{"text_format":"1","workbook":"xlsx","n_sheets":4,"sheets":["SAC","t_SAC","SAD","RH"],"not_rendered":{"charts":15,"images":15,"macros":1,"external_links":0,"defined_names":118,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"SAC","index":0,"n_rows":130,"n_cols":17,"rows_kept":130,"cut":false,"hidden":false,"merged":[]}
["Schmidt-Appleman-Criterion (SAC)"]
["This file:","https://purl.org/aero/SAC"]
[null,null,null,null,"Magnus-Equation"]
["a_w",611.20000000000005,"Pa"]
["b_w",17.62]
["c_w",243.12,"°C"]
["a_i",611.20000000000005,"Pa"]
["b_i",22.46]
["c_i",272.62,"°C"]
[null,null,null,null,"https://de.wikipedia.org/wiki/Sättigungsdampfdruck#Berechnung_des_Sättigungsdampfdrucks_von_Wasser_über_die_Magnus-Formel"]
[null,null,null,null,"https://en.wikipedia.org/wiki/Vapour_pressure_of_water",null,null,null,null,"contains also alternative equations"]
["t",-43.936142533951404,"°C",null,"No contrail above this temperatur"]
["E_w'",{"$f":"a_w*b_w*c_w*EXP(b_w*t/(c_w+t))/(c_w+t)^2","v":1.3538102189480852},"Pa/°C"]
["E_w' - G",{"$f":"E_w_strich-G","v":7.656918319387529E-7},"Pa/°C",null,"<= drive to Zero with the Solver (settings on the right)",null,null,null,null,"= a_w*b_w*c_w*EXP(b_w*t/(c_w+t))/(c_w+t)^2-G"]
["E_w",{"$f":"a_w*EXP(b_w*t/(c_w+t))","v":12.538323604177787},"Pa",null,null,null,null,null,null,"= a_w*EXP(b_w*t/(c_w+t))"]
["E_i",{"$f":"a_i*EXP(b_i*t/(c_i+t))","v":8.1683877692841858},"Pa",null,null,null,null,null,null,"= a_i*EXP(b_i*t/(c_i+t))"]
[]
["L",1.9811999999999998E-3,"°C/ft"]
["t_0",15,"°C"]
["k_a",6.8755999999999999E-6,"1/ft",null,"Constants of the ISA, Scholz"]
["k_b",4.8063399999999998E-5,"1/ft"]
["k_exp",5.2558800000000003]
["H_T",36089,"ft"]
["p_0",101315,"Pa"]
["p_T",22632,"Pa"]
[]
["H",40000,"ft",null,"Input of the flight altitude"]
[]
["p",{"$f":"IF(H<H_T,p_0*(1-k_a*H)^k_exp,p_T*EXP(-k_b*(H-H_T)))","v":18753.658935390147},"Pa",null,"Pressure from the ISA, Scholz",null,null,null,null,"= WENN(H<H_T;p_0*(1-k_a*H)^k_exp;p_T*EXP(-k_b*(H-H_T)))"]
[null,null,null,"Kerosine:"]
["EI_H2O",1.25,null,1.25,"Data for the fuel"]
["c_p",1004,"J/(kgK)",1004]
["eps",0.622,null,0.622,null,null,null,"GIERENS, Klaus, et al.,2008. A Review of Various Strategies for Contrail Avoidance. In: OASC, vol.2, pp. 1-7."]
["Q",43000000,"J/kg",43000000,null,null,null,"https://doi.org/10.2174/1874282300802010001"]
["eta",0.35,null,0.35]
[]
["G",{"$f":"EI_H2O*p*c_p/(eps*Q*(1-eta))","v":1.3538094532562532},"Pa/°C",null,"= EI_H2O*p*c_p/(eps*Q*(1-eta))"]
["t_Schumann",{"$f":"-46+9.43*LN(G-0.053)+0.72*(LN(G-0.053))^2","v":-43.470238510538778},"°C",null,"= -46+9,43*LN(G-0,053)+0,72*(LN(G-0,053))^2",null,null,null,"Approximate equation from Schumann 1996 (https://elib.dlr.de/32128), Schumann 2000 (https://elib.dlr.de/9281)"]
["t_Scholz",{"$f":"a_SLZ*LN(G)^2+b_SLZ*LN(G)+c_SLZ","v":-43.858534861970831},null,null,"= a_SLZ*LN(G)^2+b_SLZ*LN(G)+c_SLZ",null,null,null,"See on Tab \"t_SAC\". Parameters are similar to those from Schumann."]
["G0",{"$f":"E_w-G*t","v":72.019488706255345},"Pa",null,"= E_w-G*t"]
["f(t)",{"$f":"G*t+G0","v":12.538323604177783},"Pa",null,"= G*t+G0"]
["f(t)=E_w(t) ?",{"$f":"IF(E_w=f_of_t,\"true\",\"false\")","v":"true"},null,null,"Check of calculation must be \"true\"!"]
[]
["t","E_w","E_i","G*t+G0","phi = E_i/E_w"]
[-60,{"$f":"a_w*EXP(b_w*A45/(c_w+A45))","v":1.9005832334432484},{"$f":"a_i*EXP(b_i*A45/(c_i+A45))","v":1.0804269890819316},{"$f":"G*A45+G0","v":-9.2090784891198467},{"$f":"C45/B45","v":0.56847128295693938}]
[-59,2.1580720285136241,1.2363532460196305,-7.8552690358635999,0.57289711820748213]
[-58,2.4470837568804815,1.4130064150112283,-6.5014595826073389,0.57742462269150729]
[-57,2.7710553357390935,1.6129009425677314,-5.1476501293510921,0.58205295353206643]
[-56,3.1337506106185335,1.8388263172150796,-3.7938406760948311,0.58678131915932386]
[-55,3.5392866469854303,2.0938737503897915,-2.4400312228385843,0.59160897639450538]
[-54,3.9921617145835251,2.381465097471049,-1.0862217695823233,0.59653522771170875]
[-53,4.4972850420001285,2.7053841754374703,0.26758768367392349,0.60155941866523854]
[-52,5.0600084205480069,3.0698106420697409,1.6213971369301703,0.60668093547110646]
[-51,5.6861597380800797,3.4793566103390958,2.9752065901864313,0.61189920273219289]
[-50,6.3820785248092848,3.9391061806264154,4.3290160434426781,0.6172136812973682]
[-49,7.1546535945823591,4.4546580827070592,5.6828254966989391,0.62262386624562949]
[-48,8.0113628663497938,5.0321716290111462,7.0366349499551859,0.62812928498693099]
[-47,8.9603154517796142,5.6784161905267929,8.3904444032114398,0.63372949547205937]
[-46,10.010296096076241,6.4008244168518109,9.7442538564676937,0.63942408450442911]
[-45,11.170812060082898,7.2075494323155214,11.098063309723948,0.6452126661472124]
[-44,12.45214253266311,8.1075262507828576,12.451872762980202,0.65109488021969497]
[-43,13.865390663169581,9.1105376627137336,13.805682216236455,0.65707039087718688]
[-42,15.422538304514172,10.227284859277372,15.159491669492709,0.66313888526921982]
[-41,17.136503557946799,11.469463069808405,16.513301122748963,0.66930007227113797]
[-40,19.021201211131025,12.849842500633567,17.867110576005217,0.67555368128454274]
[-39,21.091606161467279,14.382354875287552,19.220920029261471,0.68189946110235045]
[-38,23.363819916857381,16.082185888367583,20.574729482517725,0.68833717883452872]
[-37,25.85514026622538,17.965873897740696,21.928538935773972,0.69486661889084977]
[-36,28.584134212105994,20.051415192506301,23.282348389030226,0.70148758201723305]
[-35,31.570714257482457,22.358376187022177,24.63615784228648,0.70819988438250492]
[-34,34.836218138797832,24.908012904412381,25.989967295542733,0.71500335671258763]
[-33,38.403492096677262,27.723398126283897,27.343776748798987,0.72189784346935926]
[-32,42.296977775381023,30.829556598870408,28.697586202055241,0.72888320207158552]
[-31,46.54280284136037,34.253608699488815,30.051395655311495,0.73595930215550465]
[-30,51.168875410507653,38.024922981022137,31.405205108567749,0.74312602487280044]
[-29,56.204982372779831,42.17527802612117,32.759014561824003,0.75038326222386165]
[-28,61.682891701831217,46.739034056930642,34.112824015080257,0.75773091642431989]
[-27,67.63645883611386,51.753314760384683,35.466633468336511,0.76516889930304099]
[-26,74.101737216597968,57.258199803461935,36.820442921592758,0.77269713172981769]
[-25,81.117093064826406,63.296928527231493,38.174252374849011,0.78031554307113105]
[]
[]
[]
[]
[]
[]
["Minimum Relative Humidity for Persistent Contrails"]
["according to Gierens (2008)"]
[]
[]
["exact:","RH_min = E_i(t) / E_w(t)"]
[]
["approx.:","RH_min = RH_a*t + RH_b"]
[]
[null,"RH_a",6.0585999999999999E-3,"1/°C"]
[null,"RH_b",0.92261000000000004]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"This according to:"]
[null,"GIERENS, Klaus, et al.,2008. A Review of Various Strategies for Contrail Avoidance. In: OASC, vol.2, pp. 1-7."]
