Burnett, Karl, SMART, Chief Engineer, Final

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MAE 4350, The University of Texas at Arlington 2014.
S.M.A.R.T. : REVERSE ENGINEERING AND MODIFYING THE NORTH AMERICAN X-15
Signatures:
Author:
Se e n:
Date:
2/26/2015
Name:
Karl Burnett
Dr. Bernd Chudoba
Dept.:
MAE
MAE
Signature:
Summary:
This report provides a realistic solution for the assigned task of reverse -engineering the X-15,
and performing a parametric sizing study to accomplish the SS-2 and DARPA XS-1 missions
with a modified X-15 as part of a capstone project for MAE 4350 Aerospace Vehicle Design I at
The University of Texas at Arlington. The successes, failures, and aspirations of the X-15
program are studied in order to learn from the past, therefore avoiding making the same
mistake twice while simultaneously making significant strides with less work input. Student
Mavericks Aerospace Research Team (S.M.A.R.T.) is divided into eight disciplines consisting of
Synthesis, Stability and Control, Geometry and Weight, Aerodynamics, Systems, Performance,
Propulsion, and Structures. As Chief Engineer, my priorities lie in streamlining communication
and data sharing between disciplines in addition to using parametric sizing studies with
information and outputs collected from all disciplines to create matching charts with a solution
space for each of the missions. This solution space is used to estimate engine size and wing size
which allows an accurate estimation of the aircraft weight and fuel fraction. The combination
of all these variables allows the idea of an aircraft to materialize into a conceptual design of an
aircraft.
Distribution:
Institution: Dept.: Name:
The University of Texas at Arlington MAE Dr. Bernd Chudoba

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WORK DISCLOSURE STATEMENT
The work I performed to document the results presented in this report was performed by myself, or it
is otherwise acknowledged.
Date: 2/26/2015
Signature:

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TABLE OF CONTENTS
Work Disclosure Statement ...............................................................................................................2
Table of Contents ..............................................................................................................................3
List of Figures ...................................................................................................................................5
List of Tables ....................................................................................................................................6
1 Introduction................................................................................................................................7
1.1 Reverse Engineering...........................................................................................................7
1.2 Modification for SS-2 and DARPA XS-1 ...........................................................................7
2 North American X-15 Background and Research........................................................................8
2.1 North American X-15 Flight 3-22-36 Mission Parameters ..................................................8
2.2 Known Features and Specifications ..................................................................................10
2.3 X-15 Flight 3-65-97 Crash and Fatality.............................................................................11
2.3.1 Accident Causes............................................................................................................12
2.3.2 Lessons Learned ...........................................................................................................12
3 Capstone Project Requirements.................................................................................................12
3.1 Defined Experimental Process and Scope .........................................................................12
3.2 Individual Responsibilities and Scope ...............................................................................13
3.3 Team Responsibilities and Scope ......................................................................................13
4 X-15 Reverse Engineering........................................................................................................14
4.1 Managing, Scheduling and Organizing .............................................................................15
4.2 Parametric Sizing Literary Knowledge Base .....................................................................15
4.3 Discipline Analysis and contribution.................................................................................16
4.4 Synthesis ..........................................................................................................................18
4.4.1 Matching Chart .............................................................................................................19
5 Future Work .............................................................................................................................30
6 Conclusions thus far .................................................................................................................30
7 Intermediate Changes ...............................................................................................................30
7.1 Team Member Attrition ....................................................................................................30
7.2 Mission Objective Changes ..............................................................................................31
8 X-15 SS-2 Re-Design ...............................................................................................................32
8.1 Minimal Modification.......................................................................................................32
8.2 Inter-Disciplinary Communication....................................................................................32

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8.3 Re-Design Process............................................................................................................32
8.4 Sizing Iterations Approaching Vehicle Convergence.........................................................33
8.4.1 Sizing Iteration Algorithm.............................................................................................34
8.5 Converged Vehicle ...........................................................................................................36
9 Results and Discussion .............................................................................................................38
9.1.1 Midterm presentation ....................................................................................................38
9.1.2 Final Presentation..........................................................................................................38
10 Conclusions and Recommendations .....................................................................................38
References.......................................................................................................................................39
Appendix A – Nomenclature ...........................................................................................................40

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LIST OF FIGURES
Figure 1-1. X-15A-1 on Display at the National Air and Space Museum ...........................................7
Figure 2-1. Ground Track of Mission 091 Along The High Range .....................................................9
Figure 2-2. Flight 3-22-36 Mission Profile.........................................................................................9
Figure 3-1. Non-Specific IDA for Synthesis ....................................................................................13
Figure 3-2. S.M.A.R.T. Organizational Chart ..................................................................................14
Figure 4-1. Original S.M.A.R.T. Timeline .......................................................................................15
Figure 4-2. Roskam Design Process [6] ...........................................................................................16
Figure 4-3. S.M.A.R.T. X-15 Reverse Engineer MDA .....................................................................17
Figure 4-4. Synthesis IDA ...............................................................................................................18
Figure 4-5. Speed of Sound versus Altitude .....................................................................................20
Figure 4-6. X-15 Coefficient of Lift vs. Mach Number ....................................................................21
Figure 4-7. X-15 Coefficient of Drag vs. Mach Number ..................................................................21
Figure 4-8. Simplification of CGR...................................................................................................22
Figure 4-9. Varying Thrust with Altitude [10] .................................................................................24
Figure 4-10. Thrust versus Altitude .................................................................................................25
Figure 4-11. X-15 Aerodynamic Accelerations versus XLR-99 Burn Time ......................................27
Figure 4-12. X-15 Altitude and Velocity versus XLR-99 Burn Time ...............................................27
TABLE 4-1. CALCULATED AND CLAIMED VELOCITIES AND ALTITUDES ...............................................28
Figure 4-13. Matching Chart of the X-15.........................................................................................29
TABLE 4-2. MATCHING CHART FINAL EQUATIONS.............................................................................29
Figure 7-1. S.M.A.R.T. Organizational Chart Post-Midterm ............................................................31
Figure 8-1. The Conceptual Design Process [11] .............................................................................33
Figure 8-2. Vehicle Sizing Iteration.................................................................................................34
Figure 8-3. Sizing Iterations Changing Empty Weight .....................................................................35
Figure 8-4. Logarithmic Trend Line of the Empty Weight versus Iteration Number .........................36
Figure 8-5. Size Comparison of the New and Original X-15 ............................................................37

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LIST OF TABLES
Table 2-1. X-15 Geometry...............................................................................................................10
Table 4-1. Main Wing Airfoil Data....................................................Error! Bookmark not defined.
Table 4-2. Vertical Tail Airfoil Data ..................................................Error! Bookmark not defined.
Table 8-1. Weight of the Modified X-15 for Varying Iterations……………………………………..36
Table 8-2. Geometric Comparison of the Original and Modified X-15……………………………...37

