487 Design aspects of launch vehicle sizing including air-breathing propulsion MSundaresan ISROVSSC,Engineer‘G’gsLVM3PROJECT,VikramSarabhaiSpaceCentre,Trivandrum,Kerala,695022,India. email:[email protected] Themanuscriptwasreceivedon21July2005andwasacceptedafterrevisionforpublicationon8May2006. DOI:10.1243/09544100JAERO30 Abstract: The overall sizing of launch vehicles is of interest, especially when air-breathing is alsoincluded.ThesizingofalaunchvehicleisdictatedbytheStateofArttechnologiespresent and the need to match the challenging demands of high-payload fraction, low cost, and also ensure reliability. This paper presents some of the important design requirements. An ideal velocityapproach,whichassumesvariousvelocitylosses,isgenerallyfollowedforinitialvehicle sizing. However, as this approach is approximate and sometimes incorrect, a new concept of accounting the drag and thrust losses during the atmospheric phase for conventional rockets and air-breathing launch vehicles using scramjet propulsion is evolved complementing the ideal velocity sizing approach. A simplistic two-dimensional trajectory simulation program with graphics for quick interactive design was developed for this purpose. The air-breathing launch vehicle trajectory is split into three flight phases. The sizing of the vehicle considering, especially, the intermediate air-breathing regime is also dealt with. A method to determine the maximum-load envelope expressed in terms of the product of flight dynamic pressure andangleofattack,namelyQ-alpha,forallweatherlaunchesusefulforinitialdesignpurposes is also suggested. The design program meant for initial design sizing purposes gives a quick insight on the vehicle performance prior to detailed design with minimum basic vehicle data forconventionalrocketsandalsoforair-breathingscramjetvehicles.Thevariousdesignfactors, suchasoptimumvelocityrequirementfortwostagetoorbitvehiclesandthesizingrequirement of the orbital stage after end of air-breathing phase, are also discussed through representative typicalvalues highlighting the design sensitivities. Keywords: launchvehicledesign,air-breathingvehiclesizing,trajectorydesignsizingprogram, launchvehicle performance 1 INTRODUCTION particular launch vehicle configuration meeting a definedmissionisanelaboratepainstakingprocess, The overall sizing of launch vehicles to meet a which also considers the state of art, development particular mission requirement is an important feasibility, cost and scheduleaspects. aspect, especially in the initial vehicle design phase. Towards the previous-mentioned factors, nume- The choice of the propulsion system and its sizing, rous studies are reported in the published literature apportionment of the stage system structural on the various aspects of launch vehicle design masses and deriving a broad mission sequence is including cost and reliability. As the area of launch very important, as it has a very large impact on the vehicle design is vast, studies are done in various launch vehicle development programme. As the phases from the initial configuration design to the overall reliability increases with lower number of detailed design stage including interactive design stage systems, it is also necessary to reduce the disciplines and overall optimization studies. Hence, system complexities and maintain operational it would be very difficult for any single paper to convenience. In actual practice, the selection of a cover the whole gamut of design issues. Still many JAERO30#IMechE2006 Proc.IMechEVol.220PartG:J.AerospaceEngineering Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 488 MSundaresan papers have addressed the overall configuration 2 DESIGN CONSIDERATIONS designaspect to alarge extent. Ryan and Townsend [1] address the salient per- Some of the important considerations for launch formance parameters of the space shuttle and vehicle sizing are mainly the following: (a) fixing the Saturn vehicle as a benchmark example, starting number of stages; (b) choice of propulsion system from the idealized rocket performance equation to and sizing; (c) range safety constraints; (d) state-of- determine the key design drivers. Robustness is the art technologies existing and near time goals; (e) key to uncoupling the design factors so that optimi- reliability and cost; (f) desired payload maximized to zation can occur, but typically robust designs define the extent possible; and (g) ground and launch low-performance systems and also the future space supportconstraintsandotherrelevantfactors.Inthe launch vehicles must develop new technologies to presentpaperthataddressesonthedesignconsider- reshapethedesignparametersensitivitiesofrobust- ations