LAUNCH VEHICLE PERFORMANCE ENHANCEMENT USING
AERODYNAMIC ASSIST
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.
_______________________
Brian Robert McDavid
Certificate of Approval:
________________________
John E. Burkhalter
Professor Emeritus
Aerospace Engineering
_________________________
Roy J. Hartfield, Jr. Chair
Professor
Aerospace Engineering
________________________
Brian Thurow
Assistant Professor
Aerospace Engineering
_________________________
George T. Flowers
Dean
Graduate School
LAUNCH VEHICLE PERFORMANCE ENHANCEMENT USING AERODYNAMIC
ASSIST
Brian Robert McDavid
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
August 9
th
, 2008
iii
LAUNCH VEHICLE PERFORMANCE ENHANCEMENT USING AERODYNAMIC
ASSIST
Brian Robert McDavid
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon request of individuals or institutions and at their expense. The author reserves all
publication rights
Signature of Author
Date of Graduation
iv
VITA
Brian Robert McDavid was born on September 14
th
, 1982, in Brunswick, Maine
to Harry and Leslie McDavid. He graduated from Bob Jones High School in Madison,
Alabama and began attending Auburn University in 2001. As an undergraduate, he was
inducted into the Aerospace Engineering Honor Society Sigma Gamma Tau and the
national engineering honor society of Tau Beta Pi. Brian graduated Cum Laude in May
2006 with a Bachelor of Aerospace Engineering degree. He entered the Auburn
University Graduate School in Fall 2006 to pursue a Master of Science degree in
Aerospace Engineering. On December 29
th
, 2006, Brian married his beautiful wife Nicole
(Cann) McDavid.
v
THESIS ABSTRACT
LAUNCH VEHICLE PERFORMANCE ENHANCEMENT USING AERODYNAMIC
ASSIST
Brian Robert McDavid
Master of Science, August 9 2008
(B.A.E., Auburn University, 2006)
66 Typed Pages
Directed by Roy J. Hartfield, Jr.
A complete preliminary design model of a three-stage solid-fuel launch vehicle
has been combined with a genetic algorithm to perform an optimization study with the
goal to enhance performance using aerodynamic assist. Three studies have been
completed which include improving the suborbital and orbital flights of a modern
intercontinental ballistic missile and improving on the orbital flight of a generic three-
stage launch vehicle. The performance is enhanced by varying the geometric definition of
the attached wing structure and the internal propellant geometry while the external
geometry remains constant. Initial system weights and propellant mass fractions were
found to decrease with the addition of the wing structure. Further enhancement involves a
payload increase by 10% with a negligible increase in system weight, and a propellant
mass decrease by 5.2% without impairing the flight performance.
vi
ACKNOWLEDGEMENTS
The author would like to thank Dr. Roy Hartfield and Dr. John Burkhalter for
their technical and professional guidance and support. The author also would like to
thank Dr. Murray Anderson, the author of the 3.1 IMPROVE Genetic Algorithm, without
which this thesis would not have been possible. The author would also like to thank his
parents Harry and Leslie and sister Amanda for their support and encouragement, and his
wife Nicole for all her patience and support provided throughout the graduate school
process.
vii
Style manual of journal used
The American Institute of Aeronautics and Astronautics Journal
Computer software used
Improve 3.1 Genetic Algorithm, Tecplot 10, Compaq Visual Fortran, Microsoft
Excel, Microsoft Word
viii
TABLE OF CONTENTS
LIST OF TABLES............................................................................................................. ix
LIST OF FIGURES ............................................................................................................ x
NOMENCLATURE ......................................................................................................... xii
1.0 INTRODUCTION .................................................................................................. 1
2.0 MODEL BACKGROUND ..................................................................................... 3
2.1 GENETIC ALGORITHM .................................................................................. 3
2.2 ADVANTAGES OF THE GENETIC ALGORITHM ....................................... 5
2.3 PRELIMINARY DESIGN MODEL .................................................................. 8
2.3.1 OBJECTIVE FUNCTION AND GA INITIALIZATION.......................... 9
2.3.2 DESIGN AND MISSION PARAMETERS ............................................. 11
2.3.3 PREDICTIVE MODEL............................................................................ 15
3.0 VALIDATION...................................................................................................... 23
4.0 AERODYNAMIC PERFORMANCE ENHANCEMENT................................... 27
4.1 MINUTEMAN-III SUBORBITAL ENHANCEMENT................................... 29
4.1.1 SUBORBITAL IMPROVEMENT ........................................................... 31
4.1.2 ORBITAL IMPROVEMENT................................................................... 39
4.2 THREE-STAGE ORBITAL ENHANCEMENT.............................................. 43
5.0 SUMMARY.......................................................................................................... 47
REFERENCES ................................................................................................................. 49
ix
LIST OF TABLES
Table 1: GA Design Variables for Minuteman-III ........................................................... 12
Table 2: Constant Mission Parameters ............................................................................. 13
Table 3: Propellant Design Variables ............................................................................... 13
Table 4: Wing and Tail Design Parameters ...................................................................... 14
Table 5: Minuteman-III Parameters.................................................................................. 14
Table 6: Mass Property Components................................................................................ 22
Table 7: Minuteman-III Validation................................................................................... 24
Table 8: PBAA/AP/Al Characteristics (English Units).................................................... 26
Table 9: MM3 Suborbital Enhancement........................................................................... 38
Table 10: MM3 Suborbital Mass Fractions ...................................................................... 38
Table 11: MM3 Orbital Enhancement .............................................................................. 43
Table 12: MM3 Orbital Mass Fractions............................................................................ 43
Table 13: Generic Three-Stage Orbital Enhancement...................................................... 46
Table 14: Generic Three-Stage Mass Fractions................................................................ 46
x
LIST OF FIGURES
Figure 1: Tournament Algorithm........................................................................................ 4
Figure 2: Crossover............................................................................................................. 7
Figure 3: Mutation .............................................................................................................. 8
Figure 4: Optimization Model Outline ............................................................................. 10
Figure 5: GA Population and Generation Setup ............................................................... 12
Figure 6: Bell Nozzle Schematic
30
.................................................................................... 18
Figure 7: Circular Arc Airfoil
30
........................................................................................ 20
Figure 8: Minuteman-III Validation Model...................................................................... 25
Figure 9: Air Density vs. Altitude..................................................................................... 27
Figure 10: Minuteman-III Dynamic Pressure................................................................... 28
Figure 11: Minuteman-III ................................................................................................. 30
Figure 12: Minuteman-III with 2540 Payload .................................................................. 31
Figure 13: Altitude vs. Time (MM3-Wings) .................................................................... 33
Figure 14: Thrust vs. Time (MM3-Wings)....................................................................... 33
Figure 15: Weight vs. Time (MM3-Wings)...................................................................... 34
Figure 16: GA Best Answer Convergence........................................................................ 34
Figure 17: Vehicle Diagram (MM3-Reduced Propellant)................................................ 36
Figure 18: Convergence for MM3-Reduced Propellant ................................................... 36
Figure 19: Vehicle Diagram (MM3-Increased Payload) .................................................. 37
xi
Figure 20: Orbital MM3 GA Convergence....................................................................... 40
Figure 21: Orbital MM3 Wings ........................................................................................ 41
Figure 22: Orbital MM3 Altitude vs. Time ...................................................................... 41
Figure 23: Orbital MM3 Thrust Profile ............................................................................ 42
Figure 24: Orbital MM3 Convergence History ................................................................ 42
Figure 25: Generic Three-Stage Vehicle .......................................................................... 44
Figure 26: Three-Stage Altitude vs. Time ........................................................................ 45
Figure 27: Three-Stage Thrust Profile .............................................................................. 45
xii
NOMENCLATURE
?
m Mass Flow Rate
GA Genetic Algorithm
r Propellant Burning Rate
a Empirical Constant
n Burning Rate Index
P
c
Chamber Pressure
P
e
Exit Pressure
P
a
Ambient Pressure
A
b
Burning Area
?
