1. FLORIDA INSITUTE OF TECHNOLOGY
Project: Vulcan
Critical Design Review
Team Members
Kristen N. Erickson
Shane Favreau
Alan Cruz – Gerena
Gabrielle S. Leesman
Alejandro Leon – Velasco
Kyle J. Levin
Ismael Naranjo – Velez
Michael J. Robison
Jared Sork
December 5th
, 2014

2. E S R A | i
Table of Contents
Table of Figures.................................................................................... Error! Bookmark not defined.
Table of Tables ..................................................................................... Error! Bookmark not defined.
1.0 Executive Summary (Kyle Levin)............................................................................................ iv
2.0 Problem Statement and Objectives.............................................................................................. 1
2.1 Project Statement (Kyle Levin) ................................................................................................. 1
2.2 Objectives (Kyle Levin)............................................................................................................. 1
2.3 Requirements ...................................................................................................................... 1
2.3.1 Project Requirements (Kyle Levin)..................................................................................... 1
2.3.2 System Requirements (Kyle Levin)..................................................................................... 1
2.3.3 Sub-System Requirements ................................................................................................ 2
2.4 List of Deliverables (Kristen Erickson)....................................................................................... 3
2.4.1 Propulsion Deliverables (Michael Robison and Gabrielle Leesman).................................... 3
2.4.2 Structures Deliverables (Alan Cruz-Gerena)....................................................................... 4
2.4.3 Avionics Deliverables (Jared Sork, Shane Favreau, Kristen Erickson) .................................. 4
3.0 Background ................................................................................................................................. 4
3.1 Motivation behind the Project (Kyle Levin)............................................................................... 4
3.2 Previous Work Similar to Project (Kyle Levin) ........................................................................... 4
3.3 Social and Societal Impacts (Kyle Levin).................................................................................... 4
4.0 Subsystem Design........................................................................................................................ 5
4.1 Propulsion ............................................................................................................................... 5
4.1.1 Design Alternatives and Tradeoffs (Michael Robison and Gabrielle Leesman).................... 5
4.1.2 Motor Chosen Design Specifics (Michael Robison and Gabrielle Leesman)....................... 11
4.1.2.1 Ignition Systems (Michael Robison and Gabrielle Leesman).......................................... 11
4.1.2.2 Nozzle Design (Michael Robison and Gabrielle Leesman).............................................. 11
4.1.2.3 Injector System (Gabrielle Leesman and Michael Robison) ........................................... 13
4.1.3 System Integration (Michael Robison, Gabrielle Leesman, Alan Cruz – Gerena)............... 13
4.1.4 Testing (Michael Robison and Gabrielle Leesman)........................................................... 14
4.1.4.2 Motor Flow Analysis (Michael Robison, Kyle Levin, Gabrielle Leesman, and Kristen
Erickson).................................................................................................................................. 21
4.2 Structure................................................................................................................................ 22
4.2.1 Design Alternatives and Tradeoffs................................................................................... 22
4.2.2 Chosen Design Specifics .................................................................................................. 28
................................................................................................................................................ 33
DRAG .............................................................................................................................................. 65

3. E S R A | ii
VELOCITY, ACCELERATION, AND ALTITUDE ...................................................................................... 69
4.2.3 Testing............................................................................................................................ 73
4.3 Avionics and Payload (Jared Sork, Shane Favreau, Kristen Erickson) ....................................... 74
4.3.1 Design Alternatives and Tradeoffs (Jared Sork, Shane Favreau, Kristen Erickson)............. 75
4.3.2 Chosen Design Specifics (Jared Sork, Shane Favreau, Kristen Erickson) ............................ 77
𝐴 = 2𝑚𝑔𝜌𝐶𝐷𝑉2 ..................................................................................................................... 80
4.3.3 Testing (Jared Sork)......................................................................................................... 86
5.0 Plan and Schedule...................................................................................................................... 86
5.1 Milestones............................................................................................................................. 86
5.2 Key Testing Dates................................................................................................................... 86
5.3 Team Organization (Kyle Levin).............................................................................................. 87
5.3.1 Basic Description of Sub System Teams (Kyle Levin) ........................................................ 87
5.3.2 Team Delegations (Kyle Levin)......................................................................................... 87
6.0 Economic Analysis ..................................................................................................................... 88
6.1 Budget................................................................................................................................... 88
6.1.1 Propulsion....................................................................................................................... 88
6.1.2 Structures ....................................................................................................................... 88
6.1.3 Avionics and Payload....................................................................................................... 91
6.1.4 Total ............................................................................................................................... 91
6.2 Revenue ................................................................................................................................ 92
6.2.1 Secured Funding ............................................................................................................. 92
6.2.2 Expected Donations ........................................................................................................ 92
6.2.3 Pursued Donations (Kyle Levin) ...................................................................................... 92
6.3 Overall Cost Analysis (Kyle Levin) ........................................................................................... 92
7.0 Statement of Ethics (Kyle Levin)................................................................................................. 92
8.0 Conclusion (Kyle Levin) .............................................................................................................. 92
9.0 References................................................................................................................................. 93
10.0 Acknowledgements (Gabrielle Leesman).................................................................................. 96
11.0 Appendices.............................................................................................................................. 97
Appendix A.................................................................................................................................. 97
........................................................................................................................................................ 98
........................................................................................................................................................ 98
Appendix B.................................................................................................................................. 98
Appendix C................................................................................................................................ 101

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Appendix D................................................................................................................................ 110
Appendix E ................................................................................................................................ 113
Appendix F ................................................................................................................................ 115
Appendix G................................................................................................................................ 120
Appendix H................................................................................................................................ 123
Appendix I ................................................................................................................................. 124
Appendix J................................................................................................................................. 124
Appendix K ................................................................................................................................ 125
Appendix L................................................................................................................................. 125
Appendix M............................................................................................................................... 126
Appendix N................................................................................................................................ 126

5. E S R A | iv
1.0 Executive Summary (Kyle Levin)
The Experimental Sounding Rocket Association Team is to design and manufacture a small scale test
bed rocket to prove that the design process and manufacturing processes used are adequate. This
test bed will potentially be the forerunner to a full scale sounding rocket that would be launching to
10,000 feet AGL while carrying a technical payload with a minimum weight of ten pounds. During
the process of creating the small scale test bed, the team will be designing, manufacturing and
testing a propulsion system, airframe, fins, nosecone, electronics bay and potentially a payload. The
goal of this small scale rocket is to prove that the concepts and designs used to create the test bed
would be usable in the potentially succeeding sounding rocket. The team will be working on use of a
hybrid propulsion system on board a frame based rocket.
In order to complete the task at hand the team has been divided into three sub-teams each of which
will concentrate on the design aspects and manufacturing of their specific sub-system but will also
be working closely with the other sub-teams for integration purposes. The three sub-teams are
propulsion, airframe and avionics. The propulsion team will be working on designing and
manufacturing the hybrid motor system for the test bed rocket as well as the engine system for the
full sized sounding rocket in the future. Meanwhile the airframe team will be designing and
fabricating the fins, main airframe and nosecone of the rocket. This sub-team is also in charge of
ensuring that the rocket will remain stable during the duration of the motor burn, this is especially
important because the rocket is a hybrid and stability will change during motor burn unlike a solid
motor rocket. The avionics team will be working towards acquiring a payload for the succeeding
competition rocket as well as for the small test bed. They will also be working on creating the
electronics bay for the rocket that will control the deployment system as well as collect flight data
and potentially control the throttle of our hybrid motor. All of these sub-teams will work in
collaboration with each other to ensure full integration is possible at the end of the design and
fabrication processes. There is also a team lead who works with all three teams to help with
integration as well as assisting teams with their provided tasks. Team lead is also in charge of
ensuring that funding is acquired and all of the management level work is completed and on time.

6. E S R A | 1
2.0 Problem Statement and Objectives
2.1 Project Statement (Kyle Levin)
The Experimental Sounding Rocket Association team is to design, manufacture a small scale test bed
rocket to prove that the design process and manufacturing processes used are adequate. This test
bed will potentially be the forerunner to a full scale sounding rocket that would be launching to
10,000 feet AGL while carrying a technical payload with a minimum weight of ten pounds. During
the process of creating the small scale test bed the team will be designing, manufacturing and
testing a propulsion system, airframe, fins, nosecone, electronics bay and potentially a payload.
These will all culminate in the small scale test bed. The goal of this small scale rocket is to prove that
the concepts and designs used to create the test bed would be usable in the potentially succeeding
sounding rocket. The team will be working on use of a hybrid propulsion system on board a frame
based rocket.
In order to complete the task at hand the team has been divided into three sub-teams each of which
will concentrate on the design aspects and manufacturing of their specific sub-system but will also
be working closely with the other sub-teams for integration purposes. The three sub-teams are
propulsion, airframe and avionics. The propulsion team will be working on designing and
manufacturing the hybrid motor system for the test bed rocket as well as the engine system for the
full sized sounding rocket in the future. Meanwhile the airframe team will be designing and
fabricating the fins, main airframe and nosecone of the rocket. This sub-team is also in charge of
ensuring that the rocket will remain stable during the duration of the motor burn, this is especially
important because the rocket is a hybrid and stability will change during motor burn unlike a solid
motor rocket. The avionics team will be working towards acquiring a payload for the succeeding
competition rocket as well as for the small test bed. They will also be working on creating the
electronics bay for the rocket that will control the deployment system as well as collect flight data
and potentially control the throttle of our hybrid motor. All of these sub-teams will work in
collaboration with each other to ensure full integration is possible at the end of the design and
fabrication processes. There is also a team lead who works with all three teams to help with
integration as well as assisting teams with their provided tasks. Team lead is also in charge of
ensuring that funding is acquired and all of the management level work is completed and on time.
2.2 Objectives (Kyle Levin)
Our mission is to design and construct a test platform to demonstrate the construction methods,
propulsion design and payload capacity of a sounding rocket that can succeed the project and be
launched to 10,000 ft. while carrying a 10lb. technical payload.
2.3 Requirements
2.3.1 Project Requirements (Kyle Levin)
The main requirement of the project will be to submit a feasibility document based on the flight of
the sub-scale rocket. This document will need to investigate the operations of each sub-system and
the possibility of scaling the sub-systems up in their current form.
2.3.2 System Requirements (Kyle Levin)
The small scale rocket system will require the full integration of the work of all three sub-teams. It
will also be required that all of the sub-systems be tested to prove the feasibility of a large scale
version of the rocket that would launch to 10,000 ft. with a 10 lb. payload on board.

