Comparison of two multidisciplinary optimization strategies for launch-vehicle design

R. D. Braun,* R. W. Powell,* R. A. Lepsch,* and D. O. Stanley*NASA Langley Research Centel: Hampton, Virginm 23681andI. M. Kroo tStanford University, Stanford, Califi_rnia 94305The investigation focuses on development of a rapid multidisciplinary analysLs and optimization capabilityfor launch-vehicle design. Two multidisciplinary optimization strategies in which the analyses are integrated indifferent manners are implemented and evaluated for solution of a single-stage-to-orbit launch-vehicle designproblem. Weights and sizing, propulsion, and trajectory i_sues are directly addressed in each optimization process.Additionally, the need to maintain a consistent vehicle model across the disciplines is discussed. Both solutionstrategies were shown to obtain similar solutions from two different starting points. These solutions suggests thata dual-fuel, single-stage-to-orbit vehicle with a dry weight of approximately 1.927 × 10s Ib, gross lit'loft weight of2.165 × 10_ Ib, and length of 181 ft is attainable. A comparison of the two approaches demonstrates that treatmentof disciplinary coupling has a direct effect on optimization convergence and the required computational effort. Incomparison with the first solution strategy, which is of the general form typically used within the launch vehicledesign community at present, the second optimization approach is shown to be 3-4 times more computationallyefficient.NomenclatureA, = nozzle exit area, f12c = nonlinear constraint vectorF_ = wing normal force, lbGLOW = vehicle gross liftoff weight, lbI_p = specific impulse, sJ = objective functionMR = mass ratioS,_f = reference aerodynamic surface area, ft2T = thrust, lbT W = thrust-to-weight ratiox = design variable vectorot = angle of attack, degZ = discipline compatibility toleranceSubscriptsc = computedvac = vacuumsl = sea levelIntroductionOR several years, various Earth-to-orbit transportation optionshave been examined with the goal of reducing operating costsrelative to the current U.S. launch fleet._'2 Many of these solutionshave focused on fully reusable systems employing various levels ofadvanced technology) Although a wide range of options have beenexamined, including single- and two-stage systems using rocketand/or air-breathing propulsion, current emphasis has been placedon single-stage-to-orbit, rocket-powered vehicles. 3-5 The design ofReceived Oct. 17, 1994; revision received Feb. 13, 1995; accepted forpublication Feb. 15, 1995. Copyright © 1995 by the American Institute ofAeronautics and Astronautics, Inc. No copyright is asserted in the UnitedStates under Title 17, US. Code. The U.S. Government has a royalty-freelicense to exercise all rights under the copyright claimed herein for Govern-mental purposes. All other rights are reserved by the copyright owner.*Aerospace Engineer, Space Systems and Concepts Division. MemberAIAAAssociate Professor, Department of Aeronautics and Astronautics. Mem-ber AIAAsuch a vehicle is a multidisciplinary process in which aerodynamics.propulsion, weights and sizing, structures, performance, heating, op-erations, and cost must be addressed. 5 Although it is imperative thateach of these disciplines be addressed at the conceptual design level,it is equally vital to be able to perform this multidisciplinary analysisand optimization rapidly so that the numerous design options maybe evaluated and understood.The present investigation focuses on development of a rapid mul-tidisciplinary analysis capability for launch-vehicle design. The spe-cific application chosen is that of a dual-fuel, single-stage-to-orbitlaunch vehicle. TWo multidisciplinary optimization strategies areimplemented and evaluated for the solution of this problem, and dif-ferences among the approaches are highlighted. Weights and sizing,propulsion, and trajectory issues are directly addressed ill the opti-mization processes. Additionally, the need to maintain a consistentvehicle model across the disciplines is discussed.404Problem Definition and Disciplinary AnalysesIn this analysis, design of a single-stage-to-orbit launch-vehicleincludes specification of the ascent trajectory through the initiallaunch azimuth, time of flighl, and pitch-angle history. Determina-tion of the appropriate component weights and sizes is performed,and the vehicle dry weight (delined as the vehicle weight with-out payload, propellant, fluids, or crew) is selected as the min-imization variable. Table 1 summarizes the design wtriables andconstraints that characterize this optimization problem. Propulsion-system characteristics to be optimized include the liftoff thrust-to-weight ratio, two nozzle area ratios, and two fuel-to-oxidizer mixtureratios. In this analysis, a dual-position nozzle is used to provide theperformance benefit of a smaller nozzle exit area at liftoff (to maxi-mize sea-level thrust) while allowing for a larger expansion at highaltitudes (to maximize vacuum thrust). Two mixture ratios requirespecification because the vehicle is operated in different propul-sive modes. Beginning with liftoff, hydrogen and kerosene are bothburned as fuel, but during a later portion of the ascent, hydrogenbecomes the sole fuel. Such a dual-fuel strategy has been shown toprovide significant dry-weight reductions. ¢'As listed in Table 1, thetransition time from mode 1 to mode 2 propulsion and the extensionof the dual-position noz7 re also optimally determined.The vehicle is sized t iver and return a 25,000-1b payload tothe Space Station folio, aunch from the Eastern Test Range at