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Burn Baby Burn

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					           Burn Baby Burn




Gina Covarrubias     John Dankanich
Kristin Gates        Jon Mah
Mike Schreiner       Selim Solmaz
Executive Summary

       The Burn Baby Burn satellite system is a university built satellite. The
manufacturing limitations of placing a thruster on the center of mass of a spacecraft lead
to pointing errors. The primary mission of the satellite is to perform analysis on the
removal of this pointing error through a two burn thrusting scheme. The secondary is
mission to de-orbit the spacecraft while testing a trapezoidal thrusting scheme to remove
pointing errors. The spacecraft is compatible with all available secondary payload launch
systems. The satellite will have a circular orbit at a 350 km altitude and an inclination
greater than 30o. The overall mass of the spacecraft is 24.85 kilograms and it has
dimensions of 30 cm X 30 cm X 35 cm. The cost of production is estimated to be
$48,000.




                                                                                        2
Table of Contents

   I.      Mission Statement and Objectives                4
   II.     Concept of Operations                           5
   III.    Major Design Requirements                       6
   IV.     Spacecraft System Overview                      9
   V.      Launch Vehicle Integration                      13
   VI.     Orbit Selection                                 14
   VII.    Power Subsystem                                 15
   VIII.   Attitude Determination and Controls Subsystem   18
   IX.     Communication and Data Handling                 37
   X.      Thermal Subsystem                               42
   XI.     Structure and Mechanisms                        47
   XII.    Propulsion                                      48
   XIII.   Summary of Spacecraft                           53
   XIV.    References                                      54
   XV.     Appendix                                        55
           A. QFD                                          55
           B. ADCS                                         56
           C. Power                                        62
           D. Communications and Data Handling             64
           E. Thermal                                      66
           F. Structure                                    68
           G. Propulsion                                   69




                                                                3
I. Mission Statement and Objectives

Mission Statement

       Due to possible center of mass or thruster offset in axially spinning-thrusting
spacecraft, the resulting angular momentum vector is not aligned with the intended flight
path. A solution to this problem is to use a “two-burn scheme” during thrusting. This
burn scheme will eliminate the average angular momentum bias, and cause the velocity
vector to point along the axis of rotation. Spacecraft customers will benefit through
decreased propellant costs and an increased mission life.

Mission Objectives

         The primary objective is to test effectiveness of the “ Two-burn scheme” in an axially spinning-
thrusting spacecraft with an intended thruster offset.
         The mission will also have secondary objectives to test the trapezoidal thrust
profile using a solid rocket motor and to de-orbit the spacecraft. An additional secondary
objective is to perform an outreach experiment. The outreach experiment will be limited
to the available mass and volume after performing the university mission. Last, the
satellite will have mirrored surfaced to aid in visualization of the craft.




                                                                                                       4
II. Concept of Operations




                        Figure 1: Illustration of the spacecraft mission.

1.Detach from launch vehicle                        10. AOS
2.Initial acquisition of signal (AOS)               11. Downlink experiment #2 data
3.Command to Spin-Up                                •Telemetry accompanies data
4.Downlink telemetry (verify rates are within       •Verify data is as expected
limits)                                             •After downlink, s/c goes to beacon mode
5.Perform experiment #1 (after performing           12. AOS
experiment, s/c goes to beacon mode)                13. Perform experiment #3 (after performing
6.AOS                                               experiment, s/c goes to beacon mode)
7.Downlink experiment #1 data                       14. AOS
•Telemetry accompanies data                         15. Downlink experiment #3 data
•Verify data is as expected                         •Telemetry accompanies data
•After downlink, s/c goes to beacon mode            •Verify data is as expected
8.AOS/downlink telemetry                            •After downlink, s/c goes to beacon mode
9.Perform experiment #2 (after performing           16. End of Life
experiment, s/c goes to beacon mode)




                                                                                              5
III. Major Design Requirements

         The primary requirement of the mission is to design a spin stabilized spacecraft platform, at a
minimal cost, to test the “Two-Burn” and “Trapezoidal” trusting schemes for velocity pointing control,
which was developed by Prof. James M. Longuski, et al. of Purdue University, West Lafayette. The
spacecraft shall have thrusters placed longitudinally along the spin axis with some intentional thruster
offset. The reasons for this are explained along with The Two-Burn scheme in detail in the following
chapters and information on the trapezoidal scheme can be found in US patent No: 6,332,592 B1.
   The major design requirements of the mission are explained below for each specific subsystem, and /or
mission phase:

1. Orbit

        In order to maximize the chances of launching as secondary payload, the mission
shall be designed for LEO (Low Earth Orbit). The spacecraft shall be designed to
perform various pointing error correction techniques and transmit the data collected to the
Purdue University ground station. The orbit shall have an inclination capable of direct
communication with the Purdue ground station. The orbit shall have a minimum of 3
passes for communication each day.
3. Launch Vehicle

         The satellite shall be designed to fit any launch vehicle available (i.e. Delta, Shuttle Hitchhiker,
Pegasus/OSP, and Minotaur), as a secondary payload. Due to the varying constraints of the different
launch vehicles, the satellite shall be designed for the maximum allowable case. The Delta rocket imposes
the greatest limits on the spacecraft dimensions, while the Pegasus will impose the largest structural
constraints.
         The spacecraft shall have maximum dimensions of 30 cm X 30 cm X 35 cm and maximum mass
of 40 kg, so the spacecraft shall fit in the Delta launch vehicle as a secondary payload.

4. Mission Life

       The satellite shall be designed for a one-week life in orbit. The experiments will
take approximately three days, allowing for a redundancy of four days.
5. Propulsion

        The satellite shall have a cold gas thruster capable of providing the thrust profiles
required to perform a test of the single and two burn maneuvers. The total velocity
change for the cold gas thruster shall be 6 m/s. The satellite shall also have a solid rocket
motor to de-orbit the spacecraft and that is capable of providing the thrust profile required
to perform the trapezoidal burn maneuver. The total velocity change for the solid rocket
motor shall be 50 m/s. The cold gas motor shall provide approximately 1 Newton of
thrust to perform the burn maneuvers. Two arrays of small solid rocket thrusters shall be
attached to the side of the spacecraft to provide the initial spin-up. The total velocity
change for the spin-up thrusters is 0.5 m/s. Both the Cold-Gas thruster and the solid
rocket motor shall have an intentional offset of 5 cm.
6. Attitude Determination & Control




                                                                                                           6
          The spacecraft shall have multiple sun sensors for precise attitude determination. The angular
velocities shall be determined by rate gyros. The sun sensors shall be used in conjunction with gyros for
reference correction. Accelerometers shall be used to detect acceleration changes of the spacecraft, which
shall be used to determine the velocity history of the spacecraft during the experiments. The spacecraft
shall spin about the maximum moment of inertia axis at a rate of 25 rpm. Two arrays of small solid
thrusters that are placed about the spin axis shall provide the initial spin in case that the launch vehicle is
incapable of providing it.
        The spacecraft shall not have an active attitude control system aside from the
axially placed main cold-gas thruster (along the spin axis) and the SRM on the opposite
face. Any nutation caused by the offset thrusters shall be damped out using passive
nutation dampers in less than three hours.

7. Power

       The power requirement for the spacecraft shall have a maximum peak power
requirement of 40 watts. The power shall be provided by primary D-cells with an
operating voltage of 24 volts. The batteries’ state of charge shall be monitored
throughout the mission.

