The project that has done in defense engineering college, Ethiopia.

1. 2010EC
[PRELIMINARY DESIGNS OF
SOLID ROCKET MOTOR]
The purpose of this research is to preliminarily design a solid propellant rocket motor that can be used
for short range air to air missile.

2. PRILIMINARY DESIGN OF SOLID PRPELLANT
ROCKET ENGINE FOR SHORT RANGE AIR-TO-AIR
MISSILE
BY: 1. Abel Birara
2. Amare Molla
3. Assefa Ambachew
4. Andargachew Salehu
DEPARTMENT OF AERONAUTICL ENGINEERING
Advisor: Colonel Dr. Fasil Ali
Debre Zeit
June, 2010 EC

4. i
DECLARATION
We hereby declare that the project entitled “PRILIMINARY DESIGN OF SOLID PROPELLANT
ROCKET ENGINE FOR SHORT RANGE AIR-TO-AIR MISSILE” submitted for the Bachelor’s Degree
is our original work and the project has not formed the basis for the award of any degree, associate ship,
fellowship or any other similar titles.
Signature of the students: 1. ______________
2. _______________
3. _______________
4. _______________
Place: Debre Zeit / Bishoftu
Date: June, 2010 EC

5. ii
CERTIFICATE
This is to certify that the project entitled “PRILIMINARY DESIGN OF SOLID PRPELLANT ROCKET
ENGINE FOR SHORT RANGE AIR-TO-AIR MISSILE ” is the work carried out by students of
Defense University college of engineering, Bishoftu, during the year 2010, in partial fulfillment of the
requirement for the award of the Degree of Bachelor of Technology in Aeronautical Engineering (focus
area of aircraft power - plants) and that the project has not formed the basis for the award previously of
any degree, diploma, associate ship, fellowship or any other similar rule.
Signature of the advisor: ____________________
Place: Debre Zeit / Bishoftu
Date: June, 2010 EC
Examiners Name and Signature
1.______________________________ _______________________
2.________________________________ ______________________
3. ______________________________ ______________________

6. iii
ACKNOWLEDGMENTS
We are heartily thankful to our advisor Dr. Fasil Ali, for the valuable guidance, suggestions,
encouragement, and support throughout the course of our research work. This thesis would not have been
possible to complete but for his valuable guidance, support, providing all the necessary documents and
interaction in technical discussion at every stage during the study.
We would like to thank Aeronautical Engineering Department head Dr. Tegegn for the timely visit FDRE
Air force by facilitate, support and by providing internet service, computers, and Encouragement during
the course of our research work.

7. iv
ABSTRACT
The purpose of this research is to preliminarily design a solid propellant rocket motor that can be
used for short range air to air missile. In this report paper general techniques are used to calculate solid
rocket motor performance characteristics in order to determine more realistic preliminary design data.
There are many design methods that can be used to determine motor performance characteristics and the
possibility of using analytical and theoretical approach is to achieve the correct design of solid rocket
motor. Solid rocket motor design requires repetitive estimates and calculations and by repeated estimates
and calculations, a refined motor is achieved that deliver the required performance. By this iterative
process, an acceptable motor design is achievable. This report can then serve as a practical primer for
solid propellant rocket motor design. It may not solve all one's design problems but will help in many
small ways. The expected outcome of this project will be well analyzed and can be used to design and
manufacture ROCKETS, MISSILES AND THEIR PROPULSION SYSTEMS for educational, practical
and experimental purpose.

8. v
TABLE OF CONTENTES
DECLARATION...................................................................................................i
CERTIFICATE....................................................................................................ii
ACKNOWLEDGMENTS..................................................................................iii
ABSTRACT.........................................................................................................iv
TABLE OF CONTENTES..................................................................................v
LIST OF FIGURES AND TABLES...............................................................viii
LIST OF ABBREVATIONS..............................................................................ix
NOMENCLATURE.......................................... Error! Bookmark not defined.
Chapter 1...............................................................................................................1
INTRODUCTION................................................................................................1
1.1 GENERAL.................................................................................................................. 1
1.2 PROBLEM STATEMENT......................................................................................... 3
1.3 OBJECTIVES OF THE STUDY................................................................................ 3
1.3.1 General objective................................................................................................. 3
1.3.2 Specific Objectives...............................................................................................3
1.4 SCOPE AND LIMITATION OF THE PROJECT......................................................3
1.5 SIGNIFICANCE OF THE STUDY............................................................................4
Chapter 2...............................................................................................................5
LITRATURE SURVEY...................................................................................... 5
2.1 BRIEF HISTORY OF SOLID PROPELLANT ROCKET MOTOR..........................5
2.2 MODERN ROCKETRY............................................................................................. 6
2.3 ROCKETS AND MISSILES...................................................................................... 7
Chapter 3.............................................................................................................10
BASIC THEORIES OF SOLID ROCKET MOTOR AND GOVERNING
EQUATIONS FOR THEIR DESIGN..............................................................10
3.1 IMPORTANT COMPONENTS OF ROCKET MOTOR.........................................10

9. vi
3.2 Combustion chamber.................................................................................................11
3.3 Nozzle c.....................................................................................................................12
3.4 Igniter........................................................................................................................ 14
3.4.1 Solid propellant grain.........................................................................................14
3.4.2 Fuel:....................................................................................................................16
3.4.3 Oxidizer:.............................................................................................................16
3.5 BASIC DESIGN PARAMETERS OF ROCKET ENGINES AND THEIR
GOVERNING EQUATIONS.............................................................................................17
3.5.1 Total Impulse..................................................................................................... 17
3.5.2 Specific impulse.................................................................................................17
3.5.3 Total thrust......................................................................................................... 18
Thrust Coefficient............................................................................................................ 19
3.5.4 Nozzle discharge coefficient..............................................................................20
3.5.5 Actual and Effective exhaust velocity................................................................21
3.5.6 Impulse-to-weight ratio......................................................................................22
3.5.7 Burning rate and density of the propellant.........................................................22
Chapter4..............................................................................................................25
ROCKET MOTOR DESIGN METHODOLOGY AND ACTUAL
PRILIMINARY DESIGN OF SOLID PROPELLANT ROCKET MOTOR
FOR SHORT RANGE AIR-TO-AIR MISSILE............................................ 25
4.1 DESIGN METHODOLOGY FOR DETERMINATION OF DESIGN PARAMETERS
25
4.2 DETERMINATION OF BASIC DESIGN PARAMETERS:...................................26
4.2.1 Case dimension.................................................................................................. 27
4.2.2 Grain configuration:...........................................................................................27
4.2.3 Nozzle design:....................................................................................................29
4.2.4 Weight estimate..................................................................................................29
4.2.5 performance........................................................................................................30
4.2.6 Erosive burning..................................................................................................31
4.3 ACTUAL DETERMINATION OF DESIGN PARAMETERS................................31
4.3.1 Determination of basic design parameters:........................................................31
4.3.2 Case Dimensions:...............................................................................................32

10. vii
4.3.3 Grain Configuration:..........................................................................................33
4.3.4 Nozzle Design:...................................................................................................35
4.3.5 Weight Estimate:................................................................................................37
4.3.6 Performance:...................................................................................................... 38
4.3.7 Erosive Burning:................................................................................................ 39
4.4 MODELING CFD SIMULATION...........................................................................40
4.4.1 Altitude performance......................................................................................... 42
4.4.2 Throttled performance........................................................................................42
4.4.3 Nested Analysis..................................................................................................42
4.4.4 Geometry............................................................................................................45
4.4.5 Mesh Selection...................................................................................................45
4.4.6 Boundary Conditions......................................................................................... 46
Chapter 5.............................................................................................................51
RESULT ANALYSIS AND CONCLUSIONS................................................51
5.1 RESULT ANALYSIS............................................................................................... 51
5.2 CONCLUSIONS AND RECOMMENDATIONS....................................................53
5.2.1 Conclusions:.......................................................................................................53
5.2.2 Recommendations:.............................................................................................54
REFERENCES.....................................................................................................................56

11. viii
LIST OF FIGURES AND TABLES
Figure 3-1 Basic solid rocket motor............................................................................................................10
Figure 3-2 detail components of solid rocket motor................................................................................... 11
Figure 3-3 axial heat transfer rate distributer..............................................................................................12
Figure 3-4 convergent divergent nozzle......................................................................................................13
Figure 3-5 length comparison of several types of nozzle............................................................................13
Figure 3-6 simple diagram of mounting options for igniters...................................................................... 14
Figure 3-7 hollow cylindrical grain.............................................................................................................15
Figure 3-8 propellant grain core shape........................................................................................................15
Figure 3-9 diagram of grain configuration..................................................................................................16
Figure 3-10 classification of grains according to their pressure-time characteristics.................................17
Figure 4-1 motor design configuration........................................................................................................25
Figure 4-2 hollow cylindrical grain.............................................................................................................40
Figure 4-3 solid rocket nozzle model..........................................................................................................41
Figure 4-4 solid rocket motor configuration............................................................................................... 41
Figure 4-5 graph of altitude performance................................................................................................... 42
Figure 4-6 graph of throttled performance……………………………………………………….42
Figure 4-7 graph of specific impulse Vs component
ratio………………………………………….……..43
Figure 4-8graph of specific impulse Vs chamber
pressure………………………………………..………43
Figure 4-9 graph of specific impulse Vs nozzle inlet condition………………..…………………………44
Figure 4-10 graph of specific impulse Vs nozzle exit condition………………………………………….44
Figure 4-11C-D nozzle dimensions………………………………………………………………..……...45
Figure 4-12 structured and unstructured mesh…………………………………………….……………...45
Figure 4-13a CD Vs iteration convergence history…………………………………….….……………...46
Figure 4-13b CD Vs iteration convergence history………………………………………..……………...47
Figure 4-14 counters of velocity magnitude………………………………………………........................47
Figure 4-15 contour of static
pressure…………………………………………………...………………...48
Figure 4-16 contour of Mach
number……………………………………………..………………………48
Figure 4-17 graph of Mack number Vs nozzle position………………………..…………………………49
Figure 4-19 velocity streamline simulation……………………………………...………………………..50
Figure 4-20 pressure simulation……………………………………………………………………….…..

