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i

Design of a Tomahawk Cruise Missile Booster Rocket Motor

by

Devon K Cowles

An Engineering Project Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

MASTER OF MECHANICAL ENGINEERING

Approved

_________________________________________Ernesto Gutierrez-Miravete Project Adviser

Rensselaer Polytechnic InstituteHartford Connecticut

May 2012



ii

copy Copyright 2012

by

Devon K Cowles

All Rights Reserved



iii

CONTENTS

LIST OF TABLES v

LIST OF FIGURES vi

LIST OF EQUATIONS vii

LIST OF SYMBOLS ix

Glossary xii

ABSTRACT xiii

1 IntroductionBackground 1

11 Rockets 1

12 Mission Requirements 2

13 Structural Requirements 3

2 Methodology 4

21 Assumptions 4

22 Flight Performance 5

23 Motor thrust requirements 6

24 Motor Casing Sizing 9

25

Material 11

251

Aluminum Alloy 11

252

Composite Material 11

3

Results 16

31

Engine Parameters 16

32

Aluminum Alloy Casing Design 16

321

Aluminum Casing Geometry 16

322

Finite Element Analysis 17

33 Composite Casing Design 21

331 Layup 21

332 Composite Casing Geometry 22



iv

333 Finite Element Analysis 24

334 Aluminum to Composite Comparison 27

4 Conclusion 29

References 30

Appendix A ndash Classical Lamination Matlab Code 31



v

LIST OF TABLES

Table 11 Mission Requirements 2

Table 12 Tomahawk Cruise Missile Specifications 2

Table 13 Available Composite Propellant 3

Table 21 E357 T-6 Casted Aluminum 11

Table 22 Hexcel Intermediate Modulus Carbon FiberResin Properties 12

Table 31 Engine Parameters 16

Table 32 Aluminum Engine Weight 17

Table 33 Laminate Properties Calculated by CLT 22

Table 34 Composite Engine Weight 23

Table 35 Laminate Properties in ANSYS 24

Table 36 Composite Casing Stress and Margins 27



vi

LIST OF FIGURES

Figure 11 Typical Rocket Components [2] 1

Figure 21 Rocket Free Body Diagram [3] 5

Figure 22 Aluminum Engine Casing Concept 10

Figure 23 Composite Engine Casing Concept 10

Figure 24 Finite Element Load and Boundary Conditions 11

Figure 31 Aluminum Alloy Casing Detail 17

Figure 32 Maximum Stress Aluminum Engine Casing Upper 18

Figure 33 Maximum Stress Aluminum Engine Casing Lower 19

Figure 34 Assembly Flight Path 19

Figure 35 Flight Performance 20

Figure 36 Rocket Angle Altitude and Velocities 21

Figure 37 Composite Casing Detail 23

Figure 38 FEA Geometry for Composite Casing 24

Figure 39 Load and Boundary Conditions Composite Casing 25

Figure 310 Maximum Total Deformation Composite Casing 26

Figure 311 Top Radius Stress Composite Casing 26

Figure 312 Flight Performance Comparison 28



vii

LIST OF EQUATIONS

Equation 21 ndash Flight path angle to ground 5

Equation 22 ndash Axial acceleration at 1000 feet 6

Equation 23 ndash Axial acceleration below1000 feet 5

Equation 24 ndash Radial acceleration above 1000 feet 6

Equation 25 ndash Radial acceleration below 1000 feet 6

Equation 26 ndash Axial velocity 6

Equation 27 ndash Radial velocity 6

Equation 28 ndash Axial dispacement 6

Equation 29 ndash Radial dispacement 6

Equation 210 ndash Horizontal distance and altitude matrix 6

Equation 211 ndash Propellant burn Area 6

Equation 212 ndash X Function 7

Equation 213 ndash Nozzle exit area 7

Equation 214 ndash Nozzle throat area 7

Equation 215 ndash Combustion chamber pressure 7

Equation 216 ndash Propellant burn rate 7

Equation 217 ndash Expansion ratio 7

Equation 218 ndash Exit pressure 8

Equation 219 ndash Ideal thrust coefficient 8

Equation 220 ndash Actual thrust coefficient 8

Equation 221 ndash Specific impulse 8

Equation 222 ndash Propellant core area 8

Equation 223 ndash Propellant core volume 8

Equation 224 ndash Combustion chamber volume 8

Equation 225 ndash Propellant volume 8

Equation 226 ndash Propellant mass 8

Equation 227 ndash Mass flow 8

Equation 228 ndash Burn time 8

Equation 229 ndash Total impulse 9



viii

Equation 230 ndash Laminae StressStrain relationship 13

Equation 231 ndash Laminae Reduced Compliance StressStrain relationship 13

Equation 232 ndash Laminae Global Reduced Compliance StressStrain relationship 13

Equation 233 ndash Transformation matrix 13

Equation 234 ndash Laminae Transformed StressStrain relationship 13

Equation 235 ndash Laminae global x stiffness 13

Equation 236 ndash Laminae global y stiffness 13

Equation 237 ndash Laminae global shear modulus 13

Equation 238 ndash Laminae Poissonrsquos ratio xy 13

Equation 239 ndash Laminae Poissonrsquos ratio yx 14

Equation 240 ndash Laminae Global Reduced Stiffness StressStrain relationship 14

Equation 241 ndash Reduced Stiffness Matrix definition 14

Equation 242 ndash Extensional stiffness matrix 14

Equation 243 ndash Couplingstiffness matrix 14

Equation 244 ndash Bending stiffness matrix 14

Equation 245 ndash Laminate LoadStrain relationship 14

Equation 246 ndash Tsai-Hill failure criteria 15

Equation 31 ndash Yield stress margin of safety 18

Equation 32 ndash Ultimate stress margin of safety 18



ix

LIST OF SYMBOLS

Motion

a ndash Acceleration (fts2)

awing ndash LiftMass of Missile Wing (32174 fts

2

)Cd ndash Coefficient of Drag

Cl ndash Coefficient of Lift

F ndash Engine Thrust (lbf )

g ndash Acceleration of Gravity on Earth (32174 fts2)

ld ratio ndash Ratio of Cl to Cd

tn ndash Time at Increment n (s)

Ψ ndash Engine Thrust Relative to Horizontal (degrees)

ρair ndash Density of Air (lbft3)

θ ndash Direction of Flight Relative to Horizontal (degrees)

v ndash Velocity in Rocket Coordinates (fts)

x ndash Axial Displacement in Rocket Coordinates (ft)

y ndash Radial Displacement in Rocket Coordinates (ft)



x

Engine

A ndash Nozzle Throat Cross-Sectional Area (in2)