8. Thermal Control

        The thermal control system shall have a thermal margin of 5°, meaning that
temperatures of 5° higher than the lower temperature limit and 5° below the upper
temperature limit will be maintained. Coating or insulating their outer surfaces shall
control temperature of compartments, and conventional electronic equipment.
9. Telecommunications and Data Handling

         The goal shall be to use the ground station available at Purdue University, through a direct
downlink from the spacecraft. Commands shall be up-linked to the spacecraft via a terminal node
controller, which shall format the data for transmission. The primary use of the downlink shall be to
transmit the attitude data, temperatures of different subsystems, and battery state of charge to the ground
station during each pass. The uplink frequency shall be in the two-meter wavelength band (~150 MHz),
and the downlink frequency shall be in the 70-centimeter wavelength band (~440 MHz). The exact
frequencies shall be as allotted. The transmitter, receiver, and terminal node controller shall use existing,
off-the-shelf technology. Communications shall use the A.X. 25 amateur radio protocol to package and
transmit the data at a rate of 1200 bits per second. The antennae shall utilize two pairs of monopole
antennae (one pair for transmit and one pair for receive), which shall be mounted on opposing corners of
the spacecraft.
        The data handling shall use a processor, a data module, several analog-to-digital
converters, a decoder, and a digital databus. The data shall be buffered in the memory
module as the experiments are performed and then, upon ground command, down-linked
data to the Purdue University ground station.
10. Structures

        A prime requirement for the structure is that it shall be designed to withstand
dynamic loads present during testing, launch phases, and zero gravity environment. The
main bulk of the structure shall consist of a durable, lightweight, cheap material that is
relatively easy to manufacture.



                                                                                                             7
8
IV. Spacecraft System Overview

        The Burn-Baby-Burn spacecraft is a spin-stabilized satellite that is spun about its
z-axis. Figure IV-1 shows the spacecraft with it body fixed coordinate system.




             Figure IV-1: External view of spacecraft with body fixed coordinates.

       The spacecraft layout is shown in figure 2, 3, and 4. Figures 2 and 3 show the
system without the batteries, while figure 5 shows the layout with the batteries included.
The stability of the spacecraft requires Iz to be the maximum moment of inertia.
Therefore the layout is designed to provide a maximum moment of inertia in the ‘z’
direction.




                        Figure IV-2: Internal layout of the spacecraft.




                                                                                         9
        All of the components except the inner battery packs are mounted directly to the
walls of the spacecraft. The main cold-gas thruster and the solid rocket motor are
intentionally offset five centimeters to cause a significant point error. Last, the CPU is a
comprehensive computer package that includes the processor, data storage, transmitter,
receiver, terminal node controller, and power regulator.




                    Figure IV-3: Layout of the spacecraft components.




                   Figure IV-4: Layout of spacecraft with dimensions.




                                                                                         10
        The mass budget for the entire spacecraft is shown in Table 1. The individual
subsystems mass budgets re shown in Tables 2 – 6. The goal for the spacecraft is to have
a total mass under forty kilograms. The total mass of the spacecraft is currently 28.5 kg.
This mass gives an 11.5 kg (29 %) margin. Because the majority of the components have
already been selected, they do not require a significant mass margin. The margin will
primarily be consumed by the estimated components in addition to a possible outreach
experiment.
           Power                        9.56 kg                          38 %

         Structure                       5.75 kg                         23 %

        Propulsion                       5.42 kg                         22 %

  Attitude Determination                 1.40 kg                          6%

 Communication and Data                  2.72 kg                         11 %

           Total                          24.85                          100 %

          Margin                          15.15                          38 %

                        Table IV-1: Overall system mass budget.



    Batteries ***          7.89 kg                           Frame*             1.39 kg

Regulator/Converter*       0.42 kg                           Shell*             3.36 kg

      Wiring*              1.25 kg                         Fasteners**           1 kg

        Total              9.56 kg                        Insulation**       0.0042 kg

                                                              Total             5.75 kg

Table IV-2: Power mass Budget.                        Table IV-3: Structure mass budget.



* Calculated ** Estimated *** Actual




                                                                                          11
       Tank*                 1.76 kg                         Transmitter*              0.5 kg

     Plumbing*               0.69 kg                          Receiver*                0.8 kg

 Spin-up Motors**             1 kg                            Antennae*                0.5 kg

  De-orbit SRM*              1.55 kg                         Processor***              0.4 kg

      Nozzle*               0.012 kg                   Terminal Node Con.*            0.32 kg

  Propellant (gas)*          0.41 kg                         Data Storage*             0.5 kg

       Total                 5.42 kg                               Total              2.72 kg

Table IV- 4: Propulsion mass budget.                Table IV-5: Com. and data mass budget.



                             Gyros***                      0.06 kg

                          Sun Sensor***                    0.31 kg

                         Accelerometers***                 0.03 kg

                      Nutation Damper**                     1 kg

                               Total                       1.4 kg

                         Table IV-6: AD & C mass budget.

* Calculated ** Estimated *** Actual



      Ix = 0.32 kg / m                  Iy = 0.36 kg / m                   Iz = 0.50 kg / m

Table IV-7. Mass moment of inertias for the spacecraft.




                                                                                                12
V. Launch Vehicle Integration




                                13
VI. Orbit Selection

        To meet the mission requirement of flexibility in launch vehicle, the spacecraft
must be able to fly in any available orbits. However, for design considerations, a specific
orbit must be chosen for calculations. The orbit inclination is determined by the
communications subsystem. The spacecraft needs to have the ability to communicate
with the Purdue University ground station at least twice per day for a minimum duration
of 8.4 minutes. The minimum inclination for communications is then 30o.
         The altitude of the orbit is determined by the mission life, the communications
system, and the size of the de-orbit motor. Our spacecraft can be in a low orbit because
the mission life is very short. Because the size and mass of the de-orbit engine increase
with altitude, the minimum altitude that allows fours days of communications before re-
entry was chosen. Four days provides enough time for all of the data to be collected and
transmitted to the ground station before the loss of the satellite. Therefore the altitude for
the mission was chosen to be 350 km.




                     Figure VI-1: Ground tracks of the orbit selected.

        The orbit for the mission is a circular orbit with an altitude of 350 km and an
inclination of 40o, which will pass directly over the Purdue University ground station.
This is the orbit is chosen for calculations, however; any inclination over 30o is
acceptable.




                                                                                           14
VII. Power Subsystem

        The power subsystem limits the lifetime of the satellite. Under optimal conditions
the mission can be completed in less than three days, so the mission lifetime requirement
is one week for redundancy. Because of the short mission life, primary cells are a
feasible option. A trade study was carried out to decide if solar cells or primary batteries
would be best suited for the mission. The three methods of power generation considered
were primary batteries, solar cells, and the combination of primary batteries with solar
cells.
        Table VII-1 shows the results of the trade study. Primary cells are very limiting
on the lifetime of the satellite and consume a large fraction of the satellite volume. The
use of solar cells can increase the duration of the mission and also greatly reduce the
amount of internal volume needed for the power subsystem. Using a combination of
solar cells and primary batteries provide both an extended lifetime and an additional level
of redundancy. The over all decision to use only primary cells and is to minimize mass
and especially the cost. In order to accurately compare the various options rough
calculations were carried out and are shown in Appendix C

                            Batteries            Solar Cells       Batteries and Solar
     Simplicity                ++                     +                      -
       Mass                    ++                    +                      -
       Cost                    ++                     -                     -
    Redundancy                  -                    +                     ++
      Volume                    -                    ++                     +
          .Table VII-1: Trade study for choosing method of power generation.


        The power requirements for each subsystem as well as the total spacecraft are
shown in table VIII-2. The power requirements are divided into the different mode of
operation. Using the power required for each mode of operation with the duration of
each mode provides the number of watt-hours the primary cells must provide. There is a
margin shown in the table for a margin in both power for each mode of operation and the
duration of each segment of the mission. The margin for the power consumed in each
mode is approximately 10%. There is also a duration margin of 100% for the insertion,
testing, and transmitting modes of operations in addition to 20% margin in the duration of
the standby mode.




                                                                                         15
                      Insertion      Testing       Standby       Transmitting
 Spin Up Motors       Capacitor
Cold Gas Thruster                      1
  De-Orbit SRM                     Capacitor
    Sun Sensor         0.05          0.05           0.05             0.05
      Gyros                            2
 Accelerometers                        1
     Processor           3             6              3               6
  Terminal Node          1             1              1               1
    Controller
    Transmitter                                                      7.5
     Receiver            3             3              3               3
  Power Losses         1.41          2.81           1.41            3.51
   Total (Watts)       8.46          16.86          8.46            21.06
  Power Margin           1             2              1               2           11 %
 Duration (Hours)       0.5           0.5           166               1
 Duration Margin        0.5           0.5            36               1           23 %
  Total (W-hrs)        9.46          18.86        1910.92           46.12         1985
Table VII-2: Power budget in various modes of operation.

