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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
5.5 Dynamic pressure (N/m2) vs altitude (km) 38
5.6 Speed (km/s) vs altitude (km) 395.7 flight path angle vs time 39
5.8 Altitude (km) vs downrange distance (km) 40
5.9 Dynamic pressure (N/m2) vs altitude (km) 42
5.10 Speed (km/s) vs altitude (km) 43
5.11 flight path angle vs time 43
5.12 Altitude (km) vs downrange distance (km) 44
5.13 Dynamic pressure (N/m2) vs altitude (km) 46
5.14 Speed (km/s) vs altitude (km) 47
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_missile8/11/2019 Completed Project Batch 3
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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)')
axis([-inf, inf, -inf, inf])
grid
figure(3)
plot(h, q)
xlabel('Altitude (km)')
ylabel('Dynamic pressure (N/m^2)')
axis([-inf, inf, -inf, inf])
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
Initial flight path angle = 90 deg
Pitchover altitude = 40 km
Burn time = 320 s
Final speed = 0.008883924 km/s
Final flight path angle = 71.0206 deg
Altitude = 0.130008 km
Downrange distance = 233.538 km
Drag loss = 0.521362 km/s
Gravity loss = 0.520493 km/s
8/11/2019 Completed Project Batch 3
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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
Initial flight path angle = 90 deg
Pitchover altitude = 40 km
Burn time = 326.667 s
Final speed = 0.00877826 km/s
Final flight path angle = 70.7761 deg
Altitude = 0.130008 km
Downrange distance = 238.538 km
Drag loss = 9.83247 km/s
Gravity loss = 0.520497 km/s
8/11/2019 Completed Project Batch 3
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Calculated outputs
Output for specific impulse 490 sec
Figure 5.9 Dynamic pressure (N/m2) vs Altitude (km)
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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
Initial flight path angle = 90 deg
Pitchover altitude = 40 km
Burn time = 333.333 s
Final speed = 0.00869341 km/s
Final flight path angle = 71.0581 deg
Altitude = 0.1300021 km
Downrange distance = 238.538 km
Drag loss = 0.519662 km/s
Gravity loss = 0.519662 km/s
8/11/2019 Completed Project Batch 3
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Calculated outputs
Output for specific impulse 500 sec
Figure 5.13 Dynamic pressure (N/m2) vs Altitude (km)
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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
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