Project Management & Design I – MAE 434W
Rocket Project
Final Report
CN: 31267
July 21, 2015
Group Members:
Wesley Harpster
Project Advisor
Dr. Thomas Alberts
Ryan Horton
James Lawrence
Karna Shah
James “Trey” Simmons
Irfan Ali Shaukat
1
TABLE OF CONTENTS
TABLE OF FIGURES ...................................................................................................... III
NOMENCLATURE ......................................................................................................... IV
ABSTRACT ...................................................................................................................... VI
1. INTRODUCTION ........................................................................................................ 1
2. LITERATURE REVIEW/BACKGROUND ................................................................ 2
3. COMPLETED METHODS .......................................................................................... 4
3.1. CENTER OF PRESSURE, CENTER OF GRAVITY, AND STATIC MARGIN ....................... 4
3.2. AVIONICS TESTING .................................................................................................. 6
3.3. TEST STAND DESIGN ............................................................................................... 7
3.4. ROCKET MOTOR DESIGN PROCESS .......................................................................... 8
4.
PROPOSED METHODS ............................................................................................. 8
4.1. COEFFICIENT OF DRAG ............................................................................................ 8
4.2. ALTITUDE ................................................................................................................ 9
4.3. AVIONICS TESTING ................................................................................................ 10
4.4. ROCKET MOTOR DESIGN PROCESS ........................................................................ 10
5.
PRELIMINARY RESULTS ...................................................................................... 13
5.1. AVIONICS TESTING ................................................................................................ 13
5.2. TEST STAND DESIGN ............................................................................................. 14
5.3. ROCKET MOTOR DESIGN PROCESS ........................................................................ 14
5.4. CENTER OF PRESSURE, CENTER OF GRAVITY, AND STATIC MARGIN ..................... 15
i
6.
DISCUSSION ............................................................................................................ 15
7.
REFERENCES .......................................................................................................... 17
8.
APPENDIX ................................................................................................................ 19
8.1. ROCKET COMPUTER-AIDED DRAWINGS ................................................................ 19
8.2. TABLES AND PLOTS ............................................................................................... 21
8.3. MATLAB CODE ...................................................................................................... 26
8.4. PICTURES ............................................................................................................... 28
8.5. GANTT CHART .................................................................................................... 31
8.6. BUDGET................................................................................................................. 32
ii
List of Figures
Figure 1: Autodesk Inventor Rocket Assembly ……………………………………..…..………..9
Figure 2: Autodesk Inventor Test Stand Design ……………………………………....….………7
Figure 3: Rocket Motor Classification…………………………………………………………….9
Figure 4: Motor Housing Thickness - Hoop Stress ….………………………………………….14
Figure 5: Motor Housing Thickness - End Stress ……………………………………………….14
Figure 6: Parachute Deployment Testing…………………………………………….…………...6
Figure 7: Theoretical vs Factory Provided Aerodynamic Values………..…………..…………..16
Figure 8: Dual Deployment with Redundancy Wiring Diagram……………………...…………10
Figure 9: Rocket Motor Design Process………………………………………….....…..……….10
Figure 10: Matlab Code for Center of Pressure………………………………………..………….6
Figure 11: Matlab Code for Coefficient of Drag………………………………………..……...…9
Figure 12: Center of Gravity Test……………..………………………………………...……...…6
Figure 13: Avionics Bay Build…………………………………………………….…………...…6
Figure 14: Parachute Ejection Charge Testing……………………………….………………...…7
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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 take a 5 pound payload 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 an 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 CSFM test stand was
designed and constructed using solid mechanics from the maximum expected thrust output of the
CSFM build. The test stand was designed to allow for testing of different diameter motor
housings depending on the level of CSFM to be tested. The test stand was modeled in Autodesk
Inventor prior to the construction and the drawings were used for assembly. Altitude prediction
was done using the coefficient of drag and an assumed thrust time. A MATLAB program was
written in order to calculate the expected altitude for various CSFM designs. These values used
in the altitude program were used to begin the rocket motor design process. The propellant
mixture that was used was 68% ammonium perchlorate, 20% aluminum powder, 12% hydroxyl
terminated polybutadiene by mass. The assumption for operating pressure, burn area, and nozzle
geometry with the known fuel characteristics provided necessary information for feasibility
prediction for the proposed design. The rocket motor was then built tested via the test stand and
launched to reach the goal altitude.
vi
1.