b
Solid Propellant Density
c
*
Characteristic Velocity
R Specific Gas Constant
? Specific Heat Ratio
T
c
Chamber Temperature
A
*
Throat Area
u
e
Exit Velocity
T Thrust
L
f
Fractional Nozzle Length
MW Molecular Weight
MM3 Minuteman-III
rpvar Propellant Outer Radius
rivar Propellant Inner Radius
fvar Fillet Radius Ratio
eps Epsilon Star Width
ptang Star Point Angle
fn Fractional Nozzle Length Ratio
diath Throat Diameter
rnose Nose Radius Ratio
thet0 Initial Launch Angle
b2tdb Tail Semi Span
crtdb Tail Root Chord Length
trt Taper Ratio Tail
tLEswp Sweep of Leading Edge in Tail Fins
xTEtl Distance to Leading Edge of Tail Fins
b2wdb Wing Semi Span
crwdb Wing Root Chord Length
trw Taper Ratio Wing
xiii
wLEswe Sweep of Leading Edge in Wings
xLEw Distance to Leading Edge of Wings
1
1.0 INTRODUCTION
During the development of the Space Shuttle, the orbiter was designed with wings
which were anticipated for use only during reentry. The initial proposal for launch was
essentially a gravity turn launch which did not make use of lifting aerodynamics. During
the design process, launch studies were being conducted by Woltosz
1,2
to ascertain the
most advantageous launch trajectory using a tool known as Rocket Ascent G-limited
Moment-balanced Optimization Program (RAGMOP). During this optimization exercise,
it was discovered that an ?upside down? launch to orbit could increase payload by 20%
(about 8,000 lb at the time)
1,2
. The reason for this improvement involved the more
efficient use of the orbiter wings for lift production in the upside down configuration
during the atmospheric portion of the ascent.
The payload advantage gained by the change in the ascent trajectory was entirely
free structurally for the Space Shuttle; however, based on the marked improvement in
performance associated with aerodynamic lifting for the shuttle, it is possible that
substantial improvement in net payload to orbit could be obtained for current launch
vehicles using aerodynamic lifting during the first stage burn despite the cost of adding
some mass in the form of wing structure (to the first stage). The potential payoff with
regard to achieving additional payload to orbit warrants the investigation described herein
which makes use of preliminary design level modeling and optimization tools. This study
includes physical modeling of the system components and digitally flying the launch
2
vehicle fitted with candidate wing design configurations through candidate ascent
trajectories. Using this general approach to preliminary design, researchers at Auburn
University have demonstrated substantial performance improvement for a Minotaur-type
vehicle using preliminary design level tools and a genetic algorithm
3
. The current
investigation uses the same preliminary design tools and includes wings to explore the
viability of the concept of using aerodynamic lifting during first phase ascent for a
generic vehicle. Two optimization studies have been completed for this thesis with the
goal of maximizing payload to orbit. The first study was conducted while changing only
the geometric definition of the add-on wing configuration (semi-span, root chord, tip
chord, sweep angle, taper ratio, and position). The first study includes a suborbital
optimization and an orbital optimization. The second study optimized an orbital launch
vehicle similar to the Minuteman-III from the ?ground-up?.
The vehicle configuration for both studies uses a three-stage solid-fuel propulsion
system. The published fuel for the Minuteman-III is polybutadiene-acrylic acid with
ammonium perchlorate and aluminum (PBAA/AP/Al). PBAA has been hardwired in the
model as the propellant selection for every study in this thesis to ensure that performance
gains are associated with the geometric design and aerodynamics rather than with
propellant characteristics. Higher overall performance is expected from launch vehicles
which incorporate advanced design optimization methods, aerodynamic lifting and
advanced propellant chemistry. The propellant choice is fixed, but the grain geometry is
selected by the genetic algorithm.
3
2.0 MODEL BACKGROUND
2.1 GENETIC ALGORITHM
Genetic algorithms (GAs) are a powerful class of evolutionary computing tools in
which elements from biology such as reproduction, inheritance, mutation, selection, and
fitness, are used to solve very complex problems in a wide range of applications. John
Holland presented the method of applying the evolutionary process to solve scientific,
mathematical, and engineering problems in his 1975 book Adaptation in Natural and
Artificial Systems
4
. The benefits of using a GA to design and optimize a model in a set
design space have been well documented. A few specific aerospace applications include
the design and optimization of propellers
5
, freight truck aerodynamics
6
, wings and
airfoils
7,8,9,10
, rockets
11,12
, missiles
13,14,15,16,17,18
, flight trajectories
19
, spacecraft
controls
20,21
, and turbines
22,23,24
.
Genetic algorithms find an optimized solution by breeding new sets of data
(members) over a defined number of generations. The process starts by randomly creating
the first set of members based on a user specified design space. The user constricts the
minimum and maximum values for each design parameter. Each individual member is a
possible solution to the problem. Koza
25
, who worked with Holland to pioneer the first
batch of GAs, states that the genetic algorithm transforms a population (set) of
individuals (or members), each with an associated fitness value, into a new generation of
4
the population using reproduction, crossover, and mutation. Specifically, each member is
analyzed by the performance codes of the design model, and a fitness is assigned to each
member based on how well the member?s performance matched the objective function.
The final solution is the member that has the best fitness at the end of the last generation.
The genetic algorithm used in this effort is the IMPROVE? code, or Implicit
Multi-Objective PaRameter Optimization Via Evolution, and was developed by
Anderson
26
. The IMPROVE? code is a binary encoded tournament based genetic
algorithm. The tournament nomenclature refers to the method employed to create the
members of the new population, and it involves three basic steps. Figure 1 summarizes
the tournament algorithm.
Figure 1: Tournament Algorithm
Two members
selected from
current
population
Fitness
comparison
Member with best
fitness stored in
temporary population
2 members in
temporary
population?
Mutation and crossover
applied to members to
form the new population
No
Yes
5
First, two members of the current population are selected at random and their fitness
values are compared. The member having the better fitness moves to a temporary
population, and the other goes back to the current population. The process repeats to
generate a two member temporary population. Mutation and crossover operations are
performed on the two members in the temporary population, creating two new members
which are placed into the new population. This process continues until the new
population is filled with the correct number of members. The tournament method
therefore creates a new population with members having characteristics, or heredity, from
the previous population but in different combinations which may result in improved
fitness.
In addition to generating the members of the new population via tournament,
elitism is employed. Elitism takes the best performing member of the current population
and moves it to the next population without changing it at all. This is to safe-guard
against the mutated members all performing worse than the best member of the previous
population and sending the GA backwards. Elitism and tournament selection ensure that
the GA will find solutions that continually approach the target fitness. It should be noted
that the use of elitism, particularly with small populations can materially reduce the
genetic diversity of the population and care should be taken to address the adequacy of
the population size when using this option.
2.2 ADVANTAGES OF THE GENETIC ALGORITHM
There are several reasons why the genetic algorithm was chosen for this effort
instead of a gradient marching method. Gradient methods march toward a local
6
maximum or minimum by taking small steps that are proportional to the gradient of the
function. This requires that the objective function be differentiable in every independent
variable. If the function is not completely differentiable, then a singularity will develop
and the ability of the routine to march towards a maximum or minimum will be ruined. In
many systems it is impossible for the objective function to be completely differentiable.
For example, propellant type is not differentiable. A second problem with gradient
methods is that convergence to local optima is more common in design spaces with many
variables. The current preliminary design model requires 37 parameters, and their
derivatives are not easily ascertained. While the GA has a greater likelihood finding a
global optimum solution, obtaining this solution is not guaranteed. However, recent
techniques such as mutation and crossover help the GA to approach the global solution.
Mutation and crossover are powerful tools that help prevent genetic algorithms
from becoming stuck in a local optimum. A design variable is represented in the
IMPROVE? genetic algorithm by a binary string such as 101100101. When the
tournament selects two members to move to the next population, crossover is one of the
methods used to produce the new member, or offspring. The IMPROVE? code uses
single point crossover. In single point crossover, a location is chosen in the binary string
of each parent, and the remaining alleles are swapped from one parent to the other.
Crossover is more easily described by looking at a simple one offspring example as
shown in Figure 2. The numbers in bold are the values transferred to the offspring.
7
Figure 2: Crossover
When crossover is applied, the offspring takes one section of each parent?s genes. The
point at which the parent string is broken depends on the randomly selected crossover
point. Crossover occurrence is based on a set probability within the genetic algorithm
setup file, so sometimes the parent is directly copied to the offspring.