7. E S R A | 2
2.3.3 Sub-System Requirements
2.3.3.1 Avionics Requirements (Kristen Erickson)
 As the rules set by the ESRA competition state, the payload must be at least 10 lbs. This
includes any parts attached to the payload so long as they are not considered part of the bay
or on board electronics.
 The payload must be able to be removed from the rocket to be judged and then reattached
to the payload bay before each launch. This will ensure that there is no foul play involved in
the payloads and allows for judging to take place.
 The payload cannot contribute to any differentiation in peak altitude of the rocket when
compared to deadweight of the same mass. The payload must be a purely independent
mechanism from the flight of the rocket.
 Drogue chute must be deployed after the rocket reaches apogee. This is to prevent teams
from using the parachutes to ensure that their rockets will not overshoot the target altitude,
which will cost points.
 Wires must be stripped and attached according to ESRA competition requirements. A
specific stripping tool must be used and there can be no exposed wiring.
2.3.3.2 Propulsion Requirements (Michael Robison and Gabrielle Leesman)
 Propellant used must be non-toxic
 Team must have an “off the shelf” motor choices for backup in case student designed motor
is not feasible or catastrophic failure of designed motor occurs
 Ability to scale motor up to the full altitude of 10,000 ft. capable of lifting a 10 lb. payload.
 Set-up and launch preparation must not put any members of the team or observers in
danger
2.3.3.3 Structures Requirements (Alan Cruz-Gerena)
 Airframe must be student designed, built, and tested
 Internal structure will be a framework that will consist of longitudinal stiffeners and ribs.
 Structure will house electronics, payload, and recovery system
 Internal structure will carry all loads: internal components (payload/electronics), inertial
loads, drag, parachutes, and thrust
 Rocket will be divided into 6 main sections: Nosecone, drogue parachute,
electronics/payload, main parachute, and fins
 Skin will be purely for aerodynamic purposes
 Skin acting as coupler must bear load necessary to break shear pins
 Internal components must be easily accessible via removal of skin
 Parachutes will be housed inside an inner tube within the structure that must withstand the
explosive blast of charge
 Electronics bay skin must be radiolucent
 Nosecone shape will be elliptical for optimum subsonic performance
 Nosecone and fin leading edge must withstand stagnation conditions (i.e. stagnation
temperatures)

8. E S R A | 3
 If Nosecone is made of Fiberglass, the glass transition temperature must be less than
stagnation temperature
 Fins will have a clipped delta shape
 Fins must be designed to avoid flutter phenomena
 Shear pins used for section separation/parachute deployment must sustain structure
throughout entire flight and only brake in shear from force exerted by internal pressure of
blast charge
 Center of pressure must be 1-2 diameters aft center of gravity
 Stiffeners must not buckle
 Ribs must not fail applied loads
 Joint section must join the adjacent sections, avoid rotation, withstand loads seen in flight,
and be able to hold rocket in horizontal position
 Fasteners must hold all loads they will be subjected to in shear
 Testing will be performed to ensure main structural constituents perform as expected
 Structure analysis will be performed by hand calculations and MATLAB
 Structure analysis will also be performed using Finite Element Analysis software such as
ANSYS
 Structure optimization (i.e. consider replacement of rocket constituents as ribs, stiffeners, or
fins with composites, or 3D printing)
2.4 List of Deliverables (Kristen Erickson)
The main deliverable for our project will be a sounding rocket. Through the course of the project,
we will be producing a small scale rocket and a large scale rocket, both with a completely student
designed airframe and hybrid rocket engine. The small scale rocket will include a structure with a
nose cone, a hybrid rocket engine, an electronics bay, a drogue parachute, and a main parachute.
The large scale rocket will include a larger structure and nosecone, hybrid engine, electronics bay
with many of the same electronics, larger drogue and main parachutes, and a payload bay. A small
manual or check list will also be produced which details the launch set-up procedures from setting
up the trail to launching the rocket.
The ESRA Intercollegiate Rocket Engineering Competition requires submission of an application
showing intent to participate in the competition, three bi-monthly updates, a self-supporting 36” x
48” poster with a technical description of the rocket, and a three-page minimum summary of the
poster and rocket. The team is also required to attend a session at the competition in order to give a
small presentation to and answer questions from the judges of the competition. Videos of the motor
test fires and launches will ideally be produced.
2.4.1 Propulsion Deliverables (Michael Robison and Gabrielle Leesman)
 A fully operational 54 mm hybrid rocket motor
 Sufficient data and proof for continuation to a larger 152 mm hybrid rocket motor. Sufficient
data is proof referring to knowledge of properly predicting the thrust output, pressure,
temperature, and overall engine performance.
 A fully operational nitrous oxide tank cooling system

9. E S R A | 4
2.4.2 Structures Deliverables (Alan Cruz-Gerena)
The structures team will design, and build a rocket capable of housing a 10 pound payload with at
least 6 inches in diameter of available space and able to reach an altitude of 10,000 feet for the
large scale. In order to prove that we are capable of performing the tasks stated above a small scale
test bed will be produced. The small scale must be able to house the payloads provided by the
school students. The multiple section construction will be designed to sustain the different loads and
conditions it will be exposed to in order to successfully perform its task such as the aerodynamic
loads, stagnation temperatures, the forces caused by the ejection charge, and the compressive
forces caused by thrust in one direction, and drag and inertial forces on the other. The structures
team will be responsible of designing, manufacturing and assembling the rocket and its components
such as skin, internal airframe (stiffeners, ribs, & section attachments), fins, and nose cone. The
structures team will deliver a structure able to sustain flight conditions, flight loads, inertial loads,
house a payload and electronic system without any radiopaque obstruction, house a recovery
system, and a propulsion system.
2.4.3 Avionics Deliverables (Jared Sork, Shane Favreau, Kristen Erickson)
The hardware for the avionics team consists of an electronics bay and a payload bay. The electronics
bay will consist of several electronic components including a flight computer, two flight altimeters, a
GPS, a wiring board and batteries. There are currently 3 different payloads being constructed for the
rocket, none of which are personally funded or produced strictly by the team. Two are middle and
elementary school projects, and the other is a payload produced by NASA. The sub team will also be
responsible for the launch day procedures and ground support set-up procedures. The recovery of
the rocket, including all parachutes, shock chord, and mounting hardware also falls under the team’s
list of deliverables.
3.0 Background
3.1 Motivation behind the Project (Kyle Levin)
The purpose of this project is to not only allow students to test their knowledge in designing and
fabricating a rocket from scratch, but also to allow these students to go the Experimental Sounding
Rocket Association competition in 2015 with their own rocket. Completion of this project would
allow students to be confident in their designs such that a full scale version of the rocket can be built
for competition.
3.2 Previous Work Similar to Project (Kyle Levin)
Many of the student on this team have previous experience with high power rocketry through the
Student Research Rocket Society on campus as well as through classes required for their major.
Some students also have experience working with rockets through positions working as research
assistants for professors or the Centurion project through the Student Research Rocket Society.
Experience on projects of this magnitude is limited however.
3.3 Social and Societal Impacts (Kyle Levin)
The rocket has the opportunity for a learning component and experimental data to be collected in
the payload section. As a result two payloads are being constructed with mentoring from the team
by a class at Indiatlantic Elementary and Stone middle school. These payloads will work on their
respected technical levels to comprehend various elements in a varying pressure environment and
potentially zero gravity information. This has a pronounced societal impact because it will allow
local students the ability to expand their learning.

10. E S R A | 5
4.0 Subsystem Design
4.1 Propulsion
4.1.1 Design Alternatives and Tradeoffs (Michael Robison and Gabrielle Leesman)
Motors are classified by their impulse; each letter following the previous is twice the impulse of its
predecessor. In Table 1, the various motor classifications can be compared. To receive maximum
thrust capabilities and best room for improvement, we designed a Class “L” motor; which generally
has a total impulse of 2,560.01 – 5,120.00 Newton-seconds. This is the impulse classification of the
small scale motor we will be testing. The full scale, 152 mm engine will be an “O” motor with a total
impulse of 20,480.01 – 40,960.00 Newton-seconds.
Class Total Impulse (N-s) Total Impulse (lbf -s)
A 1.26 – 2.50 0.29 – 0.56
B 2.51 – 5.00 0.57 – 1.12
C 5.01 – 10.00 1.13 – 2.24
D 10.01 – 20.00 2.25 – 4.48
E 20.01 – 40.00 4.49 – 8.96
F 40.01 – 80.00 8.97 – 17.92
G 80.01 – 160.00 17.93 – 35.96
H 160.01 – 320.00 35.97 – 71.92
I 320.01 – 640.00 71.93 – 143.83
J 640.01 – 1,280.00 143.84 – 287.65
K 1,280.01 – 2,560.00 287.66 – 575.30
L 2,560.01 – 5,120.00 575.31 – 1,150.60
M 5,120.01 – 10,240.00 1,150.61 – 2,301.20
N 10,240.01 – 20,480.00 2,301.21 – 4,602.40
O 20,480.01 – 40,960.00 4,602.41 – 9,204.80
P 40,960.01 – 81,920.00 9,204.81 – 18,409.6
Q 81,920.01 – 163,840.00 18,409.61 – 36,819.20
Table 1: Impulse Classifications
There are three types of motors that are currently used in most rocket deigns: solid motor, hybrid
motors, and liquid motors. Due to the restrictions of using on campus equipment, the liquid rocket
motor was deemed unfeasible. When comparing between a solid rocket motor and a hybrid motor,
it was decided that a hybrid rocket would be more beneficial. Hybrids provide a safer manufacturing
and testing option as well as non-toxic exhaust. Hybrid motors also have the ability to be completely
shut down, restarted and throttled backward or forward during flight, unlike any solid motor. All of
the advantages and disadvantages for a hybrid and solid motor comparison are displayed in Table 2
[1].
Factor Solid Hybrid
Command Shutdown & Throttle Capability NO YES
Non-toxic exhaust NO YES
Ease of Transportation & Handling NO YES
Maintenance & Launch Processing Cost MODERATE LOW
Manufacturing Cost MODERATE LOW
Readily Scalable YES YES

11. E S R A | 6
Isp GOOD GOOD
Propellant Mass Fraction GOOD FAIR
Safe, Non-explosive Propellants NO YES
Table 2: Hybrid and Solid Comparison
As shown, the hybrid motor has more benefits. The hybrid motor also has the abilities that we are
prioritizing. Ease of transportation, cost, toxicity, and throttling capabilities are all very desirable
traits when looking to design a propulsion system.
In order to attend the competition, the motor will have to transportable. Having a hybrid means that
the propellants can be stored separately and inactively. This allows for easier transportation. Solids
would require proper transportations licensing because the fuel cannot be transported while
inactive.
Along with easing transportation, the manufacturing costs for actually building a hybrid is relatively
low especially when comparing to a solid motor for multiple launches. The intent is to be able to
launch a minimum of five times: one motor testing, one practice launch, and three competition
launches. When preparing five motors, the costs continue to add, continuing the benefits of using a
hybrid motor.
Along with working with the competition it is beneficial to think about the emissions from the
motor. The environmental impact could be severe when considering the size of the motor. For this
we have chosen to work with non-toxic emissions which are achievable using hybrid motors.
The final desired trait is to be able to throttle or turn off the engine during flight. This ability is more
of a benefit that could be added in the future. The current design does not implement throttling
because it would overcomplicate the design, and it does not help to meet any of the requirements
[2].
Oxidizer Fuel Hypergolic Mixture Ratio ISP Density Impulse
Hydrogen Peroxide Kerosene NO 7.84 258 324
Nitrous Oxide HTPB (ABS) NO 6.48 248 290
Liquid Oxygen Paraffin NO ? 340 ?
Table 3: Fuel Parameters
Hybrids rockets come with a variety of fuel options. The primary options have the given parameters
shown in Table 3. Hydrogen Peroxide and Kerosene, Nitrous Oxide and HTPB, and Liquid Oxygen and
Paraffin are then compared in Table 4 [3]. We have selected to use nitrous oxide as the oxidizer and
HTPB as the fuel due to its ease of storage, relatively easy temperature regulation and its moderate
efficiency and cost to the team.
Feature Hydrogen Peroxide and
Kerosene
Nitrous Oxide and HTPB Liquid Oxygen and Paraffin