A b ndash Propellant Burning Area (in2)

Aconduit ndash Area of Core in Propellant Charge (in2)

Ae ndash Cross Sectional Area of Exhaust Cone (in2)

Cf ndash Thrust Coefficient

dc ndash Propellant Outer Diameter (in)

de ndash Diameter of Exhaust Cone (in)

ε ndash Expansion Ratio

Fn ndash Engine Thrust (lbf )

γ ndash Specific Heat Ratio

Isp ndash Specific Impulse (s)

It ndash Total Impulse (lbf -s)

k ndash Propellant Burn Rate Factor

Lc ndash Length of Propellant (in)

ṁ ndash Mass Flow Rate (lbms)

mc ndash Mass of Propellant (lbm)

n ndash Propellant Burn Rate Factor

Pc ndash Chamber Pressure (psi)

Po ndash Atmospheric Pressure (psi)

R ndash Gas Constant (lbf -inlbm-R)

r b ndash Propellant Burn Rate (ins)

t b ndash Propellant Burn Time (s)

ρ p ndash Density of Propellant (lbmin3)

Tc ndash Propellant Burn Temperature (degR)

V0 ndash Volume of No Core Propellant (in3)

Vc ndash Propellant Volume (in3)

Vconduit ndash Conduit Volume (in3)

X ndash Non-Dimensional Mass Flow Rate in Nozzle Throat



xi

Material

E ndash Youngrsquos Modulus (psi)

ε ndash Normal Strain (inin)

γ ndash Shear Strain (inin)

Fcy ndash Yield Compressive Strength (psi)

Fcu ndash Ultimate Compressive Strength (psi)

Fty ndash Yield Tensile Strength (psi)

Ftu ndash Ultimate Tensile Strength (psi)

Fsu ndash Ultimate Shear Strength (psi)

G ndash Shear Modulus (psi)

MSyld-comp ndash Yield Strength Margin of Safety ndash Compressive

MSult-comp ndash Ultimate Strength Margin of Safety ndash Compressive

MSyld-tensile ndash Yield Strength Margin of Safety ndash Tensile

MSult-tensile ndash Ultimate Strength Margin of Safety ndash Tensile

ν ndash Poissonrsquos Ratio

σ ndash Normal Stress (psi)

[Q] ndash Laminae Reduced Stiffness Matrix (psi)

[Q ] ndash Laminae Transposed Reduced Stiffness Matrix (psi)

[S] ndash Laminae Reduced Compliance Matrix (in2lb)

[S ] ndash Laminae Transposed Reduced Compliance Matrix (in2lb)

τ ndashShear Stress (psi)



xii

Glossary

Adiabatic ndash A thermodynamic process in which heat is neither added nor removed from

the system

AL ndash Aluminum powder used as a solid fuel in a solid rocket motorANSYS ndash Software created by ANSYS Inc used for finite element analysis

AP ndash A solid oxidizer made of Ammonium Perchlorate

BurnSim ndash Software created by Gregory Deputy to simulate the performance of a solid

propellant rocket motor

BATES ndash A cylindrical solid propellant configuration with a cylindrical core

CATIA ndash Software created by Dassault Systeacutemes to perform 3 dimensional computer

aided design

CLT ndash Classical Laminate Theory used to calculate laminate properties from the

properties of the individual layers

Condi Nozzle ndash A convergentdivergent nozzle

CTPB ndash A polymer binder material made of Carboxyl Terminated Polybutadiene

Isentropic ndash A thermodynamic process in which there is no change in entropy of the

system

Laminae ndash A single layer of a composite matrix

Laminate ndash A stack of laminae

Slinch ndash Unit of mass in the United States customary units 12 Slugs = 1 Slinch



xiii

ABSTRACT

The purpose of this project is to design a ground launched rocket booster to meet

specific mission requirements The mission constraints include minimum speed

maximum flight altitude as well as length and weight limits The mission is to launch a3000 lb payload such as a Tomahawk cruise missile to an altitude of 1000 feet and

accelerate the missile to 550 MPH (807 fps) To meet these mission requirements the

weight of the rocket body should be as light as possible while maintaining the required

structural integrity and reliability The motor parameters such as the nozzle size

expansion ratio propellant size and shape are determined through an iterative process

The thrust performance from a preliminary motor design is used to calculate the

resulting flight performance based on the calculated thrust overcoming gravity inertia

and aerodynamic drag of the booster rocket and cruise missile assembly The engine

nozzle parameters are then varied to meet the mission requirements and to minimize

excess capability to ensure a weight efficient motor The initial motor casing design

will be made of light weight cast aluminum The aluminum motor design will be

compared to a design made of a fiber and resin composite material The composition and

layup of the composite material and the thickness of the aluminum material will be

designed to meet industry standard safety margins based on the materialrsquos strength

properties This paper will present the calculated engine parameters as well as the

engine weight and engine size for both the aluminum casing and the composite casing



1

1 IntroductionBackground

11 Rockets

Rockets are a type of aircraft used to carry a payload at high speeds over a wide range of

distances depending on the design Rockets are powered by a reaction type engine

which uses chemical energy to accelerate and expel mass through a nozzle and relies on

the principles of Sir Isaac Newtonrsquos third law of motion [1] to propel the rocket forward

Rocket engines use either solid or liquid fuel They carry both the fuel and the oxidizer

required to convert the fuel into thermal energy and gas byproducts The gas byproducts

under pressure are then passed through a nozzle which converts the high pressure low

velocity gas into a low pressure high velocity gas

The following figure shows the different components of a typical rocket

Figure 11 Typical Rocket Components [2]



