Project Management & Design II – MAE 435
Rocket Project
Final Report
CN: 14677
December 1, 2015
Group Members:
Wesley Harpster
Ryan Horton
James Lawrence
Karna Shah
James “Trey” Simmons
Irfan Ali Shaukat
Derek Hampton (Business/IT Major)
Cindique Simmonds (EET Major)
Alexandre Misenheimer (MAE Junior)
Amanda Nolan (MAE Sophmore)
Project Advisor
Dr. Thomas Alberts
TABLE OF CONTENTS
TABLE OF FIGURES ...................................................................................................... III
NOMENCLATURE ......................................................................................................... IV
ABSTRACT ...................................................................................................................... VI
1. INTRODUCTION ........................................................................................................ 1
2. LITERATURE REVIEW/BACKGROUND ................................................................ 2
3. METHODS ................................................................................................................... 7
3.1. CENTER OF PRESSURE, CENTER OF GRAVITY, AND STATIC MARGIN ....................... 7
3.2. AVIONICS .............................................................................................................. 10
3.3. ROCKET MOTOR DESIGN PROCESS ........................................................................ 11
3.4. COMPOSITE SOLID FUEL MOTOR PREPARATION .................................................... 11
3.5. 3-D MODELING ..................................................................................................... 13
3.6. MOTOR SIMULATION ............................................................................................. 13
3.7. FINAL LAUNCH MOTOR FUEL SELECTION ………………………………………...14
4.
RESULTS .................................................................................................................. 14
4.1. CENTER OF PRESSURE, CENTER OF GRAVITY, AND STATIC MARGIN ..................... 14
4.2. AVIONICS TESTING ................................................................................................ 15
4.3. ROCKET MOTOR HOUSING DESIGN PROCESS ........................................................ 15
4.4. COMMERCIAL TEST LAUNCH ................................................................................. 16
4.5. ALTITUDE PREDICTION FAILURE INVESTIGATION ………………………………..16
4.6. CUSTOM TEST LAUNCH ......................................................................................... 17
I
4.7. FINAL CUSTOM MOTOR LAUNCH ………………………………………………...17
5.
DISCUSSION ............................................................................................................ 18
6.
CONCLUSION ……………………………………………………………………...19
7.
REFERENCES .......................................................................................................... 20
8.
APPENDIX ................................................................................................................ 22
8.1. FLIGHT DATA RESULTS ......................................................................................... 22
8.2. COMPUTER-AIDED DRAWINGS .............................................................................. 25
8.3. TABLES AND PLOTS ............................................................................................... 26
8.4. MATLAB CODES .................................................................................................... 30
8.5. PICTURES ............................................................................................................... 31
8.6. GANTT CHART....................................................................................................... 40
8.7 BUDGET……………………………………………………………………………41
II
List of Figures
Figure 1: Propellant Simulation Properties ……………………………………..…..…………...22
Figure 2: Catalyst Pressure vs. Time Curve ……………………………………....….………….22
Figure 3: Altimeter 2 Flight 2 11 October 2015 ……………………………………………...…23
Figure 4: Altimeter 2 Flight 1 11 October 2015…………………………………………..……..23
Figure 5: Altimeter 2 Flight 3 11 October 2015-Custom …………………………………….…24
Figure 6: Rocket Assembly…………………………………………….………………………...25
Figure 7: Rocket Motor Classification Table………..…………..…………………………….....26
Figure 8: Motor Housing Thickness-Hoop Stress ……………………...………………….……27
Figure 9: Motor Housing Thickness-End Stress…………………………………………………27
Figure 10: Parachute Deployment Testing………………………………………..………….….28
Figure 11: Theoretical vs. Factory Provided Aerodynamic Values……………………………...28
Figure 12: Dual Deployment with Redundancy Wiring Diagram…………………………….…29
Figure 13: Matlab Code for Center of Pressure ………………………………………….……..30
Figure 14: Matlab Code for Coefficient of Drag ……………………………………………......31
Figure 15: Center of Gravity Test……………………………….………………….....…………32
Figure 16: Single Altimeter Avionics Bay Build ………………………………………………..33
Figure 17: Dual Altimeter Avionics Bay Build………………………………………..………...34
Figure 18: Parachute Ejection Charge Testing………………………………………..……...….35
Figure 19: Certification Rocket Open Rocket 3D Model……………………………………..…35
Figure 20: Flight Simulations After Failure Investigation Weight Correction ………………....36
Figure 21: RAS Aero Rocket Model …..………………………………………………………..37
Figure 22: Open Rocket Model …..……………………………………………………………...37
Figure 23: Custom Motor Design 1 ……………………………………………………………..38
Figure 24: Final Custom Motor Design …..……………………………………………………..39
III
Nomenclature
(CNα)N
(CNα)TB
(CNα)CS
(CNα)CB
(CNα)F
x̅
x̅N
x̅TB
x̅CS
x̅CB
x̅F
𝑠
L, 𝑙𝑛
v
K T(B)
d
sf
cr
cA
l
xt
S.M.
COP
CG
𝐶𝐷0
𝐼𝑇𝑜𝑡𝑎𝑙
𝐼𝑆𝑃
t
k
m
gc
σh
P
di
th
σe
Ab
r
ρ
Ae
At
ε
pc
pe
Normal force coefficient for nose cone
Normal force coefficient for fins in the presence of the body
Normal force coefficient for conical shoulder
Normal force coefficient for conical boat tail
Normal force coefficient for fins alone
Center of pressure of rocket
Center of pressure of nose cone
Center of pressure for fins in the presence of the body
Center of pressure of conical shoulder
Center of pressure of conical boat tail
Center of pressure of fins alone
Cross sectional area
Length of nose cone
volume
Correction factor for normal force coefficient for fins in the presence of the body
Diameter of the body tube
Height of fin from body tube to tip
Length of fin attached to body tube
Length of flat portion at the tip of the fin
Length of line connecting the center point of sf with the center point of cA
Perpendicular distance from tip of fin start to start of fin against the body tube
Static Margin
Center of pressure
Center of gravity
Coefficient of Drag
Total Impulse
Specific Impulse
Operating Time
wind resistance factor
mass
acceleration due to gravity
Hoop stress
Pressure
Inside diameter
Thickness
End stress
Burn area
Burn rate
Density of fuel
Cross-sectional exit area of nozzle
Cross-sectional area at the nozzle throat
Nozzle expansion ratio - Ae/At
Operating pressure of the motor housing
Pressure at nozzle exit
IV
p0
c*
𝑤̇𝑝
M
γ
T
Pressure at maximum altitude
Characteristic velocity of the propellant
Propellant weight flow
Mach number
Specific heat ratio
Thrust
V
Abstract
The purpose of this project was to launch a high-powered rocket to a maximum height of
10,000 feet using a custom built composite solid fuel rocket motor (CSFM). The center of
pressure was found using a three dimensional theoretical analysis method. The center of gravity
was found experimentally. The static margin was calculated using both the center of pressure and
the center of gravity to determine flight stability of the rocket prior to launch. The avionics bay
was built using a MissileWorks RRC3 Altimeter System for in flight control of the parachute
deployment charges. The ejection charges were ground tested to ensure proper parachute
deployment prior to launch. The system was flight tested twice prior to beginning the CSFM
design process to ensure successful parachute deployment during the final launch. A GPS
system, a main parachute, and a drogue parachute were used to recover the rocket after the
launch. Fuel characteristics, operating pressure, burn area, and nozzle geometry were calculated
using computer programs to reach the planned altitude. Altitude and thrust predictions were done
using 3-D modeling. The propellant mixture that was used was 76.9% ammonium perchlorate,
5% aluminum powder, and 13% hydroxyl terminated polybutadiene by mass. The CSFM design
was tested twice. The first test ensured the propellant design was done correctly. The second test
was to reach 10,000 feet.
