MULTI-DISCIPLINARY DESIGN OPTIMIZATION STRATEGY IN MULTI-STAGE LAUNCH VEHICLE CONCEPTUAL DESIGN

1ST Progress Seminar Report

Submitted towards partial fulfillment of the requirement for the award of degree of Doctor of Philosophy

(Aerospace Engineering)

by

C.Geethaikrishnan (Roll No. 02401702)

Under the Guidance of

Prof. P.M. Mujumdar Prof. K. Sudhakar

Department of Aerospace Engineering Indian Institute of Technology, Bombay

August, 2003

i

CONTENTS

Page.No.

Table of contents i

Abbreviations ii

Nomenclature ii

List of Table iii

List of Figures iii

1. Introduction 1

2. Launch Vehicle Conceptual Design Process 3

3. Literature review on MDO works related to Launch Vehicle Design 7

4. Motivation for present research effort 15

5. Preliminary work on MDO strategy in conceptual design 16

6. Conclusions 20

7. References 21

ii

Abbreviation LV - Launch Vehicle

MDO - Multidisciplinary Design Optimisation

POST - Program to Optimise Simulated Trajectories

T/W - Thrust to Weight Ratio

GLOW - Gross Lift Off Weight

FASTPASS - Flexible analysis for synthesis trajectory and performance for

advanced space systems

SWORD - Strategic Weapon Optimisation for rapid Design

AMLS - Advanced Manned Launch System)

RLV - Reusable Launch Vehicle

Nomenclature SREF Reference Area

∆Vloss Velocity loss

∆V Velocity requirement

∆V1 First stage velocity increment

Isp1 Specific impulse of first stage

Isp2 Specific impulse of second stage

σ1 Structural factor of first stage

σ2 Structural factor of second stage

ms1 Structural mass of first stage

ms2 Structural mass of second stage

mp1 Propellant mass of first stage

mp2 Propellant mass of second stage

mpl Mass of payload

iii

List of Tables

Table No. Caption Page. No 1. Comparison of three MDO strategies 10

List of Figures

Fig. No. Caption Page. No.

2.1 Launch Vehicle conceptual design process 3

2.2 Coupling among disciplines in Launch Vehicle Design process 4

2.3 Vehicle sizing / performance cycle 4

2.4 Lift-off T/W trade for AMLS Vehicle 5

3.1 Iterative-loop solution strategy 8

3.2 Sequential compatibility constraint strategy 8

3.3 Collaborate optimization architecture for launch vehicle design 10

3.4 Multistep sequential procedure 12

3.5 Schematic Diagram of decomposition of segments 14

3.6 Decomposition formulation for two stage to orbit manuvere 14

5.1 Liftoff weight Vs first stage velocity 18

5.2 Payload fraction Vs first stage velocity 18

5.3 Flow diagram of preliminary study on conceptual design of launch vehicle 18

1

Chapter 1

Introduction

The design of large, complex system such as launch vehicle requires making

appropriate compromises to achieve balance among many coupled objectives such as

high performance, safety, simple operation and low cost. The earlier in the design process

that these compromises can be understood, the greater the potential for reduction of

technical, schedule and cost risks. The conceptual design is intended to reveal trends and

allow relative comparisons among alternatives early in the process while design

flexibility exists and before a large percentage of life cost are committed. The launch

vehicle conceptual design process produces a configuration, usually driven toward high

performance (often translated as low weight) for a specified mission requirement.

Configuration specification includes definition of number of stages external geometry

and internal layout, technology selection, mass properties, performance estimates,

operational scenario, and, perhaps, cost estimates. The difficulties associated with

conceptual design are (i) conceptual design is characterized by a low level system and

(ii)the relationships among design objectives and the conceptual design parameters are

often not well modeled or understood. This results in probably inefficient final design,

leaving room for significant improvements in performance and reduction in life costs. To

improve results during the conceptual design phase at least two emphases must be

pursued: (i)Improvement of disciplinary analysis, modeling and tools that capture, with

sufficient fidelity, the major relationships among design variables and system objectives

and (ii) the development of methods for coordinating the engineering analyses and

optimizing the total launch vehicle system [1].