and sensitivities, certain assumptions are nessandperformancefunctions[1].Detailedstudies madewithrespecttotheidealvelocity,structuralfac- on the conceptual design of two types of reusable tors,andpropulsionIspforvariousstagesmainlyfor two stage to orbit (TSTO) vehicles considering the highlighting a particular trend or variation and impact of mission requirements and constraints are emphasizing a particular design feature. The ideal dealtwith in reference [2]. velocity required to meet a particular mission given Olds[3]dwellscomprehensivelyonthedesignofa inequation(1)canbeusedforinitialvehiclesizing reusable single stage to orbit (SSTO) vehicle making use of rocket-based combined cycle (RBCC), which ideal velocity(VI)¼VORB:VELþVLOSSES+VE:ROT (1) combines the operating modes of an ejector, The ideal velocity should be suitably chosen by the ramjet, scramjet, and rocket in a single engine. The designeronthebasisofexperienceonthevariousvel- RBCC SSTO design uses various advanced concep- ocitylossesduetodrag,thrust,gravitylosses,typeof tual disciplinary areas on performance, aerody- propulsion system, flight sequence, range safety namics, aero-heating, propulsion, and weight factors, and launch azimuth. The ideal velocity for estimation [3]. Incidentally, the author has derived whichthevehicleistobesizedisgivenby inspiration from reference 3 for writing the present paper as a SSTO air-breathing rocket (ABR) vehicle Xn Wi had served as the benchmark for the TSTO versions vehicle ideal velocity(V )¼g (cid:1) Isp (cid:1)log I i e WFi using scramjet propulsion. There are also various i¼1 reported literature in each or selective areas of (1a) design,tonameafewlikenaturalenvironmentdefi- nition for aerospace launch vehicle design given in Theoptimumsizingofthestageswithrespecttothe reference [4] and atmospheric wind models [5] propulsionsystemdependsonthestagingvelocityfor related to aerospace launchvehicle design. eachstage.Theoptimumstagingvelocitywilldepend The purpose of this paper is to discuss some of onthestagestructuralfactorsandpropulsionsystem the important design parameters and sensitivities performance,namelyIspandidealvelocityassumed. that need to be addressed during the initial con- Onthebasisoftheidealvelocitysizingapproach,the figuration design phase itself, so as to arrive at effectofstagingvelocityonthepayloadfractionfora the most appropriate workable specifications for TSTOvehicleisshowninFig.1foranexpendablefirst the propulsion modules and stages besides satis- fying the vehicle configuration requirements on staging and overall vehicle drag and loads with respect to Q-alpha load limits. The paper addresses towards initial sizing of launch vehicles with and without air-breathing. A simplistic design approach for sizing the launch vehicle complementing an ideal velocity methodis highlighted in the following sections. The paper has attempted to make use of typical design values or factors to highlight the design sensitivities in order to have a quantitative feel, especially for air-breathing vehicles using scramjet propulsion. The aim of the design is to arrive at a skeletal wire frame type of trajectory, which is feasible, leading to system specification after that detailing and detailed design studies Fig. 1 Effect of staging velocity with expendable first can follow. stage Proc.IMechEVol.220PartG:J.AerospaceEngineering JAERO30#IMechE2006 Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 Designaspectsoflaunchvehiclesizing 489 stage.Theidealvelocityassumedis9600m/s,andthe optimum staging velocity derived thus may pose payloadfraction(asatypicalexamplecase)isplotted spent stage impact problems. Hence, under such for an all-cryogenic TSTO vehicle, considering the cases, a near optimum staging velocity giving the stagestructuralfactorsfortheexpendableandreusa- maximum payload fraction can be suitably chosen, ble stage as 0.12 and 0.25, respectively. The ideal which can also consider the range safety consider- velocity for the TSTO vehicle given in equation (2) ationsof the spentboosterstage impact. has been derived suitably in terms of the first stage Generally,theinitialsizingoftherocketisbasedon total mass WT1 and W so as to arrive at the the ideal velocity requirement derived by experience PAYL payload fraction percentage that corresponds to a from various trajectory and mission studies. The particular staging velocity assumed for plotting the ideal velocity will include the various losses due to graphinFig.1,foraknownidealvelocity atmosphericdrag,thrustlossesinatmosphere,gravity losses including maneuvers, and so on. An overall (V)¼g (cid:1)Isp (cid:1)log