DESIGN TOOL DEVELOPMENT FOR LIQUID PROPELLANT MISSILE SYSTEMS
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
_________________________________
David Baker Riddle
Certificate of Approval:
_________________________ ________________________
John E. Burkhalter Roy J. Hartfield, Chair
Professor Emeritus Associate Professor
Aerospace Engineering Aerospace Engineering
_________________________ ________________________
Christopher J. Roy George T. Flowers
Assistant Professor Interim Dean
Aerospace Engineering Graduate School
DESIGN TOOL DEVELOPMENT FOR LIQUID PROPELLANT MISSILE SYSTEMS
David Baker Riddle
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
May 10, 2007
iii
DESIGN TOOL DEVELOPMENT FOR LIQUID PROPELLANT MISSILE SYSTEMS
David Baker Riddle
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon the request of individuals or institutions and at their expense. The author reserves
all publication rights.
________________________
Signature of Author
________________________
Date of Graduation
iv
VITA
David Baker Riddle was born on September 25, 1981 in Anniston, Alabama to
William and Genie Riddle. His family moved to Madison, Alabama in 1992 where his
father began working on Redstone Arsenal as a civil engineer. After graduating from
Bob Jones High School in 2000, David followed in the footsteps of both parents and
began attending classes at Auburn University. In addition to being a full-time student, he
was also an active member of the university?s varsity track and cross-country teams.
David graduated Summa Cum Laude in December 2004 with a Bachelor of Aerospace
Engineering degree and began graduate studies in Aerospace Engineering at Auburn
University the following semester.
v
THESIS ABSTRACT
DESIGN TOOL DEVELOPMENT FOR LIQUID PROPELLANT MISSILE SYSTEMS
David Baker Riddle
Master of Science, May 10, 2007
(B.A.E., Auburn University, 2004)
89 Typed Pages
Directed by Roy J. Hartfield
The use of computer programs driven by genetic algorithms (GA?s) has become
an increasingly popular method of optimizing engineering designs. This thesis focuses
on the modeling and optimization of liquid rocket engine propelled missiles with an
emphasis on some recent upgrades to an existing suite of codes. The program is
comprised of a series of legacy codes which simulate the performance of liquid rockets
and are controlled by a GA. This program is designed so that it can be used to reverse
engineer missile designs for which some limited initial data is known. It can also be used
to optimize liquid propelled missiles in the more traditional design mode.
Several upgrades were made to the existing code to expand its capabilities and
add to the robustness of the program. A new version of the code has been developed
in which aerodynamic prediction duties are handled by Missile Datcom instead of the
Aerodsn routine used in previous versions. Plots from runs using the two different
vi
aerodynamic codes are presented and their differences discussed. Furthermore, the
program now has the ability to handle a varying specific impulse (I
sp
), and a jet vane
control system model has been added. The previous version of the liquid missile GA
code assumed that I
sp
was constant for a given fuel type. The modification described in
this thesis gives the GA the ability to choose an equivalence ratio which determines the
I
sp
. In addition to the aerodynamic control system already in place, the ability to simulate
a missile controlled by jet vanes has been added to the program. The new control system
and accompanying optimization results are examined in detail.
vii
ACKNOWLEDGEMENTS
The author would like to thank Dr. Roy Hartfield and Dr. John Burkhalter for
their direction and assistance with this thesis; without their support this project would not
have been possible. He would also like to thank the authors of the legacy codes that
served as a basis for this research including Dr. John Burkhalter, Dr. Rhonald Jenkins,
and Dr. Murray Anderson. Finally, the author wishes to thank his family and friends for
all of their encouragement, love, and support.
viii
Style manual or journal used
The American Institute of Aeronautics and Astronautics Journal
Computer software used
IMPROVE 3.1 Genetic Algorithm, General Purpose 6-DOF Simulation, Compaq Visual
Fortran, WinDiff, TecPlot, Microsoft Excel, Microsoft Word
ix
TABLE OF CONTENTS
LIST OF TABLES............................................................................................................ x
LIST OF FIGURES .........................................................................................................xi
NOMENCLATURE .......................................................................................................xii
1. INTRODUCTION ..................................................................................................... 1
2. BACKGROUND AND THEORETICAL DEVELOPMENT .................................. 5
2.1 Genetic Algorithm ............................................................................................. 5
2.2 Aerodynamics .................................................................................................... 9
2.2.1 Aerodsn..................................................................................................... 9
2.2.2 Missile Datcom ......................................................................................... 9
2.3 Mass Properties................................................................................................ 12
2.4 Six Degree-of-Freedom Model........................................................................ 13
2.5 Liquid Propulsion System................................................................................ 14
2.5.1 Background............................................................................................. 14
2.5.2 Variable Specific Impulse....................................................................... 15
2.6 Guidance System and Autopilot ...................................................................... 18
2.7 Jet Vane Control System.................................................................................. 19
2.7.1 Motivation............................................................................................... 20
2.7.2 Theory..................................................................................................... 21
2.7.3 Assumptions............................................................................................ 24
2.7.4 Methodology........................................................................................... 24
2.7.5 Verification ............................................................................................. 27
3. RESULTS................................................................................................................ 30
3.1 Model Validation ............................................................................................. 30
3.2 Unguided Results............................................................................................. 33
3.3 Aerodynamic Guided Results .......................................................................... 44
3.4 Vane Control Guided Results .......................................................................... 49
4. CONCLUSIONS AND RECOMMENDATIONS.................................................. 63
REFERENCES ............................................................................................................... 65
APPENDIX A: GA Input File ........................................................................................ 69
APPENDIX B: Global Array Variables ......................................................................... 70
x
LIST OF TABLES
Table 1: GA design variables............................................................................................ 8
Table 2: Components considered in the mass properties routine ................................... 13
Table 3: Variable specific impulse propellant combinations.......................................... 16
Table 4: LOX/H2 data table............................................................................................ 18
Table 5: Pressure coefficient depending on region (modified from Ref. 32) ................. 23
Table 6: Missile configuration and performance data (from Ref. 17) ............................ 31
Table 7: List of GA variables for SCUD-B comparison................................................. 32
Table 8: Model validation for the SCUD-B.................................................................... 33
Table 9: Case setup ......................................................................................................... 35
Table 10: Case 1 GA variables ......................................................................................... 40
Table 11: Case 2 GA variables ......................................................................................... 41
Table 12: Case 3 GA variables ......................................................................................... 42
Table 13: Case 4 GA variables ......................................................................................... 43
Table 14: GA variables for Aerodsn optimized missile.................................................... 47
Table 15: GA variables for Datcom optimized missile .................................................... 48
Table 16: GA variables for optimized, unguided missile ................................................. 52
Table 17: GA variables for optimized, aerodynamically controlled missile .................... 53
Table 18: GA variables for optimized, vane controlled missile ....................................... 54
Table 19: Target data for test cases................................................................................... 58
xi
LIST OF FIGURES
Figure 1: Aerodsn and Datcom optimized missile trajectories....................................... 12
Figure 2: Earth-centered coordinate system (from Ref. 12) ........................................... 14
Figure 3: LOX/H2 specific impulse as a function of equivalence ratio ......................... 18
Figure 4: Polish wz. 8/K-14, Scud-B (from Ref. 26)...................................................... 20
Figure 5: Regions of influence........................................................................................ 22
Figure 6: Differential pressure coefficient on a thin vane at 10? angle of attack ........... 26
Figure 7: Vane force as a function of vane deflection.................................................... 29
Figure 8: SCUD-B diagram (from Ref. 35).................................................................... 31
Figure 9: Comparison of the simulated missile with the SCUD-B................................. 33
Figure 10: Trajectory plot ................................................................................................. 37
Figure 11: Altitude as a function of time.......................................................................... 38
Figure 12: Thrust as a function of time............................................................................. 38
Figure 13: Mach number as a function of time................................................................. 39
Figure 14: Range as a function of time............................................................................. 39
Figure 15: Case 1 missile external geometry.................................................................... 40
Figure 16: Case 2 missile external geometry.................................................................... 41
Figure 17: Case 3 missile external geometry.................................................................... 42
Figure 18: Case 4 missile external geometry.................................................................... 43
Figure 19: Missile external geometry comparison............................................................ 44
Figure 20: Convergence history........................................................................................ 45
Figure 21: Aerodsn optimized, guided missile external geometry ................................... 47
Figure 22: Missile Datcom optimized, guided missile external geometry ....................... 48
Figure 23: Aerodynamically controlled flight trajectories................................................ 49
Figure 24: Ballistic missile external geometry ................................................................. 52
Figure 25: Aerodynamic control missile external geometry............................................. 53
Figure 26: Vane control missile external geometry.......................................................... 54
Figure 27: Trajectory plots for target 1............................................................................. 58
Figure 28: Trajectory plots for target 2............................................................................. 59
Figure 29: Trajectory plots for target 3............................................................................. 60
Figure 30: Trajectory plots for target 4............................................................................. 61
Figure 31: Trajectory plots for target 5............................................................................. 62
xii
NOMENCLATURE
CFD Computational Fluid Dynamics
GA Genetic Algorithm
? Sweep Angle
? Angle of Attack
C
M?
Derivative of the Moment Coefficient
C
N
Normal Force Coefficient
C
N?
Derivative of the Normal Force Coefficient
? Vane Deflection Angle
f Fuel to Oxidizer Ratio
? Equivalence Ratio
g Acceleration Due to Gravity
h
0
Total Enthalpy
h
e
Exit Enthalpy
I
sp
Specific Impulse
M Mach Number
? Mach Angle
q Dynamic Pressure
S
REF
Reference Area
u
e
Exit Velocity
1
1. INTRODUCTION
Liquid propelled missiles are complex systems with a broad range of design
options. Predicting the performance of a missile for which only a limited amount of
information is available is challenging and is not always possible. Genetic algorithms
(GA?s) have proven to be very effective in optimizing a variety of engineering designs
and are now being used to reverse engineer or predict the capabilities of missile systems
with only a few known design variables. While it is unlikely that a GA would converge
to the exact missile design of interest, GA?s are able to efficiently produce multiple close
matches to known solutions.
1-3
A genetic algorithm is based on the biological concept that a species evolves or
adapts over successive generations. Traits that improve fitness or performance are passed
from one generation to the next while unfavorable characteristics are gradually
eliminated. Over the course of many generations the average fitness of the members in a
population will gradually begin to increase and the design will converge toward the
objective. Depending on the setup, there can be multiple goals and the GA attempts to
find the combination of characteristics that results in performance which matches these
goals.
4
Genetic algorithms can be used to optimize virtually any system with multiple
design variables whose performance can be computationally simulated. The use of
genetic algorithms has become increasingly popular in the optimization of engineering
2
designs and has already been used extensively in the aerospace industry to forward
optimize designs, where constraints on performance drive the design process. The design
of helicopters,
5
spacecraft controls,
6
flight trajectories,
7
gas turbines,
8
airfoils,
9
boosted
ramjets,
10
interceptor missiles,
11,12
aircraft,
13
hybrid rockets,
14
liquid rockets,
1, -15 17
and
solid rockets
18,19
have all benefited from the application of GA?s in this manner.
More recently, genetic algorithms have been shown to be a useful tool in reverse
engineering problems, specifically in reverse engineering missile designs. In contrast to
design optimization, reverse engineering assumes some of the performance goals or
design variables are already known, and the GA attempts to discover a variable set that
matches the known goals. With a limited set of initial data, it was determined that a GA
is better able to establish the remaining unknown design parameters than a trial-and-error
method.
1
In a precursor to the current research, Burkhalter et al.
1
developed a GA-based
program that was able to partially reverse engineer ballistic solid rocket missiles. While
their program was able to discover much of the external design and some performance
characteristics, some of the design variables could not be accurately identified. Using a
derivative of this program, Metts
4
conducted much more extensive research on the
performance of the GA in reverse engineering ballistic missile designs. He found that the
GA was capable of finding quality reverse engineering matches, but human inspection
was still necessary to determine the true best performer from a small group of optimized
missile designs. This scenario often occurs because of the fact that multiple designs can
achieve identical performance goals.
The research discussed in this thesis directly builds on the work done by
Burkhalter et al.
2
The missile optimization code has been modified to use the GA in
3
optimizing liquid-fueled missiles. In addition to ballistic missiles, both aerodynamically
controlled and vane controlled missile designs are considered. The optimization code is a
combination of many individual codes which together are able to simulate the
performance of a particular missile design and then determine its fitness in relation to the
other candidate designs. A series of legacy codes predict the actual performance of
individual liquid missile designs by analyzing a candidate missile design?s aerodynamics,
mass properties, propulsion characteristics, and guidance and control system. The six
degree-of-freedom (6-DOF) model ties everything together, providing the performance
data for each missile design. The GA then determines and operates on the best solutions
for a given generation of designs depending on the user-defined objective function. Each
of the legacy codes and the GA are discussed in detail in the pages that follow.
The goal of this thesis is to upgrade an existing liquid rocket optimization
program and obtain results from relevant optimization runs. While the code can be used
for preliminary design optimization, the primary motivation that drives this research is to
be able to use the program to reverse engineer existing missile designs. If only a limited
amount of data about a specific liquid rocket is known, the GA-controlled optimization
code is able to produce complete designs with characteristics that match the known
parameters. The GA suite of codes also has the ability to optimize a current design and
discover possible modifications that might improve the missile?s performance.
The upgrades discussed in this thesis add a new level of confidence to the overall
optimization results. This process includes the ability to simulate missile types that the
program previously was unable to handle. The first upgrade to the suite of codes
involved the development of a version of the code that employs an alternate aerodynamic
4
analysis code known as Missile Datcom.
20
The next change made to the code allows for
the specific impulse (I
sp
) to vary as a function of equivalence ratio (?), where it was
formerly a constant value dependant only on the selected propellant type. Finally, a jet
vane control system is added to the current aerodynamic control system which allows for
the optimization of vane controlled missile systems. With the modifications made during
the current research, the suite of programs is now able to optimize real-world missile
designs that it was formerly incapable of simulating while adding a new level of
efficiency and accuracy to its previous abilities.
5
2. BACKGROUND AND THEORETICAL DEVELOPMENT
The liquid rocket optimization code is comprised of many individual codes that
work together to predict the performance of each missile design selected by the GA for
analysis. Many of these are referred to as legacy codes because they have remained
largely unchanged in the current research effort. Others, including the aerodynamics
routine and the liquid propulsion system model, were modified significantly. The main
codes of interest will be discussed briefly with special attention paid to the ones which
were upgraded. Some background information on the GA will first be provided followed
by discussion of the aerodynamics, mass properties, 6-DOF, liquid propulsion system,
and guidance system models. Finally, the development of the jet vane control system
will be addressed in detail.
2.1 Genetic Algorithm
The GA examined in the current research uses a set of design variables to define a
particular missile system. The optimization process begins with the user selecting a
range and resolution for each of the design variables. By randomly selecting values for
each design variable from within the user-defined boundaries, the GA then generates a
population of candidate designs. Each candidate design, otherwise known as a member,
in a generation is analyzed by the suite of performance codes. The number of members
in a generation and the number of generations that the GA should run are also values set
by the user. Next, the GA ranks the members according to the performance of each as
6
determined by the objective function. The GA employed in this effort uses a tournament
selection process which chooses the best performing member from a randomly selected
pair. The resulting member is then ?mated? with the best performer from a different pair.
The mating process combines the two members? genetic material, which is stored in
binary form. A portion of this exchanged genetic material may be mutated depending on
the mutation probability factor set in the GA options. The subsequent generation is filled
with members that result from the mating process. The process is repeated as each
member in the new population is analyzed by the performance codes and its fitness
ranked.
Over successive generations, the fitness of the designs will increase as good
designs are passed on while poor designs are eliminated. The speed and efficiency of this
process is highly dependent on the ranges of the GA variables and the number and types
of goals. Allowing wide variations in each of the design variables greatly increases the
number of possible solutions that the GA must analyze. However, if several design
variables are already known, as is usually the case in reverse engineering problems, a
solution can be reached much more quickly.
