plotG(vx,vy,char,size,color) ... Hermite Polyline modules

f535dca6-03c1-4ea9-b7a7-26d47ea29a0f 205 4 5 decimal

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

Jet-Liner Segment . . .

corrected flight altitude

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In the air, as you fly along and encounter nonstandard temperatures, indicated altitude can differ from true altitude. ... When the temperature is colder than standard, you are at an altitude lower than your altimeter indicates. @ temperature warmer than standard, you are higher than your altimeter indicates. ...................... In such conditions, an approximate correction is 4 per cent height increase for every 10°C below standard temperature as measured at the altimeter setting source. This is safe for all altimeter setting source altitudes for temperatures above –15°C. 4.3.2 Tabulated corrections

http://code7700.com/altimeter_temperature_correction.htm#correction https://en.wikipedia.org/wiki/Altimeter

Conservative pilot chart . . .

OBSERVE: NASA11(kPa) is conservative by ~ 6 m

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..... -10,210 is in error .....

t 30 - : (local temperature °C ≡ L0 0.0065 : (standard ISA temperature laps rate °C/m ≡ H 0 : (sea level elevation [m] ≡ m 1 : (meter unit ≡ h NASA11(kPa)altimeter reading ≡ 51 sys

otherwise formulated

'h' NASA(kPa) altitude

't' local °C from Pt sensor

Local °C flight altitude correction
add [m] to  altimeter reading [m] h t C h 15 t L0 H * + (- 273 t L0 H * + (+ 0.5 L0 * h H + (* - / * :

add to altimeter reading 30050 - C m 88

p[kPa] from altimeter

p NASA11 20001440714404100 p * 10129 / ln 5.256 / exp * - (* 649 / : p t Flight p NASA11 p NASA11 t C + : 31 sys

raw altimeter reading

... flight altitude [m]

't' [°C]from the airport "OR" as measured at aircraft approaching landing runway.

Altimeter reading from sensed kPa

8530 - Flight 1742

. . . in short . . .

1. altimeter reads ISA flying altitude from NASA11(kPa)

2. Flight(kPa) adds/subtracts corrected altitude [m]

3. NASA11(kPa)=m approximates ISA as "kPa sensed".

]]>

M x y Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x linterp 51 line :

'x' direction

TableIII °C/Altimeter 60901201501802102402703004506009001200150005510101015151520253550708510 - 10101515202525303045609012015020 - 101520252530354045658513017021530 - 1520253035404555608511517023028540 - 15253040455060657511014522029036550 - 20304055565758090135180270360450715 mat :

'y'

TableIII 50035 - Spline TableIII 60030 - Spline TableIII 100015 - Spline 31 mat 10811512231 mat

Landing u 1500101490 range : i 1 u rows range C i el TableIII u i el 40 - Spline : for u C 0 round vectorize augment 31 line :

Landing 1 1 sys

Local °C flight altitude correction
add [m] to  altimeter reading [h] h t C h 15 t L0 H * + (- 273 t L0 H * + (+ 0.5 L0 * h H + (* - / * :

x c 1 22.3135 x ≤ (x 101.401 ≤ (& cases :

x correct 10 x ≤ (x 1500 ≤ (& cases :

x 15 Flight x c * x 50 - Flight x c * x 50 Flight x c * 3 1 sys

x f 1 87.5 x ≤ (x 101.325 ≤ (& cases :

x 30 - C x correct * x 50 C x correct * 2 1 sys

add[m]Alti'r reading

t 15 °C * <

p 92.5 : t 50 - : 12 mat

Corrected landing approach [m alt]

x t Flight x f * p 0 p p t Flight 101.325 p t Flight 101.325 0 p 0 5 2 mat p p t Flight . 15 black 1 5 mat 3 1 sys

t 15 °C * >

subtract[m]Alt'r reading

ISA ..
flight p NASA11 p t Flight 21 mat 76999621 mat

..... More bed time reading .....

Lo 1 : (fillet the foot ≡ alt 11000 : λ 0.1 : 12 mat alt n x G alt Lo λ x * (n^+ / : x profile 10 x ≤ cases : 41 line

Some maths behind landing profile

. . . suggestive didactic . . .

1. Copy/paste this section in new WS.

2. Experiment fillet the foot Lo.

3. Observe new alt and new black cross

relative position in between .