WO þg (cid:1)Isp mission profile for a normal trajectory of an expen- I 1 e W (cid:2)WT1(1(cid:2)s) 2 dable rocket versus an ABR trajectory is shown in O 1 W (cid:2)WT1 Fig.2. (cid:1)log O (2) e (W (cid:2)WT1(cid:2)W )s þW Figure2alsoshowsthereusabilityofthefirststage O PAYL 2 PAYL landingatapredeterminedsite,whereasthesecond The first stage could also be reusable and can be of stage could be an expendable stage or reusable, different types, with respect to type of landing and which would depend on the mission requirements its location,namelyland orsea recoveryatpredeter- envisaged. For the air-breathing trajectory using mined sites. The reusable stage structural factors are scramjets, it can be considered to be essentially bound to vary say, if it is to land back with return in three phases namely: (a) ascent phase till Mach fuel supported by suitable propulsion systems numbers 2–4 (phase-I); (b) ABR phase that is from depending on whether it is to be recovered as a end of phase-I to Mach numbers that can be as sub-orbital or orbital stage. The designer has to high as .12 (phase-II); and (c) pull-up to orbit choose the suitable stage structural factors felt as phasein LEO(phase-III). appropriateforaparticularmission. The ascent phase could be a pure rocket, ejector- From Fig. 1, the optimum staging velocity for the ram rocket or turbo-ram rocket, etc. and the take- first stage is (cid:1)4500m/s and the payload fraction is off mode could be either horizontal or vertical. The 5.8 per cent for an expendable TSTO. Similarly, the air-breathing phase (phase-II) is essentially the optimum staging velocity for a reusable first stage rocketflightthroughatmospherepreferablyaltitudes can be arrived at. When there are range safety con- between 10 and 35km. The vehicle will be gaining siderations, there is every possibility that the the required velocity or Mach number, say 12, the Fig. 2 TypicaltrajectoryofexpendablerocketversusABR JAERO30#IMechE2006 Proc.IMechEVol.220PartG:J.AerospaceEngineering Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 490 MSundaresan maximum possible on the basis of ABR technology and thermal constraints. The flight will be at very low angle of attacks just enough to sustain a steady altitude gain within the desired constant dynamic pressure limit (cid:1)75kPa and as low as 30kPa during the end of ABR phase. Phase-II is critical in ABR vehicles. Depending on the terminal Mach number at the end of the ABR phase-II, the upper second stage mass and thrust requirements will be largely influenced. Lower the terminal ABR Mach number, greater will be the challenge on the propulsion system thrust rating requirements for the upper stage sizing. An SSTO vehicle using RBCC has an in-built pro- Fig. 3 TypicalABR-SSTO/TSTO:thrust/DRAGprofile pulsionsystemcapableofdeliveringadvantageously largerthrusteven during thebeginningofphase-III, i.e.therocketpull-uptoorbitphase[3].Inthecaseof TSTO rocket configurations, the above advantage, SSTO vehicle with 230 tonne lift-off weight. The dry namelyhigher thrust usuallyrequired during begin- empty weight was around 42ton with a core liquid ningofphase-IIIregime,couldbecome aconstraint hydrogen tank diameter of 6.8m. Considering the and sometimes difficult to achieve. Therefore, as an SSTO as a benchmark or reference configuration SSTO-ABR vehicles require lower stage structural [3], various TSTO-ABR versions using jettisionable factors and demanding propulsion requirements, solid boosters were conceived [7], which will give a the SSTO design will provide immense challenge similar payload to the above SSTO vehicle as and will be the dream and driving force for future depicted in Fig. 4. ABR vehicle systems. In air-breathing rockets, the generation of thrust and the presence of drag are critical during phase-II. Hence the initial vehicle sizing with 3 DESIGN SIZING PROGRAM respect to diameter, type of propulsion system for this phase, the estimation of drag and feasible Althoughthe initial sizing ofthe vehicleby theideal thrust pattern are first estimated. The method velocityapproachisrequired,itisveryapproximate, chosen to estimate the vehicle take-off mass is by and sometimes the vehicle so configured may be working backwards, namely considering the take- incorrect, especially for ABR vehicles due to the off thrust (vertical take-off and landing, VTOL) to errors in accounting for the vehicle drag with its be around three times the ABR thrust (T ) that ABR effect on vehicle velocity, and gravity losses, a would be generated, a design assumption purely strong function of the individual stage thrust levels. for initial sizing purposes. The maximum