CubeSat DeOrbit System
Final Report MAE 434W
December 3rd, 2013
Students:
Joshua Barham
Trevor Jackson
Timothy Lynch
Joseph McNamara
Joe Powell
Troy Tarnacki
Faculty Advisor:
Dr. Robert Ash
Table of Content
Abstract................................................................................................................................ii
Introduction..........................................................................................................................1
Background..........................................................................................................................2
Completed Methods.............................................................................................................2
Proposed Methods................................................................................................................5
Preliminary Results..............................................................................................................7
Discussion............................................................................................................................7
Appendices...........................................................................................................................9
References..........................................................................................................................22
List of Figures
Figure 1 - CAD model of baseplate.....................................................................................9
Figure 2 - Gasket, baseplate with screws, and baseplate cap...............................................3
Figure 3 - Baseplate with membrane, gasket, and cap assembled.......................................3
Figure 4 - Cutting wire and battery......................................................................................9
Figure 5 - Enthalpy of Sublimation of Benzoic Acid vs. Temperature.............................10
Figure 6 - Necessary mass of Benzoic Acid vs. Volume of Aerobrake and Pressure inside
Aerobrake...........................................................................................................................10
Figure 7 - Necessary Energy for Sublimation of Benzoic Acid vs. Volume of Aerobrake
and Pressure inside Aerobrake...........................................................................................11
Figure 8 - Baseplate with deployed inflatable.....................................................................6
Table 1 - Saturation Temperature as a function of Pressure with respective Elevations...12
i
Abstract
There has been an urgent need expressed by the United Nations to reduce space
debris. It is currently recommended that devices placed in orbit should have the ability to
deorbit themselves within 25 years, however, a mandate of this recommendation may be
on the horizon. This time constraint restricts CubeSats to a launch altitude of 600 km. By
utilizing technology first implemented by NASA's Echo I project a deorbit system is
being developed. This paper describes the apparatus that will utilize the sublimation of
benzoic acid to inflate a drag device, or aerobrake, that will allow for controlled and
expedited deorbit of a CubeSat.
ii
Introduction
Debris from leftover space missions creates a hazardous environment for the
International Space Station as well as expensive military and industrial satellites. The
United Nations (UN) has published debris mitigation guidelines, which mandatory
requirements expected in the near future. To resolve this accumulation of space debris,
aerodynamics brakes (aerobrakes) are being developed for CubeSats and satellites to
reduce their orbit life [1]. The use of small satellites and cube satellites (CubeSats) is
increasing because of their relatively low cost to produce and lower cost to launch due to
their low mass. Aerobrakes using mechanical mechanisms are currently being used, but
they take up a considerable amount of volume inside the CubeSat while being stored,
creating the need for an aerobrake that takes up less space when stowed. The use of
benzoic acid to inflate a balloon like aerobrake has been used by the National
Aeronautics and Space Administration's (NASA) Project Echo [2]. The use of benzoic
acid has not been used on CubeSats for deorbit, creating the potential for a small storage
volume aerobrake device.
The design for a benzoic acid driven aerobrake consists of inflating a balloon-like
device to create drag, which is attached to a CubeSat. The baseplate encompasses the
aerobrake and is pressurized by sealing a membrane material through use of a gasket
between the baseplate and cap. A high resistance heating wire is used to cut the
membrane and deploy the aerobrake, which is then inflated by the sublimation of benzoic
acid. The membrane is responsible for holding the aerobrake inflatable under pressure
inside of the baseplate. Without the membrane the benzoic acid within the inflatable
would sublimate prematurely, inflating the balloon in the lack of pressure in low earth
orbit.
A thin membrane that can be cut by a high resistance heating wire was configured
to deploy the aerobrake. A Nichrome (Nickel-Chromium) wire will be subjected to
electrical current raising the temperature of the wire. A sufficient power supply is needed
in order to supply enough power to heat the Nichrome wire to the melting point of the
membrane, cutting it and releasing the aero-brake. Once the aerobrake is released, the
vacuum pressure of low earth orbit along with solar radiation energy from the sun and the
earth will induce a phase change of the stored solid benzoic acid into a gas inflating the
aerobrake. A comprehensive thermal analysis was conducted in order to determine how
much energy input is needed to start the sublimation of benzoic acid at a given
temperature and pressure.
