completed project batch 3

8/11/2019 Completed Project Batch 3

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OPTIMIZATION OF THE 3RD

STAGE OF A SPACE LAUNCHER

POWERED BY A CDW ROCKET ENGINE

A PROJECT REPORT

Submitted by

GURUBARAN.B 09UEAR0021

MANSOOR ALI.A 09UEAR0035

NANDHINI.R 09UEAR0045

RAGUNATHAN.R 09UEAR0052

I n partial ful fi llment for the award of the degree

of

BACHELOR OF TECHNOLOGY

IN

AERONAUTICAL ENGINEERING

VEL TECH TECHNICAL UNIVERSITY

AVADI

CHENNAI


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CERTIFICATE FOR EVALUATION

College Name: VELTECH Dr. RR & Dr. SR TECHNICAL UNIVERSITY

Branch : AERONAUTICAL ENGG.

Semester : VIII

The reports of the project work submitted by the above students in partial

fulfillment for the award of Bachelor of Engineering degree in Aeronautical

Engineering of Vel Tech Dr. RR and Dr. SR Technical University were

evaluated and confirmed to be the reports of the work done by the above

students and then evaluated.

INTERNAL EXAMINER EXTERNAL EXAMINER

S.NO Register No. Name of the

Students who

have done the

project

Title of the project Name of the

Supervisor with

Designation

1. 09UEAR0052 R.RAGUNATHANOPTIMIZATION OF

THE 3RD STAGE OF A

SPACE LAUNCHER

POWERED BY A CDW

ROCKET ENGINE

Mr.S.SIVARAJ

Asst.Prof,

Dept. of

Aeronautical

Engineering

2. 09UEAR0045 R.NANDHINI

3. 09UEAR0021 B.GURUBARAN

4. 09UEAR0035 A.MANSOOR ALI


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ACKNOWLEDGEMENT

This project, though done by myself would not have been possible,

without the support of various people, who by their cooperation have helped usin bringing out this project successfully.

We are grateful to our Chancellor, Col. Dr. R. Rangarajan B.E (Elec),

B.E(Mech), MS (Auto) for his patronage towards our project.

We thank our Vice Chancellor, Dr. R. P. Bajpai Ph.D (IIT)., D.Sc

(Hokkaido,Japan)., FIETE, who had always served as an inspiration for us to

perform well. We would like to express our faithful thanks to Mr. Francois

Falempin, Head- Advanced powered Airframe, MBDA, France who has

supported us for carrying out the project.We would also like to thank Dr. P.

Mathiyalagan, Dean, School of Mechanical Engineering and the Head of the

department, Mr. G. Boopathy M.E., for having extended all the department

facilities without slightest hesitation.

We would like to express our unbounded gratefulness to our supervisor

Mr. S. Sivaraj, M.E, and rest of who has directly or indirectlyhelped in my

project work for his extremely valuable guidance and encouragement

throughout the project.

We thank all faculty members and supporting staff for the help they extended to

us for the completion of this project.


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ABSTRACT

This project aims at designing of the trajectory for third stage of launch

vehicle using continuous detonation wave engine (CDWE) and also to optimize

the trajectory with different mixture ratios. The trajectory is designed and

simulated with the commercial software MATLAB and optimization is carried

out by varying the specific impulse of a particular mixture ratio with constant

injection pressure. The optimized trajectory of the CDWE has been compared

with the liquid rocket engines trajectory with the specified specific impulse,

thrust and mixture ratio.