The second function that the genetic algorithm employs is mutation. After the
tournament selection and crossover, some of the offspring has been copied directly from
the parents, and the others have been affected by crossover. In order to ensure genetic
diversity, a small chance allowed for mutation is allowed. Each variable in the model is
represented by a binary string. The 1s and 0s that form a binary string are called alleles.
All of the members and their alleles are looped through, and if the allele is selected for
mutation, it is either changed by a small amount or replaced with a new value. Figure 3
shows an example of mutation. The allele in bold has been chosen for mutation and the
result is a change from a 0 to a 1.
Parent 1
1011010010100110
Parent 2
0011010110110101
Offspring
0011010010100110
8
Figure 3: Mutation
If the GA approaches a local solution, this random change is very useful because it very
often creates a new member that is an improvement and can escape the trap of a local
solution.
2.3 PRELIMINARY DESIGN MODEL
As can be seen from References [5-24], the genetic algorithm is effective at
optimizing a problem when paired with a capable predictive model. The model in this
effort is a suite of FORTRAN codes used to model and simulate the flight of a three-stage
solid fueled rocket. The model was developed by Jenkins, Hartfield, and Burkhalter
15
,
and was modified to include orbital trajectories by Bayley
3
. These codes accurately
predict and simulate the performance of a three-stage solid fueled rocket by modeling the
aerodynamics, mass properties, and propulsion. The six-degree of freedom code manages
all the other codes while it simulates the flight of the missile and updates the performance
characteristics synchronized in time. This approach and this particular model was
validated by Bayley using the Minotaur as a baseline for comparison.
101101011001
101111011001
9
2.3.1 OBJECTIVE FUNCTION AND GA INITIALIZATION
The results of the flight are used to determine the fitness (or how well the member
met the desired optimization goals). The fitness is calculated by sending the appropriate
performance values into the objective function, with the output being the fitness. In this
model, the objective function is a quantitative measure that the GA uses to determine
which members have better performance. Two of the objective functions for this model
are to match a user specified orbital altitude and orbital velocity. These specified values
are chosen before the GA is started. After each member is digitally flown through the
model, values for the orbital altitude and velocity are obtained. Since two of the goals are
to match these values, the objective function compares the obtained value to the desired
value by using equations 1 and 2.
altorb
altorbalt
answer
?
?
1
1 (1)
vorb
vorbv
answer
?
?
1
2 (2)
If these were the only two desired goals, the fitness would be
21 answeranswerfitness ?? (3)
In order to reach the desired altitude and velocity, answer 1 and answer 2 must be
minimized. As answer 1 approaches zero, the actual altitude becomes closer to the
desired altitude. Therefore, the member with the smallest value for the fitness is the best
performing member of the population and its characteristics are carried over into the next
generation. A second method of determining the fitness, pareto, could be used instead of
equation 3. Pareto style optimization separates the goals and attempts to minimize each
10
answer individually instead of the combined answer. Pareto was not used for the studies
in this thesis.
Figure 4 shows a very simplified and basic outline of the model code structure.
The first step in the optimization model is the initialization of the genetic algorithm. One
benefit of the GA is that it does not need an initial starting point. Instead, the GA reads an
input file created by the user which specifies the design space or range (minimum,
maximum, and resolution) for each design variable and the GA creates an initial
population by randomly selecting the values for each design parameter. The GA is binary
encoded and the values in the design space determine the number of bits required to
adequately represent each parameter by equation 4.
Figure 4: Optimization Model Outline
Genetic Algorithm
- gannl.dat
- fitness comparison
- crossover and mutation
- makeup of next generation
Predictive Model
- Mass Properties
- Propulsion
- Aerodynamics
- Six-DOF
- Other Codes
Final
Generation?
No
Yes
End
11
? ?
1
2ln
minmax
ln
?
?
?
?
?
?
? ?
?
resolution
nbits (4)
The variables in equation 4 are discussed in section 2.3.2. The number of bits required for
each parameter is important because the total number of bits influences the recommended
population size (n) by
nbitsn )0.3(? (5)
A large population size is usually needed for a complicated design problem with a large
design space. The maximum population size that the IMPROVE? code can use is set at
400. The recommended number of generations is not as explicitly defined; however a
larger number of generations is more likely to produce an optimum solution. The trade-
off is that a large number of generations and a large population size can lead to
significant computer run times. It is up to the user to determine the appropriate number of
generations and to ascertain whether the solution produced is adequate.
2.3.2 DESIGN AND MISSION PARAMETERS
A section of the gannl.dat setup file used for this study is seen in Table 1. Figure
5 shows a section from the setup file that the GA reads to set the number of populations
and generations. Table 1 and Figure 5 show how the GA reads the design variables and
how the maximum, minimum, resolution, size of the population, and number of
generations are specified. The first column is a truncated description of the design
variable name, followed by the maximum, minimum, and resolution values. The
population size and number of generations are listed at the end.
12
Table 1: GA Design Variables for Minuteman-III
Parameter Maximum Minimum Resolution
rpvar1 0.8000 0.2000 0.0100
rivar1 0.9900 0.0100 0.0100
fvar1 0.2000 0.0100 0.0100
eps1 0.9700 0.1000 0.1000
ptang1 50.0000 10.0000 1.0000
fn1 0.9900 0.6000 0.0100
diath1 35.0000 5.0000 0.1000
rpvar2 0.8000 0.2000 0.0100
rivar2 0.9900 0.0100 0.0100
fvar2 0.2000 0.0100 0.0100
eps2 0.9700 0.5000 0.1000
ptang2 50.0000 10.0000 0.1000
fn2 0.9900 0.6000 0.0100
diath2 35.0000 5.0000 0.1000
rpvar3 0.8000 0.2000 0.0100
rivar3 0.9900 0.0100 0.0100
fvar3 0.2000 0.0100 0.0100
eps3 0.9700 0.5000 0.1000
ptang3 50.0000 10.0000 0.1000
fn3 0.9900 0.6000 0.0100
diath3 35.0000 5.0000 0.1000
rnose 0.7500 0.5000 0.0100
thet0 89.0000 70.0000 1.0000
b2tdb 1.4000 0.1000 0.1000
crtdb 1.2000 0.1000 0.1000
trt 0.9900 0.5000 0.0100
tLEswp 25.0000 5.0000 0.1000
xTEtl 0.9900 0.5000 0.1000
dele0 15.0000 0.0000 0.1000
timeb1 7.0000 0.1000 0.1000
timeb2 35.0000 7.0000 0.1000
timeee 90.0000 15.0000 1.0000
b2wdb 1.5000 0.1000 0.1000
crwdb 1.2000 0.1000 0.1000
trw 0.9900 0.5000 0.1000
wLEswe 25.0000 5.0000 0.1000
xLEw 0.6500 0.0500 0.1000
Figure 5: GA Population and Generation Setup
The launch location must be specified in order to accurately simulate an orbital
trajectory. Table 2 lists four mission parameters that are constant among all the different
optimization cases.
13
Table 2: Constant Mission Parameters
The desired system mass is another important mission parameter, however the
appropriate value is different based on which optimization case is being considered. For
example, the validation of the Minuteman-III has a desired system mass of 79,432 lbm,
whereas in cases where the wings are employed to reduce required propellant mass
through aerodynamic lifting the desired system mass is smaller. These are discussed in
more detail in the appropriate section of this thesis.
The optimization starts with the GA generating a set of 37 design parameters to
describe the launch vehicle. The geometric variables that describe the propellant for each
stage, as well as two external variables are shown in Table 3.
Table 3: Propellant Design Variables
Stages 1, 2, and 3 GA Variable
Propellant Outer Radius Ratio rpvar
Propellant Inner Radius Ratio rivar
Fillet Radius Ratio fvar
Epsilon Star Width eps
Star Point Angle ptang
Fractional Nozzle Length Ratio fn
Throat Diameter diath
Other
Nose Radius Ratio rnose
Initial Launch Angle thet0
Five variables are required to describe the wings/tails as seen in Table 4. All geometric
variables are non-dimensionalized by the body diameter.