12. E S R A | 7
Storage Moderate Easy Difficult
Temperature Standard Cool Cryogenic
Efficiency Moderate Moderate High
Cost High Moderate Low
Table 4: Fuel Comparison
As for the overall design of the propulsion system, there will be a solid fuel grain, injector section,
and an oxidizer tank. Note, one alternative to this layout is depending on the static test of the 54
mm hybrid, if the combustion pressure is too low, then a pressurized tank filled with an inert gas,
either Nitrogen or Helium will be necessary and must be worked into the design. This would be
implemented in the 54 mm engine to verify the improvement of the engine as well as become a new
requirement for the 152 mm engine.
Beginning with the aft end of the rocket, the fuel that will be used in the rocket is Acrylonitrile
butadiene styrene (ABS), this is a slight modification form the preliminary design work that was
established in the earlier timeline of this project. ABS has been selected as the new fuel-of-choice
because it is much easier to produce using the 3D-printing capabilities of the Florida Institute of
Technology Materials Lab, as well as the fact that HTPB takes nearly two weeks to properly cure.
When comparing the two fuels’ chemistry, ABS has a much more stable burn throughout a wide
range of temperatures, whereas HTPB must be perfectly mixed, cured and removed from the mold
and even then, is much more affected by temperature instabilities; leading to a critical failure of the
grain. ABS is normally a pale-ish-white color. The color to the ABS will be altered to a black color, this
is necessary because black is the best color to prevent excessive heat transfer through the fuel grain
which can cause pre-burning and melting of the fuel grain. When the melting of the inside layer of
the fuel occurs, then it will begin to “clump” and slosh out of the engine. The result of this occurring
is a number of very severe motor performance problems, such as extreme pressure changes from
high to low in a short period of time. This occurs because the fuel that is being accelerated out the
nozzle needs a higher pressure to burn, then when expelled the pressure drops again. This process
can repeat several times a second and be detrimental to the overall rocket. ABS has a density of
1,070 kg/m^3 and when mixed with Nitrous Oxide, produces the more effective burn that is
required. The biggest problem when using ABS instead of HTPB is the optimal thrust decreases for
our desired capabilities; this can be seen in Table 6. It is important to note that when using ABS will
allow a much lower O/F ratio of about three, this is nearly half compared to HTPB [4].
Moving forward, the injector will be designed to allow the optimal amount of oxidizer into the pre-
combustion chamber which will be discussed in more detail in following sections. Following this is
the oxidizer tank and oxidizer, the Nitrous Oxide is liquid at 5.4 MPa, has a molecular weight of 44.0,
density of 1,222 kg/m^3 (at 20 degrees C), and a Critical Temperature and Pressure of 36.6 degrees
C and 7.27 MPa, respectively. [11] The final section of the propulsion system that may be needed is
the pressurized tank filled with either Nitrogen or Helium, as stated before, this system addition will
only occur if the combustion chamber pressure is not sufficient for proper burning. This tank would
be responsible for pushing inert gas into the oxidizer tank and “pushing” the N2O through the valve

13. E S R A | 8
at a constant velocity and keep the oxidizer tank at a constant pressure throughout the burn of the
rocket.
To get the most efficient way to design a proper hybrid motor is through the use of hybrid
combustion theory which can be seen in Figure 2. This theory is used to predict the regression rate
and oxidizer-to-fuel (O/F) ratio in the hybrid motor. This technique is often thought to be a very
complicated subject in rocket propulsion, but can be somewhat simplified through the following
assumptions:
o the slow is in a steady state
o the fuel is treated as a “flat plate”
o there is no solid oxidizer that flows past the fuel grain
o the gas is uniform
o Le = Pr = 1 (Le = k/D)
o there is no heat transfer through walls
o kinetic effects are neglected
o the flame is infinitely thin, and no oxidizer does not exist below the flame
o the boundary layer is in the turbulent phase
Figure 1: Flat Plate Regression Theory
The governing equation for determining the thermal layer thickness is the Heat Equation, which is
Equation 1.
(
𝑑𝑇
𝑑𝑡
) = ∝ (
𝑑2𝑇
𝑑𝑥2
) + 𝑟̇( 𝑡) (
𝑑𝑇
𝑑𝑥
) , ∝=
𝜆 𝑓
𝜌 𝑓∗ 𝑐𝑝 𝑓
[1]
When solving Equation 1 for steady state flows:
T(x) = ( 𝑇𝑠 − 𝑇𝑎) ∗ 𝑒(−
x
T
)
+ 𝑇𝑎 [2]

14. E S R A | 9
 𝑇 =
𝑘
𝑓
[3]
𝜏 𝑇 =
𝑘
𝑟2̇ [4]
Where the characteristic thermal thickness, Equation 3, and the characteristics time, Equation 4,
typical operation parameters of a polymeric hybrid fuel, the estimated values are as follows:
𝜏 𝑇 =
10−6
10−6
= 1 𝑠𝑒𝑐𝑜𝑛𝑑
 𝑇 =
10−6
10−3
= 10−3
𝑚𝑒𝑡𝑒𝑟𝑠
Other important equations and their respective calculations that are used in combustion theory are:
- Regression rate:
𝑟̇̅ = 𝑎𝐺0
𝑛
[5]
0.020(0.46)0.65
= 0.0121 in/sec.
- Oxygen mass flow rate:
𝑚 𝑜𝑥̇ = 𝐴 𝑝 𝐺0 [6]
0.875(0.46) = 0.4025 lbs/sec.
- Fuel mass flow rate:
𝑚 𝑓 =̇ 𝐴 𝑏 𝜌 𝑓 𝑟̇̅ [7]
54(0.046)(0.0121) = 0.0952 lbs/sec.
- Global O/F ratio:
𝑂
𝐹⁄ =
𝑚0̇
𝑚 𝑓̇⁄ [8]
0.4025/0.0952 = 4.229
- Combustion products properties:
𝑇𝑐 , 𝑀𝑐, 𝐶∗
= 𝑓( 𝑂
𝐹⁄ ) [9]
- Total mass flow rate:

15. E S R A | 10
𝑚̇ = 𝑚0̇ + 𝑚 𝑓̇ [10]
0.4977 = 0.4025 + 0.0952
- Chamber pressure:
𝑃𝑐 =
𝑚̇ 𝑐∗
𝐴 𝑛
[11]
- Thrust:
𝐹 = 𝑐𝑓 𝑃𝑛 𝐴 𝑛 [12]
- Specific impulse
𝐼𝑠𝑝 = 𝐹
𝑚̇ 𝑔0
⁄ [13]
Unlike solid-propelled rockets, hybrid fuels’ regression rates are driven primarily by the oxidizer flow
rate, which can be independently controlled. To roughly estimate the regression rate of a hybrid
motor, a closed-form regression rate model based on a flat-plate flow theory was initially developed
by Eilers and Whitmore and corrected by Whitmore and Chandler for non-unity Prandtl number,
Equation 2.
𝑟̇ = (
0.047
𝑃𝑟
0.153∗𝜌 𝑓𝑢𝑒𝑙
) ∗ (
cp(𝑇𝑜 − 𝑇 𝑓𝑢𝑒𝑙)
hnu,fuel
)
0.23
[14]
(
moẋ
Achamber
)
⅘
∗ (
mu
𝐿
)
⅕
1
[15]
𝑚 𝑜𝑥̇ = A 𝑜𝑥 ∗ cd 𝑜𝑥 ∗ √(2 ∗ ρ 𝑜𝑥 ∗ (Pox − Po)) [16]
Now to find the O/F ratio, divide the mass flow of the oxidizer by the mass flow of the fuel.
(
ṁ 𝑜𝑥
A 𝑏𝑢𝑟𝑛
∗ ρfuel ∗ ṙ) [17]
Using this method of combustion theory, a very good estimate of the various parameters can be
calculated, such as characteristic flame height, length, and intensity as well as the different flow
characteristics, mainly, the hybrid regression rate.
1
Note: mu and Pr are combustion product gas properties
Pox and ρox are incompressible oxidizer liquid propellants upstream of injector
cp, ρfuel, Tfuel and hnu are properties of solid fuel grain

16. E S R A | 11
4.1.2 Motor Chosen Design Specifics (Michael Robison and Gabrielle Leesman)
4.1.2.1 Ignition Systems (Michael Robison and Gabrielle Leesman)
For safety purposes, the motor igniters will be stored in a separate room from the motor until they
are needed in preparation for launch. The igniters will be safely loaded into the aft end of the solid
motor casing and ignited at T-0 where the spark will ignite the fuel mixture in the hybrid system. The
finer details such as length needed to properly ignite the motor are still being worked out, these
values are dependent on safety restrictions set by the university. We have however, determined that
the igniter will be placed forward of the pre-combustion chamber and aft of the injector system, this
will allow the gas to begin flowing through the injector and into the pre-combustion chamber before
the mixture is ignited and forced down the fuel port due to the high pressure difference.
4.1.2.2 Nozzle Design (Michael Robison and Gabrielle Leesman)
One of the most critical systems of this rocket is the nozzle and how it’s designed. The material that
has been chosen as the optimal nozzle is carbon-graphite. The properties that make graphite the
best candidate for the nozzle is because it has a very high melting point, will not chip away when the
gas is flowing through it, and it is cheaper than reinforced carbon, C/C, or inconel. To begin
designing the rocket’s nozzle, regardless of material, the throat area, chamber pressure, ambient
pressure, chamber temperature, molecular weight of the gas and specific heat ratio must all be
determined. It is also beneficial to use the characteristic length of the motor, also known as “L-star”
and the converging and diverging angles used for the nozzle, for the first iteration, a converging
angle of theta equal to 30 degrees and diverging angle of beta equal to 15 degrees is used. Using
Equations 3-13, the Mach number of the exiting flow is found as well as the exit temperature,
exhaust velocity, temperature at the throat, mass flow rate, area at the exit, and lengths of the
converging and diverging sections. Note, this is a conical nozzle which is the simplest form of a
supersonic rocket nozzle. A MATLAB code for this process is found in Appendix B. With the
advancement of the project and increase of knowledge of the topic, a design for an ideally expanded
rocket nozzle using the method of characteristics has begun and is attached in Appendix B. Table 6
shows the major parameters of the rocket nozzle that was designed using the MATLAB code
described in Appendix B. A secondary source as allows us to verify the performance and
characteristics of the entire rocket, this spreadsheet is attached in Appendix [A]. Note, the values
tabulated in Table 6 are derived from the “given” or “known” values in Table 7.
Location / Parameter INLET THROAT EXIT
Diameter [m] 0.03742 0.00900 0.024384
Area [m2
] 1.0998*10-3
6.36173*10-5
4.6698*10-4
Pressure [psi] 445.000 253.349 9.428
Temperature [K] 1033.15 922.455 486.385
Velocity [m/s] ≤ 1.0 622.04 1,325.08