2

12 Mission Requirements

The rocket considered in this study is a ground launched booster that is used to launch a

payload such as a Tomahawk cruise missile to a prescribed altitude and to a required

velocity The mission can be viewed in three phases In the first phase the booster is onthe ground at rest and launches vertically In the second phase the assembly transitions

from a vertical orientation to a horizontal orientation while climbing to 1000 feet In the

third phase the booster accelerates the payload horizontally to 550 MPH (807 fps) The

rocket engine must be sized appropriately to meet the mission requirements as

summarized in Table 11 The Tomahawk cruise missile specifications are listed in

Table 12 The cruise missile in this mission will use an onboard gas turbine engine to

continue flight once the missile has reached 1000 ft altitude and 550 MPH (807 fps) In

the horizontal portion of the flight the cruise missile will deploy the stowed wings to

provide lift which will allow the thrust of the booster to be used solely to accelerate the

missile to the appropriate speed Once the missile has reached the target altitude and

speed and the solid propellant has been consumed the booster will be jettisoned from the

cruise missile assembly to fall back to earth The total assembly is limited to 3500 lbm

and the payload is 2700 lbm The properties of the fuel to be used in this mission are

shown in Table 13

Table 11 Mission Requirements

Value Units

Altitude range 0 - 1000 ft

Minimum Velocity 550 MPH

Maximum Mass 3500 lbm

Payload Mass 2700 lbm

Table 12 Tomahawk Cruise Missile Specifications

RGM 109DLength (in) Diameter (in) Weight (lb)

219 209 2700



3

Table 13 Available Composite Propellant

Oxidizer AP (70)

Fuel Binder CTPB (12)

Metallic Fuel AL (16)

Curative Epoxy (2)Flame Temperature (R) 6840

Burning Rate Constants

k 0341

n 04

Density (slinchin ) 164E-4

Molecular Weight (kgkmole) 293

Gas Constant (lb-inslinch-R) 2386627

Ratio of Specific Heats 117

Characteristic Velocity (ins) 62008

13 Structural Requirements

The rocket engine casing must be able to withstand the internal engine pressure loads

and the force applied to the payload through the attachment point In some locations the

casing materials must be able to withstand high pressures and elevated temperatures dueto the combustion of the fuel

In this project the casing design will be determined based on the stress analysis using

closed form equations and the finite element method The nozzle and casing will be

sized using E357-T6 aluminum alloy and then resized using carbon fiberresin composite

materials The components will be sized based on the maximum load and pressure the

casing will be subjected to during the mission This maximum load will be referred to as

the limit load



4

2 Methodology

21 Assumptions

The following assumptions are made for the motor design to simplify the analysis

1)

The booster is an ideal rocket This is to assume the following six assumptions

are true or they are corrected for with an efficiency factor See Equation 220

2) The specific heat ratio (γ) of the exhaust gases is constant throughout the booster

The specific heat ratio is a function of temperature and temperature is assumed to

be constant due to thermal insulation and low dwell time

3) Flow through the nozzle is adiabatic isentropic and one dimensional This

assumption claims the process is reversible no heat is lost and pressure and

temperature changes only occur in the axial direction The true losses in thesystem are accounted for in the efficiency factor

4)

There is no loss of total pressure during combustion True pressure losses are

accounted for with the efficiency factor

5)

The flow area in the combustion chamber is large compared to the nozzle area so

the velocity at the nozzle entrance is negligible

6)

All of the exhaust gasses exit the nozzle in the axial direction Due to the low

altitude range of this mission the nozzle can be design such that the exhaust flow

is axial

7)

The nozzle is a fully expanding Condi nozzle Due to the narrow altitude range

of this mission the nozzle can be designed such that the exhaust is fully

expanding and not over or under expanded

8) The coefficient of drag for the payload and booster assembly is 075 The actual

drag coefficient will be based on tests

9) In the rocket combustion chamber there is a 2mm (0079 inch) liner is made of a

material of sufficient properties to keep the casing temperatures below 300

degrees Fahrenheit This assumption is reasonable based on similar designs and

preliminary thermal analysis not presented here



5

22 Flight Performance

Thrust is required to accelerate the payload fuel and motor casing mass to 1000 feet and

550 MPH (807 fps) overcoming the forces of gravity mass inertia and aerodynamic

body drag As the propellant is consumed the thrust increases and the mass of the booster assembly decreases As a result the axial and the radial acceleration velocity

and displacement are calculated in a discretized fashion for time steps of 001 seconds

The displacements are then transformed from the rocket reference frame to the ground

reference frame to determine altitude and horizontal velocity

The flight path is predetermined to transitions from a vertical flight to a horizontal path

based on the function [3]

[21]

θ is the angle of the rocket axis to the ground as shown in Figure 21 The rocket at the

beginning of the launch is vertical (θ=90deg)

Figure 21 Rocket Free Body Diagram [3]

The axial acceleration of the body is calculated by the following equation below 1000feet

[22]

The axial acceleration is calculated by the following equation when the cruise missile

wings are deployed at 1000 feet



6

[23]

The acceleration in the direction perpendicular to the cruise missile wingspan plane is

calculated as follows when below 1000 ft is

[24]


calculated as follows when the cruise missile wings are deployed at 1000 ft

+ [25]

The axial (x) and radial (y) velocity is calculated using

+ lowast [26] + lowast [27]

And the displacement is similarly calculated


The displacement values are then transformed into the ground reference frame to

determine the horizontal distance and the altitude

+ [210]

Where m=cos(θ) and n=sin(θ)

23 Motor thrust requirements

The equations above are dependent on the thrust (F) of the booster engine The thrust is

calculated using equations found in [4] For the preliminary sizing of the rocket motor

these closed form equations are used to calculate the engine performance The

maximum diameter of the engine is sized to be similar to that of the cruise missile The

length of the propellant is limited to 26 inches to minimize the length of the booster

motor Knowing the diameter and the length of the charge the burn diameter can be

calculated

∙ ∙ [211]



7

The X-function is the non-dimensional mass flow of the motor and is calculated by

lowast radic [212]

The exhaust cone diameter is a variable that can influence thrust and is adjusted as

needed in the design to get the appropriate thrust based on a given expansion ratio The

chosen diameter for this rocket motor is 13 inches The exit area is calculated from the

cone diameter

[213]

The nozzle area is calculated from the exit area and the prescribed expansion ration

epsilon The expansion ratio can be adjusted in the design phase in an iterative nature to

achieve the required thrust

lowast [214]

The chamber pressure can now be calculated based on the propellant properties and the

nozzle area

∙ ∙ lowast∙lowast [215]

The burn rate of the propellant is sensitive to the chamber pressure The burn rate is

calculated as ∙ [216]

As can be seen in the previous two equations the chamber pressure is dependent on

the burn rate and the burn area Both the burn rate and the burn area are increasing as

the propellant is consumed which provides a progressive burn rate To minimize this

effect creative cross sectional areas can be made so that the total area does not increase

with propellant consumption

In order to calculate the thrust coefficient the exit velocity or exit Mach number need to be calculated Due to the nature of the following equations an iterative process is used

to solve for Me

+ ∙ [217]



8

+ ∙ [218]

