[American Institute of Aeronautics and Astronautics 51st AIAA/ASME/ASCE/AHS/ASC Structures,...

American Institute of Aeronautics and Astronautics

1

Performance Enhancement of Air Launched Satellite

Launch Vehicle using Composite Motors

Amer Farhan Rafique1, He LinShu

2, Ma Ying

3, Ali Kamran

4, Qasim Zeeshan

5

Department of Spacecraft Technology, School of Astronautics, Beijing University of Aeronautics and Astronautics

(BUAA), 37 XueYuan Road, HaiDian District, Beijing, 100191, China

The aerospace industry's unrelenting passion to improve the performance is constantly

driving the development and use of composites. This paper presents the performance

enhancement of Air Launched Satellite Launch Vehicle by the use of Solid Rocket Motor

employing composite cases at the conceptual design stage. A light-weight motor case is

crucial to achieve the high propellant to inert mass ratio and hence the improved

performance. The mission of Air Launched Satellite Launch Vehicle is to deliver a small

satellite of 200kg to Low Earth Orbit with minimum possible Gross Launch Mass. The goal

is to minimize the Gross Launch Mass and maximize the performance of ASLV while

adhering to the design objectives and performance constraints. The objective of this effort is

to assess the effect of advanced composite materials in the conceptual design of Air

Launched Satellite Launch Vehicle structure, in order to obtain a vehicle which is, lighter,

reliable, and more importantly efficient than conventional metallic counterpart. Current

research effort applies Genetic Algorithm to optimize both configurations.

Keywords: Composite Material, Solid Rocket Motor, Satellite Launch Vehicle, Genetic

Algorithm.

I. Introduction

OMPOSITE materials play a remarkable role in current and future aerospace components. Composite materials

are attractive to aerospace applications because of their phenomenal strength and stiffness-to-density ratios.

Composites, after some reluctance on the part of designers, are finally poised to become a material of choice for

aerospace, automobile, chemical, and civil engineering. Airbus’s A380 and Boeing’s 7E7 are a typical example of

having a substantial percentage of composite structures1. Spacecrafts are high on the list of weight-critical structures.

The low coefficient of thermal expansion and high specific strength and modulus of composites make these

materials particularly attractive for space vehicles. Most of the applications in launch vehicles have been antennas,

struts, support trusses and booms. However, studies have shown exceptional potential for weight reduction in the

body of the vehicle2.

A composite material essentially consists of strong, stiff fibers in a resin matrix. Carbon and glass fiber

reinforced plastic (CFRP and GFRP), both of which are stiff and strong, are extensively used composite materials.

Composite materials can be formed into more complex shapes than their metallic counterparts. This not only reduces

the number of parts making up a given component, but also reduces the need for fasteners and joints, the advantages

of which are twofold: joints and fasteners may be the weak points of a component — a threaded hole which is a

stress concentration and, therefore, a potential crack-initiation site, and fewer fasteners and lesser joints lead to

shorter assembly time.

Weight saving has been the greatest single driving force for composite designers in the past, and some went so

far as to tailor each ply individually to save a mere ounce. With the advancement in material, design, and analysis

technologies, weight savings of 20 to 30 percent are achievable. A light-weight motor case is a key to achieve the

1 PhD Student, School of Astronautics, AIAA Student Member, [email protected], [email protected]

2 Professor, School of Astronautics, [email protected]

3 Post Doctorate Researcher, School of Astronautics, [email protected]

4 PhD Student, School of Astronautics, AIAA Student Member, [email protected]

5 PhD Student, School of Astronautics, AIAA Student Member, [email protected]

C

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th12 - 15 April 2010, Orlando, Florida

AIAA 2010-2986

Copyright © 2010 by Amer Farhan Rafique. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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mailto:[email protected]







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high propellant to inert mass ratio and hence the improved performance. Advanced composites fulfill the need to

save weight which is essential in meeting the high-performance requirements of modern vehicle systems.

One of the major advantages of composites is that it is possible to fabricate complex parts in one operation,

reducing secondary assembly requirements. This can result in lower manufacturing costs compared to metals, at

least partially offsetting the higher material cost of composites. The ability to tailor fiber orientation to meet load

and stiffness requirements is one of the great advantages of composites.

The superior mechanical properties provide weight reductions over metal designs of from 10 to 55 percent, with

20 to 30 percent being most common. This saving can be used to increase range, payload, maneuverability and

speed, or reduce fuel consumption3.