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1 INTRODUCTION
An ironic fact of life is that sometimes, the most capable and advanced machines with proof of concept
lie dormant in our museums. This is most certainly the case with respect to hypersonic space vehicles
in this day and age. North American’s X-15 fits this irony; its superb performance in such an advanced
mission profile at a relatively early time is why it is profitable to look back in history and see if there
lies the answer to future space flight. Due to the immense availability of data concerning the X-15, it
is possible to reverse-engineer and re-design the vehicle for alternative missions without the need for
too many assumptions. Through the multiple trials of parametric sizing, a greater understanding of
aerospace design at a fundamental level can be attained, which is very profitable to any student
preparing to enter the aerospace industry.
Figure 1-1. X-15A-1 on Display at the National Air and Space Museum
1.1 REVERSE ENGINEERING
The process of reverse engineering the X-15 is undertaken so that we can validate the data from our
data building and furthermore as a juxtaposition for the matching graphs of the two re-design missions.
Proving that the original X-15 could fly its missions not only increases our knowledge and familiarity
of the X-plane, but also provides as a “warm-up” for the more demanding task of a parametric sizing
study of a new mission.
1.2 MODIFICATION FOR SS-2 AND DARPA XS-1
After reverse engineering is completed, we are tasked with modifying the X-15 as little as possible in
order to achieve the mission requirements of the SS-2 and DARPA XS-1 missions. The SS-2 mission
is a space tourism mission and the DARPA XS-1 is hypersonic payload delivery to orbit. As opposed
to a clean-sheet design, we are focused on solely modifying the X-15 as little as possible in order to
save money and time.

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2 NORTH AMERICAN X-15 BACKGROUND AND RESEARCH
The X-15 program was conceived in the early 1950’s as NACA was preparing for future manned
spaceflight. By 1954, four areas of concern were identified with regards to manned spaceflight
including materials and structures needed to withstand reentry heating, aerodynamics at hypersonic
speeds, systems needed to maintain stability and control, and human capability to work effectively in
space. These areas of concern led to the feasibility study of a research aircraft capable of penetrating
the speed and altitude range of atmospheric reentry. [4]
NACA combined their effort with the Air Force and the Navy so that adequate funding could be
gathered, and an RFP was sent to the aeronautics community detailing the X-15 mission. North
American Aviation was selected to build three aircraft and Reaction Motors was selected to build the
XLR-99 rocket engines.
The original mission detailed to North American for the X-15 to accomplish was a speed of at least
Mach 6 and to be capable of reaching an altitude of at least 264,000 feet. [2] North American delivered
the first X-15 in 1958 to now NASA, which flew its first powered flight eleven months later on 17
September 1959, and the first flight with the XLR-99 ( which was behind schedule) on 15 November
1960. [4] 199 total flights with all variants of the X-15 were flown, and the program was widely
accepted as a success, meeting and succeeding its desired mission with a max Mach of 6.7 and
maximum altitude of 354,200 feet. [1] The results of the program, especially the thermal interactions
with the X-15, were the cornerstones of future space missions, especially the Space Shuttle.
2.1 NORTH AMERICAN X-15 FLIGHT 3-22-36 MISSION PARAMETERS
Flight 3-22-36, also known by mission 091, was chosen as the mission to base our reverse engineering
on due to the fact that this mission was so similar to the SS-2 mission. SS-2 reaches an altitude of 110
kilometers and mission 091 reached an altitude of nearly 108 kilometers, the highest of all X-15
missions. [3] Because of the two mission’s similarities, it is possible to decrease the time spent
researching aspects of the mission and also utilize calculations from mission 091 to apply towards SS-
2.
The High Range is the airspace used throughout the X-15 missions, and mission 091’s ground track of
293.4 miles can be seen in Fig. 2-1. The mission requirements are to reach a velocity of 3,794 miles
per hour, an altitude of 354,200 feet, an engine burn time of 85.8 seconds from the XLR-99, and then
to land at Rogers Dry Lake Bed at Edwards Air Force Base. This mission is visualized in Fig. 2-2
below.

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Figure 2-1. Ground Track of Mission 091 Along The High Range
Figure 2-1. Flight 3-22-36 Mission Profile
M=5.58
Engine Burnout
176,000 ft
t=86.8 s
Max Alt.
354,200 ft
t=206 s
45,000 ft
t=0 s
t=1 s
XLR-99 ignition
2,277 ft
t=668.6 s

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2.2 KNOWN FEATURES AND SPECIFICATIONS
Categorized as a hypersonic rocket-powered aircraft, the North American X-15 is in a class of its own,
being the only manned hypersonic “aircraft” in history. The distinguishing factor between the X-15
and other hypersonic projects, for example the Space Shuttle, is that the X-15 was specialized and
primarily utilized in the Troposphere, Stratosphere, and the Mesosphere, whereas the Space Shuttle
and other projects were tailored for the thermosphere and beyond. Recalling that in aerospace design
form follows function, one can accurately visualize the X-15 by reviewing its design mission, even
before laying eyes on the aircraft. Below in Tables 2-2 through 2-6, the dimensions and performance
of the X-15 is listed. Using form follows function, one can see how the dimensions of the X-15 were
decided on, due to the required performance of the plane. Table 2-1, acquired from Anthony Mendoza
under Geometry and Weight, shows the geometric dimensions of the X-15.
Table 2-1. X-15 Geometry
Wing
Airfoil section NACA 66005 (modified)
Total area 200 sq ft
span 22.36 ft
mean aerodynamic chord 10.27 ft
root chord 14.91 ft
tip chord 2.98 ft
taper ratio 0.2
Aspect ratio 2.5
Flap
Type Plain
Area (each) 8.3 sq ft
Span 4.5 ft
Horizontal Tail
Airfoil section NACA 66005 (modified)
Total area 115.34 sq ft
span 18.08 ft
root chord 10.22 ft
taper ratio 0.21
Aspect ratio 2.83

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Upper vertical tail
Airfoil section 10deg single wedge
span 4.58 ft
root chord 10.21 ft
tip chord 7.56 ft
taper ratio 0.74
Aspect ratio 0.51
Lower Vertical tail
Airfoil section 10deg single wedge
span 3.83 ft
root chord 10.21 ft
tip chord 8 ft
taper ratio 0.78
Aspect ratio 0.43
Fuselage
length 50.75 ft
max width 7.33 ft
max depth 4.67 ft
side area 215.66 sq ft
fineness ratio 10.91
Speed brake
Area (each) 5.57 sq ft
Span 1.67 ft
chord 3.33 ft
Deflection,deg 35
2.3 X-15 FLIGHT 3-65-97 CRASH AND FATALITY
The loss of an aircraft is a scenario that a designer has much capital invested in preventing from
becoming a reality. The loss of a human life as a result of the failure of an aircraft is the nightmare of
a designer. Every effort is made to minimize the probability of the loss of a human life on one’s
aircraft. As is evident in history, unfortunately lives are lost either through the partial or full fault of
the aircraft. In the X-15 program history, one fatality occurred on 15 November 1967, with Major
Michael J. Adams perishing.

