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ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS
GRADUATION PROJECT
February 2021
Design of and factors affecting the performance of solid rocket motor
Thesis Advisor: Prof. Dr. Alim Rüstem Aslan
Ahmet Hakan Demir
Department of Astronautical Engineering
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February 2021
ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS
GRADUATION PROJECT
Ahmet Hakan Demir
(110150127)
Department of Astronautıcal Engineering
Thesis Advisor: Prof. Dr. Alim Rüstem Aslan
Design of and factors affecting the performance of solid rocket motor
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Thesis Advisor : Prof. Dr. Alim Rüstem ASLAN ..............................
İstanbul Technical University
Jury Members : Prof.Dr. Fırat Oğuz EDİS .............................
İstanbul Technical University
Dr. Cuma YARIM ..............................
İstanbul Technical University
Ahmet Hakan Demir,student of ITU Faculty of Aeronautics and Astronautics
student 110150127, successfully defended the graduation entitled “DESIGN OF
AND FACTORS AFFECTING PERFORMANCE OF THE SOLID ROCKET
MOTOR”, which he/she prepared after fulfilling the requirements specified in the
associated legislations, before the jury whose signatures are below.
Date of Submission : 1 February 2021
Date of Defense : 8 February 2021
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To my family and my friends,
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FOREWORD
I would like to express my appreciation to my supervisor Prof. Dr. Alim Rüstem
ASLAN for his guidance. Also i am grateful to him since he taught us how to study with
a discipline in spacecraft system design lesson. Finally, I want to say my very lovable
thanks to my family for their love and patient. Without them there is no meaning of the
world.
February, 2021
Ahmet Hakan Demir
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TABLE OF CONTENTS
Page
FOREWORD ............................................................................................................. ix
ABBREVIATIONS ................................................................................................. xiv
LIST OF TABLES .................................................................................................. xvi
LIST OF FIGURES .............................................................................................. xviii
SUMMARY .............................................................................................................. xx
1. INTRODUCTION .................................................................................................. 1 1.1 Purpose of Thesis ............................................................................................... 1
1.2 Literature Review ............................................................................................... 2
1.3 Classification of Rocket Motors ......................................................................... 2
1.3.1 Solid Propellant Rocket Motors .................................................................. 3
1.3.2 Liquid Propellant Rocket Motors ................................................................ 3
1.3.3 Hybrid Rocket Motors ................................................................................ 3
2. SOLID PROPELLANT ROCKET MOTORS .................................................... 5 2.1 Main Parts of Solid Propellant Rocket Motors .................................................. 5
2.1.1 Insulator ...................................................................................................... 5
2.1.2 Igniter .......................................................................................................... 6
2.1.3 Motor Case .................................................................................................. 6
2.1.4 Propellant Grain .......................................................................................... 6
2.1.5 Nozzle ......................................................................................................... 7
3. SOLID PROPELLANT DESIGN METHODOLOGY AND GOVERNING
EQUATIONS .............................................................................................................. 9 3.1 Ballistic Parameters ............................................................................................ 9
3.1.1 Characteristic Velocity ................................................................................ 9
3.1.2 Thrust ........................................................................................................ 10
3.1.3 Nozzle Throat Area ................................................................................... 10
3.1.4 Density ...................................................................................................... 10
3.1.5 Specific Impulse ........................................................................................ 11
3.1.6 Chamber Pressure ..................................................................................... 11
3.1.7 Nozzle Expansion Ratio ............................................................................ 12
3.1.8 Burning Rate ............................................................................................. 12
4. FACTORS THAT AFFECT SOLID ROCKET MOTOR PERFORMANCE13 4.1 Burning Rate .................................................................................................... 13
4.1.1 Erosive Burning ........................................................................................ 13
4.1.2 Discussion of the Results and Effect on Operations: ................................ 16
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4.2 Grain Design Analysis and Typical Grain Configurations ............................... 16
4.2.2 End Burning Grain .................................................................................... 17
4.2.3 Internal-Burning Tube Grain ..................................................................... 18
4.2.4 Star Grain .................................................................................................. 18
4.2.5 Grain Design Comparisons ....................................................................... 19
4.2.6 Discussion of the Results and Effect on Operations ................................. 23
4.3 Design of Solid Rocket Motor For Different Kind of Operations .................... 23
4.3.1 Assumptions of the Flight: ........................................................................ 24
4.3.2 Some of the obtained ballistic parameters of the rockets .......................... 24
4.3.3 Analysis of Propellant Effect on Solid Rocket Motor Performance ......... 25
4.3.4 Discussion of the Results and Effect on Operations ................................. 26
5. CONCLUSION ..................................................................................................... 27
REFERENCES ......................................................................................................... 28
APPENDICES .......................................................................................................... 30
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ABBREVIATIONS
a : Burning rate coefficient
Ae : Nozzle exit area
At : Nozzle throat area
C* : Characteristic velocity
Cf : Thrust coefficient
DB : Double base
HMX : cyclotetramethylene tetranitmarine
Is : Specific impulse
K : Kelvin
�̇� : Mass flow rate
e : Exit pressure
c : Combustion pressure
rb : Burning rate
SPRM : Solid propellant rocket motor
: Specific heat ratio
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LIST OF TABLES
Page
Table 4.1: Grain Classification[16] .................................................................................. 17
Table 4.2: The star grains used in SPRMs ....................................................................... 19
Table 4.3: Properties of NGR-A propelant [20] ............................................................... 19
Table 4.4: Internal ballistic parameters of 5 numbered star grain[21] ............................. 21
Table 4.5: Internal ballistic parameter results of the internal end burning grain ............. 23
Table 4.6: Preliminary design parameters of the rockets ................................................. 24
Table 4.7: Performance parameters of the rockets ........................................................... 25
Table 4.8: Properties of the tested propellants ................................................................. 25
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LIST OF FIGURES
Page
Figure 1.1: Comparison of the rocket motors..................................................................... 2
Figure 2.1: Solid propellant rocket motor .......................................................................... 5
Figure 3.1: Mach number and erosive burning relation ................................................... 14
Figure 3.2: Inıtial propellant temperature and erosive burning relation........................... 15
Figure 3.3: Pressure rise and erosive burning relation[14] .............................................. 15
Figure 4.1: End burning grain configuration .................................................................... 17
Figure 4.2: Internal burning tube grain ............................................................................ 18
Figure 4.3: The design of 5 numbered star grain for RM-3 motor ................................... 20
Figure 4.4: The design internal end burning grain for RM-3 motor ................................ 20
Figure 4.5: 5 numbered star grain pressure and thrust curve[21] ..................................... 21
Figure 4.6: Results of Terzic et al [21] ............................................................................. 22
Figure 4.7: Results of the Openmotor .............................................................................. 22
Figure 4.8: Performance comparsion graphic of the propellants ..................................... 26
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DESIGN OF AND FACTORS AFFECTING THE PERFORMANCE OF SOLID
ROCKET MOTORS
SUMMARY
Solid propellant rocket motors are the most preferred propulsion systems for military
applications that require high thrust to weight ratio for comparatively short time
intervals. The range of magnitude and duration of the thrust are related to many factors.
