941165 Results of a Rocket-Based Combined-Cycle SSTO ... · optimize the design of an advanced launch vehicle for human access to low earth orbit. The vehicle makes use of rocket-based

SAE TECHNICAL PAPER SERIES 941165

Results of a Rocket-BasedCombined-Cycle SSTO Design

Using Parametric MDO Methods

John R. OldsNorth Carolina State University

Aerospace AtlanticConference and Exposition

Dayton, OhioApril 18-22, 1994

400 COMMONWEALTH DRIVE, WARRENDALE, PA 15096-001 U.S.A. Tel:(412) 766-4841 Fax: (412) 776-5760

Results of a Rocket-Based Combined-Cycle SSTO DesignUsing Parametric MDO Methods

Dr. John R. Olds*N. C. State University, Raleigh, NC

ABSTRACT

This paper reports the results of the secondphase of a research project to characterize andoptimize the design of an advanced launch vehicle forhuman access to low earth orbit. The vehicle makesuse of rocket-based combined-cycle (RBCC)propulsion — a concept combining operating modes ofan ejector, ramjet, scramjet, and rocket in a singleengine. This research builds on previous work focusedon advanced multiple mode propulsion concepts andadvanced conical acceleration-class single-stage-to-orbit (SSTO) launch vehicles.

Three systems level design variables ofinterest were optimized using multidisciplinary designoptimization (MDO) techniques. Specifically,Taguchi’s method of robust design was used toidentify a combination of variables that minimize thevehicle sensitivity to unpredictable changes in engineweights and performance. In addition, a second-orderresponse surface method (RSM) was used toapproximate the design space and predict theminimum dry weight vehicle.

The optimized vehicle results (weights,dimensions, performance) are favorably comparedwith other SSTO designs including rocket andairbreathing concepts.

NOMENCLATURE

ACC advanced carbon-carbonAl-Li aluminum-lithiumANOM analysis of the mean

APAS aerodynamic preliminary analysis systemATR air-turborocketCt thrust coefficientCCD central composite designgc gravity constant (32.2 ft/s2)HABP hypersonic arbitrary body programI* rocket equation effective specific impulseIsp specific impulseIOC initial operating capabilityLH2 liquid hydrogenLOX liquid oxygenMDO multidisciplinary design optimizationMER mass estimating relationshipMR mass ratio (lift-off weight/insertion weight)NASP national aerospace planeOMS orbital maneuvering systemPEEK polyether-ether ketonePOST program to optimize simulated trajectoriesRBCC rocket-based combined-cycleRCS reaction control systemRSM response surface methodsS/N signal-to-noise ratioSSME space shuttle main engineSSTO single-stage-to-orbitTix-Al titanium-aluminideTPS thermal protection systemT/Wo lift-off thrust-to-weight ratioUDP unified distributed panel programVMR variable mixture ratio engine∆V velocity changeφ equivalence ratioθ cowl wrap angle

INTRODUCTION

NASA and the U.S. Department of Defensehave for many years studied advanced launch vehicleconcepts for transporting crew and cargo to and fromlow earth orbit. A variety of candidate concepts have

_________________________

* - visiting assistant professor, mechanical andaerospace engineering dept. member SAE.

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been considered including two-stage and single-stageconcepts, partially and fully reusable concepts, andvehicles powered by rocket and airbreathingpropulsion systems. Currently, designers believesingle-stage, fully reusable launch vehicles maybecome feasible within the next decade and a half withmoderate advances in technology.

Airbreathing SSTO concepts have beenadvocated as strong options due to their low overallgross weights, high average Isp’s, plentiful abortoptions, mission flexibility (including hypersoniccruise), and potential for aircraft-like operations. TheU.S. National Aerospace Plane (NASP) is such anoption [1,2].

Rocket powered vehicle advocates claimlower dry (empty) weights, high engine thrust-to-weight ratios, fewer propulsion/airframe complexities,and reduced technology requirements. Several rocketSSTO vehicles are candidates including wingedvehicles powered by either SSME-derivative engines[3] or dual-fuel concepts based on derivatives of theRussian RD-701 engine [4]. Non-winged conceptssuch as the Delta Clipper [5,6] are also beingexamined.

Multi-cycle and combined-cycle propulsionsystems have been studied as ways to combine the bestcharacteristics of airbreathing and rocket launchvehicles and to strike a balance between low grossweights and low dry weights (figure 1). Multi-cyclepropulsion concepts include separate systems for eachoperating mode (e.g. a turbojet system and a rocketsystem). These systems may be operated separately orin parallel in order to maximize the performance of theoverall vehicle. Combined-cycle propulsion systemsintegrate various operating modes into a single set ofhardware components to minimize redundant systemsand reduce propulsion system weight. Air liquefactioncycles and the rocket-based combined-cycles (RBCC)[7,8,9,10] are candidates from the latter set.

This paper reports the results of the secondphase of a two phased study to optimize the design ofa conical SSTO launch vehicle with RBCC propulsion.The study goal is to minimize vehicle dry weight (dryweight is considered a better indicator of vehicle costthan propellant dominated gross weight). The firstphase results were reported in reference 11. Several

systems level variables were established in phase 1.The present work establishes the remaining variablesand makes comparisons with alternate airbreathing androcket SSTO designs.

The RBCC SSTO design consists of manytightly coupled disciplinary analyses includingperformance, aerodynamics, aeroheating, propulsion,and weight estimation. Advanced conceptual-levelcomputer programs were used to perform much of theanalysis. In order to capture all of the complexities ofthe multivariable design, two techniques from the fieldof multidisciplinary design optimization (MDO) wereemployed — Taguchi’s method of robust design andsecond-order response surface methods.

VEHICLE DESCRIPTION

Mission and Guidelines

For the purpose of this research, the candidateRBCC SSTO was sized to deliver a 10,000 lb (4,536kg) payload to a polar parking orbit of 100 Nmi. x 100Nmi. x 90° (185 km x 185 km x 90°). A fictitiousfacility at Vandenberg Air Force Base, California wasassumed as the launch site. The vehicle payload bayvolume was set to 5,300 ft3 (150 m3). When sized forthe polar reference mission, the same vehicle will becapable of delivering slightly over 20,000 lbs (9,072kg) to a 100 Nmi. x 100 Nmi. x 28.5° orbit from alaunch site at Kennedy Space Center, Florida. Thepolar mission is similar to an early NASP design

Gro

ss W

eigh

t

Dry Weight

Combined-Cycle

Rockets

Airbreathers

Figure 1 - Potential for Combined-CyclePropulsion

3

reference mission and was chosen to allow easycomparison with several alternate vehicle concepts.

While recent design emphasis has focused ondesign for operations — larger margins, additionalabort options, lower operating costs, and lower systemcomplexities, the design philosophy employed for thepresent study is more closely related to design forperformance. Again, this philosophy is consistent withthat used for the rocket and airbreathing vehiclesprovided for comparison.

In addition to circularization and deorbit∆V’s, an on-orbit ∆V of 75 fps (25.6 m/s) is includedin the vehicle OMS system. Provisions are includedfor a crew of 2 and a mission duration of 48 hours(typical for payload delivery and return missions). Aweight margin of 10% was used for all dry weightcomponents.