The second objective can be achieved by the application of multidisciplinary

design optimization(MDO) in conceptual design level. A complex interrelation exists

between mission requirements and constraints, trajectory shaping, propulsion, weights

and loads with conflicting goals which has to be matched by an appropriate optimization

strategy. MDO involves the coordination of multidisciplinary analyses to realize more

effective solutions during the design and optimization of complex systems. It will allow

system engineers to systematically explore the vast trade space in an intelligent manner

and consider many more architectures during the conceptual design phase before

converging on the final design.

2

The progress made with respect to research efforts on MDO strategy in

concurrent optimization of multi-stage launch vehicle configuration and trajectory is

presented in this report. Launch vehicle conceptual design process is explained in

Chapter 2. The works, related to the topic of interest, available in literature is

highlighted in Chapter 3. The next chapter briefs about the motivation for the present

research effort. Chapter 5 presents preliminary efforts made in the proposed work. The

conclusions are given in Chapter 6.

3

Chapter 2

Launch vehicle conceptual design process

The conceptual design of launch vehicle is highly coupled and significant data

exchange and iterations are often required among discipline and disciplinary tools as

shown in Fig 2.1

The process includes: i) specification of the mission requirements (e.g., payload

size, mass, destination, environmental constraints, on-orbit operations); ii) selection of a

vehicle approach (e.g., single or multiple stages, rocket or airbreather , expendable or

reusable, etc.,); iii) selection of associated operational scenarios (including assembly,

launch site, recovery ); iv) selection of technologies (e.g., structural materials, thermal

protection system, avionics, propulsion), v) creation of a physical layout and surface

geometry that will contain the payload, subsystems, and support equipment; vi)

estimation of aerodynamics (subsonic, supersonic, hypersonic); vii) calculation of

trajectory and flight environment; viii) execution of structural, heating, and controls

analyses based on the flight environment; ix) estimation of the vehicle weights,

dimensions and center of gravity based on mission, layout, environment and chosen

technologies and x) feedback of these results for modification and optimization of the

overall system to meet mission requirements and design objectives.

Fig 2.1 Launch vehicle conceptual design process

Mission Requirements

Structural, Control & Thermal

Analyses

Weight & C.G

Aerodynamic Analysis

Vehicle sizing

Propulsion Options

& design

Trajectory Analyses

Vehicle Configuration Dimens ions

Steering rate history

Layout & Surface

geometry

4

The conceptual design process is highly coupled and non-hierarchical and

significant data exchange and iteration are often required among disciplines and

disciplinary tools. Fig 2.2 depicts the coupling among various disciplines including cost

estimation in launch vehicle design process [1].

Fig 2.2 Coupling among disciplines in Launch vehicle design process

Determining the optimal configuration of a launch vehicle requires the evaluation of

the interactions between the vehicle systems and the impact of these systems upon the

vehicle’s ability to perform the desired mission. This interaction, as shown in fig 2.3, leads

to vehicle sizing/performance evaluations cycle.

Layout &Surface geometry

Vehicle Concept

Mission Requirements

Propulsion option

Technology options

Operational option

Aerodynamic analysis

Structural,

Control, thermal Propulsion analyses

Trajectory analysis

Configuration, Weights

and sizing

Operational analysis

Cost Analysis

Rethink/modify requirements and options

Fig 2.3 Vehicle Sizing/ Performance cycle

Vehicle performance

Vehicle Sizing

Resize vehicle

Determine Performanc

e

5

The evaluation of the sizing/performance cycle was a manual process. This

manual process has two problems:i) The vehicle must be repeatedly sized and

performance evaluated and ii) once sized, the vehicle may not be optimal [2].