12. ix
LIST OF ABBREVATIONS
ICBM - Inter-Continental Ballistic Missile
NASA - National Aeronautics and Space Administration
CFD - Computational fluid dynamics
LEO - Low Earth Orbit
JATO - Jet assisted take off
WW2 - World War two
EPDM - Ethylene Propylene Diene Monomer
AP - Ammonium perchlorate
HTPB - Poly butadiene
AN - Ammonium Nitrate
NA - Not available
SRM -Short Range Missile
SRAAMs - Short range air to air missiles
WVRAAMs - Within visual range air to air missiles
MRAAMs - Medium range air to air missile
LRAAMs - Long range air to air missile
BVRAAMs - beyond visual range air to air missile
RPA - rocket propulsion analysis

13. x
NOMENCLATURE
tb duration of propellant burning time
Do outer diameter
Di the internal diameter
L length of the motor case Rb burning rate
It The total impulse
Is Specific impulse
Ft total thrust
F The average thrust
Vb The volume required for propellant concern
Rp propellant radius
b propellant density
B web thickness
t the wall thickness
D the average diameter to the center of wall
tin.av average insulator thickness
P1 chamber pressure
Wf web fraction
ṁ mass flow rate
Ab burning area of propellant g
cf Thrust coefficient
Ae Throat area
Ae Exit area
EB erosive burning
K specific heat ratio
l longitudinal stress
Ѳ tangential stress
WTL Total weight launch
V2 The gas exit velocity

14. xi
P3 atmospheric pressure
P2 local pressure of the hot gas
CD drag coefficient
T1 chamber temperature
C The effective exhaust velocity
C* the characteristics velocity
F/Wo Thrust to weight ratio
Vb The propellant volume
Vb The total available chamber volume
tb duration of propellant burning time

15. 1
Chapter 1
1 INTRODUCTION
1.1 GENERAL
Solid propellant rocket motor is the combination of solid fuel (aluminum powder) and oxidizer
(ammonium perchlorate). Both the solid fuel and oxidizer are homogenously mixed and packed inside the
shell. Historically, solid Propellant rocket engines are designed with no moving parts. This may be true
for some cases, but some rocket designs include movable nozzles and actuators for vectoring the line of
thrust relative to the rocket axis in current scenario. The operation of the solid propellant rocket engine
depends on grain configuration, burning rate, combustion characteristics and nozzle properties [1].
General techniques are used to calculate solid rocket motor performance characteristics to determine if
certain designs are feasible. Preliminary design data are described in this report. Solid rocket motor
design requires repetitive estimates and calculations where rough approximations are made and by
repeated estimates and calculations, a refined motor is achieved that delivers the required performance.
By this Iterative process, an acceptable motor design is achievable.
This report can then serve as a practical primer for solid propellant rocket motor design. It may not solve
all one's design problems but will help in many Small ways. The theoretical design of a solid propellant
rocket motor is, in general, simple but not necessarily straight forward. Simplicity is the main feature of a
solid motor. The lack of valves and plumbing serves to increase performance reliability, reduce inert
component weight, and make them relatively easy to use. Along with the simplicity are the limitations.
The main limitation is the relatively short burn time achievable; in general, the burn times vary from a
few seconds up to a maximum burn time of about 180 seconds.
A solid rocket motor consists of a high energy propellant grain stored within an inert combustion chamber
capable of withstanding high pressure and high temperature conditions. An igniter is positioned in the
combustor to ignite the grain and at one end of the combustor is a nozzle to direct the discharge of the
combustion gases. Insulation material lines the combustor from the high temperature gases, inhibitor
material controls the propellant burning surfaces, and liner material insures a good bond between the

16. 2
propellant and insulation. Often, the liner and inhibitor are the same material. Once ignited, the propellant
burns uniformly on the uninhibited surface and regresses in a direction perpendicular to the burning
surface. Therefore, by proper grain design and inhibiting, a wide variety of performance characteristics is
achievable [6]. A solid rocket motor is a system that uses solid propellants to produce thrust.
Solid propellant rocket motor is the most commonly used compared to other rocket motors due to its
relatively simple design, high reliability, ease of manufacture and ready to use on demand etc. Since
solid-fuel rockets can remain in storage for long periods, and then reliably launch on short notice, they
have been frequently used in military applications such as missiles [12]. A solid rocket or a solid-fuel
rocket is a rocket with a motor that uses solid propellants (fuel/oxidizer).
The earliest rockets were solid-fuel rockets powered by gunpowder; they were used by the Chinese,
Indians, Mongols and Arabs, in warfare as early as the 13th century [17]. All rockets used some form of
solid or powdered propellant until the 20th
century, when liquid rockets and hybrid rockets offered more
efficient and controllable alternatives. Solid rockets are still used today in model rockets on larger
applications for their simplicity and reliability.
The lower performance of solid propellants (as compared to liquids) does not favor their use as primary
propulsion in modern medium-to-large launch vehicles customarily used to orbit commercial satellites
and launch major space probes. Solids are, however, frequently used as strap-on boosters to increase
payload capacity or as spin-stabilized add-on upper stages when higher than normal velocities are
required. Solid rockets are accused as light launch vehicles for low Earth orbit (LEO) payloads under 2
tons or escape payloads up to 1000 pounds.
Solid propellant motor designers employ a number of important parameters. The first and most common
tome used in rocketry is thrust, which is a measure of the total force delivered by a rocket motor for each
second of operation [14]. Essentially, thrust is the product of mass time’s acceleration. In actual
calculations, of course, gravity, the pressure of the surrounding medium, and other considerations must be
taken into account. The force generated is a product of weight (mass) time’s rate of acceleration. After the
thrust developed by the rocket has been determined, this value is used to compute another important
parameter, Specific Impulse (Is), which provides a comparative index to measure the number of pounds
of thrust each pound of propellant, will produce.
For designing solid propellant rocket motors, there is no single, well-defined procedure or design method.
Each class of operation has some different requirements. Individual designers and their organizations
have different approaches, background experiences, sequences of steps, or emphasis. The approach also
varies with the amount of available data on design issues, propellants, grains, hardware, or materials, with

17. 3
the degree of novelty (many "new" motors are actually modifications of proven existing motors), or the
available proven computer programs for analysis.
1.2 PROBLEM STATEMENT
For developing country like Ethiopia with limited research budget and lack of advance space technology,
it is important to find new approach for the development of low cost solid rocket motor which is among
all possibilities, an interesting option for the rapid access to modern warfare. In this project work we will
mainly perform the following activities:
 Investigate the different types of rocket engines as well as their characteristics
 Calculate the performance and determine the key design parameters of solid propellant
rocket engine
 Model and simulate the solid rocket motor with the help of CATIA, ANSYS and RPA
software
1.3 OBJECTIVES OF THE STUDY
1.3.1 General objective
To preliminarily design and analyze a solid rocket motor for short range air to air missile application.
1.3.2 Specific Objectives
 To study the complete operational phenomena and structural design components of Solid
Propellant Rocket Engine.
 To determine and compute design parameters which are necessary for the performance
analysis of rocket motor.
 To model and simulate the solid rocket motor with the help of CATIA , ANSYS and
RPA software
1.4 SCOPE AND LIMITATION OF THE PROJECT
One of the major aspects in the design of solid propellant rocket motor is the proper selection of
the propellant that can achieve missile requirements. Design of a solid propellant rocket motor
starts with a mission requirement. The mission requirement is simply what is expected from the
rocket motor. The time of operation, the thrust level, the operating environment, the geometrical
constraints and so on are given to the designer. The designer’s duty is to build up such a rocket
motor to satisfy all the needs that are given to him. In our project work the methodology for

18. 4
determination of solid rocket motor design parameters will be developed and the same parameters
will actually be computed as per the methodology developed. Modeling and simulation
operations of the solid rocket motor with the help of CATIA, ANSYS and RPA software will also
be performed along with the analysis of results. The propellant used for our rocket motor is
composite propellant since in the past three decades the composite propellants have been the most
commonly used class and have shown to have a wide range of burning rates and densities.
As far as the constraints are concerned, it was very difficult to find journals and/or report papers
on the “design of rocket engines” because of the secret nature of the armament. Lack of internet service;
lack of recent journals (since all the free journals found had been written a long time ago) and time
constraint were some of the limitations encountered during our project work.
1.5 SIGNIFICANCE OF THE STUDY
As there is no an attempt to start designing and manufacturing rockets and missiles in the country and the
project is to be performed for the first time in DEC, the importance of this project is of great value in the
future. Based on the results of the project, the data obtained can be used to design and manufacture
rockets and rocket engines. Hence the expected outcome of this project will be well analyzed and can be
used to design and manufacture ROCKETS, MISSILES AND THEIR PROPULSION SYSTEMS for
educational, practical and experimental purpose.

19. 5
Chapter 2
2 LITRATURE SURVEY
2.1 BRIEF HISTORY OF SOLID PROPELLANT ROCKET MOTOR
The solid rocket motor belongs to the family of the rocket engine (thrust achieved by mass ejection) and
its history can be considered both ancient and recent. It is possible to consider that the black powder is
the precursor of modern solid propellants: composed of natural ingredients (sulfur, charcoal and saltpeter),
the black powder has been used from the 13th
century in Asia to propelled darts, certainly the first
unguided stand-off weapons [17]. A lot of work has been performed since this time to improve the solid
propellant and to master its combustion but the main military application has been gun propellants up to
the WW2 [2, 6]. The WW2 has seen the first aeronautical applications (BACHEM Natter, JATO, and
RATO).
The main developments for military (missiles) and space activities (launchers) started in 1945. Regarding
the space activities, the first flights were carried out by liquid propellant rockets, following the world’s
first successfully flown rocket on March 15, 1926 (R. Goddard, USA). The first satellites have been put
into orbit by a liquid propellant launcher (R7 Semiorka, October 1957 - USSR); the first successful US
launch (Jupiter C, January 1958) used solid propellant rockets for the upper stages [2]. The small US
Scout has been the first of all solid propellant launchers. Most of the first intercontinental missiles or
intermediate range missiles used also liquid propellant engines, for their first generations. The current
situation is the following:
 Most of the modern strategic and tactical missiles use solid propellant propulsion. The only
competitor for solid propulsion is ramjet propulsion for tactical missiles.
 Space launchers in the western countries and in Japan are based on an assembly of liquid and
solid propelled stages; they remain all liquid propellant in Russia, Ukraine and China.
This difference of design is clearly connected to economic considerations: developments of solid
propellants are the most versatile of all. They do not require any engine for combustion but once ignited,
the combustion can't be stopped in between. They just need a cylindrical casing for storage. The
conventional solid propellants provide lesser thrust than their liquid counterpart. Solid rockets were
invented by the Chinese; the earliest versions were recorded in the 13th century. Hyder Ali, king of
Mysore, developed war rockets with an important change: the use of metal cylinders to contain the
combustion powder [4].

