- Email: [email protected]
Trajectory optimization for A S.S.T.O. using in-flight LOX collection
Acre Asrronautrcrr Vol. 41. Nos 4--10. pp. 325-334, 1997 Astronautical Federation. Published by Elsevier Science Ltd Printed in Great Britain 0094.5765198 $19.00 + 0.00 SOO94-5765(98)00047-2
C 1998 Internamnal
PII:
TRAJECTORY OPTIMIZATION FOR A S.ST.0. USING IN-FLIGHT LOX COLLECTION hf. &int-Maal & P. Hemhick EcoleRoyaleMilitak ApplicdMechanicsDepartmnt AvenuedehRrmham,30 1OOOBnmels-Belgium
Akeypintti2raspacemission(lalmchofasetellite
earthobsemtioq...)istheopthhthofthevehicle tmja&ryinordcrtobumthesmaueaquantityof maxhizetkpayload.Thisis F pmpdlam~~ mef0rcvegspaccvebicle,butcspecUyitisa fs cmcial point for a Sir&&Se-T(SSTO) i whcretkchoiceofabadt@ectoqamresultinan mdizablevdkideductothelargelargepart f+W oftbefligk L Intbissludy,wedisalssthetr@ecmy~4” * -iOn LEA fmaVaticalTakdEandHorimdranrtian (Vmrn) SST0 using SqKmnic in-flight LH2 atm@aicoxyglmcoUdonduringa~pbasc LOX (amstantspecd&~~).TbisTbis Lto oxySmiSStOdilltilCL0Xt#JkScudEllSCdiUtbe Mu kmlmkctphase.ThisSSTOhasaBlmkdEbdy aerodynamicamfi~astheonechostnby MR Ixckbaih4artinforitSncwspacclmnvhcr ok (Vm end X-33). PAW TMsSSTouscsrodcctalSinesfrrnn~toMacb PAY 1.7andalsoforthecxomqbkfliSlltpbase(that mcansfixanaltitm&bighcrtlm3OkmandaMach 2 number cvohltioll fiml 6.8 to about 20). Between tksetwofockuphases,t&SSTOispropeUedbya spbsonicramjet YE 2 Topcrfomthisstndy,wzme2cxm4mtmprognrmr r (nmingaaahamamqmter):tbektoncallowsto estimcthcm~ VW. dry Re *hgdraeeadOXYS====Jpt=)ka iixalpaylmd~andthcseamdallcpumitsthc mbtiandthcpaybdmassfbra&dTOGW. RTWt 0 1998 International Astronautical Federation. sab Published
by Elsevier
Science
Ltd
%
Tftls To l7lGW TP
‘AV~lsequdtotheapparedapeullfthcreareno
atmoqkecf&s.
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Ttw
V Vsb vtot VTOHL
Wlam Wslp
ramjet thrust-to-weight ratio (-) vehicle speed @fn/sec) specitic volume ofthe coll~oll plant (m’h.kg LEA hec)) vehicle total vohmx (m)) VerticalTake-OffandHorbxmtal Mg =ticalspe#lws=) dry mass (t) LEA a&&d mass (t) LH2massattake+JE(t) uIXmassattake+S(t) pmpellant==attal=+ff(t) engine mass (NdCet + ramjet) (t) vehidemassatstartoffinalrobet Phi= 0) ramjet mass (t) spe&icweightoftJlecollccliolI Plant w@g ENsec))
1. Intn&&m TostudytheSSTO@ectoryoptimhbon,we~ herethisu&uolyinscveIalsqqeats.Theextmmhy ofeachsegmentisfixedbyaMachmnaberanda dynamicpresanr(oraspecd&analtitb).Each segmentendllastoawqKmdwi&thebegim@of thefollowiug~fbrcMixmi@Ieasom ThepcasibkophhionmethodsaremaltipkaIMI mustbeda!Maiintwocatq+ea.The6rstca@goiy isanme@edwithwbathappensinsidctbesegmeat (ascent&cluisephases),astbechoiceabtlle ~~(alsoChi”choiaoftheb& awleofascent”),the ‘. “onoftkfuel
. . . mmmlationdthedlagorulethNst~ (i.e. notus the -*thNSt0rUSCBttbt same timea rocket and au airbnathing engine. etc...). TlIesecondcategorgtackkstbe~liQked totbefixedpoiHtaofthetra...Thissec& methodwiubeshdiedvuybri&y. InthisstlIdy,tlleoptbiwh~llavebeen appbedtoapahulartypedspaccvehidebutrbey caabeltsedfbrmanyorkxspacevehides. WCdUllalsodbllssthedifhZltOlbitiI@iOll muhodsandsb0wtheadw@qysdeadlafthem. nerearetluecdSwJltllE&ods.nle&tolEisto nalizea”poweredalltbeway”@httoort&Tht saxmdoneistoperfonqatacertainaltit&amifor aceztainflightpathangkt@ausferpoint),abUistic fligMThe&tbevehclem0vesonanellipwl tmasfero&itjoiningtbetral&rpoiattothedeahd ohit.Andhally,thelastwayisaHohmanntraa&r lwlgrhe~~tothefinalarbit
‘Inthiscasethetxau&rpointcanbew&kredasa parkingorbit.
Congress
2.
Vehicle descrithon
In this study, the trajectory that we follow is rather di&rent from a tnjectory of an all rodcet vehicle. The.difbemzcomesflDmtbefacttllatweuse airbreathing propulsion and also a cruise phase ~~xbll~aUtheoxygenweneediixthelast Figurelshowsourtypeoftmjaxozy.Wecauseeon tbisfigurethattheJiirstplulseofthefliglltislocated outsideoftheorbitplaIqandthatthecnxiseph.ase (thisisalsothecollcctionphase)isusedto~the ohitplane.AttbisQne,abighspeedtumisquired toalignthespacevellideintheoxbitpkne.Thu& thiskindoftm@tolyallowstoreachthedeaiIalCnbit hnnewxywknonealth(eveylatimde)witboutuse of a “dog-~ maneuw -*trajedory givestotbtspaccvebickavuy~launchwMow @=~6~paday). Thespacev&ideisaBkndedBo@withwrtical wandhorimnEaltaniinnw)=MJ rodcetengineshm&e-offtoMach 1.7,asubsonk ~fhnMad11.7to6.%andagainrockete1@es fixnn Mach 6.8 to saMhuh. Figme 2 (from ref.[l]) [email protected] vehideshavebeulexBSswyt&edinwindtmmels illtheusliluingthesixtieaandthe.sewnwS anSgmawhasalsobeuldlosenby~ MartinfwitSVmhpestar. Dnringthesabonicramjetmo&acruisephaseis ma&tocdkcttheoxygenfiumtheair,Dnrhgthis craist~tbZLEAisstOEdiflttELOXtanlrsfor lateruse.itisveryimpwmttow&~inthis Slldy,tlEC0lkUiOllphaseWiJltakeplaaQQ&dUIiUg cmi!Sinoldcrtosimpli@the&Sigaofthecohrion PM Tosepamtetheo~oftheatmoqMcair,we needtomkecmboardacohtionplantalhing~ chilldmvntheairtoacaarinpressweand mnpaatprewiththeheipofheatexcbaagaaAtta that,theoxygcnisexrnwedfromtbeairbyuseafa NrOrlocary~.~spacificwdght~ volumeofthiscdkchonplantaadits~ ate given in tahk 1. The vallms come hall ref.[2] excepfortJ=w ~*roFlay#parstor which COM from Rq3]. Newawe& the p&MmaCMpl&h!dbyEf.p]~beUCrtbsntbose ill t&k 1 (see c0x =9oY&issteod ofMY* in reE[3]). The M is taas iu ref.[3], tlKy separated syntlhc air(mixtureof76.86%~and23.14%4).Butae knuwtbattbenisalsoarg0n(1.2!I%)inair(with 23.14%afQaad75.56%dN3andtbattbebalk tempemwofargonisveqcbSetotbebulk tempaatmeefoxylpm~intbissaPdy,= amsidcrthatpra&auyalltbearg4mstayswithtbe oxygenThtmcansauoxggmpurityofaboutof!w% -. 1
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S.S.T.O. launch trajectory
mL4
AL4
BkJdCdBodyFii2
321
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328
wpre w&3
LEA/set))
Wcond(Lg/(kg Lw=))
22.3 3.83 4.93
Fizstofa&mamideranaprioricbsenvaluefor theangleofki&nce(i)oftheQehkleinorderto obtainafir3te&mateofthetlightpathangle(SR)by movementprojectedinthe solvingthcequati~of dktion of the speed vector:
EqtheknowlalgeoftbeMachnumber*the
. 3 aa&mhon andi,wecmevdnatcthevalueofF,D, -c4aaionplantcharacteristics-Table 1 ~:table2showsthesetofvahleswhichareused inthis.study.Aqmy,eachoptMzawvaluewiu bechangedifthischaugeprovidSauimpfmmm theRSUlOMbeXtpangnphs,thiS. resultwiubeshaded.