For this study, significant criteria that affect performance of solid propellant rocket
motor is researched with detailed. According to researches, the most effective of these
design criteria is concerned geometry of the solid propellant motor grain. It is observed
that by changing only dimensions of the grain, average pressure, thrust and specific
impulse could be increased seriously. These parameters do not impact only performance
of the rocket motors, also mass of the payload can be increased. In order to make
performance comparison between two types of the grain analysis of internal ballistic
solver is necessary. Without an internal ballistic solver pressure curve could not be
obtained. In this analysis, only type of the grain is changed and all other design
parameters are taken same for the test. Also, to verify the correctness of the analyses, the
obtained results are compared with test results and their affect on space operations is
discussed. After that effect of the erosive burning is analyzed. Factors that change
erosive burning are investigated and its effect on operations discussed too. Lastly, 3
different types of solid rocket motors are designed and all of them are assigned with a
duty. The purpose of designing here is related to analyze determining preliminary design
parameters for different conditions which are concerned altitude and payload. These
preliminary design parameters are determined by looking at successful rockets in the
past. Since altitude and operation duration are proportional to each other nozzle have to
be designed according to this criteria. Also one of the rocket is tested with three different
type of solid propellant to analyze effectiveness of the propellant on solid rocket motor’s
performance.
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KATI YAKITLI ROKET MOTORUNUN TASARIMI VE PERFORMANSINI
ETKİLEYEN FAKTÖRLER
ÖZET
Katı yakıtlı roket motorları özellikle kısa sureli çalışan ve yüksek itki- ağırlık oranlı bir
itki sistemine gereksinim duyan askeri askeri uygulamalarda en sıklıkla kullanılan itki
sistemleridir. Bu tarz sistemlerde ihtiyaç duyulan itki miktarı ve süresini belirleyen pek
çok faktor bulunmaktadır. Bu çalışmada katı yakıtlı roket motorlarının performansını en
çok etkileyen faktörler detaylı bir şekilde araştırılmıştır. Araştırmalara gore, en etkili
dizayn kriteri katı yakıtlı roket motorunun yakıt tanecik tasarımıdır. Yapılan çalışmalara
gore yakıt taneciğinin ölçüleri değiştirildiği zaman bile roketin ortalama basıncı, itkisi ve
özgül itkisi önemli bir şekilde artmaktadır. Bu parametreler sadece performası
arttırmakla kalmayıp, roketin taşıdığı görev yükünü de arttırabilir. Yakıt tanecik
tasarımında performans karşılaştırması yapılabilmesi için iç balistik programı
kullanılması zorunludur. Balistik program olmadan zamana bağlı basınç grafiği elde
edilemez. Yapılan analizde, sadece yakıt tanecik tasarımı değiştirilmiş ve diğer tüm
parametreler sabit tutulmuştur. Elde edilen balistik sonuçların doğrulanması için test
sonuçlarıyla karşılaştırılmıştır. Bu çalışmadan sonra aşınımlı yanma üzerine durulmuş
bunu etkileyen faktörlerden bahsedilmiştir ve operasyonlara olan etkisi açıklanmıştır.
Son olarak, 3 farklı roket tasarımı yapılarak her birine bir görev verilmiştir. Bu
çalışmanın yapılmasının amacı ön hazırlık parametrelerinin görev yükü ve irtifaya bağlı
olarak nasıl belirlemesi gerektiği açıklanmıştır. Bu ön koşul parametreleri geçmişte
yapılmış benzer görevlerden yararlanılarak bulunmuştur. İrtifa ve operasyon süresi de
lüle tasarımıyla bağlantılı olduğundan lüle tasarımı da bu durum baz alınarak
yapılmıştır. Ek olarak 3 farklı katı yakıt seçilerek performansı nasıl etkilediğine dair bir
analiz de yapılmıştır.
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1. INTRODUCTION
Nowadays, most of the weapon systems are used with some kind of propulsion system
that helps them move to from one location to another. For complex weapon systems like
aircrafts and so on, very complex propulsion system is required. Depending on mission
requirements, the propelling system must be able to run throughout operation, refueling
must be easy and service life must be suitable. For this kind of applications very
complex propulsion system like internal combustion engines or gas turbines are used.