20. 6
Rocket propulsion system is a non-air breathing system, in which the propulsive effort or thrust is
obtained by variation of the momentum of the system itself. They do not depend on the atmospheric air,
either as oxidizer. As its name implies, the propellant of the motor is in the solid state. The oxidizer and
the fuel is premixed and is contained and stored directly in the combustion chamber. Since the solid
propellant both includes fuel and oxidizer, solid propellant rocket motors can operate in all environmental
conditions.
In comparison to other types of rockets, solid propellant rocket motors have simple design, are easy to
apply and require little or no maintenance. Rocket motor propulsion can be classified based on the type of
propellant of rocket propulsion units used in a given vehicle, type of construction, and by the method of
producing thrust [13, 18].
The writings of Aulus Gellius, a Roman, tell a story of a Greek named Archytas who lived in the city of
Tarentum, now a part of southern Italy. Somewhere around the year 400 B.C., Archytas mystified and
amused the citizens of Tarentum by flying a pigeon made of wood. Escaping steam propelled the bird
suspended on wires. The pigeon used the action-reaction principle, which was not stated as a scientific
law until the 17th century. About three hundred years after the pigeon, another Greek, Hero of Alexandria,
invented a similar rocket-like device called an aeolipile [17]. It, too, used steam as a propulsive gas.
Johann Schmidlap invented the "step rocket," a multi-staged vehicle for lifting fireworks to higher
altitudes. A large sky rocket (first stage) carried a smaller sky rocket (second stage). When the large
rocket burned out, the smaller one continued to a higher altitude before showering the sky with glowing
cinders. Schmidlap's idea is basic to all rockets today that go into outer space.
2.2 MODERN ROCKETRY
During the latter part of the 17th century, the scientific foundations for modern rocketry were laid by the
great English scientist Sir Isaac Newton (1642-1727). Newton organized his understanding of physical
motion into three scientific laws [10]. The laws explain how rockets work and why they are able to work
in the vacuum of outer space. Newton's laws soon began to have a practical impact on the design of
rockets. About 1720, a Dutch professor, Willem Gravesend, built model cars propelled by jets of steam.
During the end of the 18th century and early into the 19th, rockets experienced a brief revival as a weapon
of war. The success of Indian rocket barrages against the British in 1792 and again in 1799 caught the
interest of an artillery expert, Colonel William Congreve. Congreve set out to design rockets for use by
the British military.

21. 7
In 1898, a Russian schoolteacher, Konstantin Tsiolkovsky (1857-1935), proposed the idea of space
exploration by rocket [15]. In a report he published in 1903, Tsiolkovsky suggested the use of liquid
propellants for rockets in order to achieve greater range. Tsiolkovsky stated that the speed and range of a
rocket were limited only by the exhaust velocity of escaping gases. For his ideas, careful research, and
great vision, Tsiolkovsky has been called the father of modern astronautics. Early in the 20th century, an
American, Robert H. Goddard (1882-1945), conducted practical experiments in rocketry. He had become
interested in a way of achieving higher altitudes than were possible for lighter-than-air balloons. He
published a pamphlet in 1919 entitled A Method of Reaching Extreme Altitudes. It was a mathematical
analysis of what is today called the meteorological sounding rocket.
Goddard's earliest experiments were with solid-propellant rockets. In 1915, he began to try various types
of solid fuels and to measure the exhaust velocities of the burning gases. While working on solid-
propellant rockets, Goddard became convinced that a rocket could be propelled better by liquid fuel. No
one had ever built a successful liquid-propellant rocket before. It was a much more difficult task than
building solid- propellant rockets. Goddard's gasoline rocket was the forerunner of a whole new era in
rocket flight. Goddard, for his achievements, has been called the father of modern rocketry [2, 13].
2.3 ROCKETS AND MISSILES
The rocket, a reaction-propulsion device that carries all of its propellants internally, has been around for
almost a millennium since its invention in China around the year 1000. But the twentieth-century saw a
technological explosion of new rocket-propulsion systems, using both solid and liquid propellants. Within
a couple of decades, rockets and missiles had begun to alter the course of the twentieth-century. With
their emergence, nations began to create new weapons, but the technology also made the dream of
spaceflight a reality.
Rockets have been used for centuries in warfare and peaceful purposes. Rockets can be divided according
to their range and speed as follows:
 Short range – Bazooka (C-24, C-6, etc.)
 Medium range – guided missiles
 Long range – ICBM (Atlas, MX, etc.)
A missile is a space-traversing unmanned vehicle that contains the means for controlling its flight path.
Missiles are also classified by the physical areas of launching and the physical areas containing the target.
The four general categories of guided missiles are:
1. Surface-to-surface;

22. 8
2. Surface-to-air;
3. Air-to-surface; and
4. Air-to-air.
Missiles are armed with high explosive warheads. Guided missiles are now developed as tactical defense
weapons to replace anti- aircraft guns which have become obsolete. Such weapons may be fired from
ground or ship (surface – to air) or from a plane to intercept aircraft or guided missile (air- to air). These
defensive missiles have relatively short range (300 to 1000 km) [12]. A guided missile is considered to
operate only above the surface of the Earth, so guided torpedoes do not meet the above definition.
Offensive missiles with a range of 5000 miles have also been tested. They have wings for lift and are
really unmanned bombers. But although they travel at supersonic speeds (2000 miles per hour), they are
far slower than Ballistic missiles, which are travelling at a speed of almost 15,000 miles per hour – ICBM.
A guided missile is a rocket with a guidance system that controls its flight all the way from launching site
to target. They have an ‘electronic-mechanical brain’, which can be controlled by radio or even by
infrared heat devices [15].
ICBMs have now been successfully tested. Their engines consume fuel mixture at a rate of one ton per
second. After the mixture has burned out, the engines and tanks fall – off, leaving only the nose cone
(warhead) in flight. The war head follows an elliptical path to its target rising 600 miles or so into the
stratosphere and travelling at a speed of 15,000 miles per hour.
Table 12.1 Selected United States Missiles
Mission category Name Diameter
(ft)
Length
(ft)
Propulsion Launch
Weight
(lb)
Surface-to-surface ( long
range)
Minuteman
III
6.2 59.8 3 stages, solid 78,000
Do Poseidon 6.2 34 2 stages, solid 65,000
Do Titan II 10 103 2 stages, liquid 330,000
Surface-to–air (or to missile) Chaparral 0.42 9.5 1 stage, solid 185
Do Improved
Hawk
1.2 16.5 1 stage solid 1,395
Do Standard
Missile
1.13 15 or 27 2 stage, solid 1,350 or
2,996

23. 9
Do Redeye 0.24 4 1 stage, solid 18
Do Patroit 1.34 1.74 1 stage, solid 1,850
Air-to-surface Maverick 1.00 8.2 1 stage, solid 475
Do Shrike 0.67 10 1 stage, solid 400
Do SRAM 1.46 14 2 stages, grains 2,230
Air-to-air Falcon 0.6 6.5 1 stage, solid 152
Do Phoenix 1.25 13 1 stage, solid 980
Do Sidewinder 0.42 9.5 1 stage, solid 191
Air-to-air Sparrow 0.67 12 1 stage, solid 515
Antisubmarine Subroc 1.75 22 1 stage, solid 4,000
Battlefield Support (surface-
to-surface short range)
Lance 1.8 20 2 stage, liquid 2,424
Do Hellfire
(antitank)
0.58 5.67 1 stage, solid 95
Do Pershing II 3.3 34.5 2 stages, solid 10,000
Do Tow
(antitank)
0.58 3.84 1 stage, solid 40
Cruise missile (subsonic) Tomahawk 1.74 21 Solid booster +
turbofan
3900

24. 10
Chapter 3
3 BASIC THEORIES OF SOLID ROCKET MOTOR AND
GOVERNING EQUATIONS FOR THEIR DESIGN
3.1 IMPORTANT COMPONENTS OF ROCKET MOTOR
A solid propellant rocket motors are mainly composed of a combustion chamber or motor case, a
converging - diverging nozzle, solid propellant or propellant grain, an igniter and if necessary an
insulator.
Hence a solid propellant rocket is formed by four main components (Fig.3. 1):
1 A case containing the solid propellant and withstanding internal pressure when the rocket is operating.
2 The solid propellant charge (or grain), which is usually bonded to the inner wall of the case, and
occupies before ignition the greater part of its volume. When burning, the solid propellant is
transformed into hot combustion products. The volume occupied by the combustion products is called
combustion chamber.
3 The nozzle channels the discharge of the combustion products and because of its shape accelerates
them to supersonic velocity.
4 The igniter, which can be a pyrotechnic device or a small rocket, starts the rocket operating when an
electrical signal is received.
Figure 3- 3- 1 Basic solid rocket motor
(From the final thesis made by P.Kuentzmann)
One can consider that the solid propellant after manufacturing is in a meta-stable state. It can remain inert
when stored (in appropriate conditions) or it can support after ignition its continuous transformation into
hot combustion products (self-combustion). The velocity of the transformation front is called burning
rate.

25. 11
Figure 3- 2 detail components of solid rocket motor
3.2 Combustion chamber
The combustion chamber (motor case) is that part of a thrust chamber where the combustion or burning of
the propellant takes place. The combustion temperature is much higher than the melting points of most
chamber wall materials. Therefore it is necessary either to cool these walls or to stop rocket operation
before the critical wall areas become too hot.
The motor case of solid propellant rocket motors has two main duties. First one is that the motor case
holds all other parts of the rocket motor, the propellant, the igniter, the nozzle, the insulating layers and
the necessary apparatus for joining the rocket motor with the rest of the missile. The second one is, it is
the combustion chamber, where the propellant burns to generate hot gases.
The motor case is nearly always cylindrical. In some applications, spherical motor case is used. This has
two main reasons. First of all, the best geometry for high pressure vessels is cylindrical or spherical
geometries. And second is that the geometry of the rest of the missile is cylindrical. Since the motor case
is also the combustion chamber, the case is subjected to very high pressure like 100 bars for large rocket
motors. Also high temperatures in the absence of good thermal insulation are received at operation. These
severe conditions require high strength materials to be used in production of motor cases. Usually high
strength alloy aluminum, heat treated high strength steels or fiber reinforced composite (Glass, Kevlar and
carbon) is used. Since aluminum has lower melting temperature, it is used in rocket motors with short
burn times or there must be given extra attention to the insulation. Fiber reinforced composites have
advantages of lowering weight and having good thermal insulation. But for manufacturing costs and
chemical stability problems, steel is the most common used material for motor cases.