4. This little piece of maths is suggestive of the

descending gradient the auto-pilot has to track.

From only few reference points wrt aircraft and

other landing conditions, infinitely many landing

profiles may be constructed from convex splines.

5. The rule of thumb for the descending distance

is ~ 3 times the crusing altitude.

]]>

alt 121 λ / G 5500

alt 12 x G x profile * alt 6 x G x profile * alt 4 x G x profile * 1 λ / alt 12 1 λ / G + 25 black 1 5 mat 4 1 sys

https://www.faa.gov/regulations_policies/handbooks_manuals/ aviation/phak/media/10_phak_ch8.pdf

Hermite polyline landing gradient example

plotG(vx,vy,char,size,color) ... Hermite Polyline modules

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

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 :

z n RepEnd m z rows : i 1 n range w i el z 1 el : for i n 1 + (m n + (range w i el z i n - el : for i m n + 1 + (m 2 n * + (range w i el z m el : for w 51 line :

data Strip nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ R k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for v 31 line 21 line :

Round OFF Matrix/Vector M n Round i 1 M rows range m i el M i el n round : for m 21 line :

user original polygon Xo 0 8.25 12.375 16.5 3715 mat transpose : Yo 1111 5.5 0015 mat transpose : 21 sys

sub 1 :

sub[1]... NOT sub-divided

New Xo sub subspace Yo sub subspace augment : New Xo 1 el Yo 1 el 12 mat New stack : 21 line

isolate New New :

X New 1 col : Y New 2 col : 21 line

t 01 0.05 range :

<= populate for more points at will

Polyline construct

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

t B t 3^- 3 t 2^* + 3 t * - 1 + 3 t 3^* 6 t 2^* - 3 t * + 3 t 3^* - 3 t 2^* + t 3^41 mat :

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat

t j XP t P 1 el X j el * t P 2 el X j 1 + el * + t P 3 el X j 2 + el * + t P 4 el X j 3 + el * + : t j YP t P 1 el Y j el * t P 2 el Y j 1 + el * + t P 3 el Y j 2 + el * + t P 4 el Y j 3 + el * + : 21 sys

U j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

collect the project xy U Unwrap V Unwrap augment : Polyline xy Strip : 21 sys

XY X Y o 7 red plotG : XoYo Xo Yo . 14 black plotG : TouchDown Polyline Polyline rows row . 25 black augment : Landed km datum 12 mat Polyline Polyline rows row stack : cruz 112 crusing altitude 11 km 12 blue 15 mat : distance 16.5 0.125 - landing distance km -->| 12 black 15 mat : Polyline Polyline . 10 red plot : 71 line

Xo Yo augment Polyline XoYo TouchDown cruz distance 6 1 sys

OBSERVE: center point ... does not need be in line

datum landing 
t[0,0.05..1]...   10 cm 
t[0,0.025..1]... 1.4 cm Landed km datum 33.05 0.00 22 mat

Radio Altimeter Accuracy ± 2 feet in the first 500 feet or ± 1.5% whichever is greater.

1200Under FAR Part 43 (basically, private flight of N-reg planes) the max allowed error is 1000ft or below - 20ft 1500ft - 25ft 2000-3999ft - 30ft 4000ft - 35ft 6000ft - 40ft 8000ft - 60ft 10000ft - 80ft 12000ft - 90ft 14000ft - 100ft

acc 02010002022 mat 10002515002522 mat 15003040003022 mat 40003560003522 mat 60004080004022 mat 800060100006022 mat 1000080120008022 mat 1200090140009022 mat 81 sys :

Altimeter ft accuracy vs altitude [ft] "Servo assisted altimeters are accurate to 1mb, ±30ft at sea level and ±100ft at 40 000ft."

acc

02010002022 mat 0.3048 * 0 6.096 304.8 6.096 22 mat

https://aerospace.honeywell.com/en/~/media/aerospace/files/datasheet/ precisionbarometerforaltimeterapplications-datasheet.pdf

calibrated wrt actual altitude runway FS 1000 m * :

0.03 FS perc 0.3 m *

resolution 0.0011 FS perc : 0.011 m *

https://www.airbus.com/content/dam/corporate-topics/publications/safety-first/ Airbus_Safety_first_magazine_24.pdf

https://www.eurocontrol.int/sites/default/files/field_tabs/content/documents/nm/ airspace/airspace-atmprocedures-flight-deck-perspective.pd

READ MORE:https://www.skybrary.aero/solutions/levelbust/BNotes/BN_Ops2.pdf

10 hPa ~ 273 ft + ~ 30 ft @ 4000 ft ~ 300 ft actual altitude 4000-300 = ~ 3700 ft

Note . . .