17. E S R A | 12
Mach ~ 0 1.0000 3.05186
Mass-flow-rate [kg/s] 0.230449
Thrust [lbs] 64.940
Burn Time 6.5
Isp 209.4
Table 5: Major Rocket Nozzle Parameters
Variable Value
Specific Gas Constant 374.5189
Specific Heat Ratio (γ) 1.240
Gravity due to Earth [m/s2
] 9.80665
Ambient Temperature [K] 288.16
Ambient Pressure [psi] 14.696
Table 6: Given and Known Parameters
𝑀𝑒 = √((
2
γ−1
) ∗ (
Pc
Pe
)
γ−1
γ
− 1) [18]
𝑇𝑒 = 𝑇𝑐 (1 +
𝛾−1
2
𝑀𝑒
2)
−1
[19]
𝑎 𝑒 = √𝛾𝑅𝑇𝑒 [20]
𝑉𝑒 = 𝑀𝑒 𝑎 𝑒 [21]
𝑃𝑒 = 𝑃𝑐 (1 +
𝛾−1
2
𝑀𝑒
2)
−𝛾
𝛾−1⁄
[22]
𝑇∗
=
2
𝛾+1
𝑇𝑐 [23]
𝑎∗
= √𝛾𝑅𝑇∗ [24]
𝑚̇ =
𝐴∗ 𝑃𝑐
√ 𝑇𝑒
√
𝛾
𝑅
(
𝛾+1
2
)
−(𝛾+1)
2(𝛾−1)
⁄
[25]
𝐴 𝑒 =
𝑚̇
𝜌 𝑒 𝑣 𝑒
[26]
𝑇 = 𝑚̇ 𝑣𝑒 + (𝑃𝑒 − 𝑃𝑎)𝐴 𝑒 [27]

18. E S R A | 13
The following equations 18-27 are the equations that were used in the MATLAB code which
produced the values in Table 6.
4.1.2.3 Injector System (Gabrielle Leesman and Michael Robison)
The injector system is one of the essential pieces in a hybrid motor system. The injector controls the
flow of the oxidizer into the engine. This will need to be monitored and machined precisely. Injectors
being clogged can cause a motor to explode due to a pressure build up.
When designing the injector system the amount of oxidizer passing through the injectors will be
essential. If too much oxidizer passes through the motor without burning, the oxidizer is being
wasted, and it could also disrupt the flow of the motor.
Pressure gages and thermocouples will be used to monitor the injection of the Nitrous Oxide. If the
nitrous oxide is not properly pressurizing the tank, the fill line can be stopped. If the Nitrous Oxide, is
not filling at the proper temperature, then the fill line can once again be stopped.
4.1.3 System Integration (Michael Robison, Gabrielle Leesman, Alan Cruz – Gerena)
For the engine to function properly within the rocket, it must be integrated into the airframe
structure securely and effectively. Beginning with the engine itself, it is composed of several rubber
O-rings, two snap rings, and a force dissipation plate, shown in the expanded motor assembly view
Figure 2.
Figure 2 - Expanded view of engine (aft section in lower left corner)
The final assembly of the motor will represent that of the image showed in Figure 3.

19. E S R A | 14
The actual attachment of the motor depicted above can be seen in section klkj;lk;ljjkl.
4.1.4 Testing (Michael Robison and Gabrielle Leesman)
4.1.4.1 Motor Casing Manufacturing Methods and Analysis
4.1.4.1.1 Motor Casing Manufacturing Methods and Analysis Overview
Rocketry, beyond the typical sport rocketry, comes with some large expenses. One of these large
expenses comes from the motor casing of the rocket. This is estimated to be about a $2,000 piece of
equipment for the ESRA Competition Team. As one of the largest expenses on the rocket is essential
to design the motor casing to be as durable as it needs to be in the worst case scenario.
The worst case scenario for the rocket that could potentially allow for the rocket to survive is when
the parachutes do not deploy at apogee and the rocket becomes ballistic. When a rocket falls on a
ballistic path, the most common area of impact on the rocket is at the aft end. Impact at the aft end
primarily includes a section of the impact involves the motor casing. The motor casing when hitting
the ground from nearly a 10,000 foot apogee would cause for the ground and the motor casing to
deform.
r
tE
2
13
1
'



 [29]
However, as noted in Roark’s Formulas for Stress and Strain, the actual critical load for this case is
observed to be 40-60% of what’s predicted by the formula. Thus, a knock-down factor of 0.6 must be
included to compensate for this discrepancy. Doing this will provide a more accurate prediction of
the load required to buckle the motor casing.

20. E S R A | 15
GPa
in
r
tE
63.1'
00984.
00635.0
1089.01
)9^10(*9.68
3
1
6.0'
13
1
6.0'
2









[30]
The target altitude for this rocket is 10,000 ft or 3,048 m. Thus, it will have the following amount of
potential energy at apogee.
MJPE
m
s
mkgPE
mghPE
099.2
3048*81.9*2.70 2



[31]
Upon impact with the ground, this energy must be dissipated, resulting in a force on the rocket.
Assuming that the rocket deforms the ground by 0.00635 m, the following force will result from this.
NMNF
m
MJ
F
d
E
F
)8^10(*31.3396.8
00635.0
099.2



[32]
The motor casing is a tube 6 inches in diameter with a wall that’s 0.25in thick. Thus the cross-
sectional area is 2.307 in2
. If this load is distributed uniformly across this cross-section, the resulting
stress would be as follows.
GPa
m
N
A
P
5.7
0014999.
)8^10(*31.3
2






[33]
From this result, it is clear that the motor casing would fail in this case. A possible alternative to this
is to make the motor casing out of carbon fiber. Carbon fiber offers a significant increase in strength
over aluminum when the fibers are aligned properly. For carbon fiber IM7, which was used to
manufacture this motor casing, the critical stress for buckling is as follows. For this case, a more
conservative knock-down factor is used, because there are likely to be manufacturing faults within
the composite laminate.
GPa
r
tE
7.42'
00984.
006.
3.01
58.289
3
1
4.0'
13
1
4.0'
2
2









[34]

21. E S R A | 16
Thus, for carbon fiber, the critical stress required for buckling is 42.7 GPa, while for aluminum the
critical stress is 7.5 GPa. For the given situation, the loading imparted by the collision is 3.31 * (10
^8) N. Thus, an aluminum motor casing will buckle, but a carbon fiber one will not.
4.1.4.1.2 Manufacturing Procedures
In order to get a better grasp on the manufacturing differences of creating a motor casing made of
simply aluminum versus creating a motor casing in a carbon composite sleeve, we set to the task of
creating two crude small scale motor casings out of aluminum and then used one of the two casings
as a mold to make a carbon fiber sleeve. The first part of this process was to make the aluminum
sections.
In order to make the motor casings a five foot length of six inch diameter, quarter inch thick
aluminum 6061-T6 was acquired from the body of a previous rocket project (JAMSTAR). Next this
aluminum tube was measured and marked in two foot lengths and then placed in the horizontal
band saw for cutting. Once these sections were cut they needed to be cleaned up so that they could
be used as a “motor casing.” To do this a hand held circular sander was used to clean all of the paint
off of the two foot sections. At this point in the process the real motor casing would be handed over
to a machinist to make snap ring grooves on the inside of the casing. To expedite the process to fit
in the time frame given for this lab, these steps were skipped as they are unimportant to knowing
the ease of manufacturing an aluminum only casing versus an aluminum casing wrapped in carbon
fiber.
Now that the aluminum “casings” were created the next step in the process was to wrap one of the
casings in carbon fiber in order to make a carbon fiber sleeve. To start the process some preparation
had to be done. First the table that was being used for composite lay-up was covered in a layer of
sheet plastic. Another piece of the same plastic was then cut in such a way that it was longer than
the two foot tube by a couple of inches and could also be wrapped around the circumference of the
tube without leaving any aluminum showing. This piece of plastic was then wrapped tightly around
the tube and taped down to the tube. This was done to assist the removal of the carbon composite
sleeve from the motor casing after it had set because the casing had a rough finish due to the fact
that the paint had to be removed. When preforming these tasks on a full sized motor casing, the
case would have a smooth finish and this step would not be necessary. This finished the preparation
of the tube, next was preparing the materials for the composite lay-up. Two different types of
carbon fiber were used to make the casing in three different directions to assist the tube in resisting
compression and buckling forces that it would undergo during its real world application.
The first type of carbon fiber used was a glass fiber backed unidirectional carbon fiber. One use for
this unidirectional carbon fiber was for the single layer of carbon fiber that was placed in the hoop
direction. In order to cut the unidirectional carbon fiber for the hoop direction two pieces of glass
backed carbon fiber were cut so that they could wrap around the tube in the hoop direction
completely without over lapping. The two pieces were cut because the roll of unidirectional carbon
fiber was not wide enough to cover the entire two foot span so a little extra was needed to cover the
whole tube. The second use of the unidirectional carbon fiber was for the four layers of axial
direction composite. These pieces were cut in lengths that were a few inches longer than the tube
so that when the ends curled during the curing process it did not affect the main product. These
pieces did not need to be cut width wise because the roll was conveniently wide enough to just wrap

22. E S R A | 17
around the tube circumference without overlapping already. The second type of carbon fiber used
in the lay-up was a multi-directional fiber IM7 (Intermediate Modulus). This cross pattern carbon
fiber was cut in the same manner as the axial direction, unidirectional composite fabric.
After the setup was complete the actual wet lay-up process began. To start this process the two
pieces of hoop direction, uniaxial carbon fiber were placed down on the plastic with the glass side
facing upwards. Then the West Systems epoxy resin was mixed in a cup for a minute. This epoxy did
not need to be measured out because the hardener and epoxy were in two separate containers with
pump tops on them that measured the exact amount necessary to cure properly, therefore only an
even amount of pumps of both resin and hardener were needed in the cup to ensure the epoxy
worked properly. The epoxy resin was mixed for one minute and then poured onto the carbon fiber
fabric. The epoxy was then painted over the unidirectional carbon fiber. Once the glass backing can
no longer be seen the carbon fiber is sufficiently impregnated with epoxy. The aluminum tube was
then placed on top of the carbon fiber in such a manner than then the carbon fiber was rolled
around the tube; the fibers were in the hoop direction. Next the carbon fiber fabric was lifted off of
the plastic and wrapped around the aluminum tube and the paint brush was used to force all of the
air out from between the carbon fiber and the aluminum tube to ensure the smoothest and tightest
fit for the carbon fiber fabric around the aluminum casing.
Following this the axial direction fibers were placed. This was done in a one at a time fashion as with
all composite lay-ups that we have done in lab to date. The aluminum tube was left on the plastic
sheet and a singular sheet of unidirectional carbon fiber was laid axially along the tube glass side up
and wrapped tightly around the tube by hand. Then epoxy resin was poured onto the carbon fiber
fabric and painted with a brush to ensure that the entire fabric was covered in resin. Once again
resin was added and painted until the glass backing was no longer visible and then the brush was
used to remove all of the air bubbles under the composite fabric. The steps for adding axial
direction carbon fiber were repeated two more times for the remaining unidirectional carbon fiber
fabric sheets that were precut, however each time a sheet was added the tube was rotated 90o
in
order to ensure that none of the seams were in the same spot on the tube because this would cause
a structural weak point on the tube, by spreading them out the seams are a non-factor in terms of
the strength of the composite. After completing the lay-up of the unidirectional carbon fiber the
IM7 multi-directional carbon fiber weave was added to the lay-up. This was done by wrapping the
IM7 weave around the tube in the same fashion as the previous unidirectional carbon fiber and then
painting it with epoxy resin as well.
Finally to complete the lay-up the carbon wrapped tube was wrapped tightly with the sheet of
plastic covering the table. This sheet of plastic was then tightly wrapped with packaging table along
the entire length in the hoop direction. This tight wrap helps the composite become one solid piece
during the curing process. After taping the composite is left to sit for twenty-four hours to allow full
curing on the final product before removal from the mold.
After the curing process is complete a few simple steps are needed to remove the newly made
carbon fiber sleeve from the motor casing. First the plastic sheeting is cut off of the composite using
a box knife very carefully in order to avoid damaging the composite. Next the assembly is taken over
to the band saw and the carbon fiber is cut flush with the end of the motor casing mold. An angle
grinder is then taken to the freshly cut end to clean up the edge. Finally the composite is slide off of

