Plot

fae2e529-fdd0-4f48-8b28-a6592d0d249a 62 4 5 true true 0 decimal

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

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Explain this document . . . [m] altitude vs measured [kPa]

1. If you have interest in knowing kPa vs altitude [m]. . . use NASA(h)

2. DO NOT use uncompensated P(h)

- - - - - - - - - - - - - - - - - - - - - - - - - -

3. This project is the inverse of Barometric, i.e: Altimetric [m vs kPa]

4. NASA(h) is not analyticaly inversible, it is solvable recursively, from

which solver we have extracted some well distributed U reference points.

5. The Barometric P(h) is analytically inversible, thus solvable for the

compensation parameter 'u'.

6. The final m(kPa) is the altitude [m] vs measured kPa.

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Atmospheric kPa <= m ...dressed as given ... h NASA 101.29 288.14 0.00649 h * - 288.08 / (5.256^* 1000 - h ≤ (h 11000 ≤ (& 22.65 1.73 0.000157 h * - exp * 11000 h ≤ (h 25000 ≤ (& 2.488 141.89 0.00299 h * + 216.6 / (11.388 -^* cases :

U 0.03 60000 0.53 35462 1.04 30747 2.05 26217 3.57 22781 5.6 19921 9.65 16453 14.72 13766 22.31 11115 32.44 8654 50.17 5563 75.49 2423 101.33 6132 mat :

0.03 60000 0.53 35462 1.04 30747 2.05 26217 3.57 22781 5.6 19921 9.65 16453 14.72 13766 22.31 11115 32.44 8654 50.17 5563 75.49 2423 101.33 6132 mat

060000 0.5 35462130747 2.1 26217 3.6 22781 5.6 19921 9.7 16453 14.7 13766 22.3 11115 32.4 8654 50.2 5563 75.5 2423 101.325 0132 mat

sol 11000 NASA p - 0 ≡ p 0200 solve : 22.7074

P.0 760 : (mmHg ≡ g 9.807 : k 1.381 1023 -^* : m 4.81556658 1026 -^* : mmHg 0.133322 kPa * ≡ 51 sys

Uncompensated Barometric Formula  
kPa  vs  altitude [m] h u P.h P.0 e m g * h * k u * / -^* 0.133322 * :

y h u P.h ≡ h solve maple 9138691407485850126655912500 y * / ln * u * 312517182998801 /

Recast the InverseFunction x u m 6905000000000012500 x * 1266559 / ln * u * 2361313072503 / - :

Solve for 'u' the compensation parameter solve x U 1 col : ω U 2 col : 12 mat j 2 U rows 1 - (range sol j 1 - el x j el u m ω j el - 0 ≡ u 0500 solve : X j 1 - el x j el : 21 line for balistic 101.325 288.15 12 mat : X sol 3 round vectorize augment balistic stack 41 line :

MCD LM β 183.541 3391.76 174.102 3346.553 - 162.042 51 mat :

solve 0.53 230.849 1.04 229.621 2.05 229.855 3.57 232.845 5.6 235.271 9.65 239.284 14.72 244.027 22.31 251.175 32.44 259.84 50.17 270.643 75.49 281.519 101.325 288.15 122 mat

Parametric Barometric compensation x f β 1 el β 2 el x β 3 el / - exp * + β 4 el x β 5 el / - exp * + :

x c 10 x ≤ (x 101.325 ≤ (& cases :

compensated [m] altitude vs input [kPa] x m 6905000000000012500 x * 1266559 / ln * x f * 2361313072503 / - :

kPa solve 1 col :

sanity i 2 U rows range Δ i el U 1 col i el m U 2 col i el - : for N U Δ 0 round vectorize augment (: N N 213 range 13 range el : 31 line :

sanity 0.53 35462228 - 1.04 3074745 2.05 26217144 3.57 227811 - 5.6 1992117 - 9.65 164534 14.72 1376620 22.31 111154 32.44 865417 - 50.17 55630 75.49 24232 101.33 66 - 123 mat

kPa m vectorize 35234307922636122780199041645713786111198637556324250121 mat

sanity 3 col Mean 4.2 -

x λ 1 0.125 x ≤ (x 101.325 ≤ (& cases :

U o 5 black plot x m x λ * 2 1 sys

Altimetric formula . . .

[m] altitude vs measured [kPa]

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The compensation function

solve o 5 black plot x f x c * 2 1 sys

sol m 11004

101.325 m 0.0

Supplementary Didactic . . .