The primary Pressure Standard is the Dead Weight Tester.

Process Plant pressure instruments are effectively calibrated

with a Secondary Pressure Standard Wallace Tiernam.

Generally, the Instrument Shop has two sets WT, one being

always fresh from last calibration lab.

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Air speed indicator: Translates the pressure difference between the dynamic impact Pitot pressure and the static pressure ... following at best the the mathematical Mach. The static pressure port is in fact a multi-port system, disposed to average at best on the ChebyShev principle ... similar to the flow measuring Annubar.

FAR 43 - Appendix E [Altimeter] Tol alt[ft] ±Hg ±ft 1000 - 31.018 200 29.921 20500 29.385 201000 28.856 201500 28.335 252000 27.821 303000 26.817 304000 25.842 356000 23.978 408000 22.225 6010000 20.577 8012000 19.029 9014000 17.577 10016000 16.216 11018000 14.942 12020000 13.750 13022000 12.636 14025000 11.104 15530000 8.885 18035000 7.041 20540000 5.538 23045000 4.355 25550000 3.425 280243 mat :

http://www.faa-aircraft-certification.com/43-appendix-e.html

Tol Tol 224 range 13 range el : X Tol 1 col : Y Tol 3 col : 12 mat 31 sys

x y axes x y / - :

visible ErrorBar ν 10 :

N i 1 Tol rows range E i el ν Y * (i el : Nest i el X i el X i el E i el + X i el X i el E i el - 22 mat : 21 line for Nest 21 line :

Lab i 1 Tol rows range E i el Y i el : read i el X i el X i el E i el + X i el E i el - 21 mat 12 mat : 21 line for read 21 line :

Tabulate "Lab" to see suggested Lab Document to be filled-in for certification as per regulation FAR 43.

j 1 N rows range Ω j el N j el 1 col N j el 2 col augment : for

Test X X augment :

Test Ω axes 3 1 sys

Q i 1 Tol rows range E i el 1 Y * (i el : Nest i el X i el E i el X i el E i el - 22 mat : 21 line for Nest 21 line :

j 1 Q rows range TOL j el Q j el 1 col Q j el 2 col augment : for

TOL axes 2 1 sys

hPa vs altitude[m] h p 1013.25 1 0.0065 h * 288.15 / - (5.255^* :

altitude[m] vs  hPa  InverseFnct
maple symbolic  from  fresh PC start x OACI 57630014 x * 4053 / ln 5.255 / exp - (* 13 / :

11000 p 226.38

useless reverse plot

1013.25 OACI 0

0 p 1013.25

2.682 OACI 30000

30000 p 2.682

x OACI x p

Electronic Altimeter ... 20 cm resolution ... [0..25 km] https://www.aircraftspruce.com/catalog/pdf/altimeter-manual.pdf

g 9.806645 : R 287.0528 : po 1013.25 : p1 226.321 : z1 11000 : To 288.15 : T1 216.65 : λ 0.0065 - : 81 sys

z ISA0 po To λ z * + To / (g - R λ * /^* : z ISA11 p1 g z z1 - (* R T1 * / - exp * : 21 sys

The two ISA segments

x c0 10 x ≤ (x 11000 ≤ (& cases : x c11 111000 x ≤ (x 25000 ≤ (& cases : 21 sys

x ISA0 x c0 * x ISA11 x c11 * 11000 600 11000 200 - 2 2 mat 5000 768 Troposphere 12 blue 1 5 mat 14000 256 Tropopause 12 red 1 5 mat 5 1 sys

ISA altitude[hPa] ... maple_solve hPa alt0 To 1 - hPa po / ln R * λ * g / - exp + (* λ / : hPa alt11 g z1 * - hPa p1 / ln R * T1 * + g / - : 21 sys

sanity check 15000 ISA11 alt11 5000 ISA0 alt0 21 mat 15000500021 mat

lowest local barometric 
ISA reference
highest local barometric 870 alt0 1013.25 alt0 1083.8 alt0 31 mat 12670571 - 31 mat

Sanity OACI [Organisation Aviation Civile Internationale] ..... convenient civil aviation [0..12 km] .....