4
The objective function has an arguably greater effect on the efficiency of the
optimization code. Experience has shown that given one goal, the GA usually finds a
solution using a relatively small number of calculations of the objective function. As
more goals are added however, optimal solutions can be more difficult to find, as the
goals are often competing with one another. For example, the user might wish to
maximize range and minimize the system weight of a missile design. Those goals are in
direct competition and finding the balance of range and weight based on the goal
7
description is computationally expensive. In addition, the user must keep the goals
evenly proportioned while adjusting a weighting factor to emphasize the more important
goal if necessary.
Many of the settings and options that control the behavior of the GA are found in
the GA input file (GANNL.DAT). An example GA input file can be found in
APPENDIX A. This file is where the bounds and resolution for each of the 27 GA
design variables are set and where the number of members in a population and the
maximum number of generations are defined. The GA can be configured for multiple
goals, and the relative importance of the goals can be adjusted by weighting factors.
There are many other parameters that control the performance of the GA located in this
file but a few notable ones are a restart switch, an elitist option, the mutation probability
factor and a seed for the random number generator. The GA itself is a complicated
program that could be the subject of its own thesis, but for the purposes of this research it
has been left unaltered from the previous versions.
2, ,4 10
Table 1 lists the 27 GA variables and provides a brief definition for each one.
Clearly, all of the possible parameters that affect the design of liquid powered missiles
could not be encapsulated in just 27 variables. These variables were selected as being the
most critical design options and have the greatest effect on a missile?s performance. The
remaining design options, which are not variable, are defined in the YYVAR.DAT file
which can be found in APPENDIX B. These parameters are read out of the file and
stored in a global array which is used by all parts of the program. While there is far too
much information stored in this file to discuss in detail, it should be noted that the major
categories of information include: constants, material densities, component masses, target
8
and launch data, external geometry variables, and reverse engineering data. Even with
this large data input, the suite of codes employed in this investigation is still arriving at
preliminary designs. Detailed design parameters such as turbopump internal parameters,
fasteners, detailed plumbing and wiring schematics are not considered in this process.
Table 1: GA design variables
Number Variable Name Description
1 kprop Propellant type
2 eqr Equivalence ratio
3 po Maximum chamber pressure (psi)
4 athroat Nozzle throat area (in
2
)
5 eps Nozzle expansion ratio
6 lf Fractional nozzle length
7 tb Burn time (sec)
8 paymass Payload mass (lbs)
9 dbody Missile body diameter (ft)
10 lnose Nose length (lnose/dbody)
11 dnose Nose diameter (dnose/dbody)
12 crfin1 Finset 1 root chord (cr/dbody)
13 trfin1 Finset 1 taper ratio
14 angLE1 Finset 1 leading edge angle (degrees)
15 b2fin1 Finset 1 semi-span (b2/dbody)
16 xcrfin1 Location of the leading edge of finset 1 (% total length)
17 crfin2 Finset 2 root chord (cr/dbody)
18 trfin2 Finset 2 taper ratio
19 angLE2 Finset 2 leading edge angle (degrees)
20 b2fin2 Finset 2 semi-span (b2/dbody)
21 xtefin2 Location of the trailing edge of finset 2 (% total length)
22 tdelay Autopilot time on delay (sec)
23 tau Autopilot time constant (sec)
24 zeta Autopilot damping coefficient
25 wcr Cross over frequency
26 pronvg Pronav gain
27 theta0 Initial launch angle (degrees)
9
2.2 Aerodynamics
2.2.1 Aerodsn
Aerodsn
21
is a fast predictor aerodynamic analysis code which has been used
successfully in several different versions of the GA missile optimization program.
Developed by the U.S. Army Missile Command in the 1980s, it is a very robust code
restricted to axis-symmetric cruciform missile shapes. More accurate CFD codes are
available, but the high computational cost of this type of analysis makes CFD impractical
for use with the GA in the preliminary design mode. Aerodsn is non-linear and assumes
that there are no boundary layers and that no separation occurs. Aerodsn uses the vehicle
geometry and other parameters necessary for successfully generating an aerodynamic
database. The required aerodynamic data is generated for the complete Mach number
range and a complete missile orientation sweep in order for the 6-DOF to determine the
aerodynamic loads and moments under any flight condition. The missile is assumed to
be symmetric so the yawing moments are determined from the pitching moment
coefficients and the side forces are determined from the normal force coefficients.
2.2.2 Missile Datcom
While Aerodsn has been used successfully as the aerodynamic prediction code for
the GA program, it was determined that the program would benefit from a full-featured
and industry standard aerodynamic code. Consequently, an alternate version of the
optimization suite has been developed which uses Missile Datcom. Missile Datcom
20
is
also a fast predictor missile aerodynamic analysis tool with a wide range of capabilities.
Even though Aerodsn borrowed some of its source code from Missile Datcom, the two
programs function differently. Missile Datcom receives the missile geometry input and
10
writes output in formats that differ greatly from that of Aerodsn. As a result, the process
of integrating Missile Datcom required a considerable amount of modification to the
optimization program as a whole.
Since the GA optimization process selects numerous missile designs which each
must be simulated to analyze their performance, the aerodynamic code must be run
repeatedly to generate the aerodynamic coefficients for each member. This fact creates a
problem with Missile Datcom as it will not run multiple cases one after another without
being completely closed between cases. Missile Datcom maintainers have acknowledged
the issue, but currently do not have a solution. The initial plan for implementing Missile
Datcom was to insert it into the liquid missile GA code as a subroutine. The Missile
Datcom subroutine would be called instead of Aerodsn each time a new missile geometry
is produced, and the coefficients could be transferred into the regular program as needed.
But because the optimization program is not exited between runs, Missile Datcom does
not work properly in this configuration.
In order to use Missile Datcom with the GA, a method of running the code which
allows Missile Datcom to be exited after each run was devised. Instead of running
Missile Datcom as a subroutine, it is compiled as a standalone executable file and called
directly from the performance prediction program. This allows Missile Datcom to
completely close after each time it is called while the liquid optimization program
continues running. A new subroutine is added to the optimization program to transfer the
missile geometry parameters into a form that Missile Datcom accepts and another
subroutine is added to retrieve the coefficients from the output file and enter them into
11
the GA code. The only modification that must be made to the actual Missile Datcom
source is to redirect the paths for the input and output files.
Although this method is functional, it is not a perfect solution for running the GA
with Missile Datcom. Whenever Missile Datcom is called, a command window is
opened for a brief moment and then immediately closed. Because of the number of
missile designs analyzed by the GA, it is normal to have a new window opening every
second. While this only causes a slight decrease in the performance of the program as a
whole, it is very inconvenient for the computer user as it steals focus from other
applications running on the machine and renders that computer almost unusable for any
other purpose while the GA is running. The development environment supplied for this
research, Compaq Visual Fortran, appears to have no compiler option that allows this
window to be suppressed. A possible solution that has been suggested is to call Missile
Datcom with a piece of C++ code that can hide the window. This option has not been
pursued within the scope of the current research effort.
The aforementioned issues have made it impractical to implement Missile Datcom
in the final version of the liquid missile GA program, but it can be used to corroborate
results obtained from the Aerodsn version. An extensive study was made comparing the
two aerodynamic codes and Figure 1 shows a plot comparing the trajectories of missiles
optimized using Missile Datcom and Aerodsn. The GA goal was set to maximize range,
and the cases had Mach number limits of 7.1 and 8.5 respectively. The trajectory plot
illustrates how similar the predictions of two aerodynamic codes were to each other. The
close agreement in the maximum range, as well as flight path, suggests Aerodsn and
Missile Datcom are providing comparable results for the aerodynamic coefficients. A
complete set of results and analysis can be found in a later section of this thesis.
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 100000 200000 300000 400000 500000 600000 700000 800000
Range (m)
Al
titude
(m
)
Aerodsn, Mach 7.1
Aerodsn, Mach 8.5
Datcom, Mach 7.1
Datcom, Mach 8.5
Figure 1: Aerodsn and Datcom optimized missile trajectories
2.3 Mass Properties
The mass properties routine is a comprehensive analysis of the missile system
component masses and moments of inertia about all three axes. Cross product moments
of inertia are assumed to be zero since missile symmetry is assumed. The moment of
inertia for each of the missile components is calculated. Once the center of gravity (CG)
of the missile is determined, the moments are transferred to the CG and subsequently
stored for future use. In this same routine, the mass and moment of inertia of the fuel and
oxidizer are also determined as a function of time. This information, with the time
dependent thrust data, is written to a file (TMASS.DAT) which is later used by the 6-
DOF model. The components that are considered in the analysis are shown in Table 2.
12
13
Also listed in the table are six generic ?boxes? which have been built into the code.
These boxes allow the user to place custom payloads or other equipment inside the
missile. The boxes can also be positioned at any location within the missile with the
exception of box1 which is always located at the nose.
Table 2: Components considered in the mass properties routine
Part No. Component
1 Box1
2 Avionics or electronics
3 Compressed gas for pressurization
4 Compressed gas tank
5 Fuel
6 Fuel tank
7 Oxidizer
8 Oxidizer tank
9 Engine assembly
10 Nozzle
11 Nosecone fairing
12 Cylindrical (main) fairing & wiring
13 Aft fins
14 Gimbals
15 Warhead
16 Forward fins
17 Servos
18 Box2
19 Box3
20 Box4
21 Box5
22 Box6
2.4 Six Degree-of-Freedom Model
The 6-DOF routine is based on the equations of motion found in Etkin.
22
It is
assumed that the missile is rigid, that all masses are stationary, and that all cross products
of inertia are negligible. The 6-DOF uses an earth-centered coordinate system, similar to
the one shown in Figure 2. The equations of motion accept aerodynamic data from
Aerodsn or Missile Datcom, mass and moments of inertia from the mass properties
routine, thrust data from the liquid rocket module, and other required information is
passed through the an array. The 6-DOF uses a 7-8
th
order Runge-Kutta numerical
integration routine to simulate the flight of the missile. The time step is a variable and is
dependent on the magnitude of the largest derivative in the equations of motion.
12
The
flight of the missile is recorded, and necessary information is stored in an array and
passed back to the GA routine for further analysis.
Figure 2: Earth-centered coordinate system (from Ref. 12)
2.5 Liquid Propulsion System
2.5.1 Background
The liquid rocket model is based on a generic set of required parameters that
define the operation of a single stage liquid rocket engine. The oxidizer and fuel are
stored in cylindrical tanks with hemispherical end caps which are sized based on the
specific missile design. Standard equations are used to predict the thrust for a variety of
fuel and oxidizer combinations at different operating combustion pressures and throat
14
15
areas. Variation of the thrust due to altitude change is also accounted for in the
equations. The pressure and temperature in the combustion chamber are assumed to be
constant, and it is also assumed that the thrust instantly drops to zero at burnout. The
nozzle is designed to connect to the combustion chamber and can be configured to extend
aft of the base of the missile or to have the nozzle exit flush with the base of the missile.
The system assumes that turbopumps are required to compress the fuel and oxidizer prior
to injection into the combustion chamber and the fuel and oxidizer tanks are under
relatively low pressure, around 100 psia. All necessary plumbing and wiring are included
as uniformly distributed mass.
19
The propellant is a design variable which can be chosen from a list of 29 included
fuel and oxidizer combinations. Propellant properties such as stoichiometric mixture
ratio, combustor total temperature, molecular weight, characteristic exhaust velocity, sea
level specific impulse, and the ratio of specific heats are included in the list with their
corresponding fuel type. Propellants with sufficient data have been approximated with a
curve fit to determine specific impulse as a function of equivalence ratio.
2.5.2 Variable Specific Impulse
A method for determining the specific impulse (I
sp
) as a function of the
equivalence ratio (?) has been implemented in the optimization code. This allows the I
sp
to be calculated based on the equivalence ratio that the GA chooses. It should be noted
however, that some of the propellants available in the program are rare, and the necessary
thermochemical data for these propellants was not readily available. As a result, these
propellant combinations are still included but have a constant specific impulse. The fuels
that currently have variable I
sp
capability are listed in Table 3.
Table 3: Variable specific impulse propellant combinations
Number Propellant Name
I
sp
(s) at ?=1
1 IRFNA/UDMH 274
2 IRFNA/Hydrazine 287
4 IRFNA/RP-1 257
5 IRFNA/JP-4 254
6 IRFNA/MMH 268
11 N
2
O
4
/UDMH 284
13 N
2
O
4
/Kerosene 283
14 N
2
O
4
/Hydrazine 291
15 N
2
O
4
/MMH 301
23 LOX/Hydrazine 314
25 LOX/UDMH 309
26 LOX/LH
2
367
The process of characterizing the thermodynamic conditions in a combustion
chamber is highly complex. The large amounts of individual chemical species that
appear make solving the chemical equations by hand impractical. Computer codes are
routinely used to determine these values instead. STANJAN
23
is one such code and was
used in calculating the I
sp
as a function of equivalence ratio for the propellants in the
optimization program. STANJAN solves for the thermodynamic conditions using linear
programming to minimize the Gibbs free energy.
The specific impulse values for the propellants with sufficient data are
approximated by a 5
th
-order curve fit that can be used to obtain the I
sp
given an
equivalence ratio. The equivalence ratio is defined as
stoich
f
f
?? (1)
where f is the fuel to oxidizer ratio by mass.
24
The I
sp
curve is valid for equivalence ratios
between 0.25 and 4.0 for most of the propellant combinations. STANJAN was used to
determine the I
sp
at approximately eight equivalence ratios for each fuel and oxidizer
16
combination. Given the initial enthalpy of the propellant, STANJAN calculates the total
temperature in the combustion chamber assuming 1000 psi (68 atm) total pressure.
Assuming entropy is constant, STANJAN then calculates the exit enthalpy of the flow
when the nozzle exit pressure is 14.7 psi (1 atm). The exit velocity is calculated by hand
and then divided by the acceleration due to gravity to obtain the specific impulse as
shown in Equation 2.
g
u
g
hh
I
e
e
sp
=
?
=
)(2
0
(2)
The resulting value is a reference I
sp
and the actual performance is adjusted based on the
flow characteristics and the selected chamber pressure. The mixture ratio is also adjusted
based on the chosen equivalence ratio so that the mass of the oxidizer and fuel, as well as
the size their respective tanks, is calculated correctly.
Figure 6 is a plot of the I
sp
as a function of equivalence ratio for one of the
available propellant combinations, LOX/LH
2
. A trend line is fitted to the curve and the
corresponding 5
th
-order equation is also shown on the plot. The data used to plot the I
sp
curve is listed in Table 4. Similar plots were made for each propellant combination and
the equation of the trend line corresponding to each propellant type was inserted into the
liquid fuels subroutine. The curve fits were compared to published data
25
to validate the
results. Except for propellant combinations containing hydrogen, the maximum specific
impulse occurs very near the stoichiometric fuel to oxidizer ratio. The I
sp
is higher for the
fuel rich LOX/H
2
mixture because the molecular weight of the fuel (H
2
) is much lower
than the molecular weight for the oxidizer (O
2
).
17
26) H2O2, Isp vs Eq. ratio
y = 1.0706x
5
- 16.383x
4
+ 99.686x
3
- 303.68x
2
+ 460.71x + 125.78
R
2
= 1
200
250
300
350
400
450
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Equivalence Ratio
Is
p
(
s
)
Figure 3: LOX/H2 specific impulse as a function of equivalence ratio
Table 4: LOX/H2 data table
Equiv. ratio Reactants h
o
(J/kg) h
e
(J/kg) u
e
(m/s) I
sp
(s)
0.25 1/2H2+O2 -1.29E+05 -2.53E+06 2192.81 223.5
0.5 H2+O2 -1.66E+05 -4.26E+06 2860.25 291.6
1.0 2H2+O2 -2.33E+05 -6.72E+06 3602.22 367.2
1.5 3H2+O2 -2.94E+05 -7.82E+06 3879.01 395.4
2.0 4H2+O2 -3.48E+05 -8.11E+06 3940.94 401.7
2.5 5H2+O2 -3.97E+05 -8.17E+06 3942.56 401.9
3.0 6H2+O2 -4.42E+05 -8.12E+06 3918.78 399.5
3.5 7H2+O2 -4.83E+05 -8.03E+06 3884.06 395.9
4.0 8H2+O2 -5.20E+05 -7.91E+06 3844.12 391.9
2.6 Guidance System and Autopilot
The guidance system is based on the proportional navigation guidance law. The
system attempts to rotate the missile at a rate proportional to the rate at which the line-of-
site to the target is moving. It is a two-axis feedback control system that uses the pitch
18
19
and yaw acceleration rates, but does not factor in the roll rate. The autopilot generates
the elevator and rudder commands based on the acceleration rates determined in the
guidance routine. The GA variables used by the guidance system and autopilot are the
time delay, autopilot time constant, damping coefficient, crossover frequency, and the
pronav gain. These variables are numbers 22 through 26 listed in Table 1.