Introduction
In the 1930’s, the interest into rocket flight began. Throughout World War II, research
into jet aircraft and space flight sparked the design and construction of the first solid fuel rocket
motors[1]. These early motors were made of gunpowder or other high powered explosives [2, 3].
The challenge associated with solid fuels was that the burn rate made it impossible to generate
enough thrust for a long enough period of time to be useful in aircraft or space applications.
Using the chemical composition of high explosives known at the time, research led to the
development of composite solid fuel motors (CSFM). These motors were made of a fuel, an
oxidizer, and a bonding agent [1-3]. Today’s high powered rocketry enthusiasts use this type of
motor regularly. For each flight, either a commercial or custom motor can be chosen.
Commercial motors have a predetermined prediction for the performance of the rocket, while
custom motors allow for the user to control the performance based on the maximum thrust,
maximum altitude, length of burn time, and specific impulse.
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 [4]. 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 $6,000.
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 [5]. 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 [5].
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 [6, 7]. The distance between these two design features
determine the stability of the rocket [6, 7]. 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 [6-8]. If this is not true the rocket will not self-correct its flight in the air and will not fly
straight up [7, 9-12].
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 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 [7, 13, 14]. 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 [7, 13, 14]. Additionally, as the rocket
approaches the Mach 1 the coefficient of drag gets much larger and causes an increase in the
overall drag force [7, 13-15].
A rocket motor consists of three major parts: propellant, nozzle, and motor housing [7].
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
3
that thrust needs to take place [7]. This allows values to be calculated in order to verify the
design will work for the particular application [7]. The process is then done in iterations until a
working design is mathematically modeled for the motor [7].
3.
Completed Methods
3.1.
Coefficient of Pressure, Center of Gravity, and Static Margin
To calculate the center of pressure for the rocket 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) [6].
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) [6].
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
The specific center of pressure for the nose cone was found using the volume, cross sectional
area, and length (Equation 3) [6].
𝐿 − 𝑣⁄𝑠(𝐿)
𝑥̅𝑁 =
𝑠(𝑜)
1−
⁄𝑠(𝐿)
(Equation 3)
4
The center of pressure for the fin section always falls on the centerline of the rocket body tube.
The calculation CNα for of 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) [6].
(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) [6].
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) [6].
(𝐶𝑁𝛼 )𝐹 =
2
𝑠
12 ( 𝑓⁄𝑑)
2
2𝑙
)
1+√1+(
𝑐𝑟 +𝑐𝐴
(Equation 6)
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) [6].
𝑥̅ 𝑇𝐵 = 𝑥𝐹 +
𝑥𝑡 𝑐𝑟 + 2𝑐𝐴
1
𝑐𝑟 𝑐𝐴
(
) + (𝑐𝑟 + 𝑐𝐴 −
)
3 𝑐𝑟 + 𝑐𝐴
6
𝑐𝑟 + 𝑐𝐴
(Equation 7)
Then the original equation can be represented in the terms of the coefficient of forces and the
specific center of pressures (Equation 8) [6].
𝑥̅ =
(𝐶𝑁𝛼 )𝑁 𝑥̅ 𝑁 +𝐾𝑇(𝐵) (𝐶𝑁𝛼 )𝐹 𝑥̅ 𝑇𝐵
∑ 𝐶𝑁𝛼
(Equation 8)
5
Following this process and using a MATLAB code (Figure 10), the center of pressure for the
rocket was found [6].
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 [6].
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 [7, 13, 14, 16]. 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 [7, 13, 14,
16].
3.2.
