The NASA(h) is recent to me.
Curiously enough, they arrived at the same conclusion years ago:
Theodore, Jean, [Ralph ?] that altitude is not homogeneous
and represented by rational/expDecay/rational segments.
In this document, we just trust NASA as an act of faith !
To determine the altitude, kPa is the measured.
You may probably use the static from the Pitot tube or else
accurate barometric device... local barometric is headache.
Given as is if any useful for your journey in air.

Jean

Inst_ISA [km_kPa] NASA airplane Copy.sm (138 KiB) downloaded 68 time(s).

Hello Jean:
The atmospheric conditions are very changeable, so it could be said that
the data are only accurate at the time they are taken.
The density of the air changes with the temperature, and the
temperature changes with the altitude, then the barometric pressure also changes.
There is a barometric formula to calculate the air pressure according to the
altitude, to which I have included the temperature function according
to the altitude to try to make the calculation more accurate.





Barometrit_Formula_Aire_CBG.sm (423 KiB) downloaded 57 time(s).


Best Regards

Carlos

Wrote

Hello Jean:
The atmospheric conditions are very changeable, so it could be said that
the data are only accurate at the time they are taken.
The density of the air changes with the temperature, and the
temperature changes with the altitude, then the barometric pressure also changes.
There is a barometric formula to calculate the air pressure according to the
altitude, to which I have included the temperature function according
to the altitude to try to make the calculation more accurate.

Thanks Carlos,
Unfortunately, SS 6179 can't open the latest SS Beta you are using,
can't read the temperature correction. Math 24 barometric is in fact
so much erroneous vs PDAS, NASA(h) it shouldn't be published as given.

Jean

Hello Jean:

I do not know why SS6179 transforms the units differently to SS7089 and gives slightly different results.

Here you have the file in the SS6179 version.

Barometric_Formula_Air_6179.sm (423 KiB) downloaded 60 time(s).




Best Regards

Carlos

Wrote

Hello Jean:
I do not know why SS6179 transforms the units differently to SS7089 and gives slightly different results.
Here you have the file in the SS6179 version.

Thanks Carlos for the SS6179 document.
Polynomic is new to me, more applications expected.
As applied to Barometric, the more abundant data set gives results
very close to NASA. The last step is the [m] altitude vs measured kPa.
Something similar to the other document ... RemToDo.
The P(h) has an inverse RootsOf, of no interest for minimal calculator.

Cheers ... Jean

Inst_ISA Barometric Formula [Carlos].sm (455 KiB) downloaded 68 time(s).

Hello Carlos.

Wrote

I do not know why SS6179 transforms the units differently to SS7089 and gives slightly different results.

Latest beta-versions of SMath Studio have huge improvements regarding accuracy, calculation performance and worksheet rendering performance. This is because currently I'm participating in a project where IAPWS equations is used and it was observed that all previous versions of SMath Studio had problems with accuracy. After reworking core of calculation engines it was observed that calculation speed became worse, so I have started work to improve performance in high accuracy calculations.
As for now SMath Studio became much more usable in both: accuracy and speed points of view (+ new rendering engine is here) and I'm doing latest preparations to release new stable build.

We are now much more close to ver. 1.0

Best regards.

Andrey,
I believe that these considerations merit a more visible position in the forum

sergio

Hello Andrey

Wrote

Hello Carlos.

Wrote

I do not know why SS6179 transforms the units differently to SS7089 and gives slightly different results.

Latest beta-versions of SMath Studio have huge improvements regarding accuracy, calculation performance and worksheet rendering performance. This is because currently I'm participating in a project where IAPWS equations is used and it was observed that all previous versions of SMath Studio had problems with accuracy. After reworking core of calculation engines it was observed that calculation speed became worse, so I have started work to improve performance in high accuracy calculations.
As for now SMath Studio became much more usable in both: accuracy and speed points of view (+ new rendering engine is here) and I'm doing latest preparations to release new stable build.

We are now much more close to ver. 1.0

Best regards.

Thank you Andrey for your extensive explanation, and we would like
to make it a substantial improvement to your excellent Software.

Best Regards

Carlos

Hello Jean

Wrote

Thanks Carlos for the SS6179 document.
Polynomic is new to me, more applications expected.
As applied to Barometric, the more abundant data set gives results
very close to NASA. The last step is the [m] altitude vs measured kPa.
Something similar to the other document ... RemToDo.
The P(h) has an inverse RootsOf, of no interest for minimal calculator.

Cheers ... Jean

Thank you very much for your excellent work.
I have tried to calculate the temperature used or measured in the NASA data,
isolating the temperature variable from the barometric formula.


I hope you find a better approach

NASA_Invert_SS6179.sm (57 KiB) downloaded 59 time(s).

Thank you

Best Regards

Carlos

Wrote

I hope you find a better approach

... Here is Carlos . . . an un-ambiguous altimetric formula.
1. NASA solved for well distributed points
2. The inverse Barometric solved for the the compensation parameter.
3. Final altimetric at least up to 40 km
4. Accuracy depends upon NASA itself and kPa resolution
Will read your latest attachment ... Jean



Inst_ISA Altimetric Formula Copy.sm (32 KiB) downloaded 56 time(s).

The Altimetric session ends here for quite a while unless more revelation.
Formula page 7/7 ... auto-compensated on actual/local ISO [101.325 kPa].
The mutual conformity wrt solved NASA(h) is stricking of realism.
Comments/suggestions ... welcome.

Jean



Inst_ISA Altimetric Formula Copy.sm (131 KiB) downloaded 51 time(s).

Hello Jean

Wrote

The Altimetric session ends here for quite a while unless more revelation.
Formula page 7/7 ... auto-compensated on actual/local ISO [101.325 kPa].
The mutual conformity wrt solved NASA(h) is stricking of realism.
Comments/suggestions ... welcome.

Jean

The Altimetric session still has a little more chapter, since the
Barometric Formula can be adjusted for the variable of gravity




Inst_ISA Altimetric Formula Gravity.sm (227 KiB) downloaded 60 time(s).

Best Regards

Carlos

Wrote

The Altimetric session still has a little more chapter, since the
Barometric Formula can be adjusted for the variable of gravity

I'm still with you Carlos ... next few days.
Just discovered problem with solve(,,,,) from which altimetric is constructed.
In the long range solutions from which the selected support points,
solutions are irregularly accurate compared to Mathcad seeded root scanner TOL e-6
This explains the observed irregular residuals.
And now, you are putting Gravity ... Oh ! ... see you, Jean.

... last brick in the wall.
1. NASA(h) Barometric ... kPa given altitude (h)
4. Nasa(p) Altimetric ... altitude (h) given kPa
................sections [2, 3] not needed for publishing
though guide line for discrete solve.
Just need the dual formulas [image below]



Inst_ISA Barometric_Altimetric Companion.sm (91 KiB) downloaded 59 time(s).

Wrote

... last brick in the wall.

... one more brick in the wall !
1. Cold airport °C landing altitude correction added
2. Spline TableIII added [observe typo in the published document]

Inst_ISA Barometric_Altimetric Companion.sm (542 KiB) downloaded 62 time(s).