design and performance optmization of hypersonic i nter-continental ballistic missile report

DESIGN & PERFORMANCE OPTIMIZATION OF

HYPERSONIC INTERCONTINENTAL

BALLISTIC MISSILE (ICBM)

A PROJECT REPORT

Submitted by

SOUVIK SANTRA SP09AEU329

SUBHAJIT ROY SP09AEU330

VIJAY KOTHARI SP09AEU335

KUSHILOV CHOWDHURY SP09AEU339

in partial fulfillment for the award of the degree

Of

BACHELOR OF ENGINEERING

IN

AERONAUTICAL ENGINEERING

St. PETER’S UNIVERSITY

St. Peter’s Institute of Higher Education and Research

(Declared Under Section 3 of UGC Act, 1956) Avadi,

Chennai – 600054.

APRIL-2013

St. PETER’S UNIVERSITY

St. Peter’s Institute of Higher Education and Research

(Declared Under Section 3 of UGC Act, 1956) Avadi,

Chennai – 600054.

BONAFIDE CERTIFICATE

Certified that this project report “DESIGN & PERFORMANCE

OPTIMIZATION OF HYPERSONIC INTERCONTINENTAL

BALLISTIC MISSILE (ICBM) - AANDHI” is the Bonafide work of

SOUVIK SANTRA (SP09AEU329), SUBHAJIT ROY (SP09AEU330),

VIJAY KOTHARI (SP09AEU335), KUSHILOV CHOWDHURY

(SP09AEU339) who carried out the project work under my supervision at

St.Peter’s University, Chennai-54.

SIGNATURE

SIGNATURE

Dr.M.CHINNAPANDIAN M.E Ph.D. Mr. M.D.RAJKAMAL M.E.

HEAD OF THE DEPARTMENT SUPERVISOR

DEPARTMENT OF AERONAUTICAL

ENGINEERING

DEPARTMENT OF AERONAUTICAL

ENGINEERING

ST.PETER’S UNIVERSITY ST.PETER’S UNIVERSITY

AVADI, CHENNAI- 600054 AVADI CHENNAI-600054

Submitted for Project Viva-Voice held on ____________________________

INTERNAL EXAMINER EXTERNAL EXAMINER

ABSTRACT

The Aim of the Project is to Design and Analyse a Hypersonic Inter

Continental Ballistic Missile -AANDHI of Mach 25 for Defence purpose and

also perform some innovations which will optimize the performance and hence

will make the missile a must have for the Worlds Super powers. The Missile

flaunts Technologies that makes it undetectable by enemy radar and

communications, furthermore the application of boat tails and variable shark

fins results in the missiles better aerodynamic efficiency compared to others.

ACKNOWLEDGEMENT

The satisfaction that accompanies the successful completion of any work

would be incomplete without mentioning those people who made it possible,

whose constant guidance and encouragement rounded our efforts with success.

First, we would like to thank God for giving us the confidence and power to

complete this work successfully.

We express our deep sense of gratitude to Dr. (Mrs.).T. BHANUMATHI,

M.B.B.S., D.G.O., Chairperson, St. Peter’s University,

Dr.K.BALAGURUNATHAN, M.E., Ph.D., Advisor and Dr.D.S.

RAMACHANDRAMURTHY M.E., Ph.D., Vice Chancellor, who has

provided motivation and facilities to us.

We would specially like to thank the Head of our Department

Dr.M.CHINNAPANDIAN M.E., Ph.D. who was instrumental in providing

vital encouragement for the successful completion of our project.

We wish to give a special thanks to our internal guide

Mr.M.D.RAJKAMAL, M.E., Lecturer with performed reverence not only for

having initiated us to develop the project, but also for giving his mental and oral

support throughout this project work and for sharing our problems and feelings.

TABLE OF CONTENTS

CHAPTER TITLE PAGE

NO.