26. 12
Figure 3- 3 axial heat transfer rate distributer
(Reference from rocket propulsion element text book page 285)
Typical axial heat transfer rate distribution for solid propellant rocket motors. The peak is always at the
nozzle throat and the lowest value is usually near the nozzle exit.
3.3 Nozzle c
It is a device fitted at the aft end of the motor case, through which the hot gas (produced by combustion)
is allowed to expand and thereby produce thrust. The mass flow rate through the throat of the nozzle and
the expansion of gases in the divergent region of the nozzle constitute the total thrust developed by the
rocket motor. The shape of the nozzle is designed to give optimum thrust due to the expansion of the
gases and to withstand the high temperature of the gases. The design of the nozzle follows similar steps as
for other thermodynamic rockets. Throat area is determined by desired stagnation pressure and thrust
level. Expansion ratio is determined by ambient pressure or pressure range to allow maximum efficiency.
Major difference for solid propellant nozzles is the technique used for cooling Ablation. Fiber reinforced
materials are used in and near the nozzle throat (carbon, graphite, and silica).
In our project work we will consider a De Laval nozzle. It is also called a Convergent-Divergent nozzle.
The important feature of the De Laval nozzle is the design of the section to the rear of the throat, which
flares outward sharply. The purpose of this configuration is to allow the exhaust gases to expand rapidly
and reach atmospheric pressure as soon as possible, so that no back pressure will be created. During this
expansion process the gases gain additional velocity (supersonic), and in a correctly designed nozzle they
will reach their greatest velocity and also achieve atmospheric pressure when they reach the exit. The

27. 13
angle of the converging section of the nozzle should be approximately 30 degrees, and the angle of the
diverging section should be approximately 15 degrees as shown below.
Figure 3- 4 convergent divergent nozzle
(From the final thesis of nozzle design made prof. Ahmed)
Figure 3- 5 length comparison of several types of nozzle [3].
High temperature of the combustion gases, ranging from approximately 2000 to 3500 K, requires the
protection of the motor case or other structural subcomponents of the rocket motor. Typical insulator
materials have low thermal conductivity, high heat capacity and usually they are capable of ablative
cooling. Most commonly used insulation materials are EPDM (Ethylene Propylene Diene Monomer) with
addition of reinforcing materials.

28. 14
3.4 Igniter
The ignition system gives the energy to the propellant surface necessary to initiate combustion. Ignition
usually starts with an electrical signal. The ignition charges have a high specific energy, and are designed
to release either gases or solid particles. Conventional heat releasing compounds are usually pyrotechnic
materials, black powder, metal-oxidant formulations and conventional solid rocket propellant.
The ignition process of a solid propellant rocket motor is a complex process that involves combustion,
heat transfer and fluid flow. The process starts with electrical signal reaching the primary charge which is
usually called as ‘squib’. By the time the secondary charge is ignited, the flame, hot gases and some
burning particles are dispersed into the motor case, onto the solid propellant. When enough heat is
transferred to the solid propellant, the surface of the propellant ignites.
Figure 3- 6 simple diagram of mounting options for igniters[6].
3.4.1 Solid propellant grain
In solid motor, the aggregate of propellant mass is known as ‘propellant Grain’. A solid propellant can
remain in the state of readiness for a long time. The Constituents of a typical solid propellant are
propellant, insulation and inhibition. Solid propellant is the largest sub-system by weight and size in any
solid rocket motor which contains all materials necessary for sustaining combustion. All propellants are
processed into a similar basic geometric form, referred to as a propellant grain. As a rule, propellant
grains are cylindrical in shape to fit neatly into a rocket motor in order to maximize volumetric efficiency.
The grain may consist of a single cylindrical segment (Figure 3.7).

29. 15
Figure 3- 7 hollow cylindrical grain (Reference from introduction to propellant grain theory)
Usually, a central core that extends the full length of the grain is introduced, in order to increase the
propellant surface area initially exposed to combustion. The grain core may have a wide variety of cross-
sections such as circular, star, cross, dog-bone, wagon-wheel, etc., however, for amateur motors; the most
common shape is circular. The grain core shape has a profound influence on the shape of the thrust-time
profile, as shown in Figure 3.8.The thrust (chamber pressure) that a rocket motor generates is proportional
to the burning area at any particular instant in time. This is referred to as the instantaneous burning area.
The burning surface at any point recedes in the direction normal (perpendicular) to the surface at that
point, the result being a relationship between burning surface and web distance burned that depends
almost entirely on the grain initial shape and restricted (inhibited) boundaries.
Figure 3- 8 propellant grain core shape[8].
The important ingredients of a solid propellant grain are fuel and oxidizer.

30. 16
3.4.2 Fuel:
The fuel is one parts of solid propellant grain. There are many kinds of fuel that could be used for solid
rocket motor propulsion. Aluminum powder fuel (15%) was used in our project. Aluminum powder fuel
has many good qualities’ some of them are:
5 Energetic performances (high reaction temperature);
6 Kinetic performances ( high combustion velocity);
7 Mechanical behavior (resistance to loads);
8 Safety and vulnerability (resistance to unwanted ignition);
9 Resistance to aging (life duration in storage)
10 Cost in production (low cost)
3.4.3 Oxidizer:
Oxidizer content is around 68% by weight of the propellant and hence has major influence on propellant
properties. These will have high oxygen content and low heat of formation. It shall have high density and
high thermal stability. Generally the oxidizer used in our project for SRM is Ammonium perchlorate
(oxidizer70 %). Ammonium perchlorate (AP) is a white powder. Its particle size controls the viscosity,
the combustion velocity, and the combustion by-product.
Figure 3- 9 diagram of grain configuration [5].
The following concepts are important to well understand the performance of rocket motor with regard to
their pressure-time characteristics: (Figure 3.10).
11 Neutral Burning: - motor burn time during which thrust, pressure, and burning surface area remain
approximately constant, typically within about +15%. Many grains are neutral burning.
12 Progressive Burning: - motor burn time during which thrust, pressure, and burning surface area
increase.

31. 17
13 Regressive Burning: - motor burn time during which thrust, pressure, and burning surface area
decrease.
Figure 3- 10 classification of grains according to their pressure-time characteristics. [3]
3.5 BASIC DESIGN PARAMETERS OF ROCKET ENGINES AND
THEIR GOVERNING EQUATIONS
The solid rocket motor designer plays with some parameters to achieve the design requirements. These
parameters are called ballistic parameters which are either the properties of the solid propellant; properties
arising from the mission requirements; grain geometry related; nozzle geometry related and some
combined. In literature these parameters are divided in to subcategories like dependent and independent
parameters, but it is sometimes very difficult to decide this dependency [11]. The important ballistic
parameters that will be used later in this study are presented and discussed below.
3.5.1 Total Impulse
The total impulse It: - is the thrust force F (which can vary with time) integrated over the burning time t
[9].
It 訸 (3.1)
For constant thrust and negligible start and stop transients this reduces to:
It = Ft (3.2)
It is proportional to the total energy released by all the propellant in a propulsion system.
3.5.2 Specific impulse
The most important metric for the efficiency of a rocket engine is impulse per unit of propellant [9]; this
is called specific impulse (usually written Isp). An engine that gives a large specific impulse is normally
highly desirable.

32. 18
The specific impulse Is: - is the total impulse per unit weight of propellant. It is an important figure of
merit of the performance of a rocket propulsion system. A higher number means better performance. If
the total mass flow rate of propellant is m’ and the standard acceleration of gravity at sea level go is
9.8066 m/sec 2
or 32.174 ft/sec 2
, then:
Is =
訸
t t訸
(3.3)
The above equation will give a time-averaged specific impulse value for any rocket propulsion system,
particularly where the thrust varies with time. For constant thrust and propellant flow this equation can be
simplified; below, mp is the total effective propellant mass.
Is = It / mp go (3.4)
For constant propellant mass flow m’, constant thrust F, and negligibly short start or stop transients:
Is = F/ (m’go) = F/w’; Is = It /mp go = It /w [8] (3.5)
The product mpgo is the total effective propellant weight w and the weight flow rate is w’. The concept of
weight relates to the gravitational attraction at or near sea level, but in space or outer satellite orbits,
"weight" signifies the mass multiplied by an arbitrary constant, namely go. In the System International (SI)
or metric system of units Is can be expressed simply in "seconds," because of the use of the constant go.
3.5.3 Total thrust
The thrust is the force produced by a rocket propulsion system acting upon a vehicle. In a simplified way,
it is the reaction experienced by its structure due to the ejection of matter at high velocity. The thrust, due
to a change in momentum, is given below. The thrust and the mass flow are constant and the gas exit
velocity is uniform and axial.
F =
訸
訸
= m’v2 =
t
(3.6)
This force represents the total propulsion force when the nozzle exit pressure equals the ambient pressure
[5].The pressure of the surrounding fluid (i.e., the local atmosphere) gives rise to the second contribution
that influences the thrust. Because of fixed nozzle geometry and changes in ambient pressure due to
variations in altitude, there can be an imbalance of the external environment or atmospheric pressure P3
and the local pressure P2 of the hot gas jet at the exit plane of the nozzle. Thus, for a steadily operating
rocket propulsion system moving through a homogeneous atmosphere, the total thrust is equal to:
F = ṁ V2+ (P2 - P3) A2 (3.7)

33. 19
The first term is the momentum thrust represented by the product of the propellant mass flow rate and its
exhaust velocity relative to the vehicle. The second term represents the pressure thrust consisting of the
product of the cross-sectional area at the nozzle exit A2 (where the exhaust jet leaves the vehicle) and the
difference between the exhaust gas pressure at the exit and the ambient fluid pressure [5].
If the exhaust pressure is less than the surrounding fluid pressure, the pressure thrust is negative. Because
this condition gives a low thrust and is undesirable, the rocket nozzle is usually so designed that the
exhaust pressure is equal or slightly higher than the ambient fluid pressure. When the ambient
atmospheric pressure is equal to the exhaust pressure, the pressure term is zero and the thrust is the same
as in Eq. 3.6. In the vacuum of space P3 = 0 and the thrust become: [5]
F = ṁ V2 +A2P2 (3.8)
The pressure condition in which the exhaust pressure is exactly matched to the surrounding fluid pressure
(P2 = P3) is referred to as the rocket nozzle with optimum expansion ratio. Equation 3.7 shows that the
thrust of a rocket unit is independent of the flight velocity. Because changes in ambient pressure affect the
pressure thrust, there is a variation of the rocket thrust with altitude. Because atmospheric pressure
decreases with increasing altitude, the thrust and the specific impulse will increase as the vehicle is
propelled to higher altitudes. This change in pressure thrust due to altitude changes can amount to
between 10 and 30% of the overall thrust.
Equation 3.7 can be expanded by modifying it as follows: [5]
F = AtP1 ㌳䁟 t䁟
t䁟
㌳䁟 䁟 ㌳ 䁟
㌳䁟
+ (p ㌳ p ) (3.9)
Ideal thrust equation [5]
The first version of this equation is general and applies to all rockets; the second form applies to an ideal
rocket with k being constant throughout the expansion process. This equation shows that the thrust is
proportional to the throat area At and the chamber pressure (or the nozzle inlet pressure) P1 , and is a
function of the pressure ratio across the nozzle P1/P2, the specific heat ratio k, and of the pressure thrust. It
is called the ideal thrust equation.
Thrust Coefficient
The thrust coefficient CF: - is non-dimensional parameter that depends only on: the combustion gases
specific heat ratio k, expansion ratio of the nozzle or (the nozzle area ratio – A2/At,) and the pressure ratio
across the nozzle Pl /P2, but independent of chamber temperature [5]. CF gives the efficiency of a nozzle
for a given propellant and nozzle geometry. It is expressed as:

