The variable definition element

The variable definition element
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The variableDef element is used to define each constant, parameter, or variable used within or generated by the defined subsystem model. It contains attributes including the variable name (used for documentation), an XML-unique varID identifier (used for automatic code generation), the units of measure of the variable, and optional axis system, sign convention, alias, and symbol declarations. Optional sub-elements include a written text description and a mathematical description, in MathML 2 content markup, of the calculations needed to derive the variable from other variables or function table outputs. An optional sub-element, isOutput, serves to indicate an intermediate calculation that should be brought out to the rest of the simulation. A final sub-element, uncertainty, captures the statistical properties of a (normally constant) parameter.

There must be a single variableDef for each and every input, output or intermediate constant or variable within the DAVEfunc model.

    variableDef+ : name, varID, units, [axisSystem, sign, alias, symbol, initialValue]
	description? :
            (description character data)
	calculation? :
	    math (defined in MathML2.0 DTD) :
	isOutput? :
	uncertainty? : effect
            (normalPDF : numSigmas | uniformPDF : symmetry )

variableDef attributes:

name: A UNICODE name for the variable (may be same as the varID).
varID: An XML-legal name that is unique within the file.
units: The units-of-measure for the signal.
axisSystem: An optional indicator of the axis system (body, inertial, etc.) in which the signal is measured. See Conventions below for best recommended practice for nomenclature.
sign: An optional indicator of which direction is considered positive (+RWD, +UP, etc.). See the section on Conventions below, for best recommended practice for abbreviations.
symbol: A UNICODE Greek symbol for the signal [to be superseded with more formal MathML or TeX element in a later release].
initialValue: An optional initial value for the parameter. This is normally specified for constant parameters only.

variableDef sub-elements:

description: An optional text description of the variable.
calculation: An optional container for the MathML content markup that describes how this variable is calculated from other variables or function table outputs. This element contains a single math element which is defined in the MathML 2 markup language.
isOutput: This optional element, if present, identifies this variable needs to be passed as an output. How this is accomplished is up to the implementer. Unless specified by this element, a variable is considered an output only if it is the result of a calculation or function AND is not used elsewhere in this DAVEfunc model.
uncertainty: This optional element, if present, describes the uncertainty of this parameter. See the section on Statistics below for more information about this element. Note that the uncertainty sub-element makes sense only for constant parameters (e.g., those with no calculation element but with an initialValue specified.

Exampleï¿½2.ï¿½Two examples of variableDef elements defining input signals

<!--                     ==========================                     -->
<!-- ====================   VARIABLE DEFINITIONS   ==================== -->
<!--                     ==========================                     -->


      <!-- ================== -->
      <!--  Input variables   -->
      <!-- ================== -->

  <variableDef name="Mach" varID="XMACH" units="" symbol="M">
    <description> 
	Mach number (dimensionless) 
    </description>
  </variableDef>

  <variableDef name="dbfll" varID="DBFLL" units="deg" sign="ted" 
                symbol="&#x3B4;bfll">
    <description>
	Lower left body flap deflection, deg, +TED (so deflections are
	always zero or positive).
    </description>
  </variableDef>

	The `name` attribute is intended for humans to read, perhaps as the signal name in an automated wiring diagram.
	The `varID` attribute is intended for the processing application to read. This must be an XML-valid identifier and must be unique within this model.
	The `description` element may be used in an automated data dictionary entry associated with the `name` attribute.
	The optional `units` attribute describes the units of measure of the variable. See the section on Conventions below for a recommended list of units-of-measure abbreviations.
	The optional `sign` attribute describes the sign convention that applies to this variable. In this case, the lower-left body-flap is positive with trailing-edge-down deflection. See the section on Conventions below for a recommended list of sign abbreviations.
	The optional `symbol` attribute allows a UNICODE character string that might be used for this variable in a symbols listing.

In this example, two input variables are defined: XMACH and DBFLL. These two variables are inputs to a table lookup function shown in example 8 below.