Composite case technology can prove to be highly beneficial not only in terms of inert mass reduction but also in

allowing a higher (maximum expected operating pressure) MEOP. A higher MEOP also allows smaller throats

hence increased area ratio for nozzle. These factors can lead to a significant increase in performance. Nozzle

architecture demands a non-ferrous (Aluminum) nozzle housing protected by thermal liners with low density and

erosion rates. The chamber insulations with micro-spheres filled materials give a high temperature resistant, thermal

protection with low density. Inclusion of low modulus rubbers and composite material shims for flexi-joint nozzles

to reduce torque for thrust vectoring thus a reduced mass of Thrust Vector Control (TVC) system.

The use of a composite chamber case to replace a heavy metallic one is not unique, but simply a trend to extend

mission effectiveness. Further use of advanced composites on launch vehicles with specialized missions will not

only reduce long term cost but increase flight performance as well. The self-sealing matrix composites materials are

now emerging in the field of aeronautical engine applications, with a demonstrated potential in a life time duration,

competitive in regard with metallic alloys, inducing weight saving4.

Main objective of current study is to design Air Launched Satellite Launch Vehicle (ASLV) with metallic Solid

Rocket Motor (SRM) (Configuration I) and Composite SRM (Configuration II) and compare the reduction in Gross

Launch Mass (GLM) and improvement in performance.

II. Use of Composite Material in Aerospace Industry

Modern composite material found their first use for the skins of the empennages of the F-14 and F-15 fighters.

Secondary structures provide the start for use of composite, but as manufacturing and development knowledge has

improved their use in primary structures have increased exponentially. Table 1 lists some aircrafts in which notable

amounts of composite materials are used in the airframe1.

Table 1. Usage of Composites in Aerospace Industry1.

Class of Aerospace Systems Examples Use of Composites

Fighter Aircraft (US)

F-16, F-14, F-18,

YF-23, F-22, F-15

JSF, UCAV

Starts with 2% composites in F-15 and increased to 19% in F-18 and 24% in F-22.

Fighter Aircraft (EUROPE)

Gripen JAS-39, Rafael,

Lavi, Mirage 2000,

Eurofighter, Mako

About 40% of the structural weight of the Eurofighter is carbon-fiber

reinforced composite material. 26% for Rafael and 20 to 25% for Gripen and Mako.

Bomber (US) B-2 Composite materials are used to offset weight penalty of radar-absorbing

material.

Transport (US-Commercial) B-777, B-767, MD-11 20% composites in Boeing 777, 50% composites in Boeing 7E7.

Transport (Airbus, European)

A-320, A-340, A-380,

Tu-204, A300-600 ST,

Falcon 900, ATR42.

Rudder, elevator and vertical tail of A300 and A310, 28% composites in

A320, 20-22% composites in A380 (weight saving is 15-30%).

There exist several examples of application of composite materials in launch vehicle structure like P80 is the

solid rocket motor to be used as the first stage of VEGA launch vehicle, as well as, as a demonstrator of cost

reduction new technologies leading to a new version of SRMs for Ariane 5. This motor case is the largest composite

case ever manufactured in Europe. Nozzle has been conceived with reduced parts architecture as well as with

components using total new materials and manufacturing technologies5. Parametric analysis shows that payload

benefit of about 33-40% can be achieved by use of composite SRM6. The CASTOR 120 combines technologies and

processes into robust and simplified design. The motor has a graphite epoxy case, HTPB propellant, flexible bearing

nozzle for thrust vector control. Forward and aft skirts are also fabricated with carbon fiber pre-impregnated with

resin7. Filament wound structures such as pressure tanks, pipes and motor cases of rockets are also widely used in

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the aerospace application6. The use of a composite chamber case to replace a heavy metallic one is not unique, but

simply a trend to extend mission effectiveness.

III. Application of Composite in ASLV Design Problem

Current trends within the global aerospace community require improvements to the Satellite Launch Vehicle

(SLV) designs that will produce better space missions in shorter schedules and constrained budgets. The design of

ASLV capable of inserting a small payload (satellite of 200kg) in Low Earth Orbit (LEO) is a complex problem that

must balance constraints and competing objectives. It involves teams of specialists working separately on their

specialized design domains (like Propulsion, Aerodynamics, Weight and sizing, Trajectory etc.), although

coordinated through a system level set of design requirements.

There can be different objective functions for SLV optimization problems. For example, one could minimize

cost, maximize payload for a fixed launch weight, maximize injection accuracy in orbit, and minimize launch weight

for placing a specific payload in a particular orbit. Traditionally, minimum take-off weight concepts have been

sought in launch vehicle design. This is because weight (or mass) is a strong driver for vehicle performance and

cost, and so take a central role in vehicle design process. For the present research effort, design objective is to

minimize the GLM of the entire vehicle to inject a specific payload into LEO and thus makes the motivational

ingredient to replace conventional metals with composites.