       After calculating how much power the primary cells must provide, the type of
primary cells must be selected. Based on a maximum mass allocation of 25% (10 kg) for
the power system, the primary cells needed to have a specific energy density greater than
200 W-hr / kg. This specific energy density limited the primary battery selection to
Lithium Thionyl Chloride, Lithium Sulfur Dioxide, and Lithium Monoflouride. Table
VII-3 shows the methodology of choosing which primary cell to use. Overall, the
Lithium Sulfur Dioxide batteries are optimal for this mission.

                        Lithium Thionyl         Lithium Sulfur           Lithium
                            Chloride               Dioxide             Monoflouride
Optimal Duration               --                     ++                    +
Discharge Curve                +                      ++                    +
 Used in Space                 +                       +                    +
      Cost                     +                      ++                    +
Specific Energy               ++                       +                    +
    Density
Table VII-3: Trade study for choosing primary battery.

        Lithium Sulfur Dioxide primary cells have been used in space and are commonly
used in military hardened applications. They have low internal resistance, and a
temperature range from –60o to 80oC. The cell types vary with specific energy densities
ranging from approximately 130 – 350 W-hr / kg. The cell chosen for the mission has a
specific energy density of approximately 250 W-hr / kg. The mass budget of the power
system is shown in table VII-4.




                                                                                      16
                       Batteries ***                    7.89 kg

                  Regulator/Converter*                  0.42 kg

                         Wiring*                        1.25 kg

                          Total                         9.56 kg

                Table VII-4: Power mass budget. *Calculated *** exact

       The volume of the power consumption is also a concern for the mission. Lithium
Sulfur Dioxide units can vary in the energy densities as well. The energy density is
proportional to the cost of the cell. Because the objective in any space mission is to
minimize the cost, the readily available D-cell was chosen. While the D-cell does not
have the highest energy density available (0.4 W-hr / cm3), it is the most cost effective
method of power generation. Because of the low energy density, the mission can only
have a maximum duration of 12 days. The entire power system cost is approximately
$2000.




                                                                                      17
VIII. Attitude Determination and Controls Subsystem

    1) Major Requirements
     The requirements on the AD & C subsystem change during mission, especially if the satellite is
performing multiple independent tasks. Usually the payload requirements at each specific mission phase
dictate the AD & C subsystem requirements for that phase. The requirement on the AD & C subsystem at
each distinct mission segment is called a control mode. Therefore, control modes of a satellite divide the
mission into segments, according to specific attitude determination and control requirements.
     Our mission analysis points out four different control modes listed below. Detailed explanations for the
each specific control mode can be found in the requirements section below.

   1.1)      Control Modes:


         Control Modes                              Explanation
     1 ) Spin-Up Mode - Acquisition of Stability through spin-up maneuver after releasing
                       from launch vehicle
     2 ) Normal Mode    - Orbit determination phase by tracking from Purdue ground station

     3 ) Thrusting Mode - 2 Thrusting experiments for evaluating the “two-burn” thrusting
                         scheme
                         - 1 thrusting for evaluating the “Ramp-up” thrusting scheme while
                        de-orbiting

     4 ) Safe Mode           - Stand-by mode in case of a major malfunction

          Table VIII-1: Control modes.
   1.2)      Performance Requirements:

    Specific requirements for each control mode were determined by the customer attributes and the
minimal cost consideration. In other words, each specific requirement is sufficient enough to assess the
validity of the thrusting experiment properly at a minimum cost.

   1.2.1)    Spin-Up Mode :

   This mode is the phase just after leaving the launch vehicle in orbit. Initially, the spacecraft will be
unstable prior to spinning. Two pairs of 4-array small solid side thrusters will achieve spin-up with the
aimed rate of 25 rpm. This angular rate has no significance, as long as it is within the range of 20 ~ 30 rpm.
This flexibility is due to the robustness of the “two-burn” and “ramp-up” thrusting schemes which provide
significant pointing error reduction, theoretically, for any given spin rate. However, due to the limitations
on thruster on-off timing at high spin rates (we can’t turn-on and turn-off the thruster very quickly as it
takes some time to reach a specific thrust value), it is not practical to apply this thrusting scheme at very-
high spin rates. Fortunately, most spacecraft are spun around 20 ~ 30 rpm since higher spin rates cause
excessive structural loads on the spacecraft. Thus we selected a nominal value of 25 rpm as the spin rate for
our spacecraft, as it is practical for our experiment while employing a commonly used spin rate. In case of
a malfunction in some of the side thruster units, the remaining thrusters will still be enough to spin the s/c
within the desired range since we have 8 separate side thruster units.
    At the end of burnout of the side thrusters, the spacecraft will be spinning with a possible nutation about
the maximum moment of inertia axis (resulting from uncertainties with initial motion and possible side
thruster misalignments etc.). The excessive nutation will be damped out using a passive nutation damper.

          Attitude Determination Requirements:



                                                                                                           18
          - All attitudes (meaning that any random attitude shall be sensed)
          - Spin rate between 10 ~ 60 rpm
        - Accuracy: Spin rate must be sensed within 0.01 rad/s accuracy

         Attitude Control Requirements:
          - Accuracy: Not important
        - Range: Spin rate between 20 ~ 30 rpm
                                      o
        - Any nutation bigger than 0.1 shall be damped after spin-up maneuver using
          a nutation damper
        - Settling time for nutation shall be less than 3 hours

   1.2.2)   Normal Mode :

    This is the phase in between thrusting maneuvers. Spacecraft will be spinning without nutation.
Attitude of the spacecraft will be monitored at this phase. Ground station will provide the orbit tracking.
The spacecraft will be waiting for any command uplink and data downlink. Thus, antennas should provide
enough coverage for communication at this phase. Attitude is random and inertially fixed due to spinning.
Random attitude means that we are not too concerned about the orientation of the satellite since any
orientation will allow us to perform our mission.

        Attitude Determination Requirements:
         - Inertially fixed due to spin
         - All attitudes (orientation + spin rate)
                                                 o
        - Attitude will be monitored within 0.5 accuracy
        - Orbit will be tracked from the ground station

       Attitude Control Requirements:
        - None




   1.2.3)   Thrusting Mode :

    This is the control mode to be used during the thrusting experiments. The initial and final orientations
of the spacecraft shall be determined precisely. Velocity changes shall be monitored during experiments.
Each experiment shall be approximately 3 minutes long (thrusting experiments are not very sensitive to
small variations in burn times).

        Attitude Determination Requirements:
          - Spin rate must be sensed within ~0.01 rad/s precision.
          - Attitude must be sensed within ~0.5 deg accuracy
          (Before and after thrusting maneuver)
        - Accelerations must be sensed with 0.01 m/s2 accuracy during thrusting

       Attitude Control Requirements:
         - None.
       - The effect of the nutation damper must be insignificant during thrusting (for
           3 min). This is a reasonable assumption although the nutation damper
           will be operational during the experiments. Since the nutation is expected to be
           eliminated in less than 3 hours, we can overlook the effect of the nutation
           damper for a three minute period.

   1.2.4)   Safe (Stand-by) Mode:




                                                                                                        19
   Safe mode is the operating condition when there is a major malfunction like a thruster problem, spin-up
booster malfunction etc. The spacecraft should cut down the energy consumption to minimum and wait for
commands from the ground station. Telemetry system should function and must be kept at full power in
order to receive commands. Attitude information will be sensed and stored for downlink if possible.

         Attitude Determination Requirements:
          - If spinning, spin rate must be measured and stored
          - Attitude shall be sensed and stored if possible
          - Orbit shall be tracked from the ground station

       Attitude Control Requirements:
        - None.