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TABLE OF CONTENTS

CHAPTER NO TITTLE PAGE NO

ABSTRACT iii

LIST OF FIGURES vii

LIST OF TABLES viiiNOMENCLATURE ix

COMPANY PROFILE 1

1. INTRODUCTION 12

1.1Detonation Engines 12

1.2Detonation Wave Engines Technology 12

1.3Types of Detonation Engine 14

1.4 Plan of Work 15

2. LITERATURE SURVEY 16

2.1 Literature review 16

3. TRAJECTORY DESIGN 19

3.1 Introduction to Trajectory 19

3.2 Types of Trajectory 20

3.3 Gravity turn Trajectory 203.4 Trajectory Optimization 21

3.5 Numerical solutions for optimizing trajectory 22

3.5.1 Computational algorithm

4. MODELLING AND SIMULATION

4.1 Introduction to MATLAB 23

4.2 Getting started to MATLAB 24

4.3 Generation of CODES 25

5. RESULTS AND DISCUSSION 33

5.1 Constant Mixture Ratio and Varying Specific Impulse

5.1.1 Graphical Evaluation 33

i. For Specific Impulse 470 33

ii. For Specific Impulse 480 37

iii. For Specific Impulse 490 41

iv. For Specific Impulse 500 45

References 49


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LIST OF FIGURES

Figure No TITLE Page No

3.1 Trajectory 18

3.2 Gravity Turn trajectory 19

4.1 Matlab Image 24

5.1 Dynamic pressure (N/m2) vs altitude (km) 34

5.2 Speed (km/s) vs altitude (km) 35

5.3 flight path angle vs time 35

5.4 Altitude (km) vs downrange distance (km) 36


5.6 Speed (km/s) vs altitude (km) 395.7 flight path angle vs time 39




5.11 flight path angle vs time 43




5.15 flight path angle vs time 475.16 Altitude (km) vs downrange distance (km) 48


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NOMENCLATURE

0 - Kink Angle

y0 - Initial Altitude (Zero)

y - Altitude

x0 - Initial Downrange distance (Zero)

x - Downrange distance

t0 - Burn out Time

v0 - Initial Velocity

n - Mass ratio


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COMPANY PROFILE

MBDA Missile System France

About:

MBDA, a world leader in missiles and missile systems, is a multi-national

group with 10,000 employees on industrial facilities in France, the United

Kingdom, Italy, Germany and the United States. MBDA has three major

aeronautical and defence shareholders - BAE Systems (37.5%), EADS (37.5%)

and Finmeccanica (25%), and is the first truly integrated European defence

company. In 2012, the Group recorded a turnover of 3 billion euros, produced

about 3,000 missiles and achieved an order book of 9.8 billion euros, new

orders came to 2.3 billion euros. MBDA works with over 90 armed forces

worldwide.

MBDA was created in December 2001, after the merger of the main missile

producers in France, Italy and Great Britain. Each of these companies

contributed the experience gained from fifty years of technological and

operational success. The restructuring of the industry in Europe was completed

with the acquisition of the German subsidiary EADS/LFK in March 2006. This

further enriched MBDAs range of technologies and products, consolidating the

Groups world-leading position in the industry.


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MBDA is the only Group capable of designing and producing missiles and

missile systems to meet the whole range of current and future operational

requirements for the three armed forces (army, navy, air force). Overall, the

Group offers a range of 45 products in service and another 15 in development.

MBDA has demonstrated its ability to bring together the best skills across the

whole of Europe, and has succeeded in becoming the prime contractor for a

series of strategic multi-national programmes. These include the six-nation

Meteor air superiority weapon, the Franco-British conventionally armed cruise

missile, Storm Shadow/SCALP, and a family of air defence systems based on

the Aster missile for France and Italy (for ground and naval based air defence)

and for the UK (naval air defence for the Royal Navys Type 45 destroyers).

Other programmes such as MEADS further serve to position MBDA at the heart

of the European defence sector as well as establishing cooperative transatlantic

links with the principal groups in the US defence industry.

In parallel to these large cooperative programmes, MBDAs name is inseparable

from a number of systems which have strengthened its reputation as an

unrivalled leader. The MILAN anti-armour weapon has been supplied to over

40 countries in the world and the Exocet anti-ship missile, in its surface,

submarine and air-launched variants, represents the main naval superiority

weapon of navies throughout the world.


