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[]
[null,"Simulace raketového motoru"]
[null,"na tuhé pohonné hmoty"]
[null,"a letu rakety"]
[]
[null,{"$f":"Motor!A2","v":"V 2.9"},null,"Nutno povolit použití maker - jinak nefunguje !"]
[]
[null,"Na listu \"Motor\" se do světle zelenkatých polí zadají parametry raketového motoru"]
[null,"a v boxu pod \"Druh elementu TPH\" se vybere typ elementu raketového paliva (trubka, kříž, hvězda….)"]
[null,"V listu \"Elementy\" je před výpočtem možné upravit parametry palivových elementů."]
[null,"Na listu \"Povrchy\" je závislost hořícího povrchu elementu na odhořrlé vzdálenosti."]
[null,"Vlastní simulace a let se spustí kliknutím na tlačítku \"Řešit výpočet integrací\" na listě Motor."]
[null,"Druh paliva se zadává na listu \"Motor\" v sekci Rychlost hoření, kde se zadávají parametry rychlostní rovnice hoření (měnit opatrně)"]
[null,"Pokud se nezadá hmotnost rakety (\"F4\"), dopočte se dle pracovního tlaku v komoře"]
[null,"Pokud se kromě hmotnosti rakety (\"F4\") nezadá ani pracovní tlak v komoře (\"D8\"), obojí se automaticky dopočte"]
[null,"a k tomu  odpovídající síla stěny spalovací komory."]
[null,"Laborujte nejen s kritickým průměrem trysky, al etaké s jejím výstupním, aby docházelo k co nejmenším ztrátám expanzí (viz sloupec V)."]
[null,"Při nereálném zadání parametrů se integreace zastaví s upozorněním."]
[null,"Na listě \"Grafy\" jsou zobrazeny parametry v závislosti na čase."]
[null,"Na listech f(  ) je znázorněna závislost průběhu parametrů na kritickémm průmněru trysky (Dkr) a rychlostním parametru hoření paliva \"a\""]
[null,"případně dalších. Spouštějí se po zadání sloupce Dkr resp. \"a\" makry zavDkr a zavRHor. Trvá několik minut."]
[null,"List \"Povrchy\" informuje o hořícím povrchu různých elementů v závislosti na odhořelé vzdálenosti."]
[null,"U malých raket s krátkou dobou hoření si zkraťte integrační interval  Dtau (\"I5\")."]
[]
[null,"Program umožňuje počítat i další stupně vícestupňové rakety zadáním počáteční výšky a rychlosti (\"R4\", \"R3\")."]
[null,"Také umožňuje počítat start vícenásobného boosteru zadáním počtu boosterů do \"I9\". Do \"F4\" pak zadáte celkovou hmotnost rakety"]
[null,"Pokud se hlásí příliš dlouhá integrace, zkuste zmenšit přesnost."]
[]
[null,"Před používáním programu doporučuji uchovat si kopii původního programu."]

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["Výpočet raketového motoru na TPH"]
["V 2.9","Vstupní data jen do zelenkavého podbarvení",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Jde o vyšší stupěň"]
["Parametry:",null,null,null,null,null,null,"Náměr (deg)",90,null,"Celk.doba letu",null,null,"par Bk ",null,null,"p.rychlost",null,"Rychlost hoření"]
["Průměr komory D (m)",null,0.2,null,"Hmot. rakety",null,null,"Koef.odporu:",0.2,null,"Teor. výška",null,null,"par b",null,null,"p.výška",null,"rp = 29163E-9*EXP(0,00243*(25-15))*p0,37"]
["Délka elementu L (m)",null,1,null,"Hmot. paliva",null,null,"DTau integr.",0.2,null,"Skut. výška (m)",null,null,"Fmax zahraz",null,null,null,null,"a",2.9162999999999998E-5,null,2.9162999999999998E-5]
["Průměr trysky  dkr (m)",null,0.04,{"$f":"PI()*C6*C6/4","v":1.2566370614359175E-3},"Výst.pr.trysky",0.05,null,"Objem TPH (m3)",null,null,"Motor výška",null,null,"L trysky (m)",{"$f":"(F6-C6)/2/0.2679","v":1.8663680477790223E-2},null,null,null,"E",2.4299999999999999E-3,null,2.4299999999999999E-3]
["Teplota hoření  (K)",null,2373,null,"Průměr tyče",0.06,null,"Doba hoření (s)",null,null,"Počet tyčí",null,null,"mTHP/mRak",{"$f":"F5/F4","v":{"$error":"#DIV/0!"}},null,null,null,"n",0.37,null,0.37]
["Pracovní tlak (Pa)",null,{"$f":"101325*D8","v":0},null,"Tah stř (N)",{"$f":"AVERAGE(J12:J200)","v":7564.3054692714286},{"$f":"F9/I7","v":{"$error":"#DIV/0!"}},"wkr (m/s)",{"$f":"SQRT(2*T9*8.314*C7/(T9+1))","v":149.3401678689643},null,"Abs. přesnost",0.02,null,"stěna k. (mm)",null,null,"Hybnost",24162.991352954239,"hustota",1600,null,1600]