Launch Site Vandenberg AFB, CA (34.6? N, 120.6? W)
Launch Direction Due North (0? Azimuth or i = 90?/polar orbit)
Desired Orbital Velocity 22,000 ft/s
Desired Orbital Altitude 750,000 ft
14
Table 4: Wing and Tail Design Parameters
Wings/Tails GA Variable
Semispan b2wdb / b2tdb
Root Chord crwdb / crtdb
Taper Ratio trw / trt
Leading Edge Sweep Angle wLEswe / tLEswp
Leading Edge Location xLEw / tLEtl
The first study takes the Minuteman-III missile and attempts to increase the
payload/reduce the propellant weight, therefore certain external geometric parameters are
hardwired into the predictive model based on Minuteman-III data. These parameters are
shown in Table 5. The payload is the only parameter that changes in some of the
optimization cases. The second study does not constrain the vehicle to match the
Minuteman-III values, therefore the only value hardwired into the model is the stage
propellant.
Table 5: Minuteman-III Parameters
Parameter Minuteman-III Value
Payload
*
2,540 lbm
Stage 1 Length 295.20 in
Stage 1 Diameter 66.00 in
Stage 1 Propellant PBAA/AP/Al
Stage 2 Length 184.00 in
Stage 2 Diameter 52.00 in
Stage 2 Propellant PBAA/AP/Al
Stage 3 Length 90.00 in
Stage 3 Diameter 52.00 in
Stage 3 Propellant PBAA/AP/Al
Constants such as material densities, program limits, target location, and physical
constants such as the radius of the earth are contained in a file called YYvar.dat.
These values can be changed easily if necessary to support new data.
15
2.3.3 PREDICTIVE MODEL
Propulsion
The propulsion code is the first to be called after the genetic algorithm is
initialized. This model analyzes the basic thrust performance and creates a full sea-level
thrust profile. Since the vehicle in this effort is three stages, the propulsion model is
called three times and the propulsion characteristics are determined for each stage
separately and in sequence. The basic theory in this model assumes steady-state
operation, which requires that the mass produced by the burning propellant is equal to the
mass output through the nozzle. Detailed derivations of the equations presented here can
be found in Sutton
27
. The burning rate is modeled by the empirical equation
n
c
apr ? (6)
where a is an empirical constant, n is the burning rate index, and P
c
is the chamber
pressure. The mass flow rate of hot gas generated by the burning propellant and flowing
away from the motor is given by
bb
rAm ??
?
(7)
where A
b
is the burning area of the propellant grain, and ?
b
is the solid propellant density
prior to the motor start.
The burning area of the propellant can be tedious to calculate by hand, but
computers have made this process much simpler. Star grains and wagon wheel grains are
considered for this vehicle. The star and wagon wheel equations have been extensively
developed by Barrere
34
and reviewed by Hartfield
29
. It is important to note that the
maximum burn area corresponds to the maximum chamber pressure, and for a star grain
16
the maximum burn area will always occur at the beginning of the burn or at the end of
phase II. Due to this fact, an initial check on chamber pressure is done once a design is
determined so that the thickness of the can be determined and a precise estimate of the
case weight can be calculated.
Isentropic flow is assumed through the nozzle, and the characteristic velocity is
defined as
? ?12
1
2
1
*
?
?
?
?
?
?
?
? ?
?
?
?
?
?
c
RT
c (8)
where T
c
is the chamber temperature and gamma is defined by the propellant.
The relationships of isentropic flow can be used to express the mass flow rate through the
nozzle as
)1(2
1
1
2*
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
c
c
RT
Ap
m (9)
*
*
c
Ap
m
c
?
?
(10)
where p
c
is the chamber pressure, A* is the throat area, R is the specific gas constant, T
c
is the chamber temperature, gamma is the specific heat ratio, and c* is the characteristic
velocity.
The chamber pressure can be expressed by
n
b
t
b
c
ca
A
A
P
?
?
?
?
?
?
?
?
?
?
1
1
*? (11)
Assuming adiabatic, steady, 1-D flow, the exit velocity is
17
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?1
1
1
2
?
?
?
?
c
ec
e
P
PRT
u (12)
The thrust of the rocket motor is finally determined by
? ?
aeee
PPAumT ???
?
(13)
A bell shaped nozzle is employed for this model because it is desirable to have a
nozzle that is minimum weight while not sacrificing performance. The geometric design
of the nozzle has been taken from Ref. 16 and Ref. 30. If a conical nozzle is used for
comparison, then the relative performance and relative weight can be determined. The
conical nozzle is a 15 degree half cone with a given expansion ratio and throat diameter.
The bell nozzle has the same expansion ratio and throat diameter, but the mass is
significantly lower. The length of the bell nozzle can be determined from equation 14,
where L
f
is the fractional nozzle length and the denominator is the equivalent known
conical nozzle length.
cone
bell
f
L
L
L
?
?
?
15
(14)
The bell nozzle diagram is shown in Figure 6.
18
Figure 6: Bell Nozzle Schematic
30
Huzel and Huang
35
contains a detailed correlation to the bell nozzle performance
equations, as derived from the method of characteristics solutions. These curves are
interpolated in the nozzle model to predict a shape and corresponding performance for
any set of design parameters. The geometric performance of the bell nozzle is a few
percent higher than the conical nozzle for all expansion ratios and length fractions. The
expansion ratio of the nozzle is limited to the body diameter.
Aerodynamics Model
The aerodynamics model is performed by Aerodsn, which is a fast predictor
aerodynamics code and has been used successfully in all of the missile optimization
codes at Auburn University for contracts with the U.S. Army, Missile and Space
Intelligence Center, and the U.S. Air Force. Aerodsn is non-linear and assumes that there
are no boundary layers, that no separation occurs, and that the vehicle is axis-symmetric.
Some improvements in Aerodsn have been incorporated, such as the modeling of a
19
variable body diameter. More accurate computational fluid dynamic (CFD) simulations
are available; however the high computational cost makes CFD an unreasonable choice
for genetic algorithm applications where thousands of missiles are simulated under a
broad range of flight conditions.
Aerodsn generates aerodynamic databases based on the vehicle geometry and
other necessary parameters. Empirical curve fits of wind tunnel data are performed and
aerodynamic constants are determined over a wide range of flow conditions. The vehicle
geometry, initial constants, and empirical data are combined to generate an aerodynamic
database to describe the flight conditions. Aerodsn can model either a cone or an ogive
shape for the nosecone and assumes the body is cylindrical in shape; this study uses an
ogive nosecone. The vehicle is smooth except for the first stage which contains the wing
and tail set. The four canards and four tail fins are set in a ?+? configuration on the first
stage. The wing and tail locations on the first stage are GA variables. Vehicles with
different wing configurations are not analyzed because Aerodsn only allows for the
cruciform configuration for the wings and tails. Aerodsn also limits the camber of the
wings. Aerodsn requires an axis-symmetric vehicle and using camber is not allowed in
Aerodsn. Future improvements will allow for different wing configurations and for
camber to be used.
The diameter of the 1
st
stage must be equal to or greater than the diameter of the
2
nd
or 3
rd
stages. For the Minuteman-III, the 2
nd
and 3
rd
stage diameters are equal. For the
first study, the stage diameters are set to the Minuteman-III value. The second study
allows the 3
rd
stage diameter to be smaller than the 2
nd
stage diameter for the generic
three-stage vehicle. The aerodynamics model is initially called before liftoff with all the
20
stages stacked together, and then it is called after stage 1 burnout, after stage 2 burnout,
and after stage 3 burnout. Essentially, the aerodynamic properties are calculated every
time the vehicle geometry changes.
The properties calculated by Aerodsn are used in conjunction with the mass
properties model to calculate all the aerodynamic forces acting on the vehicle. The
aerodynamics of the vehicle is relatively unimportant to this work. The benefit of the
lifting wings and the negative of the aerodynamic drag is only a concern during the first
stage burn. The explanation for this is explained in more detail at the start of section 4.0.
Mass Properties
The mass properties code is another important piece of the model. The airfoil
section for both the wing and tail fin sets are assumed to be circular arc airfoils. It is
assumed that the wing has no camber and that the leading and trailing edges are identical.