Vehicle Configuration

Previous research on airbreathing launchvehicles [1,12] and specifically research on rocket-based combined-cycle SSTO’s [9,13,14] has identifiedpotential advantages of a conical vehicleconfiguration. Specifically, a conical configurationoffers well behaved forebody compression, highengine capture areas, and increased structural tankefficiencies. In some cases, circular cross section tanksmay be appreciably lighter than non-circular crosssection tanks of similar volume [15]. The basic vehicleconfiguration used for this research is shown in figure2. The vehicle is fully reusable.

Figure 2 - RBCC SSTO Configuration

The vehicle consists of a large conicalforebody enclosing the crew cabin, payload bay, andan integral LH2 tank. The cone half angle was set at 5°based on phase 1 results [11]. The engine cowl iswrapped around the cylindrical section of the LH2tank. The length of the cylindrical section isdetermined by inlet geometry and the cowl wrap angleis an optimization variable. A 180° cowl wrap angle isshown in figure 2. The non-integral LOX tank and therear cryogenic OMS propellant tanks are located in thevehicle tailcone. Small RCS tanks are also located inthe vehicle nose. The delta wing (based on previouswork) is 4% thick, has an aspect ratio of 1, and has aleading edge sweep angle of 76°[12,16]. The mainlanding gear is stored in unused regions of the cowl onthe bottom of the vehicle. The nose gear is deployedfrom an area below the payload bay. The payload isloaded and deployed through a set of hinged doors ontop of the payload bay.

Technologies and Materials

The RBCC SSTO is designed to have aninitial operating capability (IOC) between the years2005 and 2010. Many advanced technologies andmaterials are used throughout the design as shown intable 1.

Table 1 - Advanced Technologies

PropellantTanks

• Graphite/PEEK filament wound LH2 tank

• Al-Li LOX tank

• composite overwrapped OMS tanks

Structures &TPS

• TixAl wing, tailcone, cowl, nosecone

• advanced metallic & ACC TPS

• active LH2 cooling in high temp areas

Propulsion • advanced RBCC engine

• cryogenic OMS & RCS systems

Subsystems• electromechanical actuators

• advanced landing systems

• lightweight avionics and power systems

Single-stage-to-orbit vehicles are extremelysensitive to weight growth. Without the weight savingadvantages of these technologies, the present RBCCSSTO design would quickly become infeasible. Manyadvanced technologies are currently being developedunder the NASP technology program.

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RBCC Engine

The vehicle is powered by a rocket-basedcombined-cycle (RBCC) propulsion system. TheRBCC engine as been the subject of several researchefforts — in the mid-1960’s [17] and more recently[8,9,10,11,13,14]. Reference 17 presents the results ofMarquardt’s broad examination of several RBCCoptions including engines with and withoutsupercharging fans, engines with and without liquid aircycles, and engines with and without scramjetcapability. Two engines were identified as the mostviable candidates for application to future launchvehicles. Both selected engines (given the designations#10 and #12) were capable of scramjet operation, butneither employed a liquid air cycle. Engine #12 had asupercharging fan in the inlet to provide additionalperformance at low speeds. Engine #10 had no fan, butwas lighter weight. Weight statements andperformance information for these engines areavailable in reference 17.

In 1988, Foster [14] reevaluated and updatedthe RBCC engine data and compared several conicalSSTO launch vehicles based on RBCC propulsion(figure 3). The work demonstrated the potential weightand performance advantages of the concept. Inaddition, Foster’s work helped identify many of thekey systems level variables used in the present study.

Figure 3 - RBCC SSTO from Reference 14

One of the preferred engines from Foster’swork is shown in figure 4. It is based on engines fromreference 17. A slightly modified and moreparameterized version of this engine concept was usedfor the present research.

The RBCC engine is an air-augmentedLOX/LH2 engine capable of operation in four distinctmodes — ejector, ramjet, scramjet, and rocket. Inejector mode, the rocket primary serves as a “pump” toentrain additional atmospheric air through the inlet.The entrained air is mixed with the rocket primaryexhaust and additional fuel and burned in anafterburner fashion. The rocket primary is turned off inramjet and scramjet modes, and oxidizer is providedsolely by atmospheric air. In rocket mode, the inlet canbe closed off, and the engine operates as a highexpansion ratio rocket.

ANALYSIS METHODS

Several conceptual level computerizedanalysis programs were used to accomplish thisdesign. These tools were typically associated withdistinct disciplines, and the level of analysis detailobtained was commensurate with conceptualaerospace vehicle design. In some cases, highlydetailed analysis (e.g. full Navier-Stokes solutions foraerodynamic coefficients) was sacrificed in favor ofreduced analysis time and the ability to quicklyconsider several configurations.

Trajectory/Performance

Ascent trajectory analysis for the RBCCSSTO was performed using 3D POST (Program toOptimize Simulated Trajectories) [18]. POSTintegrates the equations of motion for a generalizedpoint mass vehicle from lift-off to orbital insertionthrough various user defined guidance phases. Theprogram automatically adjusts trajectory parameters inorder to optimize the ascent (minimize ascentpropellant in this case) while satisfying all constraints.

Inlet

Fan(optional)

Mixer/DiffuserCombustor

Exit

Turbopump Assembly

Primary Thrust Chamber Assembly Fuel Injector

Assembly

Thermal Choke

O

F

Figure 4 - RBCC Engine Layout

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The vehicle ascent was simulated using a vertical lift-off from Vandenberg AFB, ejector mode engineoperation to Mach 3, followed by ramjet/scramjetmode engine operation along a constant 2000 psf(95,760 Pa) dynamic pressure boundary to theprescribed airbreathing to rocket mode transition Machnumber (Mtr). The engine was operated in rocketmode for acceleration to an optimum intermediateparking orbit and OMS engines were used for the finalinsertion into a 100 Nmi. (185 km) circular polar orbit.For this study, the ascent was flown untrimmed andreentry trajectories were not considered.

POST requires aerodynamic tables, engineperformance tables, and vehicle weights and sizes asinputs. POST outputs include minimum propellantrequired (in the form of a mass ratio, MR), hydrogenfuel/total propellant ratio (changes depending onairbreathing portion of the trajectory), altitude,velocity, and angle-of-attack vs. time histories, and anindication of the maximum wing loading along thetrajectory.

Aerodynamics

Aerodynamic analysis was performed usingAPAS (Aerodynamic Preliminary Analysis System)[19] for selected Mach numbers and angles of attackthroughout the speed regime (0 to Mach 25). APASconsists of two modules — UDP forsubsonic/supersonic analysis and HABP forhypersonic analysis. UDP (Unified Distributed Panelprogram) uses a panel method with linearly varyingsources and vortices. Slender body theory is used toanalyze vehicle fuselages. Viscous and wave dragterms are added empirically. HABP (HypersonicArbitrary Body Program) uses appropriate impactpressure methods (e.g. modified Newtonian, tangentcone) for different sections of the vehicle. Empiricalbase drag calculations were included for both poweredand unpowered analyses.