To obtain the optimum values of sizing parameters, vehicle performance will be

carried out to examine the value of each parameter by fixing the values of remaining

parameters. This is referred as “one variable at a time” approach. As an example, the

conceptual design of fully reusable manned launch system is briefed here [3]. The

conceptual design of a rocket-powered, two stage fully reusuable launch vehicle has been

performed as a part of advanced manned launch system(AMLS) study by NASA. The

reference geometry was chosen, the vehicle aerodynamics were evaluated, a propulsion

system was selected, ascent and entry trajectories were analyzed, a centerline heating

analysis was performed, baseline structural concepts and thermal protection system

materials were selected, and a weight and sizing analysis was performed. After

finalizing the reference vehicle, a series of parametric trade studies were also performed

on the reference vehicle to determine the effect of varying major vehicle parameters. For

example the Liftoff thrust-to-weight ratio(T/W) was chosen in the following manner:

Throughout the initial design of the two stage AMLS fully reusable vehicle, a value of

1.3 was assumed for the liftoff T/W. This was judged to be an optimal value based on the

results of previous studies; however, since such optimal parameters tend to be vehicle

dependent, a trade study was performed using a variety of T/W values. The results of this

parametric trade are presented in Fig. 2.4.

6

This trade was performed for a thrust split of 60% of the liftoff thrust of the

SSME-derivative engines on the booster and 40% on the orbiter. The curves presented in

Fig. 2.4 indicates that the minimum total gross weight occurs for a liftoff T/W of 1.5, and

the minimum total dry weight occurs for a T/W of about 1.15. However, the minimum

non propulsion dry weight occurs for a liftoff T/W of 1.3. The dry weight increases for

higher T/W values because of the additional propulsion weight needed to achieve the

required high thrust values. The gross weight increases for lower T /W values because of

the additional time and propellant required to accelerate to orbital velocities. However,

the slope of these curves is quite small. Choosing a liftoff T/W of 1.3 allows a healthy

thrust margin, minimizes nonpropulsion dry weight, and causes less than a 1 % increase

In total dry weight over the minimum value. Similarly all other parameters such as

staging Mach number are also chosen through parametric studies keeping other

parameters constant.

In this “One variable at a time” approach, the relationships among the design

variables are not considered in choosing optimum parameters. This may result in near-

optimum configuration. Instead, if “all at the same time” approach will bring out more

optimum configuration. This can be achieved by application of MDO methods in

conceptual design process.

A good amount of work related to MDO methods in launch vehicle system and

trajectory optimization. The highlights of the works available in literature is presented in

next chapter.

7

Chapter 3

Literature review on MDO works related to launch vehicle design

As stated earlier, choosing the optimal configuration requires launch vehicle

performance optimization. The performance optimization of launch vehicles implies the

tasks of system design and trajectory optimization. System design provides parameters

like the number of the stages and engine sizing. Trajectory optimization gives the control

vector that optimizes the performance for the chosen configuration. Ideally, design of the

vehicle and propulsion system and trajectory shaping should be iteratively refined

together by a coupled multidisciplinary optimization scheme to obtain optimum solution.

One approach to optimize vehicle performance is to collect all elements of the

trajectory control vector and system design variables in one vector of optimization

parameters to be manipulated by an appropriate non-linear programming algorithm. This

approach has been applied successfully to ascent mission of rocket powered single-stage-

to-orbit vehicle in multidisciplinary design environment. [4] [5]. These studies focus on

development of rapid multidisciplinary analysis and optimization capability for launch

vehicle design. To simplify the analysis, several disciplines were decoupled and

propulsion, performance and weights and sizing are considered for the study. For

propulsion system, the parameters supplied by Pratt & Whitney is used after regression

analysis. Program to optimize simulated trajectories(POST) is used for trajectory

optimization. An existing vehicle geometry, aerodynamic database were used and data

from aerodynamics, structures, heating and other subsystems were fixed or scaled

appropriately.

Two architecture referred as “Iterative loop solution strategy“ and “sequential

compatibility constraint solution” are addressed in [4] with 40 design variables and 13

constants. Iterative loop method is depicted in Fig 3.1. Here an iterative loop is set up

between the trajectory and weights and sizing disciplines. Values of GLOW, SREF, the

base diameter and the landed weight are used as loop convergence criteria. This

formulation may be referred “multidisciplinary feasible” since for each set of design

variables the looped analyses return a design candidate that is consistent across

disciplinary boundaries.