[null,"https://doi.org/10.2174/1874282300802010001"]
[]
[]
["Checking the Influence of the Altitude of the Tropopause on Pressure"]
[]
["p(H, H_T)","hPa","p_0 =",{"$f":"p_0/100","v":1013.15},"hPa"]
[]
["H","ft",null,20000,25000,30000,35000,36089,40000,45000,50000,55000,60000,65000,70000,null,"title of legend"]
["H_T","ft",20000,{"$f":" IF(D$117<$C118,p_0*(1-k_a*D$117)^k_exp,p_0*(1-k_a*$C118)^k_exp*EXP(-k_b*(D$117-$C118)))/100","v":465.58560984464981},366.12653190706061,287.91404745309768,226.40942815328913,214.86371569423667,178.04351545247212,140.00959965860054,110.10054450309049,86.580705390456217,68.08520865851446,53.540746950121701,42.103294393274631,null,"H_T = 20000 ft"]
[null,null,36089,465.58560984464981,375.97092340716307,300.86505755783213,238.39835665961203,226.29983037755792,187.51987610628152,147.46160630983147,115.96064261023326,91.188960781595142,71.709041802890809,56.390451565784254,44.34424094710004,null,"H_T = 36089 ft"]
[null,null,50000,465.58560984464981,375.97092340716307,300.86505755783213,238.39835665961203,226.29983037755792,186.87512990727714,144.76424314167357,110.68981911016655,87.044098295365018,68.449610894316407,53.827305048121886,42.328637531877433,null,"H_T = 50000 ft"]
[null,null,70000,465.58560984464981,375.97092340716307,300.86505755783213,238.39835665961203,226.29983037755792,186.87512990727714,144.76424314167357,110.68981911016655,83.422049984400147,61.868126276407672,45.063286671360494,32.161993729646518,null,"H_T = 70000 ft"]
[]
[]
[]
["Result:"]
["The influence of the altitude of the tropopause, H_T on the pressure is small!"]
[]
["Further approach:"]
["The SAC and SAD is calculated with a standard H_T = 36089 ft,"]
["even if later the SAD is evaluated for the temperatures of various other H_T."]

{"sheet":"t_SAC","index":1,"n_rows":87,"n_cols":22,"rows_kept":87,"cut":false,"hidden":false,"merged":[]}
["Calculating t_SAC for the Schmidt-Appleman-Criterion (SAC)"]
[]
["Derivation of the Approximate-Analytical Solution",null,null,null,"H [ft]","p [Pa]","G [Pa/°C]","ln(G)","t_1 [°C]","t_2 [°C]","t_3 [°C]","t_4 [°C]"]
["a_w",{"$f":"a_w","v":611.20000000000005},"Pa",null,10000,{"$f":"IF(H<H_T,p_0*(1-k_a*E4)^k_exp,p_T*EXP(-k_b*(E4-H_T)))","v":79304.183023428166},{"$f":"EI_H2O*F4*c_p/(eps*Q*(1-eta))","v":5.7248963004907907},{"$f":"LN(G4)","v":1.7448244358248626},{"$f":"b_w*c_w/(b_w-LN($G4*(c_w+t_init)^2/(a_w*b_w*c_w)))-c_w","v":-29.205045111515034},{"$f":"b_w*c_w/(b_w-LN($G4*(c_w+I4)^2/(a_w*b_w*c_w)))-c_w","v":-28.093024355749833},-27.981039117652159,-27.969787395041863]
["b_w",{"$f":"b_w","v":17.62},null,null,15000,62363.107626497898,4.5019355918788637,{"$f":"LN(G5)","v":1.5045074358248627},-31.741688833620458,-30.907063369234294,-30.824175319186679,-30.815957844282622]
["c_w",{"$f":"c_w","v":243.12},"°C",null,20000,49041.009497383246,3.5402255359085171,1.2641904358248628,-34.218877588294845,-33.645518785926924,-33.589352916998934,-33.583857596267023]
[null,null,null,null,25000,38564.797426813093,2.7839573866200227,1.0238734358248629,-36.63867746002208,-36.311456408102003,-36.279831932771458,-36.276777706343097]
["EI_H2O",{"$f":"EI_H2O","v":1.25},null,null,30000,30326.529078698644,2.1892443438712217,0.78355643582486278,-39.003059899760672,-38.907776564543212,-38.898689518009292,-38.897823077557376]
["c_p",{"$f":"c_p","v":1004},"J/(kgK)",null,35000,23848.131646653288,1.7215747698606192,0.54323943582486289,-41.313907081765421,-41.437225202234657,-41.448832773889819,-41.449925657060191]
["eps",{"$f":"eps","v":0.622},null,null,40000,18753.658935390147,1.3538094532562532,0.30292243582486283,-43.573016900609133,-43.902404093845519,-43.93301049715518,-43.935856511598502]
["Q",{"$f":"Q","v":43000000},"J/kg",null,45000,14747.474924908605,1.064606700686245,6.2605435824862721E-2,-45.782107636285872,-46.305780242395741,-46.353823956300403,-46.358236892690599]
["eta",{"$f":"eta","v":0.35},null,null,50000,11597.097793560972,0.83718386248520371,-0.17771156417513742,-47.942822312836427,-48.649694556023036,-48.713736790842006,-48.719548389687446]
[null,null,null,null,55000,9119.7088259670509,0.65834342311941108,-0.41802856417513712,-50.056732773731284,-50.936369858285332,-51.01508411639071,-51.022142258083875]
["k_a",{"$f":"k_a","v":6.8755999999999999E-6},"1/ft",null,60000,7171.5433077229964,0.51770713959771752,-0.65834556417513723,-52.125343495255009,-53.1679182927993,-53.260080909403911,-53.268248000935955]
["k_b",{"$f":"k_b","v":4.8063399999999998E-5},"1/ft",null,65000,5639.5477526764971,0.4071137843536059,-0.89866256417513724,-54.150095157334334,-55.346348175132789,-55.450829737704254,-55.459981272893117]
["k_exp",{"$f":"k_exp","v":5.2558800000000003},null,null,70000,4434.8193254955922,0.32014554317234889,-1.1389795641751372,-56.132367989621059,-57.473570339638798,-57.589327895972673,-57.599351169000101]
["H_T",{"$f":"H_T","v":36089},"ft",null,75000,3487.4467443697131,0.25175558468463954,-1.3792965641751371,-58.073484909160783,-59.55140402426548,-59.677473999347427,-59.688266953944407]
["p_0",{"$f":"p_0","v":101315},"Pa",null,80000,2742.4532776103047,0.19797518900890615,-1.6196135641751372,-59.974714464636918,-61.581582332226731,-61.717074082878298,-61.728544281696117]
["p_T",{"$f":"p_T","v":22632},"Pa"]
[]
["t_init",-40,"°C",null,null,null,"G [Pa/°C]","ln(G)","t_1 [°C]","t_2 [°C]","t_3 [°C]","t_4 [°C]","t_SLZ [°C]"]
[null,null,null,null,null,null,2.5000000000000001E-2,{"$f":"LN(G22)","v":-3.6888794541139363},{"$f":"b_w*c_w/(b_w-LN($G22*(c_w+t_init)^2/(a_w*b_w*c_w)))-c_w","v":-74.860288632808846},{"$f":"b_w*c_w/(b_w-LN($G22*(c_w+I22)^2/(a_w*b_w*c_w)))-c_w","v":-77.312795109042781},-77.501043528874135,-77.515590076760247,{"$f":"a_SLZ*H22^2+b_SLZ*H22+c_SLZ","v":-77.103000923758813}]
["Approximate-Analytical Solution",null,null,null,null,null,0.05,{"$f":"LN(G23)","v":-2.9957322735539909},-70.151089455426131,-72.366814098284379,-72.54213723655684,-72.556091492594959,-72.527278113610748]
[null,null,null,null,null,null,7.4999999999999997E-2,{"$f":"LN(G24)","v":-2.5902671654458267},-67.272153522442295,-69.329301142703571,-69.49507771611124,-69.508508389327744,-69.617463784938082]
[null,null,null,null,null,null,0.1,{"$f":"LN(G25)","v":-2.3025850929940455},-65.170701192844774,-67.105352262816268,-67.263327496423216,-67.276291055521313,-67.448530606950612]
[null,null,null,null,null,null,0.2,{"$f":"LN(G26)","v":-1.6094379124341003},-59.895003859035086,-61.496563340177801,-61.63167329942894,-61.643116578083522,-61.866758403778398]
[null,null,null,null,null,null,0.3,-1.2039728043259361,-56.661345277772654,-58.040314601360308,-58.15895303128147,-58.169194111709118,-58.368442906313305]
["t = t_SAC =","a_SLZ*LN(G)^2+b_SLZ*LN(G)+c_SLZ",null,null,null,null,0.4,-0.916290731874155,-54.296929715794391,-55.504105754321301,-55.609448895242167,-55.61866807027323,-55.781961504094106]
["t = t_SAC =",{"$f":"a_SLZ*LN(G)^2+b_SLZ*LN(G)+c_SLZ","v":-43.858534861970831},"°C",null,null,null,0.5,-0.69314718055994529,-52.421241411854282,-53.486631626830672,-53.580646027756558,-53.588963099352071,-53.716059378425797]
[null,null,null,null,null,null,0.6,-0.51082562376599072,-50.86080377181824,-51.804491098944084,-51.888538049746813,-51.896039966742848,-51.989395422232803]
["Analytical Solution: LambertW Function",null,null,null,null,null,0.7,-0.35667494393873245,-49.521410340386382,-50.357897699964695,-50.43298640697455,-50.439739934083121,-50.502369770727867]
["(exact within numerical precision of the LamberW function)",null,null,null,null,null,0.8,-0.22314355131420971,-48.3459987672816,-49.086313088702695,-49.153227507077048,-49.159285963461741,-49.194139907897735]
[null,null,null,null,null,null,0.9,-0.10536051565782628,-47.297301420135653,-47.950145360299388,-48.009515495933613,-48.014922714811007,-48.024703782684441]
