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#LyX 2.1 created this file. For more info see http://www.lyx.org/ |
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\shortcut idx |
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\end_index |
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\end_header |
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|
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\begin_body |
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|
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\begin_layout Chapter |
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Defining New Units of Measure |
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\begin_inset CommandInset label |
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LatexCommand label |
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name "cha:units" |
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|
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\end_inset |
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|
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|
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\end_layout |
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|
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\begin_layout Standard |
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Occasionally units of measure are needed that do not come predefined in |
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the ASCEND system. |
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You can define a new unit of measure by defining the conversion factor. |
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In this chapter, we examine how to do this easily for an individual user |
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and on a system-wide basis. |
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|
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\end_layout |
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|
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\begin_layout Section |
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|
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\emph on |
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Caveats |
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\end_layout |
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|
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\begin_layout Standard |
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\begin_inset Marginal |
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status collapsed |
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|
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\begin_layout Plain Layout |
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Order matters! |
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\end_layout |
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|
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\end_inset |
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|
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Order matters for defining units of measure in three ways. |
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\end_layout |
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|
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\begin_layout Itemize |
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a unit of measure must be defined before it is used anywhere. |
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\end_layout |
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|
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\begin_layout Itemize |
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the first definition ASCEND reads for a unit of measure is the only definition |
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ASCEND sees. |
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\end_layout |
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|
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\begin_layout Itemize |
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new units can be defined only from already defined units. |
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\end_layout |
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|
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\begin_layout Standard |
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Measuring units are absolutely global in the ASCEND environment -- they |
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are not deleted when the Library of types is deleted. |
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Once you define a unit's conversion factor, you are stuck with it until |
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you shut down and restart ASCEND. |
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For any unit conversion definition, only the first conversion factor seen |
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is accepted. |
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Redefinitions of the same unit are ignored. |
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\end_layout |
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|
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\begin_layout Standard |
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\begin_inset Marginal |
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status collapsed |
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|
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\begin_layout Plain Layout |
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Multiplicative unit conversions only! |
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\end_layout |
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|
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\end_inset |
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|
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The various units ASCEND uses are all obtained by conversion factors (multiplica |
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tion only) from the SI units. |
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So, for example, temperatures may be in degrees Rankine but not in Fahrenheit. |
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In this chapter we address creating new conversion factors. |
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For handling non- |
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\end_layout |
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|
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\begin_layout Standard |
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multiplicative conversions (such as the Fahrenheit or Celsius offsets) see |
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Section |
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\begin_inset space ~ |
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\end_inset |
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|
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|
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\begin_inset CommandInset ref |
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LatexCommand vref |
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reference "sec:dimeqns.Fahrenheit" |
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|
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\end_inset |
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|
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. |