34. 20
CF
㌳䁟 t䁟
t䁟
㌳䁟 䁟 ㌳ 䁟
㌳䁟
+
㌳
䁟
) [5].
(3.10)
For any fixed pressure ratio P1 /P3 , the thrust coefficient CF and the thrust F have a peak when P2 = P3.
This peak value is known as the optimum thrust coefficient and is an important criterion in nozzle design
considerations.
The use of the thrust coefficient permits a simplification to Eq. 3.9 and is defined as the thrust divided by
the chamber pressure P1 and the throat area At [4].
F = CF At P1 (3.11)
Equation 3.11 can be solved for CF and provides the relation for determining the thrust coefficient
experimentally from measured values of chamber pressure, throat diameter, and thrust. Even though the
thrust coefficient is a function of chamber pressure, it is not simply proportional to P1, as can be seen
from Eq. 3.10. However, it is directly proportional to throat area.
The thrust coefficient can be thought of as representing the amplification of thrust due to the gas
expanding in the supersonic nozzle as compared to the thrust that would be exerted if the chamber
pressure acted over the throat area only. The thrust coefficient has values ranging from about 0.8 to 1.9. It
is a convenient parameter for seeing the effects of chamber pressure or altitude variations in a given
nozzle configuration, or to correct sea-level results for flight altitude conditions.
3.5.4 Nozzle discharge coefficient
The gas discharged from the nozzle exit to the ambient atmosphere is described by: [4]
ṁ = CD AtP1 (3.12)
Where: CD – is the nozzle discharge coefficient.
In an ideal rocket motor, CD depends on the nature and temperature of the combustion gases only.
Theoretically CD is given as:
CD = k
2
kt1
)
kt1
k_1
1
R
x
Mw
T1
(3.13)
Where: T1 – the chamber temperature; Mw – the molecular weight of the combustion gases; k – is
specific heat ratio; and R – the universal gas constant.

35. 21
3.5.5 Actual and Effective exhaust velocity
In a rocket nozzle the actual exhaust velocity (V2) is not uniform over the entire exit cross-section and
does not represent the entire thrust magnitude. The velocity profile is difficult to measure accurately. For
convenience a uniform axial velocity ’c’ is assumed which allows a one-dimensional description of the
problem. This effective exhaust velocity ‘c’ is the average equivalent velocity at which propellant is
ejected from the vehicle. It is defined as:
c = Is go = F/ṁ (3.14)
It is given either in meters per second or feet per second. Since ‘c’ and Is differ only by an arbitrary
constant, either one can be used as a measure of rocket performance. In the Russian literature ‘c’ is
generally used. The exhaust speed which is termed as exhaust velocity, and after allowance is made for
factors that can reduce it, the effective exhaust velocity is one of the most important parameters of a
rocket engine (although weight, cost, ease of manufacture etc. are usually also very important).
For aerodynamic reasons the flow goes sonic ("chokes") at the narrowest part of the nozzle, the 'throat'.
Since the speed of sound in gases increases with the square root of temperature, the use of hot exhaust gas
greatly improves performance. By comparison, at room temperature the speed of sound in air is about
340 m/s while the speed of sound in the hot gas of a rocket engine can be over 1700 m/s; much of this
performance is due to the higher temperature, but additionally rocket propellants are chosen to be of low
molecular mass, and this also gives a higher velocity compared to air.
Expansion in the rocket nozzle then further multiplies the speed, typically between 1.5 and 2 times, giving
a highly collimated hypersonic exhaust jet. The speed increase of a rocket nozzle is mostly determined by
its area expansion ratio—the ratio of the area of the throat to the area at the exit, but detailed properties of
the gas is also important. Larger ratio nozzles are more massive but are able to extract more heat from the
combustion gases, increasing the exhaust velocity.
The effective exhaust velocity as defined by Eq.3.14 applies to all rockets that thermodynamically
expand hot gas in a nozzle and, indeed, to all mass expulsion systems. From Eq. 3.7 and for constant
propellant mass flow this can be modified to:
c = V2+ (P2-P3) A2 / m’ (3.15)
Equation 3.14 shows that ‘c’ can be determined from thrust and propellant flow measurements. When P2
= P3, the effective exhaust velocity ‘c’ is equal to the average actual exhaust velocity of the propellant
gases V2. When P2 is not equal to P3 then ’c’ is not equal V2. The second term of the right-hand side of

36. 22
Eq.3.15 is usually small in relation to V2; thus the effective exhaust velocity is usually close in value to
the actual exhaust velocity. When c = v2 the thrust (From Eq. 3.7) can be rewritten as:
F = (w/go) v2 = m’c (3.16)
The characteristic velocity has been used frequently in the rocket propulsion literature. Its symbol c*,
pronounced "cee-star," is defined as: [11]
c* = P1At / m’ (3.17)
The characteristic velocity c* is actually the reverse of the nozzle discharge coefficient CD (see equation
3.12) and is used in comparing the relative performance of different chemical rocket propulsion system
designs and propellants; it is easily determined from measured data of m’, Pl , and At . It relates to the
efficiency of the combustion and is essentially independent of nozzle characteristics. However, the
specific impulse Is and the effective exhaust velocity ‘c’ are functions of the nozzle geometry, such as the
nozzle area ratio A2/At. C* is simply used instead of CD in some literature, but the main aspect is not
different. Thrust-to-weight ratio
3.5.6 Impulse-to-weight ratio
The impulse to weight ratio of a complete propulsion system is defined as the total impulse It divided by
the initial or propellant-loaded vehicle weight w0. A high value indicates an efficient design. Under our
assumptions of constant thrust and negligible start and stop transients, it can be expressed as: [5].
It /wo = It / (mf +mp) go (3.18)
It /wo = Is / (mf/mp+1) (3.19)
3.5.7 Burning rate and density of the propellant
The burning rate of a solid propellant (rb) - is the distance the propellant surface regresses due to burning
of the surface material in a unit time. The combustion process is very complex, but if we simplify it, the
solid propellant particle at the surface of the propellant that is exposed to the atmosphere gasifies due to
heat transfer from the flame. Then the gasified propellant particles burn in a very short distance, giving
more heat to the remained propellant surface. This process goes continuously until all the propellant is
burned out. The speed of the burning surface regression is called burning rate of the propellant.

37. 23
The burning rate of the propellant depends on several factors. The chamber pressure is the dominant
factor affecting the burning rate. For a fixed solid propellant formulation the burning rate of the propellant
is defined by the power law as follows:
rb = a p1
n
(3.20)
Where: a – is the burning rate coefficient; and n - is the pressure exponent. The ‘a’ and ‘n’ are estimated
by testing the propellant at different pressures [10].
Density of a propellant ( b) - is an important factor when the space available for the propellant
is limited. The denser the propellant, the more propellant mass can be stored in the same volume or the
same amount of denser propellant can be fit into the same chamber with more freedom of grain geometry.
Actually the density of the propellant alone is not a very important parameter. The amount of energy that
can be obtained from a unit volume is more important than the mass of unit volume.
Volumetric Loading Fraction, Web Fraction and Erosive Burning
Solid propellant rocket motors can only function if there is a surface of propellant that is open to the
internal cavity of motor case. This is needed in order to start and sustain the burning of the propellant. So,
all solid propellant rocket motors have a void volume inside the motor case. The amount of void space is
critical for a rocket motor since the dimensional constraints are usually very strict for aerial systems. To
analyze this criterion, a parameter called volumetric loading fraction (Vl) is used. It is defined as the ratio
of the propellant volume to the total available chamber volume:
Vl = Vp / Vc (3.21)
The larger the volumetric loading fraction, the more propellant is stored in the same volume. Thus
without changing the Isp of the system, the total impulse can be increased (Eq.3.4). But on the contrary,
usually the burning area of the propellant decreases as the volumetric loading increase. So, volumetric
loading fraction of ‘one’ is not the best value. Usually 0.75 to 0.85 volumetric loading is used for tactical
missile rocket motors [11].
Web fraction (Wf) – is the ratio of the thickness of the propellant to the grain outer radius. It is the
parameter that controls the burning time of rocket motor. Since the thickness of the propellant equals to
the burning rate times the burning time, web fraction can be formulized as:
Wf = web thickness / Radius = rbtb / Rp (3.22)
Where : rb – burning rate; tb – burning time; Rp - grain outer radius
The increase in the propellant burning rate due to axial gas flow inside the combustion chamber is known
as erosive burning. To handle erosive burning two factors J and Kp, are introduced. These factors are
defined as:

38. 24
J = kp /k ; Kp = A/Ac ; k = Ab /At (3.23)
Where: Ac – is the area of a given cross section of the central part; A – is the propellant burning area
upstream of the cross section; Ab – is the propellant burning area; and At – the nozzle throat area.
Predicting the amount of erosive burning is very important at the final stage of the design. Erosive
burning results in higher pressure and thrust than the expected ones. This increase can be damaging to
the rocket motor itself or other components of the rocket system. An increase of the burning rate with
erosive burning causes the propellant at the aft end of the rocket motor to burn up before the head end,
increasing the thermal loads at the aft end of the motor case. To overcome this problem, insulation at the
aft end is usually thickened.
Since the erosive burning is maximum when the port area is minimum, the highest burning rate change is
seen usually at the ignition period and early stages of operation. The port area increases as the propellant
burns, resulting in the decrease of the erosive burning characteristics.
Generally to avoid unwanted erosive burning of propellant in a rocket motor, low length to diameter
ratio, high port to throat area ratio motors are preferred. The diameter is usually prefixed by the
mission requirements, and the length is determined by the total impulse needed. The port area cannot be
increased very much, since the volumetric loading decreases (Eq.3.21). Using tapered geometries with
larger port area at the aft end, where the erosive burning is critical, is a good solution for erosive burning
reduction without reducing the volumetric loading.

