Units/it

Alcune letture sulle unità di misura:
 * Sistema Internazionale di Misura SI
 * Sistema imperiale britannico
 * SI derived unit (in italiano si trovano nella stessa pagina del SI)
 * Grado d'arco - Unità angolari

Esempi
# -- alcuni esempi del sistema di traduzione di unità di FreeCAD -- FreeCAD.Units.parseQuantity tu('10 m') tu('3/8 in') tu('100 km/h') tu('100 km/h')/tu('m/s') tu('m^2*kg*s^-3*A^-2') # or tu('(m^2*kg)/(A^2*s^3)') tu('2*pi rad') # full circle tu('2*pi rad') / tu('gon') tu('1ft+(3+7/16)in') tu('1\'(3+7/16)"') # the ' we have to escape because of python tu('sin(pi)') b = Part.makeBox(tu('2in'),tu('2m')/100,10)
 * 1) creare un collegamento per gli esempi
 * 1) 10 meters in internal numbers
 * 1) doing math
 * 1) combined stuff
 * 1) transfer to other units
 * 1) derived units (Ohm)
 * 1) angles
 * 1) as gon
 * 1) more imperial
 * 1) or
 * 1) trigonometry
 * 1) Using translated units as parameters, this command will create a 50.8mm x 20mm x 10mm box

Unità di misura supportate
Queste sono le unità finora definite in FreeCAD. È facile aggiungere una nuova unità definita dall'utente. La definizione si trova in http://free-cad.svn.sourceforge.net/viewvc/free-cad/trunk/src/Base/UnitsApi.l?view=markup.

Lunghezza metrica "mm"   1.0;        // millimetro       (lunghezza standard interna) "m"    1000.0;     // metro "cm"   10.0;       // centimetro "dm"   100.0;      // decimetro "km"   1000000.0;  // kilometro

Lunghezza Imperiale "in" "\"" 25.4;       // inch "ft" "'"   304.8;      // foot "th"       0.0254;     // thou "yr"       914.4;      // yard

Massa metrica "kg"   1.0;        // kilogrammo       (massa standard interna) "g"    0.001;      // grammo "mg"   0.000001;   // milligrammo "t"    1000.0;     // tonnellata

Massa Imperiale "lb"   0.45359237; // pound "oz"   0.45359237; // ounce "st"   6.35029318; // Stone "cwt"  50.80234544;// hundredweights

Angolo "deg"  1.0;        // gradi         (angolo standard interno) "rad"  180/M_PI;   // radianti "gon"  360.0/400.0;// gon Tempo "s"    1.0;        // secondo         (tempo standard interno) "min"  60.0;       // minuto "h"    3600.0;     // ora

Altro del SI "A"    1.0;        // Ampere         (internal standard electric current) "K"    1.0;        // Kelvin         (internal standard thermodynamic temperature) "cd"   1.0;        // Candela        (internal standard luminous intensity) "mol"  1.0;        // Mole           (internal standard amount of substance) Volume metrico "µl"   1.0;        // microliter mm^3(volume standard derivato) "ml"   1000.0;     // milliliter cm^3 "l"    1000000.0;  // Liter      dm^3

Finalità e principi: proposta di una estensione del sistema di gestione delle unità
Nelle sezioni successive, sviluppando il concetto di sistema di unità, si propone un sistema di gestione delle unità di misura attivato nel corso dell'esecuzione di una istanza di FreeCAD. Definire tale nuovo concetto offre il vantaggio di lavorare più facilmente con tanti tipi di unità fisiche, quante si vuole, anche con quelle create dall'utente, senza aumentare la complessità di gestione delle unità, né per l'utente, né per gli sviluppatori di FreeCAD.

In breve, gli eventi di scalatura delle unità sono localizzati con precisione, e realizzati in modo globale.

Il raggiungimento di tale flessibilità è necessario specialmente quando si passa a lavorare con le proprietà dei materiali che possono avere unità molto diverse e quindi difficili da gestire manualmente una ad una.

Il ragionamento proposto permette di gestire le unità come descritto nella Guida per l'uso del Sistema Internazionale delle unità di misura (SI) e nel Sistema internazionale delle unità di misura (SI), entrambi documenti del NIST.

In questa proposta, la prima analisi nella sezione Riflessioni riguarda i possibili contesti per i quali è utile la gestione delle unità.

Nella sezione Organizzazione è presentato il modello di dati prescelto per realizzare la gestione delle unità, sulla base di 3 oggetti, la unità, il dizionario delle unità, e il sistema delle unità. Infine, è anche presentata una breve API di un quarto oggetto chiamato gestore delle unità.

Risultati
Grazie a questa estensione, si mira ad agevolare la scalatura della unità che può verificarsi tra i differenti settori di lavoro di una azienda. Ad esempio, i disegni tecnici possono essere realizzati nel sistema di unità standard, mentre la modellazione per elementi finiti può essere gestita in un sistema di unità più adatto per questo scopo.