The baseplate, to encompass the entire aerobrake system, needed to be large
enough to contain a folded aerobrake but optimized so that it would not take up any
unnecessary amount of space and add unnecessary weight. The baseplate must also be
strong enough to prohibit failure due to the internal pressure of the sealed aerobrake.
Materials selection for the baseplate will be taken into consideration for cost, ease of
manufacture, weight, and overall optimization of the system.
The purpose of the project was to find a low mass, low volume, and low cost
solution to anticipated international mandates that provides the ability to deorbit small
satellites in a controlled manner. The general increase in the rate of CubeSats being
placed into orbit in the past few years, due to their low cost nature, provides a need for a
small and low complexity system that is easily attachable to existing CubeSat chassis
Page | 1
designs. This will allow CubeSat users to continue placing small satellites into orbit while
meeting the requirements for deorbit.
Background
The first successful launch of an inflatable satellite was performed by NASA in
1960. This satellite, known as the Echo I, was constructed to act as a radio relay station
and placed into low Earth orbit for the purpose of increasing global communications.
Once in orbit, the Echo I was inflated using a sublimating powder known as benzoic acid.
Spherical in shape and comprised of a thin metallized polymide, the Echo project
demonstrated the low mass, high volume advantages of inflatable payloads used in space
operations [2].
It is this research conducted by NASA that is the basis of the Old Dominion
University (ODU) CubeSat DeOrbit System. Initiated by Dr. Robert Ash, the initial
deorbit design incorporated the use of small gas canisters to inflate a polymide balloon
[3]. Since this initial design, previous ODU CubeSat deorbit teams have used the Echo I
project as inspiration to utilize benzoic acid as the means of inflation for the aerobrake.
The original design also incorporated an aluminum door to protect the aerobrake and gas
tanks from any damage from the outside [3]. The design has recently been revised to
include the light-weight option of a polymide membrane barrier between the aerobrake
and the vacuum of space. A deployment device known as the “ODU Picosatellite Orbital
Deployer” or O-POD, was designed by a previous ODU CubeSat team as a means of
propelling the CubeSat away from the rocket placing it into orbit. The O-POD remains
attached to the rocket and can therefore be reused in future missions. It is the task of the
current ODU CubeSat team to incorporate this previous research into the development of
a functional deorbit device.
Completed Methods
The first aerobrake capsule design focused on optimization of the volume inside
the baseplate so that the maximum amount of space will be available to hold the
aerobrake and accompanying components. The first baseplate was designed for testing
purposes only. The aerobrake capsule design consists of a baseplate, membrane, gasket,
metal cap and are assembled in that order (see Figure 1, Appendix 1).
After the components are put in place screws are inserted through the cap, gasket,
membrane, and screwed into the baseplate in order to form an airtight seal between the
membrane and the baseplate. The main concepts that were to be tested was the ability of
the design to seal the membrane and test the cutting wire. By doing this the baseplate was
built overly robust, so that extra time was not needed to do a finite element analysis and
the complexity of the design could be simplified so that the machine shop would not have
to spend as much time machining a more complex part.
The membrane is responsible for holding the aerobrake inside the baseplate under
atmospheric pressure until being release by the cutting wire. The membrane must
withstand a vacuum pressure of 10^-4 torr without leaks. Testing consisted of an off the
shelf gasket being roughly cut into the shape of the baseplate (See Figure 2).
Page | 2
(Figure 2) - (Top) Gasket, (Left) Baseplate with screws,
(Right) Baseplate cap
The membrane is tensioned over the baseplate between the gasket and the
baseplate then the cap is placed on top and screwed down tight (see Figure 3).