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\end_layout |
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|
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\begin_layout Section |
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Individualised units |
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\end_layout |
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|
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\begin_layout Standard |
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There are two scenarios for individualized units of measure. |
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One in which you need a measure defined only for a specific model and another |
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in which you want to define a measure that you will use throughout your |
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modeling activities in the future. |
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The syntax for both is the same, but where best to put the UNITS statement |
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differs. |
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\end_layout |
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|
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\begin_layout Subsection |
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Units of measure for a specific model |
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\end_layout |
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|
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\begin_layout Standard |
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Units of measure that are used in only one model can be defined at the beginning |
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of the model itself or before the model, but not the units appear in the |
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model definition. |
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Let us suppose you want to measure speed in {furlong/fortnight} in a model. |
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ASCEND does not define |
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\family typewriter |
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furlong |
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\family default |
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, |
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\family typewriter |
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fortnight |
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\family default |
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, or |
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\family typewriter |
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furlong/fortnight |
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\family default |
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. |
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(Interestingly, we have been unable to find standard definitions for them!). |
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\end_layout |
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|
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\begin_layout LyX-Code |
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MODEL mock_turtle; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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d IS_A distance; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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delta_t IS_A time; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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s IS_A speed |
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\end_layout |
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|
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\begin_layout LyX-Code |
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|
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\end_layout |
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|
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\begin_layout LyX-Code |
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s = d/delta_t; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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(* We really should write s * delta_t = d; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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to avoid division by zero. |
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*) |
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\end_layout |
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|
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\begin_layout LyX-Code |
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|
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\end_layout |
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|
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\begin_layout LyX-Code |
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UNITS |
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\end_layout |
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|
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\begin_layout LyX-Code |
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furlong = {3.17*kilometer}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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fortnight = {10*day}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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END UNITS; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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|
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\end_layout |
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|
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\begin_layout LyX-Code |
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METHODS |
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\end_layout |
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|
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\begin_layout LyX-Code |
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METHOD default_self; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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d := 1 {furlong}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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t := 5 {hours}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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END default_self; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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|
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\end_layout |
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|
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\begin_layout LyX-Code |
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(* other standard methods omitted *) |
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\end_layout |
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|
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\begin_layout LyX-Code |
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|
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\end_layout |
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|
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\begin_layout LyX-Code |
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END mock_turtle; |
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\end_layout |
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|
