Re: [Boost-users] [units] Calculating air density

Subject: Re: [Boost-users] [units] Calculating air density
From: Michael Powell (mwpowellhtx_at_[hidden])
Date: 2015-08-09 13:55:06

On Sun, Aug 9, 2015 at 1:32 PM, Michael Powell <mwpowellhtx_at_[hidden]> wrote:
> On Sun, Aug 9, 2015 at 11:16 AM, Michael Powell <mwpowellhtx_at_[hidden]> wrote:
>> Hello,
>>
>> I'd like to calculate air density at altitude. Studying some notes on wikipedia:
>
> I am trying to derived a "specific gas constant" dimension, and
> corresponding units: usually in the form of (J/(kg K)).
>
> Mass and temperature dimensions are simple enough to build upon.
>
> However, energy? Not so much, or perhaps there is a better way that I
> am not grasping.
>
> /// derived dimension for specific gas constant : J M^-1 Theta^-1
> typedef derived_dimension<energy_dimension,1,
>                           mass_base_dimension,-1,
>                           temperature_base_dimension,-1>
> specific_gas_constant_dimension;
>
> Which is yielding some errors, this and a host of others:
>
> Error 19 error C2039: 'tag_type' : is not a member of
> 'boost::units::derived_dimension<boost::units::energy_dimension,1,boost::units::mass_base_dimension,-1,boost::units::temperature_base_dimension,-1,boost::units::dimensionless_type,0,boost::units::dimensionless_type,0,boost::units::dimensionless_type,0,boost::units::dimensionless_type,0,boost::units::dimensionless_type,0>'
> I:\Source\Boost.org\boost_1_58_0\installed\x64\include\boost-1_58\boost\units\detail\linear_algebra.hpp
> 701 1 Kingdom.Physics.Calculators
>
> My guess is for deriving a dimension from a derived dimension? Is
> there a better dimension to use for the energy component?
>
> Or am I wasting time trying to setup a dimension and I should simply
> build the units themselves?
>
> Or, do I really need to string together all the dimensions that
> constitute the energy dimension? or Joules ?

Which, when I "do the math" on the dimensions, I'm not positive, but
the Mass components cancel themselves out (though their actual
quantities might not actually do so...), so I end up with something
like this?

typedef derived_dimension<length_base_dimension,2,
                          time_base_dimension,-2,
                          temperature_base_dimension,-1>
specific_gas_constant_dimension;

Basically substituting and reducing from Joules (J) being energy,
which is M L^2 T^-2.

Which should happen when we say something like this:

quantity<specific_gas_constant> dry_air_ = 287.058*joules/(kilogram*kelvins);

Or this for shorthand, with appropriate unit defined:

quantity<specific_gas_constant> dry_air_ = 287.058*joules_per_kilogram_kelvins;

> I suppose, consistent with the m.o. of consistency over convenience ...
>
> Thank you...
>
>> https://en.wikipedia.org/wiki/Density_of_air
>>
>> Symbol is typically Greek Rho, whose dimensions are generally M/L^3;
>> units will probably be kg/m^3, although I am also reading about
>> slugs/ft^3.
>>
>> Which incorporates a gas constant value:
>>
>> http://en.wikipedia.org/wiki/Gas_constant
>>
>> Whose units appear to be Joules/(Volume*Temp).
>>
>> I'm not seeing anything too terribly exotic there; all these units /
>> dimensions are present in Boost.Units?
>>
>> As is usually the case, it is interesting to see how the units library
>> "reduces" the units during code writing, compilation. Very impressive
>> indeed.
>>
>> Thank you...
>>
>> Best regards,
>>
>> Michael Powell