Mathematical description of design objective is as under;

)(XGLMMin (1)

Whereas design variables X are given in Eq. (2);

),,,,,,,( ki aukppDfX misieicii (2)

Where μki is Relative Mass Coefficient of Grain, Di is Body Diameter, pci is Chamber Pressure, pei is Nozzle Exit

Pressure, ksi is Coefficient of Grain Shape, ui is Grain Burning Rate, αm is Max Angle of Attack and a is Launch

Maneuver Variable

Following are the key motivational factors for the current study of replacing metal cases with composite cases;

The strong dependency of inert mass fraction on structural material dictates the replacement for

improved candidate materials.

Chamber pressure plays a significant role in determining the overall structural coefficients of the

vehicle and may not have the optimal value because of material strength issues thus drastically limit the

performance. Composite opens the new avenue by allowing high MEOP, thus higher operating

pressures, significantly improving the ballistic performance.

Larger diameters are prone to be difficult in terms of machining and welding capabilities and cost of

manufacturing and infrastructure development is also extremely high. Composite materials reduce the

number of the manufacturing process and significant reduction in infrastructure.

In the case of composite SRM not only the number of parts are reduced but also the inspection, quality

procedures, non-destructive tests decreased to noteworthy amount. Hence maintaining quality-cost

balance at a reasonable level.

Reliability is a crucial parameter that must be taken into consideration in design of complex systems

like ASLV. The use of composites increases the whole reliability of system with a lesser number of

parts and processes.

GLM has high importance in case of ASLV as it has to be carried to a certain altitude on mother aircraft. Air

launching has several advantages, but GLM of vehicle needs to be as minimum as possible. So the use of composite

materials becomes the attractive choice for design of ASLV to meet the performance requirements. Table 2 lists the

material properties.

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Table 2. Comparison of Material Properties8.

Material Tensile Strength

(N/mm2)

Modulus of Elasticity

(N/mm2)

Density

(g/mm3)

Strength to Density

Ratio

E-glass 1930-3100 72000 2.5 1040

Carbon fiber 3500-6900 230000-300000 1.53-1.8 2800

Epoxy 83 2800 1.19 70

Kevlar 49 1310 58000 1.39 950

Steel 1400-2000 207000 7.84 205

IV. Multidisciplinary Design Analysis

ASLV demands a highly integrated process seeking tradeoffs and synergistic compromise of various parameters.

The synthesis of an effective compromise requires practical emphasis in subsystems, unbiased tradeoffs, and

evaluation of various alternatives. Starting with a well-defined baseline that has similar propulsion and performance

expedites design convergence and provides a more accurate design. Starting with a reasonable baseline enhances the

accuracy and speed of the design process. Figure 1 outlines the integrated disciplines considered in multidisciplinary

design analysis of ASLV and interconnections among these disciplines.

A. Vehicle Definition

The baseline design launches from 12 km at Mach number of 0.8. The mission of ASLV is to deliver 200 kg

payload (satellite) to LEO. Propulsion system is solid fuelled SRM and number of stages is three. Final stage motor

and payload are enclosed in fairing whose shape is known beforehand. Problem definition covers the payload weight

and volume requirements before conducting optimization.

B. Propulsion Analysis

Propulsion analysis describes essential parameters like thrust, burn time, mass flow rate and nozzle parameters8.

Chamber pressure (pc) is a vital design variable which has momentous influence on SRM specific impulse (Isp), burn

rate of propellant (ui), size of expansion nozzle and thickness of casing materials to withstand the pressure stresses.

Burning surface area (Sri) of the propellant grain primarily dictates the performance of propulsion system in SRM.

In this analysis, a variable grain shape factor (ksi) is used to represent Sri as a function of diameter of stage (Di) as

following:

Aerodynamics

Analysis

Propulsion

Analysis

Weight

Analysis

Vehicle

Configuration

Aerodynamic

Coefficients

Mach

Altitude Stage

weight Time

Thrust

Vehicle

Size

Trajectory

Analysis

MULTIDISCIPLINARY DESIGN ANALYSIS

Figure 1. Multidisciplinary Design Strategy.