2.7 Jet Vane Control System
Missiles with jet vane control systems use small, movable fins, usually composed
of graphite, placed just downstream of the nozzle to vector the thrust and control the
missile. The vanes take advantage of the high dynamic pressure of the supersonic nozzle
exit flow to produce forces and moments that are large enough to guide the missile. Just
after takeoff, while flying at low speeds, vanes provide an effective method of control,
especially before speeds are attained where aerodynamic control surfaces become
effective. The disadvantage of vanes is that they become less and less effective as flight
Mach number increases, and after burnout they are completely useless because they
require thrust to produce the controlling forces and moments. Adjusted by actuators
which are built into the missile body, the attitude of jet vanes is controlled in much the
same way as with aerodynamic fins. Figure 4 shows a missile with a jet vane control
system. The vanes are positioned just aft of the nozzle and are mounted inside the tail
fins.
Figure 4: Polish wz. 8/K-14, Scud-B (from Ref. 26)
2.7.1 Motivation
While jet vanes are not common in modern missile designs, many older missiles
still being used and upgraded today rely on vanes as their only form of control. Since a
major motivation driving the development of the optimization program is to be able to
use the GA to reverse engineer a wide range of missiles, including some that employ jet
vanes, a vane control model was determined to be a necessary upgrade. The model
should predict the aerodynamic forces and moments on the vanes which are immersed in
the supersonic exhaust flow. This modification gives the suite of codes the ability to
predict the performance of a large number of missiles, including SCUD-class missiles,
with a much higher degree of accuracy than before.
20
2.7.2 Theory
During the late 1940?s, John Evvard
27,28
and several other engineers
29-31
solved
the irrotational flow equations for a source distribution over a flat plate in supersonic
flow. Evvard?s theory divides the planar fin into regions which are affected by similar
types of disturbances. These regions are defined by the intersection of the Mach cones
produced by leading edge discontinuities and the surface of the fin. The primary
disturbance types that affect each region are infinite wing, triangular fin, and wing tip.
These disturbance types divide the wing into four regions of flow. A fifth region can also
be present in the case of swept wings when the Mach cone produced by the root chord
leading edge is reflected by the fin tip. The potential flow solution that corresponds to
the type of disturbance experienced in a particular region can be used to determine the
pressure difference between the upper and lower surfaces of the fin at angle of attack. A
generic fin is shown in Figure 5 and illustrates the different regions and the Mach lines
that divide them. The Mach lines on the surface of a flat plate are inclined at a Mach
angle, ?, which is defined as:
?
?
?
?
?
?
=
M
1
sin
1-
? (3)
21
y (span)
x (chord)
x
1
(y)
x
2
(y)
x
3
(y)
Region I
Region II
Region III
Region IV
Region V
Flow
Figure 5: Regions of influence
The regions can be identified by their location in the chord-wise direction as follows:
Region 1: x < x
1
(y) and x < x
2
(y)
Region 2: x > x
1
(y) but x < x
2
(y)
Region 3: x > x
2
(y) but x < x
1
(y)
Region 4: x > x
1
(y) and x > x
2
(y) but x < x
3
(y)
Region 5: x > x
3
(y)
In order to use the zoning laws above x
1
(y), x
2
(y), and x
3
(y) must be determined as a
function of the span-wise location, y.
( )
1
yyx ?= (4)
( ) )0.1(tan
2
yyx ?+?= ? (5)
( ) )1(
3
yyx ?+= ?? (6)
?
?
tan
1
0.1
2
=?= M (7)
22
Finally, the equations for the pressure differential between the upper and lower surfaces
of a planar fin at some angle of attack, ?, are derived in References 27 and 28 given in
Table 5. For the case of a jet vane, the angle of attack is equal to the deflection angle.
Table 5: Pressure coefficient depending on region (modified from Ref. 32)
Region
Region
Conditional
Differential Pressure Coefficient
I
x < x
1
(y)
and
x < x
2
(y)
??
=
22
,
tan
4
?
?
Ip
dC
II
x > x
1
(y)
but
x < x
2
(y)
?
?
?
?
?
?
??
??
+
+?
+?
??
=
??
?
?
?
?
??
tan
tan
cos
tan
tan
cos
tan
4
11
22
,
T
T
T
Ta
dC
IIp
III
x > x
2
(y)
but
x < x
1
(y)
()[ ]
?
?
?
?
?
?
?
?
??
?++?
??
?=
?
tan
tan2
cos
tan
4
1
22
,,
tiptip
tiptip
IpIIIp
yx
yx
dCdC
?
??
?
IV
x > x
1
(y)
and
x > x
2
(y)
but
x < x
3
(y)
()[ ]
?
?
?
?
?
?
?
?
??
?++?
??
?=
?
tan
tan2
cos
tan
4
1
22
,,
tiptip
tiptip
IIpIVp
yx
yx
dCdC
?
??
?
V x > x
3
(y)
( )
()
?
?
?
?
?
?
?
?
?++
?+???
??
=
?
tan2
tan22tan
cos
tan
4
1
22
,
tiptip
tiptip
Vp
yx
yx
dC
?
??
?
where
x
y
T ?= , ??= tanxx
tip
, and yy
tip
?= 0.1
23
Evvard?s theory provides a closed form solution that is exact for small angles of
attack. It assumes no shocks and no loss in total pressure. While these assumptions do
not hold in reality, other solutions such as supersonic potential methods or CFD analysis
would be impractical for use in the optimization program. One-dimensional linearized
supersonic aerodynamic theory could also be used to predict the forces and moments on
the vanes but it is a less accurate solution than Evvard?s theory. Evvard?s solution is a
better method because it accounts for the disturbance types found in two dimensions,
24
such as the wing tip effect, that are neglected in a one dimensional analysis. An efficient
and accurate method for this application, Evvard?s theory is extended here to estimate the
forces and moments produced by the vanes depending on their deflection angle in the
exhaust flow.
2.7.3 Assumptions
To simplify the jet vane analysis several assumptions were made. First, it is
assumed that the vanes are placed immediately downstream of the nozzle exit and the
flow of exhaust gases around the vanes is parallel. Parallel flow can be assumed because
the nozzle design generated by the performance codes turns the flow to within ten
degrees of the axial direction. In addition, the nozzle is designed to be over-expanded at
low altitudes and under-expanded at high altitudes, further affecting the direction of the
flow as it exits the nozzle. This assumption greatly simplifies the calculations because it
allows pressure gradients across the vanes to be neglected. It is further assumed that the
average flow velocity experienced by the vanes is equal to the Mach number at the nozzle
exit plane. The vanes are considered to be flat plates and testing has shown that low
aspect ratio surfaces in high Mach number flows behave accordingly.
33
Real gas effects,
vane interactions, losses, and vane erosion have all been neglected. Finally, since only
vane deflections up to 15 degrees are considered, it can be safely assumed that the
variation of the normal force on the vanes is a linear function of deflection angle.
Experimental testing
33
of vane control systems has shown this to be the case.
2.7.4 Methodology
An additional model has been added to the GA optimization code to handle the
calculations necessary to simulate a vane control system. After the applicable constants
25
are transferred in, the program iterates to determine the Mach number at the nozzle exit
based on the nozzle expansion ratio and the specific heat ratio for the chosen propellant.
The vane itself is currently set as a trapezoid shape with its dimensions normalized by the
nozzle exit plane diameter. The root chord is set at 0.9, the tip chord at 0.3, the semi-
span at 0.7 and the leading edge sweep angle is 45 degrees. This configuration is similar
to the shape of the vanes observed on several common jet vane controlled missiles. In
future revisions, the vane dimensions could be included as GA variables to further
optimize the control system. A 10 degree deflection angle is assumed in order to
determine the pressure coefficient as a linear function of angle of attack.
In order to determine the load distribution on the vane, the flat plate that
approximates the vane is divided into rectangular elements. These are currently fixed at
50 elements in the span-wise direction and 40 elements in the chord-wise direction. The
code then marches through the elements and calculates the differential pressure
coefficient for each element according to the region it lies within. The normal force
coefficient and moment coefficient about the leading edge of the vane are calculated from
the differential pressure coefficient and summed for the entire plate. Figure 6 shows the
elements and differential pressure distribution on a generic thin vane control surface at 10
degrees angle of attack as configured in the actual optimization program. Because the
vane is in a high Mach number flow which produces low Mach angles, this particular
example only contains three of the five possible regions which are defined by Evvard?s
theory.
Thrust degradation is an issue with jet vane control systems that does not affect
missiles with only aerodynamic control. An estimation of the thrust loss has been made
to account for the thrust degradation that occurs in reality. The two primary contributors
to thrust degradation are induced vane drag and viscous drag. The induced vane drag is
estimated by calculating the component of the vane normal force that is oriented
perpendicular to the axial flow. The viscous drag is estimated by assuming a skin friction
drag coefficient of 0.005. This value is a preliminary estimate and is much higher than
the 0.003 typically assumed for flat plates. The induced and viscous drag components are
summed for all four vanes and then subtracted from the thrust in the 6-DOF simulation.
This is currently a very rough estimation for the thrust degradation and the losses could
be significantly higher in reality.
Figure 6: Differential pressure coefficient on a thin vane at 10? angle of attack
The normal force and moment coefficients that are returned from the vane control
model are valid for one vane at 10 degrees deflection. These values are first converted
26
into actual forces and moments and multiplied by two to account for the two sets of
vanes, where one set acts as the elevator and the other as a rudder. The forces and
moments must be nondimensionalized by dividing by the missile reference area and
freestream dynamic pressure. Since freestream dynamic pressure is calculated during the
simulation, this step must be completed within the guidance and 6-DOF routines. The
moment coefficient must also be transferred from the vane leading edge to the missile
center of gravity. Dividing by the deflection angle provides the coefficients C
N?
and C
M?
which are the normal force coefficient and moment coefficient per radian of vane
deflection, respectively. The coefficients are now compatible with the aerodynamically
generated C
N?
and C
M?
used in the fin control case. The vane control coefficients are
substituted for the aerodynamic values in the guidance and 6-DOF routines when vane
control is activated. The aerodynamic control coefficients are used when the vane control
system becomes inactive after burnout.
2.7.5 Verification
The vane control model is verified by comparing the normal force on the vanes
calculated by the program to an approximation obtained from one-dimensional linearized
supersonic aerodynamic theory. In static ground tests, this approximation has been
shown to be an accurate method of predicting the forces and moments produced by the
vanes.
33
Linearized theory provides a relation for the lift coefficient on a thin airfoil at
small angle of attack, regardless of shape.
34
1
4
2
?
=
M
C
L
?
(8)
The lift coefficient is defined as:
27
sin-cos ??
ANL
CCC = (9)
Since linearized theory only holds for small angles of attack, the normal force coefficient
is approximately equal to the lift coefficient. The angle of attack of a vane is equal to its
deflection angle, ?, so the resulting equation for normal force coefficient is:
1
4
2
?
?
M
C
N
?
(10)
The normal force acting on a vane when assumed to be a linear function of deflection
angle is defined as:
REFN
qSCN ?
?
= (1)
where the derivative of the normal force coefficient is simply
??
?
N
N
N
C
C
d
dC
=? (12)
Since the vane deflection is limited to 15 degrees within the code, the linearized theory
approximations are expected to be valid.
The normal force values predicted by Evvard?s theory as applied in this effort
correlate well to the values derived from linearized supersonic theory. The percent
difference between the two methods of calculation was generally observed to be less than
5 percent. For example, the vane shown in Figure 6 deflected 10 degrees in a Mach 3.6
exhaust flow was predicted by Evvard?s theory to produce a normal force of 5336 N.
Assuming the same vane geometry and setup, the relation derived from linear supersonic
theory approximates the normal force to be 5502 N. A comparison plot of Evvard?s
theory calculations and values derived from linear supersonic aerodynamic theory is
shown in Figure 7. Linear supersonic theory over-predicts the normal force as expected
28
because it is only a one-dimensional analysis method and it neglects the effects of the
Mach cones that Evvard?s theory takes into account. The close agreement between the
results from Evvard?s solution and one-dimensional linearized supersonic aerodynamics
provides verification that the program is functioning correctly. Differences that do exist
can be attributed to the greater degree of accuracy that Evvard?s method affords being a
two-dimensional analysis. There is no experimental data available, however, to allow the
code to be validated.
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 2 4 6 8 10121416
Vane Deflection (deg)
V
a
ne
Fo
r
c
e
(
N
)
Evvard's Theory
Linear Supersonic Theory
Figure 7: Vane force as a function of vane deflection
29
30
3. RESULTS
The liquid missile system model has been validated against a known missile
configuration and the results are provided. Performance data for a generic short range
ballistic missile similar to the SCUD-B are given. Results from a simulated flight of the
same missile design are compared to the known performance data. Results from
unguided missile optimization runs with either Aerodsn or Missile Datcom producing the
aerodynamic coefficients will also be presented. The next section of results examines
Aerodsn and Missile Datcom produced missiles with aerodynamic control systems.
Simulating aerodynamically controlled designs highlights the differences between the
aerodynamic codes and offers a much more complete comparison than the unguided
cases. Finally, optimized missile designs featuring aerodynamic control, vane control,
and no control are compared through a series of different cases. All of the results
presented here employ the variable I
sp
upgrade that was discussed previously.
3.1 Model Validation
The liquid missile performance model is validated by flying a single run case with
a configuration very similar to the SCUD-B. A diagram of the SCUD-B is shown in
Figure 8 and the corresponding missile data
17
is given in Table 6.
Figure 8: SCUD-B diagram (from Ref. 35)
Table 6: Missile configuration and performance data (from Ref. 17)
Parameter Value
Missile Length 10.93 m 35.86 ft
Missile Diameter 0.88 m 2.887 ft
Launch Weight 5.83 metric tons 12850 lbs
Warhead Weight 1000 kg 2200 lbs
Range 300 km 186 mi
Thrust 13.35 metric tons 29436 lbs
Isp 238 sec 238 sec
Burn time 62 sec 62 sec
Chamber pressure 6.71 MPa 973.7 psi
Nozzle expansion ratio 10.32 10.32
This set of data was input into the performance model along with additional data such as
the fin geometry, and the resulting design was flown by the 6-DOF simulation. A list of
the GA variables that were used for this design is given in Table 7. The I
sp
and other fuel
parameters were set manually in the liquid fuels subroutine, and both Aerodsn and
Missile Datcom were used as aerodynamic predictors for this case. One difference of
note is the SCUD-B has a conical nose section while the simulated missile design has a
blunted ogive nose. This fact, however, should have little impact on the performance of
the simulated missile when compared to the SCUD-B.
31
32
Table 7: List of GA variables for SCUD-B comparison
Value GA variable name
4.0000000 propellant type
1.1200000 equivalence ratio
973.70000 chamber pressure (psi)
19.253000 nozzle throat area (in^2)
10.320000 nozzle expansion ratio
0.6000000 fractional nozzle length
62.000000 burn time (sec)
2200.0000 payload mass (lbs)
2.8887000 missile body diameter (ft)
3.3290000 nose length/dbody
0.1114300 nose dia/dbody
1.6138000 fin2 root chord fraction = cr/dbody
0.6197000 fin2 taper ratio
38.600000 fin2 le angle (degrees)
0.7693000 fin2 semi-span fraction = b2/dbody
1.0000000 x loc of fin2 (% totlen)
60000.000 autopilot time on delay - tdelay
0.5078700 autopilot time constant - tau
0.5800000 autopilot damping coef - zeta
63.571430 cross over frequency - cohz
2.7143000 pronav gain -pronvg
85.000000 initial launch angle (degrees)
The results of the model validation are given in Table 8 and a rendering of the
resulting missile compared to the SCUD diagram is shown in Figure 9. All other design
parameters not listed in Table 8 were either direct inputs into the model, or no data was
available for comparison. The results show close agreement between the known
missile?s performance and the performance of the model which used Aerodsn. Missile
Datcom predicts the range to be about 25 km farther than the actual SCUD. For both
models, the major design parameters are only a few percent off from the actual values.