    2) Orbit and Disturbance Environment
    In order to maximize the possibilities of launching as a secondary payload in any launch vehicle (which
is the main driver for determining the envelope of the satellite), the LEO was selected as the mission orbit.
Most of the Earth orbiting satellites are placed and lunched in the LEO, so that choosing this orbit regime
will maximize the possibilities of getting a ride into the orbit. The orbit selected has a mean altitude of 350
km with a nominal inclination of 40o. The altitude is somewhat smaller than usual LEO orbits due to the
de-orbiting requirement.
    The selected orbit parameters were used in the calculation of disturbance environment torque
calculations. Typical values for solar and magnetic exposures, aerodynamic and gravitational disturbances
for this specific orbit were assumed for the calculations, details of which are given in the Appendix-B. The
disturbance torques considered are: gravity gradient, solar pressure, magnetic and aerodynamic
disturbances of the Earth. The results of the calculations are, in summary:

               Disturbance Environment Disturbance Torque (N.m)
                                                        3.53380 × 10
                                                                       -7
                    Gravity Gradient
                                                        7.65525 × 10
                                                                    -8
                        Magnetic
                                                        3.77534 × 10
                                                                    -5
                     Solar Pressure
                                                        7.03584 × 10
                                                                    -6
                      Aerodynamic
                  Table VIII-2: Disturbance torques.

     As the results point out, the disturbance torques are very small and insignificant compared to the
stiffness of the spacecraft. Therefore, for the length of the mission and the possible disturbance
environment we do not need to have an active attitude control & compensation system since our
experiments do not require an active control other than the initial spin-up.
    The nutation frequencies due to the disturbance torques about the two smaller principal axes of the
spacecraft were found to be;

            ω ni |x = 39.0625rpm
            ω ni | y = 34.7222rpm

for the fixed spin rate of 25 rpm. The details of the calculations are given in Appendix B.

    3) Attitude Control Strategy
   As the experimental approach requires (this is an external requirement), the only spacecraft control will
be passive spin stabilization. This is realistic since, any spinning-thrusting vehicle has an inherent
gyroscopic stiffness and therefore attitude control systems are not activated without slowing down (if not
stopping) the spin of the spacecraft. Thus, the spacecraft is going to be a single spinner (pure spin) with
inertially fixed attitude in the LEO (Low Earth Orbit) with no attitude control.


                                                                                                           20
    During the trade studies, several options ranging from a 3-axis stabilized platform to a variable spin
control enabling platform and several combinations of other possible options were considered. However
due to the nature of the mission, having any control on the spinning platform requires a high degree of
sophistication that is beyond the reach of the mission mass, size limitations and the desired low cost
requirement.
    The decision of using no attitude control was chosen because of great simplicity and cost effectiveness.
The inertially fixed attitude due to spinning can also be used to determine the thrusting direction, albeit in a
limited sense, by specifying the time of thrusting for a specific location in orbit. Although this will not give
complete flexibility, it will be sufficient to achieve our mission goals. The de-orbiting requirement will be
achieved by the same control idea, again setting the time of initiation of the burn for the solid rocket
booster with the aim of decreasing the relative spacecraft velocity and possibly pushing it towards the
atmosphere for orbit decay and eventual reentry.

    4) Selection & Sizing of ADCS Hardware
   In light of above requirements, calculations and design decisions, the attitude determination equipment
was selected so that all the selected components are compatible with the accuracy requirements set in
“Major Requirements” section above. The specific hardware selected for the mission consists of 2 sun
sensors, a 3-axial accelerometer, a rate gyro and 2 nutation dampers. Nutation dampers will be of custom
design, and the compliance with the nutation damping requirements will be determined during testing The
specific information about each selected component is as follows:

   4.1)      Sun Sensors ( × 2) :
   Vendor: TNO TPD Space Instrumentation
   Part    : Sun Acquisition Sensor (SAS)
    •     Field of view: Hemispherical, typically +/- 97 degrees about bore sight.

    •     Accuracy: Better than +/- 0.5 degrees on bore sight for GEO missions under all environmental
          conditions and for the whole mission lifetime. Albedo will degrade the accuracy in LEO.

    •     Power consumption: No input power required.

    •     Electrical output: In current mode 0 - 30 mA. In voltage mode 0 - 200 mV. Output can be of
          individual detectors or of combinations of detectors (balance, sum).

    •     Operating temperature: Typically -100 C to +100 C.

    •     Mass/dimensions:
          Mass      : 0.155 kg
          Dimensions: 110 x 110 x 28 mm without connector, alignment cube, grounding stud or specific
          baffling.

    •     Reliability: Depend strongly on output arrangement (single cell or combination output) and
          philosophy with regard to redundancy; in SAS for GEO application outputs are redundant; in SAS
          for LEO application only single-cell type of output is redundant; failure probability for single cell
          voltage output 2.4 x 10-4 worst case (+100 degrees C) per year mission duration.

    •     Qualification status: Fully qualified and flight proven sensor.


A technical drawing and a photo of the part are given on the next page.




                                                                                                            21
Figure VIII – 1: Sun Sensor.




Figure VIII –2: Sun Sensor.




                               22
4.2)   Gyroscope ( × 1) :

Vendor: B E I -T E C H., I N C. SYSTRON DONNER INERTIAL DIVISION
Part : Model QRS11Micromachined Angular Rate Sensor




                                                                   23
Figure VIII-3: Gyroscope.




                            24
Figure VIII-4: Gyroscope assembly drawing.




                                             25
4.3)   Accelerometer ( × 1) :

Vendor: PCB PIEZOTRONICS
Part : 356B07 Low-Noise Triaxial ICP® Accelerometer




                                Figure VIII-5: Accelerometer    .


                                                               26
Figure VIII-6: Accelerometer assembly drawing
    4.4) Nutation Damper ( × 2) :
      A spacecraft undergoes periodic motion if it is disturbed from a stable equilibrium
position. For a pure spin-stabilized spacecraft, this periodic motion is rotational and is
known as nutation. Nutation occurs as a result of control and environment torques,
separation from the launch vehicle or, as in our experiment, it may result from offset
thrusters. The problem of nutation damping is that of aligning the nominal spin axis with
the angular momentum vector by dissipating the excess rotational kinetic energy
associated with the nutation motion. Also it should be noted that nutation damping is only
possible when the spacecraft is spinning about the maximum principle moment of inertia
axis, as in our design.
    Nutation motion can be damped by passive and active devices. A passive damper is
one which does not require attitude sensing, is driven by the motion itself, and dissipates
rotational kinetic energy. The frequency of the damper is intentionally kept near or equal
to the rigid body frequency so that it significantly affects the motion of the spacecraft.
    Nutation damping plays a significant role in this mission, since the validity of the
thrusting experiments will depend highly on the initial attitude of the spacecraft. Any
possible nutation prior to the thrusting experiments will cause additional thruster
misalignment to the existing intentional offset, and will reduce the validity of the
experiment.
    Available options for passive nutation dampers and their characteristics are shown
below;

Damper   Energy Dissipation                   Characteristics
Type     Mechanism
Pendulum fluid friction     sturdy, long life

Eddy
Current      eddy currents            delicate, high energy dissipation rate, variable
                                      damping constant
Ball-in-     rolling and fluid        sturdy, long life, remains tuned for different
Tube         friction                 spin rates

Viscous
Ring         fluid friction           Simple construction, long life

Table VIII-3: Nutation damper types.
  A simple comparison of the available options is given below:

                                          Eddy       Ball-in-     Viscous
                          Pendulum       Current     Tube         Ring

Simplicity                       -           -            +             +

safety                           +          +             +             +



                                                                                        28
support multiple spin
rates                          -            +             +             +
price                          +           -               +             -
Table VIII-4: Trade study for nutation dampers.

   According to table VIII-4, the ball-in-tube nutation damper was selected for our
spacecraft.

   Nutation dampers are custom built components and designs tend to change from one
spacecraft to another. A ball-in-tube damper consists of a closed, curved tube in which a
ball is allowed to roll freely. The damping caused by rolling friction may be augmented
by viscous damping if the tube is filled with a liquid. The ends of the tube may have
energy-absorbing bumpers. The damper behaves like a centrifugal pendulum and its
frequency of vibration is directly proportional to the spin rate of the body on which it is
mounted. Hence if such a damper is tuned initially, it remains tuned for different spin
rates.
    For our spacecraft we are going to have 2 ball-in-tube nutation dampers, so that we
comply with the requirements. The flexibility of the antennas will also contribute to the
energy damping so that our nutation settling time will be less than 3 hours. The
dimensions of the damper are shown on the figure below:




                      Figure VIII-7: Ball-in-tube nutation damper.