["Druh elemnetu TPH",null,"Trubka","ano","Impulz (N.s)",84716.558361189687,null,"Okolní tlak (Pa)",{"$f":"101320*EXP(-0.0001249*R4)","v":101320},null,"Okolní T (°C)",25,null,"Machmax ",null,null,"hTHP",0.49729958179712802,"kapa",1.3,null,1.3]
[1.0049999999999999,null,{"$f":"MAX(C12:C199)","v":0.6282381562371756},null,"Isp (N.s/kg)",1702.4064425399479,null,"Počet boosterů",null,null,1148.4106788572249,427.39102340677522,107.44339205515077,6799.4442033416108,4.1248215211332455E-11,null,84716.558361189687,11.793572164148035,"MV spalin",3.5000000000000003E-2,null,3.5000000000000003E-2]
["Čas (s)","D (m)","Shoř (m2)","mp(kg/s)","G(kg/s)","SG(kg)","Tlak (Pa)","rozdíl","wvýtok (m/s)","Tah (N)","vteo (m/s)","vsk (m/s)","p (bar)","výška(m)","dálka(m)","náměr (°)","Impuls(Ns)","rh (mm/s)","Pout (Pa)","Ae/Akr","da (m)","Tahexp ","pkr "]
[0,0,6.2831853071795798E-2,0.21111346984308116,0.11315710020733047,0,101320,null,{"$f":"wVytok(G12)","v":0},{"$f":"E12*I12","v":0},0,0,{"$f":"G12/101325","v":0.99995065383666415},0,0,null,0]
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[0.8,2.6177689084008146E-3,7.9279780214651319E-2,0.4435739716580076,0.44899626916675583,0.29746202596493604,402027.81715529185,5.4222975087482306E-3,1153.645587611652,436.10162034966083,3.2332325401596358,0,4.0202781715529188,0,0,90,323.90247687472976,3.4969033912006284,65673.932669593531,1.2536002283360694,4.4785716086021346E-2,-0.13831334737420603,2.1939772958637258]
[1,3.3285696909820068E-3,8.3745873248097222E-2,0.4838885931934116,0.48980370111459337,0.39016503579562156,438566.47886877973,5.9151079211817725E-3,1183.866627443482,508.28184303329618,4.3538557411823522,0,4.3856647886877971,0,0,90,432.28598967898341,3.6112868493224974,71642.767170577426,1.3061399613040237,4.5714592178936017E-2,-0.10286755654812316,2.3933789063987305]
[1.2,4.0623561438759281E-3,8.8356389507527736E-2,0.526852575792642,0.53329288021023435,0.49119408311381813,477506.35641863674,6.4403044175923574E-3,1212.131113072769,585.80388728982064,5.6147801745028225,0,4.7750635641863672,0,0,90,553.35445675727112,3.7267577557857003,78003.8563215537,1.3619499396940826,4.6681044370392277E-2,-7.2500525987924738E-2,2.6058846177015371]
[1.4,4.819344369798851E-3,9.311268680635458E-2,0.57257632854312679,0.5795755651940574,0.60109004660427912,518947.51772419282,6.999236650930607E-3,1238.6459579378254,668.92502042824424,7.0249339835277356,0,5.1894751772419285,0,0,90,688.0550837680654,3.8433023212367625,84773.546885700154,1.4209109058399296,4.7680787004241942E-2,-4.6332482272396176E-2,2.8320405281605794]
[1.5999999999999999,5.5997477608062006E-3,9.8016105926405084E-2,0.6211723232555495,0.62876560274465521,0.72041609315728172,562991.9002286474,7.5932794891057087E-3,1263.5869998970111,757.90624940614612,8.5938770300211562,0,5.6299190022864742,0,0,90,837.38092241323614,3.9609072240252137,91968.491025410185,1.4829389723785402,4.8710392687861433E-2,-2.3666095433976145E-2,3.0724029386745375]
[1.7999999999999998,6.4037770892624466E-3,0.10306797118950282,0.67275508760720448,0.68097892053837283,0.84975808972475919,609743.30468463362,8.2238329311683511E-3,1287.1050687528225,853.01262454848586,10.331794943638238,0,6.0974330468463362,0,0,90,1002.3715380595758,4.0795595848240263,99605.645287122898,1.5479764361754025,4.9767080463702554E-2,-3.9420716296500969E-3,3.3275383187384389]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"šířka ramene a",null,0.02,null,"Hrana s",null,0.02,null,"Úhel a ",60,{"$f":"IF(Y7=0,ATAN(Z5/Z6/2)/PI()*180,Y7)","v":60},null,null,null,null,null,"šířka ramene a",null,0.02]