This result provides a high level of confidence that the missile performance model
utilizing Aerodsn produces accurate results.
Table 8: Model validation for the SCUD-B
Parameter Known Model (Aerodsn) Model (Datcom)
Missile Length 10.93 m 11.40 m 11.40 m
Range 299.4 km 304.1 km 324.7 km
Launch Weight 5828 kg 5769 kg 5769 kg
Thrust 13.35 m tons 13.18 m tons 13.18 m tons
SCUD-B
Simulated Missile
Figure 9: Comparison of the simulated missile with the SCUD-B
3.2 Unguided Results
The following results are from a series of unguided missile optimization runs.
The primary objective of this set of missile optimizations is to obtain missile designs
using both aerodynamic prediction routines so the results can be compared. The
optimization codes are identical aside from changes made to accommodate their
respective aerodynamic prediction codes. The goal of each optimization run was to
determine the viability of a single-stage, liquid propelled ballistic missile with specific
constraints delivering a payload to a range of 700 km. The primary constraints included a
33
34
maximum thrust limit of 28 metric tons, IRFNA/RP-1 propellant, and a payload of 2000
kg. The specific goals and constraints used for these optimization runs are not important
to this thesis other than to provide a common baseline.
In order to determine the feasibility of such a missile, the GA was configured to
run a single goal case to match a range of 700 km. Alternatively, the GA could have
been set up to maximize range, but either strategy would determine whether a missile
with these requirements could achieve the range goal. Matching the thrust and payload
could have been additional GA goals, but doing so would have complicated the runs.
The optimization program works more efficiently when only a single goal is employed,
so limiting the number of goals to only those that are high priorities is advantageous. To
account for these limitations though, a thrust ceiling was fixed in the program and the
payload, being one of the 27 GA variables, was limited to be 2000 kg in all cases.
The complete GA input file, where the GA settings and design variable bounds
are defined, is provided in Appendix A. The input file in Appendix A was used for all
four of the runs conducted for this particular study. Table 9 shows the major differences
between each run. The aerodynamics column identifies which code was used for the
aerodynamic prediction for a particular case and the Mach limit column lists the
maximum allowable Mach number for each case. All of the cases were run to 100
generations with 300 members in each generation. The convergence history of each case
was recorded and all of the cases were found to be sufficiently converged with this
configuration.
35
Table 9: Case setup
Case Aerodynamics Mach Limit
1 Aerodsn 7.1
2 Aerodsn 8.5
3 Datcom 7.1
4 Datcom 8.5
A note should be made about the Mach limit, which has not been mentioned until
now and is listed in the table above. Aerodsn uses supersonic theory to predict the
aerodynamics and the accuracy of this method becomes marginal in the hypersonic range.
However, an extrapolation of the theory in this range is adequate for preliminary designs
such as the ones in question. To account for this fact, in the original Aerodsn code, an
upper bound on the Mach number was fixed at 7.1. As the plots show, the optimized
missile designs were not able to achieve the goal range with this configuration. Close
examination revealed that the Mach number bound was a limiting factor in the missile
performance. Revisions made to the Aerodsn code prior to this study provided an
increased level of confidence in the aerodynamic predictions at high Mach numbers. The
Mach number limit was raised accordingly until the GA was able to find a design capable
of reaching the target. The new Mach number upper bound of 8.5 was used in
conjunction with the previous two Mach 7.1 optimization runs to further support the
comparisons of Aerodsn and Missile Datcom.
Performance plots generated from these optimization runs are provided in Figures
10 through 14. Figure 10 plots the trajectory of each of the four resulting missile designs.
The Aerodsn, Mach 7.1 case flies slightly higher and farther than did the comparable
Missile Datcom design, but the two Mach 8.5 missiles have almost identical trajectories.
The altitude as a function of time for the cases is shown in Figure 11 and shows again
36
how the Aerodsn, Mach 7.1 design flies higher and slower than the Missile Datcom
missile. Figure 12 plots the thrust as a function of time for each missile. The Mach 8.5
missiles start with about the same thrust, but the Aerodsn missile burns out with a greater
final thrust. The lower Mach number cases have quite different thrust curves. The
Datcom thrust is much higher initially, but its curve is very flat, and the Aerodsn missile
eventually achieves the maximum thrust value. The Mach number as a function of time
is plotted in Figure 13 for all cases and the curves show good agreement. The brief dips
present in the curves are a result of temperature fluctuations within the atmosphere that
affect the speed of sound and thus the Mach number. Lastly, Figure 14 shows that the
range as a function of time is very similar for comparable cases.
Results from the four ballistic missile optimization runs demonstrate preliminary
design level agreement between the aerodynamic codes. The maximum achievable
ranges for cases with comparable Mach number limits are very similar regardless of the
aerodynamic code used. In addition, the trajectory, thrust, and Mach number as a
function of time are all very similar for comparable runs. The provided missile
renderings demonstrate that typical missile designs were achieved with only small
differences between the designs, mostly occurring in the size and placement of the fin
sets. This can be seen in Figures 15 through 18 which show the external configuration of
each of the resulting missile designs along with important performance data. Figure 19
provides an illustration of all four missile designs side-by-side for easy comparison of
their external geometries.
While the performance plots indicate close agreement between the two different
aerodynamic prediction routines at comparable Mach number limits, these results alone
cannot validate the aerodynamic prediction codes or even confirm that their predictions
are similar to one another?s. The reason for this is that much of the flight time for these
ballistic cases occurs at very high altitudes. Because the missiles have no aerodynamic
control, the primary aerodynamic force is drag, and above 10,000 m the drag force is very
small. As shown in Figure 10, these missile designs spend a considerable amount of time
at altitudes where the aerodynamics has little effect. For cruise missiles powered by air
breathing propulsion, the comparison and conclusion could be significantly different.
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 100000 200000 300000 400000 500000 600000 700000 800000
Range (m)
Al
titude
(m
)
Aerodsn, Mach 7.1
Aerodsn, Mach 8.5
Datcom, Mach 7.1
Datcom, Mach 8.5
Figure 10: Trajectory plot
37
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 50 100 150 200 250 300 350 400 450 500
Time (s)
Al
titud
e
(m
)
Aerodsn, Mach 7.1
Aerodsn, Mach 8.5
Datcom, Mach 7.1
Datcom, Mach 8.5
Figure 11: Altitude as a function of time
200000
220000
240000
260000
280000
300000
320000
0 1020304050607080
Time (s)
Th
rus
t
(
N
)
Aerodsn, Mach 7.1
Aerodsn, Mach 8.5
Datcom, Mach 7.1
Datcom, Mach 8.5
Figure 12: Thrust as a function of time
38
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
0 50 100 150 200 250 300 350 400 450 500
Time (s)
Ma
ch Nu
mb
er
Aerodsn, Mach 7.1
Aerodsn, Mach 8.5
Datcom, Mach 7.1
Datcom, Mach 8.5
Figure 13: Mach number as a function of time
0
100000
200000
300000
400000
500000
600000
700000
800000
0 50 100 150 200 250 300 350 400 450 500
Time (s)
R
a
nge
(m)
Aerodsn, Mach 7.1
Aerodsn, Mach 8.5
Datcom, Mach 7.1
Datcom, Mach 8.5
Figure 14: Range as a function of time
39
Aero Code: Aerodsn
Range: 512.1 km
Initial Mass: 10783 kg
Flight Time: 381.33 s
Figure 15: Case 1 missile external geometry
Table 10: Case 1 GA variables
Value GA variable name
4.0000000 propellant type
0.6526419 equivalence ratio
1210.3718 chamber pressure (psi)
24.418379 nozzle throat area (in^2)
14.360078 nozzle expansion ratio
0.8200000 fractional nozzle length
70.845139 burn time (sec)
4400.0000 payload mass (lbs)
3.4761906 missile body diameter (ft)
2.4126983 nose length/dbody
0.1535484 nose dia/dbody
2.8709679 fin2 root chord fraction = cr/dbody
0.2951613 fin2 taper ratio
20.047245 fin2 le angle (degrees)
0.8870968 fin2 semi-span fraction = b2/dbody
1.0000000 x loc of fin2 (% totlen)
7.9804306 autopilot time on delay - tdelay
0.7944882 autopilot time constant - tau
0.7816536 autopilot damping coef - zeta
57.857143 cross over frequency - cohz
6.6190476 pronav gain -pronvg
72.888885 initial launch angle (degrees)
40
Aero Code: Aerodsn
Range: 700.9 km
Initial Mass: 12602 kg
Flight Time: 444.1 s
Figure 16: Case 2 missile external geometry
Table 11: Case 2 GA variables
Value GA variable name
4.0000000 propellant type
1.2954991 equivalence ratio
940.31311 chamber pressure (psi)
38.152493 nozzle throat area (in^2)
23.606653 nozzle expansion ratio
0.6600000 fractional nozzle length
78.935028 burn time (sec)
4400.0000 payload mass (lbs)
3.5396826 missile body diameter (ft)
3.4047618 nose length/dbody
0.1535484 nose dia/dbody
0.6129032 fin2 root chord fraction = cr/dbody
0.8596774 fin2 taper ratio
22.834646 fin2 le angle (degrees)
0.6935484 fin2 semi-span fraction = b2/dbody
0.9857143 x loc of fin2 (% totlen)
3000.0000 autopilot time on delay - tdelay
0.5244095 autopilot time constant - tau
0.5578740 autopilot damping coef - zeta
63.571430 cross over frequency - cohz
4.3333335 pronav gain -pronvg
85.317459 initial launch angle (degrees)
41
Aero Code: Missile Datcom
Range: 503.8 km
Initial Mass: 10711.7 kg
Flight Time: 366.9 s
Figure 17: Case 3 missile external geometry
Table 12: Case 3 GA variables
Value GA variable name
4.0999999 propellant type
1.1751468 equivalence ratio
1019.56950 chamber pressure (psi)
32.385143 nozzle throat area (in^2)
9.657535 nozzle expansion ratio
0.9000000 fractional nozzle length
67.547630 burn time (sec)
4400.0000 payload mass (lbs)
3.4126985 missile body diameter (ft)
2.2142856 nose length/dbody
0.1187097 nose dia/dbody
2.1935484 fin2 root chord fraction = cr/dbody
0.3403226 fin2 taper ratio
5.6456695 fin2 le angle (degrees)
0.8387097 fin2 semi-span fraction = b2/dbody
0.9571428 x loc of fin2 (% totlen)
2998.0000 autopilot time on delay - tdelay
0.7614173 autopilot time constant - tau
0.9629921 autopilot damping coef - zeta
72.142860 cross over frequency - cohz
1.4761904 pronav gain -pronvg
84.857140 initial launch angle (degrees)
42
Aero Code: Missile Datcom
Range: 698.1 km
Initial Mass: 12084 kg
Flight Time: 440.2 s
Figure 18: Case 4 missile external geometry
Table 13: Case 4 GA variables
Value GA variable name
4.0000000 propellant type
1.0048923 equivalence ratio
946.18396 chamber pressure (psi)
36.686218 nozzle throat area (in^2)
18.692759 nozzle expansion ratio
0.8200000 fractional nozzle length
77.176353 burn time (sec)
4400.0000 payload mass (lbs)
3.5396826 missile body diameter (ft)
3.8015873 nose length/dbody
0.0722581 nose dia/dbody
1.0645162 fin2 root chord fraction = cr/dbody
0.3403226 fin2 taper ratio
10.755905 fin2 le angle (degrees)
0.5000000 fin2 semi-span fraction = b2/dbody
0.9500000 x loc of fin2 (% totlen)
2998.0000 autopilot time on delay - tdelay
0.2157480 autopilot time constant - tau
0.6388977 autopilot damping coef - zeta
72.142860 cross over frequency - cohz
1.4761904 pronav gain -pronvg
85.777779 initial launch angle (degrees)
43
44
Figure 19: Missile external geometry comparison
3.3 Aerodynamic Guided Results
While Aerodsn shows good agreement with Missile Datcom for unguided missile
designs, comparing optimized designs of guided missiles is a much better test. The
aerodynamic analysis plays a much more critical role when the aerodynamic surfaces are
actively being used to direct the missile to a target. The following results compare
guided missile designs that were optimized using the two aerodynamic codes. The goals
were set to minimize the miss distance to a target and minimize system mass, both
common goals in real-world missile development. For the optimization, the target was
set at 122 km (400,000 ft) in the x-direction (down range), 7.62 km (25,000 ft) in the y-
direction, and moving with a velocity of -15.24 m/s (-50 ft/sec) on the y-direction. Each
case had 100 members per generation and was run for 100 generations. The necessary
Missile 1 Missile 2 Missile 4 Missile 3
number of members per generation is dependent on the number of bits required to define
the design space.
4
A plot of the convergence history for these cases is given in Figure 20
and shows there is little increase in fitness for either design during the last 50 generations.
The stair-stepping convergence common to GA optimizations can also be clearly seen in
this figure.
Figure 20: Convergence history
Figures 21 and 22 show the two resulting missile designs with the corresponding
aerodynamics code, miss distance, take-off weight and flight time listed. Both missiles
were able to hit the target but there are some differences in the designs. The Missile
Datcom optimized missile is slightly longer, but much slimmer and lighter than the
Aerodsn missile. Most notably, the diameter of the Aerodsn missile is over a foot larger
than the Missile Datcom design as can be seen in Tables 14 and 15 which provide a full
45
46
list of the GA variables for each design. Both missiles have the fins placed as far aft as
possible, and the flight times only differ by 16 seconds. The trajectories of these flights
are plotted in Figure 23. The Aerodsn missile takes a much higher altitude approach than
does the Missile Datcom designed missile.
The optimized missile configurations were also flown with the aerodynamic code
not used for their optimization, and these trajectories are also shown in Figure 23. When
the Missile Datcom optimized missile was flown using Aerodsn, the program predicted
that the missile would land over 24 km from the target; it did not have the range to reach
the goal. Missile Datcom, however, predicts that the Aerodsn optimized missile will hit
the target. These results suggest that Aerodsn may be over predicting the drag on a
missile. On the other hand, Missile Datcom might be overly optimistic and could be
under predicting the drag. It is impossible to tell from this analysis which aerodynamic
predictor is more accurate, but it is a safe assumption that the Aerodsn optimized missile
is a more conservative design since both aerodynamic codes will fly it to the target. But,
if minimizing weight is a major goal, Missile Datcom clearly predicts that this flight can
be made with a much lighter missile. Regardless, the GA produced designs are similar to
current real-world missile configurations and both codes agree that the target can be
reached with aerodynamic control.