LdthenSR Aftawatds,wearnevaiuatetbe~dnivativeofsR movuImtprojecMinthe
Aftertha&weapplyanitedvepmcessto6ndisuch thatm=o dt
. ThiscaiculationgivcsIbeoptiIMlanglcof~aad llcadythe-finmess. . F uels#dficerLcmv (fs) ltispomibleto -htthC&0&OfthfS maximmOffScmrmpO&tOthcminimllmfud
ammmptionforaweUknownfkl~in fimctionofthealtitude(seerefJ4]). Wecaadsosay thasaswedonotusethndngduringthemdcct piUl%thecorwrmptioniDlUCketllUMkiSkUOWIlin fUdOllOfthCaltiade. Thc4tOObtainthCminimum
(=I AfX(bll) Qa@Pd Mcr 6)
12.8 75 2.5
fIJdCOllSU@O~We
mustjustfindtheaqieofincidemwhich@wsthe maxinmmvahwoffs.
. .
Murrrmrmdnrp) kisolm*tirnishasedonthercrearthoftheangle ofincencewhichgivathe-vahleofthe ~FOftbetjpOftHOdphCcoQ6igprationthat ofdragis wCChOOSC(BkJldCdBody),thCdMUCdat8lki3DgkOfilldbCCOfabontO.
Table-2
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I
I
Wppl(1) 210.3 208.8 210.7 WLEA (t) 219 218 222.5 WK (1) 328.4 328.63 332 -Polarorbit-A=2OOkm-CR=3.35-Spmx=92kgkcTable 3
I 1
E3ylookingattable3,wenotethatthemaximum finenesscri~givesthebestresult.Tbiscritaia allowsagainofabout2S%inPAYcompadwith theDmincriteriaamlagainofabout2O%amparal withthefsuitcliaThus,theDmincriteriais the choice to do for this mjectory lfweanalyzeattentivelythetable3,we SXth&cVenifthep@SdiStkh@!StWiththe maximumEnemescri~tkpropeb&usedfor thcfirstmcketphase(seeWLox)alemallerinthe caseoftkfsmdDmincliterss.natmeanstha& withtbcsetwocriters’s,weshaubarnless~ andthC!JllCSShJ&O@l(WL0XA4R)dUIiDgthefiISt rocket phase. EN& for these two criterss, the zb=l&
329
thiscouedonplantandthentodecRasetheweight oftheheatexchangers. Thewtcnliseaptimdimpossibilityistokcepthe Machmlmberaudthedynamicpresure(thuswefkyatamstantspeedandaltitudewithan incidenceaudathrustwhicharevaryingalongthc cnlisephase).-nles.econd~tyistokeepthc Machmmlberandtheangleofinckkce~ thednqinrhiscal~thealtitudeaadthe dynamicpresuTewillvalyduringtheullisephase.
.
*c *
Thereasonwhywechoosetomakeacmisephaseat coasmntaltitiaedconsaMspeedistofacilitetethe dbglIoftheSUbSXUCramjet&illt&(aodx,thC weight oftb subsmic ramjet). AU~theCllliSephase,We~lOObgfCKthe angleofincidewwhichgivsaverticalnsultant kceeqdtozero.Tlmtmeansthatthevehicleflies ~(then~=Q=).sO,wt-at~ timestq.bthisangieikmthefollowingnMiodip:
O=zhitl(~+L-Gw.(j$y ep(l)
thminthecaseofthelluximmfinar#r ThereforCwecansaythatthebest!&tionisto @n&ke~e~thefs~duriDgthe maximum-during theairbmbbgphase.Thismultisshownintable 4a.
v
+m(Re+A).g Tomaketheuuisephascataamstantspeed,we haveaisotoflxateachtimestepthevalueofthe thrustas follows:
F=
J
ZY+(GW(-
Theresultofsuchacaldationisshownintable4a. Table4bshowthevahtediandFatthebegiming dtkendafthecmisepbase.
I
-Spmx=92k&ec-C!ruiseatMsTable 4a
I
Withthis”ambined”@mizati~weakainagain afabout1.5%compandWiththCp@Odcalatlated withcmlyonecrite.Iia FortbiscaidatiqwechoostaMdiapriori and&awardswetryto6dtkvalueofiwhich -thep@Md~minimimTOGW. WCjUStn#dtokllOWtlERItiC8l~aadthe altitdevdationto~uatethevariatianofthe dynmicpreswreandqecdToknowthevertid acdemt@~justjuJttotothe~of -~intbeverticaldirectionthatwe can write as follows:
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48th IAF Congress
Accv =
(Log*cos(sR) - D*g*sin(SR)
+F*g.sin(SR+i))/Gw
-(g*(-
RZA) 2
w*
cwm)2
)
Re+ A
eq (3)
Thevalueof~flightpthanglecanthenbefoud itera~ as follows:
Vvert=Accv-Dt SR = arcsin( Vven 1 V) [email protected] iscleartbatfbrthenewitemionweneedtoknowtbc VUktiOIlin&itUdCWhidl~betittUlVaySilDp~ as
follows:
Dh= Vvert-Dt BcGwseofthesmauvaliatiollofvalldsRduringthe mlisewecanevaluatethethnlstasineq2(Vis almost amstant). Suchacalculationisshownintable5hrdiffemt anglesofincikm(i).Inthistable,wecanseetht largeiduemxofavexysmallmiationdi.That manSthat,ifWewanttoCIphiZethecmi&phase withaamstantangleofincihcqwenee4ltoamtrol thisvalueonthevebiclewi&averyhighprecision ThatiSthcR!4lSOIl~WeChoosetOUl&thCClUiSC phaseat-dynamicpresslaeandMachrmmkr
asbasiccarqeveniftheresultfbri=2.9oisbetter thantheredtgivenintable4.
Therearethreedifkmntwaystoi@ectapce vehicleintoadesiredorbit.Thefkstoneistbe ball&icflig&thesccondoneistheHohtaml aans&krandthelastoneisaPAW’fligbLThse tbreekindsofin~ere~atlfiglKe3 (ref01).
beginsatafixeZaltitde(&s&raltit&)anda fiXCdflightplthengktllldWhiChdSWhUllUIiV&g
onthe6nalorbitwherea~inqmlseisrquiredto reikdahthe~orbitSo,thespecevehicle evolvesonand@ticalttaasf&orbk
‘PAWmeansthattkrocketengiaesburntillthe iXLjC43.iOIlhtOttICSIIi3lOlbit.
l Hohmanuuansfer The Hohmann Uansfer is in fact a ballistic flight wheretheflightpathat@eisequaltozero. Inthis caqwecana&milakthetranskraltitudetoa parking orbit TherefoIq the perigee of the elliptical transferorbitisthepointontheparkingorbitwhere thetrandkrbeginsandtheapogeeisthepointlocated onthefinalorbitwkreanimpukisalsorequiredto rechuhk the orbit.