For powered flight/ascent, the tailcone of theRBCC SSTO was treated as part of the engine nozzlein order to be consistent with available engine data[16]. The forebody, wings, and exterior cowl weretreated as aerodynamic surfaces. For unpowered flightand landing, the entire vehicle was treatedaerodynamically. The delta wing was scaled to provide

a landing speed of less than 200 knots (102.9 m/s) atan angle of attack of 15° based on the current landingweight. The vehicle wing was located longitudinally(fore to aft) in order to provide static stability (withflaps deflected) at typical hypersonic entry and landingconditions.

APAS requires vehicle geometry, landingweight, and c.g. location as inputs. Outputs producedby APAS include aerodynamic coefficients (Cl and Cdtables vs. Mach number and angle of attack), requiredwing planform area, landing configuration wingloading, and longitudinal wing position.

Aeroheating

Aerodynamic heating analysis was performedusing Miniver [20]. Miniver uses appropriate empiricalheating methods (e.g. Eckert reference enthalpy forflat plates, Cato/Johnson for swept cylinders, etc.) toestimate heat load and heating rates for variouslocations on the vehicle body during ascent. For eachRBCC SSTO configuration and ascent trajectory,radiation equilibrium temperatures were determinedalong the forebody windward and leeward centerlines,along the cowl windward and leeward centerlines, andalong a representative wing cross section for bothwindward and leeward sides. The majority of thethermal protection system (TPS) on the RBCC SSTOis assumed to be of a passive, radiative type — eitheradvanced carbon-carbon (ACC), Inconel tiles, orTitanium tiles. Although the total heat load forairbreathing vehicles is high, the weight of the TPS isprimarily determined by material characteristicsrequired to withstand the surface temperature.Therefore, the maximum surface temperatures for thesix reference lines above were used to select TPS typefor various acreage areas of the vehicle. For theforebody and cowl, the lower 120° of surface arc wasassociated with the windward centerline temperatureand the upper 240° of surface arc was associated withthe leeward surface temperature. ACC was used forsurface temperatures below 3000°F (1922°K), Inconelwas used for temperatures below 1800°F (1255°K),and Titanium was used for temperatures below 1200°F(922°K). In the case of the wing and cowl, the primarystructure of the RBCC SSTO, Titanium-AluminideBeta 21S, was capable of withstanding surfacetemperatures up to 1500° F (1089°K) without TPS.

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Active cooling methods consisting ofcirculating liquid hydrogen (LH2) through coolingpanels and passages and heat conduction methods likeheat pipes were used in high temperatures areas suchas the vehicle nose, the wing leading edges, the cowllip, and the area immediately aft of the internal enginenozzle. These areas will be exposed to temperaturesseveral times higher than ACC is capable ofwithstanding.

Miniver requires vehicle geometry and ascenttrajectory information (altitude, velocity, and angle-of-attack vs. time) as inputs. Miniver provides maximumradiation equilibrium temperatures for various bodylocations as outputs.

Propulsion

The RBCC engine is capable of operating infour distinct modes. Complete engine performanceinformation (thrust and Isp) was created for eachengine/vehicle configuration. The engine inlet/cowlgeometry was largely determined by the maximumairbreathing Mach number (Mtr). The maximum inletheight was determined by shock-on-lip conditions atMtr for the current forebody size and length. HigherMtr’s mandate smaller inlet heights. In no case was theinlet height allowed to exceed 4.5 ft (1.38 m). Inletlength was scaled with inlet height and Mtr. LargerMtr’s require longer inlet lengths. Engines wereconsidered modular. Each engine occupied about 20°of vehicle circumference. For example, there were 18separate engines for vehicles with 360° of cowl wrap.Cowl wrap angle and inlet height combined toprescribe inlet capture area (the annular area).Diffuser/mixer, combustor, and internal nozzle lengthswere determined based on capture area. Reference 21contains additional detail on engine scaling.

For ejector mode operation up to Mach 3,engine thrust and Isp tables vs. altitude and Machnumber were determined using a quasi-1Dcompressible flow model of each of the components inthe engine flow path. The technique and componentefficiencies are described in reference 17. In ejectormode, the thrust of the overall engine is largelygoverned by the mass flow rate through the rocketprimary (rather than by the entrained air through theinlet). For a given capture area, the size of the rocket

primary was increased or decreased in order to obtainthe required vehicle thrust-to-weight ratio (T/Wo) atlift-off. Therefore, the sea-level static ratio of rocketprimary mass flow to inlet air mass flow was notconstant across all designs.

Between Mach 3 and Mtr, the engine wasoperated in ramjet and then scramjet mode. Existingdata on ramjet/scramjet engine performance for awinged-cone [16] was used to approximate RBCCperformance in these modes. The existing data wastabulated as CtAref and Isp vs. Mach number, altitude,and equivalence ratio (φ). Ct is the thrust coefficientwhere:

thrust = (Ct Aref )Ac

Aref

q (1)

thrust = thrust in lbs (cowl-to-tail)q = freestream dynamic pressure in psf (ρV2/2)Ac = annular engine capture area in ft2

Aref = reference area in ref. 16 = 207 ft2

The equivalence ratio (φ) is the ratio of massflow rate of hydrogen fuel to the mass flow rate ofhydrogen required for stoichiometric combustion. φ issimilar to a throttling parameter for thrust, butincreasing φ’s have a negative impact on Isp. φ wasallowed to vary during ascent, but in order to provideadequate engine cooling at high Mach numbers,additional hydrogen circulation is required. Therefore,φ was not allowed to fall below a line formed by φ=1at Mach 12 and φ=2.5 at Mach 18. The vehicletailcone is considered part of the engine nozzle inreference 16 (i.e. all values are “cowl-to-tail”).

In rocket mode, the RBCC engine is treatedas a throttleable, high expansion ratio rocket enginecapable of a vacuum Isp of 470 sec [14]. Rocket modevacuum thrust was determined by multiplying Isp bythe maximum ejector weight flow rate and a variablethrottle setting. An equivalent exit area wasdetermined based on vehicle tailcone geometry.

The ratio of hydrogen fuel to total ascentpropellant consumed during ascent depends on thetrajectory and the amount of time spent in each enginemode. For ejector operation, the ejector componentoperates at stoichiometric mixture ratio (LOX/LH2 =

7

8), but additional hydrogen is used in order to burn theoxygen in the entrained air at stoichiometric ratios.Therefore, the ejector mode LOX/LH2 mixture ratiodepends on flight conditions, but is always less than 8.In ramjet and scramjet modes, all propellant consumedis hydrogen since oxygen is provided by theatmosphere. In rocket mode, the engine operates at anLOX/LH2 mixture ratio of 6. The ratio of hydrogenfuel to total ascent propellant is used to determine therelative sizes of the LH2 and LOX tanks.

The engine analysis requires initial thrustrequirements (to match a given T/Wo), transitionMach number, body circumference, and forebodylength as inputs. Engine analysis outputs includeejector mode performance tables, engine length,engine capture area, inlet height, engine weight, andejector component maximum mass flow rate.