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The mastery of cutting-edge technologies is not only an advantage for MBDA

in successfully developing and producing new products. It is also a means of

guaranteeing customers that innovations can be made to existing products

during their life span in order to meet constantly changing specifications arising

from increasingly complex engagement scenarios. It is precisely this

combination which makes MBDA the defence sector partner of choice in many

countries around the world

Innovative future systems of MBDA

CVS301 VIGILUS- Revolutionary Weapon System Design for Unmanned Air

Systems

CVS401 PERSEUS - A visionary naval and land attack weapon system

CVS101 SYSTEM CONCEPT - Infantry Weapon System for 2030 and Beyond

Laser Weapons


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Chapter 1

Continuous Wave Detonation Engine

1. Introduction

As the propulsion system is a key sub-system for missiles, MBDA France

(and its former components) has always been leading a lot of effort to develop

the related technologies (generally with specialized partners) and to master their

optimum integration into its missile products. This approach is particularly

developed for the ramjet technology since the fifties but, today, a new field is

also explored with a renewed interest for the detonation wave engines.

1.1 Detonation wave engines technology

Due to its thermodynamic cycle, a detonation wave engine has theoretically a

higher performance than a classical propulsion concept using the combustion

process. Nevertheless, it still has to be proven that this advantage is not

compensated by the difficulties which could be encountered to practically

define a real engine and to implement it in an operational flying system.

During past years, MBDA France performed some theoretical and experimental

works on Pulsed Detonation Engine (PDE), mainly in cooperation with LCD

laboratory at ENSMA Poitiers. These studies aimed at obtaining a preliminary

demonstration of the feasibility of the PDE in both rocket and airbreathing

modes and at verifying the interest of such a PDE for operational application.

Further studies are still in progress with CIAM and Semenov Institute in

Moscow. On this basis, several engine concepts have been studied and


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evaluated at preliminary design level, for both space launcher and missile

application. Today, the effort is focused on the development of a small caliber

airbreathing engine able to power a UAV with very demanding requirements in

terms of thrust range.

The use of a Continuous Detonation Wave Engine (CDWE) can also be

considered to reduce the environmental conditions generated by PDE while

reducing the importance of initiation issue and simplifying some integration

aspects. As it was done for PDE, MBDA France is leading a specific R&T

program, including basic studies led with the Lavrentiev Institute of

Novosibirsk, to assess some key points for the feasibility of an operational

rocket CDWE for space launcher.

But, continuous detonation wave can have also other application for turbojets

and for ramjets. In order to address all these possible applications, a ground

demonstrator has been designed and should be developed and tested within thenext years within the framework of the National Research & Technology Center

(CNRT) Propulsion for Future located in Orleans/Bourges region.

The main feature of a CDWE is an annular combustion chamber closed on one

side (and where the fuel injection takes place) and opened at the other end.

Inside this chamber, one or more detonation waves propagate normally to thedirection of injection. The flow inside this chamber is very heterogeneous, with

a 2D expansion fan behind the leading shock. The transverse detonation wave

propagates in a small layer of fresh mixture near the injection wall. The

necessary condition for the propagation of a detonation wave is the continuous

renewal of the layer of combustible mixture. The height of this layer h must be

not less than the critical value. In the case of a LH2 / LO2 engine, the dispersion


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of liquid oxygen droplets and the quick mixing of the components should be

fast enough to decrease the value of and to enable the realisation of in small

chambers.

The first application for CDWE is the rocket mode (CDWRE) for which

continuous detonation process can lead to a compact and very efficient system

enabling lower feeding pressure and thrust vectoring with very attracting

integration capability for axi-symmetrical vehicles. But, the CDWE could also

be applied to simplified ramjet engine with short ram-combustor and possible

operating from Mach 0+ without integral booster or to Turbojet with improved

performances or simplified compression system (lower compression ratio

required).

1.3 Types of detonation engine:

1.Standing detonation engine

2.Rotating detonation engine3.Pulse detonation engine


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1.4. Plan of work:

Understanding the problem

Literature review

Generating the codes for the equations Involved.

Trajectory design

Optimizing the trajectory

Comparison of the trajectory with the given liquid rocket

engine.