PowendallAwaV Inthislneth&therodrdengiuesafecutonlywhen thespacevehicleisinjectedintotheCnalorbit_This iscednlytheworstnxthodbecausealotofenergy isvastedtothelossesduetotheearth gmvity.ThismetMwillnoIIdybeusedfbr injectionintoorbitaroundacelestialbodywithalow gravity (e-g Mars). l
. . . . ~ioftheorbl mlectumIuethod j;gMe6showsthe~ofthotitinjstion mthodolltheTOGW.ItisnotalDdgtlkttIe worst result is obtaid with the PAW injection be4xvxqassaidearlier,webumahrgequantityof overam~theearthgravity(seeAV~. itisamazingtoseethattheHohmann E aans6erisXltthebesttdUthiIttermsdTOGW. Indeed this tran&r is known (see ref.[6]. ref.[7] and ref.[S]) as the uausk which wastes the smallest quadyofenergyforachangeinorbitaIaltitude.Bnt ke,wemmtkeepinmindthatthesituationisabit follows and is difkentbecalBthisxnaEmTr whichis infldbyti.Iepull-tlpidhncedbytheatmo+eqthenbythedragonthe vehicle.Tberdo~itispossiblethattheballistic flightbumslesspmpelhtthantheHohman~ trader(thisistl~casehae,seeAV~~ wbichisa pictureofthe&ttalqudtyofpropdhtbumedaud thenofTOGW).AlIywq,wecansaythakifwe amsi&rapdl-upwihutd%kctoftkatmoqhe, theHohlmumtIanskisthecqtimalone(see AV~6).Tlms,we~saythatthebestchoice(in termsdTOGW)cimdependonthepdl-up ~ballisticflightwUUldmthavctbcbest valueofT0Gw(rhsisnotthecasehere!),this sohdhhmsalotofadvarqpontbeH&mann uausferamiwiUbeaubasicchoice.hkuLhra LEO(andtJkisthecasehere),whenwemakea Hollmanntmnskr,thevehiclearrivestotbcapogee whenthelaUll&b8seisl~Wltheahasidcof theealth(seefigure3)andso$thetnmd&Jnof -(ndiolKgUidhginIormation~~iIl Ief.[5])buweentbespaavehicleandtbelamlchbase
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IAF Congress
isnotpsiieaIlymore.Anotheradvaluageofthe bauisticflightisthesnrallalengtllofthetrajeaaryh ampacimwiththelengthofthetrajamyforthe Hobmanntnder(seeAV~.So,thetqjeUoqfl~ withabdlisticflightwilltakelcssthne.The*in lim(seenus)isrelatwylowtnltcanallowmore flexiility during spaceflights. Wecansccth%ttheAV~isalmsttbesameforthe ldisticflightandtbeHohrrmnn~evenwitb thedKnterflighttimeuftllcfirJtaDeandthelarge diffemminAV~.ItcmcsfromthefkttbattbeAV tOprwidefiXthencirarlarizationmar#rvasinthe finalorbitisbgertlmintkcaseoftheHohmam aanskr.
._. ::
..:.
‘...’
7.910
331
samedesigrlthmt(?vf4),buttheleaultwillbewoKe bCGlUWOfthCSlUdlCkWlSCiDSpCCiiiCimpulSeand
thllStwitbtheSamramjdmasS.FiIldly,ifWemaLe a9O%thmtl~evcnifthespecificimpllseisa littlebithighcr,thesiubsmicramjetwillkdesigned at M=1.7and then will be heavier.
7.850 . lntllisparqgrapb,wedlk3aIstbeploblemofthe
7.300 220 Table6 6. m lnthispfqrap&westdytbe~dthe dehxedthnrslby ilK?Qhgordecnasiogthe numberofmcket~~orthcwi&hofthe sllbmicramjqbutalsobycombiningtbelKeof dKUCOgilXStitbCttUbShCramjaatsllpasoniC spu!dAswcwillscE,tbislasts&diOnis~~
intemmdTOGWlmtlcadstoasubmicrcrrmja desigdtoworkona llamwerMachmmpberlaage.
comhedproQlrlsionwitha7O%~oftbe submnicramjetintheMachnumbcr~~1.7 upto2J.combhd~mcaasthotweuseat thesametimeandinacutainMxhmmbcrrange, therocbengiaeandthesllbaonic~togetha. Thatnwausalsoadccmseoftbespe&cinqdsed tbesubwicramjuandthenadeueascoftheSSTO pIdommm(dnetothehighet~ofLoxand LH~hrdinthem&etengiacwbicbatcusedina hgeIkhcltrange),aJWeCaaStZiILt&le8.BUtthe goaloftheamlbhdprapwamisootto~the vchideperbmmmbutwelltouseasubonic mqjudcsi~kmasmaUerMachmu&errange amillscittoitmease thespecifkimpukoft& mkuwlgineduringthecornbhd~ TkcasewingaambinedpqmlskmhfnM-1.7to Mp2.5 a Grrm M=6 to M-6.8 is evm mole amawivealldtlmwiukarmetkbasiccase~ -0p
Tabie 8 .
WW Inrhispamgmphadintkfolbwhgooe,we~
tbeproblemofthetlnustkvel-bytbemcket englnea(ofthemlmberofrocku~wetake)
aalbythesubsoJicramjet(orthewidthoftlle
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ramjct).Forthat,wenecdtoknowthe~vabofthe areaofthe.vchiclebascandthewidthofthcspace vchicktoknowifitispossibktopiaccthcsccngines onboard.ThecvaluationoftbedimensioI&ofthe spacev&icleisgivcnintheappe&x. Thethnlstofthemc&engincsiscalculatedas follows: Fz = NW-t .ToGW. ‘rhuefo~, the ratioRTWtfixthermmberofrodetcnginsandof coursctheweightofthcsera&ctcqincs.Figure5 ShowSthCCXiStUSof~optimalvalllCforRTWt (1.45). This optimal value is very CxI&bnt with reL[9]wbichgivcsauoptimalvahleinthcraugcd 1.3-1.5. Attbisoptimalpoinfwchavccaladatcdthebsc area (137.5 rn3 with the help of tie appendix (TGGW=271f V-2833 m’, SW77 & and HJ.1607). weknowakottlatthesLtlknIstiscqual to 393 tons (1.45*271),a value that can be reacbcd with 2 or 3 SSME(F&=177tat nominaJpower kvcl) whichhasancxitareaofabout4.1m’pclulginc. Thatmemlsthatwcdon0thavcalypnlbkmto~ thcroc&cngincstothebaseofthisspacevcllide.
performanccsarebettcrwiththestn#tdue.toits much higher spccitic impulse (see table 9). The iIlflIZIlCCofthCStX@il?$iSratherimpoMlt(ICdlUSioIl of2.3%ofTGGW)andmainlyallonstoavoidthe useofaibstrocketphascandalsotousetheram~ inasmaUerMachnumbcrrangc(Inthiscasethc ramjetis startedat Mach=2.5).
. . $&t+=?o+-=te quuaaonamsirtsillthe~oftheramjet width(sab)oriufbcttkchoiccofthccadeknt thenSb(and RSG(=SaWfSW).IfRSGinaegsa thUltheramjetwCightandtlUUSt)inaesses p~totheT0GWfbraamstautpaylo& Fi~6showstheinnuenceofRSGonT0GWand theanIqm&@vallleofRsGmax’.RsGmaxismt aconsbutbut ineascswithtbeRsG~wcnutc thatthtdistanasqarat@theRsGandRsGmax atrvcsdecreases.TbatmcanstbatRsG~its maJdmnmValUC(RSGmax)andthatitwillbCmOn dimallttofittheraq~intotbessTG.