For simple weapon systems like artillery rockets or surface to air rockets, cheaper,
simpler and maintenance free propulsion system is required. These systems require a one
shot operating propulsion system. After the missile or rocket reaches the desired target,
the propulsion system explodes with the payload. These type of motors are the most
common used propulsion system for such applications. Most importantly, rocket motor
does not need the surrounding air for oxidizing the propellant. Therefore rocket motor is
capable of in space or somewhere where there is no free oxygen for the propulsion
system to use. This situation makes very convenient to use rocket motor since there is no
alternative solution for space applications.
1.1 Purpose of Thesis
The aim of the study is related to discuss about general design of solid rocket motors and
understanding the main steps of designing process evaluation. Also to show the most
important factors that affect SPRM performance with numerical methods and discuss
their impacts on space operations.
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1.2 Literature Review
After World War 2, the war winner countries developed themselves in space field
rapidly. Also with the affect of Cold War, space racing became a symbol for power
demonstration[1].As a result, many contributions have been made to improve
performance of rocket motors. In 1956, Lenoir and Robillard [2] developed first erosive
burning based solid propellant rocket model and tested it. This model has been improved
and still has been using to analyze solid engine performance. In 1977, Woltosz [3]
suggested to use pattern technique to obtain solid propellant grain design. Since
propellant grain burning efficiency is related to type of solid propellant researches also
gained acceleration to find proper propellant. In 1980, Swanamithan and Madhavan [4]
attempted to find optimal propellant composition, by increasing the rate of aluminium of
the propellant. Also Nisar and Ghouzhu [5,6] used Genetic Algorith metholodology to
optimize wagon wheel and finocly grain for solid rocket motors.
1.3 Classification of Rocket Motors
Classification of rocket motors can be made in many aspects. However according to
engineering literature, the most common way of classification is regarded to usage of
type of propellant and oxidizer.
Figure 1.1: Comparison of the rocket motors
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1.3.1 Solid Propellant Rocket Motors
In solid propellant motors, both the fuel and the oxidizer are used in solid form. They are
premixed and react inside the combustion chamber at the production phase. Solid
propellant rocket motors are not complex compared to the other motors so that they do
ot need any mechanism for supplying mixture to the combustion chamber. Therefore
they are the simplest rocket motors among them.
1.3.2 Liquid Propellant Rocket Motors
In liquid propellant motors, both the fuel and the oxidizers are used in liquid form.
Unlike solid propellant rocket motors, they are stored in different tanks. In this motor
type usually hydrogen and hydrocarbons are used as fuel due to oxidize properties of
these materials. Also oxygen is usually used as oxidizer. Despite the fact that liquid
propellant rocket motors have higher specific impulse than other type of motors, they
have much more complex design and expensive. Although it requires more effort to
produce liquid propellant rocket motors, Nazis launched more than 3000 V-2 rockets
between 1939-1945 [7]. Considering technological insufficiencies at these times it was
great success since some of the developed countries still can not produce liquid
propellant rocket motors.
1.3.3 Hybrid Rocket Motors
In hybrid rocket motors, fuel and oxidizer are not stored in the same place. This situation
provides stability to the fuel since their mixture may cause some problems in motor due
to their different state properties. Therefore hybrid rocket motors avoid some of the
disadvantages of the rocket motors. However, storage of the fuel and the oxidizer in
different locations cause complexity at combustion process in hybrid motors and this
leads to low regression problem. This motor type has higher specific impulse than solid
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motor and lower than liquid motor. Although development of hybrid motors have been
started at early years, compared to other type of traditional rockets, they are not
commonly used at these days.
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2. SOLID PROPELLANT ROCKET MOTORS
As mentioned in previous chapter, solid propellant rocket motors are the most widely
used rocket motors for military applications. Their simplicity and cheapness features
make appealing to use these types of rockets for this applications. Also solid rocket
motors have high reliability since they are usually produced for single operation
conditions. They can achieve very huge thrust levels up to millions of Newtons.
Figure 2.1: Solid propellant rocket motor
2.1 Main Parts of Solid Propellant Rocket Motors
2.1.1 Insulator
In combustion process product gasses inside the motor can reach above 3000 K.
Therefore protection of the motor case and other structural components are necessary.
Most of the rocket insulators have low thermal conductivity and high heat capacity.
These properties increase heat loss between parts of the rockets so that high temperature
in combustion chamber does not affect the other parts of the rocket significantly. Most
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widely used insulator materials can be stated as EPDM (Ethylene Propylene Diene
Monomer) which has the features as it is mentioned in previous sentence[8].
2.1.2 Igniter
The aim of the igniter is to stimulate combustion reaction in a controlled and
predictable manner. Initiation of the ignition could be started with mechanical, electrical
or chemical sources. However most of the time electrical signal is used to provide safer
conditions for the motor. After initial process heat transfer occurs between igniter and
propellant surface and this allows to burning of the grain surface which stems from
formed hot gasses. Proper design of the igniter is very crucial since sufficient heat and
temperature are necessary in order to burn to grain surface.
2.1.3 Motor Case
Solid propellant rocket motor case covers the propellant grain, igniter and insulator. The
combustion process occurs in the motor case; thus, for some cases it can be stated as
combustion chamber.The case must be able to resist the internal pressure which stems
from the motor operation, thereabout 3-30 MPa. Also the case has to be designed with
sufficient safety factor to support the motor structure. The motor case is usually
constructed from either metal (titanium alloy, alloy steel, aluminum alloy 2024) or from
composite materials (glass, Kevlar 49, graphite IM) [8]. Moreover, thermal stresses
maybe sometimes critical in the combustion chamber so that determining the thickness
of the case and the selecting the material of the motor case play significant role on solid
rocket motor design.