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i

risi D

Sk

(3)

Mass of grain is calculated from design variables and propulsion analysis. Burn time (tbi), mass of ith

stage grain

(mgni) and mass flow rate (ṁgni) of ith

stage grain, as described by Ref [8] and [9], is calculated as:

3

4ignisignigni Dkm

(4)

sii

ivii

ku

Dtb

4

(5)

2ignisiigniriignigni DkuSum

(6)

Where, ρgn is density of grain, λgni is the fineness ratio of grain and ηvi is volumetric efficiency of grain. Fineness

ratio is given by Eq. (7):

gni

gnigni D

L

(7)

Lgni is length of grain. Nozzle throat area (At), expansion ratio (ε) and nozzle exit area (Ae) are calculated as:

ccco

rii

t TRp

SuA

gni

max,

max,

(8)

11

11

2

c

e

c

e

o

pp

pp

(9)

te AA (10)

12

1

12

o

(11)

Where, Rc is gas constant, Tc is temperature in combustion chamber, pe is exit pressure and γ is specific heat ratio

of gas. Vacuum specific impulse ( vacspI ) and thrust (F), as described by Ref. [8] and [9], are calculated as under:

eiagnivacspN ApmIF

..1 (12)

1

2vac a e c c

asp spc o sp

p R TI I

p g I

(13)

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Where, N is number of stages, pa is atmospheric pressure, aspI is average specific impulse and go is acceleration

due to gravity.

C. Weight Analysis

Using a combination of physics-based methods and empirical data, the weight of key components for the solid

stages is determined from Ref. [9]. The total mass of a multistage ASLV includes masses of propellants and their

tanks, related structures and payload mass. The Gross Launch Mass (GLM) (m01) for a multistage ASLV is the

cumulative sum of the following as shown below:

N

i

fiaistigniPAY mmmmmm

1

01

(14)

Where, mPAY is mass of payload, msti is mass of the ith

stage motor structure, mai is total mass of the ith

stage aft

skirt, mfi is total mass of the ith

stage forward skirt. Total mass of the ith

stage aft and forward skirt are simplified as:

asisviai mmm (15)

fsifeifi mmm (16)

oiifiai mNmm (17)

Where, msvi is mass of control system safety self-destruction system, servo, and cables inside the ith

stage aft skirt

payload, masi is mass of the ith

stage aft skirt including shell structure, equipment rack, heating protector structure,

and directly subordinate parts for integration, mfei is mass of equipment and cables inside the ith

stage forward skirt,

mfsi is mass of the ith

stage forward skirt including shell structure, equipment rack, and directly subordinate parts for

integration. The simplified form of N-stage launch vehicle mass equation comes to be:

N

i

stikignii

PAYi

KN

mm

1

0

11

(18)

Design mission dictates the mPAY. Ni, structural coefficient, has small dispersions which can be selected from

statistical data [8, 9]. Relative mass coefficient of effective grain (uki) and structure mass fraction (αsti) are given by

following relations:

oi

egni

kim

mu

(19)

gni

gniegni K

mm

(20)

gni

stisti

m

m

(21)

Kgni is sliver (un-burnt grain left in solid rocket motor) and can not be avoided but has small dispersions which

can be selected from statistical data [8, 9] and egnim is mass of effective grain. Main parameter for designing a

multistage SLV is αsti. It is dependent upon structural material, grain shape, as well as the parameters of internal

ballistics of SRM.

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The mass of the ith

stage SRM structure is shown in Eq. (22). It will be used to calculate structure mass fraction

and so GLM of ASLV.

apicabiTVCiigiininozshinozecinoz

cyiinicinicinijijqiiciccyisti

mmmmmmm

mmmmmmmmmm

,,,

,2,1,2121

(22)

Mass of the motor cylinder (mcyi), motor dome ends (mc1i, mc2i), forward and aft skirt (mqi), forward and aft

attachment (mj1i, mj2i), forward and aft insulation liner (min, c1i, min, c2i), cylindrical section insulation liner (min, cyi),

nozzle expansion cone (mnoz, eci), nozzle spherical head (mnoz, shi), nozzle insulation (mnoz, ini), igniter (migi), thrust

vector control (mTVCi), cables (mcabi) and attachment parts (mapi) are calculated using Eqs. 23-39. Factor of safety is

taken as 1.5 for metallic chamber case and 1.25 for that of composite.

b

gnicchpcycyi

pDffKm

8

3 3

(23)

222

22

32

1sin11

11

cos18

ee

cpcheic

pffDm (24)

Where, θ is normally taken as 60o ~ 65

o.