In the sequential compatibility constraint method approach, the iterative loop is

replaced by use of auxiliary variables and compatibility constraints As shown in Fig.3.2,

8

OptimizerMinimize J=dry weight

Design variables(40)Subject to inflight and terminal constraints

Initial guess at GLOW, SrefBase diameterLanded weight

propulsion

Trajectory

Weights & SizingDelta=(GLOWc-GLOW)2

+(Srefc-Sref) 2

+(Landed wtc-Landed wt) 2

+(base diameterc- base diameter) 2

GLOW=GLOWc Sref=Srefc

Landed wt =Landed wtcbase diameter =base diameterc

IsDeltasmall

Done

N0

Yes

Iterative-loop solution strategy

Fig 3.1 Iterative Loop MDO strategy

OptimizerMinimize J=dry weight

Design variables(40)Subject to inflight and terminal constraints

propulsionTrajectory

Weights & Sizing

Sequential compatibility-constraint solution

Inflight & terminal constraints

GLOWc SrefcLanded wtc

base diameterc

Dry weight

Compatibility constraintsGLOWc-GLOW =0Srefc-Sref = 0 Landed wtc-Landed wt= 0base diameterc- base diameter= 0

Fig 3.2 Sequential compatibility constraint solution

9

an auxiliary variable and a compatibility constraint are added to the optimization-problem

statement for each variable that is required as input to one discipline but is computed by

another discipline later in the analysis sequence. Hence, Sref, GLOW, the base diameter,

and the landed weight are added as design variables. In this manner, the iterative loop is

removed, and configuration control becomes an additional task of the optimizer. By

satisfying these four compatibility constraints, consistent vehicle model is guaranteed.

However, as opposed to the iterative loop approach, compatibility is required at the

solution only. This type of approach may be referred to as "simultaneous analysis and

design," since both a consistent and an optimum set of design variables converged upon

simultaneously.

This study indicates that use of the sequential compatibility constraint

approach has several advantages relative to the iterative-loop approach. These advantages

include i) being 3-4 times more computationally efficient ii) providing greater flexibility

in the way in which consistency is maintained across disciplinary boundaries, and iii) a

smoother design space. The only disadvantage of the compatibility constraint approach is

in situations when the optimizer terminates without reaching the solution on account of

poor scaling or model non-smoothness. Because multidisciplinary feasibility is only

guaranteed at a solution in this approach, the design information could be invalid.

A new design architecture “collaboration optimization”, with 95 design

variables(23 interdisciplinary) and 16 constraints, is studied in [5]. Collaborative

optimization is a new design architecture whose characteristics are well suited to large-

scale, distributed design. The fundamental concept behind the development of this

architecture is the belief that disciplinary experts should be able to contribute to the

design process while not having to fully address local changes imposed by other groups

of the system. To facilitate this decentralized design approach, a problem is decomposed

into subproblems along domain-specific boundaries. Through subspace optimization,

each group is given control over its own set of local design variables and is charged with

satisfying its own domain-specific constraints. The objective of each subproblem is to

reach agreement with the other groups on values of the interdisciplinary variables. A

system-level optimizer is employed to orchestrate this interdisciplinary compatibility

process while minimizing the overall objective. This decomposition strategy allows for

the use of existing disciplinary analyses without major modification and is also well

suited to parallel execution across a network of heterogeneous computers.

10

2313125-24840

Collaborative

6533182CombatiblityConstraint

66410482Iterative method

CommunicationRequirements

Modification time, month

FunctionEvaluation

MDOArchitecture

Fig 3.3 Collaborative optimization architecture for launch vehicle design

Table 3.1 Comparisons of MDO strategies in launch vehicle design

11

Advantages of this collaborative architecture are that it i) may not require either

modification of codes or explicit integration into an automated computing framework, ii)

allows subproblems to be optimized by the best-suited method, iii) allows for the addition

or modification of subproblems and iv) can efficiently accommodate a large number of

variables . Table 3.1 shows the performance comparison between the above three

methods for this design problem. Communication requirements are minimal because

knowledge of the other groups' constraints or local design variables is not required.