Aero Code: Aerodsn
Miss Distance: 0.01 m
Initial Mass: 6066 kg
Flight Time: 250.6 s
Figure 21: Aerodsn optimized, guided missile external geometry
Table 14: GA variables for Aerodsn optimized missile
Value GA variable name
4.09999990 propellant type
1.18982390 equivalence ratio
734.833680 chamber pressure (psi)
35.4643210 nozzle throat area (in^2)
10.0273970 nozzle expansion ratio
0.75999999 fractional nozzle length
34.6604800 burn time (sec)
4400.00000 payload mass (lbs)
4.04761890 missile body diameter (ft)
3.12698410 nose length/dbody
0.03741936 nose dia/dbody
0.50000000 fin2 root chord fraction = cr/dbody
0.25000000 fin2 taper ratio
1.92913390 fin2 le angle (degrees)
0.88709676 fin2 semi-span fraction = b2/dbody
1.00000000 x loc of fin2 (% totlen)
12.1232880 autopilot time on delay - tdelay
0.52992123 autopilot time constant - tau
0.99000001 autopilot damping coef - zeta
60.7142870 cross over frequency - cohz
2.71428560 pronav gain -pronvg
68.7460330 initial launch angle (degrees)
47
Aero Code: Missile Datcom
Miss Distance: 0.20 m
Initial Mass: 4799 kg
Flight Time: 234.1 s
Figure 22: Missile Datcom optimized, guided missile external geometry
Table 15: GA variables for Datcom optimized missile
Value GA variable name
4.0000000 propellant type
1.2778865 equivalence ratio
752.44617 chamber pressure (psi)
23.636364 nozzle throat area (in^2)
8.2837572 nozzle expansion ratio
0.7800000 fractional nozzle length
32.857841 burn time (sec)
4400.0000 payload mass (lbs)
3.0317461 missile body diameter (ft)
3.6428571 nose length/dbody
0.0316129 nose dia/dbody
0.5000000 fin2 root chord fraction = cr/dbody
0.6112903 fin2 taper ratio
27.944881 fin2 le angle (degrees)
0.5000000 fin2 semi-span fraction = b2/dbody
1.0000000 x loc of fin2 (% totlen)
24.608610 autopilot time on delay - tdelay
0.7393701 autopilot time constant - tau
0.9437008 autopilot damping coef - zeta
63.571430 cross over frequency - cohz
4.5238094 pronav gain -pronvg
74.730156 initial launch angle (degrees)
48
Figure 23: Aerodynamically controlled flight trajectories
3.4 Vane Control Guided Results
The jet vane control system model has been integrated into the liquid performance
model. Results from GA runs to optimize a variety of missiles are presented here. Three
types of missiles were considered so performance comparisons could be made. These
include a missile with no active control system, an aerodynamically controlled missile,
and a missile with a vane control system. For each of these optimization runs, the target
was placed at x=122 km (400,000 ft), y=7.62 km (25,000 ft), and at z=0 km. The target
was kept stationary and each missile had a payload of 2000 kg. The goals were set to
minimize the miss distance and minimize the take-off weight. The aerodynamic
49
50
prediction for all cases was handled by Aerodsn. The results are presented below,
starting with the missile design that results from the optimization run for each case. After
an optimized missile design of each control type was obtained, the target?s position was
moved to several different locations and each optimized design was flown again,
attempting to hit the new targets. Clearly, the unguided missile design is not affected by
a change in the position of the target, but it is still shown in each plot for reference.
The first optimized design, shown in Figure 24, is the missile with no control. It
is about 12 m long with nearly rectangular fins set a noticeable distance from the aft end
of the missile. The missile has a mass of 10300 kg and has a flight time of about 150
seconds. A complete set of design parameters for this missile is provided in Table 16.
As expected, this missile only comes within 7.5 km of the target because it lacks a control
system. The main purpose of this design is to serve as a baseline to which the other cases
can be compared. The trajectory of the missile, plotted in the Figures 27 through 31, is
unchanged regardless of the location of the target.
The external geometry of the missile with aerodynamic control is shown in Figure
25 along with other important details pertaining to its flight. The missile design appears
very reasonable at about 11 meters long with small swept fins placed as far aft as
possible. It is also quite thin with a long sharp nose. This design is predicted to hit the
target with a great deal of accuracy, coming closer than the other two designs. It is much
smaller and lighter than either the unguided or vane control missile, but its flight time is
also much longer. As can be seen from the list of GA variables in Table 17, this
particular design has a burn time of only about 32 seconds. However, it is able to use its
51
aerodynamic control to glide the rest of the way into the target. This fact explains its low
take-off weight but relatively long flight time.
Figure 26 provides the results from the vane control missile optimization run.
Compared to the missile with aerodynamic control, this design is much larger, weighing
almost 3000 kg more even though their respective optimization runs had the same goal of
minimizing the initial weight. This result is not unexpected though because this type of
control system can only provide control when the missile is thrusting. As a result, the
GA selects long burn times in order to provide control for as long as possible. This
substantially increases the weight of the missile because of the additional propellant that
must be carried. The aerodynamically controlled missile is not required to carry as much
propellant to reach the target, but it does fly significantly slower because thrust is only
provided for a short period of time. Flight time could be added as a third goal and this
would most likely bring the weight of the aerodynamically controlled missile closer to
that of the vane controlled design.
Aero Code: Aerodsn
Miss Distance: 7.46 km
Initial Mass: 10301 kg
Flight Time: 148.05 s
Figure 24: Ballistic missile external geometry
Table 16: GA variables for optimized, unguided missile
Value GA variable name
4.0999999 propellant type
1.9236791 equivalence ratio
1139.9218 chamber pressure (psi)
45.043991 nozzle throat area (in^2)
9.6046963 nozzle expansion ratio
0.8000000 fractional nozzle length
39.892525 burn time (sec)
4400.0000 payload mass (lbs)
4.1111112 missile body diameter (ft)
2.4920635 nose length/dbody
0.0210000 nose dia/dbody
0.9516130 fin2 root chord fraction = cr/dbody
0.8145161 fin2 taper ratio
1.0000000 fin2 le angle (degrees)
1.0322580 fin2 semi-span fraction = b2/dbody
0.9000000 x loc of fin2 (% totlen)
499.00000 autopilot time on delay ? tdelay
0.6015748 autopilot time constant ? tau
0.5038583 autopilot damping coef ? zeta
69.285713 cross over frequency ? cohz
1.2857143 pronav gain ?pronvg
67.825394 initial launch angle (degrees)
52
Aero Code: Aerodsn
Miss Distance: 0.1 m
Initial Mass: 6565 kg
Flight Time: 436.7 s
Figure 25: Aerodynamic control missile external geometry
Table 17: GA variables for optimized, aerodynamically controlled missile
Value GA variable name
4.0999999 propellant type
1.9442271 equivalence ratio
740.70447 chamber pressure (psi)
43.333336 nozzle throat area (in^2)
24.399218 nozzle expansion ratio
0.7400000 fractional nozzle length
31.758671 burn time (sec)
4400.0000 payload mass (lbs)
4.0476189 missile body diameter (ft)
3.5634921 nose length/dbody
0.0722581 nose dia/dbody
0.6129032 fin2 root chord fraction = cr/dbody
0.7016129 fin2 taper ratio
19.582678 fin2 le angle (degrees)
0.8870968 fin2 semi-span fraction = b2/dbody
1.0000000 x loc of fin2 (% totlen)
12.350294 autopilot time on delay ? tdelay
0.1440945 autopilot time constant ? tau
0.9900000 autopilot damping coef ? zeta
60.714287 cross over frequency ? cohz
6.3333335 pronav gain ?pronvg
68.285713 initial launch angle (degrees)
53
Aero Code: Aerodsn
Miss Distance: 18.8 m
Initial Mass: 9442 kg
Flight Time: 164.8 s
Figure 26: Vane control missile external geometry
Table 18: GA variables for optimized, vane controlled missile
Value GA variable name
4.0999999 propellant type
0.7348337 equivalence ratio
1075.3424 chamber pressure (psi)
26.666668 nozzle throat area (in^2)
15.311154 nozzle expansion ratio
0.7800000 fractional nozzle length
64.601860 burn time (sec)
4400.0000 payload mass (lbs)
3.4126985 missile body diameter (ft)
2.7698412 nose length/dbody
0.0258065 nose dia/dbody
2.0806453 fin2 root chord fraction = cr/dbody
0.2951613 fin2 taper ratio
49.779530 fin2 le angle (degrees)
1.0806452 fin2 semi-span fraction = b2/dbody
1.0000000 x loc of fin2 (% totlen)
15.982388 autopilot time on delay - tdelay
0.4803150 autopilot time constant - tau
0.6890551 autopilot damping coef - zeta
69.285713 cross over frequency - cohz
2.6190476 pronav gain -pronvg
77.031746 initial launch angle (degrees)
54
55
The optimized missile designs for an unguided case, an aerodynamically
controlled case, and a vane controlled case have been established. The resulting missiles
have been flown to various target locations which are listed in Table 19 to demonstrate
the effect of the control systems. Figure 27 plots the trajectory of each optimized missile
flying to the baseline target location. The vane controlled and aerodynamically
controlled missiles both impact the ground very near the target locations despite having
significantly different flight paths. The vane control missile turns toward the target early
in its flight and flies straight for the majority of its time in the air. The aerodynamically
controlled missile, however, takes a lower altitude approach and continually corrects its
flight path, curving back to the target during the last few seconds of flight. It is no
surprise that these designs hit the target because they were optimized to do so.
Moving the target to different locations emphasizes the effect of each control
system on the missile flights. Figures 27 through 31 present trajectory plots for the three
different missiles aimed at the target locations listed in Table 19. The second target
location has the target placed at -7.62 km (-25000 ft) in the y-direction while keeping the
distance downrange the same. This change should have little effect on the accuracy of
the missiles because only the direction of the flight changes. As Figure 28 illustrates
though, the vane controlled missile impacts over 300 m from the target while the
aerodynamic control case is right on target once again. This vane controlled design
actually flies too far in the negative y-direction. It is apparent that the vane control case
has the physical capability of reaching the target at this location, but the proportional
navigation control system does not direct it to the correct location when the target is on
the opposite side of the x-axis.
56
The third target location forces the designs to fly significantly farther away from
the launch point. Neither design is able to fly very close to the target location in this case
although the aerodynamically controlled missile lands considerably closer once again as
shown in Figure 29. This result is obviously a side effect of minimizing the take-off
weight of the missile designs; both designs lack the thrust needed to reach a target this far
from the launch point. It appears that the fin controlled missile would hit the target if it
had an adequate propulsion system, but the vane controlled design is unable to fly in the
direction of the target.
The fourth target location result, shown in Figure 30, demonstrates what happens
when the target is moved closer to the launch point. The aerodynamically controlled
missile now has no problem hitting the target. But the vane controlled missile is only
able to come within 13 km of hitting the target. This missile is able to successfully
shorten its flight, but the control system is not able to make the adjustments needed to
force the missile to land at 3.05 km in the y-direction.
The fifth and final target position tested takes advantage of the GA?s capability to
simulate a missile performance with moving targets. The target was set to move at 15.24
m/s (50 ft/sec) in the y-direction, starting from the baseline target position. The
placement of the two target dots in Figure 31 accounts for the differences in position of
the target at the time of each missile?s impact. The aerodynamically controlled missile is
still able to hit the target even though it is moving. The vane controlled missile performs
quite well, only landing about 360 m from the target. This result is surprising because
vane control theoretically should not respond well to a moving target since control is lost
57
after burnout. It is clear that this particular missile is highly optimized for hitting a target
near the baseline location, and does not perform well when moved elsewhere.
Although the results indicate that aerodynamic control seems to be a clear winner
when it comes to minimizing weight and miss distance, it does have a drawback.
Aerodynamic control systems do not provide adequate force to control the missile at low
Mach numbers. Just after launch, fins on a missile have little effect because the
freestream dynamic pressure is very low. This time period early in the flight is where a
jet vane control system is highly effective. High dynamic pressure in the nozzle, relative
to the freestream dynamic pressure, produces large forces and moments on the vanes
which steer the missile. For this reason, vanes are historically used for stabilization and
pitch control in missiles shortly after take-off. As previously discussed, vanes are
considerably less effective as the flight speed increases and of course have no effect once
burnout occurs. So while vane control systems are poor choices when attempting to hit a
moving target, they can serve an important purpose which has not been investigated in
this research.
It should also be acknowledged that many vane control missiles, such as those
similar to the SCUD, would rarely be aimed in a direction other than directly toward the
intended target. The target position for this research was deliberately placed to test the
control system models. Furthermore, SCUD class missiles have a pre-programmed flight
path that is not well-modeled by the proportional navigation system used in this research.
To accurately simulate this type of missile, more information about the specific guidance
algorithm used by the SCUD would have to be known.
Table 19: Target data for test cases
Target Position
X (ft) Y (ft) Z (ft) Vx (ft/s) Vy (ft/s)
Target 1 (baseline) 400000 25000 0 0 0
Target 2 400000 -25000 0 0 0
Target 3 500000 25000 0 0 0
Target 4 300000 10000 0 0 0
Target 5 400000 25000 0 0 50
Vane Control
18.8
164.8
Aero Control
0.10
436.7
Miss Distance (m)
Time of Flight (s)
Figure 27: Trajectory plots for target 1
58
Aero Control Vane Control
Miss Distance (m) 0.10 319.8
Time of Flight (s) 436.8 165.1
Figure 28: Trajectory plots for target 2
59
Aero Control Vane Control
Miss Distance (m) 7985.5 18108.4
Time of Flight (s) 579.5 176.3
Figure 29: Trajectory plots for target 3
60
Aero Control Vane Control
Miss Distance (m) 0.15 12749.7
Time of Flight (s) 292.1 146.7
Figure 30: Trajectory plots for target 4
61
62
Aero Control Vane Control
Miss Distance (m) 0.72 359.2
Time of Flight (s) 439.1 165.3
Figure 31: Trajectory plots for target 5
63
4. CONCLUSIONS AND RECOMMENDATIONS
A program utilizing a genetic algorithm to optimize aerodynamically controlled
missile systems has been upgraded and a method of optimizing vane controlled missile
systems has been developed. The liquid performance model was validated against a
known missile configuration. Two different aerodynamic analysis fast predictor codes
were used and their results compared to verify their predictions. A method of
determining the specific impulse as a function of equivalence ratio was also developed
and used in the optimization program. A jet vane control system model based on
Evvard?s theory was integrated into the optimization program and validated by
comparing the vane force prediction with an estimation from linear supersonic
aerodynamic theory. Optimized missiles with no control, aerodynamic control, and vane
control were produced and their performance was compared. The suite of performance
codes and accompanying GA were shown to be an effective missile optimization tool.
The GA-based optimization code is a powerful tool which allows liquid missile
systems to be optimized very quickly with a wide range of inputs and constraints. The
optimization of unguided and aerodynamically controlled missiles using Aerodsn has
been shown to be very effective but there are several suggestions and improvements that
would make the code even more robust. In regards to the variable I
sp
upgrade, propellant
combinations that still have constant values for specific impulse should be updated in the
future when the appropriate thermochemical data becomes available.
64
While the addition of Missile Datcom adds another level of sophistication to the
aerodynamic analysis capabilities of the code, it requires more computational time than
Aerodsn. For this reason, it is not recommended that it be used as the primary
aerodynamic prediction code. In addition, future versions of the program would benefit
from a more complete aeroprediction routine. It is suggested that the aeroprediction be
extended into the hypersonic range using the modified Newtonian flow model.
36
Newtonian theory provides quick and accurate results when the Mach number is large or
the flow deflection angle is large. In fact, this model was used in the preliminary design
of the Space Shuttle Orbiter.
36
For the vane control model, the dimensions of the vanes, which are
nondimensionalized by the nozzle exit plane diameter, should be input as GA variables
instead of constants. It is recommended that the thrust decrement be validated in some
way and that the real gas effects be considered in future revisions. The vane actuators
and physical configuration, which were not considered, should be accounted for within
the mass properties model and aerodynamic analysis. There is currently no adequate
method of optimizing a combined vane and aerodynamically controlled missile as the
control systems would have to share one set of guidance and autopilot parameters.
Future revisions might be able to avoid this by having separate sets of the control system
GA variables for each method of control. Furthermore, as demonstrated by the results, a
proportional navigation control algorithm is most likely not the best option for a vane
controlled missile. Other control algorithms, such as a line-of-sight model or those
unique to a specific class of missile, should be investigated in order to produce more
realistic vane control results.
65
REFERENCES
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Supersonic Speeds?, NACA Technical Note No. 1382, Flight Propulsion
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Speeds?, NACA Technical Note No. 1585, Flight Propulsion Research
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Virginia, May 1950.
30. Mirels, H., ?Theoretical Wave Drag and Lift of Thin Supersonic Ring Airfoils,?
NACA Technical Note No. 1678, Flight Propulsion Laboratory, Cleveland, Ohio,
August 1948.
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for Thin Wings at Supersonic Speeds,? NACA Technical Note No. 1689, Flight
Propulsion Research Laboratory, Cleveland, Ohio, August 1948.
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Thesis, Auburn University, Dec 16, 2005.