22222

2222

22

32

2sin11

11

cos18

eche

eche

e

cpcheic

D

dDpffDm (25)

ch

qqqqchqi

D

llDm

212

(26)

22

022

022

022

0212

12

1 226

1iiiiiiiiijij RbRbrbrbyrm

(27)

ijij mm 12 (28)

bacyinicin tRDm 2

1,4

1

(29)

2

2222

2

2

2,

1

14 cy

ecye

e

biacyinicin

D

dDtRDm

(30)

1

ln

ln21

2,

cycycygiinininp

iningibgicycycypin

iningi

cycycygiinininincycycyiin

cc

ctc

c

ccLDm

(31)

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ig

cygp

TT

TT

(32)

ec

ecc

t

et

t

e

nececinoz

E

pS

dd

fdA

Am

max

3

46

, 11 67.01sin4

(33)

3, 656.3 tshshinoz dm

(34)

innznzinnzininoz Sm , (35)

2.12

47

454.1

t

igid

m

(36)

nozTVCi mm 7.1~3.1 (37)

cicycabi Lm 3.01 (38)

148.127 )1013.6( cyiiapi LDm

(39)

D. Aerodynamics Analysis

In the preliminary design phase of ASLV, speedy and cost-effective estimations of aerodynamic stability and

control characteristics are often required. Thus, a need arises for the use of time-efficient computer software that can

predict the aerodynamic properties over a range of flight conditions. For this purpose, U.S. Air Force Missile

DATCOM 199710

has been widely used in the aerospace industry. DATCOM is capable of quickly and

economically estimating the aerodynamics of a wide variety of design configurations and in the different flow field

regions that the ASLV encounters during atmospheric flight. This study uses DATCOM for quick and economic

estimation of lift and drag coefficient.

The aerodynamic analysis for the current study was performed for a sub-orbital trajectory. The flight path was

assumed to follow a trajectory from 12 km to an altitude of about 80 km. Force coefficients were calculated for

eighteen (18) particular Mach numbers in the specified range, at fourteen (14) angles of attack for each Mach

number, ranging from -4 degrees to +22 degrees.

E. Trajectory Analysis

Since detailed data are not available at the beginning of conceptual design, it is inappropriate to use a 6 Degree-

of-Freedom (DOF) trajectory simulation. Therefore, this study implements a 3 Degree-of-Freedom (3DOF)

trajectory analysis11,12

. 3DOF model was developed and simulated in SIMULINK to analyze the flight path.

Trajectory simulation obtained from 3DOF model is computationally efficient and serves the purpose at the

conceptual design level. The trajectory analysis depends on inputs from the aerodynamic, mass and propulsion

modules. The flight program and results obtained from the other disciplines computes the flight trajectory. This

investigation treats ASLV as a point-mass and flight in 2D over a spherical and non-rotating earth is assumed. This

implies that the Coriolis and centrifugal pseudo forces are negligible. Figure 2 illustrate the forces acting on ASLV

and Eq. (40) present set of governing equations of motion.

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refD

refL

pro

e

e

e

e

o

o

SvCD

SvCL

t

R

l

vhR

R

dt

dl

vdt

dh

hR

v

v

g

mv

LF

dt

d

gm

DF

dt

dv

2

2

2

1

2

1

)(

cos

sin

coscossin

sincos

(40)

F. Interdisciplinary Design Variables

There can be large number of interdisciplinary design variables for multidisciplinary design case of ASLV.

Apart from the complexity inherited in this type of problem there exists further complexity when these variables

interact with different disciplines. For multidisciplinary design of ASLV, the design structure matrix and

interdisciplinary relationships can be considered are shown in Fig. 3.

x

v = velocity

m = mass of the vehicle

F = thrust force

go = acceleration due to gravity

φ =flight path angle

α = angle of attack

η = range angle

θ = trajectory angle

Re = radius of Earth

h = Altitude about ground

l = range

L = lift force

D = drag force

Sref = surface area.

CL = Lift coefficient

CD =Drag coefficient

Figure 2. Forces acting on ASLV.

h

x

y

D

L

T

Re

mgo l

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PROPULSION SRM dimensions

Stages propellant

mass, chamber

pressure

Burn time, thrust,

exit area, exit

pressure

SRM dimensions GEOMETRY SRM dimension,

fairing

Overall dimensions

of vehicle

Mass coefficient of

grain WEIGHT

Stages mass,

component

structural mass

Diameter of

vehicle and SRMs AERODYNAMICS

Aerodynamic

coefficients, launch

maneuver variable

Altitude, Mach no,

angle of attack TRAJECTORY

V. Optimization Strategy

Optimization deals with betterment and improvement, and was eloquently described as “The concept of

optimization is intrinsically tied to humanity’s desire to excel. Though we may not consciously recognize it, and

though the optimization process takes different forms in a different field of endeavor, this drive to do better than

before consumes much of our energy, whether we are athletes, artists, business-person, or engineers”13

.

Several heuristic tools have evolved in the past decades to facilitate optimization of difficult and complicated

problems. Although heuristic methods do not guarantee optimality, in some situations they seem to be the only way

forward to produce concrete results and due to availability of fast computational resources and easy applicability14.