Optimisation of system and trajectory together is applied to Reusable launch

Vehicle (RLV) by Tsuchiya [6]. In this study MDO method is applied to choose best

among seven typical concepts of RLV. The design variables representing geometry and

shape of vehicles, flight performance of flight trajectories are considered as design

variables. The MDO architecture used in this study is similar to “sequential compatibility

constant solution”. The study concludes that the proposed MDO optimization method is

effective for the design problem considered.

Though these MDO architectures has been applied successfully to the ascent

mission of single stage vehicle, it has shown poor convergence properties even for less

complex mission examples of an expendable multistage rocket launches, when major

system design parameters such as the mass split of stages or engine sizing were included

to optimize trajectory control and vehicle parameters simultaneously [7].

Another approach that overcome this difficulty is a multistep sequential

optimization procedure [8]. In this multistep sequential procedure, outlined in Fig.3.4,

consists of a performance optimization cycle (inner loop) and a vehicle design cycle

(outer loop). The first loop uses the data of the latter to determine the control functions

and major system parameters yielding the optimum performance. This automatic inner

loop responds to varying vehicle size needs as long as the departure from the preset

design (outer loop) remains small. Otherwise, a vehicle redesign including system

modifications and reevaluation of the aerodynamic coefficients (which are held constant

in the inner optimization cycle) is performed in separate computations in the outer it-

eration loop. The latter requires manual interaction and is supported by graphic interface

tools. This scheme outlined above is applied to enhance the performance of a reusable

rocket launcher which is part of Ariane X family [9].

12

System scaling

Flight simulation

VerificationAnd valuation

AerodynamicAerothermodynamic

Modeldefinition

MassEstimate

Designcycle

OptLoop

Two design software FASTPASS (Flexible analysis for synthesis trajectory and

performance for advanced space systems) [2] developed by Lockheed Martin

Astronautics and SWORD (Strategic Weapon Optimisation for rapid Design) [10]

developed by Lockheed Missile design and space Co. for solid motor missile are based

on the schemes similar to multistage sequential optimization process.

Though this scheme was able to solve the optimization problem of a two-stage,

winged rocket launch vehicle designed tor vertical takeoff, severe convergence problems

were encountered when it was applied to the more complex mission of an airbreathing

Sanger-type STS [7]. These difficulties were attributed in part to different performance

sensitivities of the various flight phases, controls, and major system design parameters,

and to scaling problems. A decomposition approach has been taken in the present study

to solve the overall optimization problem of a Sanger-type launch system. Decomposition

of a mission means partitioning the trajectory into subarcs such that each mission segment

can be optimized independently. These subproblems constitute the first level of

optimization. A second-level controller is then used to optimize the entire mission.

Hence, a two-level optimization procedure results, with. the master-level algorithm

optimally coordinating the solution of the subproblems. The schematic diagram of

decomposition of segments and the decomposition formulation for the two stage to

which stage missions is shown in Fig3.5 and Fig3.6 respectively

Fig.3.4 : Multistep sequential procedure

13

h

Segment 1 Segment 2

Segment 3

Schematic diagram Decomposition of segments

Master Problem: Maximize upper-stage payload mass

Independent variables: Staging Mach number Longitude at staging Load factor at pull-up

Time interval for pull-up Subproblem 1: Minimize: Booster stage ascent propellant Subject to: Staging Mach no. (master contr.) Staging longitude(master contr.) Latitude at staging heading staging Independent variables: flight heading after take-off supersonic cruis e flight length bank angle control parameter determines the length of the turn flight

Subproblem 1: Minimize: Booster stage flyback propellant Subject to: Max flight acceleration Max dynamic pressure End head towards landing site Independent variables: Angle of attack control Bank angle control Parameter determines the length of the turn flight.