ABSTRACT iii

ACKNOWLEDGEMENT iv

LIST OF FIGURES xi

LIST OF TABLES xv

LIST OF GRAPHS xvi

SYMBOLS USED xvii

1. INTRODUCTION 1

1.1 INTRODUCTION TO ICBM 1

2. LITERATURE SURVEY 2

2.1 AGNI 1 2

2.2 AGNI V 3

2.3 TITAN IIIA 4

2.4 TITAN IIIB 5

2.5 TITAN IIID 6

3. AERODYNAMICS ON MISSILES 7

3.1 AERODYNAMIC CALCULATION 7

3.2 AERODYNAMIC

CONFIGURATION DESIGN

8

3.3 SHAPE OF MISSILE BODY 8

3.4 DIMENSION 8

3.5 NOSE SHAPE 9

3.6 NOSE CALCULATION 11

3.7 NOSE LIFT CALCULATION 12

3.8 HYPERSONIC SHOCK

RELATION

13

3.9 LIFT & DRAG `13

3.10 PRESSURE GRADIENT OF

OGIVAL NOSE

16

3.11 NOSE CONE DRAG

CHARACTERISTICS

17

3.12 INFLUENCE OF THE GENERAL

SHAPE

17

3.13 INFLUENCE OF THE FINENESS

RATIO

17

3.14 BODY MID SECTION 18

3.15 AFTER BODY SHAPES 18

3.16 FIN 18

3.17 FLUID FLOW 18

3.18 PRESSURE & VISCOUS

FORCES

19

3.19 DRAG CO-EFFICIENT &

REYNOLDS NUMBER

20

3.20 FLOW PROPERTIES 20

3.21 SHOCK FORMATION 21

3.22 SUPERSONIC FLOW 22

3.23 SONIC BOOM GENERATION 22

3.24 PERFORMANCE ANALYSIS 22

3.25 BODY AXIS 23

3.26 STABILITY AND CONTROL 23

4. STRUCTURAL ANALYSIS 25

4.1 C.G CALCULATION OF AANDHI 25

4.2 SELF WEIGHT OF FIN 25

4.3 SHEAR FORCE CALCULATION 27

5. PROPULSION CALCULATIONS 28

5.1 VECHILE ACCELERATION 29

5.2 COMBUSTION CHAMBER

PROPERTIES

30

5.3 SHAPE OF NOZZLE 31

5.4 EFFECT OF FRICTION 32

6. AANDHI INNOVATIONS 33

6.1 MASKING OF IP ADDRESS 33

6.2 VALIDATION OF THE CONCEPT 34

6.3 STEPS 37

6.4 DESIGN INVOLVEMENT OF

SHARK FINS

39

6.5 VALIDATION OF THE CONCEPT 39

6.6 DOUBLE-LAYER RUBBER

RADAR ABSORBING SHEET

40

6.7 VALIDATION OF AANDHI

INNOVATION

41

6.8 DOUBLE-LAYER RUBBER

RADAR ABSORBING SHEET

42

6.9 ONE LAYER ABSORBER SHEET

STRUCTURE

43

6.10 ABSORBING SHEET WITH TWO

LAYER STRUCTURE

43

6.11 TEST SET-UP AND

EXPERIMENTAL RESULT

44

6.12 TEST SETUP 44

6.13 ABSORPTION RESULTS 45

7. MATERIAL SELECTION 46

7.1 NOSE 46

7.2 COMPARITIVE STUDY OF

MATERIALS 47

7.3 MISSILE BODY AND FINS 47

7.4 COMPARITIVE STUDY OF

MATERIALS

48

7.5 INSULATION MATERIAL 48

7.6 COMPARITIVE STUDY OF ALL

MATERIALS

49

7.7 MOTOR CASE 49


MATERIALS

51

7.9 THRUST CHAMBER 52

7.10 NOZZLE 52


THE PARTS

53

8. MISSILE DESIGN

8.1 CONVENTIONAL ICBM 54

8.2 AANDHI- BODY DESIGN

PARAMETERS

54

8.3 AANDHI STRUCTURAL

DESIGN

55

8.4 CONVECTIONAL FINS VS.

SHARK FINS 55

8.5 AANDHI WITH

CONVECTIONAL FINS

56

8.6 AANDHI WITH SHARK FINS 56

8.7 OUR GRID FIN DESIGN 57

8.8 AANDHI AASEMBLY SHARK

WITH GRID FIN

57

8.9 AANDHI REAR DESIGN 58

9. MISSILE ANALYSIS 59

9.1 CFD ANALYSIS 59

9.21 STRUCTURAL ANALYSIS 82

9.32 STEADY STATE THERMAL

ANALYSIS

87

10. RECOMMENDATIONS 88

11. FUTURE WORK 89

CONCLUSION 90

REFERENCES 91

LIST OF FIGURES

FIGURE NO. DESCRIPTION PAGE NO

2.1 AGNI 1 2

2.2 AGNI 5 3

2.3 TITAN III A 4

2.4 TITAN III B 5

2.5 TITAN III D 6

3.1 DESIGN DIMENSIONS 9

3.2 SHAPE AND GEOMETRIC

PARAMETERS OF OGIVAL NOSE

10

3.3 INFLUENCE OF NOSE SHAPE 17

3.4 AFTER BODY SHAPE 18

3.5 FLUID FLOW 18

3.6 DEPENDENCE OF FLOW REYNOLDS

NUMBER

19

3.7 PRESSURE AND VISCOUS FORCES 19

3.8 EFFECTS OF STREAMLINING

AT VARIOUS REYNOLDS

NUMBER

19

3.9 DRAG COEFFCIENT AT

VARIOUS REYNOLDS

NUMBER

20

3.10 SHOCK FORMATION 21

3.11 SONIC BOOM 22

3.12 BODY AXIS 23

6.1 MASKING OF IP ADDRESS 33

6.2 SHARK 39

6.3 CONVENTIONAL FIN 39

6.4 SHARK FIN 39

6.5 ENERGY DISTRIBUTION 42

6.6 POWER LOSS FREQUENCY 43

6.7 TWO LAYER ABSORBING SHEET 44

6.8 EXPERIM ENTAL FIGURE 45

7.1 COMPARISON OF NOSE MATERIAL 47

7.2 COMPARISON OF MATERIAL 48

7.3 COMPARISON OF INSULATION

MATERIAL

49

7.4 COMPARISON OF MOTOR

MATERIAL

51

7.5 RESULT OF MOTOR CASE

COMPARISON

51

7.6 NOZZLE 52

7.7 COMPARISON OF NOZZLE

MATERIAL

53

8.1 CONVENTIONAL ICBM 54

8.2 BODY DESIGN PARAMETER 54

8.3 STRUCTURE DESIGN 55

8.4 CONVENTIONAL FIN DESIGN 55

8.5 SHARK FIN DESIGN 55

8.6 CONVENTIONAL FIN ASSEMBLY 56

8.7 SHARK FIN ASSEMBLY 56

8.8 GRID FIN DESIGN 57

8.9 GRID FIN ASSEMBLY 57

8.10 REAR VIEW OF GRID FIN 58

9.1 VELOCITY MAGNITUDE 60

9.2 DENSITY 60

9.3 DYNAMIC PRESSURE 61

9.4 TURBULENT EDDY DISSIPATION 61


9.6 TURBULENT KINETIC ENERGY 63


9.8 VORTICITY MAGNITUDE 64

9.9 TURBULENT DENSITY 65

9.10 EDDY VISCOSITY 65


9.12 VELOCITY MAGNITUDE 66

9.13 DYNAMIC PRESSURE 66


9.15 TURBULENT INTENSITY 67

9.16 EFFECTIVE VISCOSITY 68



9.19 VELOCITY STREAMLINE 69


9.21 VORTICITY MAGNITUDE 70

9.22 ROLL CAGE MESHING 82

9.23 TOTAL DEFORMATION 82

9.24 X-AXIS DEFORMATION 83

9.25 SAFETY FACTOR 83

9.26 EQUIVALENT ELASTIC STRAIN 84

9.27 STRAIN ENERGY 84

9.28 Y-AXIS DEFORMATION 85

9.29 Z-AXIS DEFORMATION 85

9.30 VON-MISES STRESS 86

9.31 VECTOR PRINCIPLE ELASTIC

STRAIN

86

9.32 TOTAL HEAT FLUX 87

9.33 DIRECTIONAL HEAT FLUX 87

LIST OF TABLE

TABLE NO. DESCRIPTION PAGE NO.

3.1 AERODYNAMIC 8

CONFIGURATION DESIGN

3.2 LIFT/DRAG VS AOA 14


3.4 PRESSURE GRADIENT OF 16

OGIVAL NOSE

4.1 AANDHI LOAD 25

4.2 AANDHI FORCE 26

4.3 SPANWISE WEIGHT 26

5.1 STAGE WISE PROPULSION DATA 28

6.1 COMPARISON OF FIN 40

LIST OF GRAPHS

GRAPH

NO.

DESCRIPTION PAGE

NO.


3.2 PREESURE GRADIENT VS LIFT 16

4.1 SPANWISE LOCATION VS WEIGHT 27

9.1 VELOCITY MAGNITUDE VS POSITION 71

9.2 VORTICITY MAGNITUDE VS POSITION 71

9.3 TURBULENT KINETIC ENERGY VS POSITION 72

9.4 TURBULENT INTENSITY VS POSITION 72

9.5 TURBULENT DISSIPATION RATE VS POSITION 73

9.6 TURBULENT VISCOSITY VS POSITION 73

9.7 STATIC PRESSURE VS POSITION 74

9.8 PRESSURE CO-EFFICIENT VS POSITION 74

9.9 DYNAMIC PRESSURE VS POSITION 75

9.10 ABSOLUTE PRESSURE 75

9.11 TOTAL PRESSURE 76

9.12 STATIC PRESSURE VS POSITION 77

9.13 PRESSURE CO-EFFICIENT VS POSITION 77

9.14 DYNAMIC PRESSURE VS POSITION 78

9.15 ABSOLUTE PRESSURE VS POSITION 78

9.16 TOTAL PRESSURE VS POSITION 79

9.17 TURBULENT KINETIC ENERGY VS POSITION 79

9.18 TURBULENT INTENSITY VS POSITION 80

9.19 TURBULENT DISSIPATION RATE VS POSITION 80

9.20 TURBULENT VISCOSITY VS POSITION 81

9.21 TURBULENT VISCOSITY RATIO VS POSITION 81

LIST OF SYMBOLS

TOTAL LIFT CO-EFFICIENT

NORMAL FORCE

DRAG CO-EFFICIENT

CO-EFFICIENT OF PRESSURE

NOSE FINENENESS RATIO

LENGTH OF NOSE

R RADIUS OF CURVATURE

AVERAGE RADIUS OF

CURVATURE

AVERAGE LENGTH

AVERAGE LENGTH OF NOSE

AVERAGE RADIUS OF OVIGAL

NOSE

AVERAGE LENGTH RATIO

SEMI VERTEX ANGLE

SEMI VERTEX ANGLE AT

TANGENTIAL POINT

ANGLE OF ATTACK

CO-EFFICIENT OF LIFT AT NOSE

CONE ANGLE

SHOCK ANGLE

P PRESSURE

T TEMPERATURE

ρ DENSITY

SPECIFIC HEAT CONSTANT

CO-EFFICIENT OF DRAG AT

NOSE

CO-EFFICIENT OF NORMAL

FORCE AT NOSE

NORMAL FORCE CO-EFFICIENT

OF BODY

NORMAL LIFT CO-EFFICIENT OF

BODY

DRAG CO-EFFICIENT OF BODY

FRONTAL CROSS-SECTIONAL

AREA

D DRAG

NORMAL COMPONENT OF

MACH AFTER SHOCK

EXIT VELOCITY

BODY CURVATURE

PRESSUE GRADIENT

SHOCKWAVE CURVATURE

CO-EFFICIENT OF VISCOSITY

REYNOLD’S NUMBER

χ SHOCK INTERACTION

PARAMETER

SHOCK INTERACTION

PARAMETER FOR NOSE

FREE STREAM VELOCITY

VISCOSITY AT WALL

FREE STREAM DYNAMIC

VISCOSITY

FREE STEAM TEMPERATURE

WALL TEMPERATURE

a SPEED OF SOUND

CO-EFFICIENT OF MOMENT PER

ANGLE OF ATTACK

CHANGE OF NORMAL FORCE

PER ANGLE OF ATTACK

LENGTH OF BODY

DIAMETER OF BODY

FREE STREAM MACH NUMBER

MASS FLOW RATE

ATMOSPHERIC PRESSURE

EXIT PRESSURE

MASS OF PROPELLANT

INITIAL MASS

BURN OUT MASS

NORMAL ALTITUDE

MAXIMUM ALTITUDE

PAYLOAD RATIO

STRUCTURAL CO-EFFICIENT

MASS RATIO

EXIT AREA

SPECIFIC IMPULSE

THRUST CO-EFFICIENT

CHARACTERISTIC VELOCITY

THROAT AREA

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION to I.C.B.M.

An Intercontinental Ballistic Missile (ICBM) is a ballistic missile with a

range of more than 5,500 kilometres (3,400 mi) typically designed for nuclear

weapons delivery (delivering one or more nuclear warheads). Most modern

designs support multiple independently targetable re-entry vehicles (MIRVs),

allowing a single missile to carry several warheads, each of which can strike a

different target.