(Figure 3) - Baseplate with membrane, gasket, and cap assembled
To test the baseplate a 1 mil Kapton film and a 5 mil Mylar film were used as
membranes. The Kapton and Mylar films were put on the baseplate and the gasket was
Page | 3
put on top of that. The cap was placed on top of the gasket and membranes and screws
were used to screw the cap into the baseplate, compressing the gasket and membrane to
create a seal. The baseplate was put into the vacuum chamber and the air was pumped
out. The seal held to a small vacuum but leaked out of the spaces between the membrane
and baseplate as the vacuum pressure dropped below 500 millitorr. This is evident from
negative pressure inside the seal. Several different membrane and gasket materials have
been tested without complete sealing success. After doing a failure analysis the result of
the leak can be related to the aluminum cap bending where screws are absent.
The cutting wire, which melts the membrane releasing the aerobrake, has also
been tested with different materials to ensure cutting of the membrane. The wire fits inbetween the membrane material and the gasket to guarantee contact. When powered the
wire has been able to melt the membrane; cutting wire vacuum testing has not been
completed at this time but is planned.
An electrical analysis of the cutting wire was performed to determine the power
required to heat the wire above the melting temperature of a given membrane (see
Appendix 3). With the completion of the electrical analysis of the wire, a proof of
concept was required to demonstrate the capability of the selected Nichrome (NickelChromium) cutting wire to melt through a 5 mil thickness Mylar membrane. This was
accomplished by connecting the Nichrome wire to a 6 Volt, 5 Amp/hour alarm battery
(Appendix 1 Figure 4). The wire was connected by soldering the ends to copper leads and
manually connecting the lead ends to the positive and negative battery terminals.
Immediately after connecting the wire to the battery, the wire temperature began to rise
and a second team member pressed the Mylar against the wire. As expected, the wire
temperature was greater than the melting temperature of the Mylar and the membrane
began to melt.
A thermal analysis of the system was conducted in parallel so that once the
capsule system was functioning testing could begin on the inflatable system. The thermal
analysis sought to describe the thermodynamic system inside the inflatable as a numerical
model where parameters could be changed and the effects on the overall system could be
evaluated. The aerobrake can inflate easily in the vacuum environment as long as the
internal pressure after sublimation is above the external vacuum of space. Because the
aerobrake causes the CubeSat to descend in elevation, internal pressure must be sufficient
to maintain aerobrake shape at lower elevations (see Appendix 4). Pressure as a function
of elevation can be found in Appendix 2 Table 1 using data published in the Journal of
Geophysical Research [4]. Saturation temperature of benzoic acid as a function of
pressure at the selected elevation was found using the Antoine equation (see Appendix 5).
These values were then used to find the minimum amount of benzoic acid needed for
sublimation to attain desired internal pressure at a selected elevation, through use of the
Ideal Gas Law (see Appendix 6).
The energy required is based on the enthalpy of sublimation for benzoic acid. A
relation for the enthalpy of sublimation based on saturation temperature was derived
using microcalorimetry [5] (see Appendix 7). A plot of the relation can be seen in
Appendix 1 Figure 5. These values, combined with the mass of benzoic acid required,
were used to find the minimum energy required (see Appendix 8). This process was then
analyzed over a range of values by varying parameters and analyzing the results.
Inflatable volume, desired internal pressure, mass of benzoic acid required, and energy
Page | 4
required for sublimation were analyzed over a range of values (see Appendix 1 Figure
6,7).
Proposed Methods
A redesign of the base plate and cap were conducted and a design that optimizes
the sealing of a pressure vessel will be used. The baseplate and cap will be a circular
design so the stress on the cap and membrane should be evenly distributed. This design
will give the best chance for positive sealing of the pressure vessel. Once the baseplate is
machined the tests described above will be conducted again. Different gasket materials
will also be used to try and optimize the most effective gasket material for sealing the
pressure vessel. When proper sealing methods are achieved the cutting wire will be
integrated into the test system and debug any unforeseen issues. Once the sealing method
and cutting wire are proven to work and are reliable, a prototype baseplate will be
designed to reduce weight while still being able to hold up to pressure differences. A
thorough finite element analysis will be conducted with different materials and alloys to
optimize the system. Stress and deflection in the membrane will be computed using FEA
software PaTran (MSC Software, Newport Beach, CA).