Subproblem 1: Minimize: Orbiter ascent propellant Subject to: Max long. Flight acceleration Perigee velocity Perigee altitude Perigee path angle Independent variables: Angle of attack control

Fig.3.6 Decomposition formulation for two stage to orbit mission

Fig 3.5 Schematic Diagram of decomposition of segments

14

This algorithm is applied to determine the optimal ascent trajectory of an

airbreathing launch vehicle of Sanger type that delivers a maximum load to desired orbit

while staging condition and mass distribution of the two vehicles are unknown and to be

determined. This study demonstrates the capability of the decomposition method to

successfully optimize the entire mission and major design variables.

MDO methods may be divided into three groups: i)Parameters methods based

on design of experiments (DOE) techniques ii)Gradient or Calculus based methods and

iii)Stochastic methods such as geometric algorithm and simulated annealing. Parametric

methods as well as gradient based methods are applicable at conceptual design phase[11].

The above mentioned studies are all based on gradient based optimization methods.

Launch vehicle conceptual design studies have been carried out using parametric

optimization method. Stanley [12] uses parametric optimization study which employs

Taguchi design method to determine the proper levels of a variety of engine and vehicle

parameter for single-stage-to-orbit vehicle. This study considers five design parameters.

The configuration selection for rocket powered single stage vehicle configuration using

response surface methodology is presented in [13]. Five configuration parameters that

greatly affect the entry vehicle flying qualities and vehicle weight considered for study.

RSM was used to determine the minimum dry weight entry vehicle to meet constraints on

performance.

Olds has applied Taguchi’s method to conceptual design of a conical (winged-

cone) single-stage-to-orbit launch vehicle [14]. Taguchi method was used to evaluate

the effects of changing 8 design variables (2 of which were discrete) in an "all at the same

time" approach. Design variables pertained to both the vehicle geometry (cone half-

angle, engine cowl wrap around angle) and trajectory parameters (dynamic pressure

limits, heating rate limits, and airbreathing mode to rocket mode transition Mach

number). The vehicle payload was fixed at 10,000lbs to 100Nmi circular polar orbit.

Vehicle dry weight and gross weight were determined for each of the 27 point designs

performed.

Anderson et al., have investigated the potential of using a multidisciplinary

genetic algorithm approach to the design of a solid rocket motor propulsion system as a

component within overall missile system [15]. Aerodynamics and trajectory performance

disciplines were considered in this study.

15

Chapter 4

Motivation for present research effort A complex interrelation exists between mission requirements and constraints,

flight path selection, engine performance and weights, vehicle design and flight loads

with conflicting goals, which have to be matched by an appropriate optimization strategy

during conceptual design process. Ideally, design of the vehicle and propulsion system

and trajectory shaping should be iteratively refined together by a coupled, MDO scheme

to obtain the optimum solution. However this was not practical because of high

computational expenditure associated with the numerical prediction methods [8].

Therefore a multistep sequential analysis and vehicle design procedure employing

parameter optimization methods had been developed

Now with availability of various methods, good amount of work related to MDO

in launch vehicle design appear in literature. A survey on literature reveals that MDO

works related to conceptual design, that is, simultaneous optimization of system and

trajectory are limited to enhancement of an existing reference vehicle system or

subsystem optimization with respect to vehicle performance. This may be attributed to

the focused effort on the Advanced Manned Launch System (AMLS) activity since 1988.

Two vehicles, single stage and two stages were used for this AMLS mission and all

further design studies are to optimize the performance of these configuration. Also, other

recently developed vehicles are designed by evolution strategy.

An MDO strategy which has ‘zero order’ sizing capability would be useful in

developing a new vehicle. That is, given the range of realizable mass fraction and specific

impulse. The scheme should be able to decide number of stages, mass and propellant

fraction and iterate this vehicle and propulsion system and trajectory shaping and give

optimum configuration and trajectory that meets the specification. This would be useful

when no propulsion system or technological constraints are identified and the initial trade

space is being defined. This scheme may come up with a design which is non- intuitive

and much better than traditional design technique. Development of such scheme is the

aim of present research effort.