Avionics
The avionics bay electrical control board chosen was the Rocket Recovery Controller
(RRC3) altimeter avionics system from Missile Works Corporation. 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 13).
The ejection charges used to deploy the main and drogue parachutes were built using an
online design tool [17]. The charges were built to reach the design pressure of 12.5 psi inside the
6
forward and aft payload bay. The materials used for the build were FFFF black powder, finger
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 14).
3.3.
Rocket Motor Test Stand
A test stand was designed and constructed to test the various rocket motors. The vertical
orientation of the test stand used the ground as the opposing force to the natural motion. This
design ensured a reduction of moments and lateral forces that would cause the test stand to be
unstable during testing. Additionally, the test stand was built to accommodate various diameter
motor housings depending on the level of motor used during testing. The stability of the test
stand was analyzed using solid mechanics. The test stand was designed to a tolerance of 0.16
inches of radial movement of the motor housing. This was then used to find the maximum force
felt in the x-plane due to thrust direction changes based on the radial translation.
The test was assembled using the spring 2015 test stand. The I-beam used from the
spring 2015 rocket team test stand was welded to a 24 in x 24 in x 0.5 in steel plate. The radial
retaining rings were removed and reinstalled using nuts and bolts to allow for various size
retaining rings to be used. Multiple drilled bolt holes were then added in order to vary the height
of the rings depending upon the rocket motor being tested (Figure 2).
7
3.4.
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) [18].
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 [19-23]. The actual surface will
not reach this temperature, but since it exceeds the melting point for aluminum 6061-T6, a heat
shield must be used to guarantee the integrity of the motor housing under pressure [12, 21, 24,
25].
4.
Proposed Methods
4.1.
Coefficient of Drag
The coefficient of drag is dependent on the shape, flow conditions, friction, performance,
and dynamic pressure of the rocket. Since there is not a specified Mach number the rocket will
reach in flight, the values of coefficient of drag will be calculated over a range from Mach 0.1 –
Mach 2. The range of Mach numbers will solve for the Reynolds Numbers. The zero-lift drag
takes Reynolds Number into account in the coefficient of drag related to the nose cone and body
8
tube. Zero-lift drag is an addition of the coefficient of drags for the nose cone, body tube, and
base (Equation 11) [8]. Induced drag includes the performance of the fin size, number of fins,
and launching methods (Equation 12) [8].
(Equation 11)
(𝐶𝐷0 )𝑍𝑒𝑟𝑜𝐿𝑖𝑓𝑡 = (𝐶𝐷0 )𝐵𝑜𝑑𝑦 = (𝐶𝐷𝑜 )𝑁𝑜𝑧𝑧𝑙𝑒 + (𝐶𝐷0 )𝐵𝑜𝑑𝑦𝑇𝑢𝑏𝑒 + (𝐶𝐷0 )𝐵𝑎𝑠𝑒
(Equation 12)
(𝐶𝐷0 )𝐼𝑛𝑑𝑢𝑐𝑒𝑑 = (𝐶𝐷𝑜 )𝐹𝑖𝑛𝑠 + (𝐶𝐷0 )𝐼𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 + (𝐶𝐷0 )𝐿𝑎𝑢𝑛𝑐ℎ𝐿𝑢𝑔
(𝐶𝐷0 )𝑇𝑜𝑡𝑎𝑙 = (𝐶𝐷𝑜 )𝑍𝑒𝑟𝑜𝐿𝑖𝑓𝑡 + (𝐶𝐷0 )𝐼𝑛𝑑𝑢𝑐𝑒𝑑
(Equation 13)
A Matlab code will be designed to compute the drag coefficient based on the zero-lift and
induced drag equations (Figure 11). The results will be presented in a Mach number vs
coefficient of drag graph. The graph should show an increase in coefficient of drag until a Mach
of 1. At a Mach over 1, the coefficient of drag decreases. After calculating the coefficient of drag
by hand, it will be compared against a computational fluid dynamics (CFD) value done using a
3-dimensional drawing of the rocket on Autodesk (Figure 1).