23. E S R A | 18
the mold and if it does not slide off easily the assembly is placed in the freezer for a couple of hours.
This is done because the aluminum will shrink in the freezer, while the carbon fiber will actually
slightly expand causing the two to separate. This allows for the carbon fiber to be easily removed
from the aluminum motor casing. With this final step only inspection of the final product remains
and the manufacturing process is complete. See Appendix C for images of the manufacturing
process.
4.1.4.1.3 Analysis
The manufacturing process for the aluminum motor casing is a particularly easy. The majority of the
student work for creating an aluminum motor casing is acquiring materials and finding a company to
machine the part. The other major portion of the student work for the full sized motor casing is the
actual design work for the casing which involves ensuring the casing can withstand the pressures
that it will undergo during motor burn as well as creating a computer drawing of the motor casing to
bring to the company that will do the machine work on the stock material to create the motor
casing. This process is the same in both casing scenarios, whether it be carbon fiber wrapped or
simply an aluminum casing. This means the determination as to whether not to make a carbon fiber
sleeve for the casing depended on the difficulty of creating an acceptable carbon fiber sleeve in
terms of quality as well as determining if the sleeve will actually be useful under the failure scenario
for which it would be created.
The difficulty of creating the carbon fiber sleeve was not particularly high; however a high amount of
precision work must be done while laying up the composite sleeve to ensure the casing shell quality
is high. Ensuring the casing shell quality is high is important because if the quality is not spot on the
strength of the casing shell may not be strong enough to withstand the forces that it is created for.
The meticulous nature of the task makes the manufacturing process a bit more difficult; however it
does not take the manufacturing process out of the skill range of the students that would be
manufacturing the full sized casing shell. The manufacturing method used involved wrapping the
aluminum motor casing with the carbon fiber to make the shell. Although this method was effective
it was difficult to maintain quality due to the fact that the carbon fiber was being laid on the outside
of the mold we were using. A way to fix this would be to use a different type of mold for the final
product. The different mold would be a hollowed out block of metal in the shape of our motor
casing shell. This would allow us to lay the composite on the inside of the mold and therefore be
more accurate because we would simply need to press the fabric into the mold and epoxy it as
opposed to trying to keep in on the outside of a mold. Another manufacturing fault that caused
some of the defects in the final product created was the time friendly method used to lay the
composite. Our process involved placing each layer on successively in order to allow the process to
be done in a time friendly manner. We used this method because it still gave us an idea as to how
difficult the process is and what the final results would be; however if we were to use a composite
shell for our motor casing we would use a less time friendly manufacturing process. The only
difference in this non-time friendly process is the fact that we would allow each layer to set for a few
hours before adding the next layer. This setting makes it so that each layer does not move around
when applying the next layer.
Overall it can was determined by the team that the amount of work necessary to create the
composite shell would be worth the effort provided that calculations showed the composite shell
would perform the necessary task.

24. E S R A | 19
Using the FEA software, ANSYS, a good understanding of the forces and stresses that a ballistic
motor casing would undergo is obtained. By first analyzing theoretical values of the strength of the
aluminum 6061-T6 that we will be using for the main motor casing can withstand a stress of nearly
1.63 GPa, using Equation 35.
𝜎 𝑦,𝐴𝑙 =
0.6
√3
𝐸
√1−𝜈2
𝑡
(𝑟 𝑜−𝑟𝑖)2 [35]
Where E = 68.9 GPa, ν = 0.33, t = 0.00635 m, r0 = 0.11811 m, and ri = 0.10827 m
Using the worst case scenario described above, where the rocket fails to deploy either parachute
and returns on a ballistic path, the maximum forces experiences is nearly 3.31*10^5 N, from
Equation 36. Taking this value and plugging it into the stress equation, Equation 37, a maximum
stress of 7.5 GPa can be subjected to the rocket, well over the critical value given by Equation 37.
𝐹𝑚𝑎𝑥 =
𝑚𝑔ℎ
𝑑
[36]
Where m = 70.2 kg, g = 9.81 m/s, h = 3048 m, and d is the distance the casing travels through the
ground; 0.25 m
𝜎 𝑚𝑎𝑥 =
𝐹 𝑚𝑎𝑥
𝐴
=
𝑚𝑔ℎ
𝜋𝑟2 [37]
The value of maximum stress exceeding the yield value of the aluminum is supported in the ANSYS
analysis that was performed; shown in Figure 2, the entire aft section is crumpled a total of nearly 2
inches into itself as well as experiences a maximum stress of nearly 1.84 GPa, causing failure of the
case.
Figure 3: Motor Casing ANSYS Analysis

25. E S R A | 20
A close – up of the deformation is shown in Figure 3. The second material that we had performed an
analysis on is IM7, a form of carbon fiber that was nearly the same thickness as the 0.25 inch
aluminum section used previously.
Figure 4: Aluminum Casing Deformation
By calculating the maximum yield strength of this carbon fiber, which was 42.7 GPa, from Equation
29 is much greater than the aluminum’s yield strength, however E was increased to 289.58 GPa and
the thickness, t was 0.006 m.
Figure 5: Carbon Fiber Loading

26. E S R A | 21
The carbon fiber shell seen in Figure 3 that we used had definable characteristics. However, when
we completed the wet lay-up process, the amount of epoxy mixed with the carbon fiber, the
accuracy of the lay-up, and the angling of the fibers inhibited our ability to perform a proper ANSYS
analysis of the carbon fiber shell. From Figure 3 and Figure 4, we are able to see that the Carbon
Fiber shell was not sufficient in saving the aluminum tubing for the motor casing.
Figure 6: Normal Loading on Carbon Fiber
If this process were to be redone, it would be much more beneficial to do the carbon fiber wet layup
in a much more space out portion. The layers should be wrapped tightly, and the y should be done
individually to prevent any air build up. It would also be more beneficial to vacuum bag any of our
wet – lay-up items.
From this process we were able to discern that adding the carbon fiber shell to the aluminum tubing
would not be beneficial in preventing the deformation of the aluminum tubing upon impact with the
ground. This means that this does not prove to be a valid solution to our design problem.
4.1.4.2 Motor Flow Analysis (Michael Robison, Kyle Levin, Gabrielle Leesman, and Kristen
Erickson)
4.1.4.2.1 Statement of Problem
The main goal of this experiment comes from one of the biggest problems in rocketry, verifying the
proper thrust curve for a given engine. This problem is amplified when aerospace engineers design
and build experimental rocket engines. The goal is therefore to use a load cell, pressure transducer,
and possibly a high-temperature thermocouple to measure and graph the thrust curve of the Vulcan
Program subscale motor, named the XH-100 or Experimental Hybrid motor with output of 100 lbs. of
thrust. To properly gather the measurements of the sensors, a LabVIEW DAQ system and code will
be created by the team and utilized. After verification of the data acquisition and accuracy of the
measurement, this lab can be applied to various thrust stand tests that the university may wish to
conduct in the future.

27. E S R A | 22
4.1.4.2.2 Experimental Procedure
1. Caution tape off road behind machine shop for trailer and safety radius
2. Tow trailer using truck into center of road/safety area
3. Detach trailer from truck and remove
4. Place parking blocks under trailer wheels to prevent movement
5. Attach motor to holding rail
6. Plug in pressure sensors, temperature sensors and force sensor to DAQ
7. Boot up thrust stand laptop and attach to "plug and play" DAQ
8. Open custom LabVIEW program
9. Wire firing control box to motor and car battery for power
10. Attach oxidizer tank to on board motor tank and attach oxidizer tank solenoid to firing box
11. Turn on winch and use to slowly stand tower vertical on trailer
12. Place water bucket under motor outlet to prevent blowback and fire
13. Check firing box for continuity
14. Run automatic calibration through LabVIEW program
15. Begin filling of oxidizer and continue until venting occurs
16. Once venting occurs dump all of the oxidizer (first fill was to chill tank)
17. Following dump refill with oxidizer until venting occurs and continue to fill after venting begins
18. Once venting occurs start data collection on LabVIEW
19. Following commencement of data collection call out count down and then press fire button
20. Allow motor to burn out completely and press stop on LabVIEW program
4.1.4.2.3 Theoretical Values for Comparison
After experimentation, there are several vales that the test can be compared to. By using hand
calculations and with the help of a hybrid motor spreadsheet, the theoretical, or ideal, values are as
follows:
• Average Thrust: 100 lbf/sec.
• Burn Time: 6.5 sec.
• Impulse: 599.95 lbf*s
• Isp: 209.4
• Flight Tank Temperature: 80°F
• Flight Tank Pressure: 865 psi
• Combustion Chamber Pressure: 455 psi
• Coefficient of Thrust: 1.5
• Total Consumed propellant: 2.86 lbs
4.1.4.2.4 Equipment Usage
• Load Cell
• Pressure Transducer
• High Temperature Thermocouple
• SRS Thrust Trailer / Thrust Stand
• LabVIEW program “thrust_pressure.vi”
4.2 Structure
4.2.1 Design Alternatives and Tradeoffs
4.2.1.1 Initial Considerations
Throughout the designing process of this project there have been multiple design ideas that
represented possible alternatives to the final structure. An initial design of a tubular structure was
considered but since the initial requirements for the competition stated that the airframe had to be
student built with significant input on the design and bought parts had to be significantly altered.
From this requirement it was determined the best design would be a structure consisting of an
internal frame that would carry all loads and an attached skin for aerodynamic purposes.