39. 25
Chapter4
4 ROCKET MOTOR DESIGN METHODOLOGY AND
ACTUAL PRILIMINARY DESIGN OF SOLID PROPELLANT
ROCKET MOTOR FOR SHORT RANGE AIR-TO-AIR
MISSILE
4.1 DESIGN METHODOLOGY FOR DETERMINATION OF DESIGN
PARAMETERS
Design of a solid propellant rocket motor starts with a mission requirement [1]. The mission requirement
is simply what is expected from the rocket motor. The time of operation, the thrust level, the operating
environment, the geometrical constraints and so on are given to the designer. The designer’s duty is to
build up such a rocket motor to satisfy all the needs that are given to him.
In our project work the main aim is to preliminarily design solid rocket motor that can be used for short
range air to air missile. The basic input parameters for solid rocket motors are the propellant ingredients,
motor case diameter, length of the combustion chamber, length of the nozzle, motor case thickness and
nozzle diameter (Fig 4.1). In order to utilize the above input parameters solid rocket propulsion equations
were used to size the solid rocket motor. This approach includes analytical calculation and CFD
simulation results or experimental result based up on the given data to size solid rocket motor. Nozzle exit
area, nozzle throat area, chamber pressure, total mass, total thrust, specific impulse, burning rate time and
burning area are also included as basic input parameters.
Figure 4- 1 motor design configuration (reference from the final thesis of conceptual design of solid
rocket motor)

40. 26
To carry out the design calculations on solid rocket motor design characteristics, the value of basic input
design parameters are taken from various references [4, 5, 9, 11, 17, and 18].
Furthermore the following ideal rocket assumptions were considered during design:
1. The working substance is homogenous
2. The working substance obey the perfect gas law
3. There is no heat transfer across the rocket wall therefore the flow is adiabatic
4. There is no appreciable friction and all the boundary layer effects are neglected
5. The gas velocity , temperature , density and pressure all are uniform across any section
normal to nozzle axis
6. The propellant combustion is complete and dos not vary from that assumed by the
combustion equation
7. Steady state condition exist during operation of solid rocket motor
8. Expansion of the working fluid occurs in a uniform manner without shock or discontinuity
9. Flow through the nozzle is one dimensional and non-rotational
10. Chemical equilibrium is established in the combustion chamber and does not shift during
flow through the nozzle
11. Burning of the propellant grain is neutral,
Hence the following design methodology is developed for determination of rocket motor design
parameters:
4.2 DETERMINATION OF BASIC DESIGN PARAMETERS:
• The total impulse It and propellant weight at sea level Wb can be obtained from Eqns. 3.2 and 3.5
as [1, 5].:
It = Ft
Is = F/(m’go) = F/w’; Is=It /mp go= It /w
Hence: It = F x tb = Is x Wb ;
Then: Wb= It / Is (4.1)

41. 27
Where: F – desired average thrust; tb – desired duration; Is – specific impulse
 The volume required for the propellant concerned Vb is given by:
Vb = Wb/ b (4.2)
Where: b- is propellant density
 The web thickness (thickness of the propellant) ‘b’ can be found from formula 3.22:
Wf = web thickness /Radius = rbtb / Rp
b = rb x tb (4.3)
Where: wf – web fraction
rb – propellant burning rate
tb – desired burning duration
4.2.1 Case dimension
• The outside diameter is fixed at 7.0 in. (177.8 mm)
• The wall thickness’’ can be determined from equation 4.4 that describes: for a simple cylinder of
radius R and thickness ’d’ , with a chamber pressure p, the longitudinal stress l is one half of
the tangential or hoop stress Ѳ
: [8].
Ѳ= 2 l= p x R / d (4.4)
 Hence: The wall thickness can be determined as:
t = p1D / (2 ) (4.5)
Where: - is the ultimate tensile strength of heat treated steel
P1 – Chamber pressure
D – Average diameter to the center of the wall
4.2.2 Grain configuration:
• The outside diameter D0 for the grain is determined from the case thickness or wall thickness as
follows:
D0 = the fixed outside diameter -2t - 2tin.av (4.6)

42. 28
Where: t – wall thickness
tin.av – average insulator thickness
• The inside diameter Di of a simple hollow cylinder grain would be the outside diameter Do minus
twice the web thickness i.e.:
Di = D0 – 2b (4.7)
• For a simple cylindrical grain, the volume required for the propellant determines the effective
length, which can be determined from the equation:
Vb = ㌳ [8]. (4.2a)
• The web fraction would be: (see equation 3.22)
Wf = 2b/Do (4.8)
• The ratio L/Do value can also be computed as L and D0 are known:
 The initial or average burning area will be found from Eqs. 4.2 and 3.5 [9]. The burning rate of
the propellant in a motor is a function of many parameters, and at any instant governs the mass
flow rate ṁ of hot gas generated and flowing from the motor (stable combustion) :
ṁ = Ab x r x b (4.9)
• For constant propellant mass flow ṁ, constant thrust F, and negligibly short start or stop
transients:
Is = F/ (ṁgo) = F/ẇ; Is = It /mp go = It /w
Where: Ab - is the burning area of the propellant grain
r - the burning rate, and
b- the solid propellant density prior to motor start.
The total mass ‘m ‘ of effective propellant burned can then be determined by integrating Eq. 4.9:
m = 訸 訸 (4.10)
Where: Ab and ‘r‘ vary with time and pressure.
• The initial or average burning area will be found from Eq.3.5:
F = ẇ x Is = Ab x r x bx Is

43. 29
Hence: Ab = F / r x Is x b (4.11)
• The approximate volume occupied by the grain is found by subtracting the perforation volume
from the chamber volume [8]. The result 761.2 in3
is from equation 4.1.
Vb =
䁟
䁟 t ㌳ ) (L + t ) = 761.2 in3
(4.2b)
 The above equation is solved for L with the already known values of the grain outside diameter
D0 and the grain inside diameter Di of a simple hallow cylinder grain.
 The initial internal hollow tube burn area can then be found as: [9].
Ab2 = t t (4.12)
4.2.3 Nozzle design:
• The thrust coefficient CF can be found by Eq.3.10 as follows: [5].
CF
㌳䁟 t䁟
t䁟
㌳䁟 䁟 ㌳ 䁟
㌳䁟
+
㌳
䁟
)
• The throat area At can be found from Eq. 3.11as given below:
F = CF At P1
• The throat diameter can be found from the known formula as:
At = Π ) (4.13)
• Assuming the nozzle area ratio for optimum expansion is about 27 i.e. Ae/At or A2/At = 27, [5] ,
the exit area Ae and diameter De can be computed.
Ae = At x 27 ;
And from: Ae =Π ) ; (4.14)
De = (4.15)
4.2.4 Weight estimate
• The steel case weight (assume a cylinder with two spherical ends and that steel weight density is
0.3 lbf/in3
) is found by: [8].

44. 30
Wc = t Π D L + (4.16)
Where: D – is the internal nozzle exit diameter;
L – is the length;
t – is the wall thickness;
– the steel weight density
• The nozzle weight is composed of the weights of the individual parts, estimated for their densities
and geometries.
• Then we can estimate the total weight comprising of the following items:
- Case weight at sea level
- Liner/insulator weight
- Nozzle weight, including fasteners
- Igniter case and wires weight
- Igniter powder weight
- Propellant (effective) weight
- Un-usable pro - pellant weight (2%)
- Propellant and igniter powder weight
4.2.5 performance
• The total impulse - to- engine weight ratio can be found from Eq.3.2
It = Ft
Hence: It / WTE, (4.17)
• The total launch weight:
WTL = vehicle pay load + Engine weight estimate (4.18)
• The weight at burnout or thrust termination:
Wt t = WTL - propellant and igniter powder weight (4.19)
• The initial and final thrust-to-weight ratios and accelerations:

45. 31
Initial thrust to weight ratio = F/WTL (4.20)
Final thrust to weight ratio = F/Wt t (4.21)
4.2.6 Erosive burning
• It is the ratio of the port area to the nozzle throat area at start:
EB = Ap/ At (4.22)
4.3 ACTUAL DETERMINATION OF DESIGN PARAMETERS
The following data are given for determination of design parameters:
 Specific impulse (actual) ; Is = 240s
 Burning rate ; r = 0.6 in/sec
 Propellant density; b= 0.067 lbm/in3
 Specific heat ratio; k = 1.25
 Chamber pressure, nominal; Pl = 800psi
 Chamber temperature(T1 ) =4188K
 Desired average thrust; F = 4000 lbf
 Maximum missile diameter; D = 7in.
 Desired burning duration; tb = 3 sec
 Ambient pressure (P1) = 3 psi (at altitude)
 Missile payload = 78.7 lbm (includes structure)
 Approximately neutral burning is desired.
As per the methodology developed in section 4.1 and based on the parameters given above let us
actually determine the various design parameters as follows:
4.3.1 Determination of basic design parameters:
 The total impulse It and propellant weight Wb at sea level:
It = F x tb = Is x Wb = 4000 x 3 = 12,000 lbf-sec

46. 32
Wb = It / Is = 12000/240 = 50 lbf
Allowing for a loss of 2% for manufacturing tolerances the total propellant weight is:
Wb = 1.02 x 50 = 51 lbf
 The volume required for the propellant Vb is given by:
Vb = Wb/ b= 51/ 0.067 = 761.2 in3
 The web thickness ‘b’ can be found by
b = r x tb = 0.6 x 3 = 1.8in
4.3.2 Case Dimensions:
• The outside diameter is fixed at 7 in (this is maximum missile diameter)
• Heat-treated steel with an ultimate tensile strength 220,000psi is to be used.
• A safety factor of 2.0 is suggested to allow for surface scratches, combined stresses and welds,
and rough field handling.
• The value of D is the average diameter to the center of the wall
• The wall thickness ‘t’ can be determined from equation 4.4 [8], that describes for a simple
cylinder of radius R and thickness ‘d’, with a chamber pressure p, the longitudinal stress l is
one half of the tangential or hoop stress.
Ѳ= 2 l= p x R / d
From the above expression follows: d (thickness) = P x R / 2 l
 Hence the wall thickness for simple circumferential stress can be determined as: [8].
t = p1 D / (2 ) = 2 x 800 x 6.83/ (2 x 220,000) = 0.0248in
Where: - is the ultimate tensile strength of heat treated steel

47. 33
P1 – Chamber pressure. The value of P1 depends on the safety factor selected, which in turn
depends on the heating of the wall, the prior experience with the material and so on. A safety factor
of 2.0 is suggested to allow for surface scratches, combined stresses and welds, and rough field
handling.
D - The average diameter to the center of the wall and is taken as 6.83 in.
For a cylindrical case with hemispherical ends, the cylinder wall has to be twice as thick as the walls
of the end closures.
4.3.3 Grain Configuration:
• The grain will be cast into the case but will be thermally isolated from the case with an
elastomeric insulator with an average thickness of 0.1 in inside the case;
• The actual thickness will be less than 0.1in the cylindrical and forward closure regions, but
thicker in the nozzle entry area.
• The outside diameter D0 for the grain is determined from the case thickness or wall thickness as
follows:
D0 = The fixed outside diameter - 2t - 2tin.av
D0 = 7 – 2 x 0.0248 - 2 x 0.1 = 6.75 in
 The inside diameter Di of a simple hollow cylinder grain would be the outside diameter Do minus
twice the web thickness i.e.:
Di = D0 – 2b = 6.75 – 2 x 1.8 = 3.15 in
• For a simple cylindrical grain, the volume required for the propellant determines the effective
length, which can be determined from the equation 4.2a : [8]
Vb = 4
L D0
2
㌳ Di
2
)
L =
䁟
㌳ 䁟 )
=
晦
䁟 ㌳Ǥ Ǥ )
=
晦
䁟䁟䁟 Ǥ
䁟 t
• The web fraction would be:
Wf = 2b/Do = 2 x 1.8/ 6.75 = 0.533