Weights and Sizing

In order to match the required mass ratio(MR) from ascent analysis, the main hydrogen tankwas sized up or down while maintaining a constantforebody cone half-angle of 5°. All other tanks andgeometry were also resized accordingly (e.g LOX tankvolume is related to LH2 tank volume, tailcone size isrelated to LH2 tank diameter and aft cone angle). Alarger hydrogen tank will provide a larger MR. Duringthe resizing process, some geometry remained fixed.For example, the payload bay size and the crew cabinsize did not change when the LH2 tank was resized.Geometric resizing was accomplished using highlyinterdependent geometry equations on a computerizedspreadsheet. LH2 tank maximum diameter was used asthe independent variable. All other dimensions andgeometry were calculated from LH2 tank diameter.

For each trial LH2 tank diameter, a mass ratiowas determined by calculating the lift-off weight andthe insertion weight. The calculation of the weight of avehicle configuration is the most critical part ofconceptual vehicle design. In particular, single-stage-to-orbit launch vehicles are highly sensitive to smallchanges in estimated weight. The system, component,and subsystem weights for the RBCC SSTO weredetermined using relatively detailed mass estimatingrelationships (MER’s). MER’s relate the weight of acomponent to vehicle parameters such as size,

technology level, or loads. For example, wing weightis a function of size, construction method, geometry,and load. OMS propellant requirements are a functionof orbital vehicle weight, engine performance,propellant mixture ratio, and orbital velocity changerequirements. Most MER’s are derived fromregression analysis of historical data and areextrapolated to account for advanced technology. Acomplete list of MER’s used for this vehicle isavailable in reference 21. In most cases, the MER’s arederived from equations used for similar advancedSSTO vehicles including the airbreathing vehicle inreference 1 and the Tix-Al rocket vehicle in reference22. The RBCC engine weight is highly dependent onengine geometry and vehicle geometry. Specificweight values from engine point designs in reference14 and reference 17 were parameterized as noted inreference 21 for both airbreathing and rocketcomponents. These parameterized engine MER’s wereused to predict engine weight for each vehicle design.

The weight and sizing analyses are verytightly coupled. Vehicle weights were calculated onthe same spreadsheet as the vehicle geometry.Changes in LH2 tank diameter initiated an iterativesolution for new sizes, weights, and MR. LH2 tankdiameter was adjusted until the vehicle MR matchedthe required MR from ascent analysis. The weightsand sizing spreadsheet requires TPS types for variousacerage areas, LH2 propellant/total propellant ratio,required MR, peak wing loads, landing weight/wingreference area, engine dimensions, engine weights, andorbital circularization ∆V as inputs. Spreadsheetoutputs include vehicle geometry, lift-off weight,landing weight, c.g. location, and lift-off thrustrequirements.

DESIGN PROCESS

Based on the previous research of reference14, eight systems-level design variables wereoriginally selected for study in this project. Asreported in reference 11, five variables wereadequately determined in phase 1 (table 2).(Unfortunately the RBCC SSTO weights reported inreference 11 are not directly comparable to thosereported in this paper. Phase 2 work was performed ona vehicle with a larger payload bay, increased cowlstrut weights, and the elimination of a redundant

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margin on engine weights. The phase 2 results areabout 6% heavier in terms of dry weight than phase 1results, but phase 1 design variable results are stillconsidered valid). The goal of phase 2 of this projectwas to determine the optimum values for theremaining three variables (table 3 and figure 5). Theobjective was to minimize vehicle dry weight.

Table 2 - Phase 1 Design Variable Results

Variable Phase 1 Results

max. dynamic pressure 2000 psf

cone half angle 5°

stag. point heat rate limit 350 BTU/sq-ft-sec

supercharged engine? no (engine 10)

take-off mode vertical

Table 3 - Phase 2 Design Variables

Variable Low Range High Range

vehicle liftoff T/Wo 1.2 1.4

cowl wrap angle (θ) 180° 360°

scramjet to rockettransition Mach number

12 15

θ

5°

Figure 5 - Cowl Wrap Angle (θ)

Optimization Techniques

As reported in reference 11, Taguchi methodswere used to predict the near optimum settings of thedesign variables for phase 1. Taguchi methods arerelated to statistical-based design of experimentsmethods. In both methods, a fixed number ofexperimental points in the design space is strategicallyselected for analysis. The near-optimum values for thedesign variables are then predicted (interpolated) fromthe experimental results using an additive model[23,24,25]. Taguchi methods make use of orthogonalexperimental arrays and are suitable for

multidisciplinary problems with discrete variables[26]. Several successful aerospace design applicationshave been recently reported [27,28].

For phase 2 of this research, an optimizationwas performed using Taguchi’s method of robustdesign [23]. Robust design allows designers to selectvariable settings that will yield a reduced sensitivity touncontrollable, and potentially detrimental “noise”factors. Noise factors are assumed to be controllablefor the purpose of a series of experiments (i.e. pointdesigns), but are not controllable in the “real” world.Making use of orthogonal experimental arrays,Taguchi developed a technique based on signal-to-noise ratios (S/N) where each point design in anexperimental array is subjected to severalcombinations of noise factors. For each of these pointdesigns, an overall S/N is calculated as follows:

S/N = -10*log10 (14 ∑

i=1

4

yi2 ) (1)

Similar to basic Taguchi methods, the S/Nratio is maximized using an analysis of the mean(ANOM) technique on each term in an additive model.A larger S/N represents a lower sensitivity to noises,and therefore a more robust design.

For the RBCC SSTO design, three factorswere considered to be noises (table 4). In table 4, 0%represents no change from the nominal values used,+20% indicates a 20% increase (for weights), and -20% indicates a 20% drop in engine Isp at high Machnumbers. The objective of the robust designapplication was to select the values of the designvariables (table 3) that will provide a low vehicle dryweight while minimizing the vehicle’s sensitivity toengine weight growth (in the airbreathingcomponents), engine Isp degradation, and vehiclefuselage structural weight growth. That is, the robust

Table 4 - Noise Variables for Robust Design

Variable Low Range High Range

engine Isp degradation, Nisp -20% 0%

engine weight growth, Neng 0% +20%

vehicle fuselage weightgrowth, Nfuse

0% +20%

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vehicle’s dry weight should not grow excessively ifthe nominal estimates for any of the noise variableschanges by up to 20%. Additional detail is available inreference 21.

In an attempt to improve the accuracy of theoptimum, a second-order response surface method(RSM) was also employed in phase 2 (made possibleby the fact that there were only 3 continuous designvariables). In response surface methods, a centralcomposite design (CCD) experimental array is used todetermine a set of point designs that can be used to fita regression model of the form:

y = β0 + βi xi

i=1

n

∑ + βk xi x j

j = i+1

n

∑i=1

n

∑ + βl xi2

i=1

n

∑ (2)

y = dry weightxi = design variablesβi = equation constants

The second-order response surface can thenbe minimized using a non-linear optimizer. WhileRSM’s actually optimize an approximation to the truedesign space (second-order model), rather than theactual design space, they represent an excellentbalance between accuracy and design time.Techniques for constructing central composite designsare discussed in reference 29. A more detailedexplanation of the use of CCD’s and RSM’s for thisapplication is available in reference 21.