Now that proof of concept has been established to physically cut the membrane, it
is proposed that this process be completed wirelessly in a vacuum chamber. A remote
controlled circuit (Arduino Kit) will be placed within the vacuum chamber along with the
battery to remotely activate the cutting wire and demonstrate the capability to cut the
membrane without manual operation. This process will first be attempted by installing a
membrane to the CubeSat baseplate and laying the Nichrome on top of the membrane.
After the vacuum chamber reaches the lowest possible pressure (approximately 150
millitorr), the circuit will be turned on to observe how the membrane behaves after being
cut under vacuum pressures.
Once wireless capability has been established, it is then necessary to embed the
cutting wire within the baseplate and still maintain a vacuum seal. It is proposed to layer
high temperature gaskets around the membrane and cutting wire to prevent contact
between the aluminum baseplate and the wire. Failure to do so will result in a shorting of
the circuit and heat loss from the wire. After integrating the wire within the baseplate, it
is required to again remotely activate the circuit and cut the membrane. Completion of
this portion of testing will demonstrate the ability to perform integration of multiple
subcomponents of the CubeSat DeOrbit System.
The tether release has gone through several design iterations since the beginning
of the project. Currently a thermal cutting wire wrapped around the base of the balloon
(Figure 8) will initiate the separation. Further analytical work of the baseplate structure is
needed before further action can occur on the release system. A finalized baseplate
design will allow for an efficient placement of the release system to reduce the system
weight and complexity.
Page | 5
(Figure 8) - Baseplate with deployed inflatable
Previous tether release systems included: a two plate system and a double ring
design. After an initial design is agreed upon, analysis of the balloon separation can
occur. A finite element analysis program will be used to characterize the aerobrakeCubeSat separation. Systems Tool Kit (STK) (Analytical Graphics, Inc., Exton, PA) will
also be used to model the CubeSat flight characteristics. Analysis will ensure that the
CubeSat separation device will not introduce abnormal flight characteristics such as
tumbling due to uneven separation. After the computer based analysis, the separation
system will be proven functional in a vacuum environment. After successful completion
of the test, the system will be integrated onto the test structure for full scale testing.
The inflatable material will be Mylar with either Polypropylene or Polyethylene
coated on one side to provide reflectivity or absorptivity depending on the temperature
requirements of the benzoic acid. In order to determine the drag due to the balloon the
following equation will be used:
Drag = Coefficient Drag * (Surface Area) * 0.5 * (Pressure) * (Velocity)^2 (Equation 1)
The pressure and estimated velocity, depending on altitude and orbit, will be
known. The exact surface area will need to be determined. The surface area will be
estimated using the vacuum sealed volume of the balloon and the amount of space
allotted for the balloon in the CubeSat capsule. Knowing the surface area, altitude, and
pressure, STK will be used to model the CubeSat’s orbit.
The thermal analysis now seeks to determine if energy required to sublimate the
benzoic acid can be provided by solar radiation or if a heating element is necessary in the
design. The inclusion of a heating element is undesired due to the addition of mass and
complexity. Project Echo provided a variety of calculations pertaining to the availability
of energy from solar radiation and did not require a heating element [2]. STK will be
Page | 6
used to model probable orbit paths, in reference to available solar energy. The availability
of energy in the simulated orbits will be compared to the Project Echo experimental data
to verify accuracy. The availability of energy greatly affects the design of the CubeSat
DeOrbit System, not only in reference to the possibility of necessity for a heating
element, but also in the volumetric size of the inflatable.
The orbit analysis will provide necessary design criteria to ensure the final
product meets the requirements to survive an orbit test inflation, which is planned to be
done aboard an Orbital Sciences launch from Wallops Flight Facility. Orbit profiles will
be created using STK, then emulated during testing at Langley Research Center (LaRC).