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\begin_layout Standard |
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In mock_turtle we define |
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\family typewriter |
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furlong |
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\family default |
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and |
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\family typewriter |
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fortnight |
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\family default |
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conversions |
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\series bold |
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before |
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\series default |
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they are used in the methods and before any equations which use them. |
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Also, notice that, even though ASCEND rejects this model |
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\family typewriter |
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mock_turtle |
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\family default |
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, as it will because of the missing " |
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\family typewriter |
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; |
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\family default |
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" after "speed" in the fourth line, |
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\family typewriter |
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furlong |
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\family default |
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and |
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\family typewriter |
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fortnight |
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\family default |
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still get defined. |
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The |
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\family typewriter |
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UNITS |
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\family default |
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statement can appear in any context and gets processed regardless of any |
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other errors in that context. |
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\end_layout |
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|
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\begin_layout Subsection |
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UNITS OF MEASURE FOR ALL YOUR PERSONAL MODELS |
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\end_layout |
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|
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\begin_layout Standard |
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If you commonly use a set of units that is not in the default ASCEND library |
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|
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\family typewriter |
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measures.a4l |
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\family default |
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, you can create your own personal library of units in the user data directory |
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|
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\family typewriter |
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ascdata |
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\family default |
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. |
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The location of this directory is given by ASCEND at the end of all the |
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start-up spew it prints to the Console window (or xterm under UNIX) as |
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shown below. |
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You will see a path other than |
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\family typewriter |
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/usr0/ballan/ |
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\family default |
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of course. |
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\end_layout |
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|
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\begin_layout LyX-Code |
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----------------------------------- |
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\end_layout |
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|
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\begin_layout LyX-Code |
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User data directory is /usr0/ballan/ascdata |
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\end_layout |
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|
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\begin_layout LyX-Code |
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----------------------------------- |
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\end_layout |
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|
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\begin_layout Standard |
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Create the library file |
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\family typewriter |
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myunits.a4l |
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\family default |
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in your |
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\family typewriter |
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ascdata |
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\family default |
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directory. |
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This file should contain a |
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\family typewriter |
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UNITS |
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\family default |
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statement and any comments or |
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\family typewriter |
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NOTES |
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\family default |
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you wish to make. |
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This file should contain any conversions that you change often. |
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For example: |
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\end_layout |
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|
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\begin_layout LyX-Code |
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UNITS |
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\end_layout |