OACI hPa vs altitude[m] h oaci 1013.25 1 0.0065 h * 288.15 / - (5.255^* :

ISA is the physical segment, OACI is the approximated ISA. For flying conditions, either ISA/OACI are subject to °C compensation [as implemented above WS].

ISA
OACI 11000 ISA0 11000 oaci 21 mat 226.32 226.38 21 mat

altitude[m] vs  hPa  InverseFnct
maple symbolic  from  fresh PC start x OACI 57630014 x * 4053 / ln 5.255 / exp - (* 13 / :

sanity OACI vs ISA 1000 ISA0 OACI 5000 ISA0 OACI 11000 ISA0 OACI 12000 ISA11 OACI 41 mat 10005001110021198741 mat

0 ISA0 11000 ISA0 25000 ISA11 31 mat 1013.25 226.32 24.886 31 mat

More interesting stuff . . .

]]>

NASA Atmospheric kPa(m)... as published 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 :

0 NASA 11000 NASA 25000 NASA 60000 NASA 41 mat 101.4009 22.7074 2.5223 0.0279 41 mat

OACI 11000 p 0.1 * 22.64

OACI

NASA Altitude  m(kPa)... from Smath/Maple companions. kPa alt 20001440714404100 kPa * 10129 / ln 5.256 / exp * - (* 649 / 101.4009 kPa ≥ (kPa 22.7074 ≥ (& 1000017310020 kPa * 453 / ln * - (* 157 / 22.7074 kPa ≥ (kPa 2.5223 ≥ (& 100014189 - 21660125 kPa * 311 / ln 11.388 / - exp * + (* 299 / cases :

x c 1 2.5223 x ≤ (x 101.401 ≤ (& cases :

Bombardier Global 7000 crusing altitude 60000 ft in very thin atmosphere @ crusing 0.95 Mach

x alt x c * 0 18300 7.235 18300 2 2 mat 0 11000 22.707 11000 2 2 mat 16 20000 Global 7000 12 red 1 5 mat 32 13000 A 320 12 green 1 5 mat 2.522 25000 + 20 black 1 5 mat 6 1 sys

[kPa] pressure 60000 0.3048 * NASA 7.235

[m] altitude 60000 0.3048 * 18288

Airbus A 320 11000 NASA 22.707

101.325 alt 6.327203993

Thiele_13 [0 . . . 60 km]

0 error @ datum sea level 101.325 kPa

borrowed from Mathcad 11

]]>

β 20.3823482945 - 10221.7236330 - 102.254623777 7.30543254052 5.16004861812 - 1.12861221056 11.5101979221 - 2462848.97537 340.576516665 1.31098861606 13.4855096267 41.7592427147 121 mat :

β β 6 round vectorize :

x β km β 1 el x * β 2 el + β 8 el x β 3 el + β 9 el x β 4 el + β 10 el x β 5 el + β 11 el x β 6 el + β 12 el x β 7 el + / + / - / - / - / + :

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 :

data 0.0279 60000 0.5 35462130747 2.1 26217 3.6 22781 5.6 19921 9.7 16453 14.7 13773 22.3 11115 32.4 8654 50.2 5563 75.5 2423 101.325 0132 mat :

data data o 5 black plot :

XY data 113 range 12 range el : X XY 1 col : Y XY 2 col : 12 mat 21 sys

x k 1 0.0279 x ≤ (x 101.325 ≤ (& cases :

Absolute  residuals Δ Δ 0 : j 2 XY rows range Δ j el Y j el X j el β km - eval : for res X Y Δ 3 round vectorize augment : kPa alt[m] Δm 13 mat res stack 41 line :

altitude [m] vs measured pressure [kPa] ... i.e: InverseNASA(h)

data x β km x k * 2 1 sys

Δ kPa alt[m] Δm 0.0279 600000 0.5 35462 0.001 - 130747 0.001 2.1 26217 0.001 3.6 22781 0.001 5.6 199210 9.7 164530 14.7 137730 22.3 111150 32.4 86540 50.2 55630 75.5 24230 101.325 00143 mat

altitude [kPa] . . .