ThenarcbvoplCbkmsinthcoptbbtionofthe &sedpointsofatrajexy.&~thenlation sllaxsbM** eetillgbetneentwo tb&thCChOilXofthedynsrmicpresSareaadthC A4achmmdxratcaIzh&dpoint. Inthispeuagq&wcshowonlytheMucnccofa changeafthevahlcofthcdynamicpressmeofone 6xaj point (i.e. the &au&ion point where tie last KBdatphasebtg&k&syatM=6.8andQoK=55 kPa).SO,~doQnotsolvetOb&thcproblanOfthC oftleiixalpoi&.Wejustshowits
-UseofaStn@tTable 9
TabklOshowstbcbiginfl-ofasnallvariation OfthCdp8lUiCpS3UXCatihCtl7Ul&i~aihatbgmodcaaipurclock.ctengiltcmodc
Ljustthekvclofthnutofaspacevchickisavery d&icntwaytoimprovcits ““““““% thisfzanauowtotlselcssadvanc&~ thcssro(hcavkrrau&smalkxMachmmIber xangeofthe Ia@& lowu collectionratio,...). 7.Mucnaoftheuseofastrq& Tbcpexm8KBofsuchanulgincalcd8su&cdin nz[lO] & [ll] and its weight (in fact its thnlst-ttb weight ratio) is &mated ti xeL[l2]. Tabk 9 aq?3msthclesllltobtai&forthc&signpoint(DP) dQurc6withthcreultabainalwitbastn#t instcadofthefirstmckctandc0&ined~ phass.Evenwithalowcrramjettbnwt~ ratio(@lctotheaMBina&stnqt-nynjctor ~-M&th=&i@=qaal~ap(lbt(thc m the Sal@, the ‘RSomaX=~.RSb+XgiVCSthClWXblUm auowebleramjetWidthCfpldtO2aWhiChiStkbtlSC width.
@ointK).Thebigdiffhm-fmmthebighcr tW?U@OUdUtillgthClastrodretphase (sccAVfbs)fixthccascsatahigberQoKThisisdue toalongexpu&up,whatwhatalongeralmo@Mc InamNu in rwckct mode (see Tp). It is also tonotctbatitisnotpossibktoduxease toabwcrvahwtlmn55kPabccausethcntbe r timcrequindforthepuu-upmanamrbcanmes ntgative cIp
*~thcliukcxisdngkhvemthcflxal~wc chowcPrcalizcthcascuItphaacatarnstantdynamic pmmKcwhatismoptlmal~asshowniu
ref.[l31. Bu&hae, we limit the dynamic pressme at maxbmlm75kpa.
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100’ 0
2 Flii
4 6 Mach amber (-)
2721
0.064
I 6
0.066
0.06
1.4
1.6 Rmt
1
0.056
270.
0.062
(-)
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AOK(km) .. 27.6 ,“I 27.5 AVlits i_ 6.37.&j;:,,: 6.471 oan/sec) Tp (s) ‘. : &.: 1 13.59 Table 10
27.1 6.756 20.69
9. conchlsioIls The trajectory optimization is a very important point for the de-sign of a SST0 using in-flight LOX collection. It allows a gain of about 20 to 25 % in payload (for a fixed TGGW) in comparison with a poor tmje&ny optimization (fs or minimal drag). Thislargeimprovementcanallowustousealower colktion ratio and/or a heavier adkction plant and/orakaviersubsunicrarr#t_Thatcouldleadtoa SST0 using supersonic &flight LOX collection which is more comzrvative (less advanced t&UO~OgkS.
Theo@katiollofthecnlisephasedoesnothavzto bedonenecessarilytodecleaxTOGw,butwellto oprimketheinletconditionsinthec&uionplant and to avoid a too large precision on the flight pamme&s as, for example. on i in the case of the cruisephaseatamstantMachmmkrandcom$ant angle ofkkknce.. Thechoiceoftheorbitinjectionmethodisalsovery kqntantandcanpermitagainofabout4O%in telmsofTOGWin amqalkmwiththepowen?dall thewayfl@htinjazionWealsunotethattheTOGW isnotthemdyparamter:wehiwetoconsiderthe influawre of the telec0lmmmications to guide the spacevehicleaudalsotlxflighttimelength Weshowalsothatthechoiceofthedeliveredthrust leWlis~importanttoreducetheMachlNUk rangedtksubsonicramjet(caseoftheaxnbined pqndsion)butalsothatwecanimprovethespaoz vehicle@mmmcesbyimxa&lgthemlmberof rocketenginesandthewidthoftbesubsonkramjet lnthat~wehavejusttocheckifitispossibleto pUtthe~in&ktkspaceVehicle. Finally,weshowtkxtthechoiceofthefixedpointsof theQ#ctoryisveryimportant(e.g.a7%variationof TGGW kv a 1 kPa variation of QoK). This problem isstillilldeVe1opment Ref. AC.Dqer&M.L.Buck,“LiikgBodies-An attrxtk yodyr+; cordigumtion choice for z2.veh-s ML-D-U’-QS, Bktok M strengnars “Colleuion plant &mcte&ics FESTIP Technology Heat M-geme&WP9.3,FiualReport,Apr1997. RDrnevich&J.Nowobllski,“AixborneRotary separator Study”, NASA CR-191045, Dee 1992. MBarrZre,AJaunmtk,B.FraeijsdeVeub&e andJ.VandcnLerdrhovt.“Lapropukionpar fisca”. Sciences et Lctfres S.A., Likge, 1959.
5. S. Ehricke, “Space Flight Dynamks II: principles ofGuidedMissileDesign”.Mer@ l%l. 6. V. Chobo&~, “Grbital Mechanics II”, AlAA Education Series 96-42189, 19%. 7. M. oriffin & J. French, “Space Vehicle design”, AIAA Education Series 90-23705,199O. 8. C. Brown, “Spacecraft Prop&ion”, AIAA -on Series 95-11241, 1995. 9. H Immich & B. Hufenbach, “Analysis ofVariable Mixture Ratio of a RocJcet-Propellai SST0 Laucher”, AIAA 94-3314, Indkapolis, 27-29 Jun 1994. 10.R Chase, “The Design Evolution of a combined Cycle Airbreathing Powered S.S.T.O. Design Concept”, AIAA-95dolO. cbananooga 3-7 Apr 1995. ll.A Siebe&ar t P. Hewitt, “Rocket Rqjet Booskrsfbrsustai&highspeed~, AGARD, Paris, 14-17 April 1997. 12.J. Ve Qmparkm Between Ejector-Barr&t & Tuk-Ramjet fix TSTG s AIAA 93-5095, Munich, 30 NW - 3 13.D. Schmkt & J. VelapoU, “Gptimom Mission performance and Guidamx for w SSTO”. ALU 96-3904, San Diego, 29-31 Jul 19%.