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2.3.1 ACCIDENT CAUSES
Accidents are attributed to a series of events culminating in an unfortunately perfect scenario leading
to the demise of a planned mission. The initial event in the case of Flight 3-65-97 was an electrical
disturbance which degraded the stability and control response of the X-15 with respect to pilot input.
This caused a distraction for Adams, which led to the yawing of the X-15 by a maximum value at the
peak altitude of 15 degrees. Adams successfully recovered from the yaw, however a spin had already
begun due to the yaw angle. This spin was unrecoverable due to the lack of sufficient density at the
flight altitude to provide a sufficient recovering force, and the decreased response of the control
surfaces due to the original electrical disturbance. Moreover, the reaction control system’s rocket
thrusters were not powerful enough to correct the spin. This led to the disintegration of the X-15 upon
atmospheric re-entry and the death of Major Adams. [5] It was speculated that Major Adams had
vertigo, which further hindered Major Adams’s ability to recover from the spin.
2.3.2 LESSONS LEARNED
A NASA and USAF accident board concluded that the loss of control of the X-15 was attributed to
pilot distraction, misinterpretation of cockpit instrumentation, possible vertigo, and increased pilot
workload due to the original electrical disturbance. As a result of these findings, the accident board
gave two recommendations. First, install a telemetered heading indicator in the ground control room,
and also to medically screen all pilots for vertigo. One lesson that individuals can take away from this
unfortunate example is that it is always okay to abort a mission, even due to minor failures, such as the
electrical disturbance at the beginning of the X-15 flight. Stopping the chain of events from unfolding
is much easier of a task than to continue the mission and attempt to stay ahead of the curve.
3 CAPSTONE PROJECT REQUIREMENTS
A three tiered process is utilized for this project. First, The X-15 is to be reverse engineered, proving
that the X-15 could do what was claimed to have been accomplished. Once this is proven, the outputs
of the reverse engineering will be used to modify the X-15 into two new iterations of the X-15 with as
little modifications as possible. These two new vehicles are the second and third tier of this project.
The second vehicle’s mission will be sub-orbital space tourism for one passenger, similar to the mission
of Scaled Composites Spaceship Two (SS-2). The third vehicles mission is DARPA’s XS-1 mission
of a reusable first stage vehicle to orbit. Parametric sizing is the process used for all three tiers of this
project.
3.1 DEFINED EXPERIMENTAL PROCESS AND SCOPE
The scope of this project focuses on eight specific disciplines: Synthesis, Aerodynamics, Systems,
Geometry and Weight, Stability and Control, Performance, Structures, and Propulsion. Since this
project is solely dealing with conceptual design of the three vehicles, the desired outputs for each
parametric sizing are limited to the key driving parameters of the aerospace design of vehicles, which
includes but is not limited to: planform size, overall weight, engine power requirements, fuel fraction,
and total vehicle size.

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3.2 INDIVIDUAL RESPONSIBILITIES AND SCOPE
As the chief engineer of S.M.A.R.T., my responsibilities and scope include project management,
focusing the direction of the group, verifying accurate and precise work, collecting outputs from each
discipline, creating outputs based off of discipline outputs including matching charts and other
verification results, and the adherence to a schedule. This can be sufficiently summarized as the head
of the synthesis discipline, and project manager of S.M.A.R.T. These responsibilities are visually
represented into a non-specific IDA for synthesis in Fig. 3-1 below.
Figure 3-1. Non-Specific IDAfor Synthesis
3.3 TEAM RESPONSIBILITIES AND SCOPE
The responsibility of S.M.A.R.T. as a whole, is to take inputs from the knowledge base created from
the data base, and produce outputs. These outputs produced at each discipline are transferred to
synthesis as inputs, which synthesis analyzes, and creates outputs that represent the work of
S.M.A.R.T. as a whole. These synthesis outputs will include matching charts, parameters of each
vehicle found derived from the matching area, and further analysis performed based upon the
calculated vehicle parameters. S.M.A.R.T.’s organization and hierarchy is visualized in Fig. 3-2
below. The specific responsibility and scope of each discipline will change based upon which of the
three derivatives of the X-15 are being worked on, and will be detailed under each specific vehicles
chapter.
Synthesis
Disciplines
Inputs
Outputs

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Figure 3-2. S.M.A.R.T. Organizational Chart
4 X-15 REVERSE ENGINEERING
The question to be answered when reverse engineering an aerospace vehicle is first, could the vehicle
accomplish what it claimed to have accomplished. An interesting way to put this is that you must first
prove the conspiracy theorists wrong by comparing the physical and aerodynamic characteristics of
the vehicle, with that of its claimed mission. In many ways, one is proving that the vehicles form
follows its function. Once this reverse engineering is completed, a platform has been created whereby
modification of the vehicle in order to pursue another mission is possible. This is the essence of why
we are reverse engineering the X-15. It is a very successful vehicle that was claimed to have pushed
the boundary in an emerging hypersonic regime. However, before new vehicles are based off of the
original X-15, one must prove in an engineering design fashion that the vehicle was not a “dead horse”.
This will be accomplished via a parametric sizing study which will produce a matching chart and hence

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the meaningful parameters of the X-15. These outputs can then be compared to the claimed X-15
parameters, which will either confirm or bust the claims.
4.1 MANAGING, SCHEDULING AND ORGANIZING
I decided to use a moderately hands off managerial approach when dealing with individual discipline’s
decision making process. The reasoning behind this was to increase creativity and diversification
between disciplines, and to have each member base their work off of their own ideas, therefore
allowing discipline members to take ownership of their work, rather than feel micro-managed.
Granting individual’s freedom to explore is productive, however must be checked with recurring
meetings. Once a week on Wednesdays after Dr. Chudoba’s lecture, S.M.A.R.T. meets in the AIAA
room in Woolf Hall in order to re-focus our engineering creativity. The main purpose of these meetings
is to prevent any one discipline from straying too far away from the rest of the team. Further, this is a
time for easy and fast communication with other disciplines for information sharing. At the beginning
of the design process, I created an initial time frame schedule shown in Fig. 4-1 below.
Figure 4-1. Original S.M.A.R.T. Timeline
4.2 PARAMETRIC SIZING LITERARY KNOWLEDGE BASE
While many literary references are utilized throughout this design process, the two main works used
to guide S.M.A.R.T. through the parametric sizing studies are Jan Roskam’s “Airplane Design:
Preliminary Sizing of Airplanes” and the course text, Nicolai and Carichner’s “Fundamentals of
Aircraft and Airship Design: Aircraft Design”. Roskam details his oft referenced parametric sizing
process, which S.M.A.R.T.’s synthesis uses to create the matching chart for the original X-15, shown
in Fig. 4-2. Nicolai is used for specific information related to each discipline, since this reference
focuses on detailed specifics of many disciplines.

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Figure 4-2. Roskam Design Process [6]
4.3 DISCIPLINE ANALYSIS AND CONTRIBUTION
While reverse engineering the X-15, each discipline needed inputs in order to analyze the inputs which
creates meaningful outputs. Sometimes, the disciplines referenced our literature data base and
knowledge base, while other times other disciplines were able to provide their outputs as inputs for
other disciplines needing their results. A visualization of this analysis between all disciplines of the
design team is shown below in Fig. 4-3 in our multi-disciplinary analysis (MDA). Arrows entering
the left side of a discipline are inputs received, and each disciplines analysis results in an output that
leaves the right side of the discipline in Fig. 4-3. One easily notices the large amount of communication.