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|
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\begin_layout LyX-Code |
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(* Units for Norway, maybe?*) |
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\end_layout |
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|
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\begin_layout LyX-Code |
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euro = {1*currency}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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(* currency is the fundamental financial unit *) |
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\end_layout |
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|
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\begin_layout LyX-Code |
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kroner = {0.00314*euro}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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nk = {kroner}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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USdollar = {0.9*euro}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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CANdollar = {0.65*USdollar}; |
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\end_layout |
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|
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\begin_layout LyX-Code |
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END UNITS; |
| 432 |
\end_layout |
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|
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\begin_layout Standard |
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Note that this file contains a definition of |
| 436 |
\family typewriter |
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USdollar |
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\family default |
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different from that given in the standard library |
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\family typewriter |
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measures.a4l |
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\family default |
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. |
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ASCEND will warn you about the conflict. |
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You must load |
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\family typewriter |
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myunits.a4l |
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\family default |
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into ASCEND before |
| 450 |
\family typewriter |
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atoms.a4l |
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\family default |
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or any of our higher level libraries. |
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You can ensure that this happens by putting the statement |
| 455 |
\end_layout |
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|
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\begin_layout LyX-Code |
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REQUIRE "myunits.a4l"; |
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\end_layout |
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|
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\begin_layout Standard |
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on the very first line in all your model definition files. |
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\end_layout |
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|
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\begin_layout Section |
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NEW SYSTEM-WIDE UNITS |
| 467 |
\end_layout |
| 468 |
|
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\begin_layout Standard |
| 470 |
Suppose you are maintaining ASCEND on a network of computers with many users. |
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You have a standard set of models stored in a centrally located directory, |
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and you want to define units for use by everyone on the network. |
| 473 |
In this case, just edit |
| 474 |
\family typewriter |
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models/measures.a4l |
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\family default |
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, the default units of measure library. |
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ASCEND is an open system. |
| 479 |
|
| 480 |
\end_layout |
| 481 |
|
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\begin_layout Standard |
| 483 |
Make the new unit conversion definition statement(s) of the form |
| 484 |
\end_layout |
| 485 |
|
| 486 |
\begin_layout LyX-Code |
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newunit = {combination of old units}; |
| 488 |
\end_layout |
| 489 |
|
| 490 |
\begin_layout Standard |
| 491 |
as described in **Section 9.2.** In the file |
| 492 |
\family typewriter |
| 493 |
measures.a4l |
| 494 |
\family default |
| 495 |
, add your statement(s) anywhere inside the block of definitions that starts |
| 496 |
with |
| 497 |
\family typewriter |
| 498 |
UNITS |
| 499 |
\family default |
| 500 |
and ends with |
| 501 |
\family typewriter |
| 502 |
END UNITS |
| 503 |
\family default |
| 504 |
. |
| 505 |
The existing definitions are divided up into groups by comment statements. |
| 506 |
If your conversion belongs to one of the groups, it is best to put the |
| 507 |
conversion in that group. |
| 508 |
The groups are given in Table |
| 509 |
\begin_inset CommandInset ref |
| 510 |
LatexCommand ref |
| 511 |
reference "tab:units.groupOfUnits" |
| 512 |
|
| 513 |
\end_inset |
| 514 |
|
| 515 |
. |
| 516 |
\end_layout |
| 517 |
|
| 518 |
\begin_layout Standard |
| 519 |
\begin_inset Float table |
| 520 |
wide false |
| 521 |
sideways false |
| 522 |
status open |
| 523 |
|
| 524 |
\begin_layout Plain Layout |
| 525 |
\begin_inset Caption Standard |
| 526 |
|
| 527 |
\begin_layout Plain Layout |
| 528 |
Groups of units in the current measures library |
| 529 |
\begin_inset CommandInset label |
| 530 |
LatexCommand label |
| 531 |
name "tab:units.groupOfUnits" |
| 532 |
|
| 533 |
\end_inset |
| 534 |
|
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|
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\end_layout |
| 537 |
|
| 538 |
\end_inset |
| 539 |
|
| 540 |
|
| 541 |
\end_layout |
| 542 |
|
| 543 |
\begin_layout Plain Layout |
| 544 |
\begin_inset Tabular |
| 545 |
<lyxtabular version="3" rows="21" columns="1"> |
| 546 |
<features rotate="0" tabularvalignment="middle"> |
| 547 |
<column alignment="center" valignment="top"> |
| 548 |
<row> |
| 549 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 550 |
\begin_inset Text |
| 551 |
|
| 552 |
\begin_layout Plain Layout |
| 553 |
|
| 554 |
\family typewriter |
| 555 |
distance |
| 556 |
\end_layout |
| 557 |
|
| 558 |
\end_inset |
| 559 |
</cell> |
| 560 |
</row> |
| 561 |
<row> |
| 562 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 563 |
\begin_inset Text |
| 564 |
|
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\begin_layout Plain Layout |
| 566 |
|
| 567 |
\family typewriter |
| 568 |
mass |
| 569 |
\end_layout |
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|
| 571 |
\end_inset |
| 572 |
</cell> |
| 573 |
</row> |
| 574 |