2.1.4 Propellant Grain
Propellant grain is described as cast which has certain configuration and geometry. The
propellant grains can be analyzed in two general configurations: case- bonded grain and
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free standing grain. Since the bond and case are bonded to each other, case- bonded
grains directly casts the case of the motor so that extra thermal insulation is not required
for propellant grain. Free standing grains are not produced as compound of the motor
case so that the propellant is cast in some exclusive mold. They can be loaded into or
assembled into the motor case. Free standing grains can be also described as cartridge-
loaded grains [9]. With internal ballistic results of the SRM, analysis of different type of
grain designs could be evaluated and some changes could be done to satisfy flight
conditions. These mentioned propellant grain topic will be analyzed detailed in further
chapter.
2.1.5 Nozzle
In a rocket motor, the thrust force is obtained by discharging energy due to high
temperature and high pressure. The design of the nozzle is significant because total
chemical energy of the product gasses are converted useful work energy in the nozzle
which is directly related to specific impulse and thrust. In converging- diverging
nozzles, since product gasses have high pressure in the converging part of the nozzle, the
gasses will accelerate through this part. After that pressure of the gasses drop and gasses
reach sonic speed at the throat of the nozzle. Finally, the gasses accelerate through the
diverging part, which results in reduce of pressure and the gasses are discharged into to
the atmosphere from exit of the nozzle. The magnitude of the exit gasses and momentum
of the rocket are proportional to each other. Nozzles can be categorized depending on
structural assembly technique or the shape of the contour; like movable nozzle, bell
shaped nozzle and submerged nozzle.The most selected nozzle type is bell shaped
nozzle due to efficiency and ease of manufacturing. In addition, rocket motor nozzle
materials should not be underestimated. The product gasses reach very high
temperatures like 3000 K or even more. To satisfy thermal conditions in the nozzle, the
material for the solid rocket motor must be selected carefully prevent to exceed
allowable temperature conditions in the nozzle. Usually carbon fiber containing
composites and graphite are used at the nozzle since risk is the highest in this part of the
nozzle.
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3. SOLID PROPELLANT DESIGN METHODOLOGY AND GOVERNING
EQUATIONS
Initial step of designing a solid propellant rocket motor starts with determining the
mission requirements. The mission requirement can be simply defined as what is
expected from the SPRM. The duration of operation, the required thrust, the operating
environment conditions and the geometrical restraints are given to the designer. Aim of
the designer is to develop SPRM to provide all the needs that are given to him/her.The
SPRM designer can change some parameters to obtain required parameters which are
mostly done for configuration the grain design. These parameters are called as ballistic
parameters. In many resources these parameters are classified in which are dependent
and independent parameters, but for some conditions dependency can not be decided
[10].
3.1 Ballistic Parameters
At introduction part of the chapter 3, the required parameters are mentioned briefly. In
order to analyze the internal ballistic results the parameters are explained detailed in
following captions. Since some of the parameters are related to each other, some of the
explanations are done with the aid of other parameters.
3.1.1 Characteristic Velocity
Characteristic velocity is a measure of propellant thermodynamics properties and
combustion chamber design so it is independent from nozzle features. Considering this
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information characteristic velocity is used to analyze performance of the different kind
of propellants (double -base propellants, composite propellants so on ). The formulation
can be showed by :
𝐶∗ =𝑃𝑐𝐴𝑡
�̇� (3. 1)
3.1.2 Thrust
Thrust is the force that keeps the rocket moving through the air and space. It is one the
main design constraints of the rocket propulsion systems. It can be obtained by:
𝐹 = 𝐶𝐹𝑃𝑐𝐴𝑡 (3. 2)
3.1.3 Nozzle Throat Area
Nozzle throat area is a parameter that which affects the thrust of the SPRM. At the
design stages of the SPRM nozzle throat area is fixed so that thrust can not be modified
during the operation. Since some of the parameter equations are related to each other
nozzle throat area can be obtained by using expansion ratio and so on.
3.1.4 Density
Density of the propellant is significant factor considering volume limitations of the
SPRM. Since density and mass of the propellant are proportional to each other the
denser propellant is preferred in the same volume. However the density of the solid
rocket motor propellant is not effective on rocket’s performance by only itself. As it is
mentioned in nozzle chapter, conversion of the energy in the solid rocket motor is
significant since it directly affects the SPRM performance. Considering this situation,
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the obtained energy from per volume of the propellant is more significant then mass of
unit volume from it self. Therefore, density factor of the propellant has less effect on
performance of the rocket.
3.1.5 Specific Impulse
Specific impulse can be considered most significant notion for all rocket motors. It is
described as total impulse that obtained from per unit of consumed propellant. Rocket
performance efficiency and magnitude of specific impulse are proportional to each
other. Also it is very significant in the selection of the proper propellant for the mission
to satisfy ballistic requirements. Specific impulse can be defined as:
𝐼sp =𝑐∗𝐶𝐹
𝑔0=
𝐹
𝑚𝑔̇ 0 (3. 3)
3.1.6 Chamber Pressure
Chamber pressure defines the pressure value of the combustion chamber during the
operation of SPRM. This pressure value varies to different amount of values during the
whole operation. Chamber pressure is one of the most important parameter which affects
thrust of the rocket motor. Considering mechanical properties of components of motor
and motor case the maximum operating pressure is fixed to save these parts of the
SPRM. The designer has to avoid exceeding the limit of this pressure during the action
of the SPRM. Chamber pressure also represents the average pressure of SPRM which is
important performance criteria of a rocket motor. This value is obtained from pressure
curve at the duration of the operating time. The average pressure value of the SPRM
depends on the grain geometry which will be discussed detailed in further chapters.
