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cb4d01a0-1cf9-4e3e-ba62-3ee5e2a35780 36 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Standard Atmospere: altitude/pressure

1. Upper segment: altitude [km] vs measured kPa

x β kPa20 β 1 el β 2 el x β 3 el / - exp * + :

y x β kPa20 ≡ x solve maple y β 1 el - β 2 el / ln β 3 el * -

altitude [km]vs kPa p β altitude p β 1 el - β 2 el / ln β 3 el * - :

β 0.02264 127.8954 6.35874 31 mat :

11 β kPa20 20 β kPa20 21 mat 22.7 5.53 21 mat

x β kPa20 11 x ≤ (x 20 ≤ (& β 1 el β 2 el x β 3 el / - exp * + not OIAC if :

x β altitude 5.53 x ≤ (x 22.7 ≤ (& x β 1 el - β 2 el / ln β 3 el * - not OIAC if :

blue => kPa vs altitude [km] ...OIAC red => km vs measured pressure [kPa]

x β kPa20 x β altitude 2 1 sys

from measured kPa [5.5..22.7] 'y' is your altitude [km]

x β altitude 2 1 sys

2. Lower segment: altitude [m] vs measured Pa

Altitude[m] vs pressure [Pa x β H 22700 x ≤ (x 107477 ≤ (& β 1 el 1 x 101325 / (β 2 el^(- (* next segment if :

β 44330.77 0.190263 21 mat :

x β H 2 1 sys

22700 β H 101325 β H 107477 β H 31 mat 109810500 - 31 mat

3. Pressure 'kPa' vs altitude 'm'

Segment: -0.5..11 km h P 1013251 h 44330.77 / - (5.255876^* :

------------------------ EQ.1

0.001 0 P 11000 P 20000 P 31 mat * 101.325 22.632065 4.328139 31 mat

1013251 h 44330 / - (5.2^*

5.53

Thiele J_Fraction: -0.5..11 km x kPa11 66.316994 3988.071258 x 2.403022 + 1379.737008 x 28.965069 + 539.638243 x 13.217861 + / - / + / - :

----------EQ.2

Segment: 11..20 km x β kPa20 β 1 el β 2 el x β 3 el / - exp * + :

β 0.02264 127.8954 6.35874 31 mat :

-----------------EQ.3

_11 110005011000022 mat :

_20 200002020000022 mat :

plot 0.001 x P * x 1000 / kPa11 x 1000 / β kPa20_11_20 51 sys :

Alternate solving for altitude: given/measured 'kPa' x kPa11 65.344 - 0 ≡ x 30005000 solve 4096 kPa11 21 mat 4096.0249 65.344 21 mat

plot

EQ.1 & EQ.2 fit equally well the 0..11 km segment. Valid to extrapolate up to 12 km. Thiele rational EQ.2 looks cumbersome, however far superior wrt computation load. EQ.2 is a 9 Aops vs EQ.1 Y^x which is ~ 45 Aops. At the machine code level of integer arithmetic, Thiele EQ.2 is ~ 5 times faster ... Not negligible in Avionics/Aeronautics. Segment 11..20 km is "pure", simply expDecay model. A thiele rational fit would economise a bit of computation load.

plot

3. Specific 'ρ' vs altitude 'km'

A much better fit @ low computing cost !
Reserved for the  x < 11 x ρ11 1.604858 174.727169 x 43.473225 + 1286.481982 x 5.24242 + 0.000159 x 5.14073 - / + / + / - :

Much better fit to PDAS x β ρ20 β 1 el β 2 el x β 3 el / - exp * + :

β 0.0001376 1.67547 6.36715 31 mat :

α 1.30644000006 104 -^* 38518.8995295 38510.6720344 64.7372080910 68.7237058260 25.4827261347 4.84161810338 105 -^* 1483390476.38 2.74067434956 2.79372428294 575.381616331 111 mat :

x α J α 1 el α 7 el x α 2 el + α 8 el x α 3 el - α 9 el x α 4 el - α 10 el x α 5 el - α 11 el x α 6 el - / + / + / + / + / + :

x S11 1 - x ≤ (x 11 ≤ (& x ρ11 OFF segment if :

x S20 11 x ≤ (x 20 ≤ (& x β ρ20 OFF segment if :

x S85 20 x ≤ (x 85 ≤ (& x α J OFF segment if :

Air specific 'ρ' @ altitude [km]. These functions are of ultimate quality. They agree with any source ... "sources" are just as is [± 0.?] from thumb work. The source code of the functions are *.sm [snippet]. In short: above your head, is not homogeneous in term of its representability by a single or modified DE. The two rational segments have no DE representation. This point is fundamental to view atmosphere in the mind. jmGiraud [author of these 'ρ' segments] certifies for public use [14 Nov. 2016].

x S11 x S20 x S85 11 11 S11 + 12 black 20 20 S20 + 12 black 85 85 S85 + 12 black 3 5 mat 4 1 sys

Atmosphere segments ... -1 => 11... 11 => 20... 20 => 85 1 - 11 range rational ≡ 1120 range expDecay ≡ 2085 range rational ≡ 31 mat Thiele QUICK [PDAS11].sm Genfit Minimize [PDAS1120].sm Thiele QUICK [ISA2085].sm 31 mat ≡

h OIAC_11 1 - h ≤ (h 11 ≤ (& 1 22.556726 h * 103 -^* - (4.256134^if :

h OIAC_20 11 h ≤ (h 20 ≤ (& 0.2970718 157.6882945 h 11 - (* 103 -^* - exp * if :

h ρ_11 1 22.556726 h * 103 -^* - (4.256134^:

h ρ_20 0.2970718 157.6882945 h 11 - (* 103 -^* - exp * :

x OIAC_11 x OIAC_20 2 1 sys x ρ_11 x ρ_20 2 1 sys

11 ρ_11 11 ρ_20 21 mat 0.297072 0.297072 21 mat