   The tube will be filled with a viscous fluid (such as engine oil), which will cause
energy damping due to friction as the ball reciprocates in the tube. During manufacturing


                                                                                        29
phase the nutation damping capability of the device will measured with simple tests and a
suitable viscous fluid will be selected to achieve the design requirements. The total mass
of a single unit was estimated to be 0.5 kg.




Burn Thrusting Scheme

    A very good way of providing directional stability for spacecraft and rockets is to spin
them about their maximum or minimum principal axes. We know from dynamic analysis
of rigid bodies that the angular momentum of a spinning rigid body will remain constant
unless acted upon an external torque.
    Due to production tolerances, small errors in the thruster location and direction are
inevitable. Therefore an axially thrusting-spinning spacecraft or rocket will experience
unwanted transverse torques during the thrusting maneuver1, as shown in figure VIII-8.
In the




                                   Figure VIII-8: Thrusting Problem

example configuration thruster offset causes a body fixed torque in to the page. We know
that such a torque will distort the angular momentum vector in inertial coordinates and
cause it to trace a circular path as it is shown in figure VIII-9. The average angular
momentum bias angle ρ is measured from the vertical and in the YZ plane, as shown in
the reference1 and it is shown that the ∆V pointing errors occur along the axis set by ρ in
axially thrusting spin-stabilized spacecraft and rockets. In the figure, Ho shows the initial
position of the angular momentum vector and the H vector is the angular momentum
during the thrusting maneuver.

1
    Longuski J.M., T. Kia, W.G. Breckenridge, “Annihilation of Angular Momentum Bias During
    Thrusting and Spinning-up Maneuvers,” The Journal of the Astronautical Sciences , Vol. 37, No.4,
    October-December 1989, pp.443-450.


                                                                                                       30
   Figure VIII-9 The Angular Momentum and Velocity Pointing Bias During Thrusting
    A remedy for the problem lies in using a two-burn scheme as proposed1 .And indeed,
this method is the simplest and probably most effective way of achieving a solution,
provided that we have an on-off type pulse thruster.
    With the conclusion that that the velocity pointing error will occur along the direction
set by the angular momentum bias, then the basic idea lies behind eliminating the angular
momentum bias. We know that for the case of spinning and axially thrusting spacecraft
with the presence of thruster offset, there is no way of eliminating the angular momentum
bias except highly sophisticated controllers. However, with the two-burn scheme
proposed by Longuski et al.1 it is possible to eliminate the time average of the angular
momentum bias. The idea is to shift the center of the circle that is traced by the angular
momentum vector to the origin of the inertial axis system as shown in figure 3 below.




  Figure VIII-10: Initial and Final Paths of the Angular Momentum Vector in the Two-
                                       Burn Scheme

   Uncompensated angular momentum vector moves on the depicted “initial angular
momentum path”. When the angular momentum vector comes to the point A in the figure
VIII-10, along the solid line, the thruster is turned off (coasting) and consequently the
angular momentum vector stops moving since there is no external torques acting on the
spacecraft. The A point corresponds to a 60o rotation of the spacecraft and the time
required to arrive this point can be found simply from the relation t b = π / 3Ω , where, tb
denotes 1st burn time and Ω is the spin rate. We note that if we define θ as the spacecraft
rotation angle, the time relation of it is simply θ = Ω ⋅ t
   After the first ignition, the thruster is kept off for a period of “coast time” t c = π / 3Ω
and after that it is ignited again for the rest of the maneuver. In the end this causes the
angular momentum vector to fall in the track of the final path shown in dashed lines,


                                                                                            31
which has an average angular momentum bias of 0 degrees. The resulting behavior of the
velocity pointing error and angular momentum path can be obtained numerically using
the designed spacecraft parameters (MOI, thrust and an intentional offset value of 5 cm).
The promise of the two-burn scheme is evident from the plots given for numerical
simulations. Simulations were performed for 120 seconds (2 minutes).




                                                                                      32
 Figure VIII-11: Simulation of Angular Momentum Path and Velocity Path without the
                                 Two-Burn Scheme




Figure VIII-12: Non-dimensional velocity time history (the last plot is the dimensional z-
                      velocity) without the Two-Burn Scheme




                                                                                       33
Figure VIII-13: Dimensional time history of the position vector without the Two-Burn
                                      Scheme




                                                                                   34
Figure VIII-14: Simulation of Angular Momentum Path and Velocity Path with the Two-
                                    Burn Scheme




                                                                                35
Figure VIII-15: Non-dimensional velocity time history (the last plot is the dimensional z-
                        velocity) with the Two-Burn Scheme




   Figure VIII-16: Dimensional time history of the position vector with the Two-Burn
                                       Scheme

   According to the numerical results, the spacecraft departed about 0.45 m laterally
during 2 minute thrusting using the two-burn scheme as compared to the approximately 5
m lateral departure of the single-burn case. So, these are some of the results that we want
to demonstrate with our experiments.




                                                                                        36
IX. Communication and Data Handling

1) Control Modes

1.1) Transmit Mode:

       This mode is commanded when an experiment has been performed and
the data is ready to be down-linked. The processor shall be commanded to
choose from which of the data for the three experiments shall be down-linked.
Along with the data, the battery state of charge values and temp sensor data
shall also be down-linked before and after data transmission. During this time,
the receiver shall also be on. This will allow commands to be uplinked if
problems occur in the transmission.

1.2) Normal mode:

       This mode is the default mode after acquisition of signal. The transmitter
shall be off during this time, and the receiver shall be on.

1.3) Acquisition/contingency mode:

       This mode serves as both the initial signal acquisition mode and the
contingency mode. The spacecraft transmits a beacon signal allowing the
ground station to track it before sending first command. This is also a low power
mode, which will still allow the ground station to track the spacecraft.


2) Link Budget

        The design requirements assume that the altitude, h, of the satellite is 350
km at an inclination of 40 degrees. From orbit calculations (see Appendix), the
total time of the longest pass is 13 minutes, which occurs at least twice a day.
The requirement to down-link data was found to be 1200bits/sec. Each
experiment lasts 120 seconds. Each sample of accelerometer data will require at
most 1 byte per axis (3 bytes total per sample); likewise with the gyro data.
Using a sampling period of .01 seconds, the total amount of data for each
experiment is 576,000 bits. Including a margin of 5%, the total increases to
604,800 bits per experiment. Using the data rate of 1200bps, it will take
approximately 8.4 minutes of continuous transmission to down-link 1 experiment.
Total on-board data storage for three experiments is then 1,814,400 bits (226.8
Kbytes).
        Table 1 shows the link budget parameters for the satellite. Some of the
equations used are located in the Appendix.
                                      Units    Uplink       downlink
            Frequency                 MHz             150          435
            transmitter power         Watts            50            2


                                                                                 37
           transmitter power           dBW            16.99     3.01
           transmitter line loss       dB                 -1       -1
           transmit antenna length meters            0.6667   0.1667
           transmit antenna gain       dBi                14        2
           equiv. isotropic radiated
           power                       dBW            29.99     4.01
           Propagation path length km                   350      350
           space loss                  dB           -146.85 -156.101
           propagation &
           polarization loss           dB               -0.3     -0.3
           receive antenna length      meters            0.5        2
           receive antenna gain        dBi                 2       14
           system noise
           temperature                 K                614      221
           data rate                   bps              400     1200
           Eb/No                       dB        59.537716 35.97326
           C/No                        dB-Hz 85.558316 66.76508
           bit error rate                         1.00E-05 1.00E-05
           required Eb/No              dB                2.5      2.5
           Implementation loss         dB                 -2       -2
           Margin                      dB        55.037716 31.47326
                              Table IX-1: Link Budget



3) Hardware Sizing, Commands, & Requirements

       Much of the hardware chosen was based on the fact that they were used
on previous successful spacecraft. Figure 1 shows the top-level block diagram
for the telemetry, communications, command and data handling subsystem. All
the power consumption and mass data is located in the budget section of this
document.