The vacuum testing facilities at LaRC provide the ability to simulate orbit through use of
radiative heat lamps. Calculations of availability of energy to sublimate the Benzoic Acid
will be verified by the physical experiments. This will provide a high level of confidence
in the calculations, with the ability to modify the calculations for different conditions then
re-verify them through additional testing at LaRC. The baseplate, membrane, and cutting
wire systems will also undergo final vacuum, thermal, and vibration testing in accordance
with NASA’s Launch Services Program Level Poly-Picosatellite Orbital Deployer
(PPOD) and CubeSat Requirements Document [6].
Preliminary Results
With design of the system underway no numerical results have been found
pertaining to design criteria. Membrane and cutting wire testing was conducted for an
initial proof of concept. The cutting wire testing proved to be successful in heating the
cutting wire and having the ability to cut through the thickest of the membrane samples.
Testing is planned to further the analysis on the cutting wire until optimum wire diameter
and power consumption are calculated, and will be included in future documents.
Membrane and gasket testing was also conducted for an initial proof of concept. The
membranes were shown to hold a seal until approximately 500 millitorr. Leaking of the
gasket was displayed by negative pressure when the vacuum chamber was returned to
atmospheric conditions. The problem was found to be the non-diametral bolt pattern of
the baseplate. Fortunately another portion of the CubeSat DeOrbit System design team
had produced a baseplate with a diametral bolt pattern which was able to hold seal under
much lower vacuum pressure, proving that the direction we are moving will be
successful. Future testing will now begin documenting maximum values and parameters
for the abilities of the membrane, cutting wire, and inflatable aerobrake.
Discussion
The CubeSat deorbit system will provide a commercially available part for future
CubeSat missions to comply with UN space debris regulation. The system will also
incorporate a thermally actuated balloon release mechanism. This mechanism will allow
scientific access to lower earth orbits which were previously cost prohibitive. The balloon
inflation system will be driven by the sublimation of benzoic acid similarly to project
Echo, conducted by NASA in the 1960’s.
During preliminary testing several issues came up. The need arose to determine a
more efficient sealing method other than what has been proposed. It was determined that
the thermal cutting wire must be isolated from the base plate in order for the wire to
retain its thermal energy and cut the membrane; this method of thermal isolation will also
be used on the balloon release mechanism.
Page | 7
The research team consists primarily of undergraduate students. This lack of
practical experience results in longer deadlines for tasks. Access to resources at ODU
and NASA have helped the team alleviate some of the experience gap. Currently there is
a lack of testing equipment at Old Dominion. The vacuum pump used during preliminary
testing does not have a pressure gauge on it. This lack of instrumentation affects the
ability to conduct accurate tests outside of proof of concept tests. It is anticipated that the
team will have access to a proper vacuum facility at NASA Langley to conduct
preliminary flight qualification testing in the near future.
Future utilization of this technology could result in regular flights to altitudes
whose orbits decay in a matter of weeks to hours. The implications of conducting science
experiments at these elevations cannot be projected. This viable mitigation option for
space debris from CubeSats will be commercially available in the near future as a result
of this work.