4.2.
Altitude
The altitude of the rocket needs to be calculated prior to the launch to approximate the
performance of the official flight. Impulse is the area under a thrust-time curve which can be
solved by taking the integral of the thrust (F) over a certain operating time (t). The thrust curve
can be extracted from the load cell during the custom motor test. Generally, commercial motors
are classified by the impulse (Figure 3). The impulse calculated can be compared to that of
commercial motors (Equations 14-16).
𝑡
𝐼𝑡𝑜𝑡𝑎𝑙 = ∫0 𝐹 𝑑𝑡 =
𝐹0 +𝐹1
2
(𝑡1 − 𝑡0 ) +
𝐹1 +𝐹2
2
(𝑡2 − 𝑡1 ) + ⋯
−𝑚
(𝑇 − 𝑚𝑔 − 𝑘𝑣 2 )
𝑏𝑜𝑜𝑠𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = [
] ∗ 𝑙𝑛
2𝑘
(𝑇 − 𝑚𝑔)
(Equation 14)
(Equation 15)
9
𝑚
𝑐𝑜𝑎𝑠𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = [2𝑘] ∗ 𝑙𝑛
(𝑚𝑔+𝑘𝑣 2 )
(𝑚𝑔)
(Equation 16)
𝑡𝑜𝑡𝑎𝑙 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 = 𝑏𝑜𝑜𝑠𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 𝑐𝑜𝑎𝑠𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
4.3.
Avionics Testing
The rocket used to achieve a 10,000 foot launch will use a dual board RRC3 system for
redundancy. The two boards will be used from the spring 2015 rocket group’s avionics bay. This
will be assembled as previously discussed, but it will use two frames and boards on one custom
aluminum sled. The boards will then be wired using dual redundancy schematics. (Figure 8).
The Missile Works Data Acquisition and Configuration Software (mDACS) associated
with the avionics system will be used to gather data during flight. After the assembly of the dual
redundancy avionics system, the system will be reprogramed. The reprogramming will stagger
the charges in order to guarantee proper parachute deployment. Two charges will detonate at
apogee. One of those charges will detonate two seconds after the initial charge. The remaining
two charges will detonate at 800 feet and 700 feet respectively.
4.4.
Rocket Motor Design Process
The iterative design process that will be used to build the rocket fuel, motor housing and
nozzle begins by assuming a desired thrust time and maximum altitude (Figure 9) [7]. Then the
assumed values for chamber operating pressure, burn area and nozzle geometry will be selected.
Using this information and the specific propellant characteristics the specific impulse and thrust
can be determined (Equations 17-19) [7].
10
2𝛾2
2
𝐼𝑆𝑃 = 𝑐𝑑 [([𝛾−1] [𝛾+1]
𝛾−1
𝛾+1
𝛾−1
𝑝𝑒 𝛾
[1 − (𝑝 )
𝑐
𝑇 = 𝑤̇𝑝 𝐼𝑆𝑃 =
[(
𝜀=
𝑔𝑐
𝑐∗
1
2
]) +
𝑝𝑒 𝜀
𝑝𝑐
−
𝑝0 𝜀 𝑐 ∗
𝑝𝑐
]𝑔
𝑐
(Equation 17)
(Equation 18)
𝑝𝑐 𝐴𝑡 𝐼𝑆𝑃
1
1
2 𝛾−1 𝛾−1 2
)
(
) ]
𝛾+1
𝛾+1
(Equation 19)
1
1
𝛾−1 2
𝑝
𝑝
[( 𝑒 )𝛾 (1−( 𝑒 ) 𝛾 ) ]
𝑝𝑐
𝑝𝑐
These values will be compared to the design requirements, if acceptable, the process continues
on. If the values are not acceptable, new values must be assumed and these equations will be
recalculated [7].
Compute Propellant Weight Flow Rate and Weight of the Propellant Used
The values found above will be used to calculate the weight flow rate of the propellant
and the weight of the propellant (Equations 20-21).