Inthisappend&wedisaisstheproblemofthe evaluationofthewidthandthebeightoftbebaseof ourSSTG.Thevehicleshapethatweamskkhereis aconewithanel@tkal&ie(6gure7).Thisame becomesaconewithaclrudarbasewhen~~ equaltoO.44toObewiththeBlUXkd~ conflgumtion (see nE[lZ]). B with the Iwnvled@dtbe&ttalVehidevolmne(Vbot),tbe planfmmarea(Spf)andtheKllcbemaan’sparamter (T), = = calcuke the width 0, the kight (2b) andtkareaadtkSST0baseas6oLlaws:
yTOt= 2-b-h
b=2.27-a-
r
(to have b = a when r= 0.44)
@f=a-h
SIN= ma-b -(=-f@=?l 2a=hgthofthelaqpxisoftheellipse 2b==lellgthaftlIC~ercisoftkellipse h=kq#hoftkspacevehide s,=sl&ceoftheupticalbase. V&H
Tbcna2. 7r
Spf -2.27-r
C 1998 Internamnal
PII:
TRAJECTORY OPTIMIZATION FOR A S.ST.0. USING IN-FLIGHT LOX COLLECTION hf. &int-Maal & P. Hemhick EcoleRoyaleMilitak ApplicdMechanicsDepartmnt AvenuedehRrmham,30 1OOOBnmels-Belgium
Akeypintti2raspacemission(lalmchofasetellite
earthobsemtioq...)istheopthhthofthevehicle tmja&ryinordcrtobumthesmaueaquantityof maxhizetkpayload.Thisis F pmpdlam~~ mef0rcvegspaccvebicle,butcspecUyitisa fs cmcial point for a Sir&&Se-T(SSTO) i whcretkchoiceofabadt@ectoqamresultinan mdizablevdkideductothelargelargepart f+W oftbefligk L Intbissludy,wedisalssthetr@ecmy~4” * -iOn LEA fmaVaticalTakdEandHorimdranrtian (Vmrn) SST0 using SqKmnic in-flight LH2 atm@aicoxyglmcoUdonduringa~pbasc LOX (amstantspecd&~~).TbisTbis Lto oxySmiSStOdilltilCL0Xt#JkScudEllSCdiUtbe Mu kmlmkctphase.ThisSSTOhasaBlmkdEbdy aerodynamicamfi~astheonechostnby MR Ixckbaih4artinforitSncwspacclmnvhcr ok (Vm end X-33). PAW TMsSSTouscsrodcctalSinesfrrnn~toMacb PAY 1.7andalsoforthecxomqbkfliSlltpbase(that mcansfixanaltitm&bighcrtlm3OkmandaMach 2 number cvohltioll fiml 6.8 to about 20). Between tksetwofockuphases,t&SSTOispropeUedbya spbsonicramjet YE 2 Topcrfomthisstndy,wzme2cxm4mtmprognrmr r (nmingaaahamamqmter):tbektoncallowsto estimcthcm~ VW. dry Re *hgdraeeadOXYS====Jpt=)ka iixalpaylmd~andthcseamdallcpumitsthc mbtiandthcpaybdmassfbra&dTOGW. RTWt 0 1998 International Astronautical Federation. sab Published
by Elsevier
Science
Ltd
%
Tftls To l7lGW TP
‘AV~lsequdtotheapparedapeullfthcreareno
atmoqkecf&s.
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326
Ttw
V Vsb vtot VTOHL
Wlam Wslp
ramjet thrust-to-weight ratio (-) vehicle speed @fn/sec) specitic volume ofthe coll~oll plant (m’h.kg LEA hec)) vehicle total vohmx (m)) VerticalTake-OffandHorbxmtal Mg =ticalspe#lws=) dry mass (t) LEA a&&d mass (t) LH2massattake+JE(t) uIXmassattake+S(t) pmpellant==attal=+ff(t) engine mass (NdCet + ramjet) (t) vehidemassatstartoffinalrobet Phi= 0) ramjet mass (t) spe&icweightoftJlecollccliolI Plant w@g ENsec))
1. Intn&&m TostudytheSSTO@ectoryoptimhbon,we~ herethisu&uolyinscveIalsqqeats.Theextmmhy ofeachsegmentisfixedbyaMachmnaberanda dynamicpresanr(oraspecd&analtitb).Each segmentendllastoawqKmdwi&thebegim@of thefollowiug~fbrcMixmi@Ieasom ThepcasibkophhionmethodsaremaltipkaIMI mustbeda!Maiintwocatq+ea.The6rstca@goiy isanme@edwithwbathappensinsidctbesegmeat (ascent&cluisephases),astbechoiceabtlle ~~(alsoChi”choiaoftheb& awleofascent”),the ‘. “onoftkfuel
. . . mmmlationdthedlagorulethNst~ (i.e. notus the -*thNSt0rUSCBttbt same timea rocket and au airbnathing engine. etc...). TlIesecondcategorgtackkstbe~liQked totbefixedpoiHtaofthetra...Thissec& methodwiubeshdiedvuybri&y. InthisstlIdy,tlleoptbiwh~llavebeen appbedtoapahulartypedspaccvehidebutrbey caabeltsedfbrmanyorkxspacevehides. WCdUllalsodbllssthedifhZltOlbitiI@iOll muhodsandsb0wtheadw@qysdeadlafthem. nerearetluecdSwJltllE&ods.nle&tolEisto nalizea”poweredalltbeway”@httoort&Tht saxmdoneistoperfonqatacertainaltit&amifor aceztainflightpathangkt@ausferpoint),abUistic fligMThe&tbevehclem0vesonanellipwl tmasfero&itjoiningtbetral&rpoiattothedeahd ohit.Andhally,thelastwayisaHohmanntraa&r lwlgrhe~~tothefinalarbit
‘Inthiscasethetxau&rpointcanbew&kredasa parkingorbit.
Congress
2.
Vehicle descrithon
In this study, the trajectory that we follow is rather di&rent from a tnjectory of an all rodcet vehicle. The.difbemzcomesflDmtbefacttllatweuse airbreathing propulsion and also a cruise phase ~~xbll~aUtheoxygenweneediixthelast Figurelshowsourtypeoftmjaxozy.Wecauseeon tbisfigurethattheJiirstplulseofthefliglltislocated outsideoftheorbitplaIqandthatthecnxiseph.ase (thisisalsothecollcctionphase)isusedto~the ohitplane.AttbisQne,abighspeedtumisquired toalignthespacevellideintheoxbitpkne.Thu& thiskindoftm@tolyallowstoreachthedeaiIalCnbit hnnewxywknonealth(eveylatimde)witboutuse of a “dog-~ maneuw -*trajedory givestotbtspaccvebickavuy~launchwMow @=~6~paday). Thespacev&ideisaBkndedBo@withwrtical wandhorimnEaltaniinnw)=MJ rodcetengineshm&e-offtoMach 1.7,asubsonk ~fhnMad11.7to6.%andagainrockete1@es fixnn Mach 6.8 to saMhuh. Figme 2 (from ref.[l]) [email protected] vehideshavebeulexBSswyt&edinwindtmmels illtheusliluingthesixtieaandthe.sewnwS anSgmawhasalsobeuldlosenby~ MartinfwitSVmhpestar. Dnringthesabonicramjetmo&acruisephaseis ma&tocdkcttheoxygenfiumtheair,Dnrhgthis craist~tbZLEAisstOEdiflttELOXtanlrsfor lateruse.itisveryimpwmttow&~inthis Slldy,tlEC0lkUiOllphaseWiJltakeplaaQQ&dUIiUg cmi!Sinoldcrtosimpli@the&Sigaofthecohrion PM Tosepamtetheo~oftheatmoqMcair,we needtomkecmboardacohtionplantalhing~ chilldmvntheairtoacaarinpressweand mnpaatprewiththeheipofheatexcbaagaaAtta that,theoxygcnisexrnwedfromtbeairbyuseafa NrOrlocary~.~spacificwdght~ volumeofthiscdkchonplantaadits~ ate given in tahk 1. The vallms come hall ref.[2] excepfortJ=w ~*roFlay#parstor which COM from Rq3]. Newawe& the p&MmaCMpl&h!dbyEf.p]~beUCrtbsntbose ill t&k 1 (see c0x =9oY&issteod ofMY* in reE[3]). The M is taas iu ref.[3], tlKy separated syntlhc air(mixtureof76.86%~and23.14%4).Butae knuwtbattbenisalsoarg0n(1.2!I%)inair(with 23.14%afQaad75.56%dN3andtbattbebalk tempemwofargonisveqcbSetotbebulk tempaatmeefoxylpm~intbissaPdy,= amsidcrthatpra&auyalltbearg4mstayswithtbe oxygenThtmcansauoxggmpurityofaboutof!w% -. 1
48th IAF Congress
S.S.T.O. launch trajectory
mL4
AL4
BkJdCdBodyFii2
321
48th IAF Congress
328
wpre w&3
LEA/set))
Wcond(Lg/(kg Lw=))
22.3 3.83 4.93
Fizstofa&mamideranaprioricbsenvaluefor theangleofki&nce(i)oftheQehkleinorderto obtainafir3te&mateofthetlightpathangle(SR)by movementprojectedinthe solvingthcequati~of dktion of the speed vector:
EqtheknowlalgeoftbeMachnumber*the
. 3 aa&mhon andi,wecmevdnatcthevalueofF,D, -c4aaionplantcharacteristics-Table 1 ~:table2showsthesetofvahleswhichareused inthis.study.Aqmy,eachoptMzawvaluewiu bechangedifthischaugeprovidSauimpfmmm theRSUlOMbeXtpangnphs,thiS. resultwiubeshaded.