28. E S R A | 23
Within the selected design approach there were several options between increasing/decreasing the
stiffeners count. The current design correspond to a four stiffeners for each of the internal
structures sections. The biggest limitation and the crucial reason of this decision was the diameter of
the rocket, the available space, and ease of assembly/manufacture.
Different iterations were made on selecting a single stiffener configuration to a 4 stiffener
configuration. The one centric stiffener configuration allowed for an easier assemble but limited the
available space for payload section. A two stiffener configuration was not stable enough to an
option. A three stiffener configuration was a good possibility but was eliminated due to the fact that
it limited the amount of pins that would distribute the shear load they will bear. The final clear
choice was a four stiffener configuration that provided a stable design, an even distribution of load
through the fasteners, and a fairly small cross section that would resist buckling.
Another material that was considered before was a metal shim stock that could be wrapped around
the rocket but its assembly became complicated and required multiple perforations to stiffeners
which weakened the overall structure. Then a final decision was made in using a lightweight
radiolucent material such as plastic, specifically PVC that could be attached solely at the top and
bottom to the ribs instead of the stiffeners.
There were not any other significant alterations to the design or considerations. The rest of the
design has followed through with its initial concept successfully and is discussed in detail in the
following subsections corresponding to each component.
4.2.1.2 Material Selection
A series of Design matrices were made in order to select the best material to implement in our
design. The design matrices can be seen in Table, Table, Table, and Table. Several properties are
compared and weighed on a scale of 0 to 4. In the skin decision matrix aluminum or metals are not
considered because the driving parameter is low density to have lower mass, not structural strength.
Metals have a higher density than the selected plastics. Parameters based on information from
McMasterr-Carr and data sheets of materials.
Table 7: Stiffener, fin, & bulkhead material decision matrix
Material Strength
density
ratio
Cost Availability Score
Al-6061 102.22/3 $4.67/6/4 4 11
Al- 2024 116.5/3 $14.03/6/3 4 10
Al - 7075 179/4 $64.97/6/0 4 8
316
Stainless
Steal
36.25/1 $37.29/6/2 4 7

29. E S R A | 24
4130
Steel
55.4/2 $36.04/6/2 4 8
Table 8: Fastener material decision matrix
Material Strength
density
ratio
Cost Availability Score
316
Stainless
Steel
36.25/4 $5.24/25 3 4 11
18-8
Stainless
Steel
26.875/2 $5.28/100/4 4 10
Brass 17.58/1 $11.90/50
/3
4 8
Titanium 198.6/4 $6.85/1 0 5
Table 9: Skin material decision matrix
Material Strength
density
ratio
Cost Availability Score
ABS
Plastic
6.22/4 $15.58/25 3 2 9
PVC 5.28/3 $6.69/100/4 4 12
Table 10: Nosecone decision matrix
Material Strength Smooth Cost Glass
T.
Temp
Availability Score
Fiber glass 4.89 MPa
/4
4 $24.15/yd /3 N/A 4 15

30. E S R A | 25
Carbon
Fiber
4.38 Mpa/3 4 $44.95/yd/1 N/A 4 12
Aeropoxy 8.45 kN -
10.23kN/4
N/A $127.45 gal
kit / 3
91
C/4
4 15
West
System
7.75kN -
8.49kN/2
N/A $250 gal /1 50.5
C/3
4 10
4.2.1.3 Fins
The Fin, fin can and fin attachments material has been decided to be Aluminum Al – 6061 considering
that on the material comparison matrix was the material with most points considering that is the
cheapest with the highest strength density ratio of 102.22. The manufacturing of the Fin pieces which
goes around $4.67[7] for 4 sheets on the McMaster-Carr web site. Also parts are relative easier than
using composite materials. The Stress concentration and Fin flutter calculations were based on the
Aluminum specified on this paragraph.
Material
Al - 6061
Properties Metric
Density 2.7 g/cc
Cost $4.67
Tensile Yield Strength 276 MPa
Strength density ratio 102.22
Modulus of Elasticity 68.9 GPa
Figure 8: Aluminum Material Properties used to determine its usage for the Fins and components
construction. Data acquired from ASM Aerospace Materials Services Inc. Reference 1.
We also to get the calculations of the Fin flutter effect and the maximum stress experienced during
flight, the Al-6061 was used as a parameter restriction. In the AeroFin Sim the selected material is
seen in Figure 1 to ne Aluminum. The Different bending and torsion frequency values are represented
by the program. These values depend on the material, altitude conditions. Also there is Flutter,
divergence velocity results which determine the vibrations and torsion force respectively that the
rocket aerodynamics will experience.

31. E S R A | 26
Figure 9: AeroFin Sim interface for material and altitude selection of the test.
4.2.1.4 Nosecone
Nose Cone for Transonic Regime Alternative:
Fineness Ratio: ratio of nose cone length to its base diameter [13]:
Symbols:
nose cone length [m]L 
nose cone base diameterd 
Radius
Maximum radius
Distance from nose
Total nose length
r
x


n
L
f
d

Equation 38: Fineness ratio (Ref. 13)
One possible performing regime of the rocket was at transonic speeds (0.8 < M < 1.2). According to
Stroick [15], the optimum nose cone shapes for transonic speeds are the Von Karman, and the Power

32. E S R A | 27
Series x½. In addition, he states that the optimum fineness ratio for that shapes is 5. The Von Karman
nose cone has an L-D Haack shape, which belongs to the Haack Series shapes (Ref. 14). This type of
shape is mathematically constructed from the following equation:
   
 
3
1
1 1
sin 2 sin
2
cos 1 2
r C
x
  

 
  
 
[14]
C=0 for the Von Karman shape (LD Haack). This notation means that shape gives minimum drag for
the given length and diameter. When C=1/3, LV Shape is constructed to give a minimum drag for a
given length and volume [15].
The equation to obtain the Power Series X½ shape is the following:
1
2
r x [14]
It corresponds to the equation of a parabola. Again, just as a reminder “x” and “r” are ratios defined
before.
The following figure shows how the previous nose cone shapes are built:
The experimental data obtained by Stoney [14] for eight body-nose shapes lead to the conclusion that
the Von Karman shape reflected the lowest drag at transonic conditions. This experiment was made
for bodies with fineness ratio of 3. However, the important information was the drag results for these
shapes.
Crowell shows in the following graph the performance of the different nose cone shapes at different
Mach numbers; 1 being optimum and 4 being inferior poor. Again, the Von Karman shape seems to
be the best choice for a rocket at transonic speeds [13].
L
R
x = 0 x = L
x
y
C
/L
y = Ry = 0
Figure 10: Dimensions used in equations (Ref 5)

33. E S R A | 28
4.2.2 Chosen Design Specifics
4.2.2.1 Materials
The final chosen materials for each component were based on the material that best met our
requirements from the decision matrices. Table below portrays the materials chosen for each
structural component.
Table 11: Material selection for individual structural components
Item Material
Nosecone Fiber Glass
Stiffener Aluminum 6061 T6
Rib Aluminum 6061 T6
Joint rod Aluminum 6061 T6
Fin Aluminum 6061 T6
Skin PVC
Coupler Aluminum 6061 T6
Internal
cylinders Aluminum 6061 T6
Fasteners 316 Stainless Steel
3
1
0.8 1.0 1.2 1.4 1.6 1.8 2.0
1 1
1
1
1 1
1
1
2 2
2
2
2
2
22
2 2
3
3
3
3
3
3
MACH NUMBER
4
4Ogive
Cone
LV-HAACK
Von Karman
Parabola
3/4
Parabola
1/2
Parabola
x3/4
Power
x1/2
Power
Figure 11: Comparison of drag characteristics of various nose shapes in the transonic-to-low Mach
regions. Rankings are: superior (1), good (2), fair (3), inferior (4). (Ref. 13)

34. E S R A | 29
4.2.2.2 Nosecone
Nose Cone to perform in subsonic regime:
Fineness Ratio: ratio of nose cone length to its base diameter [13]:
Symbols:
nose cone length [m]L 
nose cone base diameterd 
Radius
Maximum radius
Distance from nose
Total nose length
r
x


[14]
n
L
f
d

Equation 39: Fineness ratio (Ref. 13)
The following figure shows how the previous nose cone shapes are built:
The designed sounding rocket will be performing in subsonic speeds (M<0.8). According to Stroick
[15], the optimum nose cone shape for subsonic speeds is the Elliptical shape. In addition, Stroick
states that the optimum fineness ratio for an elliptical nose cone is 2. At subsonic speeds, the most
significant contribution to drag is skin friction. According to Crowell [13], this type of friction varies
with the surface smoothness, wetted area and discontinuities on the shape.
The equation to obtain the elliptical shape is the following:
2
1y R x  [13]
The ESRA Competition 2015 small scale sounding Rocket of Florida Institute of Technology will have a
113mm diameter. The optimum nose cone choice will be the elliptical shape with a fineness ratio of 2
L
R
x = 0 x = L
x
y
C
LL
y = Ry = 0
Figure12: Dimensions used in equations (Ref 5)

35. E S R A | 30
[13]. Since the designed rocket will have a 113mm diameter, the optimal length of the nose cone is
226mm. A greater fineness ratio will contribute to the increase in skin friction drag. Moreover, it is
feasible to manufacture this shape; this because an ellipse can be easily computed. In addition, an
elliptic mold is also feasible to print.
The material to be used to construct this nose cone is fiber glass. This material is found in the market
at reasonable prices. In addition, it is a strong material and will improve the heat resistance of the
rocket structure. A smooth fiberglass surface can be manufactured to reduce skin friction drag. To
manufacture this fiber glass nose cone, PR2032 Laminating Resin with 1-hour Hardener PH3660 along
with the fiber glass will be used. These two are optimum to manufacture composites such as fiber
glass. In addition, according to the manufacturer AEROPOXY [16], their properties demonstrate good
flexural strength, high heat resistance, and can be cured at room temperature.
Florida Institute of Technology provides the students the access to 3D Printers. A mold with the
elliptical shape will be printed. The fiber glass cone will be prepared around the aforementioned
printed mold.
Some mechanical properties of PR2032 Resin with PH3660 are shown in the following table:
PR2032 with PH3660 for fiber glass
Mix Ratio 3 to 1 by Volume
Tensile Strength 352.2 MPa
Tensile Modulus 18.064 GPa
Glass Transition Temperature 91o C
Coefficient of Thermal Expansion 7.74e-05 / oC
Table 12: Mechanical Properties of PR2032 Resin with PH3660 Hardener with fiberglass (Ref. 16)
A test of strength properties of AEROEPOXY in John Coker’s website [17] demonstrated the
characteristics of the resin and hardener.
The nosecone tip must support the maximum stagnation temperature during flight. This will depend
on the glass transition temperature of the epoxy to be used.
The maximum stagnation temperature at the nose tip is calculated as follows:
Symbols:
max
Freestream Temperature
Specific Heat Ratio of Air
Maximum Speed
T
Cp
V
 


 
2
max
1
2
oT T V
Cp
 
Equation 40: Stagnation Temperature (Eqn. 4.42 Ref. 18)

36. E S R A | 31
According to Standard Atmosphere data from Appendix A of Anderson Introduction to Flight (Ref.
18), the highest air temperature the rocket will experience will be 288.16 Kelvin (15o
C); this is the
highest temperature below 10,000 ft of altitude. The calculated maximum speed is 182.03m/s. In
addition, the specific heat ratio of air is 1004.5 J/(Kg*K).
Sample Calculation
2
1
288.16 182.03
2 1004.5
304.65 31.5
o
o
o
m
T K
sJ
kgK
T K C
 
   
  
 
 
 
Glass Transition Temperature (Tg) of selected epoxy = 91o
C.
31.5 91
% 100% 100% 65.4%
91
o g
g
T T
difference x x
T
 
  
The maximum stagnation temperature the rocket will reach is around 65% the glass transition
temperature of the selected epoxy (91o
C). This means it is safe to use the selected epoxy and also
that the structure of the fiber glass nose cone will resist the conditions that it will be exposed to. In
addition, it is important to mention that this stagnation temperature will be reached for short a very
short period of time (seconds), so heating will not represent a structural problem for the nose cone at
all.