Knowing the exit velocity and the chamber pressure the thrust coefficient is calculated

as shown

+ lowast [219]

These calculations are based on an ideal nozzle with full expansion Due to thermal and

other losses the actual thrust coefficient will be about 90 of the ideal thrust

coefficient

∙ [220]

A measure of the efficiency of the rocket design is the specific impulse The specific

impulse can provide an idea of the propellant flow rate required for the given thrust The

theoretical specific impulse is calculated by

lowast∙ [221]

The area of the core in the BATES type fuel configuration or a cylindrical configuration

should be four times the area of the nozzle to prevent erosive burning From this area

the volume of the core can be calculated using the propellant length The propellant

volume is calculated by subtracting this core volume from the combustion chambervolume From this volume the mass of the propellant can be determined

∙ lowast [222] lowast [223] [224] [225] ∙ [226]

To calculate the burn time the mass flow rate is determined and then the burn time iscalculated based on the propellant mass

∙ [227]

[228]



9

An important characteristic of the motor performance is the total impulse This is the

average thrust times the burn time

∙ [229]

All of the above calculations are performed in Microsoft Excel The internal iterative

solver in Excel is used to determine the appropriate nozzle diameter and exhaust cone

diameter to meet the mission requirements The Excel spreadsheet also calculates

additional engine parameters including chamber pressure which is required to properly

size the structural components of the engine casing

The BurnSim software is then used to more accurately calculate the engine thrust

chamber pressure and the mass flow These parameters are then imported into Excel to

calculate the flight performance based on the BurnSim results

24 Motor Casing Sizing

Based on the thrust load and the chamber pressure the stresses in the initial casing

design is analyzed using closed form equations provided in Roarkrsquos Handbook [5]

ANSYS finite element software is then used to determine the stresses in the final casing

design The stresses are compared to the yield and ultimate strength of the material Anaerospace standard factors of safety of 15 for ultimate strength and 115 for yield

strength The metal alloy version of the rocket casing is to be made of a cast E357-T6

aluminum Casting the casing will minimize the number of bolted joints and maximize

the strength of the structure which will minimize the weight The aluminum casing

concept is shown in Figure 22 The filler is a light weight polymer designed to prevent

end burning of the propellant opposite the nozzle The liner is a thin coating on the

casing made of a material designed to keep the casing temperature below 300degF The

filler liner and propellant can be poured into the casing with a core plug and then cured

The plug is then removed The nozzle can be made of high temperature material

designed for the direct impingement of hot gases There are many such materials listed

in [3] The nozzle could be segmented into axially symmetric pieces to facilitate

assembly and then bonded into place The composite material version of the rocket



10

motor casing will be designed of a similar shape as shown in Figure 23 The composite

assembly will be assembled similar to the aluminum version except the Thrust Plate is

bonded to the top of the casing

Figure 22 Aluminum Engine Casing Concept

Figure 23 Composite Engine Casing Concept

Figure 24 shows a typical 2 dimensional axisymmetric finite element model used to

analyze the motor casing Pressure is applied to the internal surfaces up to the nozzle

where the pressure drops to near ambient values A thrust load is applied to the top

surface in the axial direction (depicted as ldquoCrdquo) This load application represents wherethe thrust is transferred to the payload The casing is grounded at the end of the nozzle

The load is typically distributed throughout the nozzle and not concentrated on the end

but the nozzle is structurally sturdy and not an area of concern for this project

Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11

Figure 24 Finite Element Load and Boundary Conditions

25 Material

251

Aluminum Alloy

The Table 21 shows the material properties for E357T-6 cast aluminum prepared per

AMS 4288 [6] This alloy is used since it has a relatively high strength to weight ratio

for a cast alloy

Table 21 E357 T-6 Casted Aluminum

AMS 4288 Ftu (ksi) Fty (ksi) Fcy (ksi) Fsu (ksi) E (ksi) ν ρ (lbin )

T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -

252 Composite Material

A carbon epoxy composite material from Hexcel [8] is chosen for the composite version

of the casing The properties for unidirectional fibers are shown in Table 22 The



12

maximum casing temperature is 300degF and so the strength is reduced by 10 based on

similar material trends The strength is further reduced by 50 as an industry standard

ultimate strength safety factor

Table 22 Hexcel Intermediate Modulus Carbon FiberResin Properties Ftu 1

(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280

This unidirectional material is layered several plies thick into a laminate In this project

the laminate is made of 84 layers with each layer being 0006 in thick for a total of 0504

thick Some of the layers will be at different angles from the others to tailor the material

for the mission loads This allows the composite material to be optimized to minimize

weight without sacrificing strength The overall laminate properties will be calculated

based on the material properties in Table 22 utilizing Classical Laminate Theory and

Kirchoffrsquos Hypothesis [7] The following assumptions are made

1) Lines normal to the midplane of a layer remain normal and straight and normal

during bending of the layer

2) All laminates are perfectly bonded together so that there is no dislocation

between layers

3) Properties for a layer are uniform throughout the layer

4) Each ply can be modeled using plane stress per Kirchoffrsquos Hypothesis

The following are the equations used to model the composite For details see [7]

The stress strain relationship of the laminate is defined by

This equation is expanded to



13

[230]

Using plane stress assumptions the equation can be reduced to the following

[231]

Where [S] in Equation 212 is the reduced compliance matrix This matrix istransformed for each layer to equate the properties into the laminate coordinate system

as follows

[232]

Where

[233]

This can be represented by

[234]

The global properties for the laminate can be calculated as follows

[235] [236]

[237]

[238]



14

[239]

In the laminate coordinate system the stress to strain relationship for a single layer can

be written as

[240]

where

[Q ] = [S ]-1 [241]

To create the overall laminate load to strain relationship the ABD matrix is created as

follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]

Where zk is the z-directional position of the ply number k In a symmetric layup z=0 at

the midplane and is positive in the lower layers and negative in the upper layers

The complete load to strain relationship matrix is

[245]

The maximum stress for the laminate is based on Tsai-Hill failure criteria for each

layer The laminate will be considered to have failed when any layer exceeds the

maximum allowed stress An Excel spreadsheet is used to calculate the stress in the

layers based on the laminate stress from the finite element model The layer stresses are

=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15

used with the Tsai-Hill equation to determine a static margin The Tsai-Hill failure

criteria equation is as follows

+

+

lt [246]