Early ICBMs had limited accuracy that allowed them to be used only

against the largest targets such as cities. They were seen as a "safe" basing

option, one that would keep the deterrent force close to home where it would

be difficult to attack. Attacks against military targets, if desired, still

demanded the use of a manned bomber. Second and third generation designs

dramatically improved accuracy to the point where even the smallest point

targets can be successfully attacked. Similar evolution in size has allowed

similar missiles to be placed on submarines, where they are known as

submarine-launched ballistic missiles, or SLBMs. Submarines are an even

safer basing option than land-based missiles, able to move about the ocean at

will. This evolution in capability has pushed the manned bomber from the

front-line deterrent forces, and land-based ICBMs have similarly given way

largely to SLBMs.

ICBMs are differentiated by having greater range and speed than other

ballistic missiles: intermediate-range ballistic missiles (IRBMs), medium-

range ballistic missiles (MRBMs), short-range ballistic missiles (SRBMs)—

these shorter range ballistic missiles are known collectively as theatre ballistic

missiles. The launch of a non-nuclear ICBM, however, would be considered

so threatening that it would demand a nuclear response, eliminating any

military value of such a weapon.

CHAPTER 2

LITERATURE SURVEY:-

An elaborate Literature Survey of 6 already built Inter-Continental Ballistic

Missiles (ICBM) are shown henceforth, individually, taking in mind all

characteristics data available for research.

2.1 AGNI 1

Fig 2.1 AGNI 1

SPECIFICATIONS:

Weight 12,000 kg; Length 15 m; Diameter 1.0 m

Warhead - Strategic nuclear (15kT to 250kT), conventional HE-unitary,

penetration, sub-munitions, incendiary or fuel air explosives. Engine - Single

Stage

Operational range - 700-1250 km; Flight ceiling - 370 km; Flight altitude ~ 200

km; Speed Mach - 7.5 or 2.5 km/s

2.2 AGNI-V

Fig 2.2 AGNI-V

SPECIFICATION:

Weight - 55,000[1] - 70,000 kg; Length – 20 - 40.00 m; Diameter - 1.1 - 2 m;

Maximum range - 10,000 kilometres (6,214 mi); Engine - First/second stage

solid, third liquid;

Operational range - 6,000 kilometres (3,700 mi) - 8,000 kilometres (5,000

mi); Launch platform - 8 x 8 Tatra TEL and rail mobile launcher (canisterised

missile package) (Land-based Version) Arihant Class submarine (SLBM

version); Transport - Road or rail mobile (Land-based variant) & Submarine

(Sea-Based Variant)

Manufacturer - Defence Research and Development Organisation (DRDO),

Bharat Dynamics Limited (BDL);

In service 2018-19;

2.3 TITAN IIIA

Fig 2.3 TITAN IIIA

SPECIFICATIONS:

Diameter - 3.05 metres (10.0 ft.); Mass - 161,730 kilograms (356,600 lb.);

Stages – 3; Payload to LEO 3,100 kilograms (6,800 lb.)

1st STAGE: Engines - 2 LR87-11; Thrust - 2,340kN (530,000 lbf); Specific

impulse - 302 sec; Burn time - 147 seconds;

2nd STAGE: Engines - 1 LR91-11; Thrust - 454kN (102,000 lbf); Specific


3rd STAGE: Engines - 2 AJ10-138; Thrust - 71kN (16,000 lbf); Specific impulse

- 311 sec; Burn time - 440 seconds;

Status – Retired; Launch sites - LC-20, Cape Canaveral; Total launches – 4;

2.4 TITAN IIIB

Fig 2.4 TITAN IIIB

SPECIFICATIONS:

Height - 45m (147.00 ft.); Diameter - 3.05m (10 ft.); Mass - 156,540kg

(345,110 lb.); Stages – 3; Payload to LEO - 3,000kg (7,500 lb. (23B));

1st STAGE (Titan 23B/33B): Engines - 2 x LR87-AJ-5; Thrust - 1,913kN

(430,000 lbf); Fuel - A-50; hydrazine/N2O4; Burn time - 147 seconds;

2nd STAGE: Engines - 2 x LR91-AJ-5; Thrust - 445kN (100,000 lbf); Fuel - A-

50; hydrazine/N2O4; Burn time - 205 seconds;

3rd STAGE: Engines - 1 x Bell XLR81-BA-9; Thrust - 71.1kN (16,000 lbf);

Fuel - N2O4/UDMH; Burn time - 240 seconds;

Status – Retired; Launch sites - SLC-4W, Vandenberg AFB; Total launches –

68;

2.5 TITAN IIID

Fig 2.5 TITAN IIID

SPECIFICATIONS:

Height - 36 metres (118 ft.); Diameter - 3.05 metres (10.0 ft.); Mass - 612,990

kg (1,351,400 lb.); Stages Two;

Payload to LEO - 12,300 kilograms (27,000 lb.); Fuel - A-50/N2O4;

1st STAGE: Engines - 2 LR87-11; Thrust - 2,340kN (530,000 lbf); Specific


2nd STAGE: Engines - 1 LR91-11; Thrust - 454kN (102,000 lbf); Specific

impulse – 316 sec; Burn time - 205 seconds;

Status – Retired; Launch sites - SLC-4E, Vandenberg AFB; Total launches –

22;

Successes – 22; First flight - 15 June 1971; Last flight - 17 November 1982;

CHAPTER 3

AERODYNAMICS

3.1 AERODYNAMIC CALCULATION:

1. Aerodynamic configuration design.

2. Shape of Missile Body (Dimensions)

3. Nose Calculation

4. Fin Calculation

5. Lift and Drag Calculation

6. Coefficient of Normal Lift (CN)

7. Co-efficient of Total Lift ( CL)

8. Co-efficient of Drag (CD)

9. Centre of Pressure (CP)

10. Centre of Gravity (CG)

11. Mean Aerodynamic Centre

12. Flow Variables (at altitude 1, 000, 00 feet)

13. Pressure

14. Temperature

15. Density

3.2 AERODYNAMIC CONFIGURATION DESIGN:

Components Design Parameters

Nose Fineness ratio, Bluntness ratio and shape

Body Cross section shape, diameter and length

Wing

Control fin or flap

Mounted and hinge line position

Aspect ratio, Plan form and cross section

Inlet Position Diverter and boat tail

Other appendix Conduit, cover, dome, antenna, window

Table 3.1Aerodynamic Configuration Design

3.3 SHAPE OF MISSILE BODY:

The body of a vehicle is a solid and consists of three section, i.e., nose, mid and

rear

3.4 DIMENSIONS:

Total Length: 19.4 m; Nose Fineness Ratio; ; Range: 10,000

Km; Mach No.: 25; Velocity: 8.5 kms-1;

1ST STG: Length: 8.85 m, Diameter: 1.8 m;

2ND STG: Length: 5.80 m, Diameter: 1.15 m;

3RD STG: Length: 3.35 m, Diameter: 0.70 m;

` Fig 3.1Design Dimension

3.5 NOSE SHAPE:

Considerations taken are minimum radar aberration; the packaging problem;

Missile overall length; the structural integrity of the shape; Aerodynamic

heating effects; Manufacture cost.

There are different shape of nose in missile shape but we took tangent ogival

type because of its low drag and low radar absorption characteristics

Tangent ogival:

The popularity of this shape is largely due to the ease of constructing its profile.

The nose cone length, L, must be equal to, or less than the Ogive Radius ρ. If

they are equal, then the shape is a hemisphere.

Fig 3.2 (Shape and geometric parameters of Ogival nose)

0.5

=53.1

3.6 NOSE CALCULATION: -

For our requirements we chose a moderated nose fineness ratio = = 2; The

Ogive nose is chosen because of its low drag and low radar absorption

characteristics.

The equation of the OGIVAL curve is given by-

𝑟̅ = 2 𝑅̅ {[1 - -1] 0.5+1};

;

Where:-

For our missile lift we need R 𝒙𝑚𝑖𝑑 (nose length)

In our case (R) > 𝑥̅ 𝑚𝑖𝑑.

So we get lift.