A generic circular arc cross-section is shown in Figure 7.
Figure 7: Circular Arc Airfoil
30
21
The following equations are adapted from Ref. 30. The radius of the fin and the angle
?
max
are expressed by
yyRyy
b
CC
c
t
t
c
R
const
tR
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
2
4
1
(15)
?
?
?
?
?
?
?
?
R
C
2
sin
1
max
? (16)
The cross-sectional area of the fin can be expressed as
? ? ? ? ? ?
22
maxmax
2
cos
2
2 yyAyy
b
CC
RRArea
const
tR
constconst
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?? ?? (17)
The mass of the fin is thus expressed as
? ?
?
?
?
?
?
?
???
3
3
2
3
b
yy
A
m
RR
const
?
(18)
The mass of the vehicle is not constant because it burns and ejects propellant
during flight. The mass properties code calculates the mass, products of inertia, and x-
center of gravity for every individual component. The axi-symmetric configuration of the
vehicle reduces the products of inertia to zero. The mass properties model is described in
detail in Ref. 3, and except for the addition of wing fins and tail fins remains unmodified
for this study; however it is relevant to list the five mass properties that are calculated by
this model
3
:
1. Mass of each individual component and entire launch vehicle system
2. Center of gravity relative to the nose of the rocket (xcg) of the individual
component and the entire launch vehicle system
3. X-axis moment of inertia (ixx) of the individual component and entire system
22
4. Y-axis moment of inertia (iyy) of the individual component and entire system
5. Z-axis moment of inertia (izz) of the individual component and entire system
The components that are analyzed by the mass properties code for the three-stage launch
vehicle are shown in Table 6.
Table 6: Mass Property Components
System Components Stages 1-2-3 Stage 1
Blunt Nose Bulkhead Wings
Ogive Ignitor Tails
Payload Motor Case
Electronics Liner
Insulation
Nozzle
Propellant Grain
Dynamics Simulation
The six degree of freedom model (six-DOF) is the core analysis tool used to
determine performance. All the performance characteristics are calculated inside the six-
DOF. The six-DOF code can be considered the ?project manager? of the predictive
model. The digital flight of the model is initiated and completed using a 7-8
th
order
Runge-Kutta integration routine (RK78). The RK78 routine integrates the equations of
motion. The propulsion, mass properties, and aerodynamics models are all called from
the six-DOF to update parameters real-time during the flight. The integration process
continues until the vehicle reaches the apogee of the ballistic flight trajectory. The apogee
ideally corresponds to the orbital insertion point for a low-Earth, circular orbit. Once the
six-DOF is complete, the desired goals such as orbital altitude and orbital velocity are
sent to the genetic algorithm for analysis. The goal of the optimization is to minimize the
values obtained from the six-DOF with the desired values that are set prior to the
analysis.
23
3.0 VALIDATION
To be useful as design tools, computer models of physical systems require proof
of the validity of the physical model. Validation is the process of determining if the
physical system being modeled is correct. A validated model provides a degree of
confidence in the accuracy of the physical system and the results from an optimization
study which uses the model.
Individual components of the predictive model used in the current study have
been validated independently in previous studies. The solid propellant propulsion model
was developed and validated by Burkhalter
28
, Hartfield
30
, and Sforzini
31
. The
aerodynamics model, Aerodsn, has been an industry tool since 1990. Aerodsn and the
six-DOF flight dynamics simulator have been used and validated extensively by Hartfield
et al
15,16,17
.
The three-stage solid-fuel orbital flight model for this thesis was validated using
real world data for the Minuteman-III ICBM
32,33
. The Minuteman-III is a strategic
weapon system using a ballistic missile of intercontinental range. Although the
Minuteman-III was not designed to take a payload into orbit, it was chosen for this study
because it has a known configuration that reaches suborbital altitude and velocity. Using
the known data for the Minuteman-III, the GA is used to determine the unknown
parameters. An optimization is performed to develop a vehicle having similar
characteristics to the real-world example. If the model can produce a vehicle with very
24
similar parameters to the real vehicle, then the validity and uncertainty of the model can
be ascertained.
This validation effort was a repeat of a previous effort by Bayley
3
and had
identical results. Bayley?s validation effort was reported here due to changes made in the
program. Table 7 shows the results of the validation.
Table 7: Minuteman-III Validation
25
Values in Table 7 listed in bold* were direct inputs based on known Minuteman-III data.
The rest of the parameters were determined by the GA. The results of the GA
optimization are very close to the published Minuteman-III data. An important validation
check is in the ability of the model to reproduce the performance characteristics such as
the final altitude (763,306.27 ft to 750,000.00 ft) and burnout velocity (22,071.61 ft/s to
22,000.00 ft/s). Stage weights burnout times match fairly closely as well. This validation
was performed with no wings and tails. Coincidently, an optimization case performed for
this study (discussed in section 4) that includes wings and tails was able to narrow down
on the altitude and velocity values by a large margin while only changing the system
mass by a negligible amount. Figure 8 shows a diagram of the validation vehicle next to a
photo of the physical Minuteman-III.
Figure 8: Minuteman-III Validation Model
26
The fuel for each stage is PBAA/AP/Al. Table 8 shows a list of the characteristics of the
propellant.
Table 8: PBAA/AP/Al Characteristics (English Units)
Parameter Value
a 0.0285
n 0.35
rho 0.064
Tc 6159.67
gamma 1.24
cstar 5700
Tio 519
MW 24.7
An important parameter to compare vehicles is the propellant mass fraction calculated by
inertfuel
fuel
prop
mm
m
f
?
?
(19)
The vehicles with wings should have a smaller propellant mass fraction than the vehicles
without wings.
27
4.0 AERODYNAMIC PERFORMANCE ENHANCEMENT
As discussed in section 1.0, it is very likely that substantial improvement in net
payload to orbit could be obtained for current launch vehicles using aerodynamic lifting
during the first stage burn despite the cost of adding some mass in the form of wing
structure (to the first stage). Attaching the wing structure to the first stage makes the most
use of any possible aerodynamic lifting effects. As the vehicle climbs in altitude, the
density of the air molecules drastically decreases. The flight envelope where aerodynamic
forces are non-trivial is limited to the first-stage portion of the trajectory due to the
decrease in density. Figure 9 shows graphically how density decreases as altitude
increases. At 100,000 feet, the density is 1% of the sea-level value.
0
0.0005
0.001
0.0015
0.002
0.0025
0 20000 40000 60000 80000 100000 120000
Altitude (ft)
D
e
n
s
i
t
y
(
s
l
u
g
/
f
t
^
3
)
Figure 9: Air Density vs. Altitude
28
Another important parameter for spacecraft is the dynamic pressure because it can show
the point of maximum aerodynamic load on the vehicle. Dynamic pressure is described
by equation 19. Figure 10 shows the dynamic pressure for the first stage flight of the
Minuteman-III.
2
2
1
VQ ??
(19)
0
500
1000
1500
2000
2500
3000
0 20000 40000 60000 80000 100000 120000 140000
Altitude (ft)
D
y
n
a
m
i
c
P
r
e
s
s
u
r
e
(
l
b
f
)
Figure 10: Minuteman-III Dynamic Pressure
The performance enhancement revolves around the wing and tail configuration. A
rocket with no fins is unstable, so fins are attached in order to aerodynamically stabilize
the vehicle at a specific trim angle. One of the purposes for the optimization studies
presented herein is to use the genetic algorithm to find a fin configuration that enables the
rocket to trim at a higher angle of attack. At the higher trim angle, the body and fin
system will have a higher normal force than the body alone. The trim angles for the
vehicles in this study range from slightly above 0 degrees to a maximum of 4.3 degrees.
29
Performance enhancement testing is divided into three groups with all tests
employing the wing and tail system. The propellant type is a constant and therefore is the
same for every optimization study. First, the Minuteman-III external body geometry is
kept constant to the validation model except for the addition of a wing and tail system.
Three optimization tests are performed on this configuration with a desired suborbital
altitude of 750,000 feet and velocity of 22,000 ft/s:
1. The payload and propellant fuel mass are held constant.
2. The payload is increased by 10% for a system with wings and for the
validation system.