VI
1.
Introduction
Old Dominion University has established a high powered rocket club with the goal of
attending rocket competitions against other universities. In this, Old Dominion Mechanical and
Aerospace Engineering Department could achieve national recognition for its students senior
design projects, much like the current formula team. In order to make this project more
meaningful, a baseline of knowledge must be achieved, through constant improvement at the
senior design level. Additionally, a multidisciplinary and undergraduate element must be
implemented in order to ensure the knowledge gained is never lost. This project and the previous
project have been learning the concepts of high powered rocketry and composite solid fuel motor
design (CSFM). This is the most common type of solid rocket motor currently used in military
and space applications [7]. Additionally, it is the most common fuel used in high powered
rocketry. The knowledge necessary in order to complete the project will be of monumental use in
follow on teams in competitions.
During the Fall 2014 – Spring 2015 semesters, the ODU Rocket Team built a rocket with
a commercial motor which reached an altitude of 4,000 feet. During this launch the avionics bay
deployment system incurred a fault which resulted in both main and drogue parachutes
deploying at apogee. Additionally, the Fall 2014 – Spring 2015 ODU Rocket team tested a
custom CSFM design two times which resulted in failure [1]. The Summer-Fall 2015 Rocket
Team was tasked to improve upon the research and design from the previous team. The purpose
of this project was to design and build a custom CSFM to successfully launch a rocket to an
altitude of 10,000 feet with a payload of five pounds by the end of the fall 2015 semester with a
budget of $2,500.
1
2.
Literature Review/Background
In order to begin purchasing and building a rocket, there are multiple high powered
rocket certifications that must be achieved. There are three certification levels which must be
passed prior to launching a rocket requiring an M class motor to 10,000 feet according to Tripoli
Rocketry Association guidelines [2]. Each certification must be approved by a member of the
Tripoli Rocketry Association and it must be done on an approved site. Level I certification
requires that a rocket be built and flown successfully using an H or I class motor (impulse
between 160.01 and 640.00 n-sec). The level II certification test requires a flight using a J, K, or
L class motor. The level III certification requires one successful flight using a level II class
motor and an electronic parachute deployment system. Along with the flight, a pre-flight data
capture form, rocket drawings, parts list, wiring diagram, and pre-flight checklist must be
submitted and reviewed by two Tripoli certifying members prior to the day of the launch. The
level III certification launch will use a class M or larger motor (impulse of 5120.01 n-sec or
greater). Each of the certifications require that the rocket be free of damage in order to pass [2].
The rocket being used for this project consists of a nose cone, forward payload bay, aft
payload bay, fin section and an avionics bay. The nose cone is the very tip of the rocket and
does not typically carry a payload. The forward payload bay contains the main parachute used
for recovery that deploys at apogee. The aft payload bay contains the drogue parachute used to
slow the fall of the rocket while allowing it to fall straight down for ease of recovery. The fin
section contains the motor mounts, nozzle, and motor housing and is part of the aft payload bay.
The avionics bay contains the electronic board which is responsible to ignite two or four
parachute deployment charges depending on its design.
2
In order to fly, the stability of the rocket must be determined by finding the center of
gravity and the center of pressure [3, 4]. The distance between these two design features
determine the stability of the rocket [3, 4]. Ideal rocket design calls for 1 full diameter of the
rocket body tube between the center of gravity and pressure with the center of pressure towards
the aft [3-5]. If this is not true the rocket will not self-correct its flight in the air and will not fly
straight up [4, 6-9].
There are multiple different avenues to electrical parachute deployment control. Some
electronics offer a remotely triggered explosive charge system, which is typically used for
rockets reaching an altitude of 5000 feet or less. Above that height, it becomes necessary to use
an electronic control board that uses acceleration and altitude as it primary means of parachute
ejection. This requires accelerometers and pressure sensors to be integrated into the control board
and it must be programmed to deploy each parachute at its desired point in the rockets flight
path.
The drag coefficient for any rocket must be calculated in order to predict the maximum
altitude of any flight prior to launch [4, 10, 11]. This coefficient changes throughout the flight
based on the height and speed of the rocket. As the height increases, the density of the air
decreases resulting in a lower drag force on the rocket [4, 10, 11]. Additionally, as the rocket
approaches the Mach 1, the coefficient of drag gets much larger and causes an increase in the
overall drag force [4, 10-12].
The characteristics of a rocket motor, whether commercial or custom, directly affect the
performance. In a custom motor, the characteristics are able to be altered by the fuel mixture
used and components added to it. For the rocket project, the baseline fuel selected to be used was
3
an APCP composition. This fuel type is widely used for military, space, and rocket hobbyist
applications. The question then, is which catalyst to employ. While there are various metal
oxides that can be used, each provides a different flare to the fuel. A copper oxide propellant,
which is one of the fastest and as a result hottest burning catalyzed propellants, burns blue in
color with little smoke. Red iron oxide was chosen for use in the production of our first research
motor build. This is because the propellant has a slightly lower burn rate which allows it to be a
bit forgiving during operation. This can be demonstrated through the burn rate calculation
equation below.
𝑟 = 𝑎 ∙ 𝑃𝑛
In this equation, both variables a and n are the burn rate coefficient and exponent. These
are propellant characteristic values that are specific to each propellant composition. These
values must be obtained experimentally. For red iron oxide these values are somewhat lower
causing a slower increase in burn rate with an increase in pressure.
A rocket motor consists of three major parts: propellant, nozzle, and motor housing [4].
Since many of the parameters depend on each other while designing the rocket motor, it is
necessary to make a guess based on the desired height of the rockets flight and the length of time
that thrust needs to take place [4]. This allows values to be calculated in order to verify the
design will work for the particular application [4]. The process is then done in iterations until a
working design is mathematically modeled for the motor [4].
The motor was made in a Bates Grain Configuration. In this configuration, the grains are
made in optimal lengths based on burn rate of the fuel composition and core diameter used [7,
12, 24]. This allows the motor to achieve maximum thrust nearly instantly and remain at that
4
level or just higher for the duration of the burn [7, 12, 24]. This thrust curve is most preferable
during rocket launches because it allows for the greatest use of all of the potential energy stored
in the thermochemical reaction of the rocket fuel.
The process of building a custom rocket motor is extensive in each step. First, the proper
components must be decided upon and simulated to ensure the primary goal is being met. Next,
the correct weight of components must be purchased. Lastly, the components must be mixed,
cured, and prepared for launch. Rocket fuel consists of five main parts, oxidant, fuel, binder,
additives, and catalyst [7, 12, 24]. Other additives for example plasticizers, curing agents and
catalysts can be used to either ease production or increase performance.
The oxidizer is used to provide oxygen for the combustion of the rocket motor. There are
four primary options for composite propellant oxidizer, ammonium perchlorate, ammonium
nitrate, potassium perchlorate, and potassium nitrate [7, 12, 24]. Ammonium based oxidizers
tend to be more consistent and predictable than potassium based oxidizers. “Rocket Candy” or
“Carmel Candy” is an example of a potassium based oxidizer [7]. Due to the low operating
temperature and brittle nature of these fuels, they would not be an initial choice with the
availability of composite components which are superior in ease of production and energy
output. Ammonium based oxidizers tend to be more expensive; however they provide the
necessary characteristics to withstand the ignition pressures and reach the proposed altitude [7].
The decision between ammonium nitrate and ammonium perchlorate comes down to preference
of the system that is being worked with. The low combustion temperature and slower burning
rate characteristics are highlighted in ammonium nitrate. The high burn rate and high impulse
characteristics are highlighted in ammonium perchlorate [7, 12, 24]. Since the motor housing
5
used for the rocket was able to withstand high combustion temperatures, ammonium perchlorate
was selected.