take-off Hence further to the ideal velocity sizing approach, mass of the vehicle should be around 20 per cent a two-dimensional trajectory design sizing program lower than the take-off thrust. The ABR thrust was developed considering the flat earth basically required at the beginning of phase-II depends on for arriving towards a feasible vehicle configuration. the operating dynamic pressure that is kept at con- Theprogramneedstheinitialsizingoftheindividual stant (cid:1)60–70kPa and the overall vehicle drag coef- stages including the stage structuralfactors,propul- ficient that will fix the approximate drag force. The sion data, vacuum Isp of stages, and total take-off ABR thrust is taken to be 2–2.5 times the drag mass as derived from ideal velocity estimates for force. In the design program, the equivalent C D conventional rockets highlighted in the earlier sec- value assumed is for the main core/booster stage tion. For ABR vehicles, the baseline input require- reference diameter (as against conventional wing ments to carry out the trajectory analyses is areas for computational convenience). The core/ discussed in the following sections. booster stage diameter is decided on the propellant requirement and to be compatible with the upper stages. 3.1 Additional design requirements Theenormousinfluenceoftheoverallvehicledrag for ABR rockets co-efficient, the ABR operating dynamic pressure The thrust/drag profile for a general ABR-TSTO and the diameter/size of the stage, is shown in rocket including an SSTO-ABR rocket [3] is shown Table 1 as an illustrative example. The amount of in Fig. 3. Olds [3] has graphically portrayed the fuel required during the ABR phase and the size of thrust/drag profile versus Mach number for an fuel tank (LH2) alone in order to accelerate the Proc.IMechEVol.220PartG:J.AerospaceEngineering JAERO30#IMechE2006 Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 Designaspectsoflaunchvehiclesizing 491 Fig. 4 Air-breathingstagevehicleconfiguration(schematic) vehiclefromMachnumber3to10asatypicalstudy ForTSTOvehicle,theboosterwillboostthevehicle [7]isshowninTable1.ItisseenfromTable1thatthe toMachnumber3orso,andisassumedtobeajet- ABRstagefuellengthtodiameterratioislower,when tisionablesolid-rocketmotor.However,itcouldbea theoveralldragcoefficientsarelowerandthevehicle high-pressure liquid propellant engine or, in operates at lower dynamic pressures in phase-II addition, can also work in the ejector mode-RBCC regime.Forvariousvehiclestage/boosterdiameters, for an SSTO vehicle [3]. For Turbo-fan rocket taking dynamic pressures and drag coefficients the corre- off in the horizontal mode and landing horizontally; sponding propellant required for the booster phase the T/W would be much lower and will be near and ABR cruise till Mach number 10 with solid pro- T value, and is not discussed in the Table 1. The ABR pellant for the booster phase is worked out as quantity of LH2 fuel required during the ABR shown in Table 1. phase-II is estimated on the basis of a average Table1 Sizingoftypicalair-breathingvehicles(forVTOLlaunchvehicle) Booster Propellant Dynamic ABRthrust thrust(cid:1)(kN) Max required FuelLH Fuel 2 pressure Co-efficient Drag (kN)2.5(cid:1) 3(cid:1)ABR T.O.mass(ton) toMach(cid:1)3 forABR tankL/D DIA(m) (kPa) ofdragCD(cid:3) (kN) DRAG thrust B.T/1.2(cid:1)g (ton)solid Mach3–10(ton) ratio 2.8 50 1.2 366 915 2740 228 100.0 22.6 18.5 50 0.35 107 267 801 67 29.2 6.3 5.25 30 1.2 220 550 1650 137 60.0 13.7 11.1 4.0 50 1.2 746 1865 5600 466 204.0 46.3 12.9 50 0.35 217 544 1640 136 59.5 13.7 3.6 30 1.2 449 1125 3370 280 122.0 28.0 7.7 5.0 50 0.35 340 850 2550 213 93 21.2 2.8 30 1.2 700 1754 5260 438 191 44.5 6.1 6.8 30 0.35 360 920 2760 230 (cid:1)76 23.0 1.1 SSTO3 (LH2þLOX) Note:(cid:3)REFDIAtakenforbooster/upperstageDIAquantitiativeestimatesareonlyindicativeinnature. JAERO30#IMechE2006 Proc.IMechEVol.220PartG:J.AerospaceEngineering Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 492 MSundaresan air-breathing Isp of (cid:1)1700s in order to get the additional velocity from Mach number 3 to 10. Hence we may broadly conclude that the LH2 fuel tank size reduces considerably with lower dynamic pressure and lower drag coefficient. Hence if the ABR configuration does not have a low aero-drag coefficients and the dynamic pressures are even in the high range of 60–80kPa, then the vehicle design could become impossible. Ideally, we would require a high thrust (which is a function of vehicle dynamic pressure) and with a very low overall drag co-efficient. This is a very challenging requirement, asithastoconsidertheintakesizingandpositioning, Fig. 6 Dragforceversusaltitude the booster