𝑟̅ = 2.5 {[1- 12𝑚𝑖𝑑1.25−2 (0.5− 1)2-1] 0.5+1}; 𝑟̅ = 0.791m; r = 0.565m;

Hence semi vertex angle (β) = 23.578º

Now semi vertex on the nose at any

point

𝑥̅ 𝑚 𝑖 𝑑 = 1.4m; 𝑟̅ 𝑚 𝑖 𝑑 = 0.7m; x = 0.7m; ;

Hence Ogive radius (R) = (1.4 1.25) = 1.75 m;

3.7 NOSE LIFT CALCULATION

When ; (= 23.578°, 𝛼 = 20°)

𝑐 𝑙𝑛= sin 𝛼 = 0.809749;

When 𝛼 > 𝛽 (𝛽 = 23.578° , 𝛼 = 45°)

𝑐 𝑙𝑛=0.84{0.644+0.0955(0.436+4.58) × 0.707 [0 .644{0.32+0.45(0.52)} +

0.23 ×0.89 97 × 0.733] × 0.707} = 0.79398-0.359 = 0.44

Whereas, 25.876 °;

3.8 HYPERSONIC SHOCK RELATION 𝜃= 20°= 0.35 𝑟̅ ; M=25

= 0.742;

Where 𝑙 𝑛=1.4;

𝑐𝑝=2(𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛿𝑣 − 𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛿𝑣 𝑠𝑖𝑛𝜆) =2(cos20sin23.578° − sin20cos23.578sin24.3)= 0.718

=314.3;

3.9 LIFT & DRAG:-

𝛽 𝑢 = 25.87 6°= 0 .451 ; Cos 𝛽 𝑢 = 0.8997; 𝛼 = 20° ,𝛿 𝑣 = 23.578°

Where as is the cone angle

;

; ;

Where k= 𝑀 1

Table 3.2 & 3.3 L/D vs AOA Data

𝑐𝑁𝑐 = 0.6436[0.3808] + 0.1 = 0.3464; 𝑐𝐿 = 𝑐 𝑁 𝑐𝑜𝑠 𝛼 − 𝑐𝐶sin = 0 .3466 ;

= 0.95

(3 𝑟̅ 𝑑 𝑠𝑡𝑔); 𝑐 𝑁𝑐𝑦𝑙 = 1 (2 ); 𝑐 𝑁𝑐𝑦𝑙 =0.976 (1 𝑠𝑡 𝑠𝑡𝑔 );

𝑐 𝐿𝑐𝑦𝑙 = 𝑐 𝑁𝑐𝑦𝑙Cos ; 𝑐 𝐿𝑐𝑦𝑙 = 0.917 (1 𝑠𝑡); 𝑐 𝐿𝑐𝑦𝑙 = 0.94 (2 𝑛𝑑); 𝑐 𝐿𝑐𝑦𝑙 = 0.89(3 𝑟̅𝑑);

𝑐 𝐷𝑐𝑦𝑙 =𝑐 𝐿𝑐𝑦𝑙 sin𝛼; 𝑐 𝐷𝑐𝑦𝑙 = 0.33 4(1 𝑠𝑡); 𝑐𝐷𝑐𝑦𝑙 = 0.342 (2 𝑛𝑑); 𝑐 𝐷𝑐𝑦𝑙 = 0. 325 (3𝑟̅𝑑)

L=2.1D=5985.42kN;

Velocity after Shock:

;

Now 𝐴 𝑓 = frontal cross - sectional area =

D kN

Graph 3.1 L/D Vs AOA

Now 𝑀 𝑛2= ; 𝑀2=5.73; 𝑢𝑒 = 1949.64 𝑚⁄𝑠𝑒𝑐

By Curvature

; K=M𝜃 = 8 .72;= 3.65;

Pressure Gradient, ;

Shockwave Curvature

L= ;

3.10 PRESSURE GRADIENT OF OGIVAL NOSE:

g(b) 𝑔 ′ (𝑏 ) L

0.378 5.170 -8.502 0.0426 5.532

By Curvature: ;

Pressure Gradient: - ;

Shockwave Curvature: - ;

𝟏

𝑹 𝟎 ′ 𝑹 𝟎

"

𝜹 𝑪 𝑷

𝜹𝒙

Graph 3.2 Pressure Gradient Vs Lift

0.6599 1.800 -3.640 0.2346 4.662

1.15 1.573 -4.073 0.5106 4.514

2.469 2.101 -6.820 0.77 4.684

3.968 2.487 -8.638 0.8039 4.802

5.135 2.931 -10.76 0.8921 4.929

6.780 3.65 -14.32 0.9586 5.139

Table 3.4 Pressure Gradient Of Ogival Nose

3.11 NOSE CONE DRAG CHARACTERISTICS: -

For aircraft and rockets, below Mach 0.8, the nose pressure drag is essentially

zero for all shapes. The major significant factor is friction drag, which is

largely dependent upon the wetted area, the surface smoothness of that area

and the presence of any discontinuities in the shape. For example, in strictly

subsonic rockets a short, blunt, smooth elliptical shape is usually best.

In the transonic region and beyond, where the pressure drag increases

dramatically, the effect of nose shape on drag becomes highly significant. The

VS L

Fig 3.3Influence of nose shape

factors influencing the pressure drag are the general shape of the nose cone, its

fineness ratio and its bluffness ratio.

3.12 INFLUENCE OF THE GENERAL

SHAPE: -

Comparison of drag characteristics of various

nose cone shapes in the transonic regions.

Rankings are: superior (1), good (2), fair (3),

inferior (4).

3.13 INFLUENCE OF THE FINENESS RATIO: -

The ratio of the length of a nose cone compared to its base diameter is known

as the ‘Fineness Ratio’. The length/diameter relation is also often called the

‘Caliber’ of a nose cone. At supersonic speeds, the fineness ratio has a very

significant effect on nose cone wave drag, particularly at low ratios; but there

is very little additional gain for ratios increasing beyond 5:1. As the fineness

ratio increases, the wetted area, and thus the skin friction component of drag,

is also going to increase. Therefore the minimum drag fineness ratio is

ultimately going to be a trade-off between the decreasing wave drag and

increasing friction drag.

3.14 BODY MID-SECTION: -

In general cylindrical body is used. The advantages being that: - Only Skin

friction drag is incurred; motor case can become skin of missile; Ease of

manufacturing; Good load carrying capacity;

3.15 AFTER-BODY SHAPES: -

The purpose of a boat-tail is to decrease the after body drag. Base drag arises

through flow separation behind the base. The effect of this flow separation is to

bring about a reduction of the base

Fig 3.4 After Body Shape

pressure PB below the free stream value

P .

3.16 FIN: -

The criteria affecting wing design are: -

Maximum permissible span; Required G capability incidence; required stability;

Speed and Trim angle; Structural efficiency; Minimum drag;

3.17 FLUID FLOW: -

Real fluid flow about an aerofoil

Re = ( Vl)/µ; = density of

fluid, kg/m3; V = mean velocity

of fluid, m/sec; l = characteristic

length, m; µ = coefficient of viscosity

(called simply

"Viscosity" in the earlier discussion), kg/ms;

3.18 PRESSURE AND VISCOUS FORCES: -

Fig 3.5:- Thickness of boundary layers and wake greatly exaggerated

Fig 3.6 Dependence of flow on

Reynolds number

Fig3.9 Drag co-efficient of various drag number at

various Reynolds number

3.19 DRAG COEFFICIENTS AND REYNOLDS NUMBER: -

At supercritical Reynolds numbers from 106 and larger, the laminar boundary

layer becomes turbulent and separation

is delayed; hence, the smaller CD values.

A rather abrupt transition occurs

between Reynolds numbers of 105 and

106.

These values are the critical

Reynolds numbers.

Drag coefficients of various bodies

3.20 FLOW PROPERTIES: -

Shock Interaction Parameter: - ;For nose cone: - ;

Now at 30.48 altitude: - T=233.02K; P=1.0862 × 10 3 𝑁⁄ 𝑚2; ρ=1.624kg/

𝑚3;

Since the free stream Mach no. (M)=25, the free stream velocity is

𝑉∞=M

Thus the free stream Reynolds’s no. per meter is

The nose cone is 1.4m long and therefore the shock interaction parameter is

Fig 3.8 Effects of stream lining at various Reynolds number

By using the approximate viscosity-temperature relation,

The density just outside the boundary layer(ρ)=6

Reynolds’s no. outside the boundary layer: -

Hence μ= 148

Hence

The speed of sound behind the shock: -

a= ;

Mach no. just outside the boundary layer (M) = ;

Our Reynolds Number is greater than 106 range so we have low drag

characteristics

For planar surface: -

Therefore, ;

Now, ;

3.21 SHOCK FORMATION:

3.22 SUPERSONIC FLOW: -

3.23 SONIC-BOOM GENERATION: -

Fig 3.11 Sonic Boom

Fig 3.10 Shock Formation

Fig 3.12 Body Axis

3.24 PERFORMANCE ANALYSIS: -

1. Performance of the Aerodynamic model - The force and moment induced

by flow conditions, missile attitude, and configuration.