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3.1.7 Nozzle Expansion Ratio
It defines the ratio between nozzle exit area and nozzle throat area. From the ratio it can
be understood that pressure value reduction before the exhaust process. In order to
obtain maximum acceleration from the SPRM, nozzle expansion ratio must be set at
proper value which is stated as optimum ratio. If the nozzle expansion ratio is higher
then the optimum ratio, causing a shock at the exit of nozzle which is not desirable; if
the expansion ratio is lower then the optimum value some of the energy is lost until the
conversion of useful energy. The mentioned nozzle types are called as over expanded
and under expanded nozzles respectively. The optimum expansion ratio of the SPRMs
can be obtained from equation below:
𝑨𝒕
𝑨𝒆= [
𝜸+𝟏
𝟐]
𝟏
𝜸−𝟏[
𝑷𝒆
𝑷𝒄]
𝟏
𝜸 √𝜸+𝟏
𝜸−𝟏[𝟏 − [
𝑷𝒆
𝑷𝒄]
𝜸−𝟏
𝜸] (3. 4)
3.1.8 Burning Rate
In rocket motors, propellant grain burns in a direction perpendicular to grain surface and
burn rate is the rate defines the exposed part of the consumed propellant surface.
Burning rate depends on many factors. It can be changed by the followings [8]:
1) Chamber pressure
2) Initial temperature of the propellant
3) Motor motion of the rocket (acceleration and spin induced stress)
4) Magnitude of the gas flow velocities parallel to the burning face.
𝑟𝑏 = 𝑎 ⋅ 𝑃𝑐𝑛𝑟𝑏 (3. 5)
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4. FACTORS THAT AFFECT SOLID ROCKET MOTOR PERFORMANCE
As it is stated at the beginning of the thesis, there are primarily 3 factors which affect the
SPRM performance. They are related to burning rate, burning surface and grain design
[11]. Since type of the propellant and its properties affect burning rate and burning
surface, it is discussed detailed in this chapter.
4.1 Burning Rate
Burning rate can be increased by many methods which are explained chapter 2. Since
burning rate depends on many factors, performance of the SPRM could be increased by
applying of the mentioned criteria. It provides advantageous solution because some
criteria may not be changed due to finished complete preliminary design of SPRM.
4.1.1 Erosive Burning
The erosive burning refers to increase in the burning rate of the propellant due to axial
gas flow combustion flow gasses inside the chamber [12]. According to obtained
ballistic results, it has a significant affect SPRM performance. Since pressure and the
velocity of the combustion gas values are proportional to each other, if the velocity
increases which affects the pressure, results in increase of thrust at initial stages of
burning. However erosive burning causes higher pressure than non erosive SPRMs so
that this increase may give damage some parts of the SPRM. Furthermore, insulation at
the aft end must be thickened since erosive burning induces to propellant at the aft end
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of the SPRM to burn up sooner than the head end. Erosive burning can be changed by
the following parameters [13] :
1) Axial cross flow velocity
2) Chamber pressure
3) Propellant initial temperature
4) Reynolds Number
5) Rocket motor size
6) Propellant properties
The effect of some of these parameters on erosive burning can be observed from the
figures below:
Figure 3.1: Mach number and erosive burning relation
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Figure 3.2: Inıtial propellant temperature and erosive burning relation
Figure 3.3: Pressure rise and erosive burning relation[14]
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4.1.2 Discussion of the Results and Effect on Operations:
Actually erosive burning of the SPRM should be shown by internal ballistic results. In
addition, erosive burning is very useful for the rocket at the initial stage of the rocket
flight. It can be understood from figure, the spike of the pressure provides good start for
the rocket which increases the performance of the SPRM [15]. However some designers
do not prefer erosive burning for the SPRM since the internal ballistic solver results may
be misleading which makes it difficult to understand.
4.2 Grain Design Analysis and Typical Grain Configurations
Burning area of the propellant grain changes during the motor operation. Since burning
area changes at the operation process, this change also affects chamber and thrust of the
SPRM. Therefore performance of the SPRM is strongly depended to grain design of the
propellant. Grain design analysis is related to geometrical constraints of the propellant
grain so that it is purely geometrical. Considering mission requirements, operation time
and mass so on, different type of propellants are design to satisfy these criteria.
Although most of them reach same burning time, chamber pressure and thrust curve do
not behave same which can be validated from internal ballistic results.
4.2.1 Some General Grain Configurations
Since every type of the mission may have different type of requirements (different
pressure, thrust curve, neutral boost) grain must be designed to satisfy the mission
criteria. Grain configuration can be categorized in many aspects:
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Table 4.1: Grain Classification[16]
Inner Shape of the
Grain
Outer Shape of the
Grain
Type of The Grain The dimensional
Analysis
Star, wagon,
internal burning
tube etc.
Tubular, spherical Single and double
propellant grain
Two or three
dimensional
4.2.2 End Burning Grain
End- burning grain (Figure 3.2) is the most simple grain configuration for SPRM. Since
the grain exposes directly to the chamber barrier to hot gasses, so that motor case
requires more thickened insulation. This situation increases the weight of the motor and
it invades the available chamber volume in SPRM which results in less fuel usage and
cost increase. [16] Although end- burning grain lacks from this properties of the SPRM,
it has a high volumetric loading. Since end burning grain has low thrust level, it is
mostly suitable for long duration and low thrust required missions.
Figure 4.1: End burning grain configuration
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4.2.3 Internal-Burning Tube Grain
The internal burning tube grain is one of the most selected and preferred grain type of
the SPRM. Ease of manufacture and analysis of this design make convenient to use this
type of grain. They are case bonded designed which restricts the outer surface of the
grain. The grain burns radially and its aft end usually designed unrestricted to prevent
progressive burning [16]. The parameters are given by Length L and two diameters of
the grain.
