NASA(h) Inverse Altitude[m] solved for kPa

48a0bda3-06c7-4d36-9ea2-6287c1d64f37 17 15 12 decimal

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

Part 1...solve altitude for kPa

NASA(h) is kPa vs h[m] ... we solve [m] actual altitude vs measured [kPa] 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 :

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

x nasa 11000 - x ≤ (x 60000 ≤ (& cases :

@ ISO 101.325 kPa, NASA(h) has plunged  6.33 m in the grass ! ISOerror h NASA 101.325 - 0 ≡ h 010 solve : 6.33

x NASA x nasa * 11000 64 11000 32 - 2 2 mat 25000 32 25000 32 - 2 2 mat 0 101.7 + 40 red 1 5 mat 60000 0 + 40 red 1 5 mat 5 1 sys

pressure [kPa] vs altitude [m]

L H N xd U 0 : dx H L - N 1 - / : 12 mat i 1 N range U i el L dx - (dx i * + eval : for U 31 line :

L 60000 NASA : H 101.4009 : N 200 : 13 mat u L H N xd : 21 sys

altitude i 1 u rows range m_altitude i el h NASA u i el - 0 ≡ h 0100000 solve : for u 4 round vectorize m_altitude 0 round vectorize augment 21 line :

t0 1 time :

NASA(h) solved [m_altitude] from measured kPa

altitude 101.325 0 + 40 red 1 5 mat 25000 NASA 25000 + 100 red 1 5 mat 11000 NASA 11000 + 100 red 1 5 mat 4 1 sys

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

1 time t0 - min 1.2

Part 2...Thiele altitude for kPa

ListCollect(data,select)

data select ListCollect collects index list ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 41 line :

altitude data set

altitude 0.0279 60000 0.5373 35423 1.0467 30709 1.5561 28034 2.0656 26180 2.575 24868 3.0844 23719 3.5938 22745 4.1032 21901 4.6126 21155 5.122 20488 5.6314 19884 6.1409 19332 6.6503 18825 7.1597 18355 7.6691 17917 8.1785 17507 8.6879 17122 9.1973 16760 9.7067 16416 10.2162 16090 10.7256 15780 11.235 15485 11.7444 15202 12.2538 14932 12.7632 14673 13.2726 14423 13.782 14183 14.2914 13952 14.8009 13729 15.3103 13514 15.8197 13305 16.3291 13103 16.8385 12908 17.3479 12718 17.8573 12533 18.3667 12354 18.8762 12180 19.3856 12010 19.895 11845 20.4044 11684 20.9138 11527 21.4232 11374 21.9326 11224 22.442 11078 22.9515 10932 23.4609 10792 23.9703 10654 24.4797 10519 24.9891 10386 25.4985 10255 26.0079 10126 26.5173 10000 27.0267 9875 27.5362 9752 28.0456 9631 28.555 9512 29.0644 9394 29.5738 9278 30.0832 9164 30.5926 9051 31.102 8940 31.6115 8830 32.1209 8722 32.6303 8615 33.1397 8509 33.6491 8405 34.1585 8302 34.6679 8200 35.1773 8100 35.6868 8000 36.1962 7902 36.7056 7805 37.215 7709 37.7244 7614 38.2338 7520 38.7432 7427 39.2526 7335 39.762 7244 40.2715 7154 40.7809 7064 41.2903 6976 41.7997 6889 42.3091 6802 42.8185 6716 43.3279 6632 43.8373 6547 44.3468 6464 44.8562 6382 45.3656 6300 45.875 6219 46.3844 6139 46.8938 6059 47.4032 5980 47.9126 5902 48.4221 5824 48.9315 5747 49.4409 5671 49.9503 5596 50.4597 5521 50.9691 5446 51.4785 5372 51.9879 5299 52.4973 5227 53.0068 5155 53.5162 5083 54.0256 5012 54.535 4942 55.0444 4872 55.5538 4803 56.0632 4734 56.5726 4666 57.0821 4598 57.5915 4530 58.1009 4464 58.6103 4397 59.1197 4331 59.6291 4266 60.1385 4201 60.6479 4136 61.1574 4072 61.6668 4008 62.1762 3945 62.6856 3882 63.195 3820 63.7044 3758 64.2138 3696 64.7232 3635 65.2326 3574 65.7421 3514 66.2515 3454 66.7609 3394 67.2703 3334 67.7797 3276 68.2891 3217 68.7985 3159 69.3079 3101 69.8174 3043 70.3268 2986 70.8362 2929 71.3456 2872 71.855 2816 72.3644 2760 72.8738 2705 73.3832 2649 73.8927 2594 74.4021 2540 74.9115 2485 75.4209 2431 75.9303 2377 76.4397 2324 76.9491 2271 77.4585 2218 77.9679 2165 78.4774 2113 78.9868 2061 79.4962 2009 80.0056 1957 80.515 1906 81.0244 1855 81.5338 1804 82.0432 1754 82.5527 1704 83.0621 1654 83.5715 1604 84.0809 1554 84.5903 1505 85.0997 1456 85.6091 1407 86.1185 1359 86.628 1310 87.1374 1262 87.6468 1214 88.1562 1167 88.6656 1119 89.175 1072 89.6844 1025 90.1938 978 90.7032 932 91.2127 885 91.7221 839 92.2315 793 92.7409 748 93.2503 702 93.7597 657 94.2691 612 94.7785 567 95.288 522 95.7974 478 96.3068 433 96.8162 389 97.3256 345 97.835 301 98.3444 258 98.8538 214 99.3633 171 99.8727 128 100.3821 85 100.8915 43 101.4009 02002 mat :