Page | 8
Appendix 1 - Figures
(Figure 1) - CAD model of baseplate
(Figure 4) - Cutting wire and battery
Page | 9
(Figure 5) - Enthalpy of Sublimation of Benzoic Acid vs. Temperature
(Figure 6) - Necessary mass of Benzoic Acid vs. Volume of Aerobrake and
Pressure inside Aerobrake (with ambient pressure held constant at
0.00136 mmHg)
Page | 10
(Figure 7) - Necessary Energy for Sublimation of Benzoic Acid vs. Volume of
Aerobrake and Pressure inside Aerobrake (with ambient pressure
held constant at 0.00136 mmHg)
Page | 11
Appendix 2 - Tables
Geometric Altitude
Ambient Pressure
Ambient Pressure
Saturation Temperature
(km)
(mbar)
(mmHg)
(˚C)
1.01325E+03
7.60002E+02
249.077
0
2.26320E+02
1.69750E+02
199.896
11.019
5.47470E+01
4.10640E+01
161.815
20.063
8.67980E+00
6.51040E+00
121.417
32.162
1.10900E+00
8.31800E-01
85.1195
47.35
5.89970E-01
4.42520E-01
75.4427
52.429
1.82090E-01
1.36580E-01
58.9162
61.591
1.03760E-02
7.78270E-03
25.2572
79.994
1.64370E-03
1.23290E-03
7.46534
90
3.00700E-04
2.25500E-04
-6.87372
100
7.35270E-05
5.51500E-05
-17.5102
110
2.52090E-05
1.89080E-05
-24.9408
120
(Table 1) - Saturation Temperature as a function of Pressure with respective Elevations
(ambient pressures taken from Journal of Geophysical Research [1])
Page | 12
Appendix 3
Electrical Analysis of Cutting Wire
ρ0= Electrical resistivity at room temperature (Ω*m)
α = Temperature coefficient of resistance (material property)
T0 = Room Temperature (0C)
T = Desired Temperature (0C)
Electrical Resistivity varies with temperature; therefore resistivity as a function of
temperature can be expressed as:
ρ(T) = ρ0[1- α(T-T0)]
Electrical Resistance (R) using Pouillet’s law is expressed as:
R=
R=
L is wire length (m) and A is the cross sectional area of the wire (m2).
Finally, the electrical power (W) required to heat a material to a desired temperature can
be expressed using Ohm’s Law as:
P= I2*R
I is current in amperes.
By substituting R= (ρ0[1- α(T-T0)]*L)/ A into the above equation, we have:
P=
The above equation defines the amount of power required to heat a given material to a
desired temperature based on predetermined dimensions.
Page | 13
Appendix 4
Finding desired Internal Pressure of Inflatable
For purpose of this study
If
will be taken as 0.00136 mmHg:
, then
to inflate and hold shape.
This means that all calculations for required mass of Benzoic Acid and energy input are
the absolute minimums.
Appendix 5
Finding Saturation Temperature of Benzoic Acid as a Function of Pressure
Table 1 was found using the Antoine equation:



Log is the logarithm based of 10
P = pressure (mmHg)
T= temperature ( )




A, B, C are substance-specific coefficients (constants)
A=8.57134
B=2726.2
C= 230
Manipulating equation yields:
More simply:
Page | 14
Appendix 6
Use of Ideal Gas Law to solve for Mass of Benzoic Acid Required
Molar mass of Benzoic Acid: 122.12 g/mol
Universal Gas Constant: 8.314462 J/mol K
Using the Ideal Gas Law:
Sample calculations for various inflatable volumes at ambient pressure of 0.1813 Pa:
For 0.1 m^3:
For 0.5 m^3:
For 1 m^3:
Appendix 7
Enthalpy of Sublimation as a function of Temperature
Test limitations in document were stated as:
"The lower limits of the temperature ranges of the measurements are thus determined by
the recorder system sensitivity and the upper limits by the conditions of validity of
Knudsen equation." [3]
The value of enthalpy of sublimation has thus not been determined by
measurement due to equipment restrictions. However, a function of the slope of the
enthalpy of sublimation versus temperature was found using least squares treatment of
the experimental data that can be used to find accurate values for enthalpy of sublimation
at given saturation temperatures.
The trend of the enthalpy of sublimation as a function of temperature in Kelvin given in
the document [3]:
Page | 15
Appendix 8
Finding Required Energy for Sublimation based on mass of Benzoic Acid
Using our current saturation temperature at a pressure of 0.1813 Pa,
= 281.5 K,
and disregarding deviation of the function for now, the enthalpy of sublimation is:
Sample calculations:
For 0.1 m^3:
For 0.5 m^3:
For 1 m^3:
Page | 16
Appendix 9 - Gantt Chart
Page | 17
Appendix 10 - Budget
CubeSat
DeOrbit Budget
Labor
Student Labor
Materials
CubeSat
Membranes
Cutting wires
Raw Aluminum
Hardware, Misc.