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CHAPTER 2

LITERATURE SURVEY

2.1 Literature Review

Detonation engines,Piotr Wolanski,This paper survey of jet engines based on

detonation combustion

Testing of a Continuous Detonation Wave Engine with Swirled Injection,

Eric M. Braun Nathan L. Dunn, and Frank K. Lu, The understanding of

transition in hypersonic flows is of great importance since it can help in

designing more efficient vehicles

Trajectory Optimization for Target Localization, Sameera S. Ponda

A simplified ascent trajectory optimization procedure has been developed with

application of Ares I launch vehicle

Orbit selection and ekv guidance for spacebased ICBM intercept,

Ahmet Tarik Aydin, Boost-phase intercept of a threat intercontinental ballistic

missile (ICBM) is the first layer of a multi-layer defense

A guide to MATLAB, Brian R. Hunt Ronald L. Lipsman Jonathan M.

Rosenberg

Focused introduction to MATLAB, a comprehensive software system for

mathematics and technical computing.

Practical MATLAB basics for engineers,Misza Kalechman

Introductory book of the basic mathematical concepts and principles, using the

MATLAB. Language to illustrate and evaluate numerical expressions and data

visualization of large classes of functions and problems, written for beginners

with no previous knowledge of MATLAB.


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CHAPTER 3

TRAJECTORY DESIGN

3.1 Introduction to trajectory

A trajectoryis the path that a moving object follows through space as a

function of time. The object might be a projectile or a satellite, for example. It

thus includes the meaning of orbitthe path of a planet, an asteroid or a comet

as it travels around a central mass. A trajectory can be described mathematically

either by the geometry of the path, or as the position of the

object over time.

Figure 3.1 Trajectory

3.2 Types of trajectory:

Inclined trajectory

Vertical trajectory

Gravity turn trajectory


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3.3 Gravity turn trajectory

A gravity turnor zero-lift turnis a maneuver used in launching a

spacecraft into, or descending. It is a trajectory optimization that uses gravity to

steer the vehicle onto its desired trajectory. It offers two main advantages over a

trajectory controlled solely through vehicle's own thrust. The term gravity turn

can also refer to the use of a planet's gravity to change a spacecraft's direction in

other situations than entering or leaving the orbit.

y0distance up to which the trajectory is vertical.

0kick angle

Figure .3.2 Gravity turn trajectory

Assuming zero aerodynamic drag and constant gravity field g, we can write the

force equations.


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Let,

F /mg = n over short increment of the flight path. It could be shown that

the solution for gravity turn trajectory when n is constant is represented by the

following three equations.

The constant C can be evaluated from the initial conditions that at z = z0, v0= v to get:

To apply Equations (3) (4) and (5) for a varying F /mg, the following algorithm

is devoted.

3.4 Trajectory Optimization

Trajectory optimizationis the process of designing a trajectory that

minimizes or maximizes some measure of performance within prescribed

constraint boundaries. While not exactly the same, the goal of solving a

trajectory optimization problem is essentially the same as solving an optimal

control problem.


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The selection of flight profiles that yield the greatest performance plays a

substantial role in the preliminary design of flight vehicles, since the use of ad-

hoc profile or control policies to evaluate competing configurations may

inappropriately penalize the performance of one configuration over another.

Thus, to guarantee the selection of the best vehicle design, it is important to

optimize the profile and control policy for each configuration early in the design

process.

Consider this example. Fortactical missiles, the flight profiles are determined

by the thrust andload factor (lift) histories. These histories can be controlled by

a number of means including such techniques as using anangle of

attack command history or an altitude/downrange schedule that the missile must

follow. Each combination of missile design factors, desired missile

performance, and system constraints results in a new set of optimal control

parameters.

3.5Numerical solutions for optimizing trajectory

3.5.1 Computational algorithm

Purpose:To compute the coordinates (x ,y) and the tangential velocity v

of space vehicle along gravity turn path with varying F /mg ratio

Inputs : t0,,0, v0, x0, y0, n

Computational steps :
http://en.wikipedia.org/wiki/Tactical_missilehttp://en.wikipedia.org/wiki/Load_factor_(aeronautics)http://en.wikipedia.org/wiki/Angle_of_attackhttp://en.wikipedia.org/wiki/Angle_of_attackhttp://en.wikipedia.org/wiki/Angle_of_attackhttp://en.wikipedia.org/wiki/Angle_of_attackhttp://en.wikipedia.org/wiki/Load_factor_(aeronautics)http://en.wikipedia.org/wiki/Tactical_missile


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CHAPTER 4

MODELLING AND SIMULATION

4.1 Introduction to MATLAB

MATLABis a high-level language and interactive environment for

numerical computation, visualization, and programming. Using MATLAB, you

can analyze data, develop algorithms, and create models and applications. The

language, tools, and built-in math functions enable you to explore multiple

approaches and reach a solution faster than with spreadsheets or traditional

programming languages.