16

Chapter 5

Preliminary work done in MDO strategy in conceptual design

As an effort to understand the advantage of MDO based conceptual design of ∆V,

the following work has been carried out. The conceptual design of Launch Vehicle starts

with the orbit and payload specification. The velocity requirement (∆V) can be derived

from orbit specifications. Once the ∆V is assessed, certain value of number of stages,

velocity loss (∆Vloss), structural factors (σ) and specific impulses (Isp) for each stage are

assumed based on the data base available. Based on assumed values, an optimum launch

vehicle configuration is arrived, through ‘ideal velocity calculations. In this, ∆Vloss is

due to gravity and aerodynamic of vehicle. This can be accurately assessed through

aerodynamic modeling and trajectory performance. Trajectory performance can be carried

out after sizing, geometrical modeling, weight estimation and aerodynamic modeling.

Structural factor is the outcome of sizing of propulsion system, tanks and mass estimation

of all sub systems. Specific impulse is achieved by propulsive system design. So, after

completion of final design, there may be deviations from the values assumed. This may

result in non-optimum configuration with room for improvement. These deviations can

be reduced if the above mentioned disciplines are considered in conceptual design. It

also depends on the number of disciplines brought into the conceptual design loop and

the fidelity of discipline models.

In this preliminary study, a two stage rocket is developed for deploying

20t in 400km is considered for the study. The ∆V required for 400km circular orbit is 7.7

km/s. A ∆Vloss of 1.8 m/s is considered and two stage vehicle configuration was designed

with specific impulse values of 435s and 454s which can be well achieved with cryo

propellant. Structural values of 0.17 and 0.11 is initially considered for design. These

values are based on data base available for similar type of stages.

Here, the aim of the optimization is to arrive at a configuration which

gives low liftoff weight, in other words high payload fraction. Payload fraction is defined

as the ratio of payload to liftoff weight. So, the velocity increment achieved by each stage

is to be optimized. Since the final velocity is known, the first stage velocity (∆V1) can be

independent parameter. Now, the optimization problem is “Given the payload and final

velocity to be achieved, with assumed ∆Vloss, specific impulse (Isp) and σ, optimize first

stage velocity to achieve high payload fraction.

17

For given stage velocity, the mass of structure and propellant can be estimated

using the following ideal velocity equations Lift-off weight can be calculated by

summing up all masses. The optimum final stage velocity can be obtained for minimum

lift-off weight. The variation of lift-off weight and payload fraction with respect to first

stage velocity are shown as curve (a) in Fig. 5.1 and Fig. 5.2 respectively.

.

The first stage velocity of 3.6 m/s gives the minimum lift-off weight of 366t. The

optimum configuration thus obtained would be C209 + C85. That is, based on the

assumed values, a two stage vehicle with cryo engine on both stages with 209t and 85t

propellant loading respectively will give minimum lift-off weight. The corresponding

maximum payload fraction is 5.5.

Now, further study has been done to take more accurate structural factor into

design by bringing sizing and mass estimation into loop. Propellant tanks are sized to

accommodate the propellant required for ascent flight along with possible in flight losses

and residual fluids depending on the propellant used. The volume of the payload is

(5.1)

(5.2)

(5.3)

(5.4)

(5.5)

18

Orbit SpecificationsPayload

Assumptions∆V loss

Structural factors (σ1, σ 2 )

∆Vtotalσ 1, σ 2

Initialize ∆V1

Ideal velocity calculations

ms1,mp1ms2,mp2,mpfLOW

Choice of propulsionIsp1, Isp2

Dy. PressureLoad factorArea ratiosFineness ratios

Sizing of tanks ms1e,ms2e

Isms1= ms1ems2= ms2e

Vary σ 1, σ 2

LOW

Is LOW minimum

Weight estimation

Vary∆V1

OptimumLOW &

Configuration

No

No

Yes

Yes

ig 5.3 : Flow diagram of preliminary study on conceptual design of launch vehicle

19

computed from its density derived from database and nominal density of payload is taken

as 0.14 t/m3. A preliminary mass estimation methodology is adopted. It is based on

component built up method including propellant tank, payload bay, thrust structure,

thermal protection system, avionics and other auxiliary systems. The methodologies,

given in [17] & [18] are adopted. The mass estimated using this procedure is compared

with mass obtained from ideal velocity calculation. If the values are different, then the

structural factor assumed is iterated until both match well. For each first stage velocity

value, this procedure is repeated. The methodology is explained well in Fig.5.3.