1. data set Thiele_13 from Smath solve discrete NASA(h)

NO glitch detected as plotted.

2. @ 100 km, air is so thin that two molecules meet each

other as often as you win lotery in life time !

3. The rational segment [0..20 km] is valid @ low maths.

4. NASA_m(x) in two rational segments [0..20..60 km]

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x T 1 14.7 x ≤ (x 101.325 ≤ (& cases :

x alt x β km - ( x T * 14.7 16 14.7 16 - 2 2 mat 2 1 sys

Economy rational [0 . . . 20 km]

pressure [kPa]

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data 0.0279 60000 0.5344 35462 1.049 30747 2.0539 26217 3.5733 22781 5.5993 19921 9.6511 16453 14.716 13766 22.3133 11115 32.443 8654 50.17 5563 75.4942 2423 101.325 0132 mat :

β 7.7974 - 16200.3 - 137.3143 7.939192 3.57329191 - 3985903 442.7188 0.00000061 81 mat :

<= β's from GenfitMatrix ... Minerred x β J22781 β 1 el x * β 2 el + β 6 el x β 3 el + β 7 el x β 4 el + β 8 el x β 5 el + / - / - / + :

Original
GenfitMatrix 1.53223 - 19836.6 - 159.814 8.98164 0.320738 5126400 520.985 1.83404 81 mat

XY data 513 range 12 range el : X XY 1 col : Y XY 2 col : 12 mat 21 sys

Absolute  residuals δ22781 Δ 0 : j 1 XY rows range Δ j el Y j el X j el β J22781 - eval : for X Y Δ 0 round vectorize augment 31 line :

δ22781 3.6 227810 5.6 199211 - 9.7 164533 14.7 137664 - 22.3 111151 - 32.4 86546 50.2 55636 - 75.5 24233 101.3 01 - 93 mat

0 ISA0 11000 ISA0 25000 ISA11 31 mat 1013.25 226.32 24.886 31 mat

x Eco 15 x ≤ (x 101.325 ≤ (& cases :

101.325 β J22781 0.7

x alt x β J22781 - ( x Eco *

5 alt 20642

Reconciliate NASA(kPa) altitude [0 . . . 60 km]

rational GenfitMatrix

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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 :

N 0.0279 60000 0.5344 35462 1.049 30747 2.0539 26217 3.5733 22781 5.0928 20524 5.5993 19921 9.6511 16453 14.716 13766 22.3133 11115 32.443 8654 50.17 5563 75.4942 2423 101.325 6142 mat :

Why NASA(kPa) does NOT

anchor ISA datum [101.325 . . .0]

kPa instead of hPa from illuminaties

]]>

β 37.70447993 - 2926.195206 - 46.84494347 15.22943258 3.34558857 34.6767257 - 996664.9866 67.78007379 204.2579676 700.8010171 101 mat :

α 717.279 - 20938.5 0.769787 0.0188311 19052.8 0.0144947 61 mat :

x NASA_m α 1 el x * α 2 el + α 5 el x α 3 el + α 6 el x α 4 el + / - / + 0.0279 x ≤ (x 5.092 ≤ (& β 1 el x * β 2 el + β 7 el x β 3 el + β 8 el x β 4 el + β 9 el x β 5 el + β 10 el x β 6 el + / + / + / - / + cases :

x q α 1 el x * α 2 el + α 5 el x α 3 el + α 6 el x α 4 el + / - / + : x g β 1 el x * β 2 el + β 7 el x β 3 el + β 8 el x β 4 el + β 9 el x β 5 el + β 10 el x β 6 el + / + / + / - / + : 21 sys

x Φ 10 x ≤ (x 5.092 ≤ (& cases :

x c 1 5.092 x ≤ (x 101.325 ≤ (& cases :

altitude N . 12 black plot : vx N 1 col : vy N 2 col : 12 mat 21 sys

Residuals NASA  two segments GenfitMatrix NASA2 j 1 N rows range resd j el vy j el vx j el NASA_m - eval : for vx vy resd 0 round vectorize augment 21 line :