3. For both payloads, the desired propellant fuel mass and the desired initial
system weight are reduced.
Second, the three-stage Minuteman-III geometry is used to attempt to achieve
low-earth orbit conditions of 2,430,000 feet and 24,550 ft/s with a payload of 1,000
pounds. Tests are conducted with the validation Minuteman-III system (no wings) and
compared to an enhanced Minuteman-III configuration equipped with the wing and tail
system.
The third group of tests compares the result of a generic three-stage launch
vehicle optimization performed by Bayley
3
to the result of the same optimization
procedure using the wing and tail system.
4.1 MINUTEMAN-III SUBORBITAL ENHANCEMENT
The Minuteman-III (Figure 11) is a three-stage solid ICBM and achieves a
suborbital apogee of 750,000 feet and a speed of 22,000 ft/s. The payload is 2,540
30
pounds. The predictive model successfully validated a Minuteman-III vehicle as seen in
section 3. Analysis of this system is divided into two groups: Improving the suborbital
flight, and taking the MM3 to full orbital conditions.
Figure 11: Minuteman-III
Four cases were studied to improve the suborbital flight, and one to take the three-stage
system to orbit.
31
4.1.1 SUBORBITAL IMPROVEMENT
The first suborbital test was to improve on the performance (matching the desired
altitude and velocity) of the validation case by keeping the external geometry, propellant
type, and payload the same, but adding wings and tails to the first stage. The design
variables are the geometric definition of the wing and tail (Table 4) and the internal
geometry of the propellant. The optimized vehicle is shown in Figure 12.
Figure 12: Minuteman-III with 2540 Payload
The wings presented for this vehicle are unrealistic, but serve as a proof of
concept for the idea of enhancing performance through aerodynamic assistance. With a
more accurate structural analysis, the wings presented here would break off under the
load. An improvement to the model for future analysis should include more restrictions
32
on the semi-span and chord length to limit the aspect ratio. All the suborbital
enhancement cases have this issue. In addition, the model does not show fairings over the
variable diameter stage connections. The model contains a correction factor for the drag
computations.
The new vehicle weighed less and matched the desired values for altitude and
velocity much more closely than the original validation. This vehicle attained an altitude
of 750,007 ft, a speed of 22,000.8 ft/s, and total system mass of 74,935 lbm. Noticing that
this vehicle flies to 750,007 ft and the validation model flies to 763,306 ft, it is possible
that the mass savings could be due in part to the vehicle flying to a lower altitude.
However, the remaining test cases also closely match the desired altitude, and the initial
mass is shown to be further reduced when compared to the previous case.
The additional control provided by the wing and tail system allowed the trajectory
to more closely match the desired suborbital values than the original validation case. The
ballistic trajectory can be seen in Figure 13, the thrust profile in Figure 14, and the
velocity profile in Figure 15.
33
Figure 13: Altitude vs. Time (MM3-Wings)
Figure 14: Thrust vs. Time (MM3-Wings)
34
Figure 15: Weight vs. Time (MM3-Wings)
Figure 15 displays how the weight of the system decreases with time. The smooth curves
are the loss in weight caused by the burning propellant. The points where the vehicle
disposes of a used stage are clearly seen. The first drop off is the largest in mass and
includes the first stage and the wing structure. The genetic algorithm convergence to the
optimal solution can be seen in Figure 16. The optimization was carried out for 400
generations, hit a plateau at generation 60 but improved again near generation 300.
1.00E-06
1.00E-04
1.00E-02
1.00E+00
1.00E+02
1.00E+04
1.00E+06
1.00E+08
1.00E+10
0 100 200 300 400 500
Generation
B
e
s
t
P
e
r
f
o
r
m
e
r
Figure 16: GA Best Answer Convergence
35
The next suborbital test case kept the payload (2,540 lbm) and external geometry
constant but reduced the desired first stage fuel mass by 5.2% from 45,371 pounds to
43,000 pounds. A reduction in propellant translates into a direct reduction in costs.
Again, the only variables are the wing and tail definitions and the internal propellant
geometry. Figure 17 shows a diagram of the optimized vehicle. This vehicle has a 74
degree launch angle and attains an altitude of 749,992.6 feet, a velocity of 22,000.0 ft/s,
and weighs 72,402 pounds. This vehicle weighs 2,533 pounds less than the previous case.
From the previous design, the wings have progressed towards a more aerodynamic
efficient shape. The new, thinner shape of the wings has a lower induced drag. As will be
seen in subsequent diagrams, the general trend of evolution using the genetic algorithm is
that thinner wings are designed for the vehicles having the lowest initial system mass.
The previously mentioned issues concerning the unrealistic wings apply to this case.
These wings would break if the structural model was more accurate. Genetic algorithm
best performer convergence is shown in Figure 18.
36
Figure 17: Vehicle Diagram (MM3-Reduced Propellant)
1.00E-04
1.00E-02
1.00E+00
1.00E+02
1.00E+04
1.00E+06
1.00E+08
1.00E+10
0 100 200 300 400 500
Generation
B
e
s
t
P
e
r
f
o
r
m
e
r
Figure 18: Convergence for MM3-Reduced Propellant
The next test to improve the suborbital performance of the Minuteman-III was to
increase the payload by 10%, from 2540 pounds to 2794 pounds, with a negligible
increase in the initial system mass. The design variables are the wing and tail definitions
and the internal propellant geometry. The optimization produced a vehicle that matched
the desired goals closely and had an initial system mass of only a fraction more. The
37
vehicle is seen in Figure 19 and weighs 74,959 pounds, is launched at 71 degrees, reaches
an altitude of 749,997.5 feet, and reaches a speed of 22,000.2 ft/s. The structural issues
for the wings apply to this case. Future investigations will limit the aspect ratio further to
prevent this problem.
Figure 19: Vehicle Diagram (MM3-Increased Payload)
The convergence of the best performer is similar to the previous test cases, reaching an
optimum solution around the 60
th
generation and improving only slightly afterwards.
As a comparison to the previous case, the analysis that produced the Minuteman-
III validation model (no wings) was performed using the increased payload of 2,794
pounds. This optimization case produced a vehicle that reaches an altitude of 749,998
feet, a speed of 22,000.1 ft/s, and weighs 77648.2 pounds. The original MM3 validation
38
weighed 75,807.09 pounds, leading to an increase of 1841.11 pounds in order to increase
the payload by 10%. The previous case with the wing structure only increased the system
mass by 24 pounds when the payload was increased.
Table 9: MM3 Suborbital Enhancement
Case Wings Payload (lbm) Weight (lbm) Altitude (ft) Velocity (ft/s)
Validation Model No 2,540 75,870 763,306 22,071
Enhancement 1 Yes 2,540 74,935 750,007 22,001
Enhancement 2 Yes 2,540 72,402 749,993 22,000
Validation Model No 2,794 77,648 749,988 21,997
Enhancement 3 Yes 2,794 74,959 749,998 22,000
Table 10: MM3 Suborbital Mass Fractions
Case f
prop
Validation Model 0.9102
Enhancement 1 0.9095
Enhancement 2 0.9070
Validation Model 0.9123
Enhancement 3 0.9068
Table 9 shows a summary of the basic performance characteristics for all the
suborbital performance enhancement cases that were studied. Analyzing the weight
column, it can be seen that all the cases that include the wing structure have lower initial
weights than the cases without wings. Also, increasing the payload by 10% increased the
initial weight of the validation case by a much larger amount than for the case with wings
(Enhancement 3). Table 10 shows the propellant mass fractions for each case. The
vehicles with no wings have a higher propellant mass fraction than the vehicles with
wings. This shows that when using the wings, a smaller amount of propellant is needed.
These studies serve as a proof of concept that the suborbital flight performance of the
Minuteman-III can be improved through aerodynamic lifting on the first stage.
39
4.1.2 ORBITAL IMPROVEMENT
The Minuteman-III is not an orbital vehicle, but tests were conducted to
determine if the Minuteman-III geometry from the validated model could sustain a flight
to orbital conditions. After a successful design to orbit, a second test was performed with
the goal of enhancing performance through aerodynamic lifting during the first stage
burn. This section discusses these tests and compares the results.