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 :

Thiele Table

1. Thiele Table ... Thiele(X,Y,Δ) => 'K'

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 :

Cfr(j,K,X,x)

j K X x Cfr Optimiz Symbolic j rows(K)-2 N j 1 + el K j 1 + el x X j 1 + el - K j 2 + el / + : c j el N j 1 + el : a j el K j el x X j el - c j el / + : jj j 1 - (1 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 71 line :

data altitude :

data rows 200

upper altitude segment

Select the support points select 123581216 mat : XY data select ListCollect : 21 sys

Thiele X_Kvec convergents X XY 1 col : Y XY 2 col : 12 mat Kvec X Y 0 Thiele : X Kvec 1 col : K Kvec 2 col : 12 mat 31 sys

Support points XY 0.0279 60000 0.5373 35423 1.0467 30709 2.0656 26180 3.5938 22745 5.6314 1988462 mat

Thiele 'K' convergents Kvec 0.0279 60000 0.5373 0.000021 - 1.0467 36242.50652 - 2.0656 0.00042 - 3.5938 10635.458516 - 5.6314 0.0009 - 62 mat

K 60000 0.000021 - 36242.50652 - 0.00042 - 10635.458516 - 0.0009 - 61 mat

Activate Thiele

data 0.0279 60000 0.5373 35423 1.0467 30709 1.5561 28034 2.0656 26180 2.575 24868 3.0844 23719 3.5938 22745 4.1032 21901 4.6126 21155 5.122 20488 5.6314 19884 6.1409 19332 6.6503 18825 7.1597 18355 7.6691 17917 8.1785 17507 8.6879 17122 9.1973 16760 9.7067 16416 10.2162 16090 10.7256 15780 11.235 15485232 mat

j Kvec rows 2 - : x q j K X x Cfr : Low XY o 5 black plot : 31 sys

x Φ 1 0.0279 x ≤ (x 6 ≤ (& cases :

6 25000 6 20000 - 2 2 mat x q x Φ * Low 3 1 sys

Accepted function

lower altitude segment

XY 0 :

Select the support points select 112030507012020017 mat : XY data select ListCollect : 21 sys

Thiele X_Kvec convergents X XY 1 col : Y XY 2 col : 12 mat Kvec X Y 0 Thiele : X Kvec 1 col : K Kvec 2 col : 12 mat 31 sys

Support points XY 5.122 20488 9.7067 16416 14.8009 13729 24.9891 10386 35.1773 8100 60.6479 4136 101.4009 072 mat

Thiele 'K' convergents Kvec 5.122 20488 9.7067 0.001126 - 14.8009 16642.647234 - 24.9891 0.006639 - 35.1773 36765.735481 - 60.6479 0.002972 101.4009 13344.094148 72 mat

K 20488 0.001126 - 16642.647234 - 0.006639 - 36765.735481 - 0.002972 13344.094148 71 mat

Activate Thiele

j Kvec rows 2 - : x g j K X x Cfr : support XY . 14 black plot : 31 sys

x Φ 1 0.0279 x ≤ (x 5.6314 ≤ (& cases :

x c 1 5.6314 x ≤ (x 101.325 ≤ (& cases :

x q x Φ * x g x c * support Low 4 1 sys maple confrac

x q confrac x convert maple 181406424386585814114624089646860000 x * 243192163731610251246438512589127 / - 627091605153867313820162089305371682538303283237834164348176710126781268258346375104072952404722631181883584396628163477160835567067067242806170592726156859287441687311 / + 360575720182945363107983597246423174746722714710970732264758296938606262934680158285304433869448998294747123006486712301994809761206549271991267936813483169400220417107471546902538137023013707235288395708227113285959643829230686486502184089126291403314142516531235023500 x 20786129868411053030438774807319218095868037265030388334747020979228785946659093965534381798094361584758635509409871256577122211668707789023864393315311435967262401179392145790554832818321866092980325537762069598139014984789012180921384019465041014589715021248920564398240327156127634575450551189670775171261372754317741128474069118734119009042824255909212285000 / + 332163656351259754578537976710541095660587520098934932675985126089480068521321948937628825310130781949582401050830428151708416304615703105659689484325927518346139379690439309122106483275357847436274966674826639597677753269894546560937952074026668794599128128112611746117887446291032072376125116959801122588227315850272570203621986978723189599514981317495439303050204061828254085094257609416003818628337261231570477176408810590987742683915624850429069722450901241884025135438926103830639975811100714389826148475700783888810000000 x 1497087561121837737082765716818104118049869613906678971858041868878691593790508085437387036178073600110628818397911901894532839155074178657544530648699701409799074312586818269763660268539643583988955343297047219915516879220674119381562318948212837975040039296410000 / + (* / - (* / +

