements

[TBR]

  1. NASA AMES Research Center for sponsoring and content for different engineering disciplines
  2. TopQuadrant, Inc., for Ontology Architecture, foundation ontologies and tooling support
  3. European Space Agency (ESA), for constructive dialog and input to the ontology models

References

  1. The NIST Guide for the use of the International System of Units
  2. International Vocabulary of Metrology – Basic and General Concepts and Associated Terms
  3. SI Brochure, 8th Edition
  4. Dimensional Analysis, Percy Williams Bridgman, Yale University Press (1922)

Last Updated August 24, 2013

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