[null,null,null,null,null,null,1,0,-46.349594376605125,-46.922033336285182,-46.97437872302325,-46.979171551412009,-46.966299999999997]
[null,null,null,null,null,null,2,0.69314718055994529,-39.878602982766637,-39.867079654065975,-39.865986118791056,-39.865882347618907,-39.713515925062119]
[null,null,null,null,null,null,3,1.0986122886681098,-35.892144921744801,-35.489938297525271,-35.45090407997003,-35.447119048545488,-35.237721144354239]
[null,null,null,null,null,null,4,1.3862943611198906,-32.96752899814706,-32.263373537036017,-32.193914553576519,-32.187073110402878,-31.957707153612162]
["x =","-0.5*WURZEL(b_w*c_w*G/(a_w*EXP(b_w)))",null,null,null,null,5,1.6094379124341003,-30.64154268529316,-29.687842389646136,-29.592553747142858,-29.583051758691681,-29.353859359532166]
["x =",{"$f":"-0.5*SQRT(b_w*c_w*G/(a_w*EXP(b_w)))","v":-2.2984550387840079E-4},null,null,null,null,6,1.791759469228055,-28.702503638764853,-27.53433310158178,-27.416369939872396,-27.404486286707879,-27.18766178850808,null,null,null,null,null,null,null,"a_SLZ",0.52349000000000001]
["W(x) =","LambertW(x;-1)",null,null,null,"   W-1",7,1.9459101490553132,-27.035244127226633,-25.677938180169065,-25.53962617440834,-25.525570582800015,-25.329015760759223,null,null,null,null,null,null,null,"b_SLZ",10.1007]
["W(x) =",{"$f":"LambertW(x,-1)","v":-10.75331750951659},null,null,"*","   W-1",8,2.0794415416798357,-25.569898042774128,-24.042725167108529,-23.88586310524434,-23.869800472259385,-23.698873685650128,null,null,null,null,null,null,null,"c_SLZ",-46.966299999999997]
["t = t_SAC =","-c_w-b_w*c_w/(2*B39)",null,null,null,null,9,2.1972245773362196,-24.260775506084315,-22.578947909193488,-22.404976449593732,-22.387040688394592,-22.245490865716928]
["t = t_SAC =",{"$f":"-c_w-b_w*c_w/(2*W_x)","v":-43.936148309166072},"°C",null,"* #NAME?,",null,10,2.3025850929940459,-23.076302723017221,-21.252175137526763,-21.062279076463511,-21.042581648354741,-20.933088109340702]
[null,null,null,null,"   if LamberW not defined",null,11,2.3978952727983707,-21.9937177474132,-20.037549689208817,-19.832723888815082,-19.811359382458676,-19.735863156534744]
["Compare with online calculator (e.g.):",null,null,null,null,null,12,2.4849066497880004,-20.996051684491619,-18.916516814804197,-18.697610793686948,-18.674660745644559,-18.634577736149836]
["https://www.had2know.org/academics/lambert-w-function-calculator.html",null,null,null,null,null,13,2.5649493574615367,-20.070304928743354,-17.874845207211393,-17.642594479656083,-17.618130089087316,-17.614493529220095]
["W(x) =",-2.3000000000000001E-4,"   W0",null,null,null,14,2.6390573296152584,-19.206291174897046,-16.901371229243608,-16.656420034437303,-16.630504151355552,-16.664062828151629]
[null,"and",null,null,null,null,15,2.7080502011022101,-18.395875167181543,-15.987170012759066,-15.730088237682054,-15.702776856471786,-15.774064629786253]
["W(x) =",-10.753315000000001,"   W-1",null,null,null,16,2.7725887222397811,-17.632453155074444,-15.12498994576049,-14.856286008321206,-14.827629413959585,-14.937015521176015]
[null,null,null,null,null,null,17,2.8332133440562162,-16.910588658122037,-14.308855856061115,-14.028986701896542,-13.999030366009663,-14.146756520656751]
[null,null,null,null,null,null,18,2.8903717578961645,-16.225750839296097,-13.533783743013231,-13.243162732280808,-13.211948024945855,-13.398156228962485]
[null,null,null,null,null,null,19,2.9444389791664403,-15.574122566930384,-12.795571329791784,-12.494574550389444,-12.462139313570816,-12.686893008127385]
[null,null,null,null,null,null,20,2.9957322735539909,-14.952456962381433,-12.090641407483503,-11.779612793986161,-11.745991809277115,-12.009292162637166]
[]
[null,null,null,null,null,null,null,null,null,null,"Press <ALT> F11 to see the LamberW-Function (only included in files of type *.xlsm)"]
[]
[null,null,null,null,null,null,null,null,null,null,"Function LambertW(x As Double, Optional branch As Integer = 0) As Double"]
[null,null,null,null,null,null,null,null,null,null,"    Dim w As Double, wPrev As Double, tol As Double, i As Integer"]
[null,null,null,null,null,null,null,null,null,null,"    tol = 0.000000000001"]
[null,null,null,null,null,null,null,null,null,null,"    ' Initial guess"]
[null,null,null,null,null,null,null,null,null,null,"    If branch = -1 Then"]
[null,null,null,null,null,null,null,null,null,null,"        w = Log(-x)"]
[null,null,null,null,null,null,null,null,null,null,"    Else"]
[null,null,null,null,null,null,null,null,null,null,"        w = x"]
[null,null,null,null,null,null,null,null,null,null,"    End If"]
[null,null,null,null,null,null,null,null,null,null,"    For i = 1 To 100"]
["      LambertW function: W-1 und W0. Stephan Kulla, CC BY ",null,null,null,null,null,null,null,null,null,"        wPrev = w"]
["     https://commons.wikimedia.org/wiki/File:Diagram_of_the_real_branches_of_the_Lambert_W_function.png ",null,null,null,null,null,null,null,null,null,"        w = w - (w * Exp(w) - x) / ((w + 1) * Exp(w) - (w + 2) * (w * Exp(w) - x) / (2 * w + 2))"]
[null,null,null,null,null,null,null,null,null,null,"        If Abs(w - wPrev) < tol Then Exit For"]
["Iterative Solution",null,null,null,null,null,null,null,null,null,"    Next i"]
["with t_1,  t_2,  t_3,  t_4",null,null,null,null,null,null,null,null,null,"    LambertW = w"]
[null,null,null,null,null,null,null,null,null,null,"End Function"]
[]
[]
[]
["t_n+1 =","b_w*c_w/(b_w-LN(G*(c_w+t_n)^2/(a_w*b_w*c_w)))-c_w"]
[]
["t_1 =",{"$f":"b_w*c_w/(b_w-LN(G*(c_w+t_init)^2/(a_w*b_w*c_w)))-c_w","v":-43.573016900609133},"°C","mit t_0 = t_ini =",null,{"$f":"t_init","v":-40},"°C"]
["t_2 =",{"$f":"b_w*c_w/(b_w-LN(G*(c_w+B78)^2/(a_w*b_w*c_w)))-c_w","v":-43.902404093845519},"°C"]
["t_3 =",{"$f":"b_w*c_w/(b_w-LN(G*(c_w+B79)^2/(a_w*b_w*c_w)))-c_w","v":-43.93301049715518},"°C"]
["t_4 =",{"$f":"b_w*c_w/(b_w-LN(G*(c_w+B80)^2/(a_w*b_w*c_w)))-c_w","v":-43.935856511598502},"°C"]
["t_5 =",{"$f":"b_w*c_w/(b_w-LN(G*(c_w+B81)^2/(a_w*b_w*c_w)))-c_w","v":-43.936121173596689},"°C"]
[]
["Numerical Solution (with Excel Solver)"]
[]
[]
["See Tab \"SAC\""]

{"sheet":"SAD","index":2,"n_rows":334,"n_cols":17,"rows_kept":334,"cut":false,"hidden":false,"merged":[]}
["Constructing the Schmidt-Appleman-Diagram (SAD)"]
[]
["1.) Enter altitude, H in tab \"SAC\" and operate Solver (e.g. for a calculation of a new altitude)"]
["2.) Copy new colum \"C\" into the column to the right to safe for later"]
[]
["G","Pa/°C",{"$f":"G","v":1.3538094532562532},3.3610198526021748,{"$f":"G","v":1.3538094532562532},2.1719172801401174,1.720975890616645,1.6337833407152185,1.3538094532562532,1.064606700686245,0.83718386248520371,0.65834342311941108,0.51770713959771752,0.4071137843536059,0.32014554317234889]
["G0","Pa",{"$f":"G0","v":72.019488706255345},149.10648875647044,126.25295242659809,105.79635163302788,87.67939672383018,84.041437936928773,72.458994294193644,58.975248471132915,48.173312524551676,39.261656161440875,31.933716141748164,25.925672133505408,21.012657314265486]
["H","ft",{"$f":"H","v":40000},20000,25000,30000,35000,36089,40000,45000,50000,55000,60000,65000,70000]
["H","m",{"$f":"C8*0.3048","v":12192},6096,{"$f":"E8*0.3048","v":7620},9144,10668,10999.9272,12192,13716,15240,16764,18288,19812,21336]
["p","Pa",{"$f":"p","v":18753.658935390147},46558.560984464981,{"$f":"p","v":18753.658935390147},30086.505755783211,23839.835665961204,22632,18753.658935390147,14747.474924908605,11597.097793560972,9119.7088259670509,7171.5433077229964,5639.5477526764971,4434.8193254955922]
["t_SAC,100","°C",{"$f":"t","v":-43.936142533951404},-34.171657846038833,-36.556995939242505,-38.983215462422002,-41.453686614326799,-41.997060149801399,-43.936149738567622,-46.358686546546537,-48.720135430706478,-51.022841943746812,-53.26904401732731,-55.460885188547678,-57.600302356601937]