2. Aerodynamic coefficients - CN, CA, CM, Clψ, CNδ, CMδ, CNq, CMq, Clδp;

3. Flight simulation

3.25 BODY AXIS:

3.26 STABILITY & CONTROL:

;

For Cylindrical after body,

;

;

;

Whereas, Mα =25 ;C NN=0.495; δv=23.578; c=0.5m; K=1.316; =45 ;

K= ;

C NN= KK 1 sin2α; 0.495=1.316 ×1×K 1; K 1=0.376;

C NNα=2 1.316 0.376 cos90=0;

;

;

;

;

;

Table 4.1 Aandhi load

CHAPTER 4

STRUCTURAL ANALYSIS

4.1 C.G. CALCULATION OF AANDHI:

Dimensions of fin

Major axis length=2m; Minor axis length=0.5m; Aspect Ratio = 6.9; λ=0.28

= 16.74 m (from nose);

4.2 SELF WEIGHT OF FIN

𝑘 =−0.08; 𝑦3 =−0.08;

Now, ;

3.8= ; 𝑆 𝑓 𝑖 𝑛 .7 6 = 6 3 𝑚 2 ; Weight = 2.5 × 𝑆 𝑓 𝑖 𝑛 = 1 5 9 .4 𝑘 𝑔 ;

Table 4.2 Aandhi Force

SPANWISE LOCATION WEIGHT

0 -25.6328

1 -22.8488

2 -20.2248

3 -17.7608

4 -15.4568

5 -13.3128

6 -11.3288

7 -9.5048

8 -7.8408

9 -6.3368

10 -4.9928

11 -3.8088

12 -2.7848

13 -1.9208

14 -1.2168

15 -0.6728

16 -0.2888

17 -0.0648

17.9 0

Table 4.3 Spanwise Weight

Graph 4.1 Span-Wise Location Vs Weight

Area under Curve ;

4.3 SHEAR FORCE CALCULATION:

Lift force at fin= 2 ×area under curve=36 70.616 N;

Reaction Force,

𝑉𝐴 = 5985.420 + 3670.616 − 1412640 − 304110 − 80442 − 77499 − 29430 − 18933.3 − 59841

= 1973239.264N (-ve for downward);

CHAPTER 5

PROPULSION CALCULATION: -

Stage 1st 2nd 3rd

Thrust 2400 KN 480 KN 90 KN

Total Initial Mass 200000 kg 49000 kg 16000 kg

Mass of Propellant 144000 kg 31000 kg 8200 kg

Mass of Structure and Engine 7900 kg 3000 kg 1930 kg

Payload 6100 kg

Table 5.1 Stage Wise Propulsion Data

T = ; 𝑃 𝑎=𝑃 𝑒 (Optimum expansion) ;

T=

D =

Where 𝐴𝑓= frontal cross-sectional area; 𝐶 𝐷= co-efficient of drag; = density;

𝑢 = velocity

;

I= impulse=

Now, Vehicle Acceleration: ;

Where, R = mass ratio = = initial mass; 𝑚 𝑏 = burnout mass/final mass;

𝐼

𝑚 𝑝 𝑔 𝑒

= 𝑢 𝑒 𝑞

𝑔 𝑒

ℎ 𝑏 = normal altitude; ℎ 𝑚 𝑎 𝑥̅ = maximum altitude; 𝜆 𝑟̅ = 𝑝 𝑎 𝑦 𝑙 𝑜 𝑎 𝑑 𝑟̅ 𝑎 𝑡 𝑖 𝑜 =

;

Now at 30.48km altitude,

𝑃 𝑎=atmospheric pressure=1.18 × 10 3 𝑁⁄ 𝑚2;

And

=mass flow rate of propellant=1232.5kg/sec; T = ;

𝑢𝑒𝑞=1947.246m/sec

I=28405.440kgm/sec; ;

Now 2nd stage

T = ; 𝐴𝑒= 𝜋𝑟̅ 2 = 1 .04 𝑚2;

=mass flow rate of propellant=247kg/sec; T = ; 𝑢𝑒𝑞=1943.36m/sec;

;

Now 3rd stage

T = ; 𝐴𝑒= 𝜋𝑟̅ 2 = 1 .04 𝑚2;

=mass flow rate of propellant=247kg/sec; T = ; 𝑢𝑒𝑞=1943.36m/sec;

;

5.1 VEHICLE ACCELERATION

30480 = -1647.47 𝑡𝑏+1949 𝑡𝑏-5 𝑡𝑏2; 𝑡𝑏=97.4355sec;

5.2 COMBUSTION CHAMBER PROPERTIES

R=

;

= structural co - efficient= ; ;

;

𝑇 02 = 2634.4 k; ;

𝑚 =29.04(molecular weight of propellant);

[Heating value

of

Propellant];

Nozzle Throat Area,

Now, T= ; 𝐶𝑇=thrust co-efficient=1.54;

5.3 SHAPE OF NOZZLE: -

L= where L=4m=length of nozzle; 𝑫 ∗=throat diameter; 𝑫 ∗=0.276m

as throat area ( ;

Hence𝜶 = 𝟖.𝟗𝟗 ° =nozzle divergence angle; Further𝒖 𝒆𝒒 = 𝒖 𝒆 ∅ ; ∅ = 𝟐.𝟗𝟔° ;

Hence the spherical area segment

Again ;

R=5.75m where R=radius of exit section of nozzle

Mach angle ( ;

Now hectorial component of velocity: 𝑈 2 = 𝑀 2 𝛾�̅�̅𝑇; U=391.23m/sec;

Now, 𝜃 1 − 𝑑𝜃 2 = 𝑑𝜃 3 − 𝑑𝜃 4; And the Mach no. will be uniform

𝑑𝑀1+𝑑𝑀 2=𝑑𝑀 3 + 𝑑𝑀 4; Again, 𝑑𝜃 2 = 𝑚1𝑑𝑀2; 𝑑𝜃 4=𝑚3 𝑑𝑀4;

;

Characteristic Velocity, =1268.3 m/sec;

Now, dv = Ud 𝜃 1 ; du = dU;

;

;

Assuming;

;

In which, ;

5.4 EFFECT OF FRICTION: -

Boundary layer thickness, ; Now

𝐶𝐷=0.495; �̅�̅ ∗=0.03m=throat radius;

Hence 𝛿 ∗=0.0076m; Now we that,

;

0.495 ;

2 . ; R=radius of curvature=2.24 ;

CHAPTER 6

AANDHI INNOVATIONS

1. Looping of Dummy or Temporary Address of Server (IP Address)-using

NetworkAddress Translation-to prevent hacking of Missile operator server.

2. Design Involvement of Fish Fins- two reduce drag at Super Sonic Speed.

3. Double-Layer Rubber Radar Absorbing Sheet-used to absorb the radar waves.

6.1 MASKING OF IP ADDRESS: -

When any Missile is fired to a target country, they may have the

technology of hacking the operating server. So to avoid this, our missile

“Aandhi” has a technology to translate dummy or temporary IP address of the

server to the Enemy by NETWORK ADDRESS

TRANSLATION (NAT) which is the process of modifying IP address

information in IP packet headers while in transit across a traffic routing device.

FIG 6.1 Masking of IP address

Our concept will be initiated by a “for loop” which will send false Address to

hide the Original address henceforth creating a safer networking and operating

environment.

6.2 VALIDATION OF THE CONCEPT

Program to get the IP address of the target country server:

#include <arpa/inet.h>

#include <sys/socket.h>

#include

<ifaddrs.h>

#include

<stdio.h> int main

()

{ struct ifaddrs *ifap, *ifa; struct

sockaddr_in *sa; char *addr; getifaddrs

(&ifap); for (ifa = ifap; ifa; ifa = ifa-

>ifa_next) { if (ifa->ifa_addr-

>sa_family==AF_INET) { sa =

(struct sockaddr_in *) ifa-ifa_addr;

addr = inet_ntoa(sa->sin_addr);

printf("Interface: %s\tAddress: %s\n", ifa-

>ifa_name, addr);

} }

freeifaddrs(ifap)

; return 0;

}

Output:

Interface: lo Address: 127.0.0.1

Interface: eth:0 Address: 69.72.234.7

Interface: eth0:1 Address: 10.207.9.3

An IP address is a 32-bit binary code (often written in the decimal dot form)

that contains network and host parts. The host bits define a particular computer.

The network prefix determines a network; its length depends on the network

class. Sub netting helps to organize a network by breaking it into several

subnets. To define such subnets, you must take bits from the host portion of the

IP address. That also extends the network prefix. The subnet mask explicitly

defines network and host bits as 1 and 0, respectively.

Here we have calculated a subnet mask for a computer with IP address

192.35.128.93 that belongs to network with six subnets.

A sub network, or subnet, is a logically visible subdivision of an IP network.