The fuel is the component which will fine-tune the mixture to the preferred
specifications. The two main options for fuel are aluminum and magnesium [7, 12, 24].
Aluminum tends to be used with ammonium perchlorate and magnesium tends to be used with
ammonium nitrate. In practice the addition of fuel tends to increase the specific impulse of any
motor[7, 19, 30]. This only happens to a point however as most compositions do not use more
the 18% fuel by mass.
The binder chosen for the composite rocket motor is used to bind the other components
together. There are several binders which can be chosen for a fuel composition. Examples for
binders are R45HT-LO, R45M, R20LM, and more [7, 23]. Each choice has a varying equivalent
weight, molecular weight, and chemical ratio. Based on availability, cost, and minimal difference
between the binders for the application, R45HT-LO was chosen.
The additives used are typically plasticizers and curing agents. Plasticizers, such as
dioctyl adipate, are used to ease the mixing process in fuel preparation and allow some flexibility
of cured grains without cracking [7, 12, 24]. Curing agents are used to strengthen the grains in
order to ensure they remain intact during the burn and acceleration phase of a launch. E744 was
used for the composition. Catalysts are the last portion of a propellant mixture which can affect
the final product of the composition . The three options for a catalyst are ammonium dichromate,
copper oxide, and iron oxide. Each choice has its own positive benefits, however each of them
are made to increase the burn rate which will improve performance. Iron oxide was chosen for
the composition [7, 24, 30].
6
Catalysts are typically used in rocket motors to increase the burn temperature which also
increases the burn rate. This increase in burn rate directly increases mass flow which increases
the fuels specific impulse. Essentially, the addition of a catalyst provides more thrust for every
kilogram or pound of propellant. Some typical catalysts include but are not limited to red iron
oxide, magnesium oxide, and copper oxide. These are usually transition metal oxides and are
well known for their catalytic behavior. They are also known for their explosive qualities when
in aerosol form and therefore must be handled with extreme caution.
3.
Methods
3.1.
Center of Pressure, Center of Gravity, and Static Margin
To calculate the center of pressure for the rocket, it was necessary to take every section of
a typical rocket body into consideration. The sections used were nose cone, body tube, conical
shoulder, conical boat tail, and fins. The relationship of center of pressure of the overall rocket
and each of the sections was governed by the coefficient factor of normal force and it’s specific
center of pressure (Equation 1) [3].
𝑥̅ =
(𝐶𝑁𝛼 )𝑁 𝑥̅𝑁 + ( 𝐶𝑁𝛼 ) 𝑇𝐵 𝑥̅ 𝑇𝐵 + (𝐶𝑁𝛼 )𝐶𝑆 𝑥̅𝐶𝑆 + (𝐶𝑁𝛼 )𝐶𝐵 𝑥̅𝐶𝐵
∑ 𝐶𝑁𝛼
(Equation 1)
For any nose cone with a circular cross sectional area at the base and a smooth transition
throughout, the value of CNα was known to be equal to 2 (Equation 2) [3].
8
(𝐶𝑁𝛼 )𝑁 = 2 ∫
𝜋𝑑
𝑑𝑠(𝑥)
𝑑𝑥
𝑑𝑥
𝑏𝑢𝑡
𝑑𝑠(𝑥)
𝑑𝑥
= 𝑠(𝑥) =
𝜋𝑑2
4
(𝑓𝑜𝑟 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑛𝑜𝑠𝑒 𝑐𝑜𝑛𝑒)
(Equation 2)
∴ (𝐶𝑁𝛼 )𝑁 = 2
7
The specific center of pressure for the nose cone was found using the volume, cross sectional
area, and length (Equation 3) [3].
𝐿 − 𝑣⁄𝑠(𝐿)
𝑥̅𝑁 =
𝑠(𝑜)
1−
⁄𝑠(𝐿)
(Equation 3)
The center of pressure for the fin section always falls on the centerline of the rocket body tube.
The calculation CNα for the fin section was shown above as (CNα)TB. The CNα factor for fins was
multiplied by a correction factor to adjust value for this situation (Equation 4) [3].
(𝐶𝑁𝛼 ) 𝑇𝐵 = (𝐶𝑁𝛼 )𝐹 𝐾𝑇(𝐵)
(Equation 4)
The calculation of KT(B) was a relationship between the body tube size and the size of the fins
(Equation 5) [3].
𝐾𝑇(𝐵) = 1 +
𝑟𝐴
𝑠 + 𝑟𝐴
(Equation 5)
Then (CNα)F was calculated using dimensions taken from the fins. Since known equations only
exist for certain fin shapes, it was calculated using the approximation that cA, the length of the tip
of the fin, ran to the end of the fin (Equation 6) [3].
(𝐶𝑁𝛼 )𝐹 =
2
𝑠
12 ( 𝑓⁄𝑑)
(Equation 6)
2
2𝑙
)
1+√1+(
𝑐𝑟 +𝑐𝐴
Then using fin geometry as well geometry of the entire rocket, the center of pressure of the fin
section was found in relation to the distance from the front of the nose cone (Equation 7) [3].
𝑥̅ 𝑇𝐵 = 𝑥𝐹 +
𝑥𝑡 𝑐𝑟 +2𝑐𝐴
3
(𝑐
𝑟 +𝑐𝐴
1
𝑐 𝑐
) + 6 (𝑐𝑟 + 𝑐𝐴 − 𝑐 𝑟+𝑐𝐴 )
𝑟
(Equation 7)
𝐴
8
Then the original equation can be represented in the terms of the coefficient of forces and the
specific center of pressures (Equation 8) [3].
𝑥̅ =
(𝐶𝑁𝛼 )𝑁 𝑥̅ 𝑁 +𝐾𝑇(𝐵) (𝐶𝑁𝛼 )𝐹 𝑥̅ 𝑇𝐵
∑ 𝐶𝑁𝛼
(Equation 8)
Following this process and using a MATLAB code (Figure 10), the center of pressure for the
rocket was found [3]. Additionally the rocket was 3D modeled using Open Source Rocketry and
it was found to coincide with the calculated center of pressure.
Then the center of gravity for the rocket was found. This was found by tying a rope
around the rocket and moving it until the point at which the rope alone will balance the weight of
the rocket. Then a measurement was taken from the tip of the nose cone to the point at which the
rocket balances (Figure 12).
The key piece of information derived from both of these values is the static margin [3].
𝑆. 𝑀. = (𝐶𝑂𝑃 − 𝐶𝐺)/𝑑
(Equation 9)
The design point that was chosen for the rocket was for a static margin value greater than 1.5 and
less than 4 [4, 10, 11, 13]. This range of values was chosen to allow for marginal changes in the
center of pressure that occur during flight due to weights shifting and angle of attack [4, 10, 11,
13].
9
3.2.
Avionics
The avionics bay electrical control board chosen was the Rocket Recovery Controller
(RRC3) altimeter avionics system from Missile Works Corporation. For the certification flights,
this board was mounted on a purchased carbon fiber frame. All of the electrical control
components were then mounted on a custom aluminum sled. This sled was then mounted into the
avionics bay section of the rocket using long screws, rubber and regular washers, nuts, and
covered in epoxy to minimize vibration during thrust (Figure 16).
This design was changed when a GPS and dual redundant RRC3 boards were used in the
avionics bay. The rocket used to achieve a 10,000 ft. launch utilized a dual board RRC3 system
for redundancy. The two boards were used from the spring 2015 rocket group’s avionics bay.