phase, and orbital phase stage sizing requirementbesidesthesevereaerodynamicheating environment. Hence, the ABR configuration design delivered thrust and drag force profile, respectively, requires the thrust levels to be properly matched at observed in the flight tests. The variation pattern various flight phases in order to ensure the desired observed has been approximated as simple triangu- vehicle performance. The overall ABR vehicle con- larandhalfsineforthedeliveredthrustanddragpro- figuration design is difficult, especially for multi- file mainly from simplicity considerations. As the stages and on the arrangement of stages whether it above assumption had given encouraging sensible is in tandem or parallel. results the present method was adhered to. Regard- less of the above, better simulation profiles can be tried out on the basis of study of the numerous 3.2 Conventional rockets flightdata results. Itisgenerallyseenfromvariouslaunchvehicletra- 3.2.1 Aerodynamic velocitylosses jectories[5],thelossduetodragintermsofabooster For the conventional rockets, the flight phase is ormotorIspvaries(cid:1)10–20sforexpendablevehicles essentially in two phases, namely the atmospheric andmaybecalledasequivalentdragIsp.Theequival- flight phase (phase-I) and the flight phase to orbit entdragIspisderivedbyintegratingtheareaunderthe that is in near vacuum. As only the initial sizing of drag forcecurveand dividing by the propellantmass the vehicle is being addressed to, the program has consumed during the booster phase/stage of flight included a new concept of accounting the vehicle mainly in the atmospheric region. Hence, the drag drag and atmospheric thrust losses. The drag force Isp is considered to vary at every instant in flight in curve for conventional rockets follows close to a the form of a half sine given by an approximated half-sine curve, whereas the nozzle thrust losses equation(3).Onsimilarlinesasdiscussedinthecase can be assumed to follow a triangular distribution of vehicle drag, the equivalent thrust loss Isp due to varying from sea level thrust to vacuum thrust atmospheric thrust losses is (cid:1)15–20s the thrust levels. Figures 5 and 6 show the variation of flight losses varies nearly in a linear triangular fashion and is approximately given in equation (4). The program developed estimates the instantaneous velocity of therocketbyaccountingthedragandthrustvelocity losses through an equivalent Isp approach depicted in Fig. 7 and is described subsequently. The gravity losses are estimated as per a predetermined pitch trajectory on the basis of various vehicle trajectory studiesandthevehicleissteeredalong drag Isp (at any instant,t) ¼1:5(cid:1)equivalent drag Isp(cid:1)sin(p(cid:1)t=T ) (3) BO thrust loss Isp (at any instant,t) (cid:1) (cid:2) t ¼2:0(cid:1)equivalent thrust loss Isp(cid:1) 1(cid:2) T BO Fig. 5 Variation of actual delivered thrust versus (4) vacuumthrust Proc.IMechEVol.220PartG:J.AerospaceEngineering JAERO30#IMechE2006 Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 Designaspectsoflaunchvehiclesizing 493 Fig. 7 Dragandthrustlosses Fig. 8 Typicaldesignwindprofile delivered Isp important vehicledesignparameter bothfor vehicle (cid:1) (cid:2) load estimation and vehicle controllability studies. drag Isp thrust loss Isp ¼stage Isp(cid:1) 1(cid:2) (cid:2) The extent and need for vehicle trajectory wind- stage Isp stage Isp biasing or active load relief system can then be (5) decided on the basis of the actual wind profile and effective thrust (T ) its probability of occurrence at each of the key alti- eff tudes. Nevertheless, the maximum Q-alpha bound- ¼propellant mass flow rate (WPct) ary will give us the maximum possible loads at (cid:1)delivered Isp (6) various altitudes and the nature of load variation þ T during the entire flight regime. V ¼ EFF @t(cid:2)gt sin b (7) t M (cid:2)WP t Theaboveprogramhadbeendemonstrated[6]for Vt Ct conventional rockets with reasonable accuracy The above velocity equation is used to arrive at the within 30–40m/s on the relative velocity estimates orbitalvelocity(excludesearthrotationalcomponent) besides arriving at the various vehicle parameters, atthedesiredaltitudebysuitablypitchingthevehicle namely altitude, dynamic pressures, Q-alpha, flightpathangleb.Oncetheinstantaneousvelocityis range, instantaneous vehicle mass, and other such estimated the range and altitude, the point of spent design parameters. The results are compared with stageimpactcanbeeasilyestimated. the flight test results of the Operational Indian polar satellite launch vehicle and the above exercise was also done for other launch vehicles ranging from SLV-3 with a 40kg