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Figure 4-3. S.M.A.R.T. X-15 Reverse Engineer MDA

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4.4 SYNTHESIS
As Chief Engineer, my work mainly was focused in synthesis and managerial tasks. I have two
supporting synthesis engineers, David Zaki who synthesizes Aerodynamics, Stability and Control, and
Performance. Rabin Bhandari, my other synthesis engineer, oversees Propulsion, Structure, Geometry
and Weight, and Systems.
Figure 4-4. Synthesis IDA
Final outputs by the synthesis team include a multi-dimensional analysis diagram, a semester timeline,
parametric sizing study parameters, a matching chart with comparison to the actual X-15, a summary
wall poster, and the team PowerPoint. The synthesis IDA is a summarization of how the final outputs
are resolved, and is shown in Fig. 4-4.
Two of the most labor intensive of the synthesis outputs include the matching chart and the
aerodynamic forces partial differential equation numerical analysis. The former is a standard chart
used during aerospace vehicle design to visually summarize the main vehicle characteristics, mainly
the thrust and wing loading which details the power required from the engine, and the size of the wing
required to satisfy all mission requirements. This is detailed more in 4.4.1. Due to the unique mission
requirements of the X-15, there are much less constraints on the matching charts as opposed to the
normal passenger airplane. Because of this scenario, solely producing a matching chart as the
summarization of all of the disciplines work seemed to cheapen the magnitude of the effort put forth
Known Information
from Data and
Knowledge Base
and Discipline
Outputs
Max Speed
3794 mph
Rate of Climb Matching Chart
Thrust Loading
Wing Loading
PDE Numerical
Analysis
T/W(L/D , CGR)
Landing
(Stall Speed)
W/S(Cl max, Vstall)
Four
Aerodynamic
Forces PDEs
T/W(L,D,T,W)
Numerical
Comparison of
Velocity and Altitude

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into this assignment. Therefore, it was decided to also include a PDE numerical comparison of the X-
15, which would allow the synthesis team to utilize more outputs from each discipline in visual
summarizations of our work.
4.4.1 MATCHING CHART
A parametric sizing study matching chart is a plot of thrust at sea level to weight at takeoff ratio (T/W)
versus a weight at takeoff to sing planform area ratio (W/S). Plotted on this chart are performance
constraints of the entire vehicle, including maximum velocity, stall speed, and rate-of-climb
requirements. These three constraints were the determined parameters to plot on the matching chart
since these were the defining capabilities of, and what made the X-15 the aerospace vehicle it was.
The X-15 was a hypersonic (maximum velocity) aircraft that could reach space (rate-of climb), and
that was then able to land horizontally and be re-used (stall speed requirement due to the landing
velocity).
From the following equations that I derived, a matching chart was created via plotting the
functions in Microsoft Excel.
(
T
W
)
Vmax
= f1( 𝐿, 𝐷, 𝑊) (4.1)
(
W
S
)
𝑆𝑡𝑎𝑙𝑙
= f2 (
W 𝑇𝑂
W𝐿𝑎𝑛𝑑𝑖𝑛𝑔
, VStall, 𝐶𝐿 𝑀𝑎𝑥
, 𝜌) (4.2)
(
T
W
)
𝑅𝑂𝐶
= f3 (
𝐿
𝐷 𝑚𝑎𝑥
, 𝐶𝐺𝑅) (4.3)
4.4.1.1 ATMOSPHERIC CONDITIONS
In order to do a numerical analysis of all four aerodynamic forces, it was very useful to represent
density and speed of sound as an exponential function and a polynomial function with respect to height,
respectively. Therefore, each iteration at different altitudes would have an accurate value for density
and the speed of sound at that time step. Appendix B of Nicolai’s design book has the atmospheric
data points needed to then plot the density and speed of sound points on a scatter plot in Microsoft
Excel. An example of this can be shown with Fig. 4-5 below.
𝜌 = 0.002576 ∗ 𝑒−.0000431067∗ℎ 𝑠𝑙𝑢𝑔𝑠
𝑓𝑡3
(4.4)
𝑎 = 6.71 ∗ 10−19
∗ ℎ4
− 4.59 ∗ 10−13
∗ ℎ3
+ 9.88 ∗ 10−8
∗ ℎ2
− 7.22 ∗ 10−3
ℎ + 1128
𝑓𝑡
𝑠
(4.5)

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Figure 4-5. Speed of Sound versus Altitude
4.4.1.2 LIFT AND DRAG COEFFICIENTS
Another two preparatory functions were needed before conducting a numerical analysis of the four
aerodynamic forces. These two equations are the coefficients of lift and drag as functions of velocity
and speed of sound. In order to obtain data points for the coefficients of lift and drag as functions of
velocity and speed of sound (the same as saying a function of Mach number), a NASA publication of
X-15 data was consulted. [7] The resulting graphs and their second order polynomial trend lines are
shown below in Fig. 4-6 and 4-7.
𝐶𝐿 = 0.021051 ∗ (
𝑉
𝑎(ℎ)
)
2
− 0.213623 ∗ (
𝑉
𝑎(ℎ)
)+ 0.687301 (4.6)
𝐶 𝐷 = 0.006013 ∗ (
𝑉
𝑎(ℎ)
)
2
− 0.068946 ∗ (
𝑉
𝑎(ℎ)
) + 0.256026 (4.7)
y = 6.7179E-19x4
- 4.5944E-13x3
+ 9.8826E-08x2
- 7.2235E-03x + 1.1285E+03
R² = 9.6699E-01
850
900
950
1000
1050
1100
1150
0 50000 100000 150000 200000 250000 300000 350000
SpeedofSound(feet/second)
Altitude (feet)
Speed of Sound versus Altitude

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Figure 4-6. X-15 Coefficient of Lift vs. Mach Number
Figure 4-7. X-15 Coefficient of Drag vs. Mach Number
y = 0.021051x2
- 0.213623x + 0.687301
R² = 0.972303
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6
CoefficientofLift
Mach Number
X-15 Coefficient of Lift versus Mach Number
y = 0.006013x2
- 0.068946x + 0.256026
R² = 0.982314
0
0.04
0.08
0.12
0.16
0.2
0 1 2 3 4 5 6
CoefficientofDrag
Mach Number
X-15 Coefficient of Drag versus Mach Number

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4.4.1.3 RATE OF CLIMB
All of the preparatory equations besides the four force PDE’s have been defined, so for now let us
focus first on the two constraints not needing a numerical analysis to plot on the matching chart, that
is rate of climb and stall speed.
The rate of climb is normally a constraint on the matching chart due to FAR part 23 or 25 requirements
for various missed approaches or takeoffs. However, the rate of climb constraint is used on the reverse
engineering X-15 matching chart in this case in order to prove that the X-15 could climb (reach 354,200
feet) as has been recorded by NASA. Roskam has the rate of climb equation shown in Eqn. 4.7, which
is then modified for our specific scenario of the X-15 climbing at a 45 degree climb angle with 8
degrees angle of attack. [5]
𝑇
𝑊
=
1
( 𝐿
𝐷
)
+ 𝐶𝐺𝑅 (4.7)
CGR =
( 𝑑ℎ
𝑑𝑡
)
𝑉𝑡𝑟𝑢𝑒
(4.8)
Since the true velocity and the time rate of change of altitude are related in our 45 degree climb scenario
as the hypotenuse and the leg of a 45, 45, 90 triangle, CGR reduces to 0.707, as is shown in Fig. 4-8,
due to trigonometric relationships. Eq. 4.9 details this conversion. The climb angle and the lift drag
ratio during the climb was provided by Reed Gibson from Performance.
Figure 4-8. Simplification of CGR
(
𝑑ℎ
𝑑𝑡
)
𝑉𝑡𝑟𝑢𝑒
= 𝐶𝐺𝑅 = sin(45°) = 0.707 (4.9)
45°
dh/dt
V true