LdthenSR Aftawatds,wearnevaiuatetbe~dnivativeofsR movuImtprojecMinthe
Aftertha&weapplyanitedvepmcessto6ndisuch thatm=o dt
. ThiscaiculationgivcsIbeoptiIMlanglcof~aad llcadythe-finmess. . F uels#dficerLcmv (fs) ltispomibleto -htthC&0&OfthfS maximmOffScmrmpO&tOthcminimllmfud
ammmptionforaweUknownfkl~in fimctionofthealtitude(seerefJ4]). Wecaadsosay thasaswedonotusethndngduringthemdcct piUl%thecorwrmptioniDlUCketllUMkiSkUOWIlin fUdOllOfthCaltiade. Thc4tOObtainthCminimum
(=I AfX(bll) Qa@Pd Mcr 6)
12.8 75 2.5
fIJdCOllSU@O~We
mustjustfindtheaqieofincidemwhich@wsthe maxinmmvahwoffs.
. .
Murrrmrmdnrp) kisolm*tirnishasedonthercrearthoftheangle ofincencewhichgivathe-vahleofthe ~FOftbetjpOftHOdphCcoQ6igprationthat ofdragis wCChOOSC(BkJldCdBody),thCdMUCdat8lki3DgkOfilldbCCOfabontO.
Table-2
48th IAF Congress
I
I
Wppl(1) 210.3 208.8 210.7 WLEA (t) 219 218 222.5 WK (1) 328.4 328.63 332 -Polarorbit-A=2OOkm-CR=3.35-Spmx=92kgkcTable 3
I 1
E3ylookingattable3,wenotethatthemaximum finenesscri~givesthebestresult.Tbiscritaia allowsagainofabout2S%inPAYcompadwith theDmincriteriaamlagainofabout2O%amparal withthefsuitcliaThus,theDmincriteriais the choice to do for this mjectory lfweanalyzeattentivelythetable3,we SXth&cVenifthep@SdiStkh@!StWiththe maximumEnemescri~tkpropeb&usedfor thcfirstmcketphase(seeWLox)alemallerinthe caseoftkfsmdDmincliterss.natmeanstha& withtbcsetwocriters’s,weshaubarnless~ andthC!JllCSShJ&O@l(WL0XA4R)dUIiDgthefiISt rocket phase. EN& for these two criterss, the zb=l&
329
thiscouedonplantandthentodecRasetheweight oftheheatexchangers. Thewtcnliseaptimdimpossibilityistokcepthe Machmlmberaudthedynamicpresure(thuswefkyatamstantspeedandaltitudewithan incidenceaudathrustwhicharevaryingalongthc cnlisephase).-nles.econd~tyistokeepthc Machmmlberandtheangleofinckkce~ thednqinrhiscal~thealtitudeaadthe dynamicpresuTewillvalyduringtheullisephase.
.
*c *
Thereasonwhywechoosetomakeacmisephaseat coasmntaltitiaedconsaMspeedistofacilitetethe dbglIoftheSUbSXUCramjet&illt&(aodx,thC weight oftb subsmic ramjet). AU~theCllliSephase,We~lOObgfCKthe angleofincidewwhichgivsaverticalnsultant kceeqdtozero.Tlmtmeansthatthevehicleflies ~(then~=Q=).sO,wt-at~ timestq.bthisangieikmthefollowingnMiodip:
O=zhitl(~+L-Gw.(j$y ep(l)
thminthecaseofthelluximmfinar#r ThereforCwecansaythatthebest!&tionisto @n&ke~e~thefs~duriDgthe maximum-during theairbmbbgphase.Thismultisshownintable 4a.
v
+m(Re+A).g Tomaketheuuisephascataamstantspeed,we haveaisotoflxateachtimestepthevalueofthe thrustas follows:
F=
J
ZY+(GW(-
Theresultofsuchacaldationisshownintable4a. Table4bshowthevahtediandFatthebegiming dtkendafthecmisepbase.
I
-Spmx=92k&ec-C!ruiseatMsTable 4a
I
Withthis”ambined”@mizati~weakainagain afabout1.5%compandWiththCp@Odcalatlated withcmlyonecrite.Iia FortbiscaidatiqwechoostaMdiapriori and&awardswetryto6dtkvalueofiwhich -thep@Md~minimimTOGW. WCjUStn#dtokllOWtlERItiC8l~aadthe altitdevdationto~uatethevariatianofthe dynmicpreswreandqecdToknowthevertid acdemt@~justjuJttotothe~of -~intbeverticaldirectionthatwe can write as follows:
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48th IAF Congress
Accv =
(Log*cos(sR) - D*g*sin(SR)
+F*g.sin(SR+i))/Gw
-(g*(-
RZA) 2
w*
cwm)2
)
Re+ A
eq (3)
Thevalueof~flightpthanglecanthenbefoud itera~ as follows:
Vvert=Accv-Dt SR = arcsin( Vven 1 V) [email protected] iscleartbatfbrthenewitemionweneedtoknowtbc VUktiOIlin&itUdCWhidl~betittUlVaySilDp~ as
follows:
Dh= Vvert-Dt BcGwseofthesmauvaliatiollofvalldsRduringthe mlisewecanevaluatethethnlstasineq2(Vis almost amstant). Suchacalculationisshownintable5hrdiffemt anglesofincikm(i).Inthistable,wecanseetht largeiduemxofavexysmallmiationdi.That manSthat,ifWewanttoCIphiZethecmi&phase withaamstantangleofincihcqwenee4ltoamtrol thisvalueonthevebiclewi&averyhighprecision ThatiSthcR!4lSOIl~WeChoosetOUl&thCClUiSC phaseat-dynamicpresslaeandMachrmmkr
asbasiccarqeveniftheresultfbri=2.9oisbetter thantheredtgivenintable4.
Therearethreedifkmntwaystoi@ectapce vehicleintoadesiredorbit.Thefkstoneistbe ball&icflig&thesccondoneistheHohtaml aans&krandthelastoneisaPAW’fligbLThse tbreekindsofin~ere~atlfiglKe3 (ref01).
beginsatafixeZaltitde(&s&raltit&)anda fiXCdflightplthengktllldWhiChdSWhUllUIiV&g
onthe6nalorbitwherea~inqmlseisrquiredto reikdahthe~orbitSo,thespecevehicle evolvesonand@ticalttaasf&orbk
‘PAWmeansthattkrocketengiaesburntillthe iXLjC43.iOIlhtOttICSIIi3lOlbit.
l Hohmanuuansfer The Hohmann Uansfer is in fact a ballistic flight wheretheflightpathat@eisequaltozero. Inthis caqwecana&milakthetranskraltitudetoa parking orbit TherefoIq the perigee of the elliptical transferorbitisthepointontheparkingorbitwhere thetrandkrbeginsandtheapogeeisthepointlocated onthefinalorbitwkreanimpukisalsorequiredto rechuhk the orbit.