The goal of all optimization procedures is to obtain the best results possible subject to restrictions or constraints that

are imposed. Of late, with advancement of computer technology, optimization and MDO have received new

attention. MDO gives the engineer the opportunity to find the optimal solution of the whole system accounting for

interactions between different disciplines. It should be noted that multidisciplinary solution might not be the solution

for any one discipline analyzed separate from other disciplines, but is the best solution accounting for interactions.

A. Genetic Algorithm (GA)

Conventional optimization techniques begin with a user supplied starting candidate and search iteratively for the

optimal solution by applying static heuristics. On the other hand, the Genetic Algorithm uses a population of

candidates to search several thru areas of a solution space, simultaneously and adaptively. Holland15

developed

Genetic Algorithms, which are capable of finding the global-optimal solution (or acutely near solutions) in complex

multidimensional search spaces.

Conceptual design phase of ASLV is dominated by qualitative or subjective decision making. GA can be applied

for performing optimization in the conceptual design phase as it is non-calculus and direct search based algorithm.

Below are the advantages of features of GA which make it extremely suitable for application in conceptual design

phase of ASLV;

Ability to combine discrete and continuous variables.

Population-based search.

No requirement for an initial design.

Ability to address non-convex, multimodal and discontinuous functions.

To perform the optimization process, the GA employs three operators to propagate its population from one

generation to another. The first operator is the ―Selection‖ operator that mimics the principle of ―Survival of the

Fittest‖. The second operator is the ―Crossover‖ operator, which mimics mating in biological populations. The

crossover operator propagates features of good surviving designs from the current population into the future

population, which will have better fitness value on average. The last operator is ―Mutation‖, which promotes

Figure 3. Design Structure Matrix.

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diversity in population characteristics. The mutation operator allows for global search of the design space and

prevents the algorithm from getting trapped in local minima16-17

.

GA applications have gained enormous popularity among aerospace professionals in the last decade. This is due

to the ease with which GA can be implemented and its remarkable ability to solve difficult complex problems more

efficiently. Another advantage is that the complex ideas can be implemented and tested with the rapid development

cycles. Some of the novel ideas using GA include spacecraft design, aircraft control, system modeling, airfoil

design, satellite component design, missile design, SLV design, and so on. Fig. 4 explains the flow chart of GA and

optimization parameters for design case of ASLV.

GA is the controlling routine in Fig. 5, which calls the multidisciplinary design and analyses modules. The first

step in the optimization process is to obtain a mathematical description of the ASLV system. This description then

leads to the formulation of the mathematical model of the system. A set of design variables (XS and XC) with lower

bound (LB) and upper bound (UB) is passed to GA which creates initial random population and performs its further

operations. These candidate design vectors are then passed to integrated, multidisciplinary design modules of weight

and sizing, propulsion, aerodynamics and trajectory. The algorithm executes iteratively in a closed loop till an

optimal solution is obtained. Constraints are handled by dynamic penalty function. Eq. (41) represents the symbolic

problem statement:

m

i

i xgkhxfxf1

)(,0max)()()(min

(41)

Where f(x) is the objective function, h(k) is a dynamically modified penalty value; k is the current iteration

number of the algorithm. The function gi(x) is a relative violated function of the constraints18

.

Design Variables

Optimal Solution

Population Initialization

Selection

Crossover

Mutation

Insertion

Stopping Criteria

Yes

No

Genetic Algorithm

Parameters

_____________________

Generations:

500

Population:

100

Crossover:

Two Point (0.8)

Mutation:

Uniform (0.25)

Function Tolerance:

10-6

Stall Generation Limit:

20

Elite Count:

2

Figure 4. Flow Chart of GA and Optimization Parameters for ASLV.

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VI. ASLV Design and Optimization Problem Formulation

ASLV design and optimization problem is formulated by defining design variables and design constraints as

under;

A. Design Variables

Table 3 lists discipline wise system design variables for each stage alongwith lower and upper bounds for

metallic and composite cases. There are total of 19 design variables that govern the integrated design and

optimization problem of ASLV.

Table 3. Discipline-wise Design Variables.