Con questa estensione lo scambio di dati tra questi due tipi di attività diventa più facile.

Riflessioni
In questa sezione sono evidenziati i contesti (casi) di uso del sistema di gestione delle unità. Partendo da questi contesti, dopo siamo in grado di definire le loro specifiche tecniche.

Essenzialmente sono considerati 2 contesti, come esempio.

Contesto 1: apertura di un file di dati
Questo caso probabilmente è quello più frequente. Si riceve un file contenente ad esempio un modello geometrico, o descrivente un materiale con un bel po' di proprietà. Il modello geometrico è espresso in metri, oppure le proprietà del materiale sono espresse secondo il sistema internazionale di unità di misura.

Peccato ...

You are an expert FE modelling, and you usually work with millimeter for length, MegaPascal for stress, tonne for mass...

In this context, unit management is required to scale data from an initial unit system defined in the input file to a user-defined target unit system.

Context 2: switching the unit system at runtime
In this case, you can be at the same time the guy that carries out a drawing, and the guy that will manage the FE modelling. Similarly to the previous case, the unit systems for these 2 tasks are not the same, and you need to switch the initial unit system at runtime to your favorite one.

Logic of unit scaling
In the Brainstorming section have been presented 2 contexts when using unit scaling. Some items should be highlighted from these two contexts.

Unit coherence throughout the FreeCAD running instance
The system proposed is based on a primary assumption: the user is working in a coherent unit system. For instance, this means that if the user expresses length in millimeters, necessarily areras will be expressed in terms of squared millimeters, not squared meters. This is hypothesis one.

Unit system
Because of hypothesis one, it is possible and relevant to define an unit system. An unit system applies to: According Guide for the Use of the International System of Units (SI) from NIST, they are 7 physical base units. We chose to express a unit system in terms of these 7 base units.
 * a running FreeCAD instance into which you are working
 * or it may also apply globally to the content of an input file

When working within an instance of FreeCAD, the user has thus to define first the unit system according to which she/he is working before she/he decides to switch to another unit system, or before importing data from an input file.

This unit system will apply till the user decides to change it. If she/he does, all data with dimensions will be scaled.

Considering hypothesis one, all data that the user will input manually in FreeCAD are assumed to be coherent with the chosen unit system.

The benefit to work with a unit system defined at a FreeCAD running instance level, or at data file level (instead of unit which are defined at the data level) is then that unit management is considerably simplified.

Here are some examples of unit systems.
 * meter, kilogram, second, ampere, Kelvin, mole, candela
 * millimeter, tonne, millisecond, ampere, Kelvin, mole, candela
 * millimeter, kilogramme, millisecond, ampere, Kelvin, mole, candela

Base and derived units
Derived units are created by combination of base units. For instance, an acceleration (m/s) combines at the same time length and time. An interesting picture presenting the relationships between base and derived units can be seen here also from NIST.

Thanks to the definition of unit system, it is possible for the user to work with any kind of derived units, without the need for FreeCAD developpers to foresee them in advance.

Base and derived unit symbols
According to The International System of Units (SI), the symbols to specify a units are officially approved. Two consequences can be highlighted from this.
 * it is not easy for a computer program to work with unit symbols because some are greek letters for instance. Hence they can be a bit difficult to process by a program
 * while some units and their symbols can be used widely, they may be not approved officially, like for instance tonne unit (see p32 of The International System of Units (SI))

To overcome these limitations and remain flexible, the proposed system favors the use of unit magnitudes instead of unit symbols, which remain nonetheless available for an ergonomy reason.

Data model
The three core objects of the unit management system are presented, namely the unit, the unit dictionary and the unit system.

Unit
As a foreword, it is important to highlight that a unit object in itself only indicates a dimension like length, mass, time... It doesn't specify a magnitude like meter, millimeter, kilometer... This last information is specified through the unit system.

Dimension
Compulsory string indicating the dimension of the unit. The dimension of the 7 base units are indicated below (from Guide for the Use of the International System of Units (SI)).
 * LENGTH
 * MASS
 * TIME
 * ELECTRIC CURRENT
 * THERMODYNAMIC TEMPERATURE
 * AMOUNT OF SUBSTANCE
 * LUMINOUS INTENSITY

Dimension attribute allows identifying the unit. Two units cannot share the same dimension.

Signature
Compulsory integer array of size 7 (number of base units) that defines what the unit is. The signature of the 7 base units are:
 * LENGTH: [1,0,0,0,0,0,0]
 * MASS: [0,1,0,0,0,0,0]
 * TIME: [0,0,1,0,0,0,0]
 * ELECTRIC CURRENT: [0,0,0,1,0,0,0]
 * THERMODYNAMIC TEMPERATURE: [0,0,0,0,1,0,0]
 * AMOUNT OF SUBSTANCE: [0,0,0,0,0,1,0]
 * LUMINOUS INTENSITY: [0,0,0,0,0,0,1]

From these 7 units, we are then able to express all derived units defined in Guide for the Use of the International System of Units (SI) and create new ones as needed such as for instance:
 * MASS DENSITY: [-3,1,0,0,0,0,0]
 * AREA: [0,2,0,0,0,0,0]

Signature is the attribute thanks to which unit scaling can be achieved in a generic way.