101.325 NASA_m 6

x q x Φ * x g x c * altitude 3 1 sys

NASA2 0.028 600000 0.534 354622 - 1.049 307477 2.054 2621713 - 3.573 2278115 5.093 205241 - 5.599 199211 9.651 164530 14.716 137660 22.313 111150 32.443 86540 50.17 55630 75.494 24230 101.325 60143 mat

pointer 10 - 50000 87.5 50000 87.5 50000 kPa kPa NASA_m 42 mat :

barometric kPa kPa 25 :

x n 10 x ≤ (x 101.5 ≤ (& cases :

test 64 :

pointer x NASA_m x n * altitude kPa kPa NASA_m + 40 blue 1 5 mat 4 1 sys

measured [kPa] => altitude [m kPa kPa NASA_m 12 mat 251038112 mat

InverseNASA
GenfitMatrix test alt test NASA_m 21 mat 3722372021 mat

LOWEST ever recorded pressure on Earth 87kPa /870 mbar / 652.53 mmHg /25.69 inHg 12 October 1979 Typhoon Tip, W. Pacific Ocean Largest, most intense tropical cyclone on record Peak width: 2,200 km / 1,380 miles Peak winds: 305 km/h or 190 mph ==================================================== HIGHEST ever recorded pressure on Earth Most common official citation: 108.38kPa /1083.8 mbar / 812.92mmHg / 32.01 inHg Alternative citation that is currently uncertified : 108.57 kPa/ 1085.7 mbar/ 814.32 mmHg /32.06 inHg 31 December 1968 ... Agata Lake, N. Siberia 19 December 2001 ... Tosontsengel, Mongolia Clear and extreme cold -46C/-50.8F

http://www.barometricpressureheadache.com/barometric-pressure-and-weather-conditions/

lowest local barometric 
ISA reference
highest local barometric 870 alt0 1013.25 alt0 1085.7 alt0 31 mat 12670586 - 31 mat

x Φ 1 22.75 x ≤ (x 101.325 ≤ (& cases :

x alt x NASA_m - ( x Φ * 22.75 4 22.75 4 - 2 2 mat 2 1 sys

22.75 alt 10988

plot(data,char,size,color)

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 :

3 points arithmetic [0 . . . 2 km]

very accurate [0 . . 1500 m]

]]>

data 0.279 60000 5.344 35462 10.49 30747 20.539 26217 35.733 22781 55.993 19921 96.511 16453 147.16 13766 223.133 11115 324.43 8654 501.7 5563 754.942 2423 1013.25 0132 mat :

K 17285.07323 - : H 36316152.21651 : L 1087.76235 : 13 mat

x KHL K H L x + / + :

x c 1450 x ≤ (x 1013.25 ≤ (& cases :

XY data 1113 range 12 range el : X XY 1 col : Y XY 2 col : 12 mat 21 sys

support XY o 5 black plot :

x KHL x c * support 3 1 sys

Absolute  residuals δ Δ 0 : j 1 XY rows (range Δ j el Y j el X j el KHL - eval : for X Y Δ 1 round vectorize augment 31 line :

x OACI 57630014 x * 4053 / ln 5.255 / exp - (* 13 / :

δ 501.7 55630 754.942 24230 1013.25 0033 mat

X KHL vectorize 556324235105 -^* - 31 mat

roots x OACI K H L x + / + (- 0 ≡ x 4501020 solve : 471.88 833.39 1013.25 31 mat

x OACI K H L x + / + ( - ( x c *

X 472.9 833.4 1013.25 31 mat :

α 0.00000115 - : hPa 440 : 12 mat x f K H L x + / + α x X 1 el - (* x X 2 el - (* x X 3 el - (* + : x c 1440 x ≤ (x 1013.25 ≤ (& cases : 31 sys

hPa OACI 6507

EXPLAIN ... AOPs => Arithmetic Operations 1. @ the machine code level: OACI(x) 48 AOPs. 2. @ machine code level: f(x) 11 AOPs. 3. Near landing, f(x) is so accurate that it does NOT contribute to any type of altimeter especially wrt best piezoelectric altim'r.

u 8008509009509759879951005 1007.5 1013.25 101 mat :

u f vectorize u OACI vectorize 12 mat 1949.9 1457.4 988.5 540.6 323.6 221.1 153.2 69 48.1 5.3 105 -^* - 101 mat 1949.3 1457.5 988.7 540.4 323.4 220.9 153.1 68.9 480101 mat 12 mat