                                                                          38
Figure IX-1: Block diagram for telemetry, communications, command, and data

                               handling subsystem

      The processor samples the values of temperature sensors, sun sensors,
and batteries to be made available for telemetry, and samples the values of the
gyro and accelerometer, which is stored in the data module. Table 2 shows the
command list that will be defined in the processor’s ROM.

Command             Mode                    Description
1. Spin-up          normal                  All sensors are on. Processor
thrusters                                   sends command to fire spin-
                                            up thrusters.
2. Perform          normal                  All sensors are on. Processor
experiment #1                               sends command to fire cold
                                            gas thruster for experiment #1
3. Perform          normal                  All sensors are on. Processor
experiment #2                               sends command to fire cold
                                            gas thruster for experiment #2
4. Perform          normal                  All sensors are on. Processor
experiment #3                               sends command to fire cold
                                            gas thruster for experiment #3
5. Downlink data    transmit                All sensors are on. Processor
from experiment                             routes data from experiment
#1                                          #1 and downlinks with
                                            telemetry.
6. Downlink data    transmit                All sensors are on. Processor
from experiment                             routes data from experiment
#2                                          #2 and downlinks with


                                                                             39
                                            telemetry.

7. Downlink data    transmit                All sensors are on. Processor
from experiment                             routes data from experiment
#3                                          #3 and downlinks with
                                            telemetry.
8. Abort downlink   acquisition/contingency All sensors are on.
                                            Transmitter quits sending
                                            data, and beacon is
                                            transmitted.
9. Command to       acquisition/contingency Temp sensors and battery
Power-                                      voltage monitors are
safe/overheat                               streaming data to processor.
mode                                        All other sensors are off.
                                            Once downlink telemetry
                                            command is issued, temp
                                            sensor and battery state of
                                            charge data will be made
                                            available through telemetry.
10. Command to      acquisition/contingency Temperature sensors are
Low temperature                             streaming data to processor.
mode                                        All other sensors are offOnce
                                            downlink telemetry command
                                            is issued, temp sensor data
                                            will be made available
                                            through telemetry
11. Command to      normal                  All sensors commanded on.
Normal mode                                 Transmitter is shut off.
12. Downlink        transmit                Chosen sensors are on.
Telemetry                                   Battery state of charge,
                                            temperature sensor data,
                                            gyro data, accelerometer data
                                            and sun sensor data are
                                            made available through
                                            telemetry.
                           Table IX-2: Command List

Hardware Choice:

  A.) Processor/data module:

     The processor/data module was chosen from the Citizen Explorer space-
     qualified board. The CoreModule 3SXi board built by Ampro Computers,
     Inc. utilizes a 25MHz 386SX-compatible CPU. The 4 Megabyte surface-
     mounted memory module supplies more than enough storage for the 3
     experiments (226.8 Kbytes).    Operating temperatures are 0º-70ºC


                                                                            40
      standard or -40º-85º C specially ordered. Figure 2 shows a picture of the
      board.




                    Figure IX-2: Processor board with data module

   B.) Quarter-wavelength monopole antenna:

     Monopole, omni-directional antennae were chosen since there is no active
attitude control. One pair of antennae is used for transmitting (69 cm
wavelength), and one is used for receiving (2 meter wavelength). Both of the
frequencies for transmitting and receiving were chosen because of the
requirement that the satellite be able to communicate with the Purdue University
ground station. Each pair of antennae shall be mounted on opposing corners of
the satellite. The antennae shall be made of unpainted tape measures that are
cut to a quarter of the wavelength. This follows the design of PCsat built by the
Navy.


   C.) Terminal node controller (TNC), transmitter, and receiver:

   These were chosen also based on the design of PCsat. The terminal node
controller, the KWM-1200plus (see Figure3), built by Kantronics, shall be used to
package the data per the AX.25 amateur radio protocol. It is capable of the
required 1200bps data rate for down-linking data. The transmitter (Figure 4) and
receiver (Figure 5) are also off-the-shelf amateur radio parts built by Hamtronics.
They were chosen based on the supportable frequencies (435MHz down-link,
150 MHz up-link).




                                                                                41
                 Figure IX-3: KWM-1200plus Terminal Node Controller



                     Figure IX-4: Hamtronics T304 Transmitter board



                      Figure IX-5: Hamtronics R304 Receiver board




X. Thermal Control Subsystem

X.1 Overview

 The thermal control subsystem (TCS) is an integral part of every spacecraft. It's
 purpose is to maintain all the components of a spacecraft within their respective
 temperature limits. There are several different sources of thermal energy acting on
 a spacecraft; solar radiation, albedo, earth emitted infrared, and heat generated by
 onboard equipment. Therefore, the thermal control subsystem is different for every
 spacecraft. In general, there are two types of TCS, passive and active. A passive
 system relies on conductive and radiative heat paths and has no moving parts or
 electrical power input. An active system is used in addition to the passive system
 when passive system is not adequate, for example, on manned missions. Active
 systems rely on pumps, thermostats, and heaters, use moving parts, and require
   electrical power.

   Based on the calculations contained in this section, it is concluded that soley
   insulation is needed in the satellite’s thermal control design, resulting in a passive
   thermal system. The satellite’s outer surface (0.6 m2) insulation will consist of 0.5
   mil aluminized Kapton/ITO and thin nets of Dacron. The resulting equilibrium
   temperature during eclipse, will now be within the satellite’s temperature limits.




                                                                                        42
Type                                   Kapton/ITO 0.5 mil aluminized
Absorptivity                           0.34
Emissivity                             0.55
Area Density                           7 g/m2
Area                                   0.6 m2
Total Weight                           .0042 kg
Total Cost                             $30
                 Table X-1: Thermal Control Design Specifications




Fig.(X-1) below, gives an overview of the design process for the thermal control
system.




                                                                                   43
Figure X-1: Design Process for Thermal Control System




X.2 Temperature Ranges

   The following table shows the operating temperature ranges for all of the satellite’s
   components.




                                                                                     44
Category                         Description                     Tmin (°C)    Tmax (°C)
Spacecraft Internal Units        Worst case envelope             7            50

Telecommunications               Payload Units                   -10          50

Onboard Computer                                                 -10          50

Telemetry & Command Units                                        -10          50
Electrical Power                 Batteries
                                 Power Control Unit
Attitude Control                 Sun Sensors                     -100         100

Propulsion                       Tanks, filters, valves, lines   7            55
                                 Thrusters                       7            55
Harness                          Spacecraft internal             -15          55

Thermal Control                  Multilayer Insulation (MLI)     -160        250

Structures                       Nonalignment critical           -45          65

Antennas                         TT&C                            -65          95

       Table X-2: Temperature Operating Ranges for Satellite Components


X.3 Preliminary Thermal Performance

   Thermal analysis, found in Table X-3 below, was performed based on the spherical
   satellite analysis outlined in SMAD III. Equations used, to calculate the values, are
   listed in Appendix E.




                     Figure X-2: Thermal Radiation Environment




                                                                                     45
   No. Item           Symbol Value        Units                 Source         Comments
   1     Surface      A            0.6        m2                  satellite    satellite is
         Area                                                                  .3x.3x.35 m3
   2     Diameter of D           0.437         m                  Eq. (E-1)
         sphere
         which has
         equal
         surface area
   3     Max. power QW              12         W                   satellite   given
         produced
   4     Min. power QW              9          W                   satellite   given
         produced
   5     Altitude     H           350         km                               given
   6     Radiaus of   RE          6378        km                               given
         Earth
   7     Angular      ρ          1.247        rad                 Eq.(E-2)
         radius of
         Earth
   8     Albedo       Ka         0.978         --                 Eq. (E-3)
         correction
   9     Max. Earth qI             258      W⋅m-2                Fig. (X-2)    Use for worst-
         IR emission                                                           case hot
         at surface
   10 Min. Earth      qI           216      W⋅m-2                Fig. (X-2)    Use for worst-
         IR emission                                                           case cold
         at surface
   11 Direct solar GS             1418      W⋅m-2                Fig. (X-2)    Use max. value
         flux
   12 Albedo          a           0.35         %                Fig. (X-2) Use max. value
   13 Emissivity      ε           0.92         --               White Paint
   14 Absorptivity α              0.25         --               White Paint
   15 Worst case      TMAX         -10        °C                 Eq. (E-5)
         hot temp.
   16 Worst case      TMIN         -73        °C                  Eq. (E-6)
         cold temp.
   17 Upper temp. TU                45        °C                 Table X-1     Assume 5°C
         limit                                                                 thermal margin
   18 Lower           TL            12        °C                 Table X-1     Assume 5°C
         temp. limit                                                           thermal margin
Table X-3: Preliminary Thermal Performance Estimates



The values found in Table X-3 for TMAX and TMIN appear to be significantly lower than
the expected temperatures seen by the satellite. It is concluded that the spherical model



                                                                                        46
analysis of the satellite is inaccurate for such a small satellite so close the Earth. As a
solution to this discrepancy, historical TMAX and TMIN data taken from the FalconSat2 (an
existing satellite with relatively the same size and altitude as this satellite) will be used to
complete a more accurate analysis.

