David Price Daniel Mekonnen QUDT The QUDT Ontologies are issued under a Creative Commons Attribution Share Alike 3.0 United States License. Attribution should be made to NASA AMES Research Center and TopQuadrant, Inc. Irene Polikoff Sidney Bailin The NASA Quantity - Unit - Dimension Ontology $Date: 2010-02-16 10:59:30 -0500 (Tue, 16 Feb 2010) $ Ralph Hodgson James E. Masters Quantities, Units, and Dimensions The qud, or quantity-unit-dimension ontology defines the base classes properties, and restrictions used for modeling physical quantities, units of measure, and their dimensions in various measurement systems. $Id: n1qud.n3 85 2010-02-16 15:59:30Z dmekonnen $ Quantity Kind Category Energy and work per mass amount of substance Luminance Unit Luminous Energy Unit Linear Energy Transfer Unit Mass Amount Of Substance Temperature Unit Mass Temperature Unit Magnetic Field Strength Unit A magnetic field is a vector field that permeates space and which can exert a magnetic force on moving electric charges and on magnetic dipoles (such as permanent magnets). [Wikipedia] The strength of a magnetic field at a point in space is the magnitude of the field vector at that point. This class contains the following instance(s): "Ampere per meter", "Ampere turn per inch", "Ampere turn per meter", "Oersted". Electric Charge Area Density Unit Photometry Unit Communications Unit 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. System of Units 1 Volume Per Time Unit A "Space And Time" Unit with the following instance(s): "Cubic foot per minute", "Cubic foot per second", "Cubic inch per minute", "Cubic meter per second", "Cubic yard per minute", "Gallon per day", "Gallon per minute". Logarithmic Unit Logarithmic units are abstract mathematical units that can be used to express any quantities (physical or mathematical) that are defined on a logarithmic scale, that is, as being proportional to the value of a logarithm function. Examples of logarithmic units include common units of information and entropy, such as the bit, and the byte, as well as units of relative signal strength magnitude such as the decibel. Exposure Unit Electric Flux Unit Thermal Energy Unit Area Thermal Expansion Unit When the temperature of a substance changes, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bonds. As a result, solids typically expand in response to heating and contract on cooling; this dimensional response to temperature change is expressed by its coefficient of thermal expansion. Different coefficients of thermal expansion can be defined for a substance depending on whether the expansion is measured by: * linear thermal expansion * area thermal expansion * volumetric thermal expansion These characteristics are closely related. The volumetric thermal expansion coefficient can be defined for both liquids and solids. The linear thermal expansion can only be defined for solids, and is common in engineering applications. Some substances expand when cooled, such as freezing water, so they have negative thermal expansion coefficients. For exactly isotropic materials, the area thermal expansion coefficient is very closely approximated as twice the linear coefficient. Science And Engineering Unit Current Per Angle Unit Curvature Unit The canonicall example of extrinsic curvature is that of a circle, which has curvature equal to the inverse of its radius everywhere. Smaller circles bend more sharply, and hence have higher curvature. The curvature of a smooth curve is defined as the curvature of its osculating circle at each point. The osculating circle of a sufficiently smooth plane curve at a given point on the curve is the circle whose center lies on the inner normal line and whose curvature is the same as that of the given curve at that point. This circle is tangent to the curve at the given point. That is, given a point P on a smooth curve C, the curvature of C at P is defined to be 1/R where R is the radius of the osculating circle of C at P. The magnitude of curvature at points on physical curves can be measured in diopters (also spelled dioptre) — this is the convention in optics. [Wikipedia] Continuum Mechanics Quantity Kind Mechanics Linear Velocity Unit Linear Velocity units measure change of length per unit time. Examples include meters per second, miles per hour, knots, etc. Area Angle Unit Currency Unit 1 Concentration Unit Electric Flux Density Unit Binary Prefix Unit Human Unit units for measuring human resources Luminous Intensity Unit Specific Heat Pressure Unit This class contains units of measure for specific heat capacity at a constant pressure. Angular Momentum Unit Electric Current Density Unit Electric current density is a measure of the density of flow of a conserved charge. Usually the charge is the electric charge, in which case the associated current density is the electric current per unit area of cross section, but the term current density can also be applied to other conserved quantities. It is defined as a vector whose magnitude is the current per cross-sectional area. [Wikipedia] In SI units, the electric current density is measured in amperes per square metre. This class contains the following instance(s): "Ampere per square meter". Angle Unit Length Temperature Unit Magnetic Flux Unit Magnetic flux is a measure of quantity of magnetism, taking into account the strength and the extent of a magnetic field. The SI unit of magnetic flux is the weber (in derived units: volt-seconds), and the unit of magnetic field is the weber per square meter, or tesla. [Wikipedia] This class contains the following instance(s): "Maxwell", "Unit pole", "Weber". A dimension is a relationship between a quantity system, a quantity kind of that system, and one or more