𝑤̇𝑝 =
𝐴𝑡 𝑔𝑐 𝑝𝑐
𝑐∗
𝑊𝑝 = 𝑡𝑏 𝑤̇𝑝
(Equation 20)
(Equation 21)
Then the burn rate of the propellant will be used to determine the necessary burn area to produce
the design thrust (Equation 22) [7].
𝐴𝑏 =
𝑔𝑐 𝑝𝑐 𝐴𝑡
𝜌𝑐 ∗ 𝑟
(Equation 22)
The required burn area will be used to find the geometry and size of the perforation necessary to
produce the design thrust. Then using the required propellant weight and density of the fuel the
11
length and diameter and number of grains of the propellant can be determined. This value will be
compared against the geometry of the body tube of the rocket to determine feasibility. If all
values are feasible the nozzle can be machined out of steel using the values determine throughout
the design process [7].
The motor housing design will be done and built using the previously predicted
operating pressure. Based on this pressure, the test motor housing will be designed to a safety
factor of ten. This design will be able to withstand any unexpected increase in pressure as a result
of any design flaws during fuel preparation. This will allow us to collect data on every test
despite minor increases in pressure. The data will be analyzed and the iterative design process
will be used. After three successful motor tests with consistent and predictable thrust curves that
closely match the design thrust and time assumption during the motor design process the motor
design will be ready for flight. The motor housing design that will be used during the launch will
be essentially the same; however, due to space and weight restraints the safety factor will be four
instead of ten.
The fuel that will be used for the design process will be ammonium perchlorate,
aluminum powder, and hydroxyl terminated polybutadiene (AP/Al/HTPB) [7, 12, 20, 23-28].
This fuel will apply 200 micron AP, 25 micron Al and HTPB liquid as a bonding agent [29].
The process will begin by determining the amount of fuel needed to be produced for testing and
launches. This value will then be divided on a mass basis into 68% AP, 20% Al, and 12% HTPB
[30]. The AP and Al will be mixed together first and then the HTPB added. This mixture will
be formed into cylinders using empty motor housing tubes and perforated down the center with a
cylindrical rod. It will then be placed in a press for compression and cured [26].
12
The motor design will be tested using witness materials. Immediately after curing, a
piece of the AP/Al/HTPB rocket motor will be elevated 2-3 mm using pieces of graphite.
Underneath the motor small pieces of chromium, niobium, and molybdenum will be placed as
witness materials. These materials melt at 1857, 2468 and 2617 degrees Celsius respectively
[31]. At the end of the burn the witness materials will be examined to determine which materials
melted and thus providing an estimated operating temperature. This will indicate if the motor is
burning at the expected temperature of around 2300-2400 degrees Celsius [28].
The final test prior to launch will be the test motor housing, nozzle, and fuel ignited on
the test stand. A PX-303 pressure transducer and a LC-LCJA load cell will be used on the test
stand to collect data during the burn time of the motor and housing. This data will be used to
analyze maximum operating pressure and establish a thrust curve. The thrust curve will provide
that necessary information to input into a MATLAB code to estimate the maximum height of
each motor design. The result of this code will be compared to the design specific impulse to
ensure that the design is performing as expected.
5.
Preliminary Results
5.1.
Avionics Testing
Testing of the custom designed and built ejection charges were conducted. 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 of black powder with success. The drogue chute was
13
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).
5.2. Test Stand Design
Using the solid mechanics the thrust maximum x-plane force was calculated. The
maximum height of the applied force was used to maximize the possible value of moment felt at
23.25 inches. The maximum radial translation was used as 0.16 inches. The highest expected
force of thrust is 450 lb. The force in the radial direction was calculated using 600 pounds force
for safety (Equation 23).
0.16
𝐹𝑥−𝑝𝑙𝑎𝑛𝑒 = 600 𝑙𝑏𝑓 ∙ 𝑠𝑖𝑛 √23.252
+0.162
≈ 0.1 𝑙𝑏𝑓
(Equation 23)
The test stand solid mechanics analyses provide evidence of a very safe test platform for use in
rocket motor testing at the high powered rocketry level.