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Knowing that the X-15 climbed at the max lift over drag ratio, 2.25, at an angle of attack of 8
degrees, the rate of climb constrain matching chart equation reduces down to a constant. This
makes sense due to the fact that the rate of climb should not be dependent upon the wing loading
parameter.
𝑇
𝑊
=
1
(2.25)
+ 0.707 = 1.15 (4.10)
4.4.1.4 STALL SPEED
The wings on the X-15 are obviously sized for the landing segment of the mission. The X-15 rides the
thrust vector during the initial climb portion of the mission, coasts to maximum altitude via conversion
of kinetic energy to gravitational potential energy, allows gravity to accelerate itself back through the
atmosphere, and solely needs the full area of the wings so that the landing speeds are not too
ridiculously high. At an average landing speed of 215 mph, the X-15 was once in the Guinness Book
of World Records as the fastest landing speed aircraft. [8] Knowing this, we can size the wings of the
X-15 based on the landing speed. Conversion of this speed to stall speed is most useful since Roskam
has a parametric sizing equation of wing loading for the stall speed, Eq. 4.12. Moreover, in Laurence
Loftin’s “Subsonic Aircraft”, he relates stall speed to landing approach speed, as is shown in Eq. 4.11.
[9] Assuming that the approach velocity and the landing velocity are equal for the gliding X-15, a wing
loading constraint can be used on the matching chart for landing speed, which is a known value.
V 𝑎𝑝𝑝𝑟𝑜𝑎𝑐ℎ = V𝑠𝑡𝑎𝑙𝑙 ∗ 1.3 (4.11)
𝑉𝑠𝑡𝑎𝑙𝑙 = √
2 ∗
𝑊
𝑆
𝜌 ∗ 𝐶𝐿 𝑚𝑎𝑥
(4.12)
Vapproach ≡ V𝑙𝑎𝑛𝑑𝑖𝑛𝑔 (4.13)
𝑉𝑙𝑎𝑛𝑑𝑖𝑛𝑔 = 1.3 ∗ √
2 ∗
𝑊
𝑆
𝜌 ∗ 𝐶𝐿 𝑚𝑎𝑥
(4.14)
ρ2,000 ft = 0.0022409
𝑠𝑙𝑢𝑔𝑠
𝑓𝑡3
(4.15)
C 𝐿 𝑚𝑎𝑥
= 1.15 (4.16)

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𝑊𝑡𝑎𝑘𝑒𝑜𝑓𝑓
𝑆
=
𝑉𝑙𝑎𝑛𝑑𝑖𝑛𝑔
2
∗ 𝜌 ∗ 𝐶𝐿 𝑚𝑎𝑥
3.38
∗
𝑊𝑙𝑎𝑛𝑑𝑖𝑛𝑔
(4.17)
=
34,000 𝑙𝑏𝑓
14,600 𝑙𝑏𝑓
(4.18)
𝑆
= 176.55
𝑙𝑏𝑓
𝑓𝑡2
(4.19)
Due to the hierarchy of our team, when receiving X-15 values from varying disciplines, it is most
efficient to talk directly with the lead engineer. Therefore, Junaid Ahmed provided the takeoff and
landing weights of the X-15. Abhisekh Manandhar provided the maximum coefficient of lift and the
landing speed.
4.4.1.5 AERODYNAMIC FORCES PARTIAL DIFFERENTIAL EQUATION NUMERICAL ANALYSIS
In order to verify that the maximum velocity and altitude can be attained by the X-15, a numerical
analysis was performed using four, second-order partial differential equations that describe the
accelerations due to lift, drag, thrust, and weight. The derivation of each equation is shown below,
followed by the results of the simultaneous solution of each equation.
Recalling that preparatory equations have already been derived in 4.4.1.1 and 4.4.1.2, we can proceed
with those results.
Figure 4-9. Varying Thrust with Altitude [10]
Let us first derive the partial differential equation for the acceleration due to thrust. Two more
preparatory equations must first be derived before proceeding however. These two are the equations
of mass with respect to burn time of the XLR-99 engine, and thrust with respect to altitude. Utilizing

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Fig. 4-9, a polynomial trend line equation can be created for thrust with respect to altitude. This is
shown below in Fig. 4-10. The thrust points are based off of Fig. 4-9, which was provided by
Prajwal Shrestha, the propulsion lead engineer.
Figure 4-10. Thrust versus Altitude
𝑇 = −1.869 ∗ 10−7
∗ ℎ2
+ 8.648 ∗ 10−2
∗ ℎ + 51,384 𝑙𝑏𝑓 (4.20)
Mikayla Davis, the lead systems engineer, provided the information that the flux of weight during the
XLR-99 burn was 218.92 lbf/s. Knowing that the initial weight before the XLR-99 ignition was
34,000 lbf, the mass with respect to burn time can be calculated in slugs, Eq. 4.21.
m = 1055.9 slugs − 6.799
𝑠𝑙𝑢𝑔𝑠
𝑠𝑒𝑐𝑜𝑛𝑑
∗ 𝑡 seconds (4.21)
Recalling that acceleration is a force divided by a mass, the thrust equation can be formed.
𝑑2 𝑠 𝑇
𝑑𝑡2
=
−1.869∗10−7∗ℎ2+8.648∗10−2∗ℎ+51,384
1055.9−6.799 ∗𝑡
𝑓𝑡
𝑠2
(4.22)
Since we are dealing with a vehicle capable of reaching space, it is not a safe assumption that the
acceleration due to gravity is a constant. Therefore, the gravitational acceleration equation should be
used. This equation will represent the acceleration due to gravity with respect to altitude on the X-15
during the XLR-99 burn.
𝑑2 𝑠 𝑊
𝑑𝑡2
=
𝐺∗𝑚 𝑒𝑎𝑟𝑡ℎ
𝑟2
(4.23)
y = -0.0000001869x2
+ 0.0864770618x + 51,384.7319702751
R² = 0.8914809514
0
10000
20000
30000
40000
50000
60000
70000
0 50000 100000 150000 200000 250000 300000 350000
XLR-99Thrust(lbf)
Altitude (feet)
Thrustversus Altitude