x g confrac x convert maple 3577471990161804479256830490722253956792182745160191913272986346222624238445 / - 7816930259533267752858769534403653242093702124971287375827274385425064197239025441619626070716411307416767461416158998837775097420060811857814899899425311093093495832266557589690136841885636286543132351757764390625 x 827423545339651835738713404939900157792602797057569739886315377099648131595460678118933583106106411325046781146533110625393577598641597758265464031698811870706310078828100019523865955296136694888677566293037515134363218656785078478870001461641343587651462863885777133897049703499461680489638320134053152377208956935510432116533779073958669936309532534706150000 / + 6353351470920759885923986822371811498728310263969664197352672653857686954788263153598417011034696253125544728191284369751024022860606327829448458830233159585971719802154335174070042251219242009314540505038173754590893033286571737222808214655286462847431487021813702805751633301974847446797330905822447561930472607419234051514316626774226675687307882866212898569112798491335011126237885212226793653554014006359688026157832051239796471171462939996728808306824545192150693937495831314886594012619808679040 x 1394412905947533300899115998304275493215814421239282897481020259505756377933089548713606123389699780438133017327099904451781179959051843004086761766305641703205024186579557721732007144603424689824464035000509453325283111152468964275281875536154510766830372491822198523314217088646858386762751681381815227677861562494382756963714856713506050708081187259137451041346663712701435737399637699171379170268605124705373343597640750806085391914800410804365892066524924370879071308872203769451170565234756850075154214176835495520306273429997681397273956519009499467451228890318458682083070444131111889118065036557750528249108216305938290422937421279735070054090949853596595625788978900790746743530000 / + 57174707888861961601404564856168731031287107834731961699958948338246093160187156187797546510319196189089053513568869305690658033026024306431764214186861641587127119529222039928095522910951138814789167095055190904346287445701081404501880329483039202875848216961961071928170951031060612702559414738548686025714726156740772139839475473015890470453018370862755125072097779677627909392707346903161860335670334209557927864810487008286232262288461294924408728143088482247113911477401075875142554928866233260412767437613501584510289050400793921659448013374125419097101735680790007193392946370899325836906141483017215419542844103929983167927023940186408453923296139278029627610124413668776350677982160759846482755900285265211984738171815122047899348161813448484243637263753947515600797720320182807797158755989192136234850099064431485089649173470631246938581719110997994281169802894809367476223536790514193267578440807656533361307649306682050000000 x 582917395245739133150910779159935956933071213147470635888743630204870068458498576069011478561855390249636670721054239918843384631046955257402917015600968285127026740025486557725487101331744834334437128330914451945772168608359732538656134791117004598226790194650104814496367086077003429365128212469651026170652201393876705693531481878555956885384759213370590100924404416552372691422178258780058433060309558107485333186762201153995472229802674575491390182653436134053790000 / - (* / + (* / - (* / +

β 19576.2885671219 - 149.634964537429 7.44643452345337 12.1666282557134 4837509.01773662 427.253414332934 0.049815029997549 71 mat :

α 745.938609217639 - 21240.0285213947 0.737535698760579 0.035826998148756 18107.8454343997 0.019022979991176 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 5.6314 ≤ (& β 1 el β 5 el x β 2 el + β 6 el x β 3 el + β 7 el x β 4 el - / + / - / + cases :

N 0.0279 60000 0.5373 35423 1.0467 30709 2.0656 26180 3.5938 22745 5.122 20488 5.6314 19884 9.7067 16416 14.8009 13729 24.9891 10386 35.1773 8100 60.6479 4136 101.4009 0132 mat :

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 β 5 el x β 2 el + β 6 el x β 3 el + β 7 el x β 4 el - / + / - / + : 21 sys

x Φ 10 x ≤ (x 5.6314 ≤ (& cases :

x c 1 5.6314 x ≤ (x 101.5 ≤ (& cases :

altitude N . 14 black plot :

Gloal 7500 crusing 60000 ft * 18288 m * ≡

pointer 10 - 5000072500007250000 kPa kPa NASA_m 42 mat :

barometric kPa kPa 9.7067 :

m_kPa kPa kPa NASA_m 0 round 12 mat : 9.7067 1641612 mat

pointer x q x Φ * x g x c * altitude kPa kPa NASA_m + 40 red 1 5 mat 5 1 sys

support points 0.0279 60000 0.5373 35423 1.0467 30709 2.0656 26180 3.5938 22745 5.122 20488 5.6314 19884 9.7067 16416 14.8009 13729 24.9891 10386 35.1773 8100 60.6479 4136 101.4009 0132 mat

measured [kPa] => altitude [m] m_kPa 9.7067 1641612 mat

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

x NASA_m x n *

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/barometer-calibration/

altitude x NASA_m x n * 2 1 sys