Polynomic Compensated Barometric

added from Carlos

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data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Square Minimun Function

T X Y Order f T 1 ≡ m Order 1 + : m 2 : if n X rows : 12 mat i 1 m range j 1 m range con i 1 - (j 1 - (+ : i 1 ≡ (j 1 ≡ (& A i j el n : 11 line T 1 ≡ (T 2 ≡ (| A i j el X k el (con^k 1 n sum : A i j el X k el ln (con^k 1 n sum : if if 21 line for for i 1 m range i 1 ≡ B i el Y k el k 1 n sum : B i el X k el (i 1 -^Y k el * k 1 n sum : if T 1 ≡ i 1 ≡ B i el Y k el ln k 1 n sum : B i el X k el (Y k el ln * k 1 n sum : if T 2 ≡ i 1 ≡ B i el Y k el ln k 1 n sum : B i el X k el ln Y k el ln * k 1 n sum : if cases for i 1 m range φ i el 1 : i 1 ≡ φ i el x (i 1 -^: cases for T 1 ≡ φ 1 el x : 11 line T 2 ≡ (T 3 ≡ (| cases β A 1 -^B * : ff 0 : i 1 m range ff ff β i el φ i el * + : for ff 31 line T 1 ≡ ff β 1 el exp β 2 el φ 1 el * exp * : T 2 ≡ ff β 1 el exp φ 1 el (β 2 el^* : T 3 ≡ cases ff 71 line :

Last Square Function

f( x )=f ( T , X , Y , Order)

| | | |__ Power

| | |__________ Y Data

| |_______________ X Data

|___________________ Type of

Adjustment

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T=1 Polynomic adjusment for Square Minimums method

T=3 Potential adjusment for Square Minimums method

Order= Power to which the function is rising.

Order=1 if T=2 or T=3

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4 appVersion 0.99.7100.35145

P.0 760 : g 9.807 : k 1.381 1023 -^* : m 4.81556658 1026 -^* : mmHg 0.133322 kPa * ≡ 51 sys

NASA 0.03 60000 0.53 35462 1.04 30747 2.05 26217 3.57 22781 5.6 19921 9.65 16453 14.72 13766 22.31 11115 32.44 8654 50.17 5563 75.49 2423 101.33 6132 mat :

G.Adj 0 9.807 1000 9.804 2000 9.801 3000 9.797 4000 9.794 5000 9.791 6000 9.788 7000 9.785 8000 9.782 9000 9.779 10000 9.776 15000 9.761 20000 9.745 25000 9.730 30000 9.715 40000 9.684 50000 9.654 60000 9.624 70000 9.594 80000 9.564 202 mat :

pressure [kPa]
.....
altitude [m] NASA.P NASA 1 col : NASA.Alt NASA 2 col : 21 sys

i 1 NASA.P rows range NASA.pmmHg i el NASA.P i el 0.133322 / : for

NASA.pmmHg 0.23 3.98 7.8 15.38 26.78 42 72.38 110.41 167.34 243.32 376.31 566.22 760.04 131 mat

Temperature  Barometric Formula p h T m - (g * h * p ln P.0 ln - (k * / :

i 1 NASA.pmmHg rows (range T.NASA i el 100.8 : NASA.pmmHg i el 0 ≡ T.NASA i el NASA.pmmHg i el NASA.Alt i el T : NASA.pmmHg i el 0 > (NASA.pmmHg i el 760 < (& T.NASA i el 288.15 : cases for

T.NASA 252.536 230.849 229.621 229.855 232.845 235.271 239.284 244.027 251.175 259.84 270.643 281.519 288.15 131 mat

XG G.Adj 1 col :

YG G.Adj 2 col :

X NASA.Alt : Y T.NASA : 12 mat

OrderG 1 :

T 1 :

Order 4 :

x Temp T X Y Order f :

x Gravi T XG YG OrderG f :

Polynomic

x Temp 1334532099348000046081713168433 / 186550597431004713094204707390 / - (x 21 -^* + 811609817219071957661143935200000000 / x 31 -^* + 9981161332384975981200061122700000000000 / x 41 -^* + 4323417057517580240890983928200000000000000000000 / - (x 51 -^* +

XY X Y augment :

T_VS_ALT XY o 5 black plot :

XYG XG YG augment :

G_VS_ALT XYG o 5 Red plot :

XYG x Gravi G_VS_ALT 3 1 sys XY x Temp T_VS_ALT 3 1 sys

Polynomic Barometric Formula h P.h P.0 e m h Gravi * h * k h Temp * / -^* mmHg * :

P.0 760 : g 9.807 : k 1.381 1023 -^* : m 4.81556658 1026 -^* : mmHg 0.133322 kPa * ≡ 51 sys

NASA 0.03 60000 0.53 35462 1.04 30747 2.05 26217 3.57 22781 5.6 19921 9.65 16453 14.72 13766 22.31 11115 32.44 8654 50.17 5563 75.49 2423 101.33 6132 mat :

Poly 60000 0.03 35462 0.54 30747 1.03 26217 2.04 22781 3.51 19921 5.56 16453 9.74 13766 14.92 11115 22.46 8654 32.35 5563 49.96 2423 75.39 0 101.32 132 mat :

x 060000100 range :

i 1 x length range P i el x i el P.h mmHg / 0.133322 * : 11 line for

nasa NASA 2 col NASA 1 col augment : kPa_m x P augment : support nasa o 5 black plot : Poly Poly . 14 blue plot : 41 sys

support kPa_m Poly 3 1 sys

Polynomic Barometric Formula . . .