48. 34
 The ratio L/Do value can also be computed:
L/D0 = 27.21/6.75 = 4.03
The grains with this web fraction and this L/D0 ratio, suggests the use of an internal burning tube
[10]. These grain shapes are shown as in Fig. 3.9.
 The initial or average burning area will be found from Eqs. 4.2 and 3.5 : [9] . The burning rate of
a propellant in a motor is a function of many parameters, and at any instant governs the mass flow
rate m’ of hot gas generated and flowing from the motor (stable combustion):
m’ = Ab x r x b
• It is known from the previous chapter that for constant propellant mass flow m’, constant thrust F,
and negligibly short start or stop transients:
Is = F/ (m’go) = F / w’Is = It /mp go = It /w
• Hence the initial or average burning area (the desired burn area) will be:
F = w’ x Is = Ab x r x Is x b
Ab = F/r Is b= 4000/0.6 x 240 x 0.0667 = 4000/9.6 = 416.6 in2
 The actual grain now has to be designed into the case with spherical ends, so it will not be a
simple cylindrical grain.
• The approximate volume occupied by the grain is found by subtracting the perforation volume
from the chamber volume [8] [11]. There is a full hemisphere at the head end and a partial
hemisphere of propellant at the nozzle end (0.6 volume of a full hemisphere).
Vb =
1
2 6
D0
3
1 t 0 6 ㌳ 4
) Di
2
(L+
Di
2
t 0 3
Di
2
) = 761.2 in3
 The above equation can be solved for L with the already known values of the grain outside
diameter D0 and the inside diameter Di of a simple hallow cylinder grain
 Hence substituting the values of D0 = 6.75 in and Di = 3.15 inch in the above equation, it can be
found that the effective length L = 19.82 in.
 The initial internal hollow tube burn area can then be found as:
Ab2 = Di L t
Di
2
t 0 3
Di
2
) = 291.56 in2
The desired burn area of 416.6 in2
is larger by about 125 in2
. Therefore, an additional burn surface area of
125 in2
will have to be designed.

49. 35
4.3.4 Nozzle Design:
• The thrust coefficient CF can be found by Eq.3.10 as follows:
CF
㌳䁟 t䁟
t䁟
㌳䁟 䁟 ㌳ 䁟
㌳䁟
+
㌳
䁟
)
- The value of thrust coefficient can be found for k = 1.25 and a pressure ratio of Pl / P2 =
800/3 = 266.67
- Thrust coefficient is dimensionless
- It is a key parameter for analysis as it is dependent on gas property k , the nozzle geometry ε
=A2/At - nozzle expansion ratio and the pressure distribution through the nozzle P1/P2
- Optimum thrust coefficient (peak CF ) for a given motor corresponds to P2 = P3.
- Motor thrust can simply be obtained from: F = P1 At CF
Hence: CF = 1.55
• The throat area At can be found from Eq. 3-11as given below:
F = CF At P1
Hence: At = 4000/1.55 x 800 = 3.225 in2
• The throat diameter can then be found from the known formula as:
At = Π
Dt
2
4
)
Dt = 4
At
Hence: Dt = 4 10a = 2.03 in
• Assuming the nozzle area ratio for optimum expansion is about ‘27’ i.e. Ae /At or A2 /At = 27,
the exit area Ae and diameter De can be computed.
Then: Ae = At x 27;
Hence: Ae = At x 27 = 3.225 x 27 = 87.1 in2
And from: Ae = Π )
De
2
= 4Ae/ Π
De = 4
Ae
= 4
at 1
3 14
= 10.53 in

50. 36
However the value of De is larger than the maximum vehicle diameter of ‘7 in’ (for which Ae or A2 =
38.465 in2
), which is the maximum for the outside of the nozzle exit.
 Allowing for an exit cone thickness of 0.1 in., the internal nozzle exit diameter D2 = 6.9 in and
A2 =37.37 in2
, this would allow only a maximum area ratio of:
A2/At = 37.37/3.225 = 11.59
Since the CF values are not changed appreciably for this new area ratio, it can be assumed that the
nozzle throat area is unchanged. The nozzle can have a thin wall in the exit cone, but requires heavy
ablative materials, probably in several layers near the throat and convergent nozzle regions. The thermal
and structural analysis of the nozzle is not conducted in this project.
 Solid rocket nozzle inlet section parameters ;
P1=800psi
T1 =4188 K
M1 =V1/ɑ1 = 224.7308/952.28=0.236
 Solid rocket nozzle throttle section parameters ;
Pt = P1 (2/k+1) k/k-1
Pt =800(2/2.25)1.25/2/25
= 443.9 psi
Tt =T1 (2/K+1)
Tt =4188(2/2.25) =3723K
Mt =1
 Solid rocket nozzle exit section parameters ;
P2 = P3 = 3psi
T2 = T1 (P2/P1) k-1/k
=4188 (3/800)0.25/1.25
= 1370k
sec
/
7
.
2843
800
3
1
4188
287
1
25
.
1
25
.
1
2
1
1
2 25
.
1
1
25
.
1
1
1
2
1
2 m
P
P
RT
k
k
V
K
K
































































2
2
2
a
V
M 
sec
/
743
.
1225
4188
287
25
.
1
2
2 m
kRT
a 




32
.
2
743
.
1225
7
.
2843
2 

M

51. 37
 Characteristics velocity
Cf
c
Cf
g
I
m
A
P
c o
s
t




.
1
C*
=Isgo/CF=240×9.81/1.7 =1384.9 m/sec
 Effective velocity
C=Isgo =240×9.81 =2354.4 m/sec
4.3.5 Weight Estimate:
• The steel case weight (assuming a cylinder with two spherical ends and that steel weight density
is 0.3 lbf/in3
) is found by: [8].
WC = t Π D L + 4
t D2
Wc = 0.0248 x 3.14 x 6.83 x 19.82 x 0.3 + 0.785x 0.0248 x 19.822
x 0.3
Wc = 3.163 + 2.294 = 5.457 lbf
Where: D – is the average diameter to the center of the wall; L – is the effective length; t – is the wall
thickness; – the steel weight density
 With attachment flanges, igniter and pressure tap bosses the steel case weight is increased to
11.457 lbf
• The nozzle weight is composed of the weights of the individual parts, estimated for their densities
and geometries and merely gives the result of 6.07 lbf.
• Assume unexpended igniter propellant weight of 1.15 lbf and a full igniter weight of 4.0 lbf.
• The total engine weight estimate then is:
- Case weight at sea level 11.457 lbf
- Liner/insulator 2.85 lbf
- Nozzle, including fasteners 6.07 lbf
- Igniter case and wires 1.15 lbf
….……………………………………………………………………………………….......
- Total inert hardware weight (the above items) 21.527 lbf
- Igniter powder 2.85 lbf
- Propellant (effective) weight 50 lbf

52. 38
- Un-usable pro pellant (2%) 0.9 lbf
….…………………………………………………………………………………………...
- Total weight (WTE.) 75.277 lbf
- Propellant and igniter powder weight 52.85 lbf
4.3.6 Performance:
• The total impulse-to- Engine weight ratio can be found from Eq.3.2
It = Ft
It = 4000 x 3 = 12000
It / Wtot = 12000/75.277 = 159.4
• Comparison with Is = 240 sec. shows this to be an acceptable value, indicating a good
performance.
• In comparing and contrasting the values of It and WTE , to indicate whether the design is safe or
not the following criteria can be used:
It > WTE - the design is safe
It < WTE - the design is not safe
• The total launch weight:
WTL = vehicle pay load + Engine weight estimate
WTL = 78.7 lbf + 75.3 lbf = 154 lbf
• The weight at burnout or thrust termination:
Wt t = WTL - propellant and igniter powder weight
Wt t = 154 – 52.85 = 101.15 lbf
• The initial and final thrust-to-weight ratios and accelerations:
Initial thrust to weight ratio = F/WTL = 4000/154 = 25.97
Final thrust to weight ratio = F/Wtt = 4000/101.15 = 39.54

53. 39
Therefore the acceleration in the direction of thrust is 25.97 times the gravitational acceleration at start
and 39.54 at burnout
4.3.7 Erosive Burning:
• The ratio of the port area to the nozzle throat area at start:
EB = Ap / A t = (2.82/1.432)2
= (1.97)2
= 3.88
This value is close to the limit of 4 and erosive burning is not likely to be significant. Generally to avoid
unwanted erosive burning of propellant in a rocket motor, low length to diameter ratio, high port to
throat area ratio motors are preferred.
The following table represents the summary of calculated result parameters.
Table 24.1 Table showing the calculated result parameters in two unit systems:
No Parameters Calculated
results
(in BSU)
Calculated
results
(in SI unit)
Remark
1
Basic
Design
Parame
ters
Total Impulse (It ) 12,000 lbf 54545.45 N (1N = 0.22 lbf)
2 Specific Impulse (Isp ) 240 sec 240sec Given
3 Propellant weight ( Wb) 50 lbf 222.42 N
4 Propellant volume (Vb) 761.2 in3
0.0125 m3
(1m3
= 61023.6
in3
)
5 Web thickness (b) 1.8 in 0.0457 m 1 inch = 0.0254 m
6 Case
Dimensi
ons
Max. missile diameter (D) 7 in 0.1778 m
7 Wall thickness (t) 0.0248 in 0.00063 m
8 Insulator thickness (tin) 0.1 in 0.00254 m
9
Grain
configu
ration
parame
ters
Grain outside diameter (D0) 6.75 in 0.172 m
10 Grain inside diameter (Di) 3.15 in 0.08 m
11 Effective length (L) 23.12 in 0.587 m
12 Web fraction (Wf) 0.533 0.53
13 (L/D0 ) ratio 4.03 4.03
14 Desired burn area) (Ab) 416.6 in2
0.269 m2
1m2
= 1550 in2
15
Nozzle
Design
Thrust coefficient (CF) 1.55 1.55
16 Nozzle throat area (At) 3.225 in2
0.001 m2
17 Nozzle throat diameter (Dt) 2.03 in 0.0364 m

54. 40
Parame
ters
18 Nozzle exit area (Ae) 87.1 in2
0.0241 m2
19 Nozzle exit diameter (De) 10.53 in 0.175 m
20
Perfor
mance
Parame
ters
Steel Case weight (WC) 11.457 lbf 5.2 kgf
21 Total Engine Weight 75.277 lbf 34.22 kgf (1kg = 2.2 lb)
22 Total Impulse to weight ratio 159.4 159.4
23 Total Launch Weight (WTL) 154 lbf 70 kgf 1kgf = 2.2 lbf
24 Erosive Burning (EB) 3.88 3.88
4.4 MODELING CFD SIMULATION
The complete result of software analysis (RPA - rocket propulsion analysis) is kept as separate file to
reduce the volume of our project material and can be shown for an interested examiner of the project
material. Only some thermodynamic properties and estimated delivered performance parameters are given
for the purpose of comparing with analytical computational results. The results of nested analysis in the
form of graphs are also presented. We start our actual work here by modeling the grain, the motor and the
nozzle of solid rocket motor using CATIA. After modeling of those parts we will analyze our work by
using RPA software.
Figure 4- 2 hollow cylindrical grain

55. 41
Figure 4- 3 solid rocket nozzle model
Figure 4- 4 solid rocket motor configuration
RPA is an acronym for Rocket Propulsion Analysis. RPA is a rocket engine analysis tool for rocketry
professionals, scientists, students and Amateurs. By providing a few engine parameters such as
combustion chamber pressure, used propellant components, and nozzle parameter, the program obtains
chemical equilibrium composition of combustion products, determines its thermodynamic properties, and
predicts the theoretical rocket performance. The calculation method is based on robust, proven and
industry-accepted Gibbs free energy minimization approach to obtain the combustion composition,
analysis of nozzle flows with shifting and frozen chemical equilibrium, and calculation of engine
performance for finite and infinite-area combustion chambers.