[null,null,null,null,null,null,null,null,null,null,null,"Dmax",null,{"$f":"(N5-N6)/2","v":9.0000000000000011E-2},null,"Dmax",null,{"$f":"(R5-R7)/2","v":9.0000000000000011E-2},null,"Rozev.Theta",{"$f":"V8/180*PI()","v":2.0943951023931953},120,null,"Dmax",null,{"$f":"(Motor!C4-Z5)/2*COS(Z7*PI()/180)","v":0},null,"Dmax",null,{"$f":"(Motor!C4-AD5)/2*COS(AD7*PI()/180)","v":7.0000000000000007E-2},null,"Dmax",null,{"$f":"(AH5-AH7)/2","v":9.0000000000000011E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Rameno d",null,{"$f":"V7*(COS(U8/2-PI()/V6)+SIN(U8/2-PI()/V6)/TAN(PI()/V6))","v":3.4641016151377546E-2},null,null,null,null,null,null,null,null,null,"n-počet ramen",null,6]
[null,null,null,null,null,null,null,null,null,null,null,"tryska (m)",null,0.04,null,"tryska",null,7.0000000000000007E-2,null,"tryska",null,0.04,null,"tryska",null,1.7000000000000001E-2,null,null,null,0.15,null,"tryska",null,6.8000000000000005E-2]
[null,null,null,null,null,null,null,null,null,null,null,"Izolace",null,"ano",null,"Izolace",null,"ano",null,"poměr s/d",null,{"$f":"V7/V9","v":0.57735026918962573},null,"Izolace",null,"ne",null,"Izolace",null,"ano",null,"Izolace",null,"ano"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"odhad Theta",null,{"$f":"2.3*360/V6","v":137.99999999999997}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"xLim",null,{"$f":"V5/2-V9","v":6.5358983848622459E-2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Izolace",null,"ano"]
[]
[null,null,null,null,null,null,null,null,null,null,null,"Elementy:",null,"Štěrbina",null,null,null,"Polotrubka"]
[null,null,null,null,null,null,null,null,null,null,null,"Vnější průměr Do(m)",null,{"$f":"Motor!C4","v":0.2},null,"Vnější průměr Do(m)",null,{"$f":"Motor!C4","v":0.2}]
[null,null,null,null,null,null,null,null,null,null,null,"délka šterbiny",null,0.16,null,"Vnitřní průměr di",null,0.04]
[null,null,null,null,null,null,null,null,null,null,null,"šířka šterbiny",null,1.4999999999999999E-2,null,"Hloubka h",null,0.01]
[null,null,null,null,null,null,null,null,null,null,null,"Dlim",null,{"$f":"N17-N18","v":4.0000000000000008E-2},null,"Dmax",null,{"$f":"(R17-R18)/2","v":0.08}]
[null,null,null,null,null,null,null,null,null,null,null,"1-jednost.;2-dvoust",null,1]
[null,null,null,null,null,null,null,null,null,null,null,"tryska",null,3.3000000000000002E-2,null,"tryska",null,1.4999999999999999E-2]
[null,null,null,null,null,null,null,null,null,null,null,"Izolace",null,"ano",null,"Izolace",null,"ne"]

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["Mapování povrchů hoření"]
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[]
["x","Trubka","Kříž","Hvězda","Čelní","Kužel","n-Kříž","Šterbina","poloTrubka","Tyče"]
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[5.0000000000000001E-3,9.4247779607693705E-2,0.58283185307179575,0.26819083692041817,3.1415926535897906E-2,{"$f":"Kuzel(A8)","v":7.2527674265624759E-2},0.72640168269942795,{"$f":"sterb(A8)","v":0.34526570637821763},{"$f":"polotrubka(A8)","v":2.9845130209103007E-3},{"$f":"tyce(A8)","v":1.570796326794895}]
[0.01,0.1256637061435916,0.60566370614359155,0.29638167384083636,3.1415926535897906E-2,{"$f":"Kuzel(A9)","v":7.2454773354392973E-2},0.75136743000436634,{"$f":"sterb(A9)","v":0.37046123061570768},{"$f":"polotrubka(A9)","v":3.7699111843077478E-3},{"$f":"tyce(A9)","v":1.2566370614359159}]
[1.4999999999999999E-2,0.15707963267948949,0.62849555921538736,0.32457251076125448,3.1415926535897906E-2,{"$f":"Kuzel(A10)","v":7.2333271835673313E-2},0.77633317730930473,{"$f":"sterb(A10)","v":0.39458751212526227},{"$f":"polotrubka(A10)","v":4.869468613064175E-3},0.94247779607693694]
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[2.5000000000000001E-2,0.2199114857512853,0.67415926535897897,0.38095418460209085,3.1415926535897906E-2,7.1944466975770394E-2,0.82626467191918163,0.43918409407836051,8.0110612666539661E-3,0.31415926535897887]