Where

X1=F1t if σ1gt0 and F1c if σ1lt0


Y=F2t if σ2gt0 and F2c if σ2lt0

S=F12



16

3 Results

31 Engine Parameters

The predicted engine parameters based on the chosen nozzle diameter expansion ratio

and fuel size are shown in Table 31

Table 31 Engine Parameters

Parameter Value Units

Maximum Thrust 13481 lb

Max Chamber Pressure 1104 psi

Total Impulse 120150 lbf-s

Specific Impulse 237 s

Burn Diameter 2087 in

Conduit Diameter 655 in

Propellant Length 26 in

Burn Time 1288 s

Nozzle Diameter 328 in

Nozzle Exit Diameter 802 in

Expansion Ratio 60 -

Exit Mach Number 286 -

Optimal Thrust

Coefficient161 -

Thrust Coefficient Actual 145 -

32 Aluminum Alloy Casing Design

321

Aluminum Casing Geometry

Based on the engine parameters shown in Table 31 an engine casing is designed and

optimized for weight based on the material strength as shown in Table 21 The

maximum casing temperature is 300degF and so the material properties are reduced from

the room temperature properties as shown in the table Figure 31 shows the final

dimensions of the engine casing Table 32 shows the final weight of the aluminum



17

engine casing assembly The engine casing is frac12 inch thick throughout most of the

design Some areas of the casing are thicker to accommodate the stresses due to the

thrust load transmitted to the payload through the top of the casing in addition to the

internal pressure load

Figure 31 Aluminum Alloy Casing Detail

Table 32 Aluminum Engine Weight

Component Weight (lb)

Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736

322 Finite Element Analysis

Linear elastic finite element analysis is performed using ANSYS Workbench V13 The

loads and boundary conditions are applied as shown in Figure 24 in section 2 The

results are shown in Figure 32 and Figure 33 The peak stress occurs in the top of the

casing in Figure 32 where the structure is supporting the internal pressure load as well



18

as a bending load due to the thrust load The thickness of the casing in this area is

increased to 120 inches as shown in Figure 31 Figure 33 shows the stresses for the

lower section which are not as high as in the upper section This peak stress in this

figure occurs where the structure is supporting a bending load in addition to the internal

pressure load The thickness in this area is increased to 07 inches as shown in Figure

31 to accommodate the higher stresses The margins of safety are calculated using the

maximum casing stress with a 15 safety factor on the ultimate strength and a 115 safety

factor on the yield strength

[31]

[32]

With a maximum stress of 25817 psi the margin of safety for the aluminum casing is

024 for yield strength and 001 for ultimate strength

Figure 32 Maximum Stress Aluminum Engine Casing Upper



19

Figure 33 Maximum Stress Aluminum Engine Casing Lower

The predicted flight performances based on the total assembly weight and predicted

engine thrust is shown in Figure 34Figure 35 and Figure 36 Figure 34 shows

ground distance covered by the cruise missile as it reaches the 1000 foot target altitude

This figure shows the transition from vertical to horizontal flight This transition was

chosen to provide a smooth transition

Figure 34 Assembly Flight Path

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20

Figure 35 shows the thrust altitude and the horizontal velocity over time As shown

the assembly reaches the target altitude of 1000 feet at about 10 seconds and then

continues to accelerate until it reaches the target velocity of 807 ftsec at 126 seconds

The thrust shown in Figure 35 is predicted by BurnSim The thrust profile is

progressive since the burn rate accelerates with increased burn area and increased

chamber pressure The thrust has a drop at approximately 96 seconds The hypothesis

as to why this occurs is the propellant is divided into 3 stages in BurnSim The bottom

stage is allowed to burn on the nozzle end which is open as shown in Figure 22 The

other two segments are prevented from burning on the ends As the propellant is

consumed the bottom charge is burning both axially and radially and eventually there

will no longer be an end face At this point the total burn area will drop resulting in a

pressure drop which will result in a thrust decrease This phenomenon can be further

explored with the aid of the software designer to verify accuracy

Figure 35 Flight Performance

Figure 36 shows vertical and horizontal acceleration and altitude of the assembly in

shiprsquos coordinates with respect to time These are contrasted with θ which is the angle

of the flight path with respect to the ground horizontal

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21

Figure 36 Rocket Angle Altitude and Velocities

33 Composite Casing Design

The composite version of the engine casing has the same general shape as the aluminum

version but is made of wound fibers over a sand mold The fibers are coated in an epoxy

resin The thickness of the material is tailored to optimize the weight and strength of the

structure For ease manufacturing and analysis the casing is of uniform thickness

331

Layup

The composite layup is [9020245-45]s Each layer is 0006 inches thick The sub-

laminate has 12 layers and the sub-laminate is layered 7 times The engine casing is 05

inches thick made up of a total of 84 layers The 0 degree orientation is in-line with the

casing axis but following the contour of the shell from top to bottom and the 90 degree

orientation is in the hoop direction This layup will give strength in the hoop direction

for the pressure loading with the 90 degree fibers The 0 and 45 degree fibers give the

laminate strength for bending in the curved geometry at the top and bottom of the casing

to react thrust load

The overall properties of this layup are calculated using classical laminate plate theory

The resulting three dimensional stiffness properties of the laminate as well as the

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22

Poissonrsquos ratios are shown in Table 33 The stress allowable for this laminate would

ultimately be determined through physical testing of the laminate The safety factors are

calculated based on the unidirectional material properties and CLT with Tsai-Hill failure

criteria

Table 33 Laminate Properties Calculated by CLT

Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz

10^6 psi νxy νzx νzy

1068 1068 173 254 053 053 020 038 038

332 Composite Casing Geometry


optimized for weight based on the material strength as shown in Table 22 Figure 37

shows the final dimensions of the engine casing Table 34 shows the final weight of the

composite engine casing assembly Figure 37 shows the dimensions of the composite

casing Due to the superior strength of the composite material over the aluminum the

thickness of the structure is 05 inches throughout Since the composites are lower in

density than the aluminum and the structure is thinner the composite casing is lighter

even with the additional thrust plate hardware



23

Figure 37 Composite Casing Detail

Table 34 Composite Engine WeightComponent Weight (lb)

Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24


A two dimensional axi-symmetric analysis is performed similar to the aluminum casing

The two dimensional geometry is split into segments as shown in Figure 38 so that the

coordinates of the finite elements in the curved sections can be aligned with the

curvature of the geometry This allows the material properties to be as will the fibers

aligned with the geometric curvature The material stiffness properties as applied in