The results obtained using the procedure is given as curve (b) in Fig. 5.1 & Fig.

5.2. The sizing and weight estimation-in-loop process gives optimum first stage velocity

as 4.6km/s. The optimized structural factors are 0.08 and 0.12 against the assumed values

of 0.17 and 0.11. The optimum configuration is C197 + C55. That is, two cryo stages

with 210t and 83t of cryo propellant respectively for first and second stage. The payload

fraction is 6.7 with lift-off weight of 299t.

This study shows that bringing sizing and weight estimation (with empirical

model) in loop during conceptual design has increased the payload fraction from 5.5 to

6.7 and the configuration is C197 + C56 instead of C207+C85. Similarly if other vital

disciplines like propulsion, aerodynamic and trajectory performance are considered in

conceptual design process, it will result in more efficient launch vehicle. In first phase of

studies, it is proposed to bring aerodynamic, propulsion and trajectory performance in the

loop. Then it will be extended to more number of stages.

20

Chapter 6

Conclusions

Progress made in research work related to MDO strategy in conceptual

design of multi-stage launch vehicle is presented. The conceptual design of launch

vehicle involves various disciplines and highly coupled. Considering all disciplines

with high fidelity model at conceptual design stage improves the efficiency of

launch vehicle designed. Survey of literature reveals that the MDO woks on

launch vehicle design are restricted to enhancing the existing design and single

stage vehicle. An MDO strategy capable of ‘zero order’ sizing applicable to multi-

stage vehicles would be beneficial in developing new vehicles. Present research

effort is focused in this direction. A preliminary study to demonstrate the effect of

bringing in mass estimation discipline in conceptual design indicates the payload

fraction is increased from 5.5 to 6.7.

21

Chapter 7

References

[1] Lawrence F. R., Braun R. D., Olds J.R., and Unal R, “Multidisciplinary Conceptual Design Optimization of Space Transportation Systems” Journal of Aircraft, Vol. 36, No. 1, January-February 1999, pp.218-226

[2] Szedula, J.A., FASTPASS: A Tool For Launch Vehicle Synthesis, AIAA-96-4051-CP, 1996

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[9] Hillesheimer, M., Schotlle, U. M. and Messerschmid, E., "Optimization of Two-Stage Reusable Space Transportation Systems with Rocket and Airbreathing Propulsion Concepts," International Astronautical Federation Paper 92-O863, Sept. 1992.

[10] Hempel, P. R., Moeller C. P., and Stuntz L. M., “Missile Design Optimization Experience And Developments”, AIAA-94-4344,1994-cp

[11] Lawrence, F. R.,. Braun R. D., Olds J.R., and Unal, R. “Recent experiences in Multidisciplinary Conceptual Design Optimization of Space Transportation Systems” AIAA-96-4050-CP, 1996

[12] Stanley, D. O., Unal, R., and Joyner, C. R., "Application of Taguchi Methods to Dual Mixture Ratio Propulsion System Optimization for SSTO Vehicles," Journal of Spacecraft and Rockets, Vol. 29, No. 4, 1992, pp. 453-459.

[13] Stanley, D. 0., Engelund. W. C., Lepsch. R. A., McMillin, M. L.Wt K. E.. Powell. R. W., Guinta. A. A., and Unal, R. "Rocket-Powered Single Stage Vehicle Configuration Selection and Design," Journal of Spacecraft and Rockets, Vol. 31, No. 5, 1994. pp. 792-798; also AIAA Paper93-Feb. 1993.

[14] Olds, J., and Walberg, G., ”Multidisciplinary Design of a Rocket-Based Combined-Cycle SSTO Launch Vehicle using Taguchi Methods” , AIAA 93-1096, Feb,1993.

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[15] Anderson, M., Burkhalter J., AND Jenkins R “Multidisciplinary Intelligence Systems Approach To Solid Rocket Motor Design, Part I: Single And Dual Goal Optimization. AIAA 2001-3599, July, 2001.

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