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
3RD

` 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 𝒙 𝑚𝑖𝑑 (nose length)
In our case (R) > 𝑥̅ 𝑚𝑖𝑑.
So we get lift.
𝑟̅= 2.5 {[1- 12 𝑚𝑖𝑑1.25−2 (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 𝑙 𝑛= sin 𝛼 = 0.809749;
When 𝛼 > 𝛽 (𝛽 = 23.578° , 𝛼 = 45°)
𝑐 𝑙 𝑛=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;
𝑐 𝑝=2(𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛿 𝑣 − 𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛿 𝑣 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
𝑐 𝑁𝑐 = 0.6436[0.3808] + 0.1 = 0.3464; 𝑐 𝐿 = 𝑐 𝑁 𝑐𝑜𝑠 𝛼 − 𝑐 𝐶sin = 0 .3466 ;
= 0.95
(3 𝑟̅ 𝑑 𝑠𝑡𝑔); 𝑐 𝑁 𝑐𝑦𝑙 = 1 (2 ); 𝑐 𝑁 𝑐𝑦𝑙 =0.976 (1 𝑠𝑡 𝑠𝑡𝑔 );
𝑐 𝐿 𝑐𝑦𝑙 = 𝑐 𝑁 𝑐𝑦𝑙Cos ; 𝑐 𝐿 𝑐𝑦𝑙 = 0.917 (1 𝑠𝑡); 𝑐 𝐿 𝑐𝑦𝑙 = 0.94 (2 𝑛𝑑); 𝑐 𝐿 𝑐𝑦𝑙 = 0.89(3 𝑟̅𝑑);
𝑐 𝐷 𝑐𝑦𝑙 =𝑐 𝐿 𝑐𝑦𝑙 sin𝛼; 𝑐 𝐷 𝑐𝑦𝑙 = 0.33 4(1 𝑠𝑡); 𝑐 𝐷 𝑐𝑦𝑙 = 0.342 (2 𝑛𝑑); 𝑐 𝐷 𝑐𝑦𝑙 = 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; 𝑢 𝑒 = 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 59 .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,
𝑉 𝐴 = 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 𝐴 𝑓= 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 = ;
𝑢 𝑒𝑞=1947.246m/sec
I=28405.440kgm/sec; ;
Now 2nd
stage
T = ; 𝐴 𝑒= 𝜋𝑟̅ 2 = 1 .04 𝑚2;
=mass flow rate of propellant=247kg/sec; T = ; 𝑢 𝑒𝑞=1943.36m/sec;
;
Now 3rd
stage
T = ; 𝐴 𝑒= 𝜋𝑟̅ 2 = 1 .04 𝑚2;
=mass flow rate of propellant=247kg/sec; T = ; 𝑢 𝑒𝑞=1943.36m/sec;
;
5.1 VEHICLE ACCELERATION
30480 = -1647.47 𝑡 𝑏+1949 𝑡 𝑏-5 𝑡 𝑏2; 𝑡 𝑏=97.4355sec;
5.2 COMBUSTION CHAMBER PROPERTIES
R=
;
= structural co -efficient= ; ;
;
𝑇02= 2634.4 k; ;

𝑚 =29.04(molecular weight of propellant);
[Heating value
of
Propellant];
Nozzle Throat Area,
Now, T= ; 𝐶 𝑇=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
𝛾𝑅̅̅ 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 = 𝑚1 𝑑𝑀2; 𝑑𝜃 4=𝑚3 𝑑𝑀4;
;
Characteristic Velocity, =1268.3m/sec;
Now, dv = Ud 𝜃 1
; du = dU;
;

5.4 EFFECT OF FRICTION: -
Boundary layer thickness, ; Now
𝐶 𝐷=0.495; 𝑅̅̅ ∗=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: %stAddress: %sn", 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

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

DESIGN AND PERFORMANCE OPTMIZATION OF HYPERSONIC I NTER-CONTINENTAL BALLISTIC MISSILE REPORT

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