[0.03,0.25132741228718319,0.69699111843077477,0.40914502152250909,3.1415926535897906E-2,7.1677163634587135E-2,0.85123041922412013,0.45939331794089083,1.0053096491487327E-2,0]
[3.5000000000000003E-2,0.28274333882308111,0.71982297150257057,0.4373400811318271,3.1415926535897906E-2,7.1361259685916015E-2,0.87619616652905863,0.47800327774733897,1.2409290981679671E-2,0]
[0.04,0.31415926535897903,0.74265482457436638,0.46628696281307025,3.1415926535897906E-2,7.0996755129757033E-2,0.90116191383399702,0.49482617120775663,1.5079644737230993E-2,0]
[4.4999999999999998E-2,0.3455751918948769,0.76548667764616218,0.49609715915773045,3.1415926535897906E-2,7.058364996611019E-2,{"$f":"nKriz(A16)","v":0.75000000000000056},0.34044089061098404,1.806415775814129E-2,0]
[0.05,0.37699111843077482,0.78831853071795799,0.52640422889277994,3.1415926535897906E-2,{"$f":"Kuzel(A17)","v":7.0121944194975472E-2},0.50000000000000033,0.32726136343907147,2.1362830044410575E-2]
[5.5E-2,0.40840704496667268,0.81115038378975379,0.55701978997883161,3.1415926535897906E-2,6.9611637816352906E-2,0.2500000000000005,0.31224989991991992,2.4975661596038833E-2]
[0.06,0.4398229715025706,0.83398223686155037,0.58783791407534758,3.1415926535897906E-2,6.9052730830242465E-2,6.9388939039072284E-16,0.29512709126747416,2.8902652413026066E-2]
[6.5000000000000002E-2,0.47123889803846852,0.85677453679179794,0.6187949447461264,3.1415926535897906E-2,6.8445223236644148E-2,0,0.27549954627911821,3.3143802495372285E-2]
[7.0000000000000007E-2,0.5026548245743665,0.87937130441813749,0.64985060170556308,3.1415926535897906E-2,6.7789115035557984E-2,0,0.25278449319529078,3.769911184307749E-2]
[7.4999999999999997E-2,0.53407075111026425,0.90166304360273941,0.68097831712894097,3.1415926535897906E-2,6.7084406226983945E-2,0,0.22605309110914637,4.2568580456141647E-2]
[0.08,0.56548667764616223,0.92359428585780334,0,3.1415926535897906E-2,6.6331096810922058E-2,0,{"$f":"sterb(A23)","v":0.19364916731037088},7.0497339146554885E-2]
[8.5000000000000006E-2,0.59690260418206009,0.94513960541481379,0,3.1415926535897906E-2,6.5529186787372282E-2,0,0.15198684153570663,5.3231481996663707E-2]
[0.09,0.62831853071795796,0.96629078048535777,0,3.1415926535897906E-2,6.4678676156334658E-2,0,8.8881944173156049E-2,4.9019202553453448E-2]
[9.5000000000000001E-2,0,0.98704958377071206,0,3.1415926535897906E-2,{"$f":"Kuzel(A26)","v":6.3779564917809173E-2},0,{"$f":"sterb(A26)","v":0},{"$f":"polotrubka(A26)","v":4.6546385004267332E-2}]
[0.1,0,1.0074235845819268,0,3.1415926535897906E-2,{"$f":"Kuzel(A27)","v":6.2831853071795812E-2},0,{"$f":"sterb(A27)","v":0},4.4861943093262205E-2]
[0.105,0,1.0274236374858565,0,3.1415926535897906E-2,6.183554061829459E-2,0,0,4.3625334130807651E-2]
[0.11,0,1.047062350773424,0,3.1415926535897906E-2,6.0790627557305507E-2,0,0,4.2674198325854895E-2]
[0.115,0,1.0663531413543657,0,3.1415926535897906E-2,5.9697113888828562E-2,0,0,4.1918580978231854E-2]
[0.12,0,0,0,3.1415926535897906E-2,5.8554999612863742E-2,0,0,4.1303682913612652E-2]
[0.125,0,0,0,3.1415926535897906E-2,5.7364284729411068E-2,0,0,4.0793841316219916E-2]
[0.13,0,0,0,3.1415926535897906E-2,5.6124969238470518E-2,0,0,4.0364682883395946E-2]
[0.13500000000000001,0,0,0,3.1415926535897906E-2,5.4837053140042114E-2,0,0,3.9998906962508428E-2]
[0.14000000000000001,0,0,0,3.1415926535897906E-2,5.3500536434125834E-2,0,0,3.9683855743218831E-2]
[0.14499999999999999,0,0,0,3.1415926535897906E-2,5.2115419120721707E-2,0,0,3.9410035615698794E-2]
[0.15,0,0,0,3.1415926535897906E-2,5.0681701199829711E-2,0,0,3.9170176877598842E-2]
[0.155,0,0,0,3.1415926535897906E-2,4.919938267144984E-2,0,0,3.8958613692871666E-2]
[0.16,0,0,0,3.1415926535897906E-2,4.7668463535582115E-2,0,0,3.8770862578477151E-2]
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[null,"Výpočet rakety"]
[null,"Základní vztahy pro výpočet raketového motoru."]