The practice of dividing a network into two or more networks is called sub

netting.

All computers that belong to a subnet are addressed with a common,

identical, most-significant bit-group in their IP address. This results in the

logical division of an IP address into two fields, a network or routing prefix

and the rest field or host identifier. The rest field is an identifier for a specific

host or network interface.

The routing prefix is expressed in CIDR notation. It is written as the first

address of a network, followed by a slash character (/), and ending with the bit-

length of the prefix. For example, 192.168.1.0/24 is the prefix of the Internet

Protocol Version 4 network starting at the given address, having 24 bits

allocated for the network prefix, and the remaining 8 bits reserved for host

addressing. The IPv6 address specification 2001:db8::/32 is a large network

with 296 addresses, having a 32-bit routing prefix. In IPv4 the routing prefix is

also specified in the form of the subnet mask, which is expressed in quad

dotted decimal representation like an address. For example, 255.255.255.0 is

the network mask for the 192.168.1.0/24 prefix.

Traffic between sub networks is exchanged or routed with special

gateways called routers which constitute the logical or physical boundaries

between the subnets.

The benefits of sub netting vary with each deployment scenario. In the

address allocation architecture of the Internet using Classless Inter Domain

Routing (CIDR) and in large organizations, it is necessary to allocate address

space efficiently. It may also enhance routing efficiency, or have advantages

in network management when sub networks are administratively controlled by

different entities in a larger organization.

Subnets may be arranged logically in a hierarchical architecture, partitioning

an organization's network address space into a tree-like routing structure.

6.3 STEPS

1. Determine the network class (A, B or C) based on IP address:

1.If IP addresses begin with 1 to 126, it is Class A.

2.If IP addresses begin with 128 to 191, it is Class B.

3.If IP addresses begin with 192 to 223, it is Class C.

In our example, the network is class C since the IP address 192.35.128.93 start

with 192.

2. Determine number of bits needed to define subnets: *

Number of subnets = (2^Number of bits) - 2. Hence,

1. Number of bits = Log2 (Number of subnets + 2).

2. In our example, there are six subnets:

3. Number of bits = Log2 (6 + 2) = Log2 (8) = 3. Three bits in the IP

address are used as a subnet portion.

3. Compose the subnet mask in binary form by extending the default subnet

mask with subnet bits. Default subnet mask for classes A to Care:

1. 11111111.00000000.00000000.00000000 (Class A, network part is

8 bits)

2. 11111111.11111111.00000000.00000000 (Class B, network part is

16 bits)

3. 11111111.11111111.11111111.00000000 (Class C, network part is

24 bits).

In our example, an extension of the default class C subnet mask with 3 bits

(Step 2) results in the subnet mask

11111111.11111111.11111111.11100000.

4. Convert the binary subnet mask to the decimal-dot form. The binary form

contains four octets (8 bits in each). Use following rules:

1.For "1111111" octet, write "255".

2.For "00000000" octet, write "0".

3.If octet contains both "1" and "0" use the formula:

Integer number = (128 x n) + (64 x n) + (32 x n) + (16 x n) + (8 x n) + (4 x n) +

(2 x n) + (1 x n)

Where "n" is either 1 or 0 in the corresponding position in the octet sequence.

In our example, for 11111111.11111111.11111111.11100000

11111111 ---> 255

11111111 ---> 255

11111111 ---> 255

11100000---> (128 x 1) + (64 x 1) + (32 x 1) + (16 x 0) + (8 x 0) + (4 x

0) + (2 x 0) + (1 x 0) = 224 ;( Subnet mask is 255.255.255.224.)

6.4 DESIGN INVOLVEMENT OF SHARK FINS: - Fig 6.2

6.5 VALIDATION OF THE CONCEPT:

The following is the result of the CFD analysis of Shark Fin vs. Conventional

Fin which validates our Idea

Table 6.1 Comparison of fins

.

S.NO PARAMETER UNIT SHARK FIN CONVENTIONAL FIN

1 DYNAMIC PRESSURE

Pa

6.07xe07 6.57xe07

2 TURBULENT KINETIC ENERGY m2/s3 4.025xe05 7.03 x e05

3 TURBULENT EDDY

DISSIPATION m2/s2

1.004 X e10 5.620 x e10

4 TURBULENT INTENSITY % 5.81 7.89

5 EDDY VISCOSITY Pas 1.789 1.789

6 VORTICITY MAGNITUDE 1/s 1.15Xe05 1.16xe06

As we can see in the above table that the turbulence parameters like Turbulent

Kinetic Energy, Turbulent Eddy Dissipation, Turbulent Eddy Dissipation,

Turbulent Intensity, Vorticity Magnitude is reducing which indicates that our

concept has better Aerodynamic Performance compared to the conventional

fin presently in practice.

6.6 DOUBLE-LAYER RUBBER RADAR ABSORBING SHEET:

Impedance matching principle plays an important role with the

electromagnetic wave propagation low in designing a double-layer absorbing

rubber material. The upper layer is composed of rubber, fine iron particles,

graphite, and titanium oxide (TiO2) which works as a microwave absorber in

the frequency range 8-18 GHz. The lower layer which works as a matching

layer is composed of rubber and carbon fibers. Many samples with different

thickness for both layers were designed and experimentally measured; the

results showed that the matching layer plays a key role in the absorption

principle. Tow samples with different composition and thicknesses of both

layers were chosen as the best samples, their results showed that the

reflectivity was below -10 dB for both samples in the frequency range 8-18

GHz.

6.7 VALIDATION OF AANDHI INNOVATION:

6.8 DOUBLE-LAYER RUBBER RADAR ABSORBING SHEET:

Impedance matching principle plays an important role with the

electromagnetic wave propagation low in designing a double-layer absorbing

rubber material. The upper layer is composed of rubber, fine iron particles,

graphite, and titanium oxide (TiO2) which works as a microwave absorber in

the frequency range 818 GHz. The lower layer which works as a matching

layer is composed of rubber and carbon fibers. Many samples with different

thickness for both layers were designed and experimentally measured; the

results showed that the matching layer plays a key role in the absorption

principle. Tow samples with different composition and thicknesses of both

layers were chosen as the best samples, their results showed that the

reflectivity was below -10 dB for both samples in the frequency range 8-18

GHz. Finally the practical use of this double-layer absorbing materials has a

wide range in the engineering of microwave absorbers and in military

application by applying this radar absorbing material on the military

equipment.

The idea of using radar absorbing materials to evade radar detection dates

almost as far back as the first widespread military use of radar, naturally.

During World War 2, England developed a wide and effective radar network

to protect itself from German ships and air attacks. Towards the end of the

war, aircraft (British, German, and American) started carrying radar to find

enemy ships and other aircraft. The Nazis figured out that, if a material

absorbs radar the same way the black things absorb visible light, then an

airplane covered in this material might be able to slip through British radar.

Whether or not a material absorbs radiation of a certain wavelength has to do

with the energy levels of the electrons in the atoms that make up that

material’s molecules, as well as with the masses and structures of the atoms

that make up the

Fig 6.5 Distribution of energy density in

absorbing materials

molecules. By finding a material whose molecules can vibrate in frequencies

similar to those of radar waves, and/or whose electrons can absorb quantities

of energy similar to those carried by photons of radar radiation, there is a

good chance this material would absorb radar. Carbon products were found to

absorb radar well. In addition, radar waves create small magnetic fields as

they hit iron, so many small bits of iron could create magnetic fields in such a

way to absorb most of the radar energy. It turns out that small round particles

coated with carbonyl ferrite (iron balls) are the best absorbers. An effective

electromagnetic wave absorber must satisfy maximum absorption of the

incident electromagnetic wave and at the same time dissipate this incident

wave energy into heat. It known that the electric field energy density (We )

decreases while magnetic field energy density (Wm) increases, the distribution

of energy density in a sheet absorber

with a termination metal is illustrated in

Fig.1. So to design an effective double –

layer absorber we have to choose

materials in both layers that have a

strong magnetic loss in the first layer

then strong electric loss in the second

layer also we will figure out that this

second layer will play an important role in increasing the absorption of this

tow layers absorber sheet by matching the

Impedance of this absorber sheet to the

Impedance of the free space.

Fig 6.6 Power Loss Frequency

6.9 ONE-LAYER ABSORBER SHEET STRUCTURE:

When designing a single

layer absorber using a fine

iron particles, graphite,

titanium oxide (Ti O2) and

carbon fibers, the absorption

of energy is about -8 dB in

the frequency range 8-18

GHz and is not constant at

all the frequency range, it

decreases at high frequencies this is because the absorber does not match a free

space in the high frequency region. The reflectivity versus frequency for a

sample of one layer absorber is shown in Fig. 2. To increase the absorption of

this rubber sheet we will design a tow layer absorber sheet, the first layer will

work as an electromagnetic wave absorber and the second layer as a matching

layer to the free space. Reflectivity versus frequency for a sample of one layer

absorber.