ANSYS are shown in Table 35 These values are the same as in Table 33 but

transposed to align with the coordinate system used in ANSYS In the ANSYS model

the hoop direction is the z-coordinate the axial direction is the y-coordinate and the

radial direction or through thickness is the x-coordinate

Figure 38 FEA Geometry for Composite Casing

Table 35 Laminate Properties in ANSYS

Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020

Figure 39 shows the load and boundary conditions similar to that of the aluminum

casing shown in Figure 24 The additional remote displacement is used on the top

section of the casing to represent the bonded thrust ring shown in Figure 23 This

Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25

constraint prevents the edges of the top hole from expanding or contracting radially but

allows all rotations and axial displacement Figure 310 shows the deformation of the

casing and Figure 311 shows the peak stresses in the top curved section The peak

stresses occur in areas similar to the aluminum casing as expected The margins are

calculated using Tsai-Hill failure criteria A summary of the margin of safety is listed in

Table 36

Figure 39 Load and Boundary Conditions Composite Casing



26

Figure 310 Maximum Total Deformation Composite Casing

Figure 311 Top Radius Stress Composite Casing



27

Table 36 Composite Casing Stress and Margins

Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129

The lowest margin in the composites is similar to that of the aluminum casing in the top

section which is reacting the thrust forces as well as internal pressures These margins

include the temperature knock downs as well as the 15 safety factor Since composites

behave as a brittle material in that they do not significantly plastically deform prior to

failure only ultimate margins are calculated

334 Aluminum to Composite Comparison

Comparing the total weight of the aluminum engine as shown in Table 32 to that of the

composite engine as shown in Table 34 the total weight savings is only 74 lb in an

assembly that weighs over 3000 lb As show in Figure 312 this weight savings has a

minor effect on the flight performance of the assembly



28

Figure 312 Flight Performance Comparison

983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion

A rocket motor provides a great deal of power for a short duration of time In this

project a solid fuel rocket motor is designed to produce over 13000 lb of thrust for

almost 13 seconds which is capable of lifting over 3000 lb of mass to a height of 1000feet and accelerate it to over 550 mph There are many options for size and shape of the

propellant which can have a great influence on the thrust profile A simple cylindrical

propellant shape was utilized in this project for simplicity but other options can be

explored The thrust profile is progressive in that the thrust increases with time The

chamber pressure is a moderate pressure of about 1000 psi The pressure makes it

feasible to use metal alloy and composite casings The advantage of the composite is the

high strength to weight which allows for weight savings For this design the weight

savings is only 74 lb in an assembly that weighs more than 3000 lbs This weight

savings provides marginal flight performance increase as shown in Figure 312 Further

refinements can be done for the composite casing design to decrease the thickness in

high margin locations Varying the thickness will require ply drop offs or fiver

terminations which requires special stress analysis Overall composites can be more

expensive and more technically challenging to manufacture than metal alloys A further

cost and manufacturing analysis would need to be performed to determine if the use of

composites is justified



30

References

[1] Newton Isaac The Mathematical Principles of Natural Philosophy pg 19 1729

[2]

Solid Rocket Motor Wikipedia The Free Encyclopedia WikimediaFoundation Inc 2 February 2012 Web 19 May 2008

[3] Sutton George Paul Rocket Propulsion Elements New York John Wiley ampSons 1992

[4] Ward Thomas A Aerospace Propulsion Systems Singapore John Wiley ampSons 2010

[5] Young Budynas and Sadegh Roarkrsquos Formulas for Stress and Strain NewYork McGraw-Hill 2011

[6] Metallic Materials Properties Development and Standardization (MMPDS-05)US Federal Aviation Administration

[7]

Hyer M W and S R White Stress Analysis of Fiber-reinforced CompositeMaterials Pennsylvania DEStech Publications 2009

[8]

Hexcel (2005 March) Prepreg Technology Pg 26 Retrieved February 022012 from httpwwwhexcelcomResourcesDataSheetsBrochure-Data-SheetsHexForce_Technical_Fabrics_Handbook



31

Appendix A ndash Classical Lamination Matlab Code

Tsai_hill_marginmThis program is to calculate the Tsai-Hill margin of a laminate fromFEA stress Assumption- all layers are at the same stress state in global

coordinates (not ply coordinates) Enter the sxsysxy stresses from FEA for the LAMINATE and thelaminate thickness Program will calculate the layer stresses and perform Tsai-Hillcalculation

clear allclc Normalstressx=40858 user input laminate stress Normalstressy=34018 user input laminate stress Normalstressxy=54751 user input laminate stress plystacktheta=[90045-45-4545090] user input ply orientation plystackz=[084084042042042042084084] user input of plythickness

graphitepolymer user input of ply material

h=size(plystacktheta2) determines how many layers t=0 for n=1h t=t+plystackz(1n)end calculates ply thickness

Nx=Normalstressxt Ny=Normalstressyt Nxy=Normalstressxyt Mx=0My=0 Mxy=0

z(1)=-t2 sets z0 dimension (shifted +1 for matlab purposes)

for N=2h+1 z(N)=z(N-1)+ plystackz(1N-1) end for k=1h

theta=plystacktheta(1k)pi180 Qbar=qbar(thetaE1E2poisson12shear12) for i=13

for j=13 Qbar3d(ijk)=Qbar(ij)

end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13

for j=13 for k=1h A(ij)=A(ij)+Qbar3d(ijk)(z(k+1)-z(k)) B(ij)=B(ij)+Qbar3d(ijk)2((z(k+1))^2-(z(k))^2) D(ij)=D(ij)+Qbar3d(ijk)3((z(k+1))^3-(z(k))^3) end

end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46

for j=13 ABD(ij)=B(i-3j)

end end for i=13

for j=46 ABD(ij)=B(ij-3)

end end for i=46

for j=46 ABD(ij)=D(i-3j-3)

end end

ABD abd=ABD^-1 e0k=abd[NxNyNxyMxMyMxy] e0=[e0k(1)e0k(2)e0k(3)] k=[e0k(4)e0k(5)e0k(6)] for j=122h creates matrix with 2h columns so to have top andbottom values for each layer

jmod=5j+5 converts j back to j=1h for layer properties theta=plystacktheta(jmod)pi180 epsilonxytop=e0+z(jmod)k epsilonxybottom=e0+z(jmod+1)k stiffness=qbar(thetaE1E2poisson12shear12) sigxytop=stiffness epsilonxytop sigxybottom=stiffness epsilonxybottom sig12top=tmatrix(theta)sigxytop sig12bottom=tmatrix(theta)sigxybottom epsilon12top=tmatrix(theta)epsilonxytop epsilon12bottom=tmatrix(theta)epsilonxybottom for i=13

stressxy(ij)=sigxytop(i1) stress12(ij)=sig12top(i1) strainxy(ij)=epsilonxytop(i1) strain12(ij)=epsilon12top(i1)

end for i=13

stressxy(ij+1)=sigxybottom(i1) stress12(ij+1)=sig12bottom(i1)

strainxy(ij+1)=epsilonxybottom(i1) strain12(ij+1)=epsilon12bottom(i1)

end end S =compliancematrix(E1E2E3poisson12poisson13poisson23shear12shear13shear23) deltaH=0 for i=122h

imod=5i+5



33

epsilon3(imod1)=S(13)stress12(1i)+S(23)stress12(2i) deltah(imod1)=epsilon3(imod1)plystackz(imod) deltaH=deltaH+deltah(imod1)

end for i=12h

if (stress12(1i)lt0) X1=Fcu1

else X1=Ftu1

end if (stress12(2i)lt0)