dimension vectors. There is one dimension vector for each of the system's base quantity kinds. The vector's magnitude determines the exponent of the base dimension for the referenced quantity kind. Dimension 1 1 Power Per Area Unit Permittivity Unit Dose Equivalent Unit Radiance Unit Physical Unit Volume per Time Squared Unit Area Time Temperature Unit Electric Dipole Moment Unit The electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges. [Wikipedia] This class has the following instance(s): "Coulomb meter", "Debye". Molar Heat Capacity Unit A Resource Unit is a unit for measuring the amount of various types of resources. Resource Unit A Quantity Kind is an aspect common to mutually comparable quantities. Quantity Kind 1 Thermodynamics Unit Thermodynamics Thermodynamics units are units that provide reference scales for quantifying the conversion of energy into work, as well as heat and its relation to macroscopic variables such as temperature and pressure. Power Unit Area Unit Microbial Formation Unit Conductance Unit Electrical conductance is the inverse of electrical resistance. It measures the ease with which electricity flows along a path through an electrical element. This class contains the following instance(s): "Abmho", "Mho", "Siemens", "Statmho". Volume Unit Thermal Energy Length Unit Linear Acceleration Unit Thermal Expansion Unit When the temperature of a substance changes, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bonds. As a result, solids typically expand in response to heating and contract on cooling; this dimensional response to temperature change is expressed by its coefficient of thermal expansion. Different coefficients of thermal expansion can be defined for a substance depending on whether the expansion is measured by: * linear thermal expansion * area thermal expansion * volumetric thermal expansion These characteristics are closely related. The volumetric thermal expansion coefficient can be defined for both liquids and solids. The linear thermal expansion can only be defined for solids, and is common in engineering applications. Some substances expand when cooled, such as freezing water, so they have negative thermal expansion coefficients. [Wikipedia] This class contains enumerations of the base dimensions for quantity systems. Each quantity kind system that defines a base set has a corresponding ordered enumeration whose elements are the dimension objects for the base quantity kinds. The order of the dimensions in the enumeration determines the canonical order of the basis elements in the corresponding abstract vector space. Enumeration 1 1 Velocity Unit Heat Capacity And Entropy Unit Volume per mass unit Time Area Unit Energy Density Unit Units that measure energy density, i.e. energy per unit volume. Thermal Resistivity Unit Angular Velocity Unit Thing 1 1 1 Electric Field Strength Unit The strength of the electric field at a given point is defined as the force that would be exerted on a positive test charge of +1 coulomb placed at that point; the direction of the field is given by the direction of that force. Electric fields contain electrical energy with energy density proportional to the square of the field intensity. The electric field is to charge as gravitational acceleration is to mass and force density is to volume. Electric Charge Per Amount Of Substance Unit Catalytic Activity Unit Bending Moment Or Torque Unit Dynamic Viscosity Unit Quantum Mechanics Quantity Kind Energy Per Area Unit Units that quantify energy per unit area. Magnetic Flux Density Unit Mass Amount Of Substance Unit Luminous Efficacy Unit Molar Concentration Unit Video Frame Rate Unit Length Temperature Time Unit Electricity And Magnetism Unit Electricity and Magnetism The class of units used to measure the properties of electricity and magnetism. Thermal Conductivity Unit Light Unit Optics Bio And Medical Unit Specific Heat Volume Unit This class contains units of measure for specific heat capacity at a constant volume. Electric Current Unit Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere, and electric current is measured using an ammeter. This class contains the following instance(s): "Abampere", "Ampere", "Biot", "Statampere". Data Rate Unit Area Temperature Unit Mass Unit Time Squared Unit Respiratory Rate Unit Momentum Unit Radiology Unit Radiology Rate Of Return Unit Absorbed Dose Rate Unit Temperature per time unit Electrochemistry Unit Fluid Dynamics Quantity Kind RF-Power Unit Pressure or stress rate Prefix Unit Amount Of Substance Unit Electric Charge Density Unit The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume. It is measured in coulombs per metre (C/m), square metre (C/m^2), or cubic metre (C/m^3), respectively. Since there are positive as well as negative charges, the charge density can take on negative values. [Wikipedia] A unit of measure, or unit, is a particular quantity value that has been chosen as a scale for measuring other quantities the same kind (more generally of equivalent dimension). For example, the meter is a quantity of length that has been rigorously defined and standardized by the BIPM (International Board of Weights and Measures). Any measurement of the length can be expressed as a number multiplied by the unit meter. More formally, the value of a physical quantity Q with respect to a unit (U) is expressed as the scalar multiple of a real number (n) and U: Q = nU Unit 1 1 Force Per Length Unit Thermal Insulance Unit A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement. There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, Newton's gravitational constant G, Planck's constant h, the electric permittivity of free space ε0, and the elementary charge e. Physical constants