Thermal Gasket
Vacuum
Supplies
Battery and
Charger
Benzoic Acid
Temperature
Gages
Arduino, Xbee,
Misc.
Software
Pro-E and Patran
Facilities
NASA Vacuum
Chamber
On Campus
Vacuum
Chamber
Subcontractors
and Consultants
Baseplate at
Machine Shop
3-D Printing
Consultant Nathanael Miller
(NASA)
$24,000
Calculations
$25 per hour x 6 group members x 5 hours per week x 32
weeks=$24,000
$7,500
$100
$50
$160
$25
$100
$25
$300
$30
$100
$200
$6,000
$8,000
$1,000 per hour x 8 hours=$8,000
$1,250
$50 x 25 hours=$1,250
$4,000
$1,200
$100 per hour x 40 hours=$4,000
$100 per hour x 12 hours=$1,200
$1,500
$100 per hour x 15 hours=$1,500
Page | 18
Travel
None
Contingency
30% of Budget
TOTAL
BUDGET COST
Cumulative
Budget Cost
(CBC)
Cumulative
Actual Cost
(CAC)
Cumulative
Earned Value
(CEV)
Cost
Performance
Index (CPI)
Cost Variance
(CV)
Forecasted Cost
At Completion
(FCAC)
TCPI (ToComplete
Performance
Index)
$0
$16,362.0
$70,902
0.3*SUM(B4:B30)
SUM(B4:B33)
$21,920
(Labor + (Materials - CubeSat) + (Subcontractors Consultants 3-D printing) + (Facilities - NASA Vacuum Chamber) +
Contingency)/2 + Software
(Labor + (Materials - CubeSat) + (Subcontractors Consultants 3-D printing) + (Facilities - NASA Vacuum Chamber))/2 +
Software
$25,806
0.5*Labor + 0.45*Materials + 0.1*Subcontractors Consultants
+ Software + 0.41*Facilities
$30,101
1.18
$3,886
$60,225
0.92
CPI = CEV/CAC
CV=CEV-CAC
FCAC=TBC/CPI
TCPI=(TBC-CEV)/(TBC-CAC)
Discussion of Budget
The actual budget for the project is only for the CubeSat structure which is
$1725.00. The team was awarded $1350.00 which will be going towards that structure in
its entirety. Ways to gap the cost between the CubeSat structure and the amount of money
awarded will be sought out in the following semester, although the CubeSat structure is
not necessary for testing within our scope. The expensive nature of a total CubeSat
system (approximately $7500) means that the current and future teams will be buying the
CubeSat system in portions from the manufacturer.
The Gantt chart and budget agree that the team is on track with our current goals.
Purchase of the CubeSat structure will help provide future teams with an eventual orbital
test of the CubeSat DeOrbit System, although it is not immediately necessary for the
progression of research.