MATLAB used for a range of applications, including signal processing and

communications, image and video processing, control systems, test and

measurement, computational finance, and computational biology. More than a

million engineers and scientists in industry and academia use MATLAB, the

language of technical computing.


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4.2 Getting started to MATLAB R2012b (v 8.00783):

Figure 4.1 Mat Lab image


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4.3. Generation of the code for the trajectory

Codes for Trajectory

clear all;close all;clc

deg = pi/180; % ...Convert degrees to radians

g0 = 9.81; % ...Sea-level acceleration of gravity (m/s)

Re = 6378e3; % ...Radius of the earth (m)

hscale = 7.5e3; % ...Density scale height (m)

rho0 = 1.225; % ...Sea level density of atmosphere(kg/m^3

diam = 196.85/12.*0.3048; % ...Vehicle diameter (m)

A = pi/4*(diam)^2; % ...Frontal area (m^2)

CD = 0.5; % ...Drag coefficient (assumed constant)

m0 = 16000; % ...Lift-off mass (kg)

n = 32; % ...Mass ratio

T2W = 1.01; % ...Thrust to weight ratio

Isp = 470; % ...Specific impulse (s)

mfinal = m0/n; % ...Burnout mass (kg)

Thrust = T2W*m0*g0; % ...Rocket thrust (N)

m_dot = Thrust/Isp/g0; % ...Propellant mass flow rate (kg/s)

mprop = m0 - mfinal; % ...Propellant mass (kg)

tburn = mprop/m_dot; % ...Burn time (s)

hturn = 130; % ...Height at which pitchover begins (m)

t0 = 0; % ...Initial time for the numerical integration

tf = tburn; % ...Final time for the numerical integration


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tspan = [t0,tf]; % ...Range of integration

% ...Initial conditions:

v0 = 1000; % ...Initial velocity (m/s)

gamma0 = 89.95*deg; % ...Initial flight path angle (rad)

x0 = 0; % ...Initial downrange distance (km)

h0 = 40; % ...Initial altitude (km)

vD0 = 0; % ...Initial value of velocity loss due

% to drag (m/s)

vG0 = 0; % ...Initial value of velocity loss due

%.....to gravity (m/s)

%...Initial conditions vector:

f0 = [v0; gamma0; x0; h0; vD0; vG0];

%...Call to Runge-Kutta numerical integrator 'rkf45'

% rkf45 solves the system of equations df/dt = f(t):

[t,f] = ode45('rates', tspan, f0);

%...t is the vector of times at which the solution is evaluated

%...f is the solution vector f(t)

%...rates is the embedded function containing the df/dt's

% ...Solution f(t) returned on the time interval [t0 tf]:

v = f(:,1)*1.e-3; % ...Velocity (km/s)

gamma = f(:,2)/deg; % ...Flight path angle (degrees)

x = f(:,3)*1.e-3; % ...Downrange distance (km)

h = f(:,4)*1.e-3; % ...Altitude (km)

vD = -f(:,5)*1.e-3; % ...Velocity loss due to drag (km/s)


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vG = -f(:,6)*1.e-3; % ...Velocity loss due to gravity (km/s)

for i = 1:length(t)