can take many dimensional forms, or may be dimensionless depending on the system of quantities and units used. Physical Constant 1 1 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. System of Quantity Kinds Time Unit Units that measure time. Thrust To Mass Ratio Unit Illuminance Unit A quantity is the measurement of an observable property of a particular object, event, or physical system. A quantity is always associated with the context of measurement (i.e. the thing measured, the measured value, the accuracy of measurement, etc.) whereas the underlying quantity kind is independent of any particular measurement. Thus, length is a quantity kind while the height of the Ares I rocket is a specific quantity of length; its magnitude that may be expressed in meters, feet, inches, etc. Examples of physical quantities include physical constants, such as the speed of light in a vacuum, Planck's constant, the electric permittivity of free space, and the fine structure constant. Quantity 1 a reference to the dimension that quantifies the property Mass Per Length Unit A Dimensionless Unit is a quantity for which all the exponents of the factors corresponding to the base quantities in its quantity dimension are zero. Dimensionless Unit Solid Angle Unit The solid angle subtended by a surface S is defined as the surface area of a unit sphere covered by the surface S's projection onto the sphere. A solid angle is related to the surface of a sphere in the same way an ordinary angle is related to the circumference of a circle. Since the total surface area of the unit sphere is 4*pi, the measure of solid angle will always be between 0 and 4*pi. Temperature Unit Electric Charge Volume Density Unit The volume charge density is the amount of electric charge in a volume. It is measured in coulombs per cubic metre (C/m^3). Since there are positive as well as negative charges, the charge density can take on negative values. [Wikipedia] Heart Rate Unit Two quantities proportional if they vary in such a way that one of the quantities is a constant multiple of the other. The multiple is the constant of proportionality between the two quantities. Constants of proportionality may be dimensioned in some quantity systems and dimensionless in others. For example, in the SI system, the permittivity of a vacuum has the dimensions L^-3 M^-1 T^4 I^2 and is measured in Farads per Meter; in the CGS-EMU system it has dimensions L^-2T^2 and is measured in Abfarads per Centimeter; in the CGS-ESU system it is dimensionless. Constants of proportionality are important in the definition of systems of natural units, where units are chosen in order to make certain constants of proportionality dimensionless and equal to 1. Constant of Proportionality Counting Unit Solid Mechanics Quantity Kind System of natural units Energy per Electric Charge Unit The ratio of power to electric charge is proportional to the rate of change of electric potential. Mass Per Volume Unit Gravitational Attraction Unit Mass Per Time Unit Heat Flow Rate Unit Force Unit Acceleration Unit Energy And Work Unit Linear Momentum Unit Space And Time Unit Space and Time A quantity type is an enumeration of units that are measures of the same quantity kind. Quantity type 1 Angular Acceleration Unit Chemistry Unit Chemistry Angular Mass Unit The units of angular mass have dimensions of mass * area. They are used to measure the moment of inertia. Electric Charge Line Density Unit The linear charge density is the amount of electric charge in a line. It is measured in coulombs per metre (C/m). Since there are positive as well as negative charges, the charge density can take on negative values. [Wikipedia] Pressure Or Stress Unit Magnetomotive Force Unit Magnetomotive force is any physical cause that produces magnetic flux. In other words, it is a field of magnetism (measured in tesla) that has area (measured in square meters), so that (Tesla)(Area)= Flux. It is analogous to electromotive force or voltage in electricity. MMF usually describes electric wire coils in a way so scientists can measure or predict the actual force a wire coil can generate. [Wikipedia] This class contains the following instance(s): "Ampere turn", "Gilbert", "Oersted centimeter", "Unit pole". Length Unit Capacitance Unit Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. This class contains the following instance(s): "Abfarad", "Farad", "MicroFarad", "NanoFarad", "PicoFarad", "Statfarad". Atomic Charge Unit The electric charge of an ion, equal to the number of electrons the atom has gained or lost in its ionization multiplied by the charge on one electron. This class contains the following instance(s): "atomic number". Amount Of Substance Temperature Unit Thermal Resistance Unit Decimal Prefix Unit SI Unit An SI unit Force Per Electric Charge Unit Serum Or Plasma Level Unit Photometry quantity kind Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy (including light) in terms of absolute power. Radiometry quantity kind Photometry is the field that studies the measurement of electromagnetic radiation, including visible light. Note that light is also measured using the techniques of photometry, which deal with brightness as perceived by the human eye, rather than absolute power. Specific Energy Unit Units which quantify specific energy, i.e. energy per unit mass. Energy per Electric Charge Unit The ratio of energy to electric charge arises repeatedly in electrodynamics. It is the dimensional equivalent to the electrostatic potential and electromotive force. In both cases, the SI unit is the volt, or newton meters per coulomb. This class contains the dimension objects that are the basis elements in some abstract vector space associated with a quantity kind