Therefore,
                        TU = 45o C              TMAX = 12 o C ü
                                                              ï from FalconSat2
                                                              ý
                        TL = 12 o C             TMIN = −3 C ï
                                                         o
                                                              þ

  It is seen that the worst case hot temperature (12°C) lies within the upper and lower
  temperature limits of the satellite, while the worst-case cold temperature (-3°C) falls
  below the lowest allowable operating temperature. It will, therefore, be necessary to
  use a thermal control system in order to maintain an equilibrium temperature of at least
  12°C, during eclipse.



X.4 Choosing Coating/Insulation Material

  It must first be determined how much energy needs to be dissipated. Solving the
  energy balance, Eq.(E-4), for heat dissipated yields:

                                Qdis = −120.6 W

Therefore, 120.6 W must be dissipated in order to achieve thermal equilibrium. Consider
a satellite which must dissipate heat. Qdis can be broken down into the sum of Q of the
insulation and Q of the radiator. Assuming no radiator, the coating emissivity required to
maintain the satellite at an equilibrium temperature of 12°C (lower temperature limit) is:

                                        ε = 0.55

The following table gives the thermal properties for various types of coating material:

             Material              Solar Absorptivity                 Infrared Emissivity
                                           α                                   ε
  White Apoxy                  0.248                              0.924
  Black Paint                  0.975                              0.874
  Aluminized Teflon            0.163                              0.8
  Silvered Teflon              0.08                               0.66
  Kapton/ITO      0.5       mm 0.34                               0.55
  aluminized
  Aluminum tape                  0.12                       0.06
                               Table X-4: Radiation Properties




                                                                                              47
Aluminized Kapton (0.5 mm) possesses the exact required emissivity value, and will
therefore be chosen as the insulation material. This will yield an equilibrium
temperature of 12°C during eclipse, which is an acceptable value for the satellite.

The aluminized Kapton will cover the entire outer surface of the satellite, and will
therefore have a total mass of 4.2 grams. A conservative cost estimate for the coating
is $30.




                                                                                   48
XI. Structure and Mechanisms




                               49
XII. Propulsion

                                    Cold Gas Thruster (CG)
        a. Major Requirements - The requirements as stated in the systems requirement
document (SRD) are the cold gas thruster providing approximately 1.0 Newton of thrust
for a single burn and two-burn maneuver, which combined have a total velocity change
of 6.0 meters/second. Other requirements that became factor are the size of tank, because
the spacecraft was space limited.
        b. Concept of Operation - After spacecraft is spun up using the spin-up thrusters
data will be sent to the ground to gather necessary information on attitude prior to the
first burn. After this collection the computer will send an electronic signal to the on/off
valve to open for 120 seconds then shut send another signal to close the on/off valve.
After data has been sent for the burn and data has been sent prior to the next burn after
the spacecraft has been allowed to stabilize. Again the computer will send a signal to
open the on/off valve, close the on/off valve for the already mentioned first part of the
two burn scheme then open again for the rest of the burn then close again. This
completes the operation of the (CG) thruster and any leftover propellant in tank could be
used to further de-orbit spacecraft after the solid rocket motor fires.

    Gas                                N2        Gas (kg)                          0.412
    Tank                            Sphere       Tank (kg)                          1.76
             Tank Material         D6aC Steel    Pressure Regulator (kg)            0.23
     Overall Diameter (cm)           12.52       On/Off Valve (kg)                  0.46
           Thickness (cm)             0.49       Nozzle (kg)                       0.012
                                                 Piping (kg)                      0.00146
    Pressure Regulator            TESCOM         Total (kg)                       2.87546
             Part Number        BB-13PL3KEB2
            Diameter (cm)            4.42               Table VII-2: Cold Gas Component Mass
              Height (cm)            5.72

    On/Off Valve          Metal W ork Pneumatic
             Part Number        PIV22I0SNC
            Diameter (cm)           3.45
              Length (cm)           3.00

    Nozzle                            Cone
           Nozzle Material           2219-Al
               Length (cm)            2.00
           Thickness (cm)             0.50
         Cone Angle (deg)             5.25
      Throat Diameter (cm)            0.08
        Exit Diameter (cm)            0.48

    Piping                           Copper
         Total Length (cm)             1.0
            Diameter (cm)            0.3175

   Table VII-1: Cold Gas Component Dimensions




                                                                                        50
                          Figure VII-1: Cold Gas Diagram System


c. Component Selection and Sizing - Table VII-1 gives dimensions of all components
while table VII-2 gives mass of all components and Figure VII-1 gives the schematic
of the cold gas system. The selection of nitrogen gas was determined because of its
low reactivity, safe, performance, and zero freezing due to water droplets. The design
and use of nitrogen provides 0.95 Newton of thrust, which is within 5% of the 1.0
Newton thrust desired in the SRD. The tank material was determined by comparing
various materials and consulting how much room was available in the spacecraft for
the tank. The D6aC material provided the smallest case thickness and mass for the
tank. The pressure regulator was chosen for its ability to handle the pressures; ability
to set pressure drop through system so after testing can adjust for pressure drops, and
being small. Figure VII-2 shows the appearance and workings of the pressure
regulator courtesy of Tescom Corporation.




                                                                                     51
                                   Fig VII-2: Functional Schematic
                                   of Pressure Regulator
The on/off valve was selected due to its ability to turn off or on by electric signal, light,
small, small power consumption of only 0.9 watts during operation, and able to get the
job done. The nozzle was designed for simplicity and the limiting factor does not come
from firing but from launch where it supports the rest of the system as the only
connection it has to the rest of the spacecraft. The equations and method for solving the
component selection and sizing problem can be found in the appendix.
d. Propellant Budget -
                                            1-Burn            2-Burn
                           mp (kg)           0.199             0.199
                            mr (kg)         0.00656           0.00656
                            mt (kg)          0.206             0.206
                           ∆V (m/s)           3.58              3.58
                         SRD ∆V (m/s)          3                 3
                          Margin (%)         19.34             19.34

                           Table VII-3: Cold Gas Thruster Propellant Budget

e. Trade Studies/Comparisons -
                Gas       mt (kg)     rtank(cm)     F (N)      Isp (sec)     ∆ V (m/s)
                He         0.18         10.74       0.98        169.09          7.38
                Air        0.42          5.74       0.95         71.86          7.18
                 N2        0.41          5.77       0.95         72.81          7.16
                CO2         0.46        5.25        0.92         62.87          6.96
                               Table VII-4: Propellant Gas Comparison

                Material  ρ (kg/m^3)       Ftu (GPa)        tcs (cm)       mtank (kg)
               D6aC Steel    7830             1.52            0.49           1.76
                2219 Al      2800             0.41            1.82           2.86
                Titanium     4460             1.23            0.61           1.26
                Graphite     1550             1.34            0.56           0.40

                             Table VII-5: Tank Material Comparison for N2 Gas



                             Solid Rocket Motor (SRM)
a. Major Requirements - The solid rocket motor as stated by the SRD is required to
provide approximately 43.3 m/s change of velocity while providing a trapezoidal thrust


                                                                                            52
scheme and able to fit within the space limitation. Obtaining a low maximum thrust is a
secondary objective to accomplishing the above two stated objectives.
b. Concept of Operations - After the two burn schemes and the spacecraft has stabilized
an electronic signal from the computer shall let the capacitor discharge itself igniting the
Pyrogen igniter. The Pyrogen igniter ignites the propellant grain and discharges the
nozzle plug. The propellant burns in the trapezoidal scheme, as depicted by figure VII-3,
due to the geometry of the casing until all propellant is gone and thus ending the SRM
operation.