["t_SAC,0","°C",{"$f":"-G0/G","v":-53.197655351741197},-44.363465643033599,-46.517434517002748,-48.711040977676006,-50.947486947312008,-51.439769180250117,-53.197655351741197,-55.396277736292191,-57.542094016895945,-59.637044713545428,-61.68297421310848,-63.681636755849084,-65.634701973512776]
["Dt,tot","°C",{"$f":"C11-C12","v":9.261512817789793},10.191807796994766,9.9604385777602431,9.7278255152540041,9.4938003329852094,9.442709030448718,9.2615056131735756,9.0375911897456547,8.8219585861894672,8.6142027697986165,8.4139301957811696,8.2207515673014058,8.0343996169108394]
[]
["t","E_w","phi","phi","phi","phi","phi","phi","phi","phi","phi","phi","phi",null,"Diagram for typical kerosine aircraft"]
[-60,{"$f":"a_w*EXP(b_w*A16/(c_w+A16))","v":1.9005832334432484},{"$f":"IF(OR(G*A16+G0<0, A16>t),\"n.a.\",(G*A16+G0)/B16)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.45843178586113253]
[-59,2.1580720285136241,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.19433744187142682,0.64362768579114626,null,"EI_H2O",1.25]
[-58,2.4470837568804815,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.44041713630959645,0.77917318511042366,null,"c_p",1004,"J/(kgK)"]
[-57,2.7710553357390935,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.16377600152615421,0.62650536827746039,0.87490464495961728,null,"eps",0.622]
[-56,3.1337506106185335,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.4119715911680189,0.76407626651606697,0.93884826517681108,null,"Q",43000000,"J/kg"]
[-55,3.5392866469854303,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.11919914250199969,0.60130763629392847,0.86253762251030042,0.97754824883160785,null,"eta",0.35]
[-54,3.9921617145835251,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.3723513074747184,0.7428015602469239,0.92959944469079026,0.99633504047226873]
[-53,4.4972850420001285,5.9499827379168341E-2,"n.a.","n.a.","n.a.","n.a.","n.a.",5.9499827378707001E-2,0.56725186661225135,0.84552519516190661,0.97157611654715414,"n.a.",null,"EI_H2O and Q for Kerosine "]
[-52,5.0600084205480069,0.3204336835381334,"n.a.","n.a.","n.a.","n.a.","n.a.",0.32043368353772339,0.71456403526233503,0.91694544548180557,0.99363434630153902,"n.a."]
[-51,5.6861597380800797,0.52323654755274318,"n.a.","n.a.","n.a.","n.a.",0.12635725930120029,0.52323654755237825,0.8231050395560493,0.96320465658524745,"n.a.","n.a."]
[-50,6.3820785248092848,0.67830817602985261,"n.a.","n.a.","n.a.",0.25549704326877865,0.36857442164394999,0.67830817602952742,0.90016338948012897,0.98935156873209629,"n.a.","n.a."]
[-49,7.1546535945823591,0.79428380725547409,"n.a.","n.a.","n.a.",0.46844728948896464,0.55712749599804301,0.7942838072551841,0.95176098290254152,0.99953172690174652,"n.a.","n.a."]
[-48,8.0113628663497938,0.87833182285516398,"n.a.","n.a.",0.19276647582509146,0.63316991863363536,0.70148334014470282,0.87833182285490496,0.98286982746305607,"n.a.","n.a.","n.a."]
[-47,8.9603154517796142,0.93640055959692892,"n.a.","n.a.",0.41474426725727331,0.75817976514416308,0.809527405854094,0.93640055959669732,0.99759138916298717,"n.a.","n.a.","n.a."]
[-46,10.010296096076241,0.97342313982971707,"n.a.",0.14029243735785019,0.58821004794158649,0.85057481554436509,0.88782631190223571,0.9734231398295099,"n.a.","n.a.","n.a.","n.a."]
[-45,11.170812060082898,0.9934876041269276,"n.a.",0.36868120769299861,0.72152982105248931,0.91627015037304382,0.9418462640097327,0.99348760412674186,"n.a.","n.a.","n.a.","n.a."]
[-44,12.45214253266311,0.99997833548064508,9.8104823227848484E-2,0.54870622517618783,0.82170528324930914,0.96019279456004691,0.97613490317634521,0.99997833548047843,"n.a.","n.a.","n.a.","n.a."]
[-43,13.865390663169581,"n.a.",0.330508905655997,0.68852497557408621,0.89459495865133742,0.98644414424222504,0.9944728295900982,"n.a.","n.a.","n.a.","n.a.","n.a."]
[-42,15.422538304514172,"n.a.",0.51506793436552023,0.79499023888472564,0.94509902192148321,0.99843547241662478,0.99999995606270742,"n.a.","n.a.","n.a.","n.a.","n.a."]
[-41,17.136503557946799,"n.a.",0.65968385916968741,0.87385778572086459,0.97731390132478668,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-40,19.021201211131025,"n.a.",0.77101832263891767,0.92996054776100379,0.99466170497957707,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-39,21.091606161467279,"n.a.",0.8546866638311863,0.96735479433904104,0.99999865093707141,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-38,23.363819916857381,"n.a.",0.91542112692609579,0.98944291070987855,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-37,25.85514026622538,"n.a.",0.95720827484813376,0.99907659989803987,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-36,28.584134212105994,"n.a.",0.98340477462798892,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-35,31.570714257482457,"n.a.",0.99683503067833479,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-34,34.836218138797832,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-33,38.403492096677262,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-32,42.296977775381023,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-31,46.54280284136037,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-30,51.168875410507653,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-29,56.204982372779831,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-28,61.682891701831217,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-27,67.63645883611386,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-26,74.101737216597968,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-25,81.117093064826406,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[]
[]
["Schmidt-Appleman-Diagram from Approximate Equation"]
[]
["phi = 1 - (1/Dt,tot(H)^b_t)*((H - b_H)/a_H - t)^b_t     with     Dt,tot(H) = a_tot*H + b_tot"]
[]
["H, ft",null,null,20000,25000,30000,35000,36089,40000,45000,50000,55000,60000,null,"Diagram for typical kerosine aircraft"]
["t, °C","    calculated:","Dt,tot(H)",{"$f":"a_tot*D58+b_tot","v":10.15428},9.9373500000000003,9.7204200000000007,9.5034899999999993,9.4562426459999998,9.2865599999999997,9.0696300000000001,8.8527000000000005,8.6357700000000008,8.4188399999999994]
[-60,null,null,{"$f":"IF(D16=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A60)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.43133317270269322,null,"EI_H2O",1.25]
[-59,null,null,{"$f":"IF(D17=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A61)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.14372458006669353,0.62451818222558309,null,"c_p",1004,"J/(kgK)"]
[-58,null,null,{"$f":"IF(D18=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A62)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.3910917946753607,0.77093459826323507,null,"eps",0.622]
[-57,null,null,{"$f":"IF(D19=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A63)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.10161168771329376,0.58875858840124384,0.87563107333172074,null,"Q",43000000,"J/kg"]
[-56,null,null,{"$f":"IF(D20=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A64)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",0.35124031009508128,0.74103161276262686,0.94410730486416006,null,"eta",0.35]
[-55,null,null,{"$f":"IF(D21=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A65)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.",6.0351020351821161E-2,0.55287624416767733,0.85251169531180304,0.98250015851090033]
[-54,null,null,{"$f":"IF(D22=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A66)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.",0.31184041614645919,0.71047200211918504,0.92817964184374535,0.99796777452932095,null,"EI_H2O and Q for Kerosine "]
[-53,null,null,{"$f":"IF(D23=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A67)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.",1.9951402367897608E-2,0.51697814286108335,0.82823431290683358,0.97353740299028479,"n.a."]