Page | 19
Appendix 11
MATLAB Code
Enthalpy of Sublimation of Benzoic Acid vs. Temperature Plot
T=linspace(240,360);
Hhigh=22058-(4.036*T);
Hlow=21958-(4.008*T);
Hmid=22008-(4.022*T);
hold on
plot(T,Hhigh,'r--')
plot(T,Hmid)
plot(T,Hlow,'r--'),title('Enthalpy of Sublimation of Benzoic Acid vs. Temperature');
xlabel('Temperature (K)'); ylabel('Enthalpy of Sublimation (cal/mol)');
Variation of Parameters Program
Vinflatable=needs input; %m^3
Pinflatable=needs input; %in Pa
P=needs input; %in mmHg based on elevation
R=0.0680844; %J/gK
Tsat=((2726.2-(8.57134-log10(P))*230)/(8.57134-log10(P)))+273.15%K
mass_benzoic_req=(Pinflatable.*Vinflatable)./(R*Tsat)
hig=(22008-(4.022*Tsat)) %cal/mol
higunits=(hig/122.12)*4.184 %J/g
E_req=mass_benzoic_req*higunits %J
Example of Variation of Parameters Program using values from this study
Vinflatable=1; %m^3
Pinflatable=0.1813; %in Pa
P=0.00136; %in mmHg based on elevation
R=0.0680844; %J/gK
Tsat=((2726.2-(8.57134-log10(P))*230)/(8.57134-log10(P)))+273.15%K
mass_benzoic_req=(Pinflatable*Vinflatable)/(R*Tsat)
hig=(22008-(4.022*Tsat)) %cal/mol
higunits=(hig/122.12)*4.184 %J/g
E_req=mass_benzoic_req*higunits %J
Comparison of mass of Benzoic Acid required versus aerobrake volume and desired
interior pressure
Vinflatable=linspace(0.5,3); %m^3
Pinflatable=linspace(0.1813,15); %in Pa
P=0.00136; %in mmHg based on elevation
R=0.0680844; %J/gK
Tsat=((2726.2-(8.57134-log10(P))*230)/(8.57134-log10(P)))+273.15%K
Page | 20
mass_benzoic_req=(Pinflatable.*Vinflatable)./(R*Tsat)
hig=(22008-(4.022*Tsat)) %cal/mol
higunits=(hig/122.12)*4.184 %J/g
E_req=mass_benzoic_req*higunits %J
plot3(Pinflatable,Vinflatable,mass_benzoic_req),title('Necessary mass of Benzoic Acid
vs. Volume of Aerobrake and Pressure inside Aerobrake');
xlabel('Aerobrake desired interior pressure (Pa)'); ylabel('Volume of Aerobrake
(m^3)');zlabel('Mass of Benzoic Acid required (g)')
hold on
grid on
Comparison of Energy required for sublimation of Benzoic Acid versus aerobrake
volume and desired interior pressure
Vinflatable=linspace(0.5,3); %m^3
Pinflatable=linspace(0.1813,15); %in Pa
P=0.00136; %in mmHg based on elevation
R=0.0680844; %J/gK
Tsat=((2726.2-(8.57134-log10(P))*230)/(8.57134-log10(P)))+273.15%K
mass_benzoic_req=(Pinflatable.*Vinflatable)./(R*Tsat)
hig=(22008-(4.022*Tsat)) %cal/mol
higunits=(hig/122.12)*4.184 %J/g
E_req=mass_benzoic_req*higunits %J
plot3(Pinflatable,Vinflatable,E_req),title('Necessary energy for sublimation of Benzoic
Acid vs. Volume of Aerobrake and Pressure inside Aerobrake');
xlabel('Aerobrake desired interior pressure (Pa)'); ylabel('Volume of Aerobrake
(m^3)');zlabel('Energy required for sublimation (J)')
hold on
grid on
Page | 21
References
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[6]
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D. L. Clemmons and L. R. Center, The Echo I inflation system: National
Aeronautics and Space Administration, 1964.
E. Lokcu and R. L. Ash, "A de-orbit system design for CubeSat payloads," in 2011
5th International Conference on Recent Advances in Space Technologies (RAST),
9-11 June 2011, Piscataway, NJ, USA, 2011, pp. 470-4.
N. Sissenwine, M. Dubin, and H. Wexler, "The U. S. standard atmosphere, 1962,"
Journal of Geophysical Research, vol. 67, pp. 3627-3630, 08/ 1962.
L. Malaspina, R. Gigli, and G. Bardi, "Microcalorimetric determination of the vol.
enthalpy of sublimation of benzoic acid and anthracene," Journal of Chemical
Physics,59, pp. 387-94, 07/01 1973.
N. A. S. Administration, "Launch Services Program Level Poly-Picosatellite
Orbital Deployer(PPOD) and CubeSat Requirements Document," in A, ed.
Florida: John F. Kennedy Space Center, 2011.
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