system. Enumeration element 1 1 Mechanics Unit Volume Thermal Expansion Unit When the temperature of a substance changes, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bonds. As a result, solids typically expand in response to heating and contract on cooling; this dimensional response to temperature change is expressed by its coefficient of thermal expansion. Different coefficients of thermal expansion can be defined for a substance depending on whether the expansion is measured by: * linear thermal expansion * area thermal expansion * volumetric thermal expansion These characteristics are closely related. The volumetric thermal expansion coefficient can be defined for both liquids and solids. The linear thermal expansion can only be defined for solids, and is common in engineering applications. Some substances expand when cooled, such as freezing water, so they have negative thermal expansion coefficients. For exactly isotropic materials, the volumetric thermal expansion coefficient is very closely approximated as three times the linear coefficient. [Wikipedia] Activity Unit Radiant Intensity Unit Atomic Physics Unit Atomic Physics Turbidity Unit Turbidity is the cloudiness or haziness of a fluid caused by individual particles (suspended solids) that are generally invisible to the naked eye, similar to smoke in air. Signal Detection Threshold Unit Signal relative to an underlying signal Inverse Amount Of Substance Unit 1 1 1 Quantity value A quantity value expresses the numerical value of a quantity with respect to a chosen 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. 1 1 Resistance Unit Electrical resistance is a ratio of the degree to which an object opposes an electric current through it, measured in ohms. Its reciprocal quantity is electrical conductance measured in siemens. This class contains the following instance(s): "Abohm", "Ohm", "Statohm". Luminous Flux Unit Event Unit Coefficient Of Heat Transfer Unit Molar Energy Unit Plane Angle Unit Electric Charge Unit Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. The interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces. Computing Unit Radiometry Unit Financial Unit Financial This class contains units that measure financial quantities, such as currency, transactions, rates of return, etc. Information Entropy Unit Inductance Unit An electric current flowing around a circuit produces a magnetic field and hence a magnetic flux through the circuit. The ratio of the magnetic flux to the current is called the inductance, or more accurately self-inductance of the circuit. [Wikipedia] This class contains the following instance(s): "Abhenry", "Henry", "Micro Henry", "Milli Henry", "Stathenry". Specific Heat Capacity Unit Kinematic Viscosity Unit Thermal Diffusivity Unit Linear Thermal Expansion Unit When the temperature of a substance changes, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bonds. As a result, solids typically expand in response to heating and contract on cooling; this dimensional response to temperature change is expressed by its coefficient of thermal expansion. Different coefficients of thermal expansion can be defined for a substance depending on whether the expansion is measured by: * linear thermal expansion * area thermal expansion * volumetric thermal expansion These characteristics are closely related. The volumetric thermal expansion coefficient can be defined for both liquids and solids. The linear thermal expansion can only be defined for solids, and is common in engineering applications. Some substances expand when cooled, such as freezing water, so they have negative thermal expansion coefficients. [Wikipedia] Mass Per Area Unit Absorbed Dose Unit Frequency Unit A dimension vector is an association between a quantity kind and a rational number. The quantity kind serves as the basis vector in an abstract vector space, and the rational number is the vector magnitude. The abstract vector space is determined by the chosen set of base quantity kinds for a quantity system. Dimension Vector 1 1 Molal Concentration Unit Permeability Unit This property relates a unit of measure to the unit system in which the unit is derived from the system's base units with a proportionality constant of one. derived unit of system This property relates a system of units to a base unit defined within the system. The base units of a system are used to define the derived units of the system by expressing the derived units as products of the base units raised to a rational power. base unit This property relates a system of units with a unit of measure that is either a) defined by the system, or b) accepted for use by the system and is convertible to a unit of equivalent dimension that is defined by the system. Systems of units may distinguish between base and derived units. Base units are the units which measure the base quantities for the corresponding system of quantities. The base units are used to define units for all other quantities as products of powers of the base units. Such units are called derived units for the system. system unit prefix unit coherent derived unit A coherent unit of measurement for a unit system is a defined unit that may be expressed as a product of powers of the system's base units with the proportionality factor of one. coherent unit This property relates a quantity kind to its generalization. A quantity kind, PARENT, is a generalization of the quantity kind CHILD only if 1. PARENT and CHILD have the same dimensions in every system of quantities; 2. Every unit that is a measure of quantities of kind CHILD is also a valid measure of quantities of kind PARENT. generalization This property relates a unit system with a unit of measure that