Rho = rho0 * exp(-h(i)*1000/hscale); %...Air density

q(i) = 1/2*Rho*v(i)^2; %...Dynamic pressure

end

%~~~~~~~~~~~~~~

fprintf('\n\n -----------------------------------\n')

fprintf('\n Initial flight path angle = %10g deg ',gamma0/deg)

fprintf('\n Pitchover altitude = %10g m ',hturn)

fprintf('\n Burn time = %10g s ',tburn)

fprintf('\n Final speed = %10g km/s',v(end))

fprintf('\n Final flight path angle = %10g deg ',gamma(end))

fprintf('\n Altitude = %10g km ',h(end))

fprintf('\n Downrange distance = %10g km ',x(end))

fprintf('\n Drag loss = %10g km/s',vD(end))

fprintf('\n Gravity loss = %10g km/s',vG(end))

fprintf('\n\n -----------------------------------\n')

figure(1)

plot(x, h)

axis equal

xlabel('Downrange Distance (km)')

ylabel('Altitude (km)')

axis([-inf, inf, 0, inf])

grid


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figure(2)

subplot(2,1,1)

plot(h, v)

xlabel('Altitude (km)')

ylabel('Speed (km/s)')

axis([-inf, inf, -inf, inf])

grid

subplot(2,1,2)

plot(t, gamma)

xlabel('Time (s)')

ylabel('Flight path angle (deg)')


grid

figure(3)

plot(h, q)

xlabel('Altitude (km)')

ylabel('Dynamic pressure (N/m^2)')


grid


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return

%~~~~~~~~~~~~~

function dydt = rates(t,y)

deg = pi/180; % ...Convert degrees to radians

g0 = 9.81; % ...Sea-level acceleration of gravity (m/s)

Re = 6378e3; % ...Radius of the earth (m)

hscale = 7.5e3; % ...Density scale height (m)

rho0 = 1.225; % ...Sea level density of atmosphere (kg/m^3)

diam = 196.85/12.*0.3048; % ...Vehicle diameter (m)

A = pi/4*(diam)^2; % ...Frontal area (m^2)

CD = 0.5; % ...Drag coefficient (assumed constant)

m0 = 16000; % ...Lift-off mass (kg)

n = 32; % ...Mass ratio

T2W = 1.01; % ...Thrust to weight ratio

Isp = 470; % ...Specific impulse (s)

mfinal = m0/n; % ...Burnout mass (kg)

Thrust = T2W*m0*g0; % ...Rocket thrust (N)

m_dot = Thrust/Isp/g0; % ...Propellant mass flow rate (kg/s)

mprop = m0 - mfinal; % ...Propellant mass (kg)

tburn = mprop/m_dot; % ...Burn time (s)

hturn =130; % ...Height at which pitchover begins (m)

t0 = 0; % ...Initial time for the numerical

integration

tf = tburn; % ...Final time for the numerical integration


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tspan = [t0,tf]; % ...Range of integration

% ...Initial conditions:

v0 = 1000; % ...Initial velocity (m/s)

gamma0 = 60*deg; % ...Initial flight path angle (rad)

x0 = 0; % ...Initial downrange distance (km)

h0 = 40; % ...Initial altitude (km)

vD0 = 0; % ...Initial value of velocity loss

due

% to drag (m/s)

vG0 = 0; % ...Initial value of velocity loss

due

%~~~~~~~~~~~~~~~~~~~~~~~~~

% Calculates the time rates df/dt of the variables f(t)

% in the equations of motion of a gravity turn trajectory.

%-------------------------

%...Initialize dfdt as a column vector:

dfdt = zeros(6,1);

v = y(1); % ...Velocity

gamma = y(2); % ...Flight path angle

x = y(3); % ...Downrange distance

h = y(4); % ...Altitude

vD = y(5); % ...Velocity loss due to drag

vG = y(6); % ...Velocity loss due to

gravity


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%...When time t exceeds the burn time, set the thrust

% and the mass flow rate equal to zero:

if t < tburn

m = m0 - m_dot*t; % ...Curent vehicle mass

T = Thrust; % ...Current thrust

Else

m = m0 - m_dot*tburn; % ...Current vehicle mass

T = 0; % ...Current thrust

end

g = g0/(1 + h/Re)^2; % ...Gravitational variation

% with altitude h

rho = rho0 * exp(-h/hscale); % ...Exponential density variation

% with altitude

D = 1/2 * rho*v^2 * A * CD; % ...Drag [Equation 11.1]

%...Define the first derivatives of v, gamma, x, h, vD and vG

% ("dot" means time derivative):