Symbols
Array of [real, string] (meaning [magnitude, symbol]) that lists all symbols known by FreeCAD. Thanks to this array, the unit scaling API becomes more ergonomic because symbols and related magnitudes are linked.

This array can be extended as required.

For instance, the list of symbols of the LENGTH unit, and their related magnitudes is:

[1e+12,"Tm"],[1e+09,"Gm"],[1e+06,"Mm"], [1e+03,"km"],[1e+02,"hm"],[1e+01,"dam"], [1e+00,"m"],[1e-01,"dm"],[1e-02,"cm"], [1e-03,"mm"],[1e-06,"µm"],[1e-09,"nm"], [1e-12,"pm"],[1e-15,"fm"]

Standard symbols can be found on NIST website and p23 to 26 and p32 (metric ton or tonne) of The International System of Units (SI).

Unit dictionary
All the units available in FreeCAD, and new ones created by the user, should be stored in unit dictionary, which is an XML file (FreeCAD configuration file), so as to be retrieved when needed, i.e. when achieving unit scaling.

Units
Array of units, contained in the unit dictionary.

Unit system
A unit system is the object that allows the user defining the current unit magnitude of each base units with which she/he is working. For instance, knowing that the user is working with millimeter, tonne, and second, thanks to the use of a unit system, FreeCAD can know that energy is expressed in terms of milliJoule, force in terms of Newton, and stress in terms of MegaPascal. Hence a unit system is only defined by a name (for instance Standard unit system) and a magnitude table specifying for each of the 7 base units, what is its corresponding magnitude.

Name
String allowing to the user identifying what is the unit system.

Magnitudes
By specifying the magnitude of the 7 base units, a unit system is defined.

For instance [1e-03, 1e+03, 1, 1, 1, 1, 1], meaning millimeter, tonne, second, ampere, Kelvin, mole, candela

Unit management API
Only the logic of some methods is presented, in order to highlight some features. These methods could belong to an object called Unit manager.

isValid
The unit dictionary can be an XML file (FreeCAD configuration file). It contains a list of defined units. Such a dictionary is required for the proposed unit management system to work.

It must fulfills some conditions that should be checked before activating the unit management system. These conditions are:
 * check that all base units are defined
 * check that a dimension is not defined twice through the units
 * check that a symbol is not defined twice in all the existing symbols
 * check that the signatures of all units have all the same size
 * chacke that a standard symbol (for which magnitude is 1) is defined for all units

isCompatibleWithThisSignature
A unit dictionary defines a set of units and their known magnitudes. When managing a unit, it is relevant to check that its signature is compatible with the set of units registered in the unit dictionary, so as to process it. This check includes:
 * check that the input signature length is of the same size than the unit dictionary unit signatures

scaleUnitFromSymbolToSymbol
Knowing a value, an initial unit by its symbol, the target unit by its symbol, scale the value.

scaleUnitFromSymbolToUnitSystem
Knowing a value, an initial unit by its symbol, the target unit system, scale the value.

scaleUnitFromUnitSystemToSymbol
Knowing a value, an initial unit system, the target unit by its symbol, scale the value.

Motivations for such a management: example of application
Let's assume that we are going to setup a finite element model. To build our model, we need the mesh, material properties, and to define numerical parameters. Considering that they can be tens of material properties to manage, expressed with different units, sometimes not always very common, it is interesting for the user to only have to specify a global unit system, without caring much.

FreeCAD would then just do the job.

As FreeCAD developpers and FreeCAD users do not necessarily know all units that can be defined in the material property files, it is interesting to rely on a generic system.

Let's assume that in such a file we have a fair number of exotic material properties expressed with exotic units, and that we want to work in a specific unit system.

It is easy with the proposed extension to scale any of these properties by knowing their signatures, magnitudes, and the target unit system.

For each of the properties, the scaling is obtained by multiplying the initial property value with the factor $$\frac{initialMagnitude}{targetMagnitude}$$.

The targetMagnitude is then simply obtained with the operation $$\prod_{bu} targetMagnitude_{bu}^{signature_{bu}}$$, bu standing for base unit.

It becomes thus very easy to manage any number of properties with any kind of units with very few lines of Python.

Next actions

 * Implementing Quantity and Unit classes (mostly done)
 * Implementing InputField as User front end (in progress)
 * UnitsCalculator as test bed (in progress)
 * Quantity documentation (in progress)
 * UnitsCalculator documentation
 * Update Material framework to work only with Quantities
 * Test Cases