Generation of Candidate Designs

For each combination of design variables inan experimental array, a complete, converged solutionfor a candidate RBCC SSTO was generated. Eachdesign required several passes through all of thedisciplinary analysis tools. For a given T/Wo at lift-off, cowl wrap angle, and Mtr, the analysis proceededaccording to figure 6. Iteration for loop 1 wasperformed automatically on the weights and sizingspreadsheet. All variables converged to with atolerance of <.001% after about 10-12 automaticiterations. Iteration loop 2 was a manual iterationbetween two complex spreadsheets. Exchangedvariables generally converged to within a tolerance of<.01% in 3-4 iterations. Note that each iteration ofloop 2 also required a separate execution of loop 1.

Iteration loop 3 was a manual iteration betweenseveral separate disciplinary analysis tools. In eachcase, required information was manually exchangedbetween each tool. Loop 3 was repeated until MRconverged to within 1% — typically 3-4 iterations.Each iteration of loop 3 required separate completesolutions for loop 2 and loop 1.

Since most of the design codes were separate,non-integrated computer tools, the process to producea single, converged point design typically took 6-8hours of real time. However, actual required CPU timewas as much as two orders of magnitude lower. Thisdesign process could benefit tremendously from codeintegration (i.e. one code calling the next andautomatically exchanging data). However codeintegration is time consuming and may suffer frominflexibility. The present “loosely coupled”arrangement is probably more typical of design

POSTascent perform.

Miniveraero-heating

Weightestimation

Low speed enginesizing & perform.

APASaerodynamics

Initialize DesignVariables

Converged Design?

iteration loop 1

iteration loop 3

Geometry &sizing

iteration loop 2

Figure 6 - Analysis Loops

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processes as they exist in most industry andgovernment preliminary design organizations.

RESULTS

Robust Design

To capture all desired interaction effectsusing Taguchi’s method of robust design, the threedesign variables (table 3) were placed in an L8orthogonal array and the three noise variables (table 4)were placed in an L4 orthogonal array [21]. The twoarrays were arranged as shown in table 5. Each row –column intersection in the L8 by L4 arrangementrepresents a point in the design space. 32 complete,converged point designs were generated and the dryweights (in lbs) were tabulated. Signal-to-noise ratioswere calculated for each row using equation 1.

Experimental arrays with two variable levels(“settings”) are only capable of fitting linear models.Therefore, we would expect the predicted maximumS/N to occur at one of the corners of the design space

when each design variable is limited to “low” and“high” extremes as shown in table 3. That is, thepredicted maximum S/N will be at a point representedby a combination of either the low or high bound oneach design variable. Since there are only three designvariables and eight (23) possible combinations, weshould expect that one of the rows of the L8experimental array will correspond to the predictedmaximum S/N.

By using Taguchi’s orthogonal (i.e. balanced)experimental arrays, selection of the best design pointis reduced to a very simple process. Rather thanactually fitting the S/N data to a linear model, Taguchirecommends using an analysis of the mean (ANOM)table (table 6). Each design variable in the eight rowexperimental array has two settings — low and high.Since the array is balanced, there are 4 experiments ateach of the two settings (for each variable). Theaverage S/N values at each of the two settings arecalculated and placed in the ANOM table [23]. The β’sin table 6 correspond to the coefficient that each termwould have in a linear regression model based on

Table 5 - Dry Weight Results (lbs) for L8 by L4 Robust Design Experiments

0% 0% -20% -20% Nisp

0% 20% 0% 20% Neng

T/Wo Mtr θ 0% 20% 20% 0%Nfuse S/N

1.2 12 180° 92,498 118,623 119,865 109,261 -100.875

1.2 12 360° 125,091 161,283 154,076 151,943 -103.448

1.2 15 180° 92,121 123,229 131,979 117,139 -101.368

1.2 15 360° 118,731 162,323 166,299 165,534 -103.780

1.4 12 180° 92,871 120,909 122,145 110,463 -101.001

1.4 12 360° 124,903 161,361 153,085 151,701 -103.428

1.4 15 180° 91,685 124,938 135,532 118,943 -101.502

1.4 15 360° 118,690 161,095 164,714 163,823 -103.711

Table 6 - S/N ANOM Averages for Robust Design

T/Wo Mtr θ T/Wo x Mtr T/Wo x θ Mtr x θ

L -102.368 -102.188 -101.187 -102.394 -102.433 -102.437

H -102.411 -102.590 -103.592 -102.384 -102.346 -102.342

β’s -0.021 -0.201 -1.203 0.005 0.044 0.047

11

normalized design variable values between -1 and +1.The β’s are calculated as (H-L)/2.

Interaction effects (i.e. how one variabledepends on another) are represented by “cross-terms”.Cross terms are analogous to a product term betweentwo design variables in a regression model. Forexample, for rows where T/Wo is low (1.2) and Mtr islow (12), the cross term T/Wo x Mtr is high.Interaction effects between variables are also balancedfor each of their two settings, and the average S/N’sare listed in table 6. The actual settings of theinteraction terms depend on the settings of the designvariables.

In this case, the overall S/N will bemaximized if each design variable is set to the levelthat maximizes it’s individual S/N average (keeping inmind that selection of main variable settings will affectthe interaction settings). For the RBCC SSTO,selection of the low range for each of the three designvariables will produce the largest S/N (table 7). Thispoint corresponds to row #1 and a maximum S/N of -100.875. The magnitudes of the β’s in table 6 give arelative indication of the influence of each term on theoverall S/N. Note that the largest effect on S/N is dueto cowl wrap angle, θ. A θ of 180° is stronglypreferred. Mtr is the second most significant effect (12is best), while T/Wo shows very little effect.

Table 7 - Robust Design Variable Levels

T/Wo 1.2

Mtr 12

Cowl Wrap Angle, θ 180°

The objective of the robust design is tominimize the sensitivity to uncontrollable noisefactors, while still providing a low dry weight. At thenominal noise variable settings (column 1 from table5), the robust design variable settings produce a RBCCSSTO with a dry weight of 92,498 lbs (41,957 kg).However, the design variable combination in row #7(changing T/Wo to 1.4 and Mtr to 15) would produce alower vehicle dry weight of 91,685 lbs (41,588 kg).The advantage of the robust design is clearly evident,however, by scanning across row #1 and comparingthe relative weight increases to those in row #7. If the

engine performance is below current predictions, theengine weight grows, and/or the vehicle fuselageweight grows, then the robust vehicle design will berelatively less affected than the vehicle designed withsettings corresponding to row #7. Therefore, it wouldbe wise to sacrifice a small amount of dry weight atthe nominal noise settings in order to gain the benefitsof robustness.

As applied here, Taguchi’s method of robustdesign is essentially a linearization of the design spacein terms of S/N. The best settings for each designvariable were necessarily at one end of their allowablerange or the other. The true function for S/N couldhave a maximum somewhere inside the design space.Additional S/N benefit could probably be derived fromrelaxing the lower bounds on the design variables(particularly cowl wrap angle to a value less than180°). However, the results presented here are veryuseful in characterizing the design space. For example,an earlier transition from airbreathing to rocketpropulsion (i.e. a lower Mtr) is preferred if thedesigner is concerned about a possible degradation ofengine Isp at high speeds. However, if engineperformance meets or exceeds current predictions, ahigher Mtr (up to 15) will produce a lighter vehicle.