Both boards were mounted on a purchased 3-D printed frame, which were assembled with two
zinc rods. These rods were inserted through holes located at certain points on the printed frames
and then thread locked to remain secure. One custom aluminum sled was machined on which the
GPS system was mounted. This custom sled was attached to the bottom of the secondary
altimeter using eyehooks and fastened with JB weld to avoid any vibrations or stresses on the
eyehooks or the rods. New aluminum bulk heads were also machined and milled and the whole
bay was fastened with lock nuts and thread lock. The boards were wired using dual redundancy
schematics (Figure 17). The purpose of redesigning the avionics bay was to reduce weight and
space constraints within the bay due to the addition of the custom sled and the GPS system.
The ejection charges used to deploy the main and drogue parachutes were built using an
online design tool [14]. The charges were built to reach the design pressure of 12.5 psi inside the
forward and aft payload bay. The materials used for the build were FFFF black powder, finger
10
tips of rubber gloves, an electrical motor igniter, and rubber bands. The black powder was
weighed out and placed in the tips of the glove, the igniter was inserted, and a rubber-band was
used to seal the charge. The charges were tested by assembling the rocket, bypassing the
electrical control board, and detonating the charges using a 9 volt battery. Testing was performed
on the ground by bypassing the avionics board (Figure 18).
3.3.
Rocket Motor Design Process
The design of the motor housing must take both internal pressure and temperature into
consideration. The primary forces of concern on the motor housing were as a result of the
internal pressure. All other forces were assumed to be negligible in comparison. Using this
assumption the design of a motor housing then becomes a pressure vessel calculation (Equation
10) [15].
𝜎ℎ =
𝑃(𝑑𝑖 +𝑡ℎ)
2𝑡
𝑃𝑑
𝜎𝑒 = 4𝑡ℎ𝑖
(Equation 10)
These equations were solved for t and programmed into excel to produce a graph of
necessary wall thickness based on the use of an aluminum 6061-T6 motor housing material. The
calculations were done using the yield stress of the given materials. The adiabatic flame
temperature for an AP/Al/HTPB motor is approximately 3000 K [16-20]. The actual surface will
not reach this temperature, but since it exceeds the melting point for aluminum 6061-T6, a
phenolic liner was used in every motor in order to maintain structural integrity [9, 18, 21, 22].
3.4. Composite Solid Fuel Motor Preparation
Prior to making fuel, an excel file provided by a rocket enthusiast was used in order to
determine the mass necessary in grams of each component of the fuel (Figures 23, 24). As
11
previously stated, the baseline fuel selected was an APCP composition with a red iron oxide
catalyst. After this was determined, the core diameter and nozzle throat needed to be designed to
support the fuel. Fpred and BurnSim were the two software used to complete these steps.
Multiple software programs were used for redundancy in order to ensure the design would
perform as expected.
Once the preliminary calculations were completed and the components were purchased,
the fuel was mixed. A specific order of mixture was followed to ensure that everything cured the
correct way. The liquid components were weighed and added first. This consists of a binding
agent (R45HTLO), curative (E744), and plasticizer (dioctyl adipate). The first dry component
added was the metal oxide catalyst (red Iron oxide), which ensures all of the particles are
captured by the liquid. The addition of the metal oxide catalyst was arguably the most important
due to the explosive nature of aerosolized metal oxides. Finally, the ammonium perchlorate was
added. After the fuel was mixed, it was placed in a vacuum. The vacuum increases the specific
impulse of the fuel by removing microscopic air pockets thus increasing the density.
After completion of the mixing process, the fuel was rolled and smashed into precut
propellant grain tubes where the length was previously determined during nozzle and core
diameter calculations. Proper care must be taken in order to minimize air pockets in the
propellant grains during this step. Air pockets in propellant grains would increase the burn area
drastically which in turn would increase burn rate. This self-sustaining process could quickly
result in catastrophic failure of the motor. Mold release was also used to allow the grains to free
themselves of the molds in order to reduce breaking and cracking after curing. The composition
was left to cure for 4 days, though normally the process varies between 3 hours and 3 days
depending on the binder used. When the cure completed, the composition was ready for flight.
12
3.5. 3-D Modeling
The three types of software that were used to model and simulate the rocket were Autodesk
Inventor, Open Source Rocketry, and RASAero II (Figures 6, 19, 21 and 22). These simulations
were used in order to obtain a prequalification permission to launch prior to launch day. The
primary use for Autodesk Inventor was to accurately model the bulkheads and GPS mounting
plate. Open Source Rocketry and RASAero II were used to model the rocket, and simulate the
flight based on the rocket dimensions and motor selected or designed. Based upon the model of
the rocket, the program calculates the coefficient of drag, center of mass, center of gravity and
other basic properties needed to properly simulate test flights. Each interior and exterior
component must be modeled to scale in the rocket assembly in order for the simulation to be
accurate. Prior to purchasing or machining a part, we ensured it would coincide properly with the
simulation. With a completed assembly, an estimated altitude was determined.
3.6. Motor Simulation
In order to simulate the motor build, first the fuel composition calculation spreadsheet
was used to obtain key propellant characteristics such as burn rate exponent, coefficient, C-Star,
gamma, and density. These values were then entered into both BurnSim and Fpred in order to
obtain two separate expected burn results using a Bates Grain Configuration. The results would
use the applied nozzle throat area and operating pressure in order to obtain a thrust for each
second during the burn. These values were then used in a conservative manner in order to allow
for minor fluxes in operating pressure to allow for a successful flight of the rocket without
catastrophic failure of the motor.
13
3.7. Final Launch Motor Fuel Selection
The final launch required the rocket to break 8,000 feet. This solely, drove the design
parameters. The options were to build a long 54 millimeter motor or a very short 75 millimeter
motor. In either case, some very creative fuel composition methodology would need to be
employed. Due to the extremely fast burning and unforgiving behavior of long skinny motors the
75 millimeter diameter four grain slow burn motor was chosen. This motor composition
consisted of 74.75% AP, 2.54% Al, 3.5% dioctyl adipate, 11.74% R45HT-LO, 0.75% black
copper oxide, 4.5% strontium oxide, and 0.3% tepanol. The key ingredient was the strontium
carbonate. This decreased the burn rate coefficient and exponent to less than 1, thus creating a
very stable and forgiving fuel that burns at about half the rate of our initial rocket fuel.
𝑟 = 𝑎 ∙ 𝑃𝑛
Therefore, this fuel was chosen in order to minimize the chance of catastrophic motor failure
during motor ignition and burn.
4.
Results
4.1.
Avionics Testing
Testing of the custom designed and built ejection charges were conducted for the
certification rocket and the team rocket. During testing the charge built performed as expected
outside of the rocket housing. Upon initial testing the drogue chute in the forward payload bay
was a success using 1.3 g black powder. The follow on test of the main chute in the aft payload
bay did not deploy using 2 g black powder. The black powder was then increased to 2.2 g and
tested again with another failure. The main chute was then tested in the forward bay using 1.3 g
14
of black powder with success. The drogue chute was then tested in the aft bay with 2 g of black
powder successfully. A retest was done with the drogue chute in the aft bay using 1.48 g of black
powder with success. The ejection charge designed for launch days will be the drogue chute in
the aft bay with 1.48 g of black powder and the main chute in the forward bay with 1.3 g of black
powder (Figure 5). The follow on testing of the team rocket found two successful tests at 1.68
grams of black powder in the forward bay with the main parachute and 2.3 grams in the aft bay
with the drogue parachute.
4.2. Rocket Motor Design Process
The motor housing design was graphed for both hoop stress and end stress felt in the
motor housing. The results indicate that the primary design concern for any motor housing is the
hoop stress (Figure 4 and 5). Additionally, this provides a much quicker reference for design of
various motor housings depending on design requirements. Using a safety factor of four the
motor housing would still fit inside of the main rocket that will be used for the final launch.