satellite to GSLV-MK2 that 3.2.2 Design winds carries a 2000kg GTO payload. The designer could Asanadditionalrequirement,thepossibilityofmaxi- improve on this prediction technique by going into mumpeakwindspeeds[5]occurring(95%),namely, a more elaborate three-dimensional trajectory pro- zonal (equatorial) and meridonial are considered as gram with spherical earth and assume suitable shown in Fig. 8. These winds are assumed to occur changes in the drag and thrust losses distribution at each of the key altitudes simultaneously as an pattern. extreme design condition (all weather design) Althoughthepresentprogramwasdoneusingthe during the atmospheric flightphase in the program. simplisticGWBASICsoftwarelanguage,theabilityto By including such a wind profile, corrected for the accommodate graphic presentations of the results, launch azimuth, and superimposing on the derived namely dynamic pressure, drag, thrust altitude, and vehicle instantaneous velocity allows us to get the range within the program itself had leant an easy maximum vehicle angle of attack and the envelope access for viewing the results and carrying out the of maximum Q-alpha (Parad) boundary or design necessary iterations effectively. A typical launch limits. The critical loads due to in-flight winds vehicle performance study during the initial flight would actually and possibly occur at any one of the period as derived from the design program is keyaltitudes(6–20km).Hence, theabove approach showninFig.9.Theflightdatapointsfortheinstan- givesustheworstcaseQ-alphadesignenvelopethat taneous velocity and dynamic pressures are also couldoccuratanytimeduringtheflightandisavery shown asdiscrete markerpointsfor comparison. JAERO30#IMechE2006 Proc.IMechEVol.220PartG:J.AerospaceEngineering Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 494 MSundaresan Fig. 9 Comparisonoftypicallaunchvehicleperformancefromtwo-dimensionalprogramresults withflightdata 3.3 Air-breathing rockets essentiallyanacceleratingcruisephase,thedynamic pressure will be aimed to be of near constant value In the case ofABR, the propulsion requirements are and will taper off steeply at the end of the ABR derivedmainlyonthebasisofthenearindependent phase-II. A typical drag/dynamic profile of an ABR natureofthethreeABRphases(i.e.phaseItophase is depicted in Fig. 10. In Fig. 10 during the ascent III) and the effect ofdrag on the performance ofthe phase, the drag force curve will be an incomplete ABR during the air-breathing cruise phase-II. In the near half-sine curve, as the air-breathing phase-II designprogram,theactualvehicledragandliftcoef- will take over at an altitude of 10–15km and the ficients are not required as these are estimated only drag pattern will be dictated by the ABR cruise after the initial design sizing is completed and phase characteristics as discussed in the following would require time consuming analyses and paragraph. supported by wind tunnel tests. However, when a workable trajectory is arrived at, the overall drag co-efficient (C ) can be specified meeting the par- D ticular vehicle configuration choice, which will ensure the required T /D ratio as derived from ABR the program results. 3.3.1 Drag profile for ABR rockets during the atmospheric phase (phase-Iand phase-II) During the ascent phase of the trajectory (phase-I), thedragIspwouldbehigherthanthenormalrockets as it dwells more in lower altitudes and would vary from 30 to 40s. In the case of rockets with air- breathing propulsion, both the dynamic pressure and drag pattern for the ascent phase would also follow partially the half-sine curve till the end of phase-IwhentheABRmodule/stagewillbeinitiated at a convenient altitude and desired Mach number. Fig. 10 Variation of dynamicpressure (typical)for an During the beginning of phase-II flight that is ABRvehicleduringphase-Iandphase-II Proc.IMechEVol.220PartG:J.AerospaceEngineering JAERO30#IMechE2006 Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 Designaspectsoflaunchvehiclesizing 495 Duringtheair-breathingphase(phase-II)inwhich the subsequent sections. For phase-I, we can see therocketgainsthevelocityfromsay,Machnumber that the delivered Isp pattern for the ABR rocket 2 (or 4) to 12, the drag force (D) is considerable in can also be worked out in a similar way to that of proportion to the air-breathing propulsion derived the conventional rockets; except that the thrust thrust (T ). This thrust also varies and decreases losses are near constant (sea level) and the drag ABR with increasing Mach number mainly due to lower force profile would vary similar to as shown in Ispathigheraltitudesarisingfromlowercombustion Fig. 10 for phase-I flight. The