5.3. 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.
14
5.4. 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
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) [32].
6.
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 $6,000 by December 12, 2015. In order to
achieve this some lessons learned have been 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 [4]. 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 [4]. A significant portion of the certification phase has been
15
laid out to be completed prior to the start of the fall semester. This part of the project is the point
at which the previous rocket project finished [4].
There have been some limiting factors that had a role in the projects progress. The first
limiting factor was the budget. Currently, the project has received $854.00 while the cumulative
budgeted cost to this point in the project is $1378.00. The next factor was the unattainability of
professional grade data analysis equipment. The selected method of temperature estimation was
chosen due the lack of available expected funds to purchase a thermometer capable of reading
temperatures in the ranges at which our propellant burns. The final limiting factor was
uncontrollable schedule setbacks due to the United States Navy cancelling scheduled launch
dates multiple times. This has set the project progress back four weeks.
Moving forward from the project will move back on track. On August 8, 2015 the rocket
team will attain both level I and II Tripoli High Powered Rocketry Certifications. A dual
deployment avionics bay will also be tested during these certification launches. This will allow
the team to begin the design process for the custom CSFM. This will require additional funds to
be received from sponsors. Due to that the focus for the rocket team will be funding over the
next few weeks. This will enable a continued forward progress in achieving the overall goal.
16
7.
References
[1]
H. S. Seifert, "Twenty-Five Years of Rocket Development," Journal of Jet Propulsion, vol. 25, pp.
594-603, 1955/11/01 1955.
W. Lemkin, "Rocket Fuels," Bulletin of the American Interplanetary Society, vol. 1, pp. 2-5,
1931/01/01 1931.
W. L. Ph.D, "Rocket Fuels and Their Possibilities," Bulletin of the American Interplanetary Society,
vol. 2, pp. 8-10, 1932/02/01 1932.
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.
[2]
[3]
[4]
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[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
17
[21]
[22]
[23]
[24]
[25]
[26]
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[29]
[30]
[31]
[32]
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.
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.
N. Othman and W. K. W. Ali, "Development of Ammonium Perchlorate + Aluminium Base Solid
Propellant," AIP Conference Proceedings, vol. 1225, pp. 990-995, 2010.
J. P. Renie and J. R. Osborn, "COMBUSTION MODELING OF ALUMINIZED PROPELLANTS," AIAA
Paper, 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," in Space Technology and Applications International Forum STAIF 2002. Conference on Thermophysics in Microgravity. Conference on Innovative
Transportation Systems for Exploration of the Solar System and Beyond. 19th Symposium on
Space Nuclear Power and Propulsion. Conference on Commercial/Civil Next Generation Space
Transportation, 3-6 Feb. 2002, USA, 2002, pp. 740-7.
S. Jain, Mehilal, S. Nandagopal, P. P. Singh, K. K. Radhakrishnan, and B. Bhattacharya, "Size and
shape of ammonium perchlorate and their influence on properties of composite propellant,"
Defence Science Journal, vol. 59, pp. 294-299, 2009.
G. D. Lengelle, J.; Trubert, J.F., "Combustion of Solid Porpellants," Office of national d'etudes et
de recherches aerospatiales (ONERA), Chatillon Cedex, France2004.
(August 3, 2015 ). Periodic Table: Melting Point Available:
www.chemicalelements.com/show/meltingpoint.html
M. Rocketry, "Super DX3 All Fiberglass Kit," 2009.
18
8.
Appendix
8.1.
Computer-Aided Drawings
Figure 1: Rocket Assembly
19
Figure 2: Test Stand Design
20
8.2.
Tables and Plots
Figure 3: Rocket Motor Classification Table
21
Figure 4: Motor Housing Thickness - Hoop Stress
Figure 5: Motor Housing Thickness – End Stress
22
Figure 6: 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 7: 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
23
Figure 8: Dual Deployment with Redundancy Wiring Diagram
24
Figure 9: Rocket Motor Design Process
25
8.3.