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Polynomic Barometric Formula h P.h P.0 e m h Gravi * h * k h Temp * / -^* mmHg * :

P 101.32472 100.13378 98.953705 97.784451 96.625959 95.478170 94.341028 93.214477 92.098459 90.992916 89.897792 88.813030 87.738571 86.674359 85.620336 84.576443 83.542624 82.518820 81.504974 80.501027 79.506920 78.522597 77.547999 231 mat

101.3 100.1 98.95 97.78 96.63 95.48 94.34 93.21 92.10 90.99 89.89 88.81 87.73 86.67 85.61 84.57 83.53 82.51 81.49 80.49 79.49 78.51 77.53 231 mat

Absolute  residuals wrt NASA data δ Δ 0 : X NASA 2 col : Y NASA 1 col : 12 mat j 1 NASA rows range Δ j el Y j el X j el P.h mmHg / 0.133322 * - : for Poly X Y Δ 2 round vectorize augment : header alt_m kPa ΔkPa 13 mat : header Poly stack 61 line :

δ alt_m kPa ΔkPa 60000 0.03 035462 0.53 0.04 - 30747 1.04 0.04 - 26217 2.05 0.05 - 22781 3.57 0.02 - 19921 5.6 0.07 - 16453 9.65 0.21 - 13766 14.72 0.33 - 11115 22.31 0.26 - 8654 32.44 0.01 - 5563 50.17 0.14 2423 75.49 0.08 6 101.33 0.08 143 mat

Polynomic Barometric Formula h P.h P.0 e m g * h * k h Temp * / -^* mmHg * :

x c 10 x ≤ (x 60000 ≤ (& cases :

kPa 1 :

NASA compensated Barometric pressure [mmHg] vs altitude [m]

x P.h x c * 60000 128 60000 128 - 2 2 mat 2 1 sys

0 P.h 0.133322 * mmHg / kPa 101.325

h P1.h P.0 e m g * h * k 100.8 * / -^* mmHg * :

60000 P1.h 0.0001 Pa *

Polynomic Pressure Compensation P.compens X NASA 2 col : Y NASA 1 col : 12 mat j 1 NASA rows range compens j el X j el P.h mmHg / 0.133322 * : for X compens 2 round vectorize augment 31 line :

P.compens 60000 0.03 35462 0.54 30747 1.03 26217 2.04 22781 3.51 19921 5.56 16453 9.74 13766 14.92 11115 22.46 8654 32.35 5563 49.96 2423 75.39 6 101.25 132 mat

in poly plot

======================== Other stuff =========================

test 5000 :

test NASA test P.h 0.133322 mmHg / * 21 mat 54.114 53.914 21 mat

54.114 53.946 21 mat m vectorize 5003502621 mat

10950 P.h 0.133322 mmHg / * 11000 P.h 0.133322 mmHg / * 11050 P.h 0.133322 mmHg / * 31 mat 23.023 22.85 22.677 31 mat

10950 NASA 11000 NASA 11050 NASA 31 mat 22.887 22.707 22.54 31 mat

YES,It is solvable by removing the units sol 11000 P.h 0.133322 * mmHg / p - 0 ≡ p 100 - 200 solve : 22.8495

sol 11000 NASA p - 0 ≡ p 0200 solve : 22.7074

Direct Altimetric Formula . . .

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data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

ISO 101.325 : xo 14.72 - : β 1.002 3.668 4.922 141 mat : 31 mat

x log x log10 :

p f β 1 el β 2 el p - xo + β 3 el / exp p - xo + (β 3 el β 4 el + β 3 el β 4 el * / * exp - (* + :

p Alt 10 p ISO / log 5.256 /^1 - 6.876 106 -^* - / 0.3048 * (p f * :

10 p ISO / log 5.256 /^10125 p ISO / log * 657 /^≡

x c 10 x ≤ (x 101.325 ≤ (& cases :

NASA 0.03 60000 0.53 35462 1.04 30747 2.05 26217 3.57 22781 5.6 19921 9.65 16453 14.72 13766 22.31 11115 32.44 8654 50.17 5563 75.49 2423 101.325 0132 mat :

data NASA o 5 black plot : NASA NASA 413 range 12 range el : X NASA 1 col : Y NASA 2 col : 12 mat 31 sys

m 1 :

22.31 Alt m 11134

f(p) 125 - 2.6 - 2.2 17.3 - 5.6 19 1.6 2.9 - 4 - 0111 mat

Compensated Altimetric Formula [0...25 km]

data x Alt x c * 2.05 26217 + 50 blue 1 5 mat 3 1 sys

X Alt vectorize Y - 125 - 2.6 - 2.2 17.3 - 5.6 19 1.6 2.9 - 4 - 0101 mat

10 p ISO / log 5.256 /^1 - 6.876 106 -^* - / 0.3048 * (p f *