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Vane Control Effectiveness,? AIAA-81-1897, AIAA Atmospheric Flight
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69
APPENDIX A: GA Input File
.false. ; micro
.false. ; pareto
.false. ; steady_state
.false. ; maximize
.true. ; elitist
.true. ; creep
.false. ; uniform
.true. ; restart
.true. ; remove_dup
.false. ; niche
.true. ; phenotype
0.5 ; niche diversity percentile goal
61722 ; iseed
0.9 ; pcross
0.005 ; pmutation
0.05 ; pcreep
1 ; ngoals
1. ; xgls(j)
1. ; domst
2550 ; convrg_chk (end of group2)
27 ; no_para
'kprop 1' , 4.1 , 4.0 , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'far 2' , 2.0 , 0.5 , .005 , .false. ;xmax,xmin,resolution,niche_par
'po 3' , 2000. , 500. , 5.00 , .true. ;xmax,xmin,resolution,niche_par
'athroat 4' , 60. , 10. , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'eps 5' , 30. , 3. , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'lf 6' , 0.9 , 0.6 , 0.05 , .false. ;xmax,xmin,resolution,niche_par
'tb 7' , 120.0 , 30.0 , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'paymass 8' , 4401. , 4400. , 25.0 , .false. ;xmax,xmin,resolution,niche_par
'dbody 9' , 5.0 , 1.0 , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'lnose 10' , 4.0 , 1.5 , .1 , .false. ;xmax,xmin,resolution,niche_par
'dnose 11' , .20 , .02 , .01 , .false. ;xmax,xmin,resolution,niche_par
'crfin1 12' , 0.002 , .001 , 0.001 , .false. ;xmax,xmin,resolution,niche_par
'trfin1 13' , 0.95 , 0.25 , 0.05 , .false. ;xmax,xmin,resolution,niche_par
'angLE1 14' , 60.0 , 1.00 , 1.00 , .false. ;xmax,xmin,resolution,niche_par
'b2fin1 15' , 2.0 , 0.01 , 0.01 , .false. ;xmax,xmin,resolution,niche_par
'xcrfn1 16' , 0.50 , 0.10 , 0.01 , .false. ;xmax,xmin,resolution,niche_par
'crfin2 17' , 4.00 , 0.50 , 0.20 , .false. ;xmax,xmin,resolution,niche_par
'trfin2 18' , 0.95 , 0.25 , 0.05 , .false. ;xmax,xmin,resolution,niche_par
'angLE2 19' , 60.0 , 1.00 , 1.00 , .false. ;xmax,xmin,resolution,niche_par
'b2fin2 20' , 2.00 , 0.50 , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'xtefn2 21' , 1.00 , 0.90 , 0.1 , .false. ;xmax,xmin,resolution,niche_par
'tdelay 22' , 30.0 , 1.0 , 1.0 , .false. ;xmax,xmin,resolution,niche_par
'tau 23' , 0.80 , 0.10 , 0.01 , .false. ;xmax,xmin,resolution,niche_par
'zeta 24' , 0.99 , 0.50 , 0.01 , .false. ;xmax,xmin,resolution,niche_par
'wcr 25' , 75.0 , 55.0 , 5.00 , .false. ;xmax,xmin,resolution,niche_par
'pronvg 26' , 7.0 , 1.0 , 0.20 , .false. ;xmax,xmin,resolution,niche_par
'theta0 27' , 89.0 , 60.0 , 1.00 , .false. ;xmax,xmin,resolution,niche_par
1 ; ifreq
300 ; mempops
100 ; maxgen
70
APPENDIX B: Global Array Variables
3.141592654d0 ;YY 1,1 - pi
2.0926435d7 ;YY 1,2 - re radius of the earth ft
32.174d0 ;YY 1,3 - gc acceleration of gravity ft/sec^2
57.29577951d0 ;YY 1,4 - deg/rad degrees per radian
0.0d0 ;YY 1,5 - sref reference area ft^2
0.0d0 ;YY 1,6 - lref reference length ft
Densities
0.282d0 ;YY 2,1 - rhocfair cyl fairing material lbm/in3
0.282d0 ;YY 2,2 - rhcncone nose cone fairing matl lbm/in3
0.19d0 ;YY 2,3 - rhon nozzle material lbm/in3
0.08d0 ;YY 2,4 - rhocarbn carbon lbm/in3
0.289d0 ;YY 2,5 - rhosteel steel lbm/in3
0.0975d0 ;YY 2,6 - rhoalum aluminum lbm/in3
0.00d0 ;YY 2,7 - rhopay1 payload1 lbm/in3
0.00d0 ;YY 2,8 - rhopay2 payload2 lbm/in3
0.065d0 ;YY 2,9 - rhoelec1 electronics1 lbm/in3
0.00d0 ;YY 2,10 - rhoelec2 electronics2 lbm/in3
0.0639d0 ;YY 2,11 - rhowar1 warhead1 lbm/in3
0.00d0 ;YY 2,12 - rhowar2 warhead2 lbm/in3
0.00d0 ;YY 2,13 - rhobox1 box 1 lbm/in3
0.0639d0 ;YY 2,14 - rhobox2 box 2 lbm/in3
0.00d0 ;YY 2,15 - rhopump1 oxygen pump lbm/in3
0.00d0 ;YY 2,16 - rhopump2 fuel pump lbm/in3
0.282d0 ;YY 2,17 - rhotank1 tank1 material lbm/in3
0.282d0 ;YY 2,18 - rhotank2 tank2 material lbm/in3
0.282d0 ;YY 2,19 - rhogast compressed gas tank lbm/in3
0.00d0 ;YY 2,20 - rhofin1 average dendity of fin1 lbm/in3
0.00d0 ;YY 2,21 - rhofin2 average dendity of fin2 lbm/in3
0.00d0 ;YY 2,22 - rhofin3 average dendity of fin3 lbm/in3
0.00d0 ;YY 2,23 - rhosenr1 sensor 1 material lbm/in3
0.00d0 ;YY 2,24 - rhosenr2 sensor 2 material lbm/in3
0.00d0 ;YY 2,25 - rholine1 insulator 1 material lbm/in3
0.00d0 ;YY 2,26 - rholine2 insulator 2 material lbm/in3
0.00d0 ;YY 2,27 - rhof liquid fuel lbm/in3
0.00d0 ;YY 2,28 - rhoox liquid oxidizer lbm/in3
0.00d0 ;YY 2,29 - rhototal density of missile lbm/in3
0.0105d0 ;YY 2,30 - rhoeng engine anf thrust str. lbm/in3
0.0061d0 ;YY 2,31 - rhogimbal gimbals lbm/in3
0.00d0 ;YY 2,32 - rhogas compressed gas lbm/in3
0.10d0 ;YY 2,33 - rhoservo servo actuators lbm/in3
0.00d0 ;YY 2,34 - rhobox3 box 3 lbm/in3
0.00d0 ;YY 2,35 - rhobox4 box 4 lbm/in3
0.00d0 ;YY 2,36 - rhobox5 box 5 lbm/in3
0.00d0 ;YY 2,37 - rhobox6 box 6 lbm/in3
masses
2200.0d0 ;YY 3,1 - warmass warhead mass lbm
0.0d0 ;YY 3,2 - elecmas1 elec 1 mass lbm
0.00d0 ;YY 3,3 - elecmas2 elec 2 mass lbm
0.00d0 ;YY 3,4 - insulmf1 fuel tank 1 insulator mass lbm
0.00d0 ;YY 3,5 - insulmf2 fuel tank 2 insulator mass lbm
0.00d0 ;YY 3,6 - insulmox1 ox tank 1 insulator mass lbm
0.00d0 ;YY 3,7 - insulmox2 ox tank 2 insulator mass lbm
0.00d0 ;YY 3,8 - compgas1 com.gas mass, stage 1 lbm
0.00d0 ;YY 3,9 - compgas2 com.gas mass, stage 2 lbm
0.00d0 ;YY 3,10 - comptank1 com.gas tank mass, stage 1 lbm
0.00d0 ;YY 3,11 - comptank2 com.gas tank mass, stage 2 lbm
0.00d0 ;YY 3,12 - fuelm1 fuel mass, stage 1 lbm
0.00d0 ;YY 3,13 - fuelm2 fuel mass, stage 2 lbm
0.00d0 ;YY 3,14 - oxm1 oxidizer mass, stage 1 lbm
0.00d0 ;YY 3,15 - oxm2 oxidizer mass, stage 2 lbm
0.00d0 ;YY 3,16 - ftankm1 fuel tank mass, stage 1 lbm
0.00d0 ;YY 3,17 - ftankm2 fuel tank mass, stage 2 lbm
0.00d0 ;YY 3,18 - oxtankm1 oxidizer tank mass, stage 1 lbm
0.00d0 ;YY 3,19 - oxtankm2 oxidizer tank mass, stage 2 lbm
0.00d0 ;YY 3,20 - engmass1 engine mass, stage 1 lbm
0.00d0 ;YY 3,21 - engmass2 engine mass, stage 2 lbm
71
0.00d0 ;YY 3,22 - nosfairm1 nose fairing mass, stage 1 lbm
0.00d0 ;YY 3,23 - nosfairm2 nose fairing mass, stage 2 lbm
0.00d0 ;YY 3,24 - cylfairm1 cyl fairing mass, stage 1 lbm
0.00d0 ;YY 3,25 - cylfairm2 cyl fairing mass, stage 2 lbm
0.00d0 ;YY 3,26 - finm1 total finset 1 mass lbm
0.00d0 ;YY 3,27 - finm2 total finset 2 mass lbm
0.00d0 ;YY 3,28 - finm3 total finset 3 mass lbm
0.00d0 ;YY 3,29 - gimm1 gimbal mass, stage 1 lbm
0.00d0 ;YY 3,30 - gimm2 gimbal mass, stage 2 lbm
0.00d0 ;YY 3,31 - wirem1 wiring mass, stage 1 lbm
0.00d0 ;YY 3,32 - wirem2 wiring mass, stage 2 lbm
0.00d0 ;YY 3,33 - entmas1 nozzle entrance mass 1 lbm
0.00d0 ;YY 3,34 - thrmas1 nozzle throat mass 1 lbm
0.00d0 ;YY 3,35 - bellmas1 bell nozzle mass 1 lbm
0.00d0 ;YY 3,36 - entmas2 nozzle entrance mass 2 lbm
0.00d0 ;YY 3,37 - thrmas2 nozzle throat mass 2 lbm
0.00d0 ;YY 3,38 - bellmas2 bell nozzle mass 2 lbm
0.00d0 ;YY 3,39 - nozmas1 nozzle mass 1 lbm
0.00d0 ;YY 3,40 - nozmas2 nozzle mass 2 lbm
0.00d0 ;YY 3,41 - servomas servo actuators mass lbm
0.00d0 ;YY 3,42 - sensorsmas sensors mass lbm
2.00d0 ;YY 3,43 - boxmas1 box-1 mass lbm
00.0d0 ;YY 3,44 - boxmas2 box-2 mass lbm
0.00d0 ;YY 3,45 - boxmas3 box-3 mass lbm
0.00d0 ;YY 3,46 - boxmas4 box-4 mass lbm
0.00d0 ;YY 3,47 - boxmas5 box-5 mass lbm
0.00d0 ;YY 3,48 - boxmas6 box-6 mass lbm
0.00d0 ;YY 3,49 - totalmas initial total mass lbm
center of gravity
0.00d0 ;YY 4,1 - warcg warhead cg ft
0.00d0 ;YY 4,2 - eleccg1 elec 1 cg ft
0.00d0 ;YY 4,3 - eleccg2 elec 2 cg ft
0.00d0 ;YY 4,4 - insulgf1 fuel tank 1 insulator cg ft
0.00d0 ;YY 4,5 - insulgf2 fuel tank 2 insulator cg ft
0.00d0 ;YY 4,6 - insulgox1 ox tank 1 insulator cg ft
0.00d0 ;YY 4,7 - insulgox2 ox tank 2 insulator cg ft
0.00d0 ;YY 4,8 - compgacg1 com.gas cg, stage 1 ft
0.00d0 ;YY 4,9 - compgacg2 com.gas cg, stage 2 ft
0.00d0 ;YY 4,10 - comtancg1 com.gas tank cg, stage 1 ft
0.00d0 ;YY 4,11 - comtancg2 com.gas tank cg, stage 2 ft
0.00d0 ;YY 4,12 - fuelcg1 fuel cg, stage 1 ft
0.00d0 ;YY 4,13 - fuelcg2 fuel cg, stage 2 ft
0.00d0 ;YY 4,14 - oxcg1 oxidizer cg, stage 1 ft
0.00d0 ;YY 4,15 - oxcg2 oxidizer cg, stage 2 ft
0.00d0 ;YY 4,16 - ftankcg1 fuel tank cg, stage 1 ft
0.00d0 ;YY 4,17 - ftankcg2 fuel tank cg, stage 2 ft
0.00d0 ;YY 4,18 - oxtankcg1 oxidizer tank cg, stage 1 ft
0.00d0 ;YY 4,19 - oxtankcg2 oxidizer tank cg, stage 2 ft
0.00d0 ;YY 4,20 - engcg1 engine cg, stage 1 ft
0.00d0 ;YY 4,21 - engcg2 engine cg, stage 2 ft
0.00d0 ;YY 4,22 - nosfairg1 nose fairing cg, stage 1 ft
0.00d0 ;YY 4,23 - nosfairg2 nose fairing cg, stage 2 ft
0.00d0 ;YY 4,24 - cylfairg1 cyl fairing cg, stage 1 ft
0.00d0 ;YY 4,25 - cylfairg2 cyl fairing cg, stage 2 ft
0.00d0 ;YY 4,26 - fincg1 total finset 1 cg ft
0.00d0 ;YY 4,27 - fincg2 total finset 2 cg ft
0.00d0 ;YY 4,28 - fincg3 total finset 3 cg ft
0.00d0 ;YY 4,29 - gimcg1 gimbal cg, stage 1 ft
0.00d0 ;YY 4,30 - gimcg2 gimbal cg, stage 2 ft
0.00d0 ;YY 4,31 - wirecg1 wiring cg, stage 1 ft
0.00d0 ;YY 4,32 - wirecg2 wiring cg, stage 2 ft
0.00d0 ;YY 4,33 - entcg1 nozzle entrance cg 1 in
0.00d0 ;YY 4,34 - thrcg1 nozzle throat cg 1 in
0.00d0 ;YY 4,35 - bellcg1 bell nozzle cg 1 in
0.00d0 ;YY 4,36 - entcg2 nozzle entrance cg 2 in
0.00d0 ;YY 4,37 - thrcg2 nozzle throat cg 2 in
0.00d0 ;YY 4,38 - bellcg2 bell nozzle cg 2 in
0.00d0 ;YY 4,39 - nozcg1 nozzle cg 1 in
0.00d0 ;YY 4,40 - nozcg2 nozzle cg 2 in
72
0.00d0 ;YY 4,41 - totalcg initial overall cg ft
0.00d0 ;YY 4,42 - servocg servo actuator cg ft
0.00d0 ;YY 4,43 - cgbox1 box 1 cg ft
0.00d0 ;YY 4,44 - cgbox2 box 2 cg ft
0.00d0 ;YY 4,45 - cgbox3 box 3 cg ft
0.00d0 ;YY 4,46 - cgbox4 box 4 cg ft
0.00d0 ;YY 4,47 - cgbox5 box 5 cg ft
0.00d0 ;YY 4,48 - cgbox6 box 6 cg ft
0.00d0 ;YY 4,49 - avioncg avionics cg ft
moments of inertia
0.00d0 ;YY 5,1 - warix warhead ix lbm-ft2
0.00d0 ;YY 5,2 - elecix1 elec 1 ix lbm-ft2
0.00d0 ;YY 5,3 - elecix2 elec 2 ix lbm-ft2
0.00d0 ;YY 5,4 - insuixf1 fuel tank 1 insulator ix lbm-ft2
0.00d0 ;YY 5,5 - insuixf2 fuel tank 2 insulator ix lbm-ft2
0.00d0 ;YY 5,6 - insuixox1 ox tank 1 insulator ix lbm-ft2
0.00d0 ;YY 5,7 - insuixox2 ox tank 2 insulator ix lbm-ft2