[null,"Tah raketového motoru P (v jednotkách N, SI):"]
[]
[null,"kde G je vteřinové průtočné množství pohonných látek, w je výtoková rychlost a pa tlak expandujících plynů ve výstupním průřezu trysky Sa a pH je atmosférický tlak ve výšce H. Měrný tah (specifický impuls) Isp(v jednotkách N.s/kg =m/s): udává, jak velká část tahu raketového motoru se získá z1 kg pohonných látek, spálených v motoru za 1 s,"]
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[null,"kde wef je efektivní výtoková rychlost ve výšce H. Specifický impuls je tedy mírou efektivní výtokové rychlosti plynů z motoru. Největší je ve vakuu a nižší na hladině moře. Výtoková rychlost plynů z trysky"]
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[null,"kde k je adiabatická konstanta, R - univerzální plynová konstanta 8,3145, Mv - molekulová hmotnost zplodin hoření, p0 a pa jsou tlaky ve spalovací komoře a na výstupu z trysky a T0 je teplota hoření. Je vidět, že w je tím větší, čím je větší Isp a p0 nebo čím je menší Mv. Výtoková rychlost je pro daný poměr výstupního a kritického průřezu trysky konstantní po celou dobu činnosti v důsledku toho, že ač se tlaky mění, poměr pa/p0 zůstává konstantní. Čím větší poměr průřezů, tím větší výtoková rychlost."]
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[null,"Maximální rychlost proudění se dosáhne, podaří-li se proměnit veškerou tepelnou energii v kinetickou energii plynu. Tj. po expanzi bude H = 0, resp. T = 0. Tudíž"]
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[null,"a0  je rychlost zvuku v plynu ve spalovací komoře. Maximální rychlost wmax závisí jen na počáteční teplotě T0, nezáleží na počátečním tlaku p0 (ve spalovací komoře). I když by se zdálo, že s růstem p0 poroste wmax, není tomu tak. Srůstem p0 roste totiž i r0 takže zvýšený tlak p0 udělí stejnou wmax plynu s větší r0.  wmax odpovídá pa = 0 a tudíž také pa/p0 = 0, expanzi do vakua."]
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[null,"Závislost parametrů plynu na místní rychlosti proudění"]
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[null,null,null,null,"tj. s rostoucí rychlostí klesá teplota plynu."]
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[null,"Místní rychlost zvuku"]
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[null,"Kritická výtoková rychlost"]
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[null,"Kritické parametry"]
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[null,"Průtočné množství G (kg/s)"]
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[null,"Je to maximální průtok při dosažení kritického proudění v ústí trysky"]
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[null,"Dále se zavádí ještě parametr b"]
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[null,"Parametr β má rozměr měrného tahu[N.s/kg = m/s] a nazývá se komplexem parametrů raketového motoru nebo charakteristickou rychlostí. Parametr Bk závisí na složení spalin."]
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[null,"β závisí pouze na vlastnostech pohonných látek (u chemických pohonných látek je β mezi1500 – 2000 N.s/kg). Parametr β se udává v tabulce vlastností pohonných látek. Známe-li β,můžeme nalézt Skr, nutnou k průchodu množství plynů G[kg/s] při tlaku p0 [kg/s]. Při zvětšení průtoku pohonných látek G motorem při konstantní Skr znamená zvětšení p0 ve spalovací komoře. Je to dáno tím, že rychlost v kritickém průřezu nezávisí na průtoku pohonné látky a při stále teplotě T0 se nemění. Dojde-li ke zvětšení G, zvětší se i hustota ρ pohybujícího se plynu. Při konstantní teplotě se tak hustota plynu může zvětšit pouze zvýšením tlaku v komoře"]
[null,"Plocha výstupního průřezu trysky (index a) Sa "]
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[null,"Výtoková rychlost"]
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[null,null,null,null,null,"(??)"]
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[null,"Všechny vztahy jsou totožné, jsou odvozeny z rovnice kontinuity a adiabatických vztahů. Rozšíření trysky závisí při konstantním k jen na poměru pa/p0. (tento vztah platí pro libovolný průřez Sx, dosazený za Sa. Tento poměr bývá 15 až 400. Rychlost a teplota v libovolném průřezu trysky jsou závislé na rozměrech a zákonu změny Sx podél délky trysky x. Tato rovnice platí jak pro podzvukovou, tak pro nadzvukovou část trysky."]
[null,"Poznámka: aby vůbec došlo k nadzvukovému proudění, musí být wa>wkr, tj."]
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[null,"Tepelná účinnost raketového motoru. Maximální účinnosti by raketový motor dosáhl tehdy, je-li dosaženo výtokové rychlosti wmax ,tj. úplné přeměny celkové entalpie v kinetickou energii plynů."]
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[null,"Zvýšením p0 při konstantním pa se zvýší ηt a tím i wa. Roste i měrný tak motoru. Při daném tahu motoru můžeme snížit G, tudíž i rozměry motoru a tím se zmenší i tepelné ztráty motoru. Zvýšením p0 je možné zmenšit objem komory, aniž se zmenší doba prodlevy τ plynu v komoře. Celkově lze říci, že zvýšení p0 zlepšuje charakteristiky raketového motoru."]