X2=Fcu1 Y1=Fcu2else

X2=Ftu1 Y1=Ftu2 end S1=F12 tsaihill(1i)=(stress12(1i)X1)^2-

stress12(1i)stress12(2i)(X2^2)+(stress12(2i)Y1)^2+(stress12(3i)S1)^2

ms(1i)=1tsaihill(1i)-1

end

Ex=1(abd(11)t) Ey=1(abd(22)t) Gxy=1(abd(33)t) poissonxy=-abd(12)abd(11) stress12 ms

epsilon3 deltah deltaH

epsilonz=deltaHt poissonxz=-epsilonze0(1) poissonyz=-epsilonze0(2)



GraphitepolymerE1=2465610^7 E2=130510^6 E3=E2 shear12=638000 shear13=shear12 poisson12=027 poisson13=poisson12 poisson23=1-(E2E1)(1+(E1(34shear12)-1)2sqrt(2)poisson12) shear23=E2(2(1+poisson23)) Ftu1=208800 Fcu1=139200 Ftu2=6600 Fcu2=21720 F12=8280

compliancematrixm function [S] =

compliancematrix(E1E2E3poison12poison13poison23shear12shear13shear23) S=[1E1-poison12E1-poison13E1000-poison12E11E2-poison23E2000-poison13E1-poison23E21E30000001shear230000001shear130000001shear12] end

qbarm function [qbar] = qbar(thetaE1E2poisson12shear12) S=[1E1-poisson12E10-poisson12E11E20001shear12] Sbar(11)=S(11)cos(theta)^4+(2S(12)+S(33))sin(theta)^2cos(theta)^2+S(22)sin(theta)^4

Sbar(12)=(S(11)+S(22)-S(33))sin(theta)^2cos(theta)^2+S(12)(sin(theta)^4+cos(theta)^4) Sbar(13)=(2S(11)-2S(12)-S(33))sin(theta)cos(theta)^3-(2S(22)-2S(12)-S(33))sin(theta)^3cos(theta) Sbar(21)=Sbar(12) Sbar(22)=S(11)sin(theta)^4+(2S(12)+S(33))sin(theta)^2cos(theta)^2+S(22)cos(theta)^4 Sbar(23)=(2S(11)-2S(12)-S(33))sin(theta)^3cos(theta)-(2S(22)-2S(12)-S(33))sin(theta)cos(theta)^3 Sbar(31)=Sbar(13) Sbar(32)=Sbar(23) Sbar(33)=2(2S(11)+2S(22)-4S(12)-S(33))sin(theta)^2cos(theta)^2+S(33)(sin(theta)^4+cos(theta)^4)

qbar=inv(Sbar) end

tmatrixm function [T] = tmatrix(theta) n=sin(theta)



ii

copy Copyright 2012

by

Devon K Cowles

All Rights Reserved



iii

CONTENTS

LIST OF TABLES v

LIST OF FIGURES vi


LIST OF SYMBOLS ix

Glossary xii

ABSTRACT xiii


11 Rockets 1



2 Methodology 4

21 Assumptions 4




25

Material 11

251

Aluminum Alloy 11

252


3

Results 16

31


32


321


322



331 Layup 21




iv



4 Conclusion 29

References 30




v

LIST OF TABLES














vi

LIST OF FIGURES




















vii

LIST OF EQUATIONS
































viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




iii

CONTENTS

LIST OF TABLES v

LIST OF FIGURES vi


LIST OF SYMBOLS ix

Glossary xii

ABSTRACT xiii


11 Rockets 1



2 Methodology 4

21 Assumptions 4




25

Material 11

251

Aluminum Alloy 11

252


3

Results 16

31


32


321


322



331 Layup 21




iv



4 Conclusion 29

References 30




v

LIST OF TABLES














vi

LIST OF FIGURES




















vii

LIST OF EQUATIONS
































viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




iv



4 Conclusion 29

References 30




v

LIST OF TABLES














vi

LIST OF FIGURES




















vii

LIST OF EQUATIONS
































viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




v

LIST OF TABLES














vi

LIST OF FIGURES




















vii

LIST OF EQUATIONS
































viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




vi

LIST OF FIGURES




















vii

LIST OF EQUATIONS
































viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




vii

LIST OF EQUATIONS
































viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




viii






















ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




ix

LIST OF SYMBOLS

Motion



2















x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




x

Engine































xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




xi

Material























xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




xii

Glossary


the system







aided design






system






xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




xiii

ABSTRACT





















1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




1


11 Rockets













2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




2

















shown in Table 13


Value Units







219 209 2700



3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




3


Oxidizer AP (70)





k 0341

n 04















the limit load



4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




4

2 Methodology

21 Assumptions


1)









4)



5)



6)



is axial

7)












5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




5










[21]





[22]





6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




6

[23]



[24]



+ [25]







+ [210]









calculated

∙ ∙ [211]



7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




7


lowast radic [212]




cone diameter

[213]




lowast [214]


nozzle area










to solve for Me

+ ∙ [217]



8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




8

+ ∙ [218]


as shown

+ lowast [219]



coefficient

∙ [220]




lowast∙ [221]





∙ lowast [222] lowast [223] [224] [225] ∙ [226]


∙ [227]

[228]



9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




9



∙ [229]



























10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




10












Propellant

Casing

Nozzle

Liner

Filler

Propellant

Filler

Liner Nozzle

Casing

Thrust Plate

Igniter Housing

Integral igniter

housing



11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




11


25 Material

251

Aluminum Alloy



for a cast alloy



T=72degF 45 36 36 28 104E3 033 0097

T=300degF 39 37 - - 106E3 - -






12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




12





(psi)