4.3. Center of Pressure, Center of Gravity and Static Margin
The calculation for the stability of the rocket was solved using the center of pressure,
center of gravity and static margin. The center of pressure was determined to fall at 54.3 inches
down from the tip of the nose cone. The center of gravity was found experimentally to be 45.3
inches from the tip of the nose cone. These values were used to produce a designed static margin
of 2.25 (Equations 1-9). The rocket nose cone provided from the kit was swapped out for a
previous rockets nose cone due to material issues. Therefore, the geometry only changed slightly
and we were able to compare our theoretical calculated values against the values provided with
the kit. The static margin for the rocket as purchased was 1.75. The distance between the center
15
of pressure and center of gravity was 7 inches which leads to the conclusion that our rocket is
stable and ready for flight as built (Figure 7) [23].
4.4. Commercial Test Launch
The first flight using the K695R motor was simulated at 3,675 feet. The altimeters
recorded a maximum altitude of 4,029 feet.
%𝐸𝑟𝑟𝑜𝑟 =
|3675 − 4029|
∗ 100% = 9.633%
3675
The value of 9.633% error is a bit on the high side but still acceptable for rocketry standards.
The more troubling part is the simulations are designed to be best case scenario and therefore are
rarely over shot by more than 1-2%.
The second flight which was on a L1250DM was projected to go to 9,360 feet, however;
it went 11,960 feet.
%𝐸𝑟𝑟𝑜𝑟 =
|9360 − 11960|
∗ 100% = 27.77%
9360
The 27% error seen in the second flight is completely unacceptable.
4.5. Altitude Prediction Failure Investigation
Due to the large unexpected error in the predicted slight simulation for the commercial
L1250-DM motor, a failure investigation was conducted. Upon examination of the 3-D model
nothing appears to be out of the ordinary. The only way to achieve a significant increase in
altitude was to decrease the overall rocket weight significantly. Based upon this, the rocket was
dissembled and reweighed 3 times on two separate scales. The rocket weighed approximately
three pounds lighter than what it was simulated at. After adjusting the model the flight
16
simulations were consistent with actual maximum altitude of flight (Figure 20, Figure 3 and
Figure 4).
𝐾695𝑅 𝑆𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑃𝑜𝑠𝑡 𝑊𝑒𝑖𝑔ℎ𝑡 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 %𝐸𝑟𝑟𝑜𝑟 =
𝐿1250 − 𝐷𝑀 𝑃𝑜𝑠𝑡 𝑊𝑒𝑖𝑔ℎ𝑡 𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 %𝐸𝑟𝑟𝑜𝑟 =
|4029 − 4142|
∗ 100% = 2.73%
4142
|11960 − 12087|
∗ 100% = 1.05%
12087
4.6. Custom Test Launch
There was only one flight completed using the Ammonium Perchlorate Composite
Propellant (APCP). The altimeters recorded a maximum altitude of 2,503 feet.
%𝐸𝑟𝑟𝑜𝑟 =
|3156 − 2503|
∗ 100% = 20.69%
3156
The estimated altitude from the rocket simulation was based on a J-800 motor because of
the similar thrust-time curves. The error was largely due to significant discrepancies in the rocket
model prior to the flight
4.7. Final Custom Launch
The final custom motor launch was a complete success. The expected altitude was 8,179
feet and the actual achieved altitude was 8,111 feet.
%𝐸𝑟𝑟𝑜𝑟 =
|8179 − 8111|
∗ 100% = 0.8314%
8179
The motor performed within 1% of the expected altitude and came off without a hitch. This
verified our rocket model and altitude simulation process. Additionally, our motor design
approach was verified through this as well.
17
5.
Discussion
The summer 2015 – fall 2105 rocket project was tasked to launch a rocket using a custom
CSFM to a height of 10,000 feet using a budget of $2,500 by December 12, 2015. In order to
achieve this, some lessons learned were applied from the fall 2014 – spring 2015 rocket project.
The test stand design was modified from a horizontal to a vertical orientation to provide an
inherently stable design eliminating the need to anchor the stand down [1]. Additionally, the fuel
that has been selected for the CSFM build has been changed from a potassium nitrate and sugar
mixture to AP/Al/HTPB due to the significant amount of current research available. Also, in the
previous rocket project an expert cited the possibility of their fuel selection being a cause for the
failure in the motor testing [1]. The rocket project at this point has achieved all of the initial tasks
with some unavoidable edits to the original goal. Due to Tripoli Rocketry Association we were
unable to actually attain an altitude of 10,000 feet on a custom motor. Additionally, the launch
was not done with a payload on board. Due to the maximum launch height of 9,000 feet, we
chose to break 8,000 feet using the empty mass of the rocket. The CSFM design can easily be
scaled up using burn simulations and flight simulations in order to achieve 10,000 feet. In
addition an additional five pounds payload flight can easily be completed after simulations. The
next step in the progression for this project should be to start preparations for competition. The
necessary base knowledge and skills have been passed down and demonstrated by
undergraduates who should be able to perform well in a rocket competition.
18
6.
Conclusion
The team was able to complete 100% of the project scope. Due to Tripoli regulations, we
were not able to fly to 10,000 feet on the custom motor flight. The same design process could be
employed with the goal of achieving a higher altitude and the same result could be achieved.
Additionally, the five pound payload could be added anywhere to any rocket model and the
custom motor would then be designed in a manner in which to ensure a 5 pound payload reached
the desired altitude. The only reason the payload was not included is because originally that part
of the competition was to be designed by the SEDS who failed to continue working on their
portion of the project.
19
7.
References
[1]
C. B. Nathan Akers, Paul Campbell, Charles Juenger, Brian Mahan, Chris Skiba, Michael Weber,
Michael Wermer, "Rocket Project Final Report ", ed. Old Dominion University 2015, p. 62.
T. R. A. Inc., "High Powered Rocketry Certification," ed, p. 4.
J. S. Barrowman and J. A. Barrowman, "The theoretical prediction of the center of pressure,"
Catholic University Master’s thesis, 1966.
E. Fleeman, Tactical Missile Design, Second ed. Reston, VA: American Institute of Aeronautics
and Astronautics, Inc., 2006.
S. M. (July 21, 2015). Chapter 3 - Drag Force and Drag Coefficient. Available:
http://faculty.dwc.edu/sadraey/Chapter%203.%20Drag%20Force%20and%20its%20Coefficient.
pdf
X.-b. Li, J.-w. Dong, Y.-j. Wang, and Z.-z. Jin, "Zero-lift drag coefficient identification of rocket
target," Journal of Solid Rocket Technology, vol. 33, pp. 5-8, 02/ 2010.
E. R. Prince, S. Krishnamoorthy, I. Ravlich, A. Kotine, A. C. Fickes, A. I. Fidalgo, et al., "Design,
Analysis, Fabrication, Ground-Test, and Flight of a Two-Stage Hybrid and Solid Rocket," in 49th
AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 14-17 July 2013, Reston, VA, USA, 2013, p.
25 pp.
R. A. Struble, "The Trajectory of a Rocket With Thrust," Journal of Jet Propulsion, vol. 28, pp.
472-478, 1958/07/01 1958.
N. Kubota (2015). Propellants and Explosives : Thermochemical Aspects of Combustion (3 ed.).
Available: http://ODU.eblib.com/patron/FullRecord.aspx?p=1998813
S. Mark and T. Richard, "Evaluation of CFD code CFD-ACE for application to rocket problems," in
36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, ed: American Institute of
Aeronautics and Astronautics, 2000.
T. Brown, B. Fred, H. Thomas, H. Wayne, T. Brown, B. Fred, et al., "Drag and moment
coefficients measured during flight testing of a 2.75-in. rocket," in 35th Aerospace Sciences
Meeting and Exhibit, ed: American Institute of Aeronautics and Astronautics, 1997.