37. E S R A | 32
Figure 13: Drawing of Vulcan Small Scale Rocket Nosecone
Figure shows a drawing of the nosecone of the small scale rocket. The diameter and length are
specified.
4.2.2.3 Fins
To determine the design of the fin shapes, dimensions and airfoil we used multiple formulas that are
based on measuring the fin flutter and center of pressure for the small scale rocket.
Symmetrical single rounded flat plate cross section with
clipped delta shape planform (14) is most efficient at
subsonic speeds see reference 7. It has higher strength and
a stiffer cross section which helps against fin flutter.
Delta Wings Shape
The fin shape is dependent of the speed regime the rocket
will be flying at. The optimal shape for subsonic speeds has
been determined to be the clipped delta shape (See Figure
8) due to their decrease in drag, and increase speed
An efficient clipped delta shaped fin typically has a fin root
chord length equal to the semi-span length to provide a
Figure 14: Clipped Delta shape obtained from
Apogee Components, "Peak Of Flight"
Newsletter by Hennin, Bart

38. E S R A | 33
balance between strength and aerodynamic efficiency. In the Final design we use this as a reference
and the simulations do corroborate the necessity of the Delta Wing.
Fin Flutter phenomena is accounted for by calculating the minimum thickness at which flutter would
occur
Equation 41: From the Flutter Boundary Equation
𝑉𝑓 = 𝑎√
𝐺
(1.337𝐴𝑅3 𝑃(𝜆+1)
2(𝐴𝑅+2)(
𝑡
𝑐
)3
Where: 𝑎 = √𝛾𝑅𝑇 𝜆 =
𝐶𝑡
𝐶 𝑟
These calculations are based in the 3 clipped delta wing design (Figure) for maximum stability, also
the constants are assumed for the max possible temperature at sea level.
Constants and Variables Results:
AR= 0.4615; a=340.27; Vf= 365.27 m/s; P=101325 Pa; G= 26 GPa; c= 0.4572m; 𝜆 = 0.444
𝑡 = √
(1.337( 𝐴𝑅3))(𝑃)(𝜆 + 1)(𝑉𝑓
2
)
2(𝐴𝑅 + 2)(𝑎2)(𝐺)
3
𝑡 = √
(1.337(0.46153))(101325)(0.444 + 1)(356.762)
2(0.4615 + 2)(340.272)(26 ∗ 109)
3
Equation 42: Sample calculation of minimum Fin thickness to avoid Fin Flutter
T=2.54966x10-3
m => 2.55 mm
Figure 15: Delta wings area illustration. Used to calculate thickness of airfoil in equation 1. Reference 3

39. E S R A | 34
Airfoil shape of the fins
The decided Airfoil shape is going to be a symmetrical airfoil shape, which is the same as seen in (figure
16) for subsonic flow. Knowing that the rocket will not surpass transonic flow speeds the decision of
using this shape is based feasible manufacturing techniques. The main rectangular body of the airfoil
represents an easier shape to manufacture were the bottom triangular shape does not represent a
major manufacturing inconvenience.
Symmetrical airfoil cross section is most efficient at subsonic speeds see Figure. It also has higher
strength and a stiffer cross section which helps against fin flutter, this can be corroborated by the
simulation high stress that the fins are able to support
Figure 16: Fin Airfoils Functionality and placement to body tube. Reference 3

40. E S R A | 35
Design Fin Shape and Dimensions
Figure 17: Vulcan Rocket Fin CREO design December 2014
1. Delta wing shape design (Figure) used for subsonic velocity
2. Parallel axis pin location and double diameter of Pin stress concentration area safety feature
in x and y axis from the connection of L shape.
3. Rounded shape on leading edge that to avoid stress point on the center line of the edge
4. Fin shape dimensions are dependent of standard wing design characteristics based on Fun
Flutter standards (RED COLOR).
5. Span & Root= 21.9 cm; Tip = 10.9 cm; & In thickness = 0.2 cm
Fin Can Attachment Design
The main focus is to be able to successfully mount and fin attachment design (Error! Reference source
not found.) that will not compromise main structures of the rocket. We will accomplish such by
creating a fin system that will be able to fast reassemble and replace in case of accident. The best idea
the group could come out with a simple Fin Can connection from the rocket structure to an
independent structure. Doing so we must follow the safe factors procedure and measurements as
NASA rocket standards. (This involves a standard two length diameter for beside the stress
concentration areas)

41. E S R A | 36
The limit parameters are to not compromise the rocket skin by perforation and decrease its
aerodynamics features, plus there should be not reliability on a stress force concentration on the outer
skin. Also this compromise also applies to the stiffeners or ribs. Is there is multiple drills will weak the
structure and may not support the load.
Fin can Overall Design Features:
 Triple Fin triangular design for optimum stability.
 Single delta airfoil with clipped leading edge use for
sub sonic
 Single Fin to fin can attachment for weight reduction
and avoidance of tension or shear.
 Solid bottom plate connection to the rocket motor
and main structure frame.
The thickness of the Fin can was determine by standards of
Fin cans and later test under Fin flutter AeroFin Sim
program to accurate demonstrate (Figure …)the Can will
stand the maximum Stress force Applied of (2.482 x 108
)
NT/m2
at an air velocity of 150.29 m/s and 10,000 ft
altitude.
Can Design and Dimension Chosen
While designing then characteristics of the Fin can we reach to calculate a Can thickness based on the
outer diameter matches the rocket structure frame and an inner diameter which foils and holds the
rocket motor in the bottom section of the structure. The stress concentration perforations areas are
aligned parallel Pin hole with stress concentration area safety feature of minimum 2 diameters in same
axis. The can characteristics (figure 18) correspond to a middle wall thick ness of 0.2 cm & 1.26 m
height, this are based on the height of the motor engine and the minimum simulated wall thickness
possible that will stand the necessary loads and stresses been the thinnest possible to save material
and reduce weight.
Figure 18: Frontal View of CAD Creo Design of the triple fin can and
main frame attachments.

42. E S R A | 37
Figure 19: Fin can tube thickness and main connections selected
The bottom plate (Error! Reference
source not found.) is considered to
be the connection between the main
structure without compromising the
stiffeners and the ribs.
It is necessary to mounted on top
with the motor top plate and the
bottom rib will seat on top while is
connected to the solid plate. This
reduce on possible shear at the can
joints to the Fins.
The 0.5 cm diameter outer pins
diameter symmetric design circle
correspond to the solid plate
connection to the bottom airframe
main structure. The four symmetric
points are also positioned exactly to follow the patron of the stiffener. So this symmetry will help to
now the stiffener position and when the Fins are mounted do not collide to the Stiffener position.
Figure 20: Bottom Pate connection between Fin can and Airframe main
structure

43. E S R A | 38
The fin can will be lateral connected to the solid bottom plate with an L shape, the inner radius of
the other four pin points correspond to this connection. The Fin can inner radius is two diameters
more open that this symmetric holes.
(L) Shape Fin to Fin Can connection
Parallel Pin hole 0.5 cm with stress concentration area
safety of 2 diameters in Y axis. 5 cm distance between Pin’s
points for both left and right section.
X axis perpendicular between Plates to avoid flow torsion
rupture of the middle joint. Y axis distance difference of 2
cm between P1 & P2, but same Y axis separation of 5 cm in
each section. This difference is used to avoid torsional
vibrations which will occur if the Pins connections are not
parallel.
Slight thickness difference of thickness and Lengths
between FA & CA. Fin Attachment has bigger area and
volume because the direct torsion of the flutter effect.
Smaller area for Can attachment to considering design
position advantage and to avoid interference with the
square area of the stiffener.
1. T1= 1 cm; T2=0.5 cm
2. L1 & L2 = 2 cm
3. H1 & H2= 15 cm
The L shape connection design was chose due that is the
simples shape joint to manufacture and mostly almost all
the basic rocket design do have (L) shape structure
connection (Figure 12) also called Faring.
The torsion value that this joint will experience is inits worst
55o
Angle of attack 4248.62 Hz Torsion Frequency, Fin
force-load applied to joint and fin of 0.076 NT & and a
Bending Moment of 1688.61 Hz. Know that this are the
starting failure regime range the actual joint and fins are
safe during a normal flight with any other AOA that is
smaller than 55o
Figure 7: (L) Shape Fin connection close up
structure

44. E S R A | 39
Fin Final Attachment Detail Structure
Finally the four main components of the Fin attachment. Fin stresses during worst case scenario were
determine, given us the safety range were we can operate with this Thickness, dimensions and
material properties of the Fin and main components.
Figure 8: Final Joint of the 4 main Fin can connections. Fins, L shape joint, Fin can, Bottom plate
Cp and Cg attachment Calculations
Calculations: the density of AL -6061 IS 2700 kg/m^3 was use, the Matlab Code is done to run it
changing the density in case is required to change the chosen material.
Constants and Variables Results:
W_Can = 0.0332 (N)
W_Lshape = 1.1719 (N) x 3
W_Fin = 1.5173 (N) x 3
W_SolidPlate = 0.9493 (N)
W_Tube =120.5867 (N)
Weight_smalltotal = 1639.7 (N)
Area_smalltotal =1.2733 (m^2)
volume_smalltotal = 0.1547(m^3)

45. E S R A | 40
Figure 9: Nasa Cg calculation considering the weight of all the tube components.
CG= ((W_Can * 0.635) + (W_Lshape * 0.08) + (W_Fin *11.4) + (W_SolidPlate * 0.05))+ (W_Tube *
1.2191)/Weight_smalltotal
These calculations are based in the NASA source CP and CG equations display in (figure 20 and figure
21)
Figure 21: Center of Gravity of a Rocket based on NASA source. NASA CP calculation considering
the Area of all the tube but its internal components don’t count.