Exampleï¿½3.ï¿½A simple local variable

      <!-- ================== -->
      <!--  Local variables   -->
      <!-- ================== -->

<!-- PRELIMINARY BUILDUP EQUATIONS -->

<!--  LOWER LEFT BODY FLAP CONTRIBUTIONS -->

<!--    table output signal   -->
  <variableDef name="Cldbfll_0" varID="CRBFLL0" units="">
    <description>
	Output of CRBFLL0 function; rolling moment contribution of
	lower left body flap deflection due to alpha^0 (constant
	term).
    </description>
  </variableDef>

This example defines CRBFLLO which is the "independent variable" output from the table lookup function shown in example 8 below.

Exampleï¿½4.ï¿½A more complete example using a calculation element

<!--    lower left body flap lift buildup -->
  <variableDef name="CLdbfll" varID="CLBFLL" units="">
    <description>
	Lift contribution of lower left body flap deflection
	CLdbfll = CLdbfll_0 + alpha*(CLdbfll_1 + alpha*(CLdbfll_2 
                            + alpha*CLdbfll_3)) 
    </description>
    <calculation>  
      <math>
	<apply>  
	  <plus/>
	  <ci>CLBFLL0</ci>
	  <apply>
	    <times/>
	    <ci>ALP</ci>
	    <apply>
	      <plus/>
	      <ci>CLBFLL1</ci>
	      <apply>
		<times/>
		<ci>ALP</ci>
		<apply>
		  <plus/>
		  <ci>CLBFLL2</ci>
		  <apply> 
		    <times/>
		    <ci>ALP</ci>
		    <ci>CLBFLL3</ci>
		  </apply> <!--            a*c3   -->  
		</apply> <!--        (c2 + a*c3)  -->
	      </apply> <!--        a*(c2 + a*c3)  -->
	    </apply> <!--    (c1 + a*(c2 + a*c3)) -->
	  </apply> <!--    a*(c1 + a*(c2 + a*c3)) -->
	</apply> <!-- c0 + a*(c1 + a*(c2 + a*c3)) -->
      </math>
    </calculation>
  </variableDef>

	This FORTRANish equation is simply for human readers and is not parsed by the processing application.
	A `calculation` element always embeds a MATHML-2 `math` element.
	Each `apply` tag pair surrounds a math operation (in this example, a `plus`) operator) and the arguments to that operation (in this case, a variable `CLBFLL` defined elsewhere is added to the results of the nested `apply` operation).
	Inner-most apply multiplies variables `ALP` and `CLBFLL3`.
	The comments here are useful for humans to understand how the equation is being built up; the processing application doesn't use these comments.

Here the local variable CLBFLL is defined as a calculated quantity, based on several other input or local variables (not shown). Note the description element is used to describe the equation, in FORTRANish human-readable text. The calculation element describes this same equation in MathML 2 content markup syntax; this portion should be used by parsing applications to create either source code, documentation, or run-time calculation structures.

Exampleï¿½5.ï¿½An output variable based on another calculation element


      <!-- ================== -->
      <!--  Output variables  -->
      <!-- ================== -->

  <variableDef name="CL" varID="CL" units="" sign="up" symbol="CL">
    <description>
	Coefficient of lift
	CL = CL0 + CLBFUL + CLBFUR + CLBFLL + CLBFLR + 
     		CLWFL + CLWFR + CLRUD + CLGE + CLLG
    </description>
    <calculation>
      <math>
	<apply> 
	  <plus/>
	  <ci>CL0</ci>
	  <ci>CLBFUL</ci>
	  <ci>CLBFUR</ci>
	  <ci>CLBFLL</ci>
	  <ci>CLBFLR</ci>
	  <ci>CLWFL</ci>
	  <ci>CLWFR</ci>
	  <ci>CLRUD</ci>
	  <ci>CLGE</ci>
	  <ci>CLLG</ci>
	</apply>
      </math>
    </calculation>
    <isOutput/> 
  </variableDef>

	Here `<apply>` simply sums the value of these variables, referenced by their `varID`s.
	The `isOutput` element signifies to the processing application that this variable should be made visible to models external to this DAVEfunc.

This is an example of how an output variable (CL) might be defined from previously calculated local variables (in this case, CL0, CLBFL, etc.).

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