Figure 4.2: Internal burning tube grain
4.2.4 Star Grain
Star grain is a radially burning grain cylindrical type of grain with specific geometric
properties. There are more independent geometric variables are used to define
characterization of the star grain compared to other types of grain. These independent
variables can be defined as: D out , r1, r2, 𝟂, ζ, N. Since variety of parameters are used to
define star grain, design of the star grains are more appealing to designers due to
flexibility. To satisfy flight conditions many parameters can be changed repetitively and
can be tested with internal ballistic analysis. Therefore, many significant space missions
are applied with star grain, as seen in the table below [17,18,19]
19
Table 4.2: The star grains used in SPRMs
Name of the SPRM Type of the grain used
Ariane 5 P-230 15 numbered star grain
Space Shuttle 11 numbered star grain
The Advanced Star grain
VEGA P80 12 numbered star grain
As it can be observed from the figure above star grain is used for some space
applications. Star grain is selected for these missions to satisfy thrust and pressure curve
conditions.
4.2.5 Grain Design Comparisons
Since grain design is very crucial for performance of the rocket motor, two type of grain
designs are compared for the same rocket motor. The grain length kept same for the
same rocket motor and the motor is tested with both star grain and internal-end burning
grain. In addition, same propellant is used for internal ballistic results.
Table 4.3: Properties of NGR-A propelant [20]
NGR-A Double Base Propellant
Density(kg/m^3) 1600
Specific heat J(kg K) 1450
Temperature of combustion(K) 2351
Gas constant (J/(kgK) 344
Thermal conductivity (W/mK) 0.1853
The molar mass (g/mol) 24.18
RM-3 rocket motor is used for the analysis which have diameter of nozzle throat 29.4
mm and 12.87 of nozzle expansion ratio. Also the grain drawings are obtained by using
CATIA which are shown below:
20
Figure 4.3: The design of 5 numbered star grain for RM-3 motor
Figure 4.4: The design internal end burning grain for RM-3 motor
İnternal ballistic results of the star grain rocket motor is given below:
21
Figure 4.5: 5 numbered star grain pressure and thrust curve[20]
From this experimental analysis some internal ballistic parameters are obtained which
are given below:
Table 2.4: Internal ballistic parameters of 5 numbered star grain[21]
P average Specific Impulse Burning Time
12.26 MPa 258.06 sec 1.47 sec
To make comparison between two types of the grains, same procedure should be
applied. Despite the fact that internal-end burning grain rocket motor pressure curve is
given, there is no information about its ballistic parameters. In order to accomplish this
comparison, internal ballistic solver (openMotor) is used. Main assumptions of the
program are given below [22]:
- The combustion gasses are in ideal form.
- Combustion gas properties have constant values throughout the motor.
- Erosive burning affect is not included
- Chamber gases inertia effect could be neglected.
22
To validate the ballistic solver results, the results are compared with the curve which
is given below:
Figure 4.6: Results of Terzic et al [21]
Figure 4.7: Results of the Openmotor
23
Table 4.5: Internal ballistic parameter results of the internal end burning grain
P average Specific Impulse Burning Time
9.821 MPa 250.183 sec 1.5 s
4.2.6 Discussion of the Results and Effect on Operations
As it can be observed from the obtained results, specific impulse value is higher for the
star grain rocket motor. Since more volumetric efficiency is created in star grain more
specific impulse is obtained. In addition, average pressure values and pressure. curve
behavior should not be underestimated for both designs. It can be understood that the
star grain rocket motor starts the ignition with higher pressure value and this situation
gives better start-up pressure value which also increases the performance of the engine.
Also pressure value for the star grain rocket motor is almost constant which increases
efficiency of the motor. Furthermore, the range of possible payloads can be increased
with star grain design since more average pressure is obtained. To sum up, star grain is
more effective than internal end burning grain due to mentioned factors. Since there are
so many parameters are involved in star grain design this configuration can be improved
and better results could be obtained. However, internal end burning grain lacks from
these advantages. At the beginning of the burning, proper surface area does not exist for
the internal end burning grain and burning stars with low pressure. At final point, it rises
to very high levels and therefore flow separation occurs and performance of the rocket
decreases [23].
4.3 Design of Solid Rocket Motor For Different Kind of Operations
Until this section some of the performance factors are analyzed detailed. However other
environmental factors and mass conditions should not be underestimated. Depending on
altitude, nozzle design and force requirements change. In order to compare these
requirements, 3 type of SPRM designs are studied and analyzed some internal ballistic
parameters which has a significant affect on SPRM performance.
24
Table 4.6: Preliminary design parameters of the rockets
Type of The Rocket The Sounding
Rocket
Experimental
Rocket 1
Experimental
Rocket 2
Payload 4 kg 4 kg 700 gr
Altitude 100000 m 10000 m 700m
Throat Area the of
Nozzle
0.005453 m2 0.0028 m2 0.00025 m2
Nozzle Area Ratio 100 2.5 2.3
Chamber Pressure 4.895x106 Pa 2.5 x 106 Pa 2x106 Pa
The sounding rocket is designed for weather observations, the experimental rockets are
designed for testing of rescue system to analyze performance results. The determined
parameters are determined from similar type of missions [8,24,25]:
4.3.1 Assumptions of the Flight:
1- Drag and lift forces are neglected due to insufficient area information of the vehicles.
2- Atmospheric pressure varies depending on altitude.
3- Gravity force is constant through the flight.
4- The rockets are launched in vertical trajectory.
5- Start and stop transients are neglected.
4.3.2 Some of the obtained ballistic parameters of the rockets
By using design parameters from table 4-5, weight of the propellant, case weight,
specific impulse and force are found. The calculations are done in Matlab. For the grain
calculations simple cylinder configuration is used.