[null,"Účinnost využití paliva:"]
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[null,"Je-li V0 objem spalovací komory, pak lze zavést charakteristickou délku spalovací komory poměrem L≈ V0/Skr. Obvykle mívá parametr L hodnoty v rozmezí 0,6 – 1,5 m. Je-li dále Vvt objem, vzniklý spálením G, tj. Vvt = GRT0/p0, potom doba prodlevy plynu v komoře je τ = V0/Vvt = V0p0/GRT0 . Volba parametru τ určuje objem spalovací komory. Nicméně přesné určení rozměrů spalovací komory plyne z analýzy procesů hoření a plynové dynamiky ve spalovací komoře."]
[null,"Tah raketového motoru:",null,null,null,null,null,"pH je okolní tlak v dané výšce"]
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[null,"Konická a zvonovitá tryska"]
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[null,"U konické trysky se při tvorbě tahu uplatní pouze axiální složky průtoku hmoty a výtokové rychlosti. Je-li úhel rozevření trysky a, pak"]
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[null," Nejvýhodnější je úhel rozevření a = 15°. Délka trysky Ld je pak úměrná rozdílu průměrů"]
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[null,"Pro zkrácení trysky (a tedy i snížení její hmotnosti) se používá zvonovitý tvar trysky, která se nejdříve za kritickým průměrem nejdříve rozšiřuje s úhlem 20°-50° což vede k větší expanzi a u ústí se tok narovnává v úhlu 2°-5°. Tím se délka zvonovité trysky snižuje na 70-80% délky trysky pouze konické."]
[null,"Pokud je pa > pH mluvíme o neúplné expanzi; plyn vytékající z trysky se při přebytečném tlaku pa rozpíná a mísí s vnějším prostředím. Rychlost se dále nezvětšuje, protože se tvoří víry."]
[null,"Pokud je pa < pH Za hranicemi trysky se tok zpomaluje a rychlost se zmenšuje na podzvukovou. Přitom vznikají rázové vlny, které srůstem pH se přibližují k trysce, případně do ní vstupují. Vzniká pak odtrhávání toku od stěn a tvoří se víry. Maximálního tahu je dosaženo, pokud pa = pH."]
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[null,"Rychlost hoření prachu v závislosti na pracovním tlaku v komoře se řídí buď lineárním nebo exponenciálním zákonem hoření:"]
[null,"rh = a +b.p (lineární zákon), rh = a.pn (exponenciální zákon), a, b, Ba n jsou empirické konstanty. Také se zavádí teplotní citlivost E na počáteční teplotu elementu TPL. Pak je exponenciální zákon ve tvaru "]
[null,"rh = a.exp[E.(t - tokolí)]pn    E bývá 0,002 až 0,008; n 0,2 až 0,6. Někdy se rychlost hoření vyjadřuje pomocí standardní rychlosti hoření (při 70 bar; 7MPa)  r = r7.(p/7)n   (pokud tlak v MPa)."]
[null,"Jelikož měrná hmotnost prachu je mnohem větší než měrná hmotnost vzniklých spalin a s použitím exponenciálního zákona závislosti rychlosti hoření na tlaku ve spalovací komoře dostaneme závislost tlaku ve spalovací komoře na povrchu hoření TPH ve stacionárním případě ve tvaru:"]
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[null,"Kde F = Sh/Skr poměr mezi hořícím povrchem a kritickým průřezem trysky se nazývá zahrazením. rP je hustota elementu. Analýza stability hoření TPH ukazuje, že stabilní hoření nastává pro TPH s n < 1, kdy se tlakové fluktuace zmenšují. Naopak u TPH s n > 1 se odchylky tlaku od stacionární hodnoty zvyšují a tak motor buď přestane hořet, nebo exploduje. Většina TPL, které se používají, mají n = 0,2÷0,8."]
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[null,"V leteckých startovacích raketách je používáno palivo NRDC:"]
[null,"Pikrát Amonný .................. 45%"]
[null,"Dusičnan Sodný ................. 45%"]
[null,"Pryskyřičnaté pojivo ......... 10%"]
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[null,"Také se používalo palivo GALCIT, které obsahuje:"]
[null,"KClO4 (chloristan draselný)........... 75%"]
[null,"Přírodní asfalt ............................... 25%"]
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[null,"Obě tyto hmoty dosahují výtokové rychlosti okolo 1800m/s, však pro některé své vlastnosti se nehodí pro bojové rakety."]
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[null,"Sovětský raketový kordit:"]
[null,"Nitrocelulóza ..................... 56,5% (obsah dusíku 12,2%)"]
[null,"Nitroglycerin ..................... 28%"]
[null,"DNT ................................... 12%"]
[null,"Centralit ............................ 4,5%"]
[null,"Tento kordit dosahuje výtokové rychlosti okolo 2000m/s."]
