multi-disciplinary design optimization … · prof. k. sudhakar department of aerospace engineering...
TRANSCRIPT
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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