<row> |
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
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\begin_inset Text |
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|
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\begin_layout Plain Layout |
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|
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\family typewriter |
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time |
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\end_layout |
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|
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\end_inset |
| 585 |
</cell> |
| 586 |
</row> |
| 587 |
<row endhead="true"> |
| 588 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
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\begin_inset Text |
| 590 |
|
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\begin_layout Plain Layout |
| 592 |
|
| 593 |
\family typewriter |
| 594 |
molecular quantities |
| 595 |
\end_layout |
| 596 |
|
| 597 |
\end_inset |
| 598 |
</cell> |
| 599 |
</row> |
| 600 |
<row endhead="true"> |
| 601 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 602 |
\begin_inset Text |
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|
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\begin_layout Plain Layout |
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|
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\family typewriter |
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money |
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\end_layout |
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|
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\end_inset |
| 611 |
</cell> |
| 612 |
</row> |
| 613 |
<row endhead="true"> |
| 614 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 615 |
\begin_inset Text |
| 616 |
|
| 617 |
\begin_layout Plain Layout |
| 618 |
|
| 619 |
\family typewriter |
| 620 |
reciprocal time (frequency) |
| 621 |
\end_layout |
| 622 |
|
| 623 |
\end_inset |
| 624 |
</cell> |
| 625 |
</row> |
| 626 |
<row endhead="true"> |
| 627 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 628 |
\begin_inset Text |
| 629 |
|
| 630 |
\begin_layout Plain Layout |
| 631 |
|
| 632 |
\family typewriter |
| 633 |
area |
| 634 |
\end_layout |
| 635 |
|
| 636 |
\end_inset |
| 637 |
</cell> |
| 638 |
</row> |
| 639 |
<row endhead="true"> |
| 640 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 641 |
\begin_inset Text |
| 642 |
|
| 643 |
\begin_layout Plain Layout |
| 644 |
|
| 645 |
\family typewriter |
| 646 |
volume |
| 647 |
\end_layout |
| 648 |
|
| 649 |
\end_inset |
| 650 |
</cell> |
| 651 |
</row> |
| 652 |
<row endhead="true"> |
| 653 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 654 |
\begin_inset Text |
| 655 |
|
| 656 |
\begin_layout Plain Layout |
| 657 |
|
| 658 |
\family typewriter |
| 659 |
force |
| 660 |
\end_layout |
| 661 |
|
| 662 |
\end_inset |
| 663 |
</cell> |
| 664 |
</row> |
| 665 |
<row endhead="true"> |
| 666 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 667 |
\begin_inset Text |
| 668 |
|
| 669 |
\begin_layout Plain Layout |
| 670 |
|
| 671 |
\family typewriter |
| 672 |
pressure |
| 673 |
\end_layout |
| 674 |
|
| 675 |
\end_inset |
| 676 |
</cell> |
| 677 |
</row> |
| 678 |
<row endhead="true"> |
| 679 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 680 |
\begin_inset Text |
| 681 |
|
| 682 |
\begin_layout Plain Layout |
| 683 |
|
| 684 |
\family typewriter |
| 685 |
energy |
| 686 |
\end_layout |
| 687 |
|
| 688 |
\end_inset |
| 689 |
</cell> |
| 690 |
</row> |
| 691 |
<row endhead="true"> |
| 692 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 693 |
\begin_inset Text |
| 694 |
|
| 695 |
\begin_layout Plain Layout |
| 696 |
|
| 697 |
\family typewriter |
| 698 |
power |
| 699 |
\end_layout |
| 700 |
|
| 701 |
\end_inset |
| 702 |
</cell> |
| 703 |
</row> |
| 704 |
<row endhead="true"> |
| 705 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 706 |
\begin_inset Text |
| 707 |
|
| 708 |
\begin_layout Plain Layout |
| 709 |
|
| 710 |
\family typewriter |
| 711 |
absolute viscosity |
| 712 |
\end_layout |
| 713 |
|
| 714 |
\end_inset |
| 715 |
</cell> |
| 716 |
</row> |
| 717 |
<row endhead="true"> |
| 718 |
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> |
| 719 |
\begin_inset Text |
| 720 |
|
| 721 |
\begin_layout Plain Layout |
| 722 |
|
| 723 |
\family typewriter |
| 724 |
electric charge |
| 725 |
\end_layout |
| 726 |
|
| 727 |
\end_inset |
| 728 |
</cell> |
| 729 |
</row> |
| 730 |
<row> |
| 731 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 732 |
\begin_inset Text |
| 733 |
|
| 734 |
\begin_layout Plain Layout |
| 735 |
|
| 736 |
\family typewriter |
| 737 |
miscellaneous electromagnetic |
| 738 |
\end_layout |
| 739 |
|
| 740 |
\end_inset |
| 741 |
</cell> |
| 742 |
</row> |
| 743 |
<row> |
| 744 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 745 |
\begin_inset Text |
| 746 |
|
| 747 |
\begin_layout Plain Layout |
| 748 |
|
| 749 |
\family typewriter |
| 750 |
swiped from C math.h |
| 751 |
\end_layout |
| 752 |
|
| 753 |
\end_inset |
| 754 |
</cell> |
| 755 |
</row> |
| 756 |
<row> |
| 757 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 758 |
\begin_inset Text |
| 759 |
|
| 760 |
\begin_layout Plain Layout |
| 761 |
|
| 762 |
\family typewriter |
| 763 |
constant based conversions |
| 764 |
\end_layout |
| 765 |
|
| 766 |
\end_inset |
| 767 |
</cell> |
| 768 |
</row> |
| 769 |
<row> |
| 770 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 771 |
\begin_inset Text |
| 772 |
|
| 773 |
\begin_layout Plain Layout |
| 774 |
|
| 775 |
\family typewriter |
| 776 |
subtly dimensionless measures |
| 777 |
\end_layout |
| 778 |
|
| 779 |
\end_inset |
| 780 |
</cell> |
| 781 |
</row> |
| 782 |
<row> |
| 783 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 784 |
\begin_inset Text |
| 785 |
|
| 786 |
\begin_layout Plain Layout |
| 787 |
|
| 788 |
\family typewriter |
| 789 |
light quantities |
| 790 |
\end_layout |
| 791 |
|
| 792 |
\end_inset |
| 793 |
</cell> |
| 794 |
</row> |
| 795 |
<row> |
| 796 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 797 |
\begin_inset Text |
| 798 |
|
| 799 |
\begin_layout Plain Layout |
| 800 |
|
| 801 |
\family typewriter |
| 802 |
miscellaneous rates |
| 803 |
\end_layout |
| 804 |
|
| 805 |
\end_inset |
| 806 |
</cell> |
| 807 |
</row> |
| 808 |
<row> |
| 809 |
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> |
| 810 |
\begin_inset Text |
| 811 |
|
| 812 |
\begin_layout Plain Layout |
| 813 |
|
| 814 |
\family typewriter |
| 815 |
time variant conversions |
| 816 |
\end_layout |
| 817 |
|
| 818 |
\end_inset |
| 819 |
</cell> |
| 820 |
</row> |
| 821 |
</lyxtabular> |
| 822 |
|
| 823 |
\end_inset |
| 824 |
|
| 825 |
|
| 826 |
\end_layout |
| 827 |
|
| 828 |
\end_inset |
| 829 |
|
| 830 |
|
| 831 |
\end_layout |
| 832 |
|
| 833 |
\begin_layout Section |
| 834 |
Send them in |
| 835 |
\end_layout |
| 836 |
|
| 837 |
\begin_layout Standard |
| 838 |
We are always on the lookout for useful unit conversions to add to |
| 839 |
\family typewriter |
| 840 |
measures.a4l |
| 841 |
\family default |
| 842 |
. |
| 843 |
If you create a |
| 844 |
\family typewriter |
| 845 |
myunits.a4l |
| 846 |
\family default |
| 847 |
containing unit conversion definitions of general use (i.e. |
| 848 |
not currency exchange rates and other time-varying conversions), please |
| 849 |
mail us a copy and include your name in a comment. |
| 850 |
Thank you very much. |
| 851 |
\end_layout |
| 852 |
|
| 853 |
\end_body |
| 854 |
\end_document |
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