56. 42
4.4.1 Altitude performance
The performance of the chamber in the specified ambient conditions.
Figure 4- 5 graph of altitude performance
4.4.2 Throttled performance
The performance of the chamber at the specified throttle values.
Figure 4-6 graph of throttled performance
4.4.3 Nested Analysis
Using nested analysis, we can evaluate the performance of the rocket chamber for the range of
parameter/s, stepping of up to four independent variables (component ratio, chamber pressure, nozzle
inlet conditions, and nozzle exit conditions). We can plot the diagrams of:
- "Specific impulse vs. variable parameter",
- "Chamber temperature vs. variable parameter",
- "Characteristic velocity vs. variable parameter" or
"Thrust coefficient vs. variable parameter". The following figures represent the same

57. 43
Figure 4-7 graph of specific impulse Vs component ratio
Figure 4.7 graph of specific impulse Vs component ratio
Figure 4-8graph of specific impulse Vs chamber pressure
Figure 4.8 graph of specific impulse Vs chamber pressure

58. 44
Figure 4-9 graph of specific impulse Vs nozzle inlet condition
Figure 4.9 Graph of specific impulse Vs nozzle inlet condition
Figure 4-10 graph of specific impulse Vs nozzle exit condition

59. 45
Figure 4.10 Graph of specific impulse Vs nozzle exit condition
The commercial code ANSYS Fluent was used to undertake the fluid simulation throughout this research.
The fluid domain is modeled as thousands of smaller divisions (elements) where the variables for each are
calculated individually. There are several considerations for the simulation process which affect the scope
and quality of the model, they will be described and analyzed throughout consecutively.
4.4.4 Geometry
Figure 4-11C-D nozzle dimensions
4.4.5 Mesh Selection
A successful mesh independence study provides a mesh that “arrives at the least number of elements that
can yield accurate computational results”. After the modeling is completed the meshing is to be done. The
module used to perform meshing is Fluid Flow (Fluent). The meshing method used here is Automatic
Method and the mesh type is selected as All Quad.
a. Unstructured mesh b. Structured mesh
Figure 4-12 structured and unstructured mesh

60. 46
The mesh obtained initially will be unstructured mesh (fig.4.12a) and this cannot be used to obtain
accurate results. Since the edges are prismatic the mesh can be converted into structured meshing (figure
4.12b) by using Mapped Face Meshing.
4.4.6 Boundary Conditions
1. Inlet
2. Outlet
3. Walls
Specification of the boundary zones has to be done in WORKBENCH only, as there is no possibility to
specify the boundary zones in FLUENT. Therefore proper care has to be taken while defining the
boundary conditions in WORKBENCH. With all the zones defined properly the mesh is exported to the
solver. The solver used in this problem is ANSYS FLUENT. The exported mesh file is read in Fluent for
solving the problem.
The following two graph show ‘cd’ Vs iteration convergence history. The two consecutive graphs (Figure
4.4a and Figure 4.4b) show the wrong and correct representations of ‘cd’ Vs iteration convergence
history which can be explained by the difference of air medium and combustion product properties
analysis. The correct representation proves that our design is safe and can be continued to the next steps
of the job.
Figure 4-13a CD Vs iteration convergence history
CD Vs iteration convergence history (wrong one – air medium)

61. 47
Figure 4-13b CD Vs iteration convergence history
CD Vs iteration convergence history (correct one – combustion product)
The following figures show the contours of various parameters analyzed by ANSIS of FLUENT
release.
Figure 4-14 counters of velocity magnitude

62. 48
Figure 4-15 contour of static pressure
From figures 4.14 and 4.15 it follows that at the inlet of the nozzle or at subsonic region, the pressure
increases and velocity decreases or maximum pressure and minimum velocity occurs at the inlet of the
nozzle. At the outlet of the nozzle maximum velocity is achieved whereas the pressure is almost
approaching to zero.
Figure 4-16 contour of Mach number

63. 49
From Figure 4.16 it can clearly be seen that minimum value of velocity is achieved at subsonic condition
and maximum at supersonic condition. Both the graph and the image show the same conditions i.e. at
subsonic (M < 1); sonic (M = 1), and supersonic (M > 1) conditions the above described results are
achieved.
Figure 4-17 graph of Mack number Vs nozzle position
Figure 4-18 graph of static pressure Vs nozzle position

64. 50
The following figures show the velocity and pressure simulation results analyzed by ANSIS of FLUENT
release.
Figure 4-19 velocity streamline simulation
Figure 4-20 pressure simulation

65. 51
Chapter 5
5 RESULT ANALYSIS AND CONCLUSIONS
5.1 RESULT ANALYSIS
The objective of our project is to preliminarily design a rocket motor to be fitted for short range air to air
missile. The present work is purely analytical and dealt with the computation of design flow parameters
of a rocket motor and verification of its results with software simulation results. The verification shows
that the results are found to be in agreement among them-selves and with the one given in literature.
Proper materials for rocket motor requirement are chosen for combustion chamber, nozzle and insulator
components. An attempt is also made to make the sizes of the components to reduce the weight of the
rocket motor, which is one of the main considerations in the design of rocket motor components for air to
air missile applications. The suggested layout for the rocket motor with the calculated dimensions is
furnished in the drawing shown in figure 4.4. In selecting a solid propellant rocket for short range air to
air missile, it is planned to bring in the merits of its simplicity and easy to manufacture along with others.
The comparison table of computational result parameters with simulation result parameters of a designed
rocket motor is presented as given below.
Table 35.1 Comparisons of computational results with simulation results of designed rocket motor
Engine main parameters
(Thermodynamic properties)
Designed engine
Calculated Results Simulation Results Unit
Nozzle inlet pressure 5.5 5.2577 MPa
Nozzle throat pressure 3.0600 3.1751 MPa
Nozzle outlet pressure 0.02 0.0293 MPa
Nozzle inlet temperature 4188 4188.3480 0
K
Nozzle throat temperature 3723K 4042.1330 0
K
Nozzle outlet temperature 1370k 2597.7838 0
K
Specific heat ratio (K) 1.25 1.2549
Actual inlet exhaust velocity (V1 ) 223 224.73 m/s
Actual throat exhaust velocity(Vt) 701.06 929.14
Actual exit exhaust velocity(V2) 2577 2614.6

66. 52
Nozzle inlet Mack number (M1) 0.23 2.3834
Nozzle throat Mack number (Mt) 1 1
Nozzle exit Mack number (M2) 2.36 2.4
Area ratio (Ae/At) 27 24.0000
Engine main parameters
(Optimum delivered
performance values)
Designed engine
Calculated Results Simulation Results Unit
Characteristic velocity (c*) 1384.9 1410.4700 m/s
Effective exhaust velocity (c ) 2354 2220.2500 m/s
Specific impulse (by weight Is) 240 226.4000 sec
Thrust coefficient (CF) 1.55 1.5741
The following table may also serve as a comparison tool to compare the current available air to
air missiles with the proposed short range air to air missile to which our designed engine is going to be
fitted.
Table 45.2 Comparisons of proposed missile with other standard air to air missiles
Missile
parameters
Representatives of other Standard air to air Missiles Proposed
Missile
Falcon
(USA)
R- 27
(Russia)
Sidewinder
(USA)
Sparrow (USA) Abyssinia I
Type of missile Air-to air Short range air
to air
Short range Air-
to air
Medium range
Air-to air
Short range Air-
to air
Length 1.98 m
(6 ft 6 in)
Length 4.08 m
(13.4 ft.)
9 feet 11 inches
(3.02 m)
12 ft (3.7 m) 2 m
Diameter 163 mm
(6.4 in)
230 mm (9.1
in)
5 in (127.0 mm) 8 in (200 mm) 7 in (177.8 mm)
Warhead 3.4 kg
(7.5 lb)
39 kg (86 lb.) 20.8 lb (9.4 kg) High explosive
blast-
fragmentation
17.6 lbs (8 kg)
Propellant Solid fuel
rocket
Solid
propellant
rocket motor
Solid -fuel rocket solid rocket Solid propellant
rocket motor
Operational 9.7 km 80 km-130km 0.6 to 22 miles 11 km (6.8 mi) 10 km (6.2 mi)

67. 53
range (6.0 mi) (1.0 to 35.4 km)
Speed Mach 3 --------- Mack 2.5+
Mach 4 Mack 2.5
Missile launch
Weight --------
253 kg (558
lb.)
188lbs
(85.3 kg)
510 lb
(230 kg)
154 lbs
( 70 kg)
The analysis and computations made in chapter four are performed to the best of us, and therefore can be
enough to be taken for granted. Results obtained are close to the standard design data carried out prior to
this project (refer the above table).
Deviations of expected results have been observed due to errors that can be accounted to improper
selection of coefficients, which could have required experimental investigations of rocket engine models
or real engines in laboratory conditions or engine test cells. Deviations may also be accounted to
assumptions made on engines aimed at easing the engine to be designed during computations.
5.2 CONCLUSIONS AND RECOMMENDATIONS
5.2.1 Conclusions:
- The present work is purely analytical and dealt with design flow parameters computation of a
rocket motor and verification of its results with software simulation results. We consider that the
objective we have stetted at the beginning of the project is achieved.
- Due to reference limitations (especially current journals and technical papers) and time constraint
we have dealt with preliminary design aspects only. Even with these constraints we believe that
this report can serve as a good reference for advanced and detail designs of rocket motors.
- As a future continuation the rest of rocket motor detail design can be performed based on the data
obtained in this project and can be taken as a future scope of study.
- The results obtained are very close to reality and can be enough to be taken for granted for further
detail design. The results obtained go in line with the accepted ranges and are found to be in
agreement with the one given in literatures [1, 2, 5, 7, 9, 11] (refer table 2.1).