N. Hall. (July 20, 2015). The Drag Coefficient. Available: https://www.grc.nasa.gov/www/K12/airplane/dragco.html
A. Fedaravičius, S. Kilikevičius, and A. Survila, "913. Optimization of the rocket's nose and nozzle
design parameters in respect to its aerodynamic characteristics," Journal of Vibroengineering,
vol. 14, pp. 1885-1891, 2012.
J. Anderson. (August 3, 2015 ). Black Powder. Available:
http://www.rockethead.net/black_powder_calculator.htm
J. K. N. Richard G. Budynas, Shigley's Mechanical Engineering Design, Ninth ed. New York, NY:
McGraw-Hill, 2008.
A. M. Hegab, H. H. Sait, A. Hussain, and A. S. Said, "Numerical modeling for the combustion of
simulated solid rocket motor propellant," Computers & Fluids, vol. 89, pp. 29-37, 1/20/ 2014.
R. J and O. J, "Combustion modeling of aluminized propellants," in 15th Joint Propulsion
Conference, ed: American Institute of Aeronautics and Astronautics, 1979.
Y. Chang, L. W. Hunter, D. K. Han, M. E. Thomas, R. P. Cain, and A. M. Lennon, "Solid rocket
motor fire tests: Phases 1 and 2," AIP Conference Proceedings, vol. 608, p. 740, 2002.
L. Luigi De, P. Christian, R. Alice, S. Marco, M. Elisa, M. Filippo, et al., "Aggregation and Incipient
Agglomeration in Metallized Solid Propellants and Solid Fuels for Rocket Propulsion," in 46th
AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, ed: American Institute of
Aeronautics and Astronautics, 2010.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
20
[20]
[21]
[22]
[23]
V. Sekkar and T. S. K. Raunija, "Hydroxyl-Terminated Polybutadiene-Based Polyurethane
Networks as Solid Propellant Binder-State of the Art," Journal of Propulsion and Power, vol. 31,
pp. 16-35, 2015/01/01 2014.
J. D. G. Lengelle, J.F. Trubert. (2003, June 29). Combustion of Solid Propellants (January 2004 ed.)
[Research Article].
J. R. E. Grant, L. R, and S. M, "A study of the ignition of solid propellants in a small rocket motor,"
in Solid Propellant Rocket Conference, ed: American Institute of Aeronautics and Astronautics,
1964.
M. Rocketry, "Super DX3 All Fiberglass Kit," 2009.
21
8.
Appendix
8.1. Flight Data Results
Figure 1: Propellant Simulation Properties
Figure 2: Catalyst Pressure vs Time Curve
22
Figure 3: Altimeter 2 Flight 2 10 October 2015
Figure 4: Altimeter 2 Flight 1 10 October 2015
23
Figure 5: Altimeter 2 Flight 3 11 October 2015 – Custom
24
8.2.
Computer-Aided Drawings
Figure 6: Rocket Assembly
25
8.3.
Tables and Plots
Figure 7: Rocket Motor Classification Table
26
Figure 8: Motor Housing Thickness - Hoop Stress
Figure 9: Motor Housing Thickness – End Stress
27
Figure 10: Parachute Deployment Testing
Test 1
Test 2
Test 3
Test 4
Test 5
Test 6
Test 7
Charge Size (g) Chute Used
1.3 N/A
1.3 drogue
2 main
2.2 main
1.3 drogue
2 main
1.48 drogue
Results
drogue
main
aft bay
forward bay
Purpose
Test to see if the charge will detonate
drogue deployment fwd bay
main deployment aft bay
main deployment aft bay
main deployment fwd
drogue deployment aft bay
drogue deployment aft bay
Result
Success
Success
Fail
Fail
Success
Success
Success
1.48g
1.3g
Figure 11: Theoretical vs Factory Provided Aerodynamic Values
Theoretical Values
COP
COG
Static Margin
54.3 in
45.3 in
2.25
Factory Provided Values
COP
COG
Static Margin
48 in
41 in
1.75
28
Figure 12: Dual Deployment with Redundancy Wiring Diagram
29
8.4.
Matlab Codes
Figure 13: Matlab Code for Center of Pressure
%This code will calculate the center of pressure for a rocket
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%SURFACE AREA OF NOSE CONE AND COP FOR CONE%%%%%
h_nose = 0.5; %this is the height of incremental measure
D_nose = [0.35 0.60 0.79 0.92 1.09 1.25 1.42 1.56 1.67 1.80 1.94 2.12 2.18
2.393 2.4985 2.50 2.615 2.6955 2.810 2.8691 2.935 3.016 3.113 3.185 3.2515
3.3410 3.398 3.409 3.527 3.5895 3.646 3.698 3.751 3.807 3.856 3.9 3.932
3.9765 4.005 4.024 4.036 4.045 4.05 4.054 4.057 4.057 4.057 4.057]; %diameter
measurements
B = length(D_nose); %end of loop setting
i = 1;
Nose_Vf = 0;
CN_Alpha_nose = 2; %eqn 1
while i <= B
Nose_V = pi()*(D_nose(i)/2)^2*h_nose;
Nose_Vf = Nose_Vf + Nose_V;
i = i+1;
end
COP_Cone_Section = (24 - (Nose_Vf/((pi()*4^2)/4))); %Eqn 2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%SURFACE AREA OF FINS AND COP FOR FINS%%%%%
s = 3.776;
Xf = 64;
cr = 11.04;
ca = 4.54;
l = 4.406;
Xt = 6.50;
d = 4;
ra = 2;
CN_Alpha_Fins = (12*(s/d)^2)/(1+sqrt(1+(2*l/(cr+ca)))); %eqn 3
CN_Alpha_TB = (1+ra/(s+ra))*CN_Alpha_Fins;
COP_Fin_Section = Xf + (Xt/3)*((cr+2*ca)/(cr+ca))+(1/6)*(cr+ca((cr*ca)/(cr+ca)));
%Note: Fin geometry assumed square in rear for calculations purposes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%COP%%%%%
COP =
(CN_Alpha_nose*COP_Cone_Section+CN_Alpha_TB*COP_Fin_Section)/(CN_Alpha_nose+C
N_Alpha_TB);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%Stability Check%%%%%
CG = 54.2632-9;
Static_Margin = (COP - CG)/d;
30
Figure 14: Matlab Code for Coefficient of Drag
%Mach Number
M = linspace(0.1,2,20);
%Input Data
%l = missile body length
prompt1 = 'missile body length: ';
l = input(prompt1);
%ln = nose length
prompt2 = 'nose length: ';
ln = input(prompt2);
%d = missile body diameter
prompt3 = 'missile body diameter: ';
d = input(prompt3);
%q = dynamic pressure
prompt4 = 'dynamic pressure: ';
q = input(prompt4);
%Nozzle Exit Area
prompt5 = 'nozzle exit area: ';
Ae = input(prompt5);
%Sref = cross sectional area
prompt6 = 'cross sectional area: ';
Sref = input(prompt6);
%Equations
Cdbodyfriction = 0.053*(l/d)*[M/(q*l)].^0.2;
if M>1
Cdbasecoast = 0.25/M;
else
Cdbasecoast = (0.12+0.13*M.^2);
end
if M>1
Cdbasepower = ((1-(Ae/Sref))*(0.25/M));
else
Cdbasepower = ((1-(Ae/Sref))*(0.12+0.13.*M.^2));
end
Cdbodywave = ((1.586+(1.834./M.^2))*(atan(0.5/(ln/d))).^1.69);
Cdbodycoast = Cdbodywave+Cdbasecoast+Cdbodyfriction;
Cdbodypower = Cdbodywave+Cdbasepower+Cdbodyfriction;
Cd_zerolift = Cdbodyfriction+Cdbodywave+Cdbasecoast+Cdbasepower
Cd_induced = Cdbodycoast + Cdbodypower
Cd = Cdbodyfriction + Cdbodywave + Cdbodycoast + Cdbodypower + Cdbasepower +
Cdbasecoast
Cd2 = Cd_zerolift + Cd_induced
plot(M,Cd)
31
8.5.