%v_dot = T/m - D/m - g*sin(gamma); % ...Equation 11.6

%...Start the gravity turn when h = hturn:

if h


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vG_dot = -g;

else

v_dot = T/m - D/m - g*sin(gamma);

gamma_dot = -1/v*(g - v^2/(Re + h))*cos(gamma); % ...Equation 11.7

x_dot = Re/(Re + h)*v*cos(gamma); % ...Equation 11.8(1)

h_dot = v*sin(gamma); % ...Equation 11.8(2)

vG_dot = -g*sin(gamma); % ...Gravity loss rate

end

vD_dot = -D/m; % ...Drag loss rate

%...Load the first derivatives of f (t) into the vector dfdt:

dydt(1) = v_dot;

dydt(2) = gamma_dot;

dydt(3) = x_dot;

dydt(4) = h_dot;

dydt(5) = vD_dot;

dydt(6) = vG_dot;

dydt=dydt';

End


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CHAPTER 5

RESULTS AND DISCUSSION

5.1 constant mixture ratio and varying specific impulse

The trajectory has been designedbyvarying the specific impulse ofa particular mixture ratio with constant injection pressure

5.1.1Graphical evaluation

The graphical evaluation shows the vales for specific impulse for 470 sec

I. Graphical values

Initial flight path angle = 90 deg

Pitchover altitude = 40 km

Burn time = 313.333 s

Final speed = 0.00869341 km/s

Final flight path angle = 71.1157 deg

Altitude = 0.1300021 km

Downrange distance = 238.538 km

Drag loss = 0.519662 km/s

Gravity loss = 0.519662 km/s


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Calculated outputs

Outputs for specific impulse 470 sec

Figure 5.1 Dynamic pressure (N/m2) vs altitude (km)


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Flightpath angle (deg) vs Time (sec)

Figure 5.2 Speed (km/s) vs altitude (km)

Figure 5.3 flight path angle vs time


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Figure 5.4 Altitude (km) vs downrange distance (km)


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Variation of specific impulse

With variation with specific impulse we get a trajectory for each change and

outputs for the values.

II. Graphical values



Burn time = 320 s








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Calculated outputs

Output for specific impulse 480 sec

Figure 5.5 Dynamic pressure (N/m2) vs Altitude (km)


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Figure 5.6 Speed (km/sec) vs Altitude (km)

Figure 5.7 Flight path angle (deg) vs Time (sec)

Altitude (km) vs downrange distance (km)


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Figure 5.8Altitude (km) vs downrange distance (km)


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Variation of specific impulse

With variation with specific impulse we get a trajectory for each change and

outputs for the values.

III. Graphical values











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Calculated outputs




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Figure 5.10 Speed (km/sec) vs Altitude (km)

figure 5.11 Flight path angle (deg) vs Time (sec)


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Figure 5.12 Altitude (km) vs downrange distance (km)


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IV.Graphical values











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Calculated outputs




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figure 5.14 Speed (km/sec) vs Altitude (km)

Figure 5.15 Flight path angle (deg) vs Time (sec)


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Figure 5.16 Altitude (km) vs downrange Distance (km)


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List of references

1. Ascent, stage separation and glideback performance of a partially

reusable small launch vehicle, Bandu N. Pamadi, Paul V. Tartabini and

Brett R. Starr Vehicle Analysis Branch

2. Computational algorithm for gravity turn maneuver By M. A. Sharaf &

L.A.Alaqal

3. Development of trajectory simulation capabilities for the planetary entrysystems synthesis tool By Devin Matthew Kipp

4. Orbit selection and ekv guidance for spacebased ICBM intercept By

Ahmet Tarik Aydin

5. Programming with M-Files: A Rocket Trajectory Analysis Using ForLoops By Darryl Morrell

6. Sounding Rocket Technology Demonstration for Small Satellite Launch

Vehicle Project. By John Tsohas, Lloyd J. Droppers, Stephen D. Heister

Purdue University West Lafayette

7. Rapid Trajectory Optimization for the ARES I Launch Vehicle

By Greg A. Dukeman

8. Graphics and GUIs withMATLABT H I R D E D I T I O N

By Patrick marchand

completed project batch 3

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