is not defined by or part of the system, but is allowed for use within the system. An allowed unit must be convertible to some dimensionally eqiuvalent unit that is defined by the system. allowed unit a property to relate an observable thing with a quantity (qud:Quantity) quantity element kind system quantity kind prefix unit of system reference quantity The default element in an enumeration default a property to relate an observable thing with a quantity value (qud:QuantityValue) value system base quantity kind value for quantity This property relates a unit of measure with a unit system that does not define the unit, but allows its use within the system. An allowed unit must be convertible to some dimensionally eqiuvalent unit that is defined by the system. allowed unit of system This property relates a unit of measure to the system of units in which it is defined as a base unit for the system. The base units of a system are used to define the derived units of the system by expressing the derived units as products of the base units raised to a rational power. base unit of system This property relates a unit of measure with a system of units that either a) defines the unit or b) allows the unit to be used within the system. unit of system This property relates a unit of measure with the unit system that defines the unit. defined unit of system dimension vector quantity kind of system An element of an enumeration element derived quantity kind of system A reference to the unit of measure of a quantity (variable or constant) of interest. unit base quantity kind of system system dimension system derived quantity kind This property relates a unit of measure to the system of units in which it is defined as a derived unit. That is, the derived unit is defined as a product of the base units for the system raised to some rational power. derived unit of system This property relates a unit system with a unit of measure that is defined by the system. defined unit reference thing quantity value This property relates a system of units to a unit of measure that is defined within the system in terms of the base units for the system. That is, the derived unit is defined as a product of the base units for the system raised to some rational power. derived unit A coherent unit of measurement for a unit system is a defined unit that may be expressed as a product of powers of the system's base units with the proportionality factor of one. coherent unit of system This property relates a quantity kind to its specialization(s). For example, linear velocity and angular velocity are both specializations of velocity. specialization unit for numeric value The symbol for a unit is a glyph that is used to represent the unit in a compact form. For example, the symbol for the US Dollar is $. This contrasts with unit:abbreviation, which gives a short alphanumeric abbreviation for the unit. (I.e. USD for US Dollar). symbol The standard uncertainty of a quantity is the estimated standard deviation of the mean taken from a series of measurements. standard uncertainty The relative standard uncertainty of a measurement is the (absolute) standard uncertainty divided by the magnitude of the exact value. relative standard uncertainty A unit code is a numeric string that uniquely identifies a unit code order conversion coefficient literal description A negative change limit between consecutive sample values for a parameter. The Negative Delta may be the encoded value or engineering units value depending on whether or not a Calibrator is defined. negative delta limit An abbreviation for a unit is a short (usually 5 characters or less) string that is used in place of the full name for the unit in contexts where space is limited, or where using the abbreviation will enhance readability. abbreviation A positive change limit between consecutive sample values for a parameter. The Positive Delta may be the encoded value or engineering units value depending on whether or not a Calibrator is defined. Positive delta limit exact match The currency exponent indicates the number of decimal places between a major currency unit and its minor currency unit. For example, the US dollar is the major currency unit of the United States, and the US cent is the minor currency unit. Since one cent is 1/100 of a dollar, the US dollar has a currency exponent of 2. However, the Japanese Yen has no minor currency units, so the yen has a currency exponent of 0. currency exponent A system of units is coherent with respect to a system of quantities and equations if the system of units is chosen in such a way that the equations between numerical values have exactly the same form (including the numerical factors) as the corresponding equations between the quantities. In such a coherent system, no numerical factor other than the number 1 ever occurs in the expressions for the derived units in terms of the base units. coherent unit system This property associates a system of quantities with an enumeration that enumerates the base dimensions of the system in canonical order. base dimension enumeration unit system vector magnitude basis element conversion offset conversion multiplier dimension inverse reference unit Communications Biology Information Not Used With SI Unit Non SI Unit A Non-SI unit. Typically an imperial measure. A type specification for all units that are not used in the SI standard. Used With SI Unit A type specification for all units that are used in the SI standard. SI Base Unit A Base Unit is a unit adopted by convention for a base quantity. Base Unit All SI units are derived from the SI Base units SI Derived Unit A DerivedUnit is a type specification for units that are derived from other units. Derived Unit