Matlab Codes
Figure 10: 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;
26
Figure 11: 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)
27
8.4.
Pictures
Figure 12: Center of Gravity Test
28
Figure 13: Avionics Bay Build
29
Figure 14: Parachute Ejection Charge Testing
30
8.5.
Gantt Chart
31
8.6.
Budget
Main Budget
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:
Thus far funding totals $854.00.
-
$354.00 were received from the Old Dominion University Mechanical Engineering
Department
$500.00 were received from NASA
Additional Funds:
In order to get the budget back on track additional funds are necessary:
-
$1378.00 - $854.00 = $524
32
Budget Analysis
TBC
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)
1
2
3
4
5
$750.00 $1,500.00 $2,250.00 $ 3,000.00 $ 3,750.00
$750.00 $1,500.00 $2,250.00 $3,337.60 $4,087.60
$750.00 $1,500.00 $2,250.00 $3,000.00 $3,750.00
1.00
1.00
1.00
0.90
0.92
$0.00
$0.00
$0.00
-$337.60
-$337.60
$33,653.00 $33,653.00 $33,653.00 $37,440.08 $36,682.67
$33,653.00 $33,653.00 $33,653.00 $33,990.60 $33,990.60
1.000000
1.000000
1.000000
1.011136
1.011419
6
$5,300.00
$5,366.60
$4,925.00
0.92
-$441.60
$36,670.50
$34,094.60
1.015612
7
8
9
10
$6,640.00 $9,543.00 $12,253.00 $14,878.00
$6,616.60 $8,756.68 $11,451.68 $14,076.68
$5,541.25 $6,793.75 $8,495.00 $9,245.00
0.84
0.78
0.74
0.66
-$1,075.35 -$1,962.93 -$2,956.68 -$4,831.68
$40,183.79 $43,376.42 $45,365.91 $51,240.94
$34,728.35 $35,615.93 $36,609.68 $38,484.68
1.039774 1.078844 1.133176 1.246812
1) Calculations
End of Week 11
-
Total Budgeted Cost (TBC) = $33,653.00
Cumulative Budget Cost (CBC) = $17,503.00
Cumulative Actual Cost (CAC) = $16,849.68
Cumulative Earned Value (CEV) = $10,893.00
Cost Performance Index (CPI) = $0.65
Cost Variance (CV) = -$5,956.68
Forecasted Cost at Completion (FCAC Formula 1) = $52,055.66
Forecasted Cost at Completion (FCAC Formula 2) = $39,609.68
To-Complete Performance Index (TCPI) = 1.354494
2) Plot CBC, CAC, and CEV Curves
Budgeted vs Actual vs Earned Value
$40,000.00
Cumulative Budget Cost
$35,000.00
$30,000.00
Cumulative
Budgeted Cost
Cumulative
Actual Cost
Cumulative
Earned Value
$25,000.00
$20,000.00
$15,000.00
$10,000.00
$5,000.00
$0.00
0
5
10
15
20
25
30
Weeks
33
11
$17,503.00
$16,849.68
$10,893.00
0.65
-$5,956.68
$52,055.66
$39,609.68
1.354494
3) Based on the budget analysis, the project is not on track. Throughout the MAE 434W
semester the rocket team researched the custom motor design process and prepared for
the level 1, 2 and 3 certifications. Thus far $854.00 was received from the ODU
Mechanical Engineering Department and NASA. The money spent was solely on the
rocket build and preparation for the certifications. In order to further research and begin
building the custom motor, the total project funding must reach $1378.00. A total of six
potential sponsors have been contacted and all demonstrate interest in donating funds to
the project. One of these sponsors will be considering a $5000.00 donation. Additionally,
the level I and II certifications will be held on August 8, 2015. The completion of the
level I and II certifications paired with the additional funds from sponsorships will put
this project back on track by the end of September.
34