46. E S R A | 41
CP= ((Area_Tube * 1.2191) + (Area_Lshape * 0.08) + (Area_Fin *11.4) + (Area_SolidPlate *
0.05))/Area_smalltotal
Cp and Cg attachment Results.
(Please see the Attached Code in Appendix E to understand the method to calculate this results.)
• CG =1.731251
• CP =0.9569
To see all the AeroFin Simulations on 10 o
and 55O
angle of attack, plus the Fin Flutter Velocity
(279.83 m/s) and Divergence velocity (485.39 m/s).
4.2.2.4 Internal Structure
The internal structure will consist of a framework of 4 stiffeners held in place in both the x-z plane
and the y-z plane (refer to Coordinate system in figure 22) by a rib and a fastener (See figure 23). The
internal structure will carry all loads. The skin will be purely for aerodynamic purposes.
Figure 22: Diagram of stiffener-rib interface with coordinate system

47. E S R A | 42
Figure 23: CAD model of internal structure section performed with Creo Parametric
The stiffeners will mainly be exposed to a compressive load from the thrust in one direction and the
inertial force and drag on the other which is why a buckling analysis was performed. The ribs will
have loads present from the skin and the internal components inertial force such as
electronics/payload.
The overall structure must also allow for separate rocket section attachment and separation for
recovery system deployment. In figure 23 the joint designed for section attachment consists of a
series of four rods that will slide into the adjacent section in order to keep the section stable and
avoid rotation. The sections will be held by a coupler fixed on one side and fastened using shear pins
that shear away once the ejection charge is deployed. One side will be fixed while the other will have
the shear pins.
The overall structure is divided into 6 sections: nosecone, drogue parachute, electronics/payload
bay, main parachute, and fins. Below in figure 24 the sections are labeled in the design layout of our
internal structure

48. E S R A | 43
Figure 24: Design of rocket with internal sections labeled performed with Creo Parametric
Figure 25: CAD model of section joint detached performed using Creo Parametric

49. E S R A | 44
4.2.2.5 Internal Structure Analysis
Symbols
Initial Mass [ ]oM Kg
Structure Mass [ ]sM Kg
Payload Mass [ ]LM Kg
Propeller Mass [ ]pM Kg
Burnout mass [ ]bM Kg
[ ]b o pM M M Kg 
Mass Ratioo
o
M
R
M mt

 &
Nozzle exit velocity [m/s]eu 
Rocket velocity [m/s]u 
2
max = Maximum rocket acceleration [m/s ]a
2
Acceleration of gravity [m/s ]g 
Weight [N]W 
angle between velocity vector and gravity 
Time [s]t 
Burning time [s]bt 
coasting time [s]coastt 
Average Shearing Stress in a section [Pa]ave 
Applied Load [N]P 
2
Cross Sectional Area [m ]A 
Diameter of Pin [m]d 
Base [m]b 

50. E S R A | 45
Height [m]a 
4
Moment of Inertia [m ]I 
Radius of gyration [m]k 
Stress [Pa] 
Modulus of elasticity [Pa]E 
Effective Length [m]Le 
Critical Stress [Pa]cr 
Stiffener length [m]L 
Altitude [m]h 
semimajor axis=nose cone lengtha 
semiminor axis=nosecone diameter/2b 
 Dynamic Viscosity [kg/ (s)]m 
Freestream speed [m/s]V 
Local Speed [m/s]localV 
2
local cross sectional area [m ]localA 
2
1 Area of control surface [m ]A 

51. E S R A | 46
Buckling Analysis
Buckling analysis was performed on the stiffeners to ensure structural integrity because they will be
subjected to a compressive force applied from the thrust in one direction and the drag/inertial force
from the other direction. Below in Table are the parameters used in the analysis and the result
Table 13: Parameters used in Buckling analysis and results
Parameters Symbol Value
Mass of structure (kg) m 12
Column length (m) L 1.7232
Drag (N) D 50
Gravity (m/s^2) g 9.807
Weight (N) w 117.684
Acceleration (m/s^2) a 31.17
load factor (1+(a/g)) n 4
Factor of Safety (FS) FS 3
Total applied load P 1475.172
Cross section dimensions (cm) a 0.5x0.5
Minimum selected value (cm) a 1x1
31
12
I ba
Equation 43: Area moment of Inertia around neutral axis for a rectangular cross section (Ref. 11)
z
z
I
k
A

Equation 44: Radius of gyration about x axis (Eqn. 10-6 Ref. 10)
Ultimate load
. .
Allowable load
F S 
Equation 45: Factor of safety using loads (Eqn. 1.25 Ref. 7)
In this analysis, the ultimate load represents the critical buckling load, and the allowable load
represents the applied load

52. E S R A | 47
. . crP
F S
P

Equation 46: Factor of safety for buckling analysis
P
A
 
Equation 47: Stress (Eqn. 1.5 Ref. 7)
2
2cr
E
Le
k

 
 
 
 
Equation 48: Critical Stress (Eqn. 10.13 Ref. 8)
Equation can also be written as:
cr cr
cr
P P
A ab
  
Equation 49: Critical Stress
The area of a rectangle is:
A ab
Equation 50: Area of a rectangle
In the XY plane:
Combining Equation and Equation and solving for radius of gyration:
12
z
a
k 
Equation 51: Radius of gyration xy plane
12
z
Le L
ak

Equation 52: Effective slenderness ratio xy plane
In the XZ Plane:
Combining equation 51 and equation 52 and solving for radius of gyration:

53. E S R A | 48
12
y
b
k 
Equation 53: Radius of gyration xz plane
12
y
Le L
bk

Equation 54: Effective slenderness ratio xz plane
Most efficient design will have the slenderness ratios equated to have the two buckling modes
equal:
y z
Le Le
k k

12 12
L L
a b

a b Square cross section will be the most efficient
Now equation 54 can be rewritten as:
2
cr cr
cr
P P
A a
  
Equation 55: Critical Stress
Setting equation 55 equal to equation 56 and solving for a:
1/42
2
12 crP L
a
E
 
  
 
Equation 56: Minimum width required to avoid buckling
The applied load P is calculated from inertial forces
P Wn
Equation 57: Inertial Applied load
max
1
a
n
g
 
Equation 58: Load Factor

54. E S R A | 49
oW M g
Sample Calculation
With given/known parameters from Table
Calculations:
  
2
2
2
31.17 /
12 9.81 / 1 491
9.81 /
m s
P Wn Kg m s N
m s
 
    
 
Using 4 stiffeners, and assuming uniform load distribution, the applied load at each stiffener will be
1/4P=154.5N
    . . 3.0 154.5 1475crP F S P N N  
Using Equation:
  
 
1/41/4 22
2 2 9
12 309 1.269212
0.05
70 10
cr
N mP L
a m
E x Pa 
  
         
Pin Shear Analysis for fasteners
The fasteners must support the shear load caused by inertial force and drag force of rocket, and
support individual section loads. Below in Table are the parameters used in the analysis and the
result
Table 14: Parameters used in Pin shear analysis and results
Parameters Symbol Value
Mass (kg) m 12
Gravity (m/s^2) g 9.807
Weight (N) w 117.684
Acceleration (m/s^2) a 37.2
load factor (1+(a/g)) n 5
Factor of Safety (FS) FS 3
Total applied load P 1692.252
Calculated cross Fastener diameter (mm) d 1.36
Minimum selected diameter (mm) d 2

55. E S R A | 50
cr
ave
P
A
 
Equation 59: Shearing Stress to determine pin diameter for stiffeners (Eqn. 1.8 Ref. 7)
Solving Equation for area, considering a circular area, and then solving for the diameter:
2
4
cr
ave
d P
A


 
4 cr
ave
P
d


Equation 60: Minimum pin diameter for stiffeners
Sample calculation
Given:
Material: 316 Stainless Steel
205ave yield MPa   (Ref. 10)
1692crP N
Calculations:
Using Equation
 4 1692
0.00136
290
N
d m
MPa
 
Rib Analysis
The ribs are required to support individual section loads (ex: electronics, and payload), maintain
shape of structure, and carry skin. To ensure they can support the loads an analysis was performed
using theory of circular plates considering a centric load and a fixed boundary condition from Theory
of Plates and Shells by S. Timoshenko, and S Woinowsky-Krieger (Ref 19). Below in table 15 are the
parameters used in the analysis and the results.

56. E S R A | 51
Table 15: Parameters used and results for rib analysis
Parameters Symbol
Load critical
rib Drouge rib Non-critical rib
Electronics/pa
yload rib
Mass (kg) m 12 0.5 0 2
Gravity (m/s^2) g 9.807 9.807 9.807 9.807
Weight (N) w 117.684 4.9035 0 19.614
Acceleration (m/s^2) a 31.17 31.17 31.17 31.17
load factor (1+(a/g)) n 4 4 4 4
Factor of Safety (FS) FS 3 3 3 3
Total applied load(N) P 1475.172 61.4655 0 245.862
Thickness selected (mm) a 6 2 2 4
Total Stress (Mpa) σ 83 42 0 35
Yield Stress (Mpa) σy 240 240 240 240
Equation 61: Equation for maximum tensile stress at bottom surface of plate with centric load and
clamped edges (Ref 19)
(1 )(0.485ln( ) 0.52)
P a
h h
   
Where P=load, h=thickness of plate, a=radius, and ν= Poissons ratio of 0.33 for Al 6061
Sample calculation
Material: Aluminum 6061 T6
Using Equation we calculate the max stress and compare to yield strength
1475 0.0465
(1 0.33)(0.485ln( ) 0.52)
.006 0.006
N
   
83 95yieldMPa MPa   

57. E S R A | 52
Skin Analysis
The skin’s purpose is to shield interior of rocket and for aerodynamic purposes since it will not be
bearing any main loads; however the coupler section of section must withstand the force required to
break the shear pins so a simple bearing stress analysis was performed to ensure it would not fail.
The material selected for the coupler was Aluminum 6061 T6 while the rest of the skin will be made
of PVC. Below in Table are the parameters used in the analysis and the results.
Table 16: Parameters and results for Bearing stress analysis on skin
Parameters Symbol Value
Force Applied (N) F 170.3
Factor of Safety (FS) FS 3
diameter of hole (mm) d 3
Total applied load(divided by N=4=pin count) P 510.9
Calculated thickness of skin (mm) t 1.8
Minimum selected thickness (mm) t 2
Equation 62: Equation of Bearing Stress (Ref. 8)
bearing
F
td
 
Where F=Force applied, t=thickness of materials, d=diameter of hole
Solving for t:
Equation 63: Equation of Bearing stress solved for thickness
bearing
F
t
d

Sample calculation
We will input the materials yield strength to be equal to the bearing stress. Safety factor is taken
into account in the load
bearing
F
t
d


58. E S R A | 53
511
95 (0.003 )
t
MPa m

1.8t mm
Section Joint analysis
The section joint‘s main purpose is the connect two sections of the rocket that must detach to
deploy recovery system. They must slide in and out with simple translational motion along the
longitudinal axis. They will also avoid rotation between sections. It must also withstand weight of
rocket in horizontal position. Below in Table are the parameters used in the analysis and the results.
Table 17: Parameters and results for section joint analysis
Parameters Symbol Value
Mass (kg) m 12
Gravity (m/s^2) g 9.807
Weight (N) w 117.684
Acceleration (m/s^2) a 37.2
load factor (1+(a/g)) n 5
Factor of Safety (FS) FS 3
Total applied load P 1692.252
Calculated rod diameter (mm) d 2
Minimum selected rod diameter (mm) d 3.175
cr
ave
P
A
 
Equation 64: Shearing Stress to determine rod diameter for section joint (Eqn. 1.8 Ref. 7)

59. E S R A | 54
Solving Equation for area, considering a circular area, and then solving for the diameter:
2
4
cr
ave
d P
A


 
4 cr
ave
P
d


Equation 65: Minimum rod diameter for section joint
Sample calculation
Given:
Material: Aluminum 6061
140yield MPa  (Ref. 8)
511crP N
Calculations:
Using Equation
 4 511
0.002
1400
N
d m
MPa
 
After performing the calculations a series of results and conclusions were made regarding overall
dimensions and the principal dimensions and masses are listed in the tables below (Table, Table)