Second-Order Response Surface

In order to increase the accuracy of theoptimization and to create a better model for “what-if”type analysis, an extra set of point designs wasgenerated and added to the 32 experiments of table 5.Previous experiments were conducted at only twosettings for each variable — thereby yielding only alinear model. The seven additional points (one centerpoint and six “star” points) in table 8 allow theformation of a 39 row central composite design (CCD)experimental array and the use of a second-orderresponse surface model [21].

The 32 point designs performed for the robustdesign do not allow two factor interaction termsbetween noise variables to be estimated. The sevenruns added for the CCD allow estimation of second-order terms for the three main design variables, but notfor the noise variables. Both of the omitted effects areassumed to be small in this example.

12

A least squares regression fit of the 39experimental point designs yields the followingsecond-order model for dry weight (in lbs):

Dry Weight(lbs) =

126,668 +159T̂

W

+ 2,447M̂tr +18,310θ̂

−7,692 N̂isp + 6,821N̂eng +10,502 N̂ fuse

−85T̂

W* M̂tr

− 584

T̂

W* θ̂

− 55

T̂

W* N̂isp

+29T̂

W* N̂eng

+167

T̂

W* N̂ fuse

− 349(M̂tr * θ̂ )

−3,005(M̂tr * N̂isp ) + 508(M̂tr * N̂eng )

+963(M̂tr * N̂ fuse ) − 914(θ̂ * N̂isp )

+2,771(θ̂ * N̂eng ) − 263(θ̂ * N̂ fuse ) + 657T̂

W

2

+1,084(M̂tr )2 + 3,616(θ̂ )2

Equation 3 - Second-Order Response Surface

In equation 3, the three design variables andthree noise variables have been normalized so that anormalized value of -1 corresponds to the originalvariable low range and +1 corresponds to the originalvariable high range as given in tables 3 and 4respectively. Therefore, the variables on the right handside of equation 3 are dimensionless. The magnitudesof the equation coefficients indicate the relative impact

that each term will have on vehicle dry weight asvariables are moved from one end of their range toanother. For example, the cowl wrap angle has thelargest influence on vehicle dry weight, and the noisevariables have a significant impact. As with the S/Nanalysis, T/Wo has only a small influence on thedesign. Note the strong interaction between Mtr andengine Isp (Nisp). As engine Isp degrades (normalizedNisp becomes more negative), a lower (more negative)Mtr is preferred.

Equation 3 can be minimized (subject tovariable range limits). The point that minimizes dryweight is shown in table 9. As expected, the threenoise variables are optimized to their nominal(baseline values). Recall that any perturbations tonoises would have a negative impact on the vehicle. θis limited (somewhat artificially) by the lower end ofits allowable range. It is highly probable thatadditional dry weight savings could be realized with acowl wrap angle of less than 180°. As discussedpreviously, a Mtr near 15 tends to produce a lighter(but less robust) launch vehicle. The optimum Mtr fordry weight is 14.6. Again, T/Wo has only a smalleffect on the dry weight.

At the minimum conditions, the modelpredicts a dry weight of 89,660 lbs (40,670 kg). Anactual experiment at that point produced a vehicle dryweight of 91,578 lbs (41,540 kg) — an acceptabledifference of 2.1%. Recall that the previous lowest dryweight was 91,685 lbs (41,588 kg) at row #7, column#1 of the 32 experiment robust design array. Thedesign variable values are very similar for the twopoints. For this case, the second-order model does notimprove significantly on the linear model.

Table 8 - Additional Point Designs for CCD

T/Wo Mtr θ Nisp Neng Nfuse Dry Weight(lbs)

1.3 13.5 270° -10% +10% +10% 127,552

1.1 13.5 270° -10% +10% +10% 129,163

1.5 13.5 270° -10% +10% +10% 128,921

1.3 10.0 270° -10% +10% +10% 128,467

1.3 17.0 270° -10% +10% +10% 136,295

1.3 13.5 360° -10% +10% +10% 109,221

1.3 13.5 180° -10% +10% +10% 149,310

13

In addition to providing an approximation ofthe minimum vehicle dry weight, equation 3 is veryuseful to the designer for quickly answering “what-if”questions without having to reevaluate an entirevehicle point design. For example, the impacts ofengine Isp degradation or engine weight growth caneasily be approximated.

Final Vehicle Design

Even though the second-order responsesurface method produced the lowest dry weight, therobust design variable settings were selected for thefinal design (table 7). The robust design is lesssensitive to changes in the noise variables and only hasa slight weight penalty at nominal noise values.

The final RBCC SSTO configuration isshown in figure 7. The vehicle dry weight is 92,498lbs (41,957 kg) and the gross lift-off weight (fueled) is506,575 lbs (229,781 kg). The overall vehicle length is198 ft (60.35 m), the maximum LH2 tank diameter is22.3 ft (6.8 m), and the total engine length (cylindricalbody section) is 33.5 ft (10.2 m). The theoretical wingplanform area is 2,550 ft2 (237 m2). The required massratio (MR) for ascent is 4.393 and the total ascentpropellant mixture ratio (LOX/LH2) is 2.831. Moredetail on the vehicle geometry is available in reference21.

Reference 13 discusses the concept ofeffective specific impulse, I* , as a measure of theoverall vehicle Isp taking into account ascenttrajectory losses. For the RBCC SSTO, the effectivespecific impulse, I* , is 512 sec as calculated by therocket equation (equation 4). ∆Vt is the total inertialchange in velocity from launch to orbit insertion (i.e.the ideal ∆V minus drag, thrust vector, and gravity

losses). For the final design, the ideal ∆V is 32,893 ft/s(10,026 m/s) and the ∆Vt is 24,404 ft/s (7,438 m/s).

I* = ∆Vt

gc ln(MR)(4)

Figures 8a and 8b display the angle of attack(alpha), dynamic pressure, inertial velocity, andaltitude history for the optimized ascent trajectory forthe final vehicle design. An extremely simplifiedweight statement is listed in table 10. More detailedweight statement information is available in theappendices of reference 21.

For each point design in this study, newengine performance information (Isp and thrust) wasgenerated based on current engine geometry (inletheight, capture area), vehicle geometry (forebodyangle, body diameter), and ascent trajectory (airflowrates, velocities, altitudes). Graphs of cowl-to-tail Isp ,equivalence ratio (φ), aerodynamic drag, and cowl-to-tail thrust vs. Mach number for the final RBCC SSTOdesign and trajectory are given in figures 9 and 10.Note that equivalence ratio was limited to linearinterpolation between four reference point values. Thevalues for φ at each of the four reference points wereoptimized by POST for each ascent trajectory. Otherpoint design vehicles had different engine performancecharacteristics.

For the final vehicle, the engine weight,including cowl, is 23,338 lbs (10,586 kg). The sea-level static engine thrust-to-weight ratio is 26.04 inejector mode. Without the cowl, the engine thrust-to-weight ratio is 40.9.