Δev u OACI u f - vectorize : 0.61 - 0.15 0.17 0.13 - 0.21 - 0.20 - 0.17 - 0.09 - 0.07 - 5.25 105 -^* 101 mat

u Δev augment 1013.25 1 1013.25 1 - 2 2 mat 2 1 sys x OACI x f - ( x c * u Δev augment 1013.25 0.5 1013.25 0.5 - 2 2 mat 0 3 1 sys

x Jfrac 10803171625 / - 35490321924738153976562500 x 34028048113125000 / + (* / + :

x OACI x Jfrac - ( x c * x OACI K H L x + / + ( - ( x c * 2 1 sys

roots x OACI x Jfrac - 0 ≡ x 4501020 solve : 472.47 867.49 975.58 31 mat

X 472.47 867.49 975.58 31 mat :

α 0.00000102 - : hPa 440 : 12 mat x f x Jfrac α x X 1 el - (* x X 2 el - (* x X 3 el - (* + : x c 1440 x ≤ (x 1013.25 ≤ (& cases : 31 sys

x OACI x f - ( x c *

850 OACI 1458

u 8008509009509759879951005 1007.5 1013.25 101 mat :

u f vectorize u OACI vectorize 12 mat 1950.8 1457.8 988.5 540.3 323.4 220.9 153.1 68.9 480101 mat 1949.3 1457.5 988.7 540.4 323.4 220.9 153.1 68.9 480101 mat 12 mat

Δev u OACI u f - vectorize : 1.50 - 0.23 - 0.19 0.09 0.00 0.02 - 0.02 - 0.01 - 0.00 0.02 101 mat

u Δev augment 1013.25 0.5 1013.25 0.5 - 2 2 mat 0 3 1 sys

Last 400 m ± 2cm

u 965 :

u OACI u f - 0.033

u f vectorize u OACI vectorize 12 mat 409.65 409.69 12 mat

Thiele Quick 3 points F_frac

Optimiz NUMERIC X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

XY 501.7 5563 754.942 2423 1013.25 032 mat :

Y XY 2 col :

X XY 1 col :

length Thiele j XY rows : 3

Thiele on length of support points 'j'
algo style ... Optimiz => NONE k X x Cfr N j 1 + el k j 1 + el : c j el N j el : a j el k j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el k jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

The continued fraction ... Optimiz => NONE k X x Cfr k 1 el x 501710 / - k 2 el x 377471500 / - k 3 el / + / +

examine Thiele K's X Y 0 Thiele 501.7 5563 754.942 0.0807 - 1013.25 22848.0736 - 32 mat

K 5563 0.0807 - 22848.0736 - 31 mat :

x J_frac K 1 el x 501710 / - K 2 el x 377471500 / - K 3 el / + / + confrac x convert maple :

Optimiz NONE x J_frac 10803171625 / - 35490321924738153976562500 x 34028048113125000 / + (* / +

Explain something about . . . 3 points arithmetic

3 points arithmetic and the advanced counterpart continued fractions

origin from the age before Microprocessors where made available for

the Process Control Technologies. Numerical PID where available

in 1980, but for advanced models ... zap ! So, we were confined to

rational models, continued fraction models.

As demonstrated, we don't care much high accuracy @ high altitude

but as you reach the runway, accuracy is critical. The last demo

J_frac(x) is pretty convincing @ minimal arithmetic [+, -, *, /] just

ignoring avanced exp, ln, X^Y ...

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Project Note:

The 3 support points come from an horrible empirical approximation related

to the depth of insertion of the moulinet [ a rough volumetric flow measuring

device in large pipe sizes not covered by ISO-5167 Orifice Plate].

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XY 15 0.121229 135 0.119489 635 0.118596 32 mat :

X XY 1 col : Y XY 2 col : data XY . 12 black plot : 31 line

β 0.118226 0.261451 72.045495 31 mat :

Model function x β f β 1 el β 2 el β 3 el x + / + :

FIT range, populate U 07001 range : i 1 U rows range FIT i el U i el β f eval : for U FIT augment 41 line :

data FIT XY 3 1 sys