The first test was to take the validation model to orbit. The desired goals were
changed from suborbital conditions to a desired altitude of 2,430,000 feet and desired
velocity of 24,550 ft/s. The payload was changed from the Minuteman-III suborbital
value of 2,540 pounds to a more typical orbital payload of 1,000 pounds. As before, the
only variables that are allowed to change are the wing and tail geometry definitions and
the internal propellant geometry. The genetic algorithm was able to converge to a design
that achieved the desired orbital conditions, reaching an altitude of 2,430,024 feet and a
velocity of 24,551 ft/s. The diagram of the vehicle is the same as previous Minuteman-III
validation configurations (such as Figure 8) because the external geometry is constant.
The vehicle weighs 75,760 pounds, which is similar to the 75,870 pounds that the
validation case weighs to reach suborbital conditions. This vehicle is 110 pounds lighter
than the validation case yet achieves a higher altitude and faster velocity. The 1,540
pound reduction in payload was directly applied to the first and second stage propellant
mass. The validation case had a first and second stage propellant mass of 45,371 pounds
and 13,668 pounds respectively, and the current vehicle has first and second stage
propellant mass of 46,750 pounds and 14,413 pounds respectively. Figure 20 shows the
40
genetic algorithm convergence history of the best performer. Similar to the previous
convergence plots shown, a near-best solution is found around generation 60, and is
refined over the course of the rest of the generations.
1.00E-04
1.00E-02
1.00E+00
1.00E+02
1.00E+04
1.00E+06
1.00E+08
1.00E+10
0 50 100 150 200 250
Generation
B
e
s
t
P
e
r
f
o
r
m
e
r
Figure 20: Orbital MM3 GA Convergence
The next case attempts to take the Minuteman-III geometry with the wing
structure to the same orbital conditions as the previous case. The vehicle chosen as the
best performer achieves an altitude of 2,429,956 feet and a velocity of 24,551 ft/s. The
initial system weight is 75,486 pounds, only 274 pounds lighter than the previous MM-3
vehicle. The mass of the propellant is slightly less than the previous vehicle, with 46,557
pounds for the first stage and 14,311 pounds for the second stage. The small wings make
a very slight improvement for this case. Figure 21 shows a diagram of this vehicle. Figure
22 shows the altitude versus time plot, Figure 23 shows the thrust profile, and Figure 24
shows the convergence history.
41
Figure 21: Orbital MM3 Wings
Figure 22: Orbital MM3 Altitude vs. Time
42
Figure 23: Orbital MM3 Thrust Profile
1.00E-03
1.00E-01
1.00E+01
1.00E+03
1.00E+05
1.00E+07
1.00E+09
1.00E+11
0 100 200 300 400
Generation
B
e
s
t
P
e
r
f
o
r
m
e
r
Figure 24: Orbital MM3 Convergence History
Table 11 summarizes the performance goals of the two orbital designs.
Table 12 shows the propellant mass fractions for these two vehicles. The propellant mass
43
fractions are very similar, and the fraction for the vehicle with wings is only slightly
smaller than for the vehicle without wings.
Table 11: MM3 Orbital Enhancement
Case Wings Payload (lbm) Weight (lbm) Altitude (ft) Velocity (ft/s)
Validation Model No 1,000 75,760 2,430,024 24,551
Enhancement 1 Yes 1,000 75,486 2,429,956 24,551
Table 12: MM3 Orbital Mass Fractions
Case f
prop
Validation Model 0.91313
Enhancement 1 0.91302
4.2 THREE-STAGE ORBITAL ENHANCEMENT
The generic three-stage solid fuel model includes more variables than the
validation model. The stage lengths and stage diameters are not hard-wired to match the
Minuteman-III and are included in the design space for the GA. Wall thickness
parameters were known for the MM3 but are calculated for the generic model, therefore
the initial system weight is on a different scale than for the MM3 cases. Due to this
discrepancy, the comparisons for vehicles with the wing structure to a baseline case are
done using the optimizations performed by Bayley
3
. The same design optimizations are
performed but with the addition of the wing structure and the results are compared.
The baseline vehicle attains an altitude of 2,439,276 feet, a velocity of 24,595 ft/s,
and has an initial system mass of 89,906 pounds. The specific details of the flight can be
seen in Ref. 3. The wing structure was added to this model and the optimization
performed again. The same wing and tail variables that were added to the Minuteman-III,
44
seen in Table 4, are added to the generic three-stage model. The result of this
optimization is a much lighter vehicle. The desired goals are matched well. The vehicle
attains an altitude of 2,429,965 feet and a velocity of 24,550 ft/s. The initial system mass
of the vehicle dropped from 89,906 pounds to 80,002 pounds. Figure 25 shows a diagram
of the vehicle.
Figure 25: Generic Three-Stage Vehicle
The first stage propellant mass dropped from 48,939 pounds to 45,002 pounds. The
second stage propellant mass dropped from 18,965 pounds to 17,029 pounds. The altitude
plot and thrust profile are shown in Figure 26 and Figure 27.
45
Figure 26: Three-Stage Altitude vs. Time
Figure 27: Three-Stage Thrust Profile
46
Table 13 shows a summary of the performance goals for the generic three-stage vehicles.
Table 13: Generic Three-Stage Orbital Enhancement
Case Wings Payload (lbm) Weight (lbm) Altitude (ft) Velocity (ft/s)
3-Stage No 1,000 89,906 2,439,276 24,595
3-Stage Enhance Yes 1,000 80,002 2,429,965 24,550
Table 14: Generic Three-Stage Mass Fractions
Case f
prop
3-Stage 0.9078
3-Stage Enhance 0.8904
Table 14 shows the propellant mass fractions for the generic three stage optimizations.
The vehicle with the wings has a slightly lower propellant mass fraction than the vehicle
without wings.
47
5.0 SUMMARY
Launch vehicle performance enhancement using aerodynamic assistance during
early flight has proven to be successful for the current design models. The Minuteman-III
suborbital performance was shown to improve by using a wing and tail system. It was
shown that by only changing the geometric definition of the wings, tails, and propellant
geometry the payload could be increased by 10% with no increase in the initial total
system mass. It was also shown that the first stage propellant mass could be decreased
while achieving the same performance parameters using the winged vehicle. Every
comparison case of the baseline Minuteman-III to a version with wings showed that the
vehicle with wings had a lower initial system weight.
The impact of the wings was not as large when the Minuteman-III was changed
from a suborbital flight to an orbital flight. The MM3 external geometry is locked in, so
the only way to improve the performance is by using fins to increase the trim angle,
modifying the propellant geometry, and varying the launch angle. With an orbital altitude
of 2,430,000 feet (compared to the suborbital altitude of 750,000 feet) and a ballistic
trajectory, the required launch angle was 89 degrees. This left little room for the wings to
have a large effect on the performance. It was shown that there is a total weight savings
even with the launch angle at 89 degrees, but it was not as large as for the suborbital
flights.
48
The non-optimized generic three-stage solid fuel vehicle showed a big weight
savings, a little over 11%, when using wings. The small effect of the wings allowed the
first, second, and third stage geometries and propellant grains to be redesigned
significantly and this all contributed to the weight reduction.
This study indicates that performance enhancement through aerodynamic assist
on launch vehicles is a valid proposal and warrants subsequent studies. There are several
improvements that should be undertaken for future work. While the current model
calculates the weight of the wings, it does not model the support structure in detail. To
more accurately represent the total weight penalty for adding wings, the support structure
should be modeled structurally to ensure adequate structural integrity of the entire
vehicle. Additionally, improved fin settings could be introduced in order to change the
angle of attack of the wings during flight. A trajectory modification is recommended for
the future. The current trajectory is non-guided and follows a mostly ballistic path. A
guided trajectory is suggested for study in order to have a trajectory where the vehicle is
kept for a longer period of time in the flight envelope for aerodynamic assistance.
Another improvement is to modify the Aerodsn package to allow for non-cruciform fin
configurations to be analyzed.
Additional improvements could include more detailed modeling of the
aerodynamic effects during the atmospheric flight, the addition of a gimbaled control
system and higher fidelity modeling of the entire structure. For a more comprehensive
preliminary design study to look at proposed new launch vehicle applications, more
modern propellants should be considered along with winged liquid propellant two stage
systems.