main governing efficiency at hypersonic regimes beside intake equations for deriving the vehicle instantaneous efficiency. velocity for phase-II is given subsequently 3.3.2 Instantaneous vehicle velocity estimation deliveredABR(T )¼propellantfuelmass eff during ABR phase-II flow rate(WPct)(cid:1)IspABR (9) AsitisnoteasilypossibletoestimatetheABRthrust @V T t ¼ EFF (ABRphase-IIflight, lift anditsdistributioninthebeginningstagesofvehicle @t M t sizing itself, the following method is suggested. trimmedfornearconstant‘Q’) (10) Generally,theratiooftheair-breathingthrustgener- ated during phase-II to drag, namely, T /D is ABR The vehicle instantaneous velocity estimation for desired to be around 2–2.5. This aspect is mainly phase-I and phase-III for ABR vehicle is similar to consideredinthedesignprograminwhichthedeliv- as given in section 3.2. ered or effective thrust is derived by reducing the The altitude, range, vehicle dynamic pressures, drag component. The air-breathing thrust at the and angle of attack due to winds are estimated beginning of phase-II is estimated as an initial esti- using the above derived velocity directly through mate from the vehicle drag force during the ABR simple trajectory equations and are not elaborated cruise phase on the basis of the selected vehicle in this paper. The flight path angle b is suitably stage/booster diameter and the desired overall drag varied on a initial predetermined path to meet the coefficient of the vehicle and operating dynamic desired velocity requirements at the end conditions pressureregime. of each phase of flight (i.e. phase-I to phase-III) Hence, the thrust T (propellant mass flow ABR rate(cid:1)Isp ) generated during the initiation of the and would require modifications of propulsion ABR inputs with respect to propellant loading and burn ABR cruise phase can be estimated as evident from time. During the ABR cruise phase-II, the vehicle the discussions above. The vehicle instantaneous flightpath(b)issoadjustedtogivetheneardesired velocity is derived using this effective thrust (that is constant dynamic pressure that will ensure the reducing the drag component) and the variation of required thrust. At the same time, the drag force is thrust follows from a typical anticipated ABR-Isp also plotted using the assumed overall C values profile versus Mach number. The ABR-Isp that D with instantaneous velocity generated to ensure could be taken for design would possibly vary from that the T/D ratios are nearly maintained. The 2300s at lower Mach numbers to 1100–900s at whole exercise is repeated untill the overall require- hypersonic Mach numbers of 12 or so. That is the mentsaremet.Althoughthisseemstobeanon-opti- T thrust profile during the ABR regime will ABR mum approach, it nevertheless serves the purpose followthe Ispprofile for initial launchvehicle sizing. deliveredABR-thrust¼(T (cid:2)drag) (8) ABR T T wheredrag¼ ABR for ¼2.5inphase-IIflight 3.3.3 Summary of design inputs andprogram 2:5 D highlight Nevertheless the whole ABR design is a highly The inputs for the program are (a) initial take-off iterative exercise. The design suggestions only serve massofthevehiclebasedonidealvelocityapproach to reduce the iterative exercise in the beginning andashighlightedinTable1forABR;(b)thebooster stagesofvehiclesizingandwillleadtoafirmskeletal thrust, Isp, flight path angle, maximum measured design over which the finer details can be built or peakwindspeeds(95percent)probabilityofoccur- worked out. Similarly, the sizing of the second rence at each of the key altitudes (8–20km), struc- stage,namelythefinalstagetoorbitcanbeindepen- tural masses, and atmospheric data; (c) for the ABR dently sized after assessing the terminal ABR Mach phase, the thrust distribution, Isp variation, C ; (d) D number that can be achieved considering various upper orbital stage propulsion thrust and Isp; (e) technology options, state of art, and feasibility. The flight path angle; (f) ejectable masses as desired. sizing aspects of the second stage are discussed in The program actually traces out the predetermined JAERO30#IMechE2006 Proc.IMechEVol.220PartG:J.AerospaceEngineering Downloaded from pig.sagepub.com at Purdue University on July 2, 2015 496 MSundaresan two-dimensional trajectory by consuming the boos- Table 2 Sizing of rocket from end of ABR phase to orbit terpropellant untillphase-I conditions areachieved (forLEOpayloadof10ton) and the booster thrust is terminated. The vehicle Velocity mass after booster burnout and ejection would atthe form the initial condition for phase-II flight. In this endof Stage manner, the whole trajectory is traced out meeting ABRphase-II Structural Propellant Diameter length (m/s) factor mass(ton) (M) (m) the end conditions and operating conditions for all the flight phasesspecified. 