[-52,null,null,{"$f":"IF(D24=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A68)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.",0.27294191866658546,0.67940130669532972,0.91069298655411546,0.99487691779428689,"n.a."]
[-51,null,null,{"$f":"IF(D25=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A69)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.",0.10512276466637427,0.48115562992334371,0.80296805004144733,0.96281013438634644,"n.a.","n.a."]
[-50,null,null,{"$f":"IF(D26=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A70)^b_t)","v":"n.a."},"n.a.","n.a.",0.23458452564495091,0.33969484923611515,0.64794767135336617,0.89181345596551342,0.99017556212678393,"n.a.","n.a."]
[-49,null,null,{"$f":"IF(D27=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A71)^b_t)","v":"n.a."},"n.a.","n.a.",0.44548640862019928,0.53203151444452412,0.77686643661491206,0.95043547561035058,0.9994443431417388,"n.a.","n.a."]
[-48,null,null,{"$f":"IF(D28=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A72)^b_t)","v":"n.a."},"n.a.",0.19679937864016694,0.6162235818129973,0.6853597861722216,0.87169942308907156,0.98384107869575899,"n.a.","n.a.","n.a."]
[-47,null,null,{"$f":"IF(D29=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A73)^b_t)","v":"n.a."},"n.a.",0.41003630927524182,0.7500680499712522,0.80309681923635101,0.93654180764805628,0.99784198073382979,"n.a.","n.a.","n.a."]
[-46,null,null,{"$f":"IF(D30=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A74)^b_t)","v":"n.a."},0.1596103596457451,0.58432750666032363,0.85049958753659283,0.88889623142395036,0.97590830221571168,"n.a.","n.a.","n.a.","n.a."]
[-45,null,null,{"$f":"IF(D31=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A75)^b_t)","v":"n.a."},0.37486084284534626,0.72269740995440557,0.92126115055203806,0.94671819054887862,0.99494298587359609,"n.a.","n.a.","n.a.","n.a."]
[-44,null,null,{"$f":"IF(D32=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A76)^b_t)","v":0.12303520602480733},0.55234541921549585,0.82835205169175863,0.96644611842575834,0.98094569916168151,0.99994400850416809,"n.a.","n.a.","n.a.","n.a."]
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[-42,null,null,{"$f":"IF(D34=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A78)^b_t)","v":0.52035218879776346},0.80538404591262525,0.95554311661023017,0.99931959694545647,0.99999800135626549,"n.a.","n.a.","n.a.","n.a.","n.a."]
[-41,null,null,{"$f":"IF(D35=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A79)^b_t)","v":0.66667332431664761},0.88705791686422342,0.98494974871031349,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-40,null,null,{"$f":"IF(D36=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A80)^b_t)","v":0.78171206734521048},0.94329840428863376,0.997729251012614,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-39,null,null,{"$f":"IF(D37=\"n.a.\",\"n.a.\",1-(1/D$59^b_t)*((D$58-b_H)/a_H-$A81)^b_t)","v":0.86838245147411375},0.97785858495982125,"n.a.",{"$f":"IF(G37=\"n.a.\",\"n.a.\",1-(1/G$59^b_t)*((G$58-b_H)/a_H-$A81)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-38,null,null,0.92981560035546351,0.99499997252588435,{"$f":"IF(F38=\"n.a.\",\"n.a.\",1-(1/F$59^b_t)*((F$58-b_H)/a_H-$A82)^b_t)","v":"n.a."},"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-37,null,null,0.96943032039195898,0.99989358516601035,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-36,null,null,0.99105644917521774,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-35,null,null,0.999197898620097,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-34,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-33,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-32,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-31,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-30,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-29,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-28,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-27,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-26,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-25,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[]
[]
["Error of the Schmidt-Appleman-Diagram from Approximate Equation"]
[]
["The Approximate Equation was calculated for a typical altitude of 40000 ft. Errors occur for lower relative humidity (towards 0%) at high and low altitudes."]
[]
["H, ft",null,null,20000,25000,30000,35000,36089,40000,45000,50000,55000,60000]
["t, °C"]
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[-59,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I17=\"n.a.\",\"n.a.\",(I61-I17))","v":"n.a."},"n.a.","n.a.",-5.0612861804733289E-2,-1.910950356556318E-2]
[-58,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I18=\"n.a.\",\"n.a.\",(I62-I18))","v":"n.a."},"n.a.","n.a.",-4.9325341634235742E-2,-8.2385868471885892E-3]
[-57,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I19=\"n.a.\",\"n.a.\",(I63-I19))","v":"n.a."},"n.a.",-6.2164313812860444E-2,-3.7746779876216552E-2,7.2642837210346034E-4]
[-56,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I20=\"n.a.\",\"n.a.\",(I64-I20))","v":"n.a."},"n.a.",-6.0731281072937626E-2,-2.3044653753440114E-2,5.2590396873489764E-3]
[-55,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I21=\"n.a.\",\"n.a.\",(I65-I21))","v":"n.a."},-5.8848122150178525E-2,-4.8431392126251138E-2,-1.0025927198497375E-2,4.9519096792924877E-3]
[-54,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I22=\"n.a.\",\"n.a.\",(I66-I22))","v":"n.a."},-6.0510891328259209E-2,-3.2329558127738856E-2,-1.4198028470449042E-3,1.6327340570522209E-3]
[-53,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I23=\"n.a.\",\"n.a.\",(I67-I23))","v":-3.9548425010809393E-2},-5.0273723751168009E-2,-1.7290882255073026E-2,1.9612864431306498E-3,"n.a."]
[-52,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(I24=\"n.a.\",\"n.a.\",(I68-I24))","v":-4.7491764871137931E-2},-3.5162728567005308E-2,-6.2524589276901077E-3,1.2425714927478682E-3,"n.a."]
[-51,null,null,"n.a.","n.a.","n.a.","n.a.",-2.1234494634826018E-2,{"$f":"IF(I25=\"n.a.\",\"n.a.\",(I69-I25))","v":-4.2080917629034542E-2},-2.0136989514601966E-2,-3.9452219890101503E-4,"n.a.","n.a."]
[-50,null,null,{"$f":"IF(D26=\"n.a.\",\"n.a.\",(D70-D26))","v":"n.a."},"n.a.","n.a.",-2.0912517623827731E-2,-2.8879572407834841E-2,{"$f":"IF(I26=\"n.a.\",\"n.a.\",(I70-I26))","v":-3.0360504676161248E-2},-8.3499335146155484E-3,8.2399339468763877E-4,"n.a.","n.a."]
[-49,null,null,"n.a.","n.a.","n.a.",-2.2960880868765354E-2,-2.5095981553518887E-2,{"$f":"IF(I27=\"n.a.\",\"n.a.\",(I71-I27))","v":-1.7417370640272045E-2},-1.3255072921909417E-3,-8.7383760007719857E-5,"n.a.","n.a."]
[-48,null,null,"n.a.","n.a.",4.0329028150754842E-3,-1.6946336820638064E-2,-1.6123553972481219E-2,{"$f":"IF(I28=\"n.a.\",\"n.a.\",(I72-I28))","v":-6.6323997658334077E-3},9.712512327029188E-4,"n.a.","n.a.","n.a."]
[-47,null,null,"n.a.","n.a.",-4.7079579820314965E-3,-8.1117151729108716E-3,-6.4305866177429838E-3,{"$f":"IF(I29=\"n.a.\",\"n.a.\",(I73-I29))","v":1.4124805135895535E-4},2.5059157084261763E-4,"n.a.","n.a.","n.a."]