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𝑑2 𝑠 𝑊
𝑑𝑡2
=
14.072∗1015
(ℎ+20.925∗106)2
𝑓𝑡
𝑠2
(4.24)
With the thrust and weight accelerations derived, we will move on to lift and drag. Both of these
derivations will include the coefficient equations, the speed of sound with respect to altitude
equations, and the density as a function of altitude equation. Let us start with lift.
𝐿 = 𝐶𝐿 ∗ 𝑞 ∗ 𝑆 (4.25)
𝑑2 𝑠 𝐿
𝑑𝑡2
=
𝐶 𝐿 ∗𝑆∗𝜌∗𝑉2
2∗(1055.9−6.799∗𝑡)
(4.26)
Junaid Ahmed, lead engineer of Geometry and Weight, provided the planform area as 200 square
feet. Using this value, and the preparatory equations plugged in, we derive the final acceleration due
to lift, in the direction of lift equation. The speed of sound equation is not plugged in so as to avoid
an unnecessarily long equation filling up the page.
𝑑2 𝑠 𝐿
𝑑𝑡2
=
(0.021051∗( 𝑉
𝑎(ℎ)
)
2
−0.213623∗( 𝑉
𝑎(ℎ)
)+0.687301) ∗(0.2576∗𝑒−.0000431067∗ℎ)∗𝑉2
(1055.9−6.799∗𝑡)
𝑓𝑡
𝑠2
(4.27)
Deriving the drag equation is the exact same as the lift equation, however the coefficient of drag is
substituted for the coefficient of lift. Therefore, we can simply replace Eq. 4.27 with the coefficient
of drag equation, and have derived the acceleration due to drag equation.
𝑑2 𝑠 𝐷
𝑑𝑡2
=
(0.006013∗( 𝑉
𝑎(ℎ)
)
2
−0.068946∗( 𝑉
𝑎(ℎ)
)+0.256026) ∗(0.2576∗𝑒−.0000431067∗ℎ)∗𝑉2
(1055.9−6.799∗𝑡)
𝑓𝑡
𝑠2
(4.28)
With all aerodynamic acceleration equations derived in their own direction, we can now numerically
iterate all four equations simultaneously. Two different summations of all four accelerations are
needed in order to calculate two different accelerations, vertical acceleration and directional
acceleration. A temporal step size of 0.1 seconds was chosen, with initial conditions of an altitude of
40,000 feet and a velocity of 774.48 ft/s, which is Mach=0.8 at 40,000 feet altitude on a standard day.
The new altitude and velocity after each step size is calculated by utilizing the kinematic equations.
𝑎 𝑦 =
𝑑2 𝑠 𝑇
𝑑𝑡2
∗ cos(90 − ( 𝛼 + 𝜃)) +
𝑑2 𝑠 𝐿
𝑑𝑡2
∗ cos( 𝛼 + 𝜃) −
𝑑2 𝑠 𝐷
𝑑𝑡2
∗ cos(90 − 𝜃) −
𝑑2 𝑠 𝑊
𝑑𝑡2
(4.29)
𝑎 𝑑 =
𝑑2 𝑠 𝑇
𝑑𝑡2
∗ cos( 𝛼) −
𝑑2 𝑠 𝑊
𝑑𝑡2
∗ cos(270 + 𝜃) −
𝑑2 𝑠 𝐿
𝑑𝑡2
∗ cos(90 − 𝛼) −
𝑑2 𝑠 𝐷
𝑑𝑡2
(4.30)
ℎ𝑓 = 𝑉𝑖 ∗ cos(90 − 𝜃) ∗ 𝛥𝑡 +
(𝑎 𝑦∗𝛥𝑡2)
2
+ ℎ𝑖 (4.31)
𝑉𝑓 = 𝑎 𝑑 ∗ 𝛥𝑡 + 𝑉𝑖 (4.32)

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Figure 4-11. X-15 Aerodynamic Accelerations versus XLR-99 Burn Time
Figure 4-12. X-15 Altitude and Velocity versus XLR-99 Burn Time
0
25
50
75
100
125
150
0 10 20 30 40 50 60 70 80 90
Acceleration
(ft/s^2)
time
(s)
X-15 Aerodynamic Accelerations Versus XLR-99Burn Time
Thrust
Drag
Lift
Weight
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0
50000
100000
150000
200000
250000
300000
350000
400000
0 20 40 60 80
Velocity
(ft/s)
Altitude
(ft)
time
(s)
Altitude and Velocity During XLR-99 Burn
Altitude
Actual Burn-
Out Altitude
Velocity
Actual
Maximum
Velocity

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The results of the Aerodynamic Acceleration PDE’s Numerical Analysis can be summarized in Fig.
4-11 and Fig. 4-12. The errors associated between the claimed velocity and altitude at burn out, and
the calculated velocity and altitude at burn out can be viewed in Table 4-1. The two errors associated
with the claimed versus calculated altitude and velocity are certainly within the range of error
expected by a first-order approximation method. Therefore the numerical analysis is proof for the X-
15 being able to do what has been claimed to have been done.
TABLE 4-1. CALCULATED AND CLAIMED VELOCITIES AND ALTITUDES
Velocity at Burn Out Altitude at Burn Out
Claimed 5,565 ft/s 160,000 ft
Calculated 5,046 ft/s 180,877 ft
Error -6.44% 16.39%
4.4.1.6 MAXIMUM VELOCITY
The maximum speed for mission 091 was claimed as M=5.58, 3,794 mph, 5,564.53 ft/s. None of the
referenced texts were able to provide an equation for thrust loading to size the engine based on such a
high value. Since this constraint was believed to be the critical constraint, that is to say the constraint
that determines the size of the engine, the numerical PDE analysis for the four aerodynamic forces was
used to verify that the X-15’s actual thrust loading led to a maximum velocity near this claimed value.
This turned out to be true, so the value on our matching chart for thrust loading based upon the
maximum velocity constraint will be the same as the actual thrust loading of the X-15. We allow
ourselves to do this since our numerical analysis led us to the same result as reality.
𝑇
𝑊
=
50,000 𝑙𝑏𝑓
34,000 𝑙𝑏𝑓
= 1.47 (4.33)
4.4.1.7 MATCHING RESULTS
The final combination of all the equations and variables are visually represented in Fig. 4-13, the
matching chart. The actual X-15 falls right on the matching space, and gives us confidence that the X-
15 indeed could do what was claimed, which allows us to now design new vehicles based off of this
proven concept. The equations used for the matching chart are located in Table 4-2. The X-15 has a
lot less number of constraints plotted as opposed to normal aircraft. This is due to the lack of necessity
to conform to FAR requirements since the X-15 is not a civilian transport aircraft.

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Figure 4-13. Matching Chart of the X-15
TABLE 4-2. MATCHING CHART FINAL EQUATIONS
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 50 100 150 200 250
ThrustLoading
WingLoading (psf)
Matching Chart
Max Speed
Rate of Climb
Landing
Actual X-15
Equations
Stall
Speed
𝑊𝑇𝑂
𝑆
=
𝑉𝑙𝑎𝑛𝑑𝑖𝑛𝑔
2
∗ 𝜌 ∗ 𝐶𝐿 𝑚𝑎𝑥
3.38
∗
Maximum
Speed
𝑇𝑆𝐿
𝑊𝑇𝑂
=
−1.869 ∗ 10−7
∗ ℎ2
+ 8.648 ∗ 10−2
∗ ℎ + 51,384
(1055.9 − 6.799 ∗ 𝑡) ∗ 𝑔
Rate of
Climb
𝑇𝑆𝐿
𝑊𝑇𝑂
=
1
(
𝐿
𝐷
)
+ 𝐶𝐺𝑅

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5 FUTURE WORK
Over the course of the next 6 weeks, S.M.A.R.T. is tasked with designing a minimally altered X-15
capable of a space tourism mission in addition to another vehicle that is minimally altered from the X-
15 capable of single stage to orbit missions. Inter-discipline communication will be vital during these
design stages even more so than what was needed in the reverse engineering process since no longer
can a team member solely research values, but rather must receive all values from team members.
6 CONCLUSIONS THUS FAR
Our confidence is very high that the X-15 is capable of claimed milestones such as hypersonic flight
and sub-orbital space access capability. Now that this confidence has been attained and valuable data
and analysis performed, we are able to push on to designing vehicles based off of the X-15 platform,
thus reducing the costs that clean sheet design vehicles attain and doing more with less.
7 INTERMEDIATE CHANGES
The key to success in the aerospace industry is flexibility. This principle’s importance is of such
magnitude due to the usual extended length of time necessary to produce a commercially or militarily
viable vehicle. With the change in time comes also a change in certain requirements, ergo the necessity
for flexibility.
7.1 TEAM MEMBER ATTRITION
Due to unfortunate circumstances, three team members dropped the aerospace design class halfway
through the semester including both performance engineers, Danny Luong and Reed Gibson, as well
as one aerodynamics engineer, Rima Rai. Because of these losses, a restructuring of the S.M.A.R.T.
hierarchy is necessary, which is detailed in Fig. 4-14. The restructuring consisted of eliminating the
systems discipline, due to this discipline being the least relevant discipline. Mikayla Davis, the former
systems lead engineer, became the sole engineer in the performance discipline. Further, the
aerodynamics discipline shrank by one engineer, Rima Rai. This is the totality of the changes made to
our hierarchy.