25
Table 4.7: Performance parameters of the rockets
Type of The
Rocket
The Sounding
Rocket
Experimental
Rocket 1
Experimental
Rocket 2
Force 49100N 9435N 662.5 N
Specific
impulse
290 sec 217 sec 213.85 sec
Case weight 352.66 kg 17.62 kg 0.4443 kg
Propellant
weight
11658.5kg 434.79 kg 15.49 kg
Burning rate 30.66 mm/sec 23.4 mm/sec 22.28 mm/sec
Vehicle
diameter
1.5 m 0.6 m 0.3m
Desired
operation time
60s 10s 5s
4.3.3 Analysis of Propellant Effect on Solid Rocket Motor Performance
To analyze propellant effect on solid rocket motor performance, 3 types of solid rocket
motor propellants are used. The differences of the propellants can be stated as aluminum
rate, flame temperature and amonium chlorate ingredients. The plot is obtained from
MatLAB and the calculations are done for experimental rocket 1.
Table 4.8: Properties of the tested propellants
Propellant
Type
DB DB/AP/Al DB/AP-
HMX/Al
Flame
Temperature
2550 K 3880 K 4000 K
Density 1610(kg/m3) 1800(kg/m3) 1800(kg/m3)
Metal Content 0 % 20-21 % 20 %
26
Performance results of the propellants are obtained from MATLAB which is given
below:
Figure 4.8: Performance comparison graphic of the propellants
4.3.4 Discussion of the Results and Effect on Operations
According to the results, the obtained performance parameter varies between each other.
Obtained thrust force is high for the sounding rocket since more throat area and nozzle
area are involved in the calculations. Considering the used in past sounding rockets,
generally they operate between 5-20 minutes time interval. However in this study, the
desired operation time the sounding rocket is taken as 6 minutes to 1 minute due to very
unrealistic amount of propellant requirements. Since the thrust force is high compared to
other type of sounding rockets, it is able to complete its task in given time. It is observed
that specific impulse, thrust and nozzle area ratios are higher than the experimental
rockets. Although performance of the sounding rocket is better than the experimental
rockets, it carries more propellant which increases cost of the operation. In addition,
27
since more propellant occupies more volume, the volume of the vehicle also have to be
increased which affects the material usage and cost.
As the chamber pressure increases, more thickness of steel requires to stand pressure
force. However, high combustion chamber pressure decreases the constraints of the
nozzle which provides more volume in the space vehicle. As it is mentioned in the first
chapter, thrust, specific impulse and nozzle constraints have to be determined according
to type of mission.
Also it can be understood figure 4-11, type of the propellant seriously affects
performance of the SPRM. However, there is a proportional rate between and cost and
efficiency of the propellant. Therefore, finding optimal type of the solid propellant may
results in to exceed budget limit of the project so that determination of the proper
propellant should be selected according to budget, available vehicle volume, required
thrust and specific impulse.
5. CONCLUSION
In conclusion, it is clear that changing type of the propellant and nozzle dimensions are
more effective than changing grain design. However, configuration of the nozzle and
using different type of the propellant affect many design steps for solid motors. For
instance, using highly qualified propellant impacts the budget limit. Since these motors
are produced for mostly profit making purposes, it is not a wise choice to use optimum
propellant composition. To mention nozzle configuration, increasing nozzle area and
throat area result in better specific impulse performance however, larger nozzle increases
the weight of the rocket which reduces to thrust to total weight ratio of the rocket and it
is not something desirable. Despite the fact that some grain types are very challenging to
produce, by changing only dimensions and the type of the grain specific impulse can be
increased with less changing other parameters of the motor so that is more beneficial and
practical than other performance affecting factors.
28
REFERENCES
[1] Todd, A History for the IB Diploma Paper 2 The Cold War: Superpower tensions
and rivalries. Cambridge University Press, 2015
[2] Lenoir., M. & Robillard., G. A Mathematical Model to Predict the Effects of Erosive
Burning in Solid Rocket Motor Propellant, 1957
[3] Woltosz, W.S., The Application of Numerical Optimization Techniques to Solid-
Propellant Rocket Engine Design , M.S Thesis, Auburn University,Auburn ,Alabama,
March 1977
[4] Swaminathan, V., Madhavan, N.S., A direct Random Search Technique for the
Optimization of Propellant System, Indian Instute of Science , The Journal of the
Aeronautical Society of India, Vol. 32, No 1-4
[5] Nisar K., Guozhu, L., A Hybrid Approach for Design Optimization of Wagon Wheel
Grain for SRM, AIAA 2008-4893
[6] Nisar, K., Guozhu, L., A Hybrid Optimization Approach for SRM FINOCYL Grain
Design, Chinese Journal of Aeronautics 21(2008) 481-487
[7] Ramsey, Syed . Tools of War: History of Weapons in Modern Times Alpha
Editions,2016
[8] Sutton, G., P., Biblarz, Rocket Propulsion Elements, John Wiley & Sons, 9th
edition, 2017,
[9] A. Propellant Grain And Grain Configuration - Chamber Pressure. Bedford
Astronomy Club. Retrieved from https://www.astronomyclub.xyz/chamber-
pressure/propellant-grain-and-grain-configuration.html, January 13,2021
[10] Netzer D. W., Propulsion Analysis for Tactical Solid Propellant Rocket Motors
,NASA SP -8076,1972
[11] Fry, R.S. SOLID PROPELLANT TEST MOTOR SCALING, The Johns Hopkins
University, Chemical Propulsion Information Agency, September 2001
[12] Barrere et al ,Rocket Propulsion , Elsevier Publishing Co, 1960, 829 pp
[13] C. E. Rogers,Erosive Burning Design Criteria For Solid Rocket Motor, NEVADA
AEROSPACE SCIENCE ASSOCIATES, 2002.