[-46,null,null,"n.a.",1.9317922287894917E-2,-3.8825412812628635E-3,-7.522800777226557E-5,1.0699195217146462E-3,{"$f":"IF(I30=\"n.a.\",\"n.a.\",(I74-I30))","v":2.485162386201778E-3},"n.a.","n.a.","n.a.","n.a."]
[-45,null,null,"n.a.",6.1796351523476512E-3,1.1675889019162611E-3,4.9910001789942315E-3,4.871926539145921E-3,{"$f":"IF(I31=\"n.a.\",\"n.a.\",(I75-I31))","v":1.4553817468542229E-3},"n.a.","n.a.","n.a.","n.a."]
[-44,null,null,2.4930382796958847E-2,3.6391940393080136E-3,6.6467684424494911E-3,6.2533238657114243E-3,4.8107959853362914E-3,{"$f":"IF(I32=\"n.a.\",\"n.a.\",(I76-I32))","v":-3.4326976310339319E-5},"n.a.","n.a.","n.a.","n.a."]
[-43,null,null,{"$f":"IF(D33=\"n.a.\",\"n.a.\",(D77-D33))","v":9.4976550859726672E-3},6.3410233116036885E-3,1.0129365546092339E-2,4.2083545492445085E-3,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-42,null,null,5.2842544322432294E-3,1.0393807027899604E-2,1.0444094688746963E-2,8.841245288316868E-4,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a."]
[-41,null,null,6.9894651469601943E-3,1.3200131143358829E-2,7.6358473855268061E-3,"n.a.",{"$f":"IF(H35=\"n.a.\",\"n.a.\",(H79-H35))","v":"n.a."},"n.a.",{"$f":"IF(J35=\"n.a.\",\"n.a.\",(J79-J35))","v":"n.a."},"n.a.","n.a.","n.a."]
[-40,null,null,1.0693744706292807E-2,1.3337856527629977E-2,3.0675460330369386E-3,"n.a.","n.a.","n.a.",{"$f":"IF(J36=\"n.a.\",\"n.a.\",(J80-J36))","v":"n.a."},"n.a.","n.a.","n.a."]
[-39,null,null,{"$f":"IF(D37=\"n.a.\",\"n.a.\",(D81-D37))","v":1.3695787642927448E-2},1.0503790620780218E-2,"n.a.",{"$f":"IF(G37=\"n.a.\",\"n.a.\",(G81-G37))","v":"n.a."},"n.a.","n.a.",{"$f":"IF(J37=\"n.a.\",\"n.a.\",(J81-J37))","v":"n.a."},"n.a.","n.a.","n.a."]
[-38,null,null,1.4394473429367727E-2,5.5570618160057927E-3,{"$f":"IF(F38=\"n.a.\",\"n.a.\",(F82-F38))","v":"n.a."},"n.a.","n.a.","n.a.",{"$f":"IF(J38=\"n.a.\",\"n.a.\",(J82-J38))","v":"n.a."},"n.a.","n.a.","n.a."]
[-37,null,null,1.2222045543825222E-2,8.1698526797047144E-4,"n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J39=\"n.a.\",\"n.a.\",(J83-J39))","v":"n.a."},"n.a.","n.a.","n.a."]
[-36,null,null,7.651674547228815E-3,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J40=\"n.a.\",\"n.a.\",(J84-J40))","v":"n.a."},"n.a.","n.a.","n.a."]
[-35,null,null,2.3628679417622145E-3,"n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J41=\"n.a.\",\"n.a.\",(J85-J41))","v":"n.a."},"n.a.","n.a.","n.a."]
[-34,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J42=\"n.a.\",\"n.a.\",(J86-J42))","v":"n.a."},"n.a.","n.a.","n.a."]
[-33,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J43=\"n.a.\",\"n.a.\",(J87-J43))","v":"n.a."},"n.a.","n.a.","n.a."]
[-32,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J44=\"n.a.\",\"n.a.\",(J88-J44))","v":"n.a."},"n.a.","n.a.","n.a."]
[-31,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J45=\"n.a.\",\"n.a.\",(J89-J45))","v":"n.a."},"n.a.","n.a.","n.a."]
[-30,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J46=\"n.a.\",\"n.a.\",(J90-J46))","v":"n.a."},"n.a.","n.a.","n.a."]
[-29,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J47=\"n.a.\",\"n.a.\",(J91-J47))","v":"n.a."},"n.a.","n.a.","n.a."]
[-28,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J48=\"n.a.\",\"n.a.\",(J92-J48))","v":"n.a."},"n.a.","n.a.","n.a."]
[-27,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J49=\"n.a.\",\"n.a.\",(J93-J49))","v":"n.a."},"n.a.","n.a.","n.a."]
[-26,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J50=\"n.a.\",\"n.a.\",(J94-J50))","v":"n.a."},"n.a.","n.a.","n.a."]
[-25,null,null,"n.a.","n.a.","n.a.","n.a.","n.a.","n.a.",{"$f":"IF(J51=\"n.a.\",\"n.a.\",(J95-J51))","v":"n.a."},"n.a.","n.a.","n.a."]
[]
[]
["Calculation of the Approximate Equation for the Schmidt-Appleman-Diagram"]
[]
["Calculate the correction that has to be applied to get from phi = 100% to the actual phi at temperatures lower than t_SAC"]
[]
[null,null,null,null,"Dt_tot:",8,10,12]
["valid for 40000 ft or \"40k\"",null,"a_t =  ",3.08445825837715E-3,"a_t:",{"$f":"1/(F$146^b_t)","v":4.4931122664851643E-3},{"$f":"1/(G$146^b_t)","v":2.5156117144778433E-3},{"$f":"1/(H$146^b_t)","v":1.5661138505692618E-3}]
["Dt_tot,40k = 9,246 °C",null,"b_t =  ",2.5993563915546996]
["Delta t, °C","phi","Dphi","Dphi_calc_9,246","error^2","Dphi_calc_8","Dphi_calc_10","Dphi_calc_12"]
[12,null,null,{"$f":"a_t*A150^b_t","v":1.9694981033824521},{"$f":"(D150-C150)^2","v":3.878922779227076},{"$f":"(1/F$146^b_t)*$A150^b_t","v":2.8689563436604417},{"$f":"(1/G$146^b_t)*$A150^b_t","v":1.6062763978260275},{"$f":"(1/H$146^b_t)*$A150^b_t","v":1}]
[11,null,null,1.5708316013521977,2.4675119198067099,2.2882211867997633,1.2811333617828451,0.79757964663912229]
[10,null,null,1.2261265284405707,1.5033862637457256,1.786091327459804,1,0.62255786199275776]
[9,5.9499827378707001E-2,{"$f":"1-B153","v":0.94050017262129304},0.93238496842637664,6.5856539125188788E-5,1.3581997186524062,0.76043128241602886,0.47341247337333392]
[8,0.32043368353772339,0.67956631646227661,0.68648590897329942,4.788076051860295E-5,0.99999999999999989,0.55988178466898975,0.3485588068322158]
[7,0.52323654755237825,0.47676345244762175,0.48516547592035714,7.0593998436396419E-5,0.70673770514236056,0.39568956764797109,0.24633965124775956]
[6,0.67830817602952742,0.32169182397047258,0.32499099210299104,1.0884510366625341E-5,0.47341247337333386,0.26505502047682278,0.16501208685849739]
[5,0.7942838072551841,0.2057161927448159,0.20232569721054314,1.1495459967923517E-5,0.29472665726400582,0.16501208685849725,0.10272957199758928]
[4,0.87833182285490496,0.12166817714509504,0.11327847243863676,7.0387145061568188E-5,0.16501208685849758,9.2387261682289973E-2,5.7516416108291876E-2]
[3,0.93640055959669732,6.3599440403302676E-2,5.3627441817128065E-2,9.9440755802668453E-5,7.8118780176176739E-2,4.373728206120233E-2,2.722898880939632E-2]
[2,0.9734231398295099,2.6576860170490102E-2,1.8692317133242244E-2,6.2166018906213686E-5,2.7228988809396337E-2,1.524501484933677E-2,9.490903850650944E-3]
[1,0.99348760412674186,6.5123958732581366E-3,3.08445825837715E-3,1.1750756291515947E-5,4.4931122664851643E-3,2.5156117144778433E-3,1.5661138505692618E-3]
[0,0.99997833548047843,2.1664519521569225E-5,0,4.6935140610045409E-10,0,0,0]
[null,"copy from",null,"sum",{"$f":"SUM(E153:E162)","v":4.5045641382810938E-4}]
[null,"table above",null,"drive sum to min. with solver (setting on the right)"]
[]
[null,"Dphi = a_t(H)*Dt^b_t",null,null,null,null,null,"Dt(Dphi = 1) =",{"$f":"(1/a_t)^(1/b_t)","v":9.2456943980527324},"°C"]
[null,null,null,null,null,null,null,"Dt_tot,40k =",{"$f":"(1/a_t)^(1/b_t)","v":9.2456943980527324},"°C"]
[null,"General equation with modified a_t(H) from Dt_tot(H):"]
[null,"Dt_tot = a_tot*H + b_tot",null,null,null,"see below"]
[null,"a_t(H) = 1/(Dt_tot(H)^b_t)"]
[null,"Dphi = a_t(H)*((H - b_H)/a_H - t)^b_t",null,null,null,"see above"]
[null,"phi = 1 - Dphi"]
[]
[null,"Important for the approximate equation for the Schmidt-Appleman-Diagram:"]
[null,"H_SAC = f (t_SAC), to answer the question: \"At what altitude do contrails start to form depending on temperature?\""]
[]
[null,"t_SAC","°C",{"$f":"D11","v":-34.171657846038833},{"$f":"E11","v":-36.556995939242505},-38.983215462422002,-41.453686614326799,-41.997060149801399,-43.936149738567622,-46.358686546546537,-48.720135430706478,-51.022841943746812,-53.26904401732731,-55.460885188547678,-57.600302356601937]
[null,"H_SAC","ft",{"$f":"D8","v":20000},{"$f":"E8","v":25000},30000,35000,36089,40000,45000,50000,55000,60000,65000,70000]
[]
[]
[null,"a_H",-2118.8000000000002,"ft/°C","from trendline"]
[null,"b_H",-52772,"ft","from trendline"]
[]
[]
[null,"   H_SAC = a_H*t _SAC+ b_H"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"With the above, we obtain an equation:"]
[null,"phi = 1 - a_t*(((H - b_H)*1/a_H) - t)^b_t"]
[]
[null,"This means for a relative humidity larger than phi, we will have a contrail."]