Fcu 1

(psi)

Ftu 2

(psi)

Fcu 2

(psi)

F12

(psi)

E1

(psi)

E2

(psi)

G12

(psi) ν12

room

temperature348000 232000 11000 36200 13800

2466000 1305000 638000 027300degF 313200 208800 9900 32580 12420

15 Safety

Factor208800 139200 6600 21720 8280











between layers








13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




13

[230]


[231]


as follows

[232]

Where

[233]


[234]


[235] [236]

[237]

[238]



14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




14

[239]


be written as

[240]

where

[Q ] = [S ]-1 [241]


follows

( )sum=

minusminus= N

1k 1k k ij

_

ij zzQAk

[242]

( )sum=

minusminus= N

1k

21k

2k ij

_

ij zzQBk

[243]

( )sum=

minusminus= N

1k

31k

3k ij

_

ij zzQDk

[244]




[245]





=

0XY

0Y

0X

0XY

0Y

0X

66

26

26

22

16

12

161211

66

26

16

26

22

12

16

12

11

662616662616

262212262212

161211161211

XY

Y

X

XY

Y

X

κ

κ

κ

γ

ε

ε

D

D

D

D

D

D

DDD

B

B

B

B

B

B

B

B

BBBBAAA

BBBAAA

BBBAAA

M

M

M N

N

N



15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




15



+

+

lt [246]

Where




S=F12



16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




16

3 Results













Burn Time 1288 s





Optimal Thrust

Coefficient161 -



321









17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




17








Engine Casing 172

Fuel 507

LinerFiller 50

Nozzle 7

Total 736








18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




18









[31]

[32]






19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




19








983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983089983090983088983088

983089983092983088983088

983088 983090983088983088 983092983088983088 983094983088983088 983096983088983088 983089983088983088983088 983089983090983088983088 983089983092983088983088 983089983094983088983088 983089983096983088983088 983090983088983088983088

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983111983154983151983157983150983140 983108983145983155983156983137983150983139983141 983080983142983156983081

983110983148983145983143983144983156 983120983137983156983144

983137983148983156983145983156983157983140983141 (983142983156983081



20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




20


















983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983090983088983088983088

983092983088983088983088

983094983088983088983088

983096983088983088983088

983089983088983088983088983088

983089983090983088983088983088

983089983092983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087

983155 983141 983139 983081

983124 983144 983154 983157 983155 983156 983080 983148 983138 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983124983144983154983157983155983156 (983148983138983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




21







331

Layup











983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088

983089983088

983090983088

983091983088

983092983088

983093983088

983094983088

983095983088

983096983088

983097983088

983088 983090 983092 983094 983096 983089983088 983089983090

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081 983137 983150 983140

983126 983141 983148 983151 983139 983145 983156 983161

983080 983142 983156 983087 983155 983141 983139 983081

θ 983080 983140 983141 983143 983154 983141 983141 983155 983081

983124983113983149983141

983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

θ (983140983141983143983154983141983141983155983081

983137983148983156983145983156983157983140983141 (983142983156983081

983144983151983154983145983162983151983150983156983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081983158983141983154983156983145983139983137983148 983158983141983148983151983139983145983156983161

(983142983156983087983155983141983139983081



22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




22




criteria


Ex

10^6 psi

Ey

10^6 psi

Ez

10^6 psi

Gxy

10^6 psi

Gxz

10^6 psi

Gyz


1068 1068 173 254 053 053 020 038 038












23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




23



Engine Casing 97

Fuel 507

LinerFiller 50

Nozzle 7

Thrust Plate 1

Total 662



24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




24













Ex

106

psi

Ey

106

psi

Ez

106

psi

Gxy

106

psi

Gxz

106

psi

Gyz

106

psi νxy νzx νzy

173 1068 1068 053 053 254 006 006 020




Top

Top Radius

Barrel

Bottom Radius

Bottom

Throat

Cone Radius

Cone

Throat Top

Radius



25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




25






Table 36




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




26





27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




27


Stress (psi)

LocationAxial

min

Axial

max

Hoop

min

Hoop

max

Shear

min

Shear

maxMargin

Cone -20144 -47292 -48973 -56672 -31246 7948 2081Cone radius -13465 -6717 -60744 -18762 -72242 67468 3716

Nozzle -97186 -80954 -27453 29522 -42646 18322 5415

Throat Top

Radius-14915 24486 -413 28774 -20148 50471 0696

Bottom -13401 24279 15498 28629 -12322 18099 0718

Bottom

Radius-54632 17727 30158 23340 -11887 18518 1163

Barrel 37015 13574 13057 24296 -11448 11166 1198

Top Radius -14147 29048 29513 19953 -14829 11581 0793

Top -21888 34018 82417 40858 12488 54751 0129













28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




28


983088

983089983088983088

983090983088983088

983091983088983088

983092983088983088

983093983088983088

983094983088983088

983095983088983088

983096983088983088

983097983088983088

983088

983090983088983088

983092983088983088

983094983088983088

983096983088983088

983089983088983088983088

983088 983090 983092 983094 983096 983089983088 983089983090

983112 983151 983154 983145 983162 983151 983150 983156 983137 983148 983126 983141 983148 983151 983139 983145 983156 983161 983080 983142 983156 983087 983155 983141 983139 983081

983105 983148 983156 983145 983156 983157 983140 983141 983080 983142 983156 983081

983124983113983149983141

983105983148983157983149983145983150983157983149 983158983155 983107983151983149983152983151983155983145983156983141 983110983148983145983143983144983156 983120983141983154983142983151983154983149983137983150983139983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983107983151983149983152983151983155983145983156983141 983107983137983155983145983150983143

983105983148983156983145983156983157983140983141

983105983148983157983149983145983150983157983149 983107983137983155983145983150983143

983126983141983148983151983139983145983156983161



29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




29

4 Conclusion




















30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




30

References


[2]






[7]


[8]




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




31












end end

end

A=[000000000]B=[000000000]D=[000000000] for i=13


end end



32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




32

for i=13 for j=13

ABD(ij)=A(ij) end

end for i=46


end end for i=13


end end for i=46


end end




end for i=13




imod=5i+5



33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end




33


end for i=12h


else X1=Ftu1


X2=Fcu1 Y1=Fcu2else




end











qbar=inv(Sbar) end









qbar=inv(Sbar) end


02935booster_missile.pdf

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