Discipline Design Variable Symbol Units

Structure + Propulsion Relative Mass Coefficient of Grain μki ratio

Structure + Propulsion + Aerodynamics Body Diameter Di m

Structure + Propulsion Chamber Pressure pci bar

Structure + Propulsion + Trajectory Nozzle Exit Pressure pei bar

Structure + Propulsion Coefficient of Grain Shape ksi

Propulsion + Trajectory Grain Burning Rate ui mm/s

Aerodynamics + Trajectory + Structure Max Angle of Attack αm deg

Aerodynamics + Trajectory + Structure Launch Maneuver Variable a

B. Design Constraints

Mission velocity (vf) and corresponding altitude (altf) are trajectory constraints. The overall structure of the

system should be extremely strong to survive the high g-loads. Therefore, a constraint is implemented to restrict (Ox)

below 12g for 1st and 2

nd stage. During launch maneuver, αm is constrained to be below 22 deg and ensured that it is

zero during transonic phase. Nozzle exit diameters (Dei) are constrained to be less than stage diameters (Di). First

and second stage diameters are constrained to be equal. Flight path angle should be zero at orbit insertion.

Constraints are formulated as under:

Multidisciplinary

Design Analysis

Module

GENETIC ALGORITHM

Propulsion

Analysis

Trajectory Analysis

Optimal Design

(X*M)

Find: Optimum Design Variables (X*)

Satisfy: Constraints

Minimize: GLM (Mg)

Aerodynamic Analysis

Design Variables

(XM)

Weight Analysis

METTALIC

SRM

Multidisciplinary

Design Analysis

Module

Propulsion

Analysis

Trajectory Analysis

Aerodynamic

Analysis

Weight Analysis

COMPOSITE

SRM

Design Variables

(XC)

Optimal Design

(X*C)

Figure 5. Overall Design and Optimization Approach

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) ( 0 :11

)3.18.0( 0 :10

:9

:8

:7

22 :6

2 :5

12 :4

12 :3

450 :2

7600 :1

as;given is Where

11 ,10 ,9 ,0

8.....,2,1 ,0

21

13

12

1

2

1

insertionorbitatC

MC

DDC

DDC

DDC

C

OC

OC

OC

altC

vC

C

iC

iC

a

e

e

m

y

x

x

f

f

i

i

(42)

VII. Composite vs. Metallic Motor Case Comparison (Results)

Multidisciplinary design and optimization of Air Launched Satellite Launch Vehicle using Genetic Algorithm is

successfully implemented with the aim of improving performance and reducing Gross Launch Mass under stringent

mission objectives and performance constraints. The results of simulation tests demonstrate that reasonable solutions

are obtained for both the cases of composites and metallic motor cases. The required circularization velocity is

achieved for corresponding altitude (Figure 6). It was observed that for the same payload (200kg) composite system

is attaining the more altitude than that of metallic counterpart. In addition, axial overloads of ASLV with composite

are significantly lower than the other one. Optimized design variables (X*M and X*c) lie between their upper and

lower bounds (Table 4). Gross Launch Mass is almost equal for both cases, but performance is significantly better

for the same mission requirements.

Both the problems were executed five times to reduce some of the stochastic error that can normally be present

in each run of optimization algorithm. The best feasible fitness value is the minimum GLM ever encountered that

does not violate the constraints.

0 100 200 300 400 500 600 700

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Time, (s)

Velo

city,

(m/s

)

STEEL

COMPOSITE

0 100 200 300 400 500 600 7000

100

200

300

400

500

600

Time, (s)

Altitude,

(km

)

STEEL

COMPOSITE

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Figure 6. Performance Results with Mettalic and Composites

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

Time, (s)

Angle

of

Att

ack,

(deg)

STEEL

COMPOSITE

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time, (s)

Late

ral O

verload,

(g)

STEEL

COMPOSITE

0 100 200 300 400 500 600 7000

100

200

300

400

500

600

Time, (s)

Thru

st,

(kN

)

STEEL

COMPOSITE

0 100 200 300 400 500 600 7000

5

10

15

Time, (s)

Axia

l O

verload,

(g)

STEEL

COMPOSITE

0 100 200 300 400 500 600 7000

5

10

15

20

25

Time, (s)

Mass,

(Mg)

STEEL

COMPOSITE

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Table 4. Optimum Design Variables.