[null,"We will have a persistent contrail, if the relative humidity is much larger than RH_min. For RH_min see Tab \"SAC\"."]
[]
[]
[]
["H_SAC",null,"ft",20000,25000,30000,35000,{"$f":"H_T","v":36089},40000,45000,50000,55000,60000,65000,70000]
["Dt,tot  from SAD",null,"°C",{"$f":"D13","v":10.191807796994766},9.9604385777602431,9.7278255152540041,9.4938003329852094,9.442709030448718,9.2615056131735756,9.0375911897456547,8.8219585861894672,8.6142027697986165,8.4139301957811696,8.2207515673014058,8.0343996169108394]
["Dt,tot  calculated   (a)",null,"°C",{"$f":"a_tot*D203+b_tot","v":10.15428},9.9373500000000003,9.7204200000000007,9.5034899999999993,9.4562426459999998,9.2865599999999997,9.0696300000000001,8.8527000000000005,8.6357700000000008,8.4188399999999994,8.2019099999999998,7.9849800000000002]
["Dt,tot  calculated   (b)",null,"°C",{"$f":"t_SAC_0_100-t_SAC_0_0-(L_SAC_100-L_SAC_0)*D$203","v":10.154199999999998},9.937249999999997,9.7202999999999982,9.5033499999999975,9.4560982899999981,9.2863999999999969,9.0694499999999962,8.8524999999999974,8.6355499999999967,8.4185999999999961,8.2016499999999972,7.9846999999999966]
[]
[null,null,"a_tot",-4.3386000000000001E-5,"°C/ft","from trendline"]
[null,null,"b_tot",11.022,"°C","from trendline"]
[]
["Dt,tot  calculated   (a)",null,"Dt_tot = a_tot*H + b_tot"]
[]
["Dt,tot  calculated   (b)",null,"Dt_tot = t_SAC_0_100-t_SAC_0_0-(L_SAC_100-L_SAC_0)*H"]
[]
[]
[]
[]
[]
[]
[]
[]
["Evaluating and Planning Flights for Contrail Avoidance"]
["t_SAC = f ( H_SAC), to answer the question: \"At what temperature do contrails start (and end) to form depending on altitude?\""]
[]
["H_SAC",null,"ft",{"$f":"D8","v":20000},{"$f":"E8","v":25000},30000,35000,36089,40000,45000,50000,55000,60000,65000,70000]
["t_SAC,100",null,"°C",{"$f":"D11","v":-34.171657846038833},{"$f":"E11","v":-36.556995939242505},-38.983215462422002,-41.453686614326799,-41.997060149801399,-43.936149738567622,-46.358686546546537,-48.720135430706478,-51.022841943746812,-53.26904401732731,-55.460885188547678,-57.600302356601937]
["t_SAC,0",null,"°C",{"$f":"D12","v":-44.363465643033599},{"$f":"E12","v":-46.517434517002748},-48.711040977676006,-50.947486947312008,-51.439769180250117,-53.197655351741197,-55.396277736292191,-57.542094016895945,-59.637044713545428,-61.68297421310848,-63.681636755849084,-65.634701973512776]
["Dt,tot",null,"°C",{"$f":"D226-D227","v":10.191807796994766},9.9604385777602431,9.7278255152540041,9.4938003329852094,9.442709030448718,9.2615056131735756,9.0375911897456547,8.8219585861894672,8.6142027697986165,8.4139301957811696,8.2207515673014058,8.0343996169108394]
["average Dt,tot",null,"°C",{"$f":"AVERAGE(D228:O228)","v":9.1017433993619736}]
["t_ICAO,H_T=36089 ft",null,"°C",{"$f":"IF(D$225<H_T,t_0-L*D$225,t_0-L*H_T)","v":-24.623999999999995},-34.529999999999994,-44.435999999999993,-54.341999999999999,-56.499526799999998,-56.499526799999998,-56.499526799999998,-56.499526799999998,-56.499526799999998,-56.499526799999998,-56.499526799999998,-56.499526799999998]
["t_ICAO,H_T,pole",null,"°C",{"$f":"IF(D$225<H_T_pole,t_0-L*D$225,t_T_pole)","v":-24.623999999999995},-34.529999999999994,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993,-44.435999999999993]
["t_ICAO,H_T,lat,tropo",null,"°C",{"$f":"t_0_lat-L*D$225","v":-19.623999999999995},-29.529999999999994,-39.435999999999993,-49.341999999999999,-51.499526799999998,-59.24799999999999,-69.153999999999996,-79.059999999999988,-88.965999999999994,-98.871999999999986,-108.77799999999999,-118.684]
["t_ICAO,H_T,lat,strato",null,"°C",{"$f":"t_T_lat","v":-53.648335677208834},-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834,-53.648335677208834]
["t_ICAO, H_T,equator",null,"°C",{"$f":"IF(D$225<H_T_equator,t_0-L*D$225,t_T_equator)","v":-24.623999999999995},-34.529999999999994,-44.435999999999993,-54.341999999999999,-56.499526799999998,-64.24799999999999,-74.153999999999996,-84.059999999999988,-84.059999999999988,-84.059999999999988,-84.059999999999988,-84.059999999999988]
[]
["m/ft",0.30480000000000002]
["t_0,lat",20,"°C",15,"°C  (ICAO)"]
["H_T,pole",30000,"ft",{"$f":"H_T_pole*m_ft/1000","v":9.1440000000000001},"km"]
["Latitude, B",53.5,"deg",53.5,"deg  (Hamburg)"]
["H_T,lat(B)",{"$f":"D240/m_ft*1000","v":37173.599675554637},"ft",{"$f":"a_lat*(1+COS(2*B*PI()/180))+b_lat","v":11.330513181109053},"km"]
["H_T,lat",{"$f":"B240","v":37173.599675554637},"ft",{"$f":"H_T_lat*m_ft/1000","v":11.330513181109055},"km"]
["H_T,equator",50000,"ft",{"$f":"H_T_equator*m_ft/1000","v":15.24},"km"]
["t_T,pole",{"$f":"t_0-L*H_T_pole","v":-44.435999999999993},"°C"]
["t_T",{"$f":"t_0-L*H_T","v":-56.499526799999998},"°C"]
["t_T,lat",{"$f":"t_0_lat-L*H_T_lat","v":-53.648335677208834},"°C"]
["t_T,equator",{"$f":"t_0-L*H_T_equator","v":-84.059999999999988},"°C"]
["L_SAC,0",4.2831999999999999E-4,"°C/ft","from trendline"]
["L_SAC,100",4.7171000000000002E-4,"°C/ft","from trendline"]
["t_SAC,0,0",-35.94,"°C","from trendline"]
["t_SAC,0,100",-24.917999999999999,"°C","from trendline"]
["t_SAC,100 = t_SAC,0,100 - L_SAC,100*H"]
["t_SAC,0 = t_SAC,0,0 - L_SAC,0*H"]
[]
[]
["Calculating Possible Intersections of t_SAC and t_atmosphere"]
[]
["Troposphere:",null,null,"Flight Level, FL:"]
["H_SAC,100",{"$f":"(t_0-t_SAC_0_100)/(L-L_SAC_100)","v":26444.693240763438},"ft",{"$f":"ROUND(B258/1000,0)*10","v":260}]
["H_SAC,lat,100",{"$f":"(t_0_lat-t_SAC_0_100)/(L-L_SAC_100)","v":29757.070268766274},"ft",{"$f":"ROUND(B259/1000,0)*10","v":300}]
["H_SAC,0",{"$f":"(t_0-t_SAC_0_0)/(L-L_SAC_0)","v":32803.564988923812},"ft",{"$f":"ROUND(B260/1000,0)*10","v":330}]
["H_SAC,lat,0",{"$f":"(t_0_lat-t_SAC_0_0)/(L-L_SAC_0)","v":36023.388800164859},"ft",{"$f":"ROUND(B261/1000,0)*10","v":360}]
["Stratosphere:"]
["H_SAC,pole,0",{"$f":"IF((t_SAC_0_0-t_T_pole)/L_SAC_0>H_SAC_0,(t_SAC_0_0-t_T_pole)/L_SAC_0,\"n.a.\")","v":"n.a."},"ft",{"$f":"IF(B263=\"n.a.\",\"n.a.\",ROUND(B263/1000,0)*10)","v":"n.a."}]