PowendallAwaV Inthislneth&therodrdengiuesafecutonlywhen thespacevehicleisinjectedintotheCnalorbit_This iscednlytheworstnxthodbecausealotofenergy isvastedtothelossesduetotheearth gmvity.ThismetMwillnoIIdybeusedfbr injectionintoorbitaroundacelestialbodywithalow gravity (e-g Mars). l
. . . . ~ioftheorbl mlectumIuethod j;gMe6showsthe~ofthotitinjstion mthodolltheTOGW.ItisnotalDdgtlkttIe worst result is obtaid with the PAW injection be4xvxqassaidearlier,webumahrgequantityof overam~theearthgravity(seeAV~. itisamazingtoseethattheHohmann E aans6erisXltthebesttdUthiIttermsdTOGW. Indeed this tran&r is known (see ref.[6]. ref.[7] and ref.[S]) as the uausk which wastes the smallest quadyofenergyforachangeinorbitaIaltitude.Bnt ke,wemmtkeepinmindthatthesituationisabit follows and is difkentbecalBthisxnaEmTr whichis infldbyti.Iepull-tlpidhncedbytheatmo+eqthenbythedragonthe vehicle.Tberdo~itispossiblethattheballistic flightbumslesspmpelhtthantheHohman~ trader(thisistl~casehae,seeAV~~ wbichisa pictureofthe&ttalqudtyofpropdhtbumedaud thenofTOGW).AlIywq,wecansaythakifwe amsi&rapdl-upwihutd%kctoftkatmoqhe, theHohlmumtIanskisthecqtimalone(see AV~6).Tlms,we~saythatthebestchoice(in termsdTOGW)cimdependonthepdl-up ~ballisticflightwUUldmthavctbcbest valueofT0Gw(rhsisnotthecasehere!),this sohdhhmsalotofadvarqpontbeH&mann uausferamiwiUbeaubasicchoice.hkuLhra LEO(andtJkisthecasehere),whenwemakea Hollmanntmnskr,thevehiclearrivestotbcapogee whenthelaUll&b8seisl~Wltheahasidcof theealth(seefigure3)andso$thetnmd&Jnof -(ndiolKgUidhginIormation~~iIl Ief.[5])buweentbespaavehicleandtbelamlchbase
48th
IAF Congress
isnotpsiieaIlymore.Anotheradvaluageofthe bauisticflightisthesnrallalengtllofthetrajeaaryh ampacimwiththelengthofthetrajamyforthe Hobmanntnder(seeAV~.So,thetqjeUoqfl~ withabdlisticflightwilltakelcssthne.The*in lim(seenus)isrelatwylowtnltcanallowmore flexiility during spaceflights. Wecansccth%ttheAV~isalmsttbesameforthe ldisticflightandtbeHohrrmnn~evenwitb thedKnterflighttimeuftllcfirJtaDeandthelarge diffemminAV~.ItcmcsfromthefkttbattbeAV tOprwidefiXthencirarlarizationmar#rvasinthe finalorbitisbgertlmintkcaseoftheHohmam aanskr.
._. ::
..:.
‘...’
7.910
331
samedesigrlthmt(?vf4),buttheleaultwillbewoKe bCGlUWOfthCSlUdlCkWlSCiDSpCCiiiCimpulSeand
thllStwitbtheSamramjdmasS.FiIldly,ifWemaLe a9O%thmtl~evcnifthespecificimpllseisa littlebithighcr,thesiubsmicramjetwillkdesigned at M=1.7and then will be heavier.
7.850 . lntllisparqgrapb,wedlk3aIstbeploblemofthe
7.300 220 Table6 6. m lnthispfqrap&westdytbe~dthe dehxedthnrslby ilK?Qhgordecnasiogthe numberofmcket~~orthcwi&hofthe sllbmicramjqbutalsobycombiningtbelKeof dKUCOgilXStitbCttUbShCramjaatsllpasoniC spu!dAswcwillscE,tbislasts&diOnis~~
intemmdTOGWlmtlcadstoasubmicrcrrmja desigdtoworkona llamwerMachmmpberlaage.
comhedproQlrlsionwitha7O%~oftbe submnicramjetintheMachnumbcr~~1.7 upto2J.combhd~mcaasthotweuseat thesametimeandinacutainMxhmmbcrrange, therocbengiaeandthesllbaonic~togetha. Thatnwausalsoadccmseoftbespe&cinqdsed tbesubwicramjuandthenadeueascoftheSSTO pIdommm(dnetothehighet~ofLoxand LH~hrdinthem&etengiacwbicbatcusedina hgeIkhcltrange),aJWeCaaStZiILt&le8.BUtthe goaloftheamlbhdprapwamisootto~the vchideperbmmmbutwelltouseasubonic mqjudcsi~kmasmaUerMachmu&errange amillscittoitmease thespecifkimpukoft& mkuwlgineduringthecornbhd~ TkcasewingaambinedpqmlskmhfnM-1.7to Mp2.5 a Grrm M=6 to M-6.8 is evm mole amawivealldtlmwiukarmetkbasiccase~ -0p
Tabie 8 .
WW Inrhispamgmphadintkfolbwhgooe,we~
tbeproblemofthetlnustkvel-bytbemcket englnea(ofthemlmberofrocku~wetake)
aalbythesubsoJicramjet(orthewidthoftlle
332
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ramjct).Forthat,wenecdtoknowthe~vabofthe areaofthe.vchiclebascandthewidthofthcspace vchicktoknowifitispossibktopiaccthcsccngines onboard.ThecvaluationoftbedimensioI&ofthe spacev&icleisgivcnintheappe&x. Thethnlstofthemc&engincsiscalculatedas follows: Fz = NW-t .ToGW. ‘rhuefo~, the ratioRTWtfixthermmberofrodetcnginsandof coursctheweightofthcsera&ctcqincs.Figure5 ShowSthCCXiStUSof~optimalvalllCforRTWt (1.45). This optimal value is very CxI&bnt with reL[9]wbichgivcsauoptimalvahleinthcraugcd 1.3-1.5. Attbisoptimalpoinfwchavccaladatcdthebsc area (137.5 rn3 with the help of tie appendix (TGGW=271f V-2833 m’, SW77 & and HJ.1607). weknowakottlatthesLtlknIstiscqual to 393 tons (1.45*271),a value that can be reacbcd with 2 or 3 SSME(F&=177tat nominaJpower kvcl) whichhasancxitareaofabout4.1m’pclulginc. Thatmemlsthatwcdon0thavcalypnlbkmto~ thcroc&cngincstothebaseofthisspacevcllide.
performanccsarebettcrwiththestn#tdue.toits much higher spccitic impulse (see table 9). The iIlflIZIlCCofthCStX@il?$iSratherimpoMlt(ICdlUSioIl of2.3%ofTGGW)andmainlyallonstoavoidthe useofaibstrocketphascandalsotousetheram~ inasmaUerMachnumbcrrangc(Inthiscasethc ramjetis startedat Mach=2.5).
. . $&t+=?o+-=te quuaaonamsirtsillthe~oftheramjet width(sab)oriufbcttkchoiccofthccadeknt thenSb(and RSG(=SaWfSW).IfRSGinaegsa thUltheramjetwCightandtlUUSt)inaesses p~totheT0GWfbraamstautpaylo& Fi~6showstheinnuenceofRSGonT0GWand theanIqm&@vallleofRsGmax’.RsGmaxismt aconsbutbut ineascswithtbeRsG~wcnutc thatthtdistanasqarat@theRsGandRsGmax atrvcsdecreases.TbatmcanstbatRsG~its maJdmnmValUC(RSGmax)andthatitwillbCmOn dimallttofittheraq~intotbessTG.