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[null,"Americký raketový balsit:"]
[null,"Nitrocelulóza .....................51,5% (obsah dusíku 13,35%)"]
[null,"Nitroglycerin .....................43,5%"]
[null,"Centralit ............................1,3%"]
[null,"Dietylftalát ........................3,25%"]
[null,"Síran draselný ...................1,25%"]
[null,"Saze ....................................0,2%"]
[null,"Dosahuje výtokové rychlosti 2200 m/s (vyšší výtokové rychlosti se dosáhlo na úkor jiných vlastností)"]
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[null,"Německý diglykolý raketový prach:"]
[null,"Nitrocelulóza .....................61,5% (obsah dusíku 12,6%)"]
[null,"Diglykol .............................35%"]
[null,"Difenyluretan ....................2,10%"]
[null,"Etylfenyluretan .................1,40%"]
[null,"Dosahuje výtokové rychlosti okolo 2000 m/s."]
[null,"Všeobecně nutno zdůraznit, že koloidní hmoty zůstávají svými vlastnostmi za pohonnými hmotami složenými., a proto se od jejich používání postupně upouští."]
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[null,"Amatérská směs:"]
[null,"KNO3……………………………….. 74,5 %"]
[null,"Cukr ………………………………… 25,5 %"]
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[null,"NH4NO3……………………………….. 85-90 %"]
[null,"elastomér ……………………………… 25,5 %"]
[null,"Rychlost hoření  0,096 cm/s at 6,8 bar a 0,016 cm/s at 20,6 bar (?). Teplota hoření je cca. 1800K a ISP=180."]
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[null,"KNO3……………………………….. 72 %"]
[null,"Dřevěné uhlí .…………………… 24 %"]
[null,"Síra  …………………………………  4 %"]
[null,"The burning rate of this rocket fuel depends much less on pressure than that of black powder. This widens the accetable limits of the ratio nozzle area/fuel surface area."]
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[null,"Space Shuttle Boosters propellant"]
[null,"Aluminum powder...................................16"]
[null,"Ammonium perchlorate...........................69.9"]
[null,"Fe2O3 catalyst...........................................0.07"]
[null,"Rubber based binder of polybutadiene acrylic acidacrylonitrile.....12.04"]
[null,"Epoxy curing agent...................................1.96"]
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[null,"ESTES C-class rocket engine propellant"]
[null,"KNO3.........................................71.79"]
[null,"Síra............................................13.45"]
[null,"Černé uhlí..................................13.81"]
[null,"Dextrin........................................0.95"]
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[null,"     Propellant 1"]
[null,"    20% R20LM HTPB (Low molecular weight HTPB)"]
[null,"    20% Magnesium powder(-650 mesh)"]
[null,"    60% Ammonium Nitrate powder"]
[null,"    (Curing ratio = 0.19) Rubinate M MDI Curing Agent"]
[null,"    Burn rate coefficient = 0.0061  (? inch/sec)"]
[null,"    Burn rate exponent = 0.507 "]
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[null,"    Propellant 2"]
[null,"    19% R20LM HTPB (Low molecular weight HTPB)"]
[null,"    16% Aluminum powder (-400 mesh or 20 micron)"]
[null,"    65% Ammonium Perchlorate (200 micron)"]
[null,"    (Curing ratio = 0.19) Mondur MR MDI Curing Agent"]
[null,"    Burn rate coefficient = 0.0374"]
[null,"    Burn rate exponent = 0.28 "]
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[null,"Note: Curing agent ratio = (Wt. of curing agent)/(Wt. of binder) = (0.8) * (Equivalent weight of curing agent)/(Equivalent weight of binder)"]
[null,"This assumes 80% linkage for a flexible propellant. Other curing agents can be used, but an adjustment to the curing agent ratio will have to be made."]
[null,"http://homepages.sover.net/~sbjohn/chemistry/chemx/fuels.html"]
[null,"https://www.nakka-rocketry.net/anexp.html"]
[null,"http://www.wydawnictwa.ipo.waw.pl/cejem/vol-9-4-2012/Shekhar.pdf"]
[null,"http://ijseas.com/volume2/v2i4/ijseas20160451.pdf"]
[null,"http://www.transformacni-technologie.cz/40.html"]
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[null,"Orientační rychlosti hoření raketového paliva:"]
[null,"Tlak (bar)","Rychlost (mm/s)"]
[null,40,"2023-08-05"]
[null,70,"2023-12-07"]
[null,100,"2014-09-01"]
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[null,"Vyjádření pomocí Machova čísla M"]
[null,"Rychlost zvuku a a Machovo číslo M:"]
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[null,"Poměr průřezu trysky ke kritickému"]
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[null,"Tah motoru:"]
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[null,"Hodnota Cf u motoru s cukr/KNO3 směsí bývá 1,5, zatímco teoretická by byla okolo 1,64. Ztráty jsou v důsledku dvojrozměrného toku."]