29
[14] Zarchan P., Editor-in-chief, Tactical Missile Propulsion , American Institute of
Aeronautics and Astronautics , Virginia I, 1996
[15] Kosanke K., Terminology of Model Rocketry , Peak of Flight, ISSUE 321,
September 2012
[16] Solid Propellant Grain Design and Internal Ballistics, NASA, SP-8076, 1972
[17] Gigou, J. Solid-propellant stage development for Ariane-5, ESA-bulletin 69 (Also
published as AIAA paper 92-156).
[18] Mitchell, R., Thomas, J., and Levinsky C. ASRM: Turning in solid performance,
Aerospace America, July 1992
[19] R. Barbera & S. Bianchi VEGA: The European Small launcher Programme; ESA
Bulletin 109, February 2002.
[20] Terzic et al Numerical simulation of internal ballistic parameters of solid
propellant rocket motors, University of Sarajevo, Faculty of Mechanical Engineering,
April 2012
[21] Terzic et al Prediction of Internal Ballistic Parameters of Solid Propellant Rocket
Motors, University of Sarajevo, , Faculty of Mechanical Engineering, January 2011
[22] R. reilleya/openMotor. GitHub. Retrieved from https://github.com/reilleya/
[23] Stein S., Benefits of the Star Grain Configuration for a Sounding Rocket, United
States Air Force Academy Department of Astronautics, CO, 80841
[24] Bilgic H., Coban S., Yapıcı A., Katı Yakıtlı Roket ALP-01 Tasarımı, Modellenmesi
ve Simülasyonu, İskenderun Technical University, Faculty of Engineering and Natural
Sciences, March 2019
[25] Bollermann et al., DESIGN, DEVELOPMENT AND FLIGHT TEST OF THE
SUPER LOKI STABLE BOOSTER ROCKET SYSTEMS, Space Data Corporation,
Phoenix, Arizona, June 1973
30
APPENDICES
APPENDIX A
31
32
APPENDIX B
%Performance calculations regarding to altitude and payload mass % k=1.25; Tx=3120 ; P2=1.958*10^3; At=0.005453; h=0:0.01:100000; P1=4.895*10^6; Px=101325; R=348; g=9.81; D=1.5; a=0.0003018; n=0.3; sigma=1.5168*10^9; roprop=1000; rocase=0.5; t=360; rosteel=8303.97;
for i=1:length(h)
P3(i)=Px*exp(-0.000012*h(i)); % altitude and pressure relation %
Nratio=((k+1)/2)^(1/(k-1))*((P2/P1)^(1/k))*sqrt((k+1)/(k-1)*(1-
(P2/P1)^((k-1)/k))); % Nozzle Area Ratio Equation %
r=a*(P1)^n; % burning rate equation %
mflow=P1*At*k*sqrt(((2/(k+1))^((k+1)/(k-1)))/(k*R*Tx));% flow rate
calculation %
Cex= sqrt((2*k)/(k-1)*R*Tx*(1-((P2/P1)^((k-1)/k)))); % Exhaust Velocity
FOrmula %
Ceff(i)= Cex + (P2-P3(i))*(At/mflow);% effective exhaust velocity %
F(i)= mflow*Ceff(i); % OBtaining thrust %
I(i)=Ceff(i)/9.81;
Fm=mean(F);
Im=mean(I);
end
It=Fm*t; % Total Impulse%
mpropellant=(It/Im)/1.02;
33
Vb=mpropellant/roprop; % Volume occupied by propellant %
b=r*t; % web thickness
% Dimesioning the case
d=(1.98*P1*D)/(2*sigma);
% Grain configuration
Do= D- 2*d-2*0.254; % outside diameter of the grain%
Di= Do- 2*b; % Inside diameter of the grain %
L=(4*Vb)/(pi*(Do^2-Di^2)); % Length of the grain %
W=d*D*L*sigma + (pi/4)*d*D^2*rosteel% Weight estimate for Case %
figure(1) plot(h,F,h,Fy,h,Fz) xlabel('Altitude(m)') ylabel('Thrust Force(N)') title ('Sounding Rocket')
legend DB DB/AP/Al DB/AP-HMX/Al
figure(2) plot(h,I,h,Iy,h,Iz) xlabel('Altitude(m)') ylabel('Specific Impulse (sec)') title ('Sounding Rocket')
legend DB DB/AP/Al DB/AP-HMX/Al
%Erosive Burning calculations for % R=279.94; % specific heat ratio % Cs= 1400 ; % specific of the solid propellant J/kg.K % a= 3*10^-5; % pre- exponent factor m/s % n=0.4; % 0.4 % Tstag= 3610; % Stagnation temperature k % pstag= 7000000 ; % stagnation pressure Mpa% Pr=0.4922; % Prandtl number % Ts=1000; % Average surface burning temperature of the propellant K % Ti=300; % Inıtial propellant temperature K % D=0.1; % hydrauli diameter of the port grain % u=1.0049* 10^-4 ; % Viscosity of combustion products Poise % ropro=1750; % density of the propellant kg/m^3% M=0.5; % Mach Number % beta=60; %B value % Cp=1975;
34
syms rdot;
gama=Cp/(Cp-R); % Gama Value%
p=pstag*(1+ ((gama-1)/2)*M^2)^(-gama/(gama-1)); % combustion pressure
value %
k= (1/(ropro*Cs))*((Tstag-Ts)/(Ts-Ti)); % Expression for the k value %
G=M*pstag*sqrt(gama/(R*Tstag))*(1+((gama-1)/2)*M^2)^((-gama-
1)/(2*(gama-1))); % MAss Flux %
rnon=a*p^(n); % burning rate with non erosive part
Fun=rdot== rnon + (0.0288*(G^(0.8))*Cp*(u^(0.2))*(Pr^(-
0.667))*k)/((D^0.2)*exp((beta*rdot*ropro)/G));% calculation of total
burning rate%
rdot=abs(solve(Fun,rdot))
rdot=double(rdot)
rero=rdot - rnon;