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Figure 7-1. S.M.A.R.T. Organizational Chart Post-Midterm
7.2 MISSION OBJECTIVE CHANGES
The original objective that was presented at the beginning of the semester was to complete three
phases, including a reverse engineering of the X-15, and two minimal modifications to the X-15 in
order for the vehicle to achieve a suborbital space tourism mission, and an orbital mission. Due to
time constraints, the orbital mission has been removed from this semesters objectives. This allows
more time to focus on the space tourism mission, which directly results in a higher quality of work.

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8 X-15 SS-2 RE-DESIGN
The second and last mission to be completed during this semester is to have the X-15 complete the
mission profile of Scaled Composites’ SpaceShipTwo and the payload capacity of SpaceShipOne.
That is to say, to reach an altitude apogee of 110 kilometers while carrying two passengers in addition
to the one pilot.
8.1 MINIMAL MODIFICATION
A defining requirement to keep in mind is the request by the customer to minimally modify the X-15.
This is the central pillar from which our design framework will be built around. One way to interpret
this requirement is to say that each discipline is to alter the X-15 in the least bit possible while also
satisfying one’s discipline’s objective which results in the X-15 meeting this new mission. A
secondary branch of this requirement that must be followed as well, is the knowledge that the smallest
adjustment on one discipline’s design modification may cause a huge adjustment needed with another
discipline. Therefore, occasionally a discipline needs to not necessarily choose the smallest
modification due to the total modification amount drastically increasing. This is one of the many
reasons that inter-disciplinary communication is a must in aerospace design.
8.2 INTER-DISCIPLINARY COMMUNICATION
During the reverse engineering process of the X-15, analysis was performed by each discipline based
off of inputs from historical data. If there was a gap in communication between disciplines, then a
discipline that needed information about the X-15 on the subject of another discipline could simply do
the research themselves. This is not the case for our space tourism mission. A vehicle is being designed
with which there is no historical data. Due to this, inter-disciplinary communication is vital because
in order for one discipline to proceed, it needs the outputs from another discipline’s analysis. If work
is not finished in a timely manner by solely one discipline, then the whole design process can halt and
not resume until just one discipline finishes their analysis. To overcome this challenge, I have
motivated my two supporting synthesis engineers, Rabin Bhandari and David Zaki, to continuously
communicate with their respective discipline lead engineers on a daily basis. This synthesis
communication assures that any lack of information is addressed as soon as possible in order to prevent
halts in progress. This concept is even more important than normal due to the recent discovery that
our final presentations’ due date has been moved two weeks ahead of schedule.
8.3 RE-DESIGN PROCESS
The totality of the re-design process can be attributed to the increased payload and the slight increase
in apogee altitude. Since this is not a clean sheet design, the work load and time required to reach a
converged vehicle design is significantly shorter.

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8.4 SIZING ITERATIONS APPROACHING VEHICLE CONVERGENCE
In order to converge upon a final size of an aerospace vehicle, an initial empty weight estimate is
required. This initial empty weight is the weakest part of the conceptual design of a clean sheet
aerospace vehicle. However, with a moderate re-design, this can be a somewhat accurate estimate.
Figure 8-1. The Conceptual Design Process [11]
Fig. 8-1 details the clean sheet conceptual design process as illustrated by Nicolai. Following this
whole process in not necessary with a vehicle re-design, especially when minimal changes to the
vehicle is desired. Because of the customer’s request for minimum modification, as a team, we decided
that the main modifications to the original X-15 will be a lengthened fuselage to account for the
addition of two passengers sitting in tandem and the added fuel requirement, and also to increase
aerodynamic surfaces wetted area while keeping aspect ratio and wing loading constant to account for
the increased weight of the modified X-15. Positioning of the larger surfaces will be placed in positions

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that keep the current stability and aerodynamic derivatives as close to the original X-15 as possible.
The original powerplant, the XLR-99, will not change, and it is assumed that this engine will be capable
of taking the even heavier modified X-15 to the desired apogee altitude of 110 kilometers. This will
be confirmed or disproved by the performance team, and if necessary, a new powerplant will be
selected. The increase in volume of the modified X-15 to accommodate for the necessary increase in
fuel will arise from a lengthened fuselage only, and the aerodynamic surfaces will not house any of the
added fuel. Furthermore, the mission logistics will be assumed as not to change. That is to say that
the modified X-15 will be carried to 40,000 feet by a B-52 and released at this altitude at which point
the X-15 will take over from there. Adherence to portions of Fig. 8-1 is always necessary to some
point, and in our case, the bulk of the workload is associated with the sizing iterations necessary to
converge to the final vehicle capable of taking our X-15 and its pilot and two passengers to the apogee
altitude of 110 kilometers. The assumptions stated in this paragraph are the defining principles that
will ultimately shape our modified X-15. If any assumptions were to change that are stated in this
paragraph, then one can expect a very different final converged vehicle to be the solution.
Figure 8-2. Vehicle Sizing Iteration
8.4.1 SIZING ITERATION ALGORITHM
The first iteration empty weight estimate will be the empty weight of the original X-15, plus the added
weight due to the extended fuselage that allows the fitting of two passengers sitting in tandem. As is
shown in Fig. 8-2, input, analysis, and output from each discipline will ultimately determine the values
of the rest of the steps in our sizing algorithm. The result will not be close to the exact sized vehicle
Empty Weight
Fuel Weight
Take Off Weight
Vehicle Size

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necessary to complete the mission, however a vehicle size that more closely resembles the final
converged modified X-15 will be the result. Many iterations are necessary to be completed to arrive at
the converged solution. The change in empty weight with respect to sizing iterations completed is
visualized below in Fig. 8-3.
Figure 8-3. Sizing Iterations Changing Empty Weight
Using the derived partial differential equations for the forces on the X-15 during the XLR-99 burn, and
knowing the constant fuel flux of the XLR-99 rocket engine, the performance and propulsion
disciplines were able to work together to determine the weight in fuel needed to bring the modified X-
15 to a speed and altitude level where a coast up to 110 kilometers was possible. This fuel weight was
compiled for the first iteration, and the aerodynamics and stability & control disciplines sized the
aerodynamic surfaces to satisfy our original assumptions of constant wing loading and aspect ratio and
constant stability. With the larger surfaces came an increase in weight, determined by the structures
and geometry & weight disciplines, which added to the fuel weight gave us the takeoff weight of the
modified X-15 for the first iteration. These iterations required input, analysis, and outputs from every
discipline, and due to the large amount of interdisciplinary communication needed, the iterations took
a lot of time to complete.
This exact process was followed for the first three iterations. In order to determine the size of the
converged X-15, which was going to require much more iterations than the three performed iterations,
the empty weights for the first three iterations were matched to a logarithmic trend line, and the X-15
was determined to be converged when the empty weight changed by only 0.01 pounds after one
iteration. This was determined to happen at the 10,000th
iteration along the logarithmic trend line.
Figure 8-4 below is a visualization of this trend line.
Sizing Iterations Completed
ChangeinEmptyWeight
Converged Vehicle Empty Weight