Table 9 - Minimum Dry Weight for Second-OrderResponse Surface

T/Wo 1.27

Mtr 14.6

Cowl Wrap Angle, θ 180°

Nisp 0%

Neng 0%

Nfuse 0%

Figure 7 - Final RBCC SSTO Design

14

0 200 400 600 800 1000time (sec)

dynp (psf)

alpha (deg.)

alpha

dynp

20

10

0

-10

3000

2000

1000

0

Figure 8a - Dynamic Pressure and alpha vs. Time forFinal Design

time (sec)

0 200 400 600 800 1000

0

2

4

630000

20000

10000

0

veli

alt

alt (kft)veli (fps)

Figure 8b - Altitude and Inertial Velocity vs. Time forFinal Design

Mach

0 5 1510 20 25

0

1000

2000

3000

40001.2

1.0

0.8

0.6

0.4

φ isp

isp (sec)φ

scramjet-rockettransition

ejector-ramjettransition

Figure 9 - Isp and φ vs. Mach for Final Design

Mach0 5 1510 20 25

drag

thrust

thrust (Mlbs)

drag (Mlbs)

rocket mode(3g throttle)

ejector mode1.25

1.00

0.75

0.50

0.25

0

1.25

1.00

0.75

0.50

0.25

0

ramjet/scramjetmodes

Figure 10 - Thrust and Drag vs. Mach for Final Design

Table 10 - Simplified Weight Statement

Item lbs kg

Structures 37,685 17,094

TPS 11,297 5,124

Engine (no-cowl) 17,809 8,078

Other Weights 16,457 7,465

Margin (10%) 9,250 4,196

Dry Weight 92,498 41,957

Crew and Gear 1,890 857

Payload 10,000 4,536

Ascent Prop 391,265 177,477

Other Fluids 10,922 4,954

Gross Weight 506,575 229,781

The passive components of the vehicle’sthermal protection system are primarily determined byradiation equilibrium temperatures on various parts ofthe vehicle surface. For the final RBCC SSTO design,33% of the total body area (excluding wings) wasprotected by advanced carbon-carbon and 34% byInconel TPS. The remaining areas (including portionsof the wings) were either actively cooled or left astitanium-aluminide “hot structure” as appropriate.

ISSUES AND CONCERNS

The final vehicle design has been logicallyselected and care has been taken to account for all ofthe major effects in a very complex design space.However, there are a number of issues and concernspertaining to analysis methods and tools that remain tobe considered by future researchers. For variousreasons (time, lack of detailed expertise, etc.), the

15

following issues received only cursory treatment inthis research.

1) Lift-off Mode

Phase 1 of this research [11] indicated a clearweight advantage of vertical lift-off vs. horizontal lift-off. In some cases, horizontal lift-off vehicles werepenalized as much as 25,000 lbs (11,340 kg) in termsof dry weight. The RBCC engine operates in a highthrust ejector mode at lift-off. It can lift-off verticallyand take advantage of reduced wing weight andreduced landing gear requirements. However, sincecowl wrap angle was optimized to 180°, there is aproblem with asymmetric thrust at lift-off. Acombination of RCS augmentation from the nosethrusters, engine thrust vectoring, and aerodynamiccontrols (with sufficient speed) will be required toensure that the vehicle lifts-off smoothly and is able tomake an early transition to nearly horizontal flight.The engines may have to be separated into 90°modules and placed at the sides of the vehicle in orderto reduce asymmetric thrust. Additional work isneeded in this area.

2) Reentry Trajectory

The RBCC SSTO is designed for a shuttle-like unpowered, lifting reentry from orbit. The wingedcone configuration provides a relatively high lift-to-drag ratio (L/D = 1.7 at trimmed reentry conditions) socross range capability and reentry loads were notconsidered issues. However, the position of the cowl(particularly the cowl lip) on the lower surface of thevehicle will present a heating problem. During ascentthe cowl lip is actively cooled with hydrogen flowingto the engine. Reentry heating is not expected to be assevere as ascent heating, but may still require specialactive cooling provisions for some parts of the body.

3) Ascent Control and Trim

The ascent trajectory trim and aerodynamiccontrol requirements were not simulated for thisresearch. While angles of attack are relatively low, thelengthy acceleration time in the atmosphere couldcause trim losses to become significant. Decreases inramjet/scramjet performance at angles-of-attack werenot taken into account. In addition, precise

aerodynamic control and quick aerosurface reactiontimes will be required to maintain a constant dynamicpressure boundary during scramjet operation.Additional research is recommended in these areas todetermine the overall impact on the vehicle design.

4) Landing Conditions

Phase 1 of this research [11] demonstrated thedry weight advantage of a vehicle designed using theRBCC engine without the supercharging fan.However, engine with the supercharging fan hasadvantages at landing that should be considered —powered go-around, loiter, self-ferry, etc. Decisionmakers should consider whether these advantages areworth the additional vehicle weight incurred. Inaddition, aerodynamic performance during landingshould be examined with more detail analysis tools.The aerodynamic analysis tool used for this research isincapable of accurate prediction for conditions withthe large degree of separated flow likely to exist for acone at high angle of attack. Additional work couldhelp refine landing speed and wing loadingrequirements.

5) Vehicle Geometry

The research was limited to the optimizationof a few parameters of a conical configuration only.One of the primary advantages of a conical shape is ahigh engine capture area. However, since the cowlwrap angle was optimized to 180° (with indicationsthat the true optimum could be even lower), thequestion is raised as to whether a conical configurationis the preferred geometry. There are structuraladvantages to the circular cross section propellant tankin a conical geometry, but the upper surface of thecone compresses air that is not fed into an engineresulting in increased drag. Alternate vehicleconfigurations (including those with 2-D inletcompression surfaces) should be considered todetermine the advantages of one shape over another. Ifthe shape is changed, most of the systems-level designvariables will also have to be reconsidered. It isunreasonable to assume that optimized variables likeT/Wo and Mtr are independent of vehicle shape.Multidisciplinary design optimization (MDO) toolssuch as those employed in the current research wouldbe valuable in such a shape comparison study.

16

VEHICLE COMPARISONS

In reference 30, Freeman compares severaladvanced launch vehicle design options. Four of thevehicles are advanced technology SSTO’s — anSSME powered rocket, a rocket with a variablemixture ratio (VMR)/dual expansion nozzle engine, amulti-cycle SSTO combining air-turborocket (ATR)and rocket propulsion, and an advanced conicalairbreather combining a turbo-based low speed cycle,ramjet, scramjet, and rocket modes. Wilhite [22] laterupdated and improved the structural MERs for the tworocket vehicles. The two airbreathing concepts arehorizontal launch.

Freeman’s vehicles are all designed to similarguidelines as the current RBCC SSTO (i.e. design forperformance, advanced technologies, 10% dry weightmargins, 10,000 lb (4,536 kg) payload to a 100 Nmi.(185 km) circular polar orbit, small crew sizes, andtwo day mission duration). Some of Freeman’sconcepts do employ slush hydrogen propellants.However, comparisons to the current vehicle areappropriate. These four concepts are shown with thecurrent vehicle in figure 11.

The conical airbreather (conical AB) SSTO isvery similar in geometry to the RBCC SSTO vehicle,but there are several distinct differences. The RBCCSSTO uses ejector mode operation for the initial stageof flight. The conical airbreather uses a turbo-basedlow speed cycle. The RBCC engine has a lower Isp inejector mode than the turbo-based low speed cycle, butthe RBCC engine is considerably lighter for a giventhrust. In addition, the cowl wrap angle on the conicalairbreather is 360° compared to 180° for the RBCCSSTO. But perhaps most significant is the airbreathingto rocket transition (Mtr) during ascent. The RBCCSSTO transitions at Mach 12 while the conicalairbreather remains in scramjet mode to over Mach 20!