ThenarcbvoplCbkmsinthcoptbbtionofthe &sedpointsofatrajexy.&~thenlation sllaxsbM** eetillgbetneentwo tb&thCChOilXofthedynsrmicpresSareaadthC A4achmmdxratcaIzh&dpoint. Inthispeuagq&wcshowonlytheMucnccofa changeafthevahlcofthcdynamicpressmeofone 6xaj point (i.e. the &au&ion point where tie last KBdatphasebtg&k&syatM=6.8andQoK=55 kPa).SO,~doQnotsolvetOb&thcproblanOfthC oftleiixalpoi&.Wejustshowits
-UseofaStn@tTable 9
TabklOshowstbcbiginfl-ofasnallvariation OfthCdp8lUiCpS3UXCatihCtl7Ul&i~aihatbgmodcaaipurclock.ctengiltcmodc
Ljustthekvclofthnutofaspacevchickisavery d&icntwaytoimprovcits ““““““% thisfzanauowtotlselcssadvanc&~ thcssro(hcavkrrau&smalkxMachmmIber xangeofthe Ia@& lowu collectionratio,...). 7.Mucnaoftheuseofastrq& Tbcpexm8KBofsuchanulgincalcd8su&cdin nz[lO] & [ll] and its weight (in fact its thnlst-ttb weight ratio) is &mated ti xeL[l2]. Tabk 9 aq?3msthclesllltobtai&forthc&signpoint(DP) dQurc6withthcreultabainalwitbastn#t instcadofthefirstmckctandc0&ined~ phass.Evenwithalowcrramjettbnwt~ ratio(@lctotheaMBina&stnqt-nynjctor ~-M&th=&i@=qaal~ap(lbt(thc m the Sal@, the ‘RSomaX=~.RSb+XgiVCSthClWXblUm auowebleramjetWidthCfpldtO2aWhiChiStkbtlSC width.
@ointK).Thebigdiffhm-fmmthebighcr tW?U@OUdUtillgthClastrodretphase (sccAVfbs)fixthccascsatahigberQoKThisisdue toalongexpu&up,whatwhatalongeralmo@Mc InamNu in rwckct mode (see Tp). It is also tonotctbatitisnotpossibktoduxease toabwcrvahwtlmn55kPabccausethcntbe r timcrequindforthepuu-upmanamrbcanmes ntgative cIp
*~thcliukcxisdngkhvemthcflxal~wc chowcPrcalizcthcascuItphaacatarnstantdynamic pmmKcwhatismoptlmal~asshowniu
ref.[l31. Bu&hae, we limit the dynamic pressme at maxbmlm75kpa.
333
48th IAF Congress
100’ 0
2 Flii
4 6 Mach amber (-)
2721
0.064
I 6
0.066
0.06
1.4
1.6 Rmt
1
0.056
270.
0.062
(-)
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48th IAF Congress
AOK(km) .. 27.6 ,“I 27.5 AVlits i_ 6.37.&j;:,,: 6.471 oan/sec) Tp (s) ‘. : &.: 1 13.59 Table 10
27.1 6.756 20.69
9. conchlsioIls The trajectory optimization is a very important point for the de-sign of a SST0 using in-flight LOX collection. It allows a gain of about 20 to 25 % in payload (for a fixed TGGW) in comparison with a poor tmje&ny optimization (fs or minimal drag). Thislargeimprovementcanallowustousealower colktion ratio and/or a heavier adkction plant and/orakaviersubsunicrarr#t_Thatcouldleadtoa SST0 using supersonic &flight LOX collection which is more comzrvative (less advanced t&UO~OgkS.
Theo@katiollofthecnlisephasedoesnothavzto bedonenecessarilytodecleaxTOGw,butwellto oprimketheinletconditionsinthec&uionplant and to avoid a too large precision on the flight pamme&s as, for example. on i in the case of the cruisephaseatamstantMachmmkrandcom$ant angle ofkkknce.. Thechoiceoftheorbitinjectionmethodisalsovery kqntantandcanpermitagainofabout4O%in telmsofTOGWin amqalkmwiththepowen?dall thewayfl@htinjazionWealsunotethattheTOGW isnotthemdyparamter:wehiwetoconsiderthe influawre of the telec0lmmmications to guide the spacevehicleaudalsotlxflighttimelength Weshowalsothatthechoiceofthedeliveredthrust leWlis~importanttoreducetheMachlNUk rangedtksubsonicramjet(caseoftheaxnbined pqndsion)butalsothatwecanimprovethespaoz vehicle@mmmcesbyimxa&lgthemlmberof rocketenginesandthewidthoftbesubsonkramjet lnthat~wehavejusttocheckifitispossibleto pUtthe~in&ktkspaceVehicle. Finally,weshowtkxtthechoiceofthefixedpointsof theQ#ctoryisveryimportant(e.g.a7%variationof TGGW kv a 1 kPa variation of QoK). This problem isstillilldeVe1opment Ref. AC.Dqer&M.L.Buck,“LiikgBodies-An attrxtk yodyr+; cordigumtion choice for z2.veh-s ML-D-U’-QS, Bktok M strengnars “Colleuion plant &mcte&ics FESTIP Technology Heat M-geme&WP9.3,FiualReport,Apr1997. RDrnevich&J.Nowobllski,“AixborneRotary separator Study”, NASA CR-191045, Dee 1992. MBarrZre,AJaunmtk,B.FraeijsdeVeub&e andJ.VandcnLerdrhovt.“Lapropukionpar fisca”. Sciences et Lctfres S.A., Likge, 1959.
5. S. Ehricke, “Space Flight Dynamks II: principles ofGuidedMissileDesign”.Mer@ l%l. 6. V. Chobo&~, “Grbital Mechanics II”, AlAA Education Series 96-42189, 19%. 7. M. oriffin & J. French, “Space Vehicle design”, AIAA Education Series 90-23705,199O. 8. C. Brown, “Spacecraft Prop&ion”, AIAA -on Series 95-11241, 1995. 9. H Immich & B. Hufenbach, “Analysis ofVariable Mixture Ratio of a RocJcet-Propellai SST0 Laucher”, AIAA 94-3314, Indkapolis, 27-29 Jun 1994. 10.R Chase, “The Design Evolution of a combined Cycle Airbreathing Powered S.S.T.O. Design Concept”, AIAA-95dolO. cbananooga 3-7 Apr 1995. ll.A Siebe&ar t P. Hewitt, “Rocket Rqjet Booskrsfbrsustai&highspeed~, AGARD, Paris, 14-17 April 1997. 12.J. Ve Qmparkm Between Ejector-Barr&t & Tuk-Ramjet fix TSTG s AIAA 93-5095, Munich, 30 NW - 3 13.D. Schmkt & J. VelapoU, “Gptimom Mission performance and Guidamx for w SSTO”. ALU 96-3904, San Diego, 29-31 Jul 19%.
Inthisappend&wedisaisstheproblemofthe evaluationofthewidthandthebeightoftbebaseof ourSSTG.Thevehicleshapethatweamskkhereis aconewithanel@tkal&ie(6gure7).Thisame becomesaconewithaclrudarbasewhen~~ equaltoO.44toObewiththeBlUXkd~ conflgumtion (see nE[lZ]). B with the Iwnvled@dtbe&ttalVehidevolmne(Vbot),tbe planfmmarea(Spf)andtheKllcbemaan’sparamter (T), = = calcuke the width 0, the kight (2b) andtkareaadtkSST0baseas6oLlaws:
yTOt= 2-b-h
b=2.27-a-
r
(to have b = a when r= 0.44)
@f=a-h
SIN= ma-b -(=-f@=?l 2a=hgthofthelaqpxisoftheellipse 2b==lellgthaftlIC~ercisoftkellipse h=kq#hoftkspacevehide s,=sl&ceoftheupticalbase. V&H
Tbcna2. 7r
Spf -2.27-r