0.00d0 ;YY 5,8 - compgaix1 com.gas ix, stage 1 lbm-ft2
0.00d0 ;YY 5,9 - compgaix2 com.gas ix, stage 2 lbm-ft2
0.00d0 ;YY 5,10 - comtanix1 com.gas tank ix, stage 1 lbm-ft2
0.00d0 ;YY 5,11 - comtanix2 com.gas tank ix, stage 2 lbm-ft2
0.00d0 ;YY 5,12 - fuelix1 fuel ix, stage 1 lbm-ft2
0.00d0 ;YY 5,13 - fuelix2 fuel ix, stage 2 lbm-ft2
0.00d0 ;YY 5,14 - oxix1 oxidizer ix, stage 1 lbm-ft2
0.00d0 ;YY 5,15 - oxix2 oxidizer ix, stage 2 lbm-ft2
0.00d0 ;YY 5,16 - ftankix1 fuel tank ix, stage 1 lbm-ft2
0.00d0 ;YY 5,17 - ftankix2 fuel tank ix, stage 2 lbm-ft2
0.00d0 ;YY 5,18 - oxtankix1 oxidizer tank ix, stage 1 lbm-ft2
0.00d0 ;YY 5,19 - oxtankix2 oxidizer tank ix, stage 2 lbm-ft2
0.00d0 ;YY 5,20 - engix1 engine ix, stage 1 lbm-ft2
0.00d0 ;YY 5,21 - engix2 engine ix, stage 2 lbm-ft2
0.00d0 ;YY 5,22 - nosfaiix1 nose fairing ix, stage 1 lbm-ft2
0.00d0 ;YY 5,23 - nosfaiix2 nose fairing ix, stage 2 lbm-ft2
0.00d0 ;YY 5,24 - cylfaiix1 cyl fairing ix, stage 1 lbm-ft2
0.00d0 ;YY 5,25 - cylfaiix2 cyl fairing ix, stage 2 lbm-ft2
0.00d0 ;YY 5,26 - finix1 total finset 1 ix lbm-ft2
0.00d0 ;YY 5,27 - finix2 total finset 2 ix lbm-ft2
0.00d0 ;YY 5,28 - finix3 total finset 3 ix lbm-ft2
0.00d0 ;YY 5,29 - gimix1 gimbal ix, stage 1 lbm-ft2
0.00d0 ;YY 5,30 - gimix2 gimbal ix, stage 2 lbm-ft2
0.00d0 ;YY 5,31 - wireix1 wiring ix, stage 1 lbm-ft2
0.00d0 ;YY 5,32 - wireix2 wiring ix, stage 2 lbm-ft2
0.00d0 ;YY 5,33 - entix1 nozzle entrance ix 1 lbm-ft2
0.00d0 ;YY 5,34 - thrix1 nozzle throat ix 1 lbm-ft2
0.00d0 ;YY 5,35 - bellix1 bell nozzle ix 1 lbm-ft2
0.00d0 ;YY 5,36 - entix2 nozzle entrance ix 2 lbm-ft2
0.00d0 ;YY 5,37 - thrix2 nozzle throat ix 2 lbm-ft2
0.00d0 ;YY 5,38 - bellix2 bell nozzle ix 2 lbm-ft2
0.00d0 ;YY 5,39 - nozix1 nozzle ix 1 lbm-ft2
0.00d0 ;YY 5,40 - nozix2 nozzle ix 2 lbm-ft2
0.00d0 ;YY 5,41 - totalix initial overall ix lbm-ft2
0.00d0 ;YY 5,42 - wariy warhead iy lbm-ft2
0.00d0 ;YY 5,43 - eleciy1 elec 1 iy lbm-ft2
0.00d0 ;YY 5,44 - eleciy2 elec 2 iy lbm-ft2
0.00d0 ;YY 5,45 - insuiyf1 fuel tank 1 insulator iy lbm-ft2
0.00d0 ;YY 5,46 - insuiyf2 fuel tank 2 insulator iy lbm-ft2
0.00d0 ;YY 5,47 - insuiyox1 ox tank 1 insulator iy lbm-ft2
0.00d0 ;YY 5,48 - insuiyox2 ox tank 2 insulator iy lbm-ft2
0.00d0 ;YY 5,49 - compgaiy1 com.gas iy, stage 1 lbm-ft2
0.00d0 ;YY 5,50 - compgaiy2 com.gas iy, stage 2 lbm-ft2
0.00d0 ;YY 5,51 - comtaniy1 com.gas tank iy, stage 1 lbm-ft2
0.00d0 ;YY 5,52 - comtaniy2 com.gas tank iy, stage 2 lbm-ft2
0.00d0 ;YY 5,53 - fueliy1 fuel iy, stage 1 lbm-ft2
0.00d0 ;YY 5,54 - fueliy2 fuel iy, stage 2 lbm-ft2
0.00d0 ;YY 5,55 - oxiy1 oxidizer iy, stage 1 lbm-ft2
0.00d0 ;YY 5,56 - oxiy2 oxidizer iy, stage 2 lbm-ft2
0.00d0 ;YY 5,57 - ftankiy1 fuel tank iy, stage 1 lbm-ft2
0.00d0 ;YY 5,58 - ftankiy2 fuel tank iy, stage 2 lbm-ft2
0.00d0 ;YY 5,59 - oxtankiy1 oxidizer tank iy, stage 1 lbm-ft2
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0.00d0 ;YY 5,60 - oxtankiy2 oxidizer tank iy, stage 2 lbm-ft2
0.00d0 ;YY 5,61 - engiy1 engine iy, stage 1 lbm-ft2
0.00d0 ;YY 5,62 - engiy2 engine iy, stage 2 lbm-ft2
0.00d0 ;YY 5,63 - nosfaiiy1 nose fairing iy, stage 1 lbm-ft2
0.00d0 ;YY 5,64 - nosfaiiy2 nose fairing iy, stage 2 lbm-ft2
0.00d0 ;YY 5,65 - cylfaiiy1 cyl fairing iy, stage 1 lbm-ft2
0.00d0 ;YY 5,66 - cylfaiiy2 cyl fairing iy, stage 2 lbm-ft2
0.00d0 ;YY 5,67 - finiy1 total finset 1 iy lbm-ft2
0.00d0 ;YY 5,68 - finiy2 total finset 2 iy lbm-ft2
0.00d0 ;YY 5,69 - finiy3 total finset 3 iy lbm-ft2
0.00d0 ;YY 5,70 - gimiy1 gimbal iy, stage 1 lbm-ft2
0.00d0 ;YY 5,71 - gimiy2 gimbal iy, stage 2 lbm-ft2
0.00d0 ;YY 5,72 - wireiy1 wiring iy, stage 1 lbm-ft2
0.00d0 ;YY 5,73 - wireiy2 wiring iy, stage 2 lbm-ft2
0.00d0 ;YY 5,74 - entiy1 nozzle entrance iy 1 lbm-ft2
0.00d0 ;YY 5,75 - thriy1 nozzle throat iy 1 lbm-ft2
0.00d0 ;YY 5,76 - belliy1 bell nozzle iy 1 lbm-ft2
0.00d0 ;YY 5,77 - entiy2 nozzle entrance iy 2 lbm-ft2
0.00d0 ;YY 5,78 - thriy2 nozzle throat iy 2 lbm-ft2
0.00d0 ;YY 5,79 - belliy2 bell nozzle iy 2 lbm-ft2
0.00d0 ;YY 5,80 - noziy1 nozzle iy 1 lbm-ft2
0.00d0 ;YY 5,81 - noziy2 nozzle iy 2 lbm-ft2
0.00d0 ;YY 5,82 - totaliy initial overall iy lbm-ft2
0.00d0 ;YY 5,83 - wariz warhead iz lbm-ft2
0.00d0 ;YY 5,84 - eleciz1 elec 1 iz lbm-ft2
0.00d0 ;YY 5,85 - eleciz2 elec 2 iz lbm-ft2
0.00d0 ;YY 5,86 - insuizf1 fuel tank 1 insulator iz lbm-ft2
0.00d0 ;YY 5,87 - insuizf2 fuel tank 2 insulator iz lbm-ft2
0.00d0 ;YY 5,88 - insuizox1 ox tank 1 insulator iz lbm-ft2
0.00d0 ;YY 5,89 - insuizox2 ox tank 2 insulator iz lbm-ft2
0.00d0 ;YY 5,90 - compgaiz1 com.gas iz, stage 1 lbm-ft2
0.00d0 ;YY 5,91 - compgaiz2 com.gas iz, stage 2 lbm-ft2
0.00d0 ;YY 5,92 - comtaniz1 com.gas tank iz, stage 1 lbm-ft2
0.00d0 ;YY 5,93 - comtaniz2 com.gas tank iz, stage 2 lbm-ft2
0.00d0 ;YY 5,94 - fueliz1 fuel iz, stage 1 lbm-ft2
0.00d0 ;YY 5,95 - fueliz2 fuel iz, stage 2 lbm-ft2
0.00d0 ;YY 5,96 - oxiz1 oxidizer iz, stage 1 lbm-ft2
0.00d0 ;YY 5,97 - oxiz2 oxidizer iz, stage 2 lbm-ft2
0.00d0 ;YY 5,98 - ftankiz1 fuel tank iz, stage 1 lbm-ft2
0.00d0 ;YY 5,99 - ftankiz2 fuel tank iz, stage 2 lbm-ft2
0.00d0 ;YY 5,100 - oxtankiz1 oxidizer tank iz, stage 1 lbm-ft2
0.00d0 ;YY 5,101 - oxtankiz2 oxidizer tank iz, stage 2 lbm-ft2
0.00d0 ;YY 5,102 - engiz1 engine iz, stage 1 lbm-ft2
0.00d0 ;YY 5,103 - engiz2 engine iz, stage 2 lbm-ft2
0.00d0 ;YY 5,104 - nosfaiiz1 nose fairing iz, stage 1 lbm-ft2
0.00d0 ;YY 5,105 - nosfaiiz2 nose fairing iz, stage 2 lbm-ft2
0.00d0 ;YY 5,106 - cylfaiiz1 cyl fairing iz, stage 1 lbm-ft2
0.00d0 ;YY 5,107 - cylfaiiz2 cyl fairing iz, stage 2 lbm-ft2
0.00d0 ;YY 5,108 - finiz1 total finset 1 iz lbm-ft2
0.00d0 ;YY 5,109 - finiz2 total finset 2 iz lbm-ft2
0.00d0 ;YY 5,110 - finiz3 total finset 3 iz lbm-ft2
0.00d0 ;YY 5,111 - gimiz1 gimbal iz, stage 1 lbm-ft2
0.00d0 ;YY 5,112 - gimiz2 gimbal iz, stage 2 lbm-ft2
0.00d0 ;YY 5,113 - wireiz1 wiring iz, stage 1 lbm-ft2
0.00d0 ;YY 5,114 - wireiz2 wiring iz, stage 2 lbm-ft2
0.00d0 ;YY 5,115 - entiz1 nozzle entrance iz 1 lbm-ft2
0.00d0 ;YY 5,116 - thriz1 nozzle throat iz 1 lbm-ft2
0.00d0 ;YY 5,117 - belliz1 bell nozzle iz 1 lbm-ft2
0.00d0 ;YY 5,118 - entiz2 nozzle entrance iz 2 lbm-ft2
0.00d0 ;YY 5,119 - thriz2 nozzle throat iz 2 lbm-ft2
0.00d0 ;YY 5,120 - belliz2 bell nozzle iz 2 lbm-ft2
0.00d0 ;YY 5,121 - noziz1 nozzle iz 1 lbm-ft2
0.00d0 ;YY 5,122 - noziz2 nozzle iz 2 lbm-ft2
0.00d0 ;YY 5,123 - totaliz initial overall iz lbm-ft2
0.00d0 ;YY 5,124 - servoix servo ix lbm-ft2
0.00d0 ;YY 5,125 - servoiy servo iy lbm-ft2
0.00d0 ;YY 5,126 - servoiz servo iz lbm-ft2
target data
400000.0d0 ;YY 6,1 - xtarg x location of target ft
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25000.0d0 ;YY 6,2 - ytarg y location of target ft
0.0d0 ;YY 6,3 - ztarg z location of target ft
0.0d0 ;YY 6,4 - vxtarg x velocity of target ft/sec
-50.0d0 ;YY 6,5 - vytarg y velocity of target ft/sec
0.0d0 ;YY 6,6 - vztarg z velocity of target ft/sec
initiation of launch data
30.0d0 ;YY 7,1 - xlamda initial latitude deg
86.5d0 ;YY 7,2 - y0 initial longitude deg
1.00d0 ;YY 7,3 - z0 initial altitude deg
0.00d0 ;YY 7,4 - u0 initial u-velocity ft/sec
0.00d0 ;YY 7,5 - v0 initial v-velocity ft/sec
0.00d0 ;YY 7,6 - w0 initial w-velocity ft/sec
-1.0d0 ;YY 7,7 - tht0 initial Euler angle deg
00.0d0 ;YY 7,8 - phi0 initial Euler angle deg
00.0d0 ;YY 7,9 - psi0 initial Euler angle deg
0.00d0 ;YY 7,10 - q0 initial pitch rate deg/sec
0.00d0 ;YY 7,11 - p0 initial roll rate deg/sec
0.00d0 ;YY 7,12 - r0 initial yaw rate deg/sec
0.00d0 ;YY 7,13 - clpct fin cant multiplier
0.00d0 ;YY 7,14 - dxcg0 initial CG-CP offset ft
-1.0d0 ;YY 7,15 - tdelay auto-pilot on delay time sec
-1.0d0 ;YY 7,16 - tau autopilot time const
-1.0d0 ;YY 7,17 - zeta autopilot pitch damping
-1.0d0 ;YY 7,18 - wcr cross over frequency Hz
-1.0d0 ;YY 7,19 - pronvgn pronav gain (guidance)
60.0d0 ;YY 7,20 - rol_wcr cross over freq (roll) rad/sec
45.0d0 ;YY 7,21 - des_ph desired phase mar in roll deg
program lengths,limits and constants
40000.0d0 ;YY 8,1 - tmaxd max flight run time sec
285000.0d0 ;YY 8,2 - fbd max bending stress-1 lb/in2
135000.0d0 ;YY 8,3 - sigmad max motor case stress lb/in2
9000.0d0 ;YY 8,4 - pcmax 1 max chamber pressure lb/in2
50.0d0 ;YY 8,5 - pcmin 1 min chamber pressure lb/in2
0.0d0 ;YY 8,6 - pcmax 2 max chamber pressure lb/in2
0.0d0 ;YY 8,7 - pcmin 2 min chamber pressure lb/in2
500.0d0 ;YY 8,8 - gmax max g-limit
1.50d0 ;YY 8,9 - sfd motor case safety factor
0.0d0 ;YY 8,10 - tipchek dis to TE of fin2 tip ft
15.0d0 ;YY 8,11 - delmax1 maximum fin deflection 1 deg
00.0d0 ;YY 8,12 - delmax2 maximum fin deflection 2 deg
00.0d0 ;YY 8,13 - delmax3 maximum fin deflection 3 deg
00.0d0 ;YY 8,14 - rodradi1 actuator1 rod radius in
00.0d0 ;YY 8,15 - rodradi2 actuator2 rod radius in
0.00d0 ;YY 8,16 - warlen length of warhead ft
0.00d0 ;YY 8,17 - eleclen1 length of electronics 1 ft
0.00d0 ;YY 8,18 - eleclen2 length of electronics 2 ft
0.00d0 ;YY 8,19 - comgas1 length comp gas tank ft
0.00d0 ;YY 8,20 - tanklen length comp gas tank ft
0.00d0 ;YY 8,21 - fueltank1 length of fuel tank 1 ft
0.00d0 ;YY 8,22 - fueltank2 length of fuel tank 2 ft
0.00d0 ;YY 8,23 - oxtank1 length of oxidizer tank 1 ft
0.00d0 ;YY 8,24 - oxtank2 length of oxidizer tank 2 ft
0.00d0 ;YY 8,25 - enginel1 length of engine 1 ft
0.00d0 ;YY 8,26 - enginel2 length of engine 2 ft
0.00d0 ;YY 8,27 - ncone1 length of nosecone 1 ft
0.00d0 ;YY 8,28 - ncone2 length of nosecone 2 ft
0.00d0 ;YY 8,29 - fair1 cyl fairing length, stage 1 ft
0.00d0 ;YY 8,30 - fair2 cyl fairing length, stage 2 ft
0.00d0 ;YY 8,31 - giml1 gimbal length, stage 1 ft
0.00d0 ;YY 8,32 - giml2 gimbal length, stage 2 ft
0.00d0 ;YY 8,33 - wirel1 wiring length, stage 1 ft
0.00d0 ;YY 8,34 - wirel2 wiring length, stage 2 ft
100.d0 ;YY 8,35 - pprop propellant press. level psi
100.d0 ;YY 8,36 - delp regulator delta p psi
6000.d0 ;YY 8,37 - pair pressurization tank press psi
530.0d0 ;YY 8,38 - tair pressurization tank temp deg R