Pictures
Figure 15: Center of Gravity Test
32
Figure 16: Single Altimeter Avionics Bay Build
33
Figure 17: Dual Altimeter Avionics Bay Build
34
Figure 18: Parachute Ejection Charge Testing
Figure 19: Certification Rocket Open Rocket 3D Model
35
Figure 20: Flight Simulations After Failure Investigation Weight Correction
36
Figure 21: RAS Aero Rocket Model
Figure 22: Open Rocket Model
37
Figure 23: Custom Motor Design 1
Propellant designation
Propellant density
77_5
0.06 lb/in^3
GRAINS TO BE CAST
Grain #1
Diameter
Length
Core (mandrel) dia.
Number of grains
Expected waste, %
Ingredient
Ammonium perchlorate 400 um
Ammonium perchlorate 200 um
Ammonium perchlorate 90 um
Aluminum atomized -400 mesh
Red Iron Oxide
R45HTLO
R45M HTPB
Dioctyl adipate
Castor oil
E744
IPDI
Dibutyltin dilaurate
PAPI
Tepanol
Total wt.
Percent solids
PREPARATION STEPS
Mix liquid ingredients
Add metals
Add curative
Vacuum process
Grain #2
1.25
2
0
16
2
Grain #3
1.8
3.2
0.625
6
NEEDED
Actual Used:
THIS BATCH
0.00
1755.22
0.00
113.98
2.28
0.00
0.00
296.34
0.00
68.39
0.00
45.59
0.00
0.00
2281.78
95.00%
0
0
Original batch:
Weight
Percent
0.00
0.0%
77.00
76.9%
0.00
0.0%
5.00
5.0%
0.10
0.1%
0.0%
0.0%
13.00
13.0%
0.00
0.0%
3.00
3.0%
0.0%
2.00
2.0%
0.0%
0.0%
0.0%
0.00
0.0%
100.1
DATA AND COMMENTS
Cure
38
Figure 24: Final Custom Motor Design
Propellant designation
Propellant density
MG3
0.058 lb/in^3
(95% theoretical density)
GRAINS TO BE CAST
Grain #1
Diameter
Length
Core (mandrel) dia.
Number of grains
Expected waste, %
Ingredient
Ammonium perchlorate 200 um
Strontium Carbonate
Black Copper Oxide
Aluminum -325 mesh
R45 HTLO
Dioctyl adipate
Castor oil
Dibutyltin dilaurate
Tepanol
IPDI
E744
PAPI
Grain #2
1.8
2.6
0.75
0
3
Grain #3
1.8
3.1
0.625
0
NEEDED
Actual Used:
THIS BATCH
891.55
53.67
8.95
29.82
0.00
139.55
41.74
0.00
0.00
3.58
0.00
25.05
0.00
2.55
5.1
1
2
Original batch:
Weight
Percent
74.75
74.7%
4.50
4.5%
0.75
0.7%
2.50
2.5%
0.0%
11.70
11.7%
3.50
3.5%
0.0%
0.0%
0.30
0.3%
2.10
0.0%
2.1%
0.0%
Silicone Oil 3 drops per Kg.
Total wt.
Percent solids
PREPARATION STEPS
Mix liquid ingredients
Add metals
Add curative
Vacuum process
1193.90
82.42%
100.1
DATA AND COMMENTS
Cure
39
8.6.
Gantt Chart
40
8.7 Budget
Main Budget Including Labor Costs
Task #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Task Title
Research & Project Specification
Inventor Design
Chemistry
Rocket Build
Avionics
Thermometer
Pressure Gauges
Load Cell
Thermodynamics
Level I Certification
Level II Certification
Test Stand Design
Gas Dynamics
Pre-Flight Data Form
Drawings
Parts List
Wiring Diagram
Pre-Flight
Test Stand Build
Matlab Code
Level III Certification
Engine Build
Commercial Motor Test
Custom Motor Test
Data Analysis
Re-Build Motor
Re-Test Motor
Test Launch
Managerial Duties
Names
Wes, Trey, Karna, James, Irfan, Ryan
Trey, James, Irfan
Ryan, Trey, Wes, Irfan
Wes, Trey, Karna
Wes, Trey, Karna
James, Irfan
James, Irfan
James, Irfan
Ryan, Trey, Wes, Irfan
Wes, Trey, Karna
Wes, Trey, Karna
James, Irfan
Ryan, Trey, Wes, Irfan
Wes, Trey, Karna
Wes, Trey, Karna
Wes, Trey, Karna
Wes, Trey, Karna
Wes, Trey, Karna
James, Irfan
Ryan, Trey, Wes, Irfan
Wes, Trey, Karna
Wes, Trey, Karna, Irfan, Ryan
James, Irfan
Wes, Trey, Karna, Ryan
Wes, Trey, Karna, James, Irfan, Ryan
Wes, Trey, Karna, James, Irfan, Ryan
Wes, Trey, Karna, James, Irfan, Ryan
Wes, Trey, Karna, James, Irfan, Ryan
Wes, Trey
Work Days Labor Rate Labor Costs Materials Equipment Facilities Subcontractors Travel Contingency Total Costs
25
$150.00
$3,750.00
$3,750.00
10
$75.00
$750.00
$750.00
5
$100.00
$500.00
$500.00
5
$75.00
$375.00 $300.00
$675.00
5
$75.00
$375.00
$90.00
$465.00
5
$50.00
$250.00
$140.00
$390.00
5
$50.00
$250.00
$260.00
$510.00
5
$50.00
$250.00
$355.00
$605.00
10
$100.00
$1,000.00
$1,000.00
5
$75.00
$375.00
$103.00
$70.00
$20.00
$568.00
5
$75.00
$375.00
$45.00
$20.00
$440.00
10
$50.00
$500.00 $85.00
$585.00
10
$100.00
$1,000.00
$1,000.00
15
$75.00
$1,125.00
$1,125.00
15
$75.00
$1,125.00
$1,125.00
15
$75.00
$1,125.00
$1,125.00
15
$75.00
$1,125.00
$1,125.00
15
$75.00
$1,125.00
$1,125.00
10
$50.00
$500.00
$500.00
10
$100.00
$1,000.00
$1,000.00
5
$75.00
$375.00
$350.00
$20.00
$745.00
35
$125.00
$4,375.00 $2,200.00
$6,575.00
40
$50.00
$2,000.00
$20.00
$2,020.00
5
$100.00
$500.00 $500.00
$20.00
$1,020.00
5
$150.00
$750.00
$100.00
$850.00
5
$150.00
$750.00 $1,000.00
$1,750.00
5
$150.00
$750.00
$40.00
$790.00
5
$150.00
$750.00
$40.00
$790.00
20
$50.00
$1,000.00
$1,000.00
325
$28,125.00 $4,085.00
$1,443.00
$70.00
$0.00 $ 180.00
$0.00 $33,903.00
Conclusion of Budget:
The total budget for the entire project will be $33,903.00
Funds Received:
The ODU Rocket Team received $3,086.00 for the Summer 2015 and Fall 2015 semesters.
-
The ODU Mechanical and Aerospace Engineering department donated $1,586.45
The National Aeronautics and Space Association (NASA) donated $500.00
Old Dominion University donated $1000.00
]Funds Spent:
The ODU Rocket Team spent $3,468.15 during the Summer 2015 and Fall 2015 semesters.