The gross weights and dry weights of the fivedesign options are shown in table 11 and figures 12and 13. Wilhite’s updated structural MER’s have beenapplied to both rocket vehicles. The updated VMRrocket was previously published in reference 22. TheRBCC SSTO compares very favorably in terms ofboth dry weight and gross weight. It is neither thelightest dry weight (the VMR rocket is lighter) nor thelightest gross weight (the conical AB is lighter), but itis second in both cases. This result is consistent withthe earlier hypothesis that a combined-cycle vehiclemight lie between rockets and airbreathers (figure 1),but the RBCC SSTO results lie closer to the preferredextreme than expected.

Table 11 - Advanced SSTO Comparisons

ConceptDry

Weight(klbs)

GrossWeight(klbs)

BodyLength

(ft)

VMR Rocket 90 1,108 125

SSME Rocket 99 1,107 134

RBCC SSTO 92 507 198

Conical AB 157 451 220

ATR SSTO 214 1,087 210

Although airbreathing engines tend to havehigher Isp’s than rocket engines, the rocket engineshave a significant advantage in terms of engine sea-level thrust-to-weight ratio as shown in figure 14.Airbreathing engines are heavier due to inlets, cowls,etc. Note, the T/Wo for the ATR SSTO is for the air-turborocket at sea level. The vehicle also switches to

SSME Rocket

VMR Rocket

ATR Airbreather

Conical Airbreather

RBCC SSTO

Length (ft)

2001000

Figure 11 - SSTO Design Options

17

an SSME-derived rocket engine at higher Machnumbers. The RBCC SSTO engine T/Wo lies betweenthe airbreathing and rocket extremes.

All of the values used for these comparisonsare the results of conceptual, not detailed, design. Theactual numbers are sure to change as the analysis isrefined and some of the issues and concerns areresolved for all of the vehicles. In fact, all of thevehicles will need some adjustments to make themmore “design for operations” oriented. However, therelatively favorable comparisons indicate that theRBCC SSTO is a very viable option for a nextgeneration launch vehicle. The vehicle, andparticularly the propulsion cycle, should continue toreceive attention from advanced vehicle designers anddecision makers.

CONCLUSIONS

A conical SSTO launch vehicle using rocket-based combined-cycle propulsion was successfullydesigned and optimized by using multidisciplinarydesign optimization tools. Three systems-level designvariables were determined. Five design variables hadbeen determined in an earlier phase of this study. Asecond-order response surface was created toapproximate the changes in dry weight as the designvariables are changed. The second-order modelenables designers to quickly answer “what-if”questions about design changes.

Perhaps the most important conclusion is thatthe cowl wrap angle should be 180° (or less) ratherthan 360° as favored by previous researchers. Thecowl wrap angle has the most significant effect onoverall vehicle dry weight of all the variablesconsidered. A larger cowl wrap angle produces alarger capture area and a higher thrust. These effectscombine to produce a lower vehicle mass ratio, butthis advantage is far outweighed by the increase inengine and cowl weight so that the resulting overallvehicle dry weight increase. Therefore, the lower cowlwrap angle (and lower engine weight) is preferred.This conclusion is highly dependent on the thrust-to-weight ratio of the airbreathing engine components.

Using Taguchi’s method of robust design, itwas determined that a scramjet-to-rocket modetransition Mach number of 12 will produce a vehiclethat is less sensitive to unpredicted changes high speed

VMRRocket

SSMERocket

RBCC SSTO

Conical AB

ATRSSTO

0

50

100

150

200

250

Figure 12 - Dry Weight (klbs) Comparison

VMRRocket

SSMERocket

RBCC SSTO

Conical AB

ATRSSTO

0

200

400

600

800

1000

1200

Figure 13 - Gross Weight (klbs) Comparison

VMRRocket

SSMERocket

RBCC SSTO

Conical AB

ATRSSTO

0

40

80

120

160

Figure 14 - Engine Installed T/Wo Comparison

18

engine performance, engine weight, and body weight.While a Mtr of close to 15 provides a slightly betterdry weight, the advantages of robustness wereconsidered more significant. Vehicles with higherMtr’s use a relatively higher percentage of LH2 fueland tend to have lighter gross weights and lowerMR’s. In this case the advantage is reflected in lowerdry weights. However, this conclusion is highlydependent on ramjet/scramjet engine Isp (hence theargument for robust design). Significant degradationsof engine Isp could quickly erode the advantages ofhigher transition Mach numbers. Therefore, the morerobust Mtr of 12 was selected for the final vehicledesign in this study.

Throughout the design process, the initialvehicle lift-off T/Wo was shown to be one of the leastsignificant effects on dry weight and S/N. Higher lift-off T/Wo vehicles have lower gravity losses, acceleratefaster to Mach 3, and therefore have more time inairbreathing modes. The advantages translate to alower MR. However, these advantages are almostexactly canceled by the increase in ejector componentengine weight.

When compared to other advanced launchvehicle concepts, the RBCC SSTO proved to be verycompetitive. Advocates for combined-cycle propulsionargue that there is a potential to combine the bestcharacteristics of rocket and airbreathing propulsion.This was largely proven to be true. The RBCC SSTOhas a dry weight comparable to a rocket and a grossweight comparable to an airbreathing vehicle.

The MDO tools used (robust design andsecond-order response surface methods) were veryimportant to the success of this research. Oldfashioned “one-variable-at-a-time” trade studies wouldhave been inadequate in the multivariable, complexdesign space of this vehicle. The growing field ofMDO should continue to receive support andencouragement.

RECOMMENDATIONS

In addition to the resolution of the issues andconcerns mentioned in a previous section, there areseveral areas where additional research isrecommended. These areas are related specifically to

the conical RBCC design and the efforts to determinethe optimum variable settings and to characterize thevehicle design space.

1) Extend the variable range for cowl wrap angle tovalues below 180°. Indications are that the trueoptimum lies below 180° and that significantweight savings could be obtained. Additionalexperimental point designs will be required toensure that the optimum is interpolated (rather thanextrapolated) from known point designs.

2) Include additional noise variables in the robustdesign technique. The method was very successfulat locating a robust design point. Additional noisevariables could include payload weight growth, dryweight margin growth, and boundary layertransition criteria (for heating).

ACKNOWLEDGMENTS

This work was supported by cooperativeagreement number NCC1-168 between North CarolinaState University and NASA-Langley Research Centerand by NASA Grant NAGW-1331 to the MarsMission Research Center at North Carolina StateUniversity. The author also appreciates the supportand assistance of Dr. Bill Escher at NASA-HQ, DickFoster at Astronautics Corporation, Dr. GeraldWalberg at NCSU, Dr. Resit Unal at Old DominionUniversity, Dr. Alan Wilhite at NASA-LaRC, andmembers of the Vehicle Analysis Branch at NASA-LaRC including Doug Stanley, Roger Lepsch, DickPowell, Walt Engelund, Ian “Mac” MacConochie,Larry Rowell, and Kay Wurster.

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