0.00d0 ;YY 8,39 - nozlen overall nozzle length ft
0.00d0 ;YY 8,40 - aspect actual missile fineness ratio
0.00d0 ;YY 8,41 - boxlen1 length of box 1 ft
75
0.00d0 ;YY 8,42 - boxlen2 length of box 2 ft
0.00d0 ;YY 8,43 - boxlen3 length of box 3 ft
0.00d0 ;YY 8,44 - boxlen4 length of box 4 ft
0.00d0 ;YY 8,45 - boxlen5 length of box 5 ft
0.00d0 ;YY 8,46 - boxlen6 length of box 6 ft
0.00d0 ;YY 8,47 - servolen length of servo actuators ft
0.00d0 ;YY 8,48 - areanose surface area of nose ft^2
0.00d0 ;YY 8,49 - vnose1 volume of nose section ft^3
external geometry default variables
0.00d0 ;YY 9,1 - lcentr1 cyl. section length 1 ft
-1.0d0 ;YY 9,2 - dcyl1 centr sec dia - stage 1 ft
0.00d0 ;YY 9,3 - lcentr2 cyl. section length 2 ft
0.00d0 ;YY 9,4 - dcyl2 centr sec dia - stage 2 ft
0.00d0 ;YY 9,5 - dumy variable
0.00d0 ;YY 9,6 - totlen total body length ft
0.0d0 ;YY 9,7 - typfin1 0-blades; 1-wrap around 1
4.0d0 ;YY 9,8 - nfin1 number of fins in fin set 1
60.0d0 ;YY 9,9 - sweple1 sweep of le in fin set 1 deg
0.4d0 ;YY 9,10 - xlefin1 dis to LE of finset 1 (% body)
00.0d0 ;YY 9,11 - xhlfin1 dis to hinge line-Fin set 1 in
1.00d0 ;YY 9,12 - crfin1 root chord length-Fin set 1 ft
0.99d0 ;YY 9,13 - tapfin1 taper ratio of fin1 1
0.50d0 ;YY 9,14 - b2fin1 semi-span-fin set 1 ft
0.10d0 ;YY 9,15 - tmaxfin1 fin1 thickness ratio set 1
0.0d0 ;YY 9,16 - typfin2 0-blades; 1-wrap around 2
4.0d0 ;YY 9,17 - nfin2 number of fins in fin set 2
-1.0d0 ;YY 9,18 - sweple2 sweep of le in fin set 2 deg
0.0d0 ;YY 9,19 - xlefin2 dis to LE of finset 2 (% body)
0.0d0 ;YY 9,20 - xhlfin2 dis to hinge line-Fin set 2 ft
0.0d0 ;YY 9,21 - crfin2 root chord length-Fin set 2 ft
-1.0d0 ;YY 9,22 - tapfin2 taper ratio of fin2 2
0.0d0 ;YY 9,23 - b2fin2 semi-span-Fin set 2 ft
0.10d0 ;YY 9,24 - tmaxfin2 thickness ratio of fin2 2
00.0d0 ;YY 9,25 - typfin3 0-blades; 1-wrap around 3
00.0d0 ;YY 9,26 - nfin3 number of fins in fin set 3
00.0d0 ;YY 9,27 - sweple3 sweep of le in fin set 3 deg
00.0d0 ;YY 9,28 - xlefin3 dis to LE of Fin set 3 (% body)
00.0d0 ;YY 9,29 - xhlfin3 dis to hinge line-Fin set 3 ft
0.00d0 ;YY 9,30 - crfin3 root chord length-Fin set 3 ft
0.00d0 ;YY 9,31 - tapfin3 taper ratio of finset 3
0.00d0 ;YY 9,32 - b2fin3 semi-span-Fin set 3 ft
0.10d0 ;YY 9,33 - tmaxfin3 thickness ratio finset 3
0.00d0 ;YY 9,34 - dtail diameter of body at fin2 in
0.00d0 ;YY 9,35 - fin1del fin1 deflection:1-yes, 0-no
1.00d0 ;YY 9,36 - fin2del fin2 deflection: 1-yes, 0-no
0.00d0 ;YY 9,37 - ybarfin1 spnwise loc of fin1 CP ft
0.00d0 ;YY 9,38 - ybarfin2 spnwise loc of fin2 CP ft
0.00d0 ;YY 9,39 - ybarfin3 spnwise loc of fin22 CP ft
0.00d0 ;YY 9,40 - lnose length of the nose ft
-1.0d0 ;YY 9,41 - dnose ratio of (nose dia)/DB
00.0d0 ;YY 9,42 - bnose radius of nose ft
0.00d0 ;YY 9,43 - rchamb radius of combust chamber in
0.50d0 ;YY 9,44 - hang fin2 tip hang over / Dbody
1.00d0 ;YY 9,45 - internal noz 1 - yes; 0 - no
liquid rocket motor default variables
-1.0d0 ;YY 10,1 - prop_typ1 propellant combo 1
0.0d0 ;YY 10,2 - prop_typ2 propellant combo 2
-1.0d0 ;YY 10,3 - po1 chamber pressure 1 psi
0.00d0 ;YY 10,4 - po2 chamber pressure 2 psi
-1.0d0 ;YY 10,5 - athroat1 area of throat stage 1 in2
00.0d0 ;YY 10,6 - athroat2 area of throat stage 2 in2
-1.0d0 ;YY 10,7 - eps1 expansion ratio stage 1
0.00d0 ;YY 10,8 - eps2 expansion ratio stage 2
75.0d0 ;YY 10,9 - thein1 convergence angle for noz1 deg
0.00d0 ;YY 10,10 - thein2 convergence angle for noz2 deg
00.0d0 ;YY 10,11 - angexit1 noz exit angle stage 1 deg
00.0d0 ;YY 10,12 - nozlen1 nozzle length stage 1 in
0.382d0 ;YY 10,13 - sigtht1 nozzle contour fraction 1 in
00.0d0 ;YY 10,14 - nozlen2 nozzle length stage 2 in
76
0.382d0 ;YY 10,15 - sigtht2 nozzle contour fraction 2 in
00.0d0 ;YY 10,16 - thangle1 throat angle match 1 deg
00.0d0 ;YY 10,17 - thangle2 throat angle match 2 deg
-1.0d0 ;YY 10,18 - fnl fractional nozzle length 1
0.00d0 ;YY 10,19 - fn2 fractional nozzle length 2
0.98d0 ;YY 10,20 - etamu1 nozzle 1 efficiency
0.98d0 ;YY 10,21 - etamu2 nozzle 2 efficiency
0.00d0 ;YY 10,22 - thrust1 engine1 thrust =f(time) lbs
0.00d0 ;YY 10,23 - thrust2 engine2 thrust =f(time) lbs
0.00d0 ;YY 10,24 - tvac1 vacuum thrust, stage 1 lbs
0.00d0 ;YY 10,25 - tvac2 vacuum thrust, stage 2 lbs
-1.0d0 ;YY 10,26 - tb1 motor burn time, stg 1 sec
0.00d0 ;YY 10,27 - tb2 motor burn time, stg 2 sec
0.00d0 ;YY 10,28 - volf1 fuel tank volume, stg 1 ft3
0.00d0 ;YY 10,29 - volf2 fuel tank volume, stg 2 ft3
0.00d0 ;YY 10,30 - volox1 oxidizer tank volume, stg 1 ft3
0.00d0 ;YY 10,31 - volox2 oxidizer tank volume, stg 2 ft3
0.00d0 ;YY 10,32 - endf1 fuel tank radius, stg 1 ft
0.00d0 ;YY 10,33 - midf1 fuel tank ctr len, stg 1 ft
0.00d0 ;YY 10,34 - endf2 fuel tank radius, stg 2 ft
0.00d0 ;YY 10,35 - midf2 fuel tank ctr len, stg 2 ft
0.00d0 ;YY 10,36 - endox1 oxidizer tank radius, stg 1 ft
0.00d0 ;YY 10,37 - midox1 oxi tank cntr len, stg 1 ft
0.00d0 ;YY 10,38 - endox2 oxi tank radius, stg 2 ft
0.00d0 ;YY 10,39 - midox2 oxi tank cntr len, stg 2 ft
0.00d0 ;YY 10,40 - rmix1 propellant mix ratio, stg 1
0.00d0 ;YY 10,41 - rmix2 propellant mix ratio, stg 2
0.00d0 ;YY 10,42 - mdot1 prop consume rate, stg 1 lbm/sec
0.00d0 ;YY 10,43 - mdot2 prop consume rate, stg 1 lbm/sec
-1.0d0 ;YY 10,44 - eqr equivalence ratio
0.00d0 ;YY 10,45 - thrust10 initial motor thrust 1 lbs
0.00d0 ;YY 10,46 - thrust20 initial motor thrust 2 lbs
200.0d0 ;YY 10,47 - xrecord max. no. table record points
1.0d0 ;YY 10,48 - typgas compres gas type:he-1,air-2
nozzle contour variables
00.0d0 ;YY 11,1 - theti1 arc-circle upstream angle deg
00.0d0 ;YY 11,2 - aone1 parabolic arc constant
00.0d0 ;YY 11,3 - bone1 parabolic arc constant
00.0d0 ;YY 11,4 - rzero1 parabolic arc constant
00.0d0 ;YY 11,5 - entlen1 length of entrance section in
00.0d0 ;YY 11,6 - xstar1 axial loc of the throat 1 in
00.0d0 ;YY 11,7 - xp x loc of circ¶b in
00.0d0 ;YY 11,8 - yp y loc of circ¶b in
00.0d0 ;YY 11,9 - aone2 parabolic arc constant
00.0d0 ;YY 11,10 - bone2 parabolic arc constant
00.0d0 ;YY 11,11 - rzero2 parabolic arc constant
00.0d0 ;YY 11,12 - entlen2 length of entrance section in
00.0d0 ;YY 11,13 - xstar2 axial loc of the throat 2 in
00.0d0 ;YY 11,14 - xnozzle2 x location nozzle 2 in
0.1d0 ;YY 11,15 - tnoz1 nozzle thickness, stage 1 in
00.0d0 ;YY 11,16 - tnoz2 nozzle thickness, stage 2 in
atmospheric data and aero constants
00.0d0 ;YY 12,1 - pinf atmospheric pressure psf
00.0d0 ;YY 12,2 - tinf atmospheric temperature deg R
12.0d0 ;YY 12,3 - nalp number of alpha's in aero tables
37.0d0 ;YY 12,4 - nphi number of roll angls in aero tables
14.0d0 ;YY 12,5 - nmach number of Mach #'s in aero tables
0.0d0 ;YY 12,6 - member member number in the generation
0.0d0 ;YY 12,7 - igen generation number
27.0d0 ;YY 12,8 - novar No. of variables in 'gannl.dat'
22.0d0 ;YY 12,9 - nparts No of main parts in the missile
1.0d0 ;YY 12,10 - ispeed 0- subsonic; 1 supersonic
aerodynamic constants data
00.0d0 ;yy 13,1 - tma(1) table mach number (1)
00.0d0 ;yy 13,2 - tma(2) table mach number (2)
00.0d0 ;yy 13,3 - tma(3) table mach number (3)
0.0d0 ;yy 13,4 - tma(4) table mach number (4)
0.0d0 ;yy 13,5 - tma(5) table mach number (5)
0.0d0 ;yy 13,6 - tma(6) table mach number (6)
77
0.0d0 ;yy 13,7 - tma(7) table mach number (7)
0.0d0 ;yy 13,8 - tma(8) table mach number (8)
00.0d0 ;yy 13,9 - tma(9) table mach number (9)
00.0d0 ;yy 13,10 - tma(10) table mach number (10)
00.0d0 ;yy 13,11 - tma(11) table mach number (11)
00.0d0 ;yy 13,12 - tma(12) table mach number (12)
00.0d0 ;yy 13,13 - tma(13) table mach number (13)
00.0d0 ;yy 13,14 - tma(14) table mach number (14)
0.0d0 ;yy 13,15 - talp(1) table alpha (1) deg
0.0d0 ;yy 13,16 - talp(2) table alpha (2) deg
0.0d0 ;yy 13,17 - talp(3) table alpha (3) deg
0.0d0 ;yy 13,18 - talp(4) table alpha (4) deg
00.0d0 ;yy 13,19 - talp(5) table alpha (5) deg
00.0d0 ;yy 13,20 - talp(6) table alpha (6) deg
00.0d0 ;yy 13,21 - talp(7) table alpha (7) deg
00.0d0 ;yy 13,22 - talp(8) table alpha (8) deg
00.0d0 ;yy 13,23 - talp(9) table alpha (9) deg
00.0d0 ;yy 13,24 - talp(10) table alpha (10) deg
00.0d0 ;yy 13,25 - talp(11) table alpha (11) deg
00.0d0 ;yy 13,26 - talp(12) table alpha (12) deg
GA variable data
00.0d0 ;yy 14,1 - xray(1) propellant type
00.0d0 ;yy 14,2 - xray(2) equivalence ratio
00.0d0 ;yy 14,3 - xray(3) chamber pressure psi
00.0d0 ;yy 14,4 - xray(4) nozzle throat area in2
00.0d0 ;yy 14,5 - xray(5) nozzle expansion ratio
00.0d0 ;yy 14,6 - xray(6) fractional nozzle length
00.0d0 ;yy 14,7 - xray(7) burn time sec
00.0d0 ;yy 14,8 - xray(8) payload mass lbm
00.0d0 ;yy 14,9 - xray(9) missile body diameter ft
00.0d0 ;yy 14,10 - xray(10) length of nose/dbody
00.0d0 ;yy 14,11 - xray(11) dia of nose/dbody
00.0d0 ;yy 14,12 - xray(12) fin1 root chord/dbody
00.0d0 ;yy 14,13 - xray(13) fin1 taper ratio
00.0d0 ;yy 14,14 - xray(14) fin1 le angle deg
00.0d0 ;yy 14,15 - xray(15) fin1 b/2 ratio = b2fin1/dbody
00.0d0 ;yy 14,16 - xray(16) x loc of fin 1 % body length
00.0d0 ;yy 14,17 - xray(17) fin2 root chord/dbody
00.0d0 ;yy 14,18 - xray(18) fin2 taper ratio
00.0d0 ;yy 14,19 - xray(19) fin2 le angle deg
00.0d0 ;yy 14,20 - xray(20) fin2 b/2 ratio = b2fin2/dbody
00.0d0 ;yy 14,21 - xray(21) xTE loc of fin 2 % body length
00.0d0 ;yy 14,22 - xray(22) autopilot time delay sec
00.0d0 ;yy 14,23 - xray(23) autopilot time constant
00.0d0 ;yy 14,24 - xray(24) autopilot damping
00.0d0 ;yy 14,25 - xray(25) cross over frequency hz
00.0d0 ;yy 14,26 - xray(26) pronav gain
00.0d0 ;yy 14,27 - xray(27) initial launch angle deg
reverse engineering/trajectory data
62.0d0 ;YY 15,1 - taltburn motor burnout time sec
24.5d0 ;YY 15,2 - altburn motor burnout altitude km
266.64d0 ;YY 15,3 - tflight total flight time sec
92.00d0 ;YY 15,4 - altmax apogee km
901.68d0 ;YY 15,5 - maxrange maximum range km
1.0d0 ;YY 15,6 - numgoals number of GA traj match goals
12.55d0 ;YY 15,7 - fineness desired missile fineness ratio
900000.d0 ;YY 15,8 - maxThrust maximum limit on thrust lbs