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Figure 8-4. Logarithmic Trend Line of the Empty Weight versus Iteration Number
8.5 CONVERGED VEHICLE
With the converged empty weight known, the original assumptions were applied to arrive at the final
modified X-15 size, including its geometry and weight. Shown below in Table 8-1 are the weights for
the modified X-15 at varying iterations.
TABLE 8-1. WEIGHT OF THE MODIFIED X-15 FOR VARYING ITERATIONS
Iteration Fuel Weight (lbf) Empty Weight (lbf) Take Off Weight (lbf)
0 17,400 14,600 32,000
1 20,953 16,461 37,414
2 22,119 16,578 38,697
3 22,832 16,618 39,450
10,000 27,620 17,720 45,340
With the known weights for the modified X-15 vehicle, the geometry was determined by the
Aerodynamics, Stability & Control, and the Geometry & Weight disciplines. Once again, our initial
assumptions were that the aspect ratios of all aerodynamic surfaces would stay the same, the wing
loading would remain constant, and the size and placement of the non-wing surfaces would be such
that the stability of the new X-15 remain as close as possible to the original X-15’s stability. The result

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of these assumptions led to a vehicle very closely resembling the original X-15, with the only
noticeable differences being the increase in size and length.
Figure 8-5. Size Comparison of the New and Original X-15
TABLE 8-2. GEOMETRIC COMPARISON OF THE ORIGINAL AND MODIFIED X-15
Original X-15 Modified X-15
Wing Span 22.36 ft 24.63 ft
Length 49.33 ft 63.04 ft
Total Wing Planform Area 200.00 ft^2 242.74 ft^2
Original X-15
Modified
X-15

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9 RESULTS AND DISCUSSION
The results and their corresponding discussions of our X-15 project are divulged during a midterm
presentation and ultimately a final presentation. During these presentations, team S.M.A.R.T.
discusses the processes used to obtain meaningful results that lead to the desired conclusions of the
requested objectives enumerated at the beginning of the semester. The primary medium used to
accomplish this is Microsoft PowerPoint.
9.1.1 MIDTERM PRESENTATION
The midterm presentation was held on Friday, 24 October 2014. The results up to this presentation
were solely those dealing with the reverse engineering process of the X-15. The presentation of the
results was with an introduction by myself, the chief engineer, followed by a discussion by each
discipline concerning their results. Each member of each discipline participated in this discussion.
After all disciplines presented, I spoke with regards to synthesis, which gathered each discipline’s
outputs as inputs, and formed an overarching output/result in the form of a matching chart and physical
differential equation analysis.
9.1.2 FINAL PRESENTATION
The final presentation was held on Friday, 21 November 2014. The results up to this presentation were
those dealing with both the reverse engineering process of the X-15, and the mostly complete design
process of the modified X-15. As with the midterm presentation, an introduction by myself
commenced our presentation, followed by a discussion by each discipline concerning their results and
analysis process. Each member did not participate, since the day before the final presentation, both of
our propulsion engineers, Prajwal Shrestha and John Lasely quit our team and quit the class. In their
place, their synthesis engineer, Rabin Bhandari, discussed their results and analysis. The presentation
came to a conclusion during a final discussion concerning the synthesis portion of this project, in which
I brought together all the results from our disciplines into one overarching big picture.
10 CONCLUSIONS AND RECOMMENDATIONS
Over this past semester, our team’s knowledge over aerospace vehicle design grew drastically during
a reverse engineering process and space tourism modification of the North American X-15. With the
combination of in-class lectures detailing technical specifics of design and out of class team meetings,
research, and progress, a first order accurate analysis of the X-15 was performed. A general feel and
sense of what all is entailed with aerospace design and the challenges that are brought with this type
of field were learned. One recommendation of mine would be that rather than a modification of an
existing aircraft be performed throughout the semester, instead a clean sheet design be performed so
that the entire conceptual design process be practiced.

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REFERENCES
[1] Jenkins, Dennis R. Hypersonics Before the Shuttle: A Concise History of the X-15 Research Airplane. Washington D.C.:
NASA, 2000. N. pag. Web.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
Taylor, John W., ed. "North American X-15-A." Jane's All the World's Aircraft. 1963-1964 ed. London: Jane's
Information Group, 1963. N. pag. Print.
Taylor, John W., ed. "North American X-15-A." Jane's All the World's Aircraft. 1967-1968 ed. London: Jane's Information
Group, 1967. N. pag. Print
Mack, Pamela E., ed. "The X-15 Hypersonic Flight Research Program: Politics and Permutations at NASA." From
Engineering Science to Big Science: The NACA and NASA Collier Trophy Research Project Winners.
Washington D.C.: NASA, 1998. N. pag. Web.
Evans, Michelle. The X-15 Rocket Plane: Flying the First Wings into Space. Lake Forest, CA: Mach 25 Media, 2013. N.
pag. Web.
Roskam, Jan. Airplane Design: Preliminary Sizing of Airplanes. Vol. 1. Ottawa, Kansas: Roskam Aviation and
Engineering Corporation, 1985. N. pag. 8 vols. Print.
Saltzman, Edwin J., and Darwin J. Garringer. Summaryof Full-Scale Lift and Drag Characteristics of the X-15 Airplane.
Washington D.C.: NASA, 1966. N. pag. Print.
Matranga, Gene J. Analysis of X-15 Landing Approach and Flare Characteristics Determined from the First 30 Flights.
Washington D.C.: NASA, 1961. N. pag. Print.
Loftin, Jr., Laurence K. SubsonicAircraft: Evolution and the Matching ofSize to Performance. Hampton, Virginia: NASA,
1980. N. pag. Print.
Jenkins, Dennis R. X-15: Extending the Frontiers of Flight. Washington D.C.: NASA, 2012. N. pag. Print.
Nicolai, Leland M., and Grant E. Carichner. Fundamentals of Aircraft and Airship Design. Vol. 1. Reston, VA: American
Institute of Aeronautics and Astronautics, 2010. N. pag. 2 vols. Print.

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APPENDIX A – NOMENCLATURE
Variables Subscripts
a Speed of Sound d Direction Opposite Drag
C Coefficient D Drag
D Drag f Final
g Gravitational Acceleration i Initial
h Altitude Above Sea Level L Lift
L Lift T Thrust
q Dynamic Pressure W Weight
r Distance from Earth’s Center y Vertical Direction
s
S
t
T
V
W
CGR
ρ
θ
Position in the Direction of Force
Wing Planform Area
Time
Thrust
Velocity
Weight
Climb Gradient
Density
Angle Above the Horizon
ROC Rate of Climb

Burnett, Karl, SMART, Chief Engineer, Final

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