3700 1...0.20 1...50 1...12 Thewholetrajectorysimulationexercisecallingfor (nearM¼12) 2...0.25 2...75 4.0 2...16 an iterative procedure is programmed using GWBA- 3...0.275 3...125 3...28 SIC language and is made easier by an interactive 2400 1...0.15 1...75 1...16 mode having graphics inbuilt for this purpose. As (nearM¼8) the program was developed basically as an initial 2...0.20 2...150 4.0 2...32 engineering tool, it is limited to making system 3...0.22 3...300 3Large choicesandpredictamissionfeasibility.Itisadvan- tageousmainlybecausethenormalandaxialaerody- namic coefficients are not needed for initially ideal velocity that is further required from the end running the program. However, when the actual off ABR phase-II to the relative velocity required for aerodynamic coefficients are once estimated, the LEO orbit in addition to the velocity losses of drag force distribution can be calculated using the 1300m/s for a typical cryogenic (LOX/LH2) stage. derived vehicle instantaneous velocity and altitude The values shown in Table 2 are only indicative and and the revised drag pattern compared with the are mainly for portraying a particular trend as dis- initial assumptions. Any design mismatches arising cussed subsequently. The diameter 4m is again will be sorted out and a revised trajectory run can taken as a typical case for the rocket stage. The bemade.Thiscanbefollowedupbydetailedtrajec- stagediameterbasicallydependsontheoverallcon- torystudies,whichincludesliftingbodies,aftereach figuration sizing of the vehicle, the propellant loa- of the systemdesigns includingaerodynamic coeffi- ding, aerodynamics,and propulsion. cients are finalized. From Table 2, the dependency of the stage struc- tural factor and velocity at the end of air-breathing phase is clearly seen. The propellant mass require- 4 DESIGN CONSTRAINTS FOR SIZING ABR ment increases three times, i.e. 50–150t on for the ROCKETS FOR PHASE-III same structural factor of 0.20, when the velocity at the end of ABR phase is reduced from Mach Generally for ABR, the primary fuel choice is LH2/ number 12 to 8. The propellant mass is estimates LOX for both during the ABR phase-II and the for LOX/LH2 propellant that is normally low thrust second or final stage, which takes the payload to cryogenic-engines. The velocity losses are high for orbit. However, there are the following factors/con- low thrust to stage mass ratios and could be straints that influence the vehicle sizing to a large in some cases as high as 1500m/s from the end of extent namely: (a) low density of LH2 leads to large ABR phase-II, i.e. pull-up to orbit. On the basis tankage size; (b) terminal Mach number at the end of the above especially due to the limitations of of ABR phase-II; (c) rocket thrust available at the cryogenicstagethrust,sometimesitismorefeasible pull-up stage after end of ABR phase-II; (d) expend- to go in for a LOX/kerosene stage as it has a higher able or re-usable second stage. equivalent density and higher thrust rating. The The last three factors influence the second stage higher thrust capability engines allows for lower rocket sizing to a large extent and combining with velocity losses due to gravity from ABR pull-up to the first factor makes the design very challenging. orbit phase and can be aslow as 600m/s. The velocity losses due to gravity for the second HenceaLOX/keroseneupperstageiscompetitive, stage to orbit rocket for ABR can be as high as although the propellant mass is much larger. The 1500m/s compared with500m/s for a directrocket overall sizing of ABR vehicles is finally dictated by mode. Sometimes the mission will simply, just not the overall vehicle hypersonic drag coefficients, succeed because of the low thrust /weight ratios of which has to be kept low, perhaps between 0.35 cryogenic LOX/LH2 rockets combined with higher and 0.50, assuming reference area to be the main stage mass structural factors that are associated vehicle booster/rocket largest diameter. Figure 11 with re-usability. Table 2 shows typically the sensi- shows a typical design sizing curve for both LH2 tivity of the second stage propellant mass required andkerosenefuelsystems.Figure11showstheesti- with the variation of terminal Mach number at the mate of propellant mass, stage structural factors end of that phase. The second stage is sized for the versus overall stage volume required for every Proc.IMechEVol.220PartG:J.AerospaceEngineering JAERO30#IMechE2006 Downloaded from pig.sagepub.com at Purdue University on July 2, 2015