-
Approximately $971.56 was spent for testing
Approximately $696.51 was spent for launch preparation
Approximately $250.08 was spent for miscellaneous equipment
Approximately $50.00 was spent on shipping
$1,500.00 was owed back to Mechanical and Aerospace Engineering department based
on the loans initially given
41
Budget Analysis:
Certification
Testing
Design
Total
Cumulative Budgeted Cost (CBC)
Cumulative Actual Cost (CAC)
Calculated Earned Value (CEV)
Cost Performance Index (CPI)
Cost Variance (CV)
Forecast Cost at Completion (Eq. 1)
Forecast Cost at Completion (Eq.2)
To-Complete Performance Index (TCPI)
Certification
Testing
Design
Total
Cumulative Budgeted Cost (CBC)
Cumulative Actual Cost (CAC)
Calculated Earned Value (CEV)
Cost Performance Index (CPI)
Cost Variance (CV)
Forecast Cost at Completion (Eq. 1)
Forecast Cost at Completion (Eq.2)
To-Complete Performance Index (TCPI)
TBC
$9,388.00
$6,190.00
$18,075.00
$33,653.00
1
$0.00
$0.00
$750.00
$750.00
$750.00
$750.00
$750.00
1.00
$0.00
$33,653.00
$33,653.00
1.000000
2
$0.00
$0.00
$750.00
$750.00
$1,500.00
$1,500.00
$1,500.00
1.00
$0.00
$33,653.00
$33,653.00
1.000000
13
TBC
$0.00
$9,388.00
$6,190.00 $250.00
$18,075.00 $2,825.00
$33,653.00 $3,075.00
$22,053.00
$19,603.04
$17,893.00
0.91
-$1,710.04
$36,869.23
$35,363.04
1.121711
3
$0.00
$0.00
$750.00
$750.00
$2,250.00
$2,250.00
$2,250.00
1.00
$0.00
$33,653.00
$33,653.00
1.000000
14
$0.00
$250.00
$625.00
$875.00
$22,928.00
$20,478.04
$18,768.00
0.92
-$1,710.04
$36,719.28
$35,363.04
1.129795
4
$0.00
$0.00
$750.00
$750.00
$3,000.00
$3,337.60
$3,000.00
0.90
-$337.60
$37,440.08
$33,990.60
1.011136
15
$0.00
$250.00
$625.00
$875.00
$23,803.00
$21,353.04
$19,643.00
0.92
-$1,710.04
$36,582.69
$35,363.04
1.139028
5
$0.00
$0.00
$750.00
$750.00
$3,750.00
$4,087.60
$3,750.00
0.92
-$337.60
$36,682.67
$33,990.60
1.011419
16
$0.00
$250.00
$625.00
$875.00
$24,678.00
$22,228.04
$21,143.00
0.95
-$1,085.04
$35,380.04
$34,738.04
1.094971
6
$675.00
$375.00
$500.00
$1,550.00
$5,300.00
$5,366.60
$4,925.00
0.92
-$441.60
$36,670.50
$34,094.60
1.015612
17
$0.00
$250.00
$625.00
$875.00
$25,553.00
$23,103.04
$24,143.00
1.05
$1,039.96
$32,203.40
$32,613.04
0.901425
7
$465.00
$375.00
$500.00
$1,340.00
$6,640.00
$6,616.60
$5,541.25
0.84
-$1,075.35
$40,183.79
$34,728.35
1.039774
18
$0.00
$250.00
$625.00
$875.00
$26,428.00
$23,978.04
$25,018.00
1.04
$1,039.96
$32,254.10
$32,613.04
0.892510
8
$898.00
$1,505.00
$500.00
$2,903.00
$9,543.00
$8,756.68
$6,793.75
0.78
-$1,962.93
$43,376.42
$35,615.93
1.078844
19
$0.00
$250.00
$625.00
$875.00
$27,303.00
$24,853.04
$25,893.00
1.04
$1,039.96
$32,301.37
$32,613.04
0.881822
9
$1,875.00
$335.00
$500.00
$2,710.00
$12,253.00
$11,451.68
$8,495.00
0.74
-$2,956.68
$45,365.91
$36,609.68
1.133176
20
$0.00
$250.00
$1,000.00
$1,250.00
$28,553.00
$26,299.55
$26,768.00
1.02
$468.45
$33,064.06
$33,184.55
0.936295
10
$1,875.00
$250.00
$500.00
$2,625.00
$14,878.00
$14,076.68
$9,245.00
0.66
-$4,831.68
$51,240.94
$38,484.68
1.246812
21
$0.00
$850.00
$0.00
$850.00
$29,403.00
$27,149.55
$27,618.00
1.02
$468.45
$33,082.19
$33,184.55
0.927969
11
$1,875.00
$250.00
$500.00
$2,625.00
$17,503.00
$16,849.68
$10,893.00
0.65
-$5,956.68
$52,055.66
$39,609.68
1.354494
22
$0.00
$0.00
$1,750.00
$1,750.00
$31,153.00
$27,899.55
$28,468.00
1.02
$568.45
$32,981.02
$33,084.55
0.901198
23
$0.00
$0.00
$750.00
$750.00
$31,903.00
$28,649.55
$29,318.00
1.02
$668.45
$32,885.71
$32,984.55
0.866402
1. Calculations
End of Week 24
-
12
$725.00
$250.00
$500.00
$1,475.00
$18,978.00
$18,324.68
$13,393.00
0.73
-$4,931.68
$46,044.98
$38,584.68
1.321736
Total Budgeted Cost (TBC) = $33,653.00
Cumulative Budget Cost (CBC) = $33,653.00
Cumulative Actual Cost (CAC) = $30,399.55
Cumulative Earned Value (CEV) = $30,399.55
Cost Performance Index (CPI) = $1.00
Cost Variance (CV) = $0.00
Forecasted Cost at Completion (FCAC Formula 1) = $33,653.00
Forecasted Cost at Completion (FCAC Formula 2) = $33,653.00
To-Complete Performance Index (TCPI) = 1.00
42
24
$1,000.00
$0.00
$750.00
$1,750.00
$33,653.00
$30,399.55
$30,399.55
1.00
$0.00
$33,653.00
$33,653.00
1.000000
2. Plot CBC, CAC, and CEV Curves
Estimated Budget + Labor Costs
40000
Cumulative Budget Cost
35000
30000
Cumulative Budgeted
Cost (CBC)
25000
Cumulative Actual
Cost (CAC)
20000
Calculated Earned
Value (CEV)
15000
10000
5000
0
0
10
20
30
Weeks
43
3. Summary of Budget
Based on the budget analysis, the project has been completed. This conclusion can be driven from
the Cost Performance Index (CPI) being $1.00, and the Cumulative Actual Cost (CAC) and Cumulative
Earned Value (CEV) being the same. In comparison to the Cumulative Budgeted Cost (CBC) we spent
approximately $3,253.45 less than originally budgeted for. This difference came from the availability of
funds that we had access to. Unfortunately we did not have enough money as originally planned to
allow us to purchase certain parts. Thankfully we were still able to complete the project with this minor
budget issue. In the first weeks of the project we fell behind on progress. Around week 17 we were able
to catch up to everything that needed to be done. This is shown by our CPI eclipsing 1.00.
The budget based solely on items purchased, leaving out labor, travel etc, ended at a balance of
-$381.70. $3,086.45 was received overall and $3,468.15 was spent. This is because originally we
expected to receive more money from Old Dominion University so we budgeted accordingly.
Unfortunately we only received $1,000 of the $3,000 which we originally planned for. We are thankful
for the assistance from the ODU Mechanical and Aerospace Engineering department to allow us to
complete our project.
44