6.10 ABSORBING SHEET WITH TWO LAYERS STRUCTURE:

The structure of a double- layer absorber with metal substrate is shown in Fig.

3. Many samples were prepared and the two samples with best absorption

results will be presented in this paper. The first layer of sample one is

composed of (fine particle of iron 40%, graphite 5%, titanium oxide (TiO2)

25%, and natural rubber 30%, with thickness of 1.8 mm) to achieve high

permeability which leads to a large magnetic loss and at the same time high

absorption, the second layer of sample one is composed of (carbon fibres 70%

and natural rubber 30%, with thickness of 2.5 mm) which mainly working as

a matching layer. The first layer of sample two is composed of ( fine particle

of iron 40% , graphite 5% , titanium oxide (TiO2) 25%, and natural rubber

30%, with thickness of 1.8 mm) while the second layer of sample two is

composed of (carbon fibers 40%, titanium oxide (TiO2) 30% and natural

rubber 30% with thickness of 3 mm) which has a better absorption results

since both carbon and titanium oxide have low permittivity and permeability,

and this is the reason of increasing the thickness of the second layer in the

second sample to achieve the matching as we can conclude from these

relations.

Fig 6.7 Two layer Absorbing Sheet

6.11 TEST SETUP AND EXPERIMENTAL RESULTS:

6.12 TEST SETUP:

Many Samples of double layer absorbers were made; tow samples with best

results were presented. The schematic diagram of the reflectivity

measurement setup is shown in Fig. 4. Samples with rectangle shape (25 cm

X 25 cm) were prepared for reflectivity measurements and samples with

different dimensions for mechanical properties measurements were prepared.

6.13 ABSORPTION RESULTS:

The reflectivity measurements of samples 1 and 2 are shown in Tables 1, 2

and Figures 5, 6. As shown in these figures the average measured power loss

for sample 1 is -12.78 dB which means 94.7% loss and the average measured

power loss for sample2 is -13.94 dB which means 95.91% loss. For both

samples the absorption are almost constant along all the frequency range.

Finally we can say that the absorption of these tow samples of the double

layers absorber sheets is improved by introducing the matching layer (second

layer).

Fig 6.8 Experimental Figure

CHAPTER 7

MATERIAL SELECTION:

To start the material selection at first we have to consider the parts for which

the material is to be selected. The parts we selected for material selection are

as follow: - 1. Nose; 2.Missile Body; 3.Insulation; 4.Fins; 5.Motor Case;

6.Thrust Chamber; 7.Nozzle;

7.1 NOSE:

Nose is the very important part of missiles.it is located at front of missiles,

due to this missiles can easily penetrate into any surface moreover due to its

sharp edge it reduces the drag .The materials to be selected for fabrication are

according to the type of dome seekers ,the different types of dome seekers are

as follow:

Multimode (RF/IR); RF only; Mid-Wave IR;

The properties that this seekers should have are as follow:

Dielectric Constant; Transverse Strength; Thermal Expansion; Erosion

Resistance; Maximum Short-Duration Temperature; Combined mid

wave/long wave infrared bypass;

Materials used in different types of dome seekers are as follow:

Multimode (RF/IR): - Zinc Sulphide; Zinc Selenide;

Zinc Sulphide is more advantageous than Zinc Selenide because it is a

dielectric constant, transverse strength, rain erosion and moreover it is used

below Mach no. 3 and for Mach no greater than 3 we have to use other

materials like quartz, sapphire diamond.

RF only: - Pyrocream; Polyimide;

Fig 7.1 Comparison of Nose Material

Pyrocream is used commonly for supersonic missiles and Polyimide is used in

relatively low speed missiles.

Mid Wave IR: - Magnesium Fluoride; Alon;

Both this materials are used in supersonic speed but Alon is less susceptible to

rain, dust erosion and it can able to operate at high Mach no. also.

7.2 COMPARATIVE STUDY OF MATERIAL:

By considering all the above factor we have concluded that to take silicon

nitride to use as the material of our nose of the missile since our missile is

moving at hypersonic speed.

7.3 MISSILE BODY AND FINS:

Airframe is the main structure of any type of aircraft. In this part of the missiles

material to be selected should be of high strength, stiffness, high temperature

etc.

The materials needed for airframe structure are as follow: Aluminium; Steel;

Titanium; Epoxy and S994 glass; Graphite Reinforce

Fig 7.2 (Comparison of material)

By considering all the factors we have concluded that we have chosen steel

named Steel PH 15-7Mo as our material for the airframe because the

temperature our missiles is high.

7.5 INSULATION MATERIAL:

Insulation material are the material which is used to protect the surface from

excessive heating from combustion or any other heating devices.

Parts of missiles that is needed for insulation are as follow:

High Speed Airframes; Engines; Motor case;

Material that we generally used for insulation of different parts are as follow:

Graphite; Bulk Ceramics; Porous Ceramics; Low Density Plastics; Low Density

7.4 COMPARATIVE STUDY OF MATERIAL :

Fig 7.3 (Comparision of Insulation Material)

7.6 COMPARATIVE STUDY OF ALL THE MATERIALS:

As we have taken the materials for airframe and other parts of the missiles as

high speed steel so we are considering

Medium density plastic composites as it allow temperature till 5000°R and it

has good performance as insulator and as our missiles is also at hypersonic

speed.

7.7 MOTOR CASE:

Motor case is the pressure and load carrying structure enclosing the propellant

grain .Cases are nearly curved hemispherical end enclosure. Highest

performance in motor case required lightest possible inert weight, lightest

structure to contain the chamber pressure (typically 400 psi to 1000psi) in a

modern rocket and to withstand the load the vehicle encountered during its

flight.

The material generally used for motor case are as follow:

Steel; Aluminium; Epoxy Laminate; Titanium; Composites.

Com posites ; Medium Density Composites ;

Steel: The conventional quench and temper steels have been used extensively in

the past, and a great deal of information is available on material properties and

fabrication-process experience at strength levels up to about 240 ksi. The 9

nickel-4 cobalt quench and temper steels are currently available in 0.250 to

0.450 carbon grades (ref. 56), with tensile strengths in the range of 180 to 220

ksi and 260 to 300 ksi, respectively. The 0.250 grade can be cold-formed,

machined, and welded in moderate to heavy sections in the fully heat-treated

condition. The 0.450 grade (primarily a forging alloy) should be welded in the

annealed or normalized condition with preheat and post weld heat treatment to

obtain desirable properties. The 9 nickel-4 cobalt steels and any other work-

harden able steels can develop residual stresses depending on the fabrication

processes and thermal treatments used during case fabrication.

Titanium: Titanium alloys have been used and are currently considered for

use in solid rocket motor cases primarily because their strength-to-density

ratio offers the advantage of increased vehicle performance. In comparison to

steel with comparable geometry, the titanium alloys provide less resistance to

buckling. General material-property data and design considerations in the use

of titanium alloys may be obtained in references 52, 55, and 63. Current

alloys are available with ultimate strengths to about 190 ksi. The alloy

generally exists in three forms, or combinations: (1) alpha, or single-phase,

non-heat-treatable alloy up to 130ksi ultimate strength; (2) alpha-beta, dual-

phase, heat-treatable to 180 ksi; and (3) beta-phase, heat-treatable to 190 ksi.

The forming characteristics and weld ability of these materials are discussed

in reference 36, pp. 3-5. Titanium alloys generally are not susceptible to

corrosion but experience has shown that certain compounds under some

conditions can produce stress corrosion in titanium alloys.

Aluminium: Although not generally used in motor cases for space vehicles,

aluminium alloys may be useful for small cases and for cases where corrosion

may

Fig 7.4 Comparison of Motor material

Fig 7.5 Result of Motor Case Comparison

be a specific design problem. The material exists in both heat-treatable and

nonheat-treatable alloys, with yield strength properties ranging from about 35 to

70 ksi (kip/square inch).

Epoxy Laminate: It is being used in moderate cost and performance rocket

Composites: It is being used in rare case because the cost of composites is very

high in refer to other materials.

7.8 COMPARATIVE STUDY OF ALL THE MATERIALS:

After the comparative study off all the

materials which are used for making the

motor case of missiles. We have

considered to use steel for our missile

(Aandhi).