Design Variable Symbol Units Metallic Composite Metallic

Optimum

Composite

Optimum LBM UBM LBC UBC

Relative Mass Coefficient of Grain

μk1 ratio 0.60 0.75 0.70 0.80 0.699 0.732

μk2 / μk1 ratio 1.00 1.10 1.00 1.10 1.000 1.051

μk2 / μk1 ratio 1.00 1.10 1.00 1.10 1.000 0.952

Body Diameter D1,2 m 1.25 1.40 1.25 1.40 1.299 1.257

D3 m 0.80 0.90 0.80 0.85 0.850 0.815

Chamber Pressure

pc1 bar 55.0 65.0 65.0 75.0 64.59 70.02

pc2 bar 55.0 65.0 65.0 75.0 60.25 72.48

pc3 bar 55.0 65.0 40.0 60.0 60.01 47.71

Nozzle Exit Pressure

pe1 bar 0.10 0.16 0.12 0.16 0.140 0.149

pe2 bar 0.10 0.16 0.10 0.16 0.130 0.128

pe3 bar 0.08 0.12 0.05 0.10 0.099 0.076

Coefficient of Grain Shape

ks1 1.50 2.30 1.50 2.30 2.243 1.626

ks2 1.50 2.30 1.50 2.30 2.299 2.100

ks3 1.50 2.30 1.50 2.30 1.931 1.959

Grain Burning Rate

ui mm/s 5.00 8.00 5.00 6.50 5.794 5.538

ui mm/s 5.00 8.00 5.00 6.50 6.999 6.161

ui mm/s 5.00 8.00 5.00 4.50 6.364 4.510

Max Angle of Attack αm deg 1.00 22.0 1.00 22.0 21.96 21.48

Launch Maneuver Variable a 0.01 0.10 0.01 0.10 0.016 0.011

VIII. Conclusion

Light-weight motor case is a key to achieve the high propellant to inert mass ratio and thus leading to enhanced

performance. This research effort elaborates substitution of composite for metallic SRMs used in the ASLV, and its

effect of on weight reduction and performance improvement. Composite materials provide the exceptional capability

to enhance performance of the vehicle. The conceptual design approach of this research replaces material data bank

from metallic to composite disregarding the manufacturing details to reach feasible solution at reasonable

computational cost. Further study on manufacturability and selection of composites is recommended to improve the

fidelity of the design process and move on to preliminary design stage.

References 1Deo, R.B., Starnes, J.H., Holzwarth, R.C., ―Low-cost composite materials and structures for aircraft applications‖, RTO AVT

Specialists’ Meeting on “Low Cost Composite Structures”, RTO-MP-069(II), 2001. 2Thompson, H.D., Smith, G.B. and Bixler, C.H., Advanced Composite Satellite Equipment Support Module Study, Fibrous

Composites in Structural Design, E.M. Lenoe, D.W. Oplinger and J.J. Burke, Eds., Plenum Press, New York, 1980. 3Carl Zweben, ―Advanced Composites; A Revolution for the Designer‖, AIAA-81-0894. 4Alain Lacombe, Patrick Spriet, Alain Allaria, Eric Bouillon, Georges Habarou, ―Ceramic Matrix Composites to make

Breakthroughs in Aircraft Engine Performance,‖ 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and

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Development,‖ 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2004, AIAA Paper 2004-4220. 6A.Dufour, M.Calabro, L Lecardonnel, D.Jeannot, ―ARIANE 2010 Composite Case SRM: An Example of Multidisciplinary

Approach,‖ 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2001, AIAA Paper 2001-3724. 7J Hilden, ―Thiokol corporation’s Castor120 Solid Propellant Booster Program,‖ AIAA Space Programs and Technologies

Conference, 1992, AIAA Paper 1992-1658. 8Sutton, G.P. and Biblarz, O., Rocket Propulsion Elements, 7th ed., New York: Wiley-Interscience, 2001. 9LinShu, H., Launch Vehicle Design. Beijing University of Aeronautics and Astronautics Press, Beijing, 2004. 10Blake, W.B., Missile DATCOM: User’s manual-1997 FORTRAN 90 revision, Oklahoma: Wright-Patterson AFB, 1998. 11Zipfel, P.H., Modeling and Simulation of Aerospace Vehicle Dynamics, Reston: AIAA, 2007.

12Fleeman F., Eugene L., Tactical Missile Design, AIAA Education Series, Reston: 2001. 13Garret N V., Numerical Optimization Techniques for Engineering Design, 3rd ed., Second Printing, Vanderplaats Research

and Development, Inc. Colorado Springs, 1999. 14Reeves, C.R., Modern Heuristic Techniques for Combinatorial Problems, New York: John Wiley & Sons; 1993. 15Holland, J.H., Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology,

Control, and Artificial Intelligence, MIT Press, Cambridge, MA, 1992. 16Goldberg D., Genetic Algorithms in Search, Optimization and Machine Learning, 1st ed., Addison-Wesley Longman,

Reading, MA, 1989. 17Davis L., The Handbook of Genetic Algorithms, Van Nostrand Reingold, New. York, 1991. 18Crossley, W.A., and Williams, E.A., ―A Study of Adaptive Penalty Functions for Constrained Genetic Algorithm-based

Optimization, AIAA Aerospace Sciences Meeting and Exhibit, 1997, AIAA Paper 1997-0083.

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