["H_SAC,pole,100",{"$f":"IF((t_SAC_0_100-t_T_pole)/L_SAC_100>H_SAC_100,(t_SAC_0_100-t_T_pole)/L_SAC_100,\"n.a.\")","v":41377.117296644108},"ft",410]
["H_SAC,ICAO,0",{"$f":"(t_SAC_0_0-t_T)/L_SAC_0","v":48000.389428464703},"ft",480]
["H_SAC,ICAO,100",{"$f":"(t_SAC_0_100-t_T)/L_SAC_100","v":66951.149647028884},"ft",670]
["H_SAC,lat,0",{"$f":"IF((t_SAC_0_0-t_T_lat)/L_SAC_0>H_SAC_lat_0,(t_SAC_0_0-t_T_lat)/L_SAC_0,\"n.a.\")","v":41343.704887021006},"ft",410]
["H_SAC,lat,100",{"$f":"IF((t_SAC_0_100-t_T_lat)/L_SAC_100>H_SAC_lat_100,(t_SAC_0_100-t_T_lat)/L_SAC_100,\"n.a.\")","v":60906.77678490775},"ft",610]
["H_SAC,equator,0",{"$f":"IF((t_SAC_0_0-t_T_equator)/L_SAC_0>H_SAC_100,(t_SAC_0_0-t_T_equator)/L_SAC_0,\"n.a.\")","v":112345.90960029882},"ft",1120]
["H_SAC,equator,100",{"$f":"IF((t_SAC_0_100-t_T_equator)/L_SAC_100>H_SAC_100,(t_SAC_0_100-t_T_equator)/L_SAC_100,\"n.a.\")","v":125377.88047741193},"ft",1250]
[]
[]
["Calculating a SAD with Lines of Equal Relative Humidity"]
[]
["H","ft",20000,70000]
["Dt_tot","°C",{"$f":"a_tot*C$275+b_tot","v":10.15428},{"$f":"a_tot*D$275+b_tot","v":7.9849800000000002}]
["a_t(H)","1/°C",{"$f":"1/C$276^b_t","v":2.4174646800060196E-3},{"$f":"1/D$276^b_t","v":4.5151142698865035E-3}]
["phi:","Dphi:","Dt:","Dt:"]
[0.5,{"$f":"1-$A279","v":0.5},{"$f":"($B279/C$277)^(1/b_t)","v":7.77749426416998},6.1159566359714299]
[0.8,{"$f":"1-$A280","v":0.19999999999999996},5.4669858951467312,4.2990515362023425]
[0.95,{"$f":"1-$A281","v":5.0000000000000044E-2},3.2072224478916929,2.5220505148534604]
[]
["t_SAC,100","°C",{"$f":"D226","v":-34.171657846038833},{"$f":"O226","v":-57.600302356601937}]
["phi:","Dphi:","t:","t:"]
[{"$f":"A279","v":0.5},{"$f":"1-$A285","v":0.5},{"$f":"C$283-C279","v":-41.949152110208814},-63.716258992573366]
[{"$f":"A280","v":0.8},{"$f":"1-$A286","v":0.19999999999999996},-39.638643741185561,-61.899353892804278]
[{"$f":"A281","v":0.95},{"$f":"1-$A287","v":5.0000000000000044E-2},-37.378880293930528,-60.122352871455398]
[]
["t_SAC,100",null,{"$f":"t_SAC_0_100-L_SAC_100*C$275","v":-34.352199999999996},{"$f":"t_SAC_0_100-L_SAC_100*D$275","v":-57.9377}]
["t_SAC,0",null,{"$f":"t_SAC_0_0-L_SAC_0*C$275","v":-44.506399999999999},{"$f":"t_SAC_0_0-L_SAC_0*D$275","v":-65.922399999999996}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Calculating the Altitude of the Tropopause, H_T"]
["Depending on the Latitude, B"]
[]
[null,"H_T = a_lat*(1-(COS(2*B)))+b_lat",null,null,"standard values"]
["H_T,amplitude","a_lat",4,"km",3.5,"km"]
["H_T,pole","b_lat",8.5,"km",9,"km"]
[]
["latitude, B","h_measured","H_T calc"]
[-90,9,{"$f":"a_lat*(1+COS(2*A314*PI()/180))+b_lat","v":8.5}]
[-80,9,8.7412295168563663]
[-70,9.5,9.4358222275240884]
[-60,10,10.5]
[-50,11,11.80540728933228]
[-40,13,13.194592710667722]
[-30,15.2,14.5]
[-20,16,15.564177772475912]
[-10,16.8,16.258770483143635]
[0,16.399999999999999,16.5]
[10,16.399999999999999,16.258770483143635]
[20,15.8,15.564177772475912]
[30,13,14.5]
[40,10.4,13.194592710667722]
[50,9.6999999999999993,11.80540728933228]
[60,8.9,10.5,null,null,null,null,null,null,null,null,null,null,null,null,null,"Mean height z (km) of the global tropopause (1979–93; 1200 UTC): annual mean"]
[70,8.4,9.4358222275240884,null,null,null,"GEERTS, B., LINACRE, E., 1997: The height of the tropopause. University of Wyoming, Department of Atmospheric Science.",null,null,null,null,null,null,null,null,null,"[(a), all], northern summer [(b), JJA], and northern winter [(c), DJF]. The height increment is 500 m."]
[80,8,8.7412295168563663,null,null,null,"http://www-das.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html",null,null,null,null,null,null,null,null,null,"Figure 1"]
[90,8,8.5,null,null,null,"https://perma.cc/42TC-K7EF"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Klaus P. Hoinka, 1999. Temperature, Humidity, and Wind at the Global Tropopause. In: Monthly Weather Review, Vol. 127 (1999), No. 10, pp. 2248–2265."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"https://doi.org/10.1175/1520-0493(1999)127%3C2248:THAWAT%3E2.0.CO;2"]

{"sheet":"RH","index":3,"n_rows":194,"n_cols":1,"rows_kept":194,"cut":false,"hidden":false,"merged":[]}
["Literature Review: Relative Humidity, RH"]
[]
["Klaus P. Hoinka, 1999. Temperature, Humidity, and Wind at the Global Tropopause. In: Monthly Weather Review, Vol. 127 (1999), No. 10, pp. 2248–2265."]
["https://doi.org/10.1175/1520-0493(1999)127%3C2248:THAWAT%3E2.0.CO;2"]
[]
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[]
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[]
[]
[]
[]
[]
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[]
[]
[]
[]
["Mean annual rh (%) at the global tropopause (1979–93; 1200 UTC). The increment is 5%."]
["Shading in the relative humidity field indicates 0%–10% (none), 10%–20% (weak), 20%–30% (moderate), 30%–40% (strong), and greater than 40% (very strong)."]
["Figure 8"]
[]
[]
["RUZMAIKIN, Alexander, AUMANN, Hartmut H., MANNING, Evan M. , 2014. Relative Humidity in the Troposphere with AIRS . In: Journal of the Atmospheric Sciences, Vol. 71 (2014), No. 7, pp. 2516–2533."]
["https://doi.org/10.1175/JAS-D-13-0363.1"]
[]
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[]
[]
["Zonally averaged, nonsaturated, latitude–height distributions of RH for (left) January and (right) July in (top to bottom) 2003, 2007, and 2011."]
["The colored RH (%) shadings of 10, 30, 60, 80, 90, 100 are displayed and RH is only plotted for good-quality data (QC = 0, 1)."]
["White areas indicate that there are no retrievals of this quality or the RH < 10%."]
["Figure 1"]
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["Height vs latitude RH climatologies of (left) January and (right) July from AIRS 11 yr of measurements (1 Sep 2002–31 Aug 2013)."]
["Figure 2"]
[]
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["The RH profiles in the tropics for (left) January and (right) July in (top to bottom) 2003, 2007, and 2011. "]
["In all cases, with a slight exception of January 2011, the minimum RH is reached at 300 hPa."]
["Figure 4"]