49
REFERENCES
1. Lyons, J. T.; Woltosz, W. S.; Abercrombie, G. E.; Gottlieb, R. G NASA-CR-129000,
TR-243-1078, 1972.
2. Woltosz, W., Personal Communication.
3. Bayley, D., Hartfield, R.J., Burkhalter, J.E., and Jenkins, R.M., ?Design Optimization
of a Space Launch Vehicle Using a Genetic Algorithm,? AIAA Paper 2007-1863,
presented at the 3rd AIAA Multidisciplinary Design Optimization Specialist
Conference, Honolulu, Hawaii, April 23-26, 2007.
4. Holland, J. H., Adaptation in Natural and Artificial Systems, The University of
Michigan Press, Ann Arbor, MI, 1975.
5. Burger, C. and Hartfield, R.J., ?Propeller Performance Optimization using Vortex
Lattice Theory and a Genetic Algorithm?, AIAA-2006-1067, presented at the Forty-
Fourth Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 9-12, 2006.
6. Doyle, J., Hartfield, R.J., and Roy, C. ?Aerodynamic Optimization for Freight Trucks
using a Genetic Algorithm and CFD?, AIAA 2008-0323, presented at the 46th
Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2008.
7. Anderson, M.B., ?Using Pareto Genetic Algorithms for Preliminary Subsonic Wing
Design?, AIAA Paper 96-4023, presented at the 6
th
AIAA/NASA/USAF
Multidisciplinary Analysis and Optimization Symposium, Bellevue, WA, September
1996.
50
8. Oyama, A., Obayashi, S., Nakahashi, K., ?Transonic Wing Optimization Using
Genetic Algorithm?, AIAA Paper 97-1854, 13th Computational Fluid Dynamics
Conference, June 1997.
9. Jang, M., and Lee, J., ?Genetic Algorithm Based Design of Transonic Airfoils Using
Euler Equations?, AIAA Paper 2000-1584, Presented at the 41st
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference, April 2000.
10. Jones, B.R., Crossley, W.A., and Anastasios, S.L., ?Aerodynamic and Aeroacoustic
Optimization of Airfoils Via a Parallel Genetic Algorithm?, AIAA Paper 98-4811,
7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and
Optimization, September 1998.
11. Schoonover, P.L., Crossley, W.A., and Heister, S.D., ?Application of Genetic
Algorithms to the Optimization of Hybrid Rockets?, AIAA Paper 98-3349, 34th
AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 1998.
12. Nelson, A., Nemec, M., Aftosmis, M., and Pulliam, T., ?Aerodynamic Optimization
of Rocket Control Surfaces Using Cartesian Methods and CAD Geometry,? AIAA
2005-4836, 23rd Applied Aerodynamics Conference, Toronto, Canada, June 6-9,
2005.
13. Anderson, M.B., Burkhalter, J.E., and Jenkins, R.M., "Design of an Air to Air
Interceptor Using Genetic Algorithms", AIAA Paper 99-4081, presented at the 1999
AIAA Guidance, Navigation, and Control Conference, Portland, OR, August 1999.
14. Anderson, M.B., Burkhalter, J.E., and Jenkins, R.M., ?Intelligent Systems Approach
to Designing an Interceptor to Defeat Highly Maneuverable Targets?, AIAA Paper
51
2001-1123, presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno,
NV, January 2001.
15. J.E. Burkhalter, R.M. Jenkins, and R.J. Hartfield, M. B. Anderson, G.A. Sanders,
?Missile Systems Design Optimization Using Genetic Algorithms,? AIAA Paper
2002-5173, Classified Missile Systems Conference, Monterey, CA, November, 2002.
16. Hartfield, Roy J., Jenkins, Rhonald M., Burkhalter, John E., ?Ramjet Powered Missile
Design Using a Genetic Algorithm,? AIAA 2004-0451, presented at the forty-second
AIAA Aerospace Sciences Meeting, Reno NV, January 5-8, 2004.
17. Jenkins, Rhonald M., Hartfield, Roy J., and Burkhalter, John E., ?Optimizing a Solid
Rocket Motor Boosted Ramjet Powered Missile Using a Genetic Algorithm?, AIAA
2005-3507 presented at the Forty First AIAA/ASME/SAE/ASEE Joint Propulsion
Conference, Tucson, AZ, July 10-13, 2005.
18. Riddle, David B., ?Design Tool Development for Liquid Propellant Missile System,?
MS Thesis, Auburn University, May 10, 2007.
19. Mondoloni, S., ?A Genetic Algorithm for Determining Optimal Flight Trajectories?,
AIAA Paper 98-4476, AIAA Guidance, Navigation, and Control Conference and
Exhibit, August 1998.
20. Karr, C.L., Freeman, L.M., and Meredith, D.L., "Genetic Algorithm based Fuzzy
Control of Spacecraft Autonomous Rendezvous," NASA Marshall Space Flight
Center, Fifth Conference on Artificial Intelligence for Space Applications, 1990.
21. Krishnakumar, K., Goldberg, D.E., ?Control System Optimization Using Genetic
Algorithms?, Journal of Guidance, Control, and Dynamics, Vol. 15, No. 3, May-June
1992.
52
22. Tong, S.S., ?Turbine Preliminary Design Using Artificial Intelligence and Numerical
Optimization Techniques?, Journal of Turbomachinery, Jan 1992, Vol 114/1.
23. Selig, M.S., and Coverstone-Carroll, V.L., ?Application of a Genetic Algorithm to
Wind Turbine Design?, Presented at the 14th ASME ETCE Wind Energy
Symposium, Houston, TX, January 1995.
24. Torella, G., Blasi, L., ?The Optimization of Gas Turbine Engine Design by Genetic
Algorithms?, AIAA Paper 2000-3710, 36th AIAA/ASME/SAE/ASEE Joint
Propulsion Conference and Exhibit, July 2000.
25. Koza, J. R., Genetic Programming, The MIT Press, Cambridge, MA, 1992.
26. Anderson, M.B., ?Users Manual for IMPROVE? Version 2.8: An Optimization
Software Package Based on Genetic Algorithms?, Sverdrup Technology Inc. / TEAS
Group, Eglin AFB, FL, March 6, 2001.
27. Sutton, G., Biblarz, O., Rocket Propulsion Elements, John Wiley & Sons, Inc., New
York, 2001.
28. Anderson, M.B., Burkhalter, J.E., and Jenkins, R.M., ?Multi-Disciplinary Intelligent
Systems Approach to Solid Rocket Motor Design, Part II: Multiple Goal
Optimization,? AIAA Paper 2001-3600, presented at the 37th
AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Salt Lake City,
UT, July 2001.
29. Hartfield, Roy J., Jenkins, Rhonald M., Burkhalter, John E., and Foster Winfred,
?Analytical Methods for Predicting Grain Regression in Tactical Solid-Rocket
Motors,? Journal of Spacecraft and Rockets, Vol.41 No. 4, July-August 2004,
pp.689-693.
53
30. Burkhalter, J.E., Jenkins, R.M., and Hartfield, R.J., ?Genetic Algorithms for Missile
Analysis ? Final Report?, Submitted to Missile and Space Intelligence Center,
Redstone Arsenal, AL, 35898, February 2003.
31. Sforzini, R.H., ?An Automated Approach to Design of Solid Rockets Utilizing a
Special Internal Ballistics Model?, AIAA Paper 80-1135, Presented at the 16
th
AIAA/SAE/ASME Joint Propulsion Conference, July 1980.
32. U.S. Air Force Fact Sheet, LGM-30 Minuteman-III,
http://www.af.mil/factsheets/factsheet.asp?id=113
33. System Description of the LGM-30 Minuteman-III, http://www.globalsecurity.org
34. Barrere, M., Jaumotte, A., Veubeke, B.,and Vandenkerckhove, J., Rocket Propulsion,
Elsevier Publishing Company, Amsterdam, 1960.
35. Huzel, Dieter K. and Huang, David H., Design of Liquid Propellant Rocket Engines,
Rocketdyne Division, North American Rockwell, Inc, Washington, D.C.,
1971 (updated version currently published by AIAA)