[null,"Charakteristická rychlost c* je odrazem účinnosti hoření, Isp je specifický impuls (v jednotkách N.s/kg =m/s)"]
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[null,"Poměry na kolmé rázové vlně (Rankine-Hugoniotovy rovnice):"]
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[null,"Orbitální mechanika"]
[null,"Rychlost družice v bodech eliptické dráhy"]
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[null,"Kde M hmotnost Země 5,7 x 1024 kg, G gravitační konstanta 6,67×10-11 N.m2.kg-2"]
[null,"a velikost velké poloosy elipsy (m), r vzdálenost satelitu od středu Země (m). Velká poloosa dráhy je aritmetický průměr z vzdáleností obou apsid od těžiště centrálního tělesa. M.G = 3,8019.1014 , odmocnina z M.G = 1,9498.107 "]
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[null,"Kruhová rychlost ",null,null,null,null,"úniková"]
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[null,"Oběžná doba eliptické dráhy:",null,null,null,null,"kde  m =G(M1+M2) , a velká poloosa "]
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[null,"Specifická orbitální energie eliptické oběžné dráhy je záporná a rovnice pro zachování "]
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[null,"orbitální energie"]
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[null,"Pokud chceme vzdálit polohu jedné apsidy (perigeum, apogeum) od centrálního tělesa, musí družice zažehnout svůj motor v protilehlé apsidě a pozor – ve směru letu! Jinými slovy – satelit musí zrychlit. Pokud naopak chceme snížit polohu apsidy, musíme i tentokrát zapálit motor v protilehlé apsidě, tentokrát ale proti směru letu. Družice tedy zpomalí, což ovlivní polohu protilehlé apsidy. Přechod na vyšší kruhovou dráhu tedy vyžaduje dvě změny rychlosti. Z rozdílů rychlostí v původní a nové apsidě spočítáme potřebné Dv."]
[null,"Přechod na vyšší dráhu při změně sklonu oběžné dráhy. Místo aby vk2 = vea + Dv2, tak je dáno vektorově obecným trojúhelníkem:  Dv22 = vea2+ Dv22-2.vea. Dv2.cos(a) "]
[null,"kde vk2 kruhová rychlost na vyšší dráze, vea rychlost apoapsidě eliptické dráhy, Dv2 potřebná změna rychlosti, a úhel změny dráhy."]
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[null,"Model rakety k simulaci"]
[null,"Model tvoří soustava obyčejných diferenciálních rovnic, která se řeší numericky v čase"]
[null,"y(1)","odhořená lineární vzdálenost TPH (D) (m)"]
[null,"y(2)","hořící povrch Sh  (m2)"]
[null,"y(3)","průtočné hmotové množství mP, G  (kg/s)"]
[null,"y(4)","skutečná rychlost v (m/s) včetně vlivu gravitace a odporu vzduchu"]
[null,"y(5)","dosažená výška h (m)"]
[null,"y(6)","impuls I  (N.s)"]
[null,"y(7)","dálka x  (m)"]
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[null,"Počáteční podmínky: y(i) = 0  kromě  y(2) = počáteční hořící povrch Sh0 = Povrch(element,0,1)"]
[null,"Rovnice modelu:"]
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[null,"Am = a.exp(E.(t-tokol)).rP "]
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[null,null,null,null,null," rovnovážný tlak ve spalovací komoře"]
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[null,"y1","odhořelá vrstva paliva",null,"y2","hořící povrch"]
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[null,null,null,"numerická derivace Povrch(element, y1) podle y1"]
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[null,"y3","vyhořelá hmota paliva",null,"y4","rychlost rakety",null,"y5","výška"]
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[null,null,null,null,null," rP hustota TPH"]
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[null,"kde cx koef. odporu (0,2),  v = y4 rychlost rakety, mcelk celková hmotnost rakety včetně TPH"]
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[null,null,null,null,"y6","impuls"]
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[null,"Po dohoření paliva, když Sh = 0 je výhodnější integrovat setrvačný let už jen jako dvě rovnice pro rychlost v a výšku h."]
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[null,null,null,null,null,null,"s poč. podmínkami na konci chodu motoru"]
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[null,"Na konci výstupních integračních intervalů Dt se dopočítávají veličiny:"]
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[null,null,null,null,null,"tah (N)   G = dy3/dτ"]
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[null,null,"a  da odpovídající expanzi na okolní tlak pH. Také se dopočte expanzní tlak pa pro daný výstupní průměr trysky da čili Sa. a je úhel rozšíření trysky."]
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[null,"V případě obecného, šikmého letu se integrují dvě složky rychlosti vx a vy a dvě vzdálenosti – délka a výška, tedy čtyři rovnice, místo dvou (celkem osm)."]
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[null,"v2 = vx2 + vy2 ","  "]
[null,null,null,null,null,"     "]
[null,null,null,null,"     "]
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[null,"s poč. podmínkami na konci chodu motoru; axy je okamžitý úhel dráhy"]
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[null,"Takovýto model má v aktivní dráze letu stále konstantní náměr (jako by byl řízen po přímce). Chceme-li zohlednit gravitací klesající náměr, je nutné integrovat v aktivním letu další diferenciální rovnici pro náměr a. Z důvodů integrační stability by se derivace měla počítat až pro celkovou ryclost  > 30 m/s."]
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[null,null,null,null,null,"kde v je ryclost"]
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[null,"Odkaz na kurs návrhu raket:    https://www.youtube.com/watch?v=vQiIt-jX0BM&list=PL99EA5ECCC34949DB&index=1"]
[null,"(anglicky Indian Institute of Technology Madras)"]