We have selected steel for the following

factors:

High performance; Relatively low cost;

High Fracture Toughness; good forming;

Good forging characteristics;

Fig 7.6 Nozzle

7.9 THRUST CHAMBER:

The thrust chamber is a very essential part of the missiles due to which is used

provide thrust to the vehicle due to which it is able to move forward. In the

thrust chamber propellant burning takes place due to which we are able to

achieve thrust we need to move forward.

The material to be selected for fabrication of thrust chamber is difficult since it

should have the following factors:

High Temperature; High Resistance; Corrosion Resistance; High Pressure;

The material generally used in fabrication of thrust chamber is Steel. Since Steel

has high temperature, corrosion resistance etc.

The steel we are using for our

missiles is 4SCDN-4-10 high

strength alloy steel.

7.10 NOZZLE:

It is the part which is attached to

the end part of the motor case

which is used to convert the

chemical energy coming from the

combustion chamber into kinetic

energy.

The parts included in rocket nozzle are:

Housing; Dome Closeout; Blast Tube; Throat; Exit cone;

7.11 COMPARATIVE STUDY OF ALL THE PARTS:

MATERIALS

As we are using a high heating motor we have chosen all the material of nozzle

section as high heating.

Fig 7.7 Comparison of nozzle material

CHAPTER 8

MISSILE DESIGN:

8.1 CONVENTIONAL ICBM: Fig 8.1

8.2 AANDHI: - BODY DESIGN PARAMETERS: Fig 8.2

8.3 AANDHI STRUCTURAL DESIGN: Fig 8.3

8.4 CONVENTIONAL FINS VS. SHARK FINS: Fig 8.4 & 8.5

8.5 AANDHI WITH CONVENTIONAL FINS: Fig 8.6

8.6 AANDHI WITH SHARK FINS: Fig 8.7

8.7 OUR GRID FIN DESIGN: FIG 8.8

8.8 AANDHI ASSEMBLY SHARK + GRID FIN: FIG 8.9

8.9 AANDHI REAR DESIGN: FIG 8.10

CHAPTER 9

MISSILE ANALYSIS:

9.1 CFD ANALYSIS CONSIDERATIONS:-

DOMAIN TYPE: CUBOID;

TYPE OF MESH: TETRAHEDRON

MESH SIZE: 10 mm

MESH GRADE: HARD

TYPE OF FLOW: TURBULENT (EPSILON)

INLET VELOCITY: 8600 m/s (25 MACH)

OUTLET GAUGE PRESSURE: 0 Pa

NUMBER OF NODES: 22654

SOLUTION INITIALIZATION: STANDARD

CALCULATION ITERATIONS: 500

9.2 SHARK FIN:

9.3 VELOCITY MAGNITUDE: Fig 9.1

9.4 DENSITY: Fig 9.2

9.5 DYNAMIC PRESSURE: Fig 9.3

9.6 TURBULENT EDDY DISSIPATION: Fig 9.4

FIG 9.4

FIG 9.5

9.7 TURBULENT KINETIC ENERGY: FIG 9.6

FIG 9.7

9.8 VORTICITY MAGNITUDE: Fig 9.8

9.9 TURBULENT INTENSITY: Fig 9.9

9.10 EDDY VISCOSITY: Fig 9.10

FIG 9.11

9.11 CONVENTIONAL FIN:

9.12 VELOCITY MAGNITUDE: Fig 9.12

9.13 DYNAMIC PRESSURE: Fig 9.13

9.14 TURBULENT EDDY DISSIPATION: Fig 9.14

9.15 TURBULENT INTENSITY: Fig 9.15

9.16 EFFECTIVE VISCOSITY: Fig 9.16

9.17 EDDY VISCOSITY: Fig 9.17

FIG 9.18

9.18 VELOCITY STREAMLINE: FIG 9.19

9.19 TURBULENT KINETIC ENERGY: FIG 9.20

9.20 VORTICITY MAGNITUDE: Fig 9.21

9.21 SHARK FIN GRAPHS:

9.22 VELOCITY MAGNITUDE: GRAPH 9.1

GRAPH 9.2

9.23 TURBULENT KINETIC ENERGY: GRAPH 9.3

9.24 TURBULENT INTENSITY: GRAPH 9.4

9.25 TURBULENT DISSIPATION RATE: GRAPH 9.5

9.26 TURBULENT VISCOSITY: GRAPH 9.6

9.27 STATIC PRESSURE: GRAPH 9.7

9.28 PRESSURE COEFFICIENT: GRAPH 9.8

9.29 DYNAMIC PRESSURE: GRAPH 9.9

9.30 ABSOLUTE PRESSURE: GRAPH 9.10

9.31 TOTAL PRESSURE: GRAPH 9.11

9.32 CONVENTIONAL FIN:

9.33 STATIC PRESSURE: GRAPH 9.12

9.34 PRESSURE COEFFICIENT: GRAPH 9.13

9.35 DYNAMIC PRESSURE: GRAPH 9.14

9.36 ABSOLUTE PRESSURE: GRAPH 9.15

9.37 TOTAL PRESSURE: GRAPH 9.16

9.38 TURBULENT KINETIC ENERGY: GRAPH 9.17

9.39 TURBULENT INTENSITY: GRAPH 9.18

9.40 TURBULENT DISSIPATION RATE: GRAPH 9.19

9.41 TURBULENT VISCOSITY: GRAPH 9.20

9.42 TURBULENT VISCOSITY RATIO: GRAPH 9.21

9.43 STRTUCTURAL ANALYSIS (LOAD APPLIED 5985420N

AT NOSE)

9.44 ROLL CAGE (MESHING): FIG 9.22

9.45 TOTAL DEFORMATION: FIG 9.23

9.46 DIRECTIONAL DEFORMATION(X AXIS): FIG 9.24

9.47 SAFETY FACTOR: FIG 9.25

9.48 EQUIVALENT ELASTIC STRAIN: FIG 9.26

9.49 STRAIN ENERGY: FIG 9.27

9.50 DIRECTIONAL DEFORMATION(Y AXIS): FIG 9.28

9.51 DIRECTIONAL DEFORMATION (Z AXIS): FIG 9.29

9.52 EQUIVALENT (VON MISES) STRESS: FIG 9.30

9.53 VECTOR PRINCIPAL ELASTIC STRAIN: FIG 9.31

9.54 STEADY STATE THERMAL

9.55 TOTAL HEAT FLUX: FIG 9.32

9.56 DIRECTIONAL HEAT FLUX: FIG 9.33

CHAPTER 10

RECOMMENDATIONS

STEPS REQUIRED FOR OUR IDEA TO BE TAKEN UP BY DEFENCE

ORGANISATION:

1. Manufacturing of our Missile Aandhi in 1:1 Ratio with help from

scientists in defence laboratories.

2. A real time comparison of our Shark Fins with other conventional fins in

practice.

3. Hypersonic Wind Tunnel Testing.

4. Comparison of Experimental data with computational data obtained and

evaluated.

5. Experimental validation of the idea.

10.1 FEASIBILITY OF OUR CONCEPT:

We are not over confident but we are sure that our innovation can be made

into reality if we can work more experimentally. Computationally we have

proved all our innovations and we hope it will give a boon to the missile

industry. And we hope that this project will be taken up in the Research and

Development Domain.

CHAPTER 11

FUTURE WORK

We would like to carry out the following work in near future:

1. Research work to be carried out at DRDL if given a

chance.

2. Experimental Analysis of GRID SHARK FIN.

CONCLUSION

Our project is on the design and analysis of an Intercontinental Hypersonic

Ballistic Missile with the following three innovations: -

1. Masking of I.P. address.

2. Shark Fin Design.

3. Double Layer Rubber Radar Absorber Sheet.

The unique thing about our project is we have validated all our concept by the

use of the computational tools and resources available to our disposal.

We have performed and proved the Idea of I.P. Address masking with the

help of a C++ programing wherein we were able to mask our I.P. Address by

creating an array of false irrelevant I.P. Addresses.

In case of our Shark Fin design we have compared the flow results of a

Conventional Fin and found that the properties related to turbulence is much

lower than the latter. Hence better than the Conventional Fins now in practice.

The Double Layer Rubber Radar Absorbing Sheet is already a proven

concept and we are just applying the concept to our missile so that it may be

invisible to enemy radar.

Thus we have been able to achieve the desired results for our project and

would like to take this up for modifications in future.

REFERENCES

We have taken reference from the following sources:

1. CIA Annual report of 1990

2. Fundamental of Aerodynamics by Dr.J.D. Anderson

3. Gas Dynamics by E. Rathakrishnan

4. Google Scholar

5. Hypersonic Aerodynamics by Robert Wesley Truitt.

6. Hypersonic Gas Dynamics by Anderson.

7. NASA technical report,1988

8. www.nasa.gov

9. www.drdo.gov.in

10. www.isro.org

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