                                   Figure VII-3: Thrust Profile of SRM

c. Component Selection and Sizing - Table VII-6 illustrates the SRM’s component
dimensions and Table VII-7 displays the mass breakdown of the component and figure
VII-4 shows the diagram of the SRM.




                                                                                          53
Propellant                     TP-H-3340
                                                           Propellant (kg)       1.059
              Aluminum           18%
                                                           Tank (kg)             0.192
 Ammonium Perchlorate            71%
                                                           Insulation (kg)       0.207
     Hydroxy-terminated          11%
                                                           Nozzle (kg)           0.028
  Polybutadiene (HTPB)
                                                           Igniter (kg)          0.057
Tank                           Cylinder w/
                                                           Plug (kg)             0.005
                              Hemispherical
                                                           Total (kg)            1.548
                                End Caps
                Material       D6aC Steel            Table VII-7: Solid Rocket Motor Component Mass
   Overall Diameter (cm)          11.85
             Length (cm)          7.06
         Thickness (cm)            0.1
Insulation                       Ablative
                Material     Carbon/Phenolic
         Thickness (cm)            0.62

Nozzle                             Cone
         Material (Body)       D6aC Steel
        Material (Insert)   Pyrolytic Graphite
            Length (cm)            0.21
       Cone Angle (deg)            12.0
   Throat Diameter (cm)             1.0
     Exit Diameter (cm)            1.09
     Plug Diameter (cm)            1.01
    Table VII-6: Solid Rocket Motor Component
                    Dimensions

                                                        Figure VII-4: Diagram of SRM

The propellant selection was chosen for its common use, low cost, and ability to be
obtained by Purdue University. It had to have the propellant grain design of end burning,
because only possible way to have a low thrust and be able to accomplish the task of the
trapezoidal thrust scheme. The casing is to be made of D6aC steel, because of its high
strength and common usage in solid rocket motors, such as the space shuttle solid rocket
boosters. The insulation material will be made of carbon/phenolic, because of its
relatively low erosion rate. The low erosion rate is needed along with minimum char
build-up to provide the desired thrust and to prevent blockage of the throat during
thrusting. The nozzle is to have D6aC steel as the body with pyrolytic graphite insert in
the throat region due to the high temperatures and the necessity that the throat erosion be
kept to a minimum so that the trapezoidal thrust is possible. The pyrogen igniter was
selected because of minimum power input and common usage. Finally a nozzle plug is
needed to prevent debris from entering the rocket while the cold gas thruster performing
its experiments.

d. Propellant Budget –




                                                                                          54
                                    mp (kg)            1.059
                                     mr (kg)            0.0
                                     mt (kg)           1.059
                                    ∆V (m/s)           43.3
                                  SRD ∆V (m/s)         43.3
                                   Margin (%)           0.0

                            Table VII-8: Solid Rocket Motor Propellant Budget


e. Trade Studies/Comparisons -

               Material     ρ (kg/m^3)     Ftu (GPa)       tcs (cm)          mtank (kg)
             2219-Al           2800          0.413          0.0321            0.0219
             Titanium          4460          1.230          0.0108            0.0117
             D6aC Steel        7830          1.520          0.0087            0.0166
             4130 Steel        7830          0.862          0.0154            0.0293
             Graphite          1550          1.343          0.0099            0.0037
             Kevlar            1380          0.964          0.0138            0.0046
             Fiberglass        1990          1.100          0.0121            0.0058

                             Table VII-9: Solid Rocket Motor Case Material



                Material           Erosion Rate (cm/s)         tinsul (cm)        minsul (kg)
       Pyrolytic Graphite                  0.05                   0.232             0.119
       Polycrystalline Graphite            0.10                   0.464             0.188
       3-D Carbon/Carbon                   0.10                   0.464             0.210
       Carbon/Phenolic                     0.18                   0.835             0.288
       Graphite/Phenolic                   0.28                   1.298             0.467
       Silica/Phenolic                     1.30                   6.027             3.699
       Glass/Phenolic                      1.50                   6.955             5.040
       Paper/Phenolic                      1.90                   8.809             4.463
                           Table VII-10: Insulation for Solid Rocket Ablative Material




                                                                                                55
   XIII. Summary of Spacecraft


a) Requirement Compliance

       Design of the spacecraft and all the subsystems are based major design

requirements given in section III of the report. The specific requirements on each

subsystem level and the corresponding design decisions were explained in detail within

subsystem overviews.

       In summary, our designed spacecraft complies with most of the subsystem level

requirements and all of the major mission requirements, while allowing for some

contingency margins. Compliance with some subsystem level requirements couldn’t be

determined within the scope of the project objectives, as these require more sophisticated,

in-depth study. Simplified analyses were used for such complicated decisions.

b) Cost Estimation

                  Power                                         $ 2,000
                  ADCS                                         $ 44,550
   Communications and Data Handling                              $ 430
                 Thermal                                          $ 30
        Structure and Mechanisms                                 $ 200
                Propulsion                                       $ 780
          Total for Production                                 $ 47,990
                  Launch                                        200,000
                   Total                                       $ 247,990
Table XIII-1: Cost estimation assuming labor is at no cost.

c) Areas Needing Further Design Consideration

       1. Nutation Damper Testing.
       2. Venting of Sulfur Dioxide during battery short.
       3. Construction of SRM plug.




                                                                                        56
 XIV. References
[1] Longuski J.M., T. Kia, W.G. Breckenridge, “Annihilation of Angular Momentum
Bias During Thrusting and Spinning-up Maneuvers,” The Journal of the Astronautical
Sciences , Vol. 37, No.4, October-December 1989, pp.443-450.

[2] Javorsek II, D. and J.M. Longuski, “Velocity pointing errors associated with spinning
thrusting spacecraft,” Journal of Spacecraft and Rockets, Vol. 37, No. 3 , May-June
2000, pp.359-365

[3] Wertz, R. J., and W. J. Larson, Space Mission Analysis and Design, 3rd Ed., Kluwer
Academic Publishers, Microcosm Press, El Segundo CA 1999.

[4] Wertz, James R., Spacecraft Attitude Determination and Control, D. Reidel
Publishing Company, Dordrecht, Holland,1984.

[5] Chobotov, Vladimir A., Spacecraft Attitude Dynamics and Control, Krieger
Publishing Company, Malabar-Florida, 1991.

[6] Longuski, James M., AAE 507 Principles Of Dynamics, Class Notes, Fall 2001
semester, Purdue University, West Lafayette, 2001.

[7] Greenwood, D.T., Principles of Dynamics, 2nd edition, Prentice-Hall,1988

[8] Humble, R. W., Henry, G. N., and Larson, W. J.1995. Space Propulsion Analysis and
Design, 1st ed-Revised. New York: Primis Custom Publishing

[9] Javorsek, Daniel II, and Longuski, J., "Velocity Pointing Errors Associated with
Spinning Thrusting Spacecraft," Journal of Spacecraft and Rockets, Vol. 37, No.3, 2000,
pp. 359-365.


Internet References

[10] http://www.hdssystems.com/LithiumBattery.htm
[11] http://www.firefox-fx.com/
[12] http://www.tescom.com
[13]
http://www.globalspec.com/Frames?URL=%2FSpecSearch%2FMatchingSuppliers%3
FQID%3D1413807%26Comp%3D1412%26state%3Dspecsearchable
[14] www.ampro.com
[15] www.kantronics.com
[16] www.hamtronics.com




                                                                                      57
Appendix A: QFD
                                 Ground Station
                             Power consumption                                                                                                                                                                                                   `
                                 accelorometers
                                   Fuel quantity
                     Angular Momentum History
                              Comm Architecture                                                                                                                                                                                --
                                             Life                                                                                                                                                                              ++
                                 Loss of Velocity
                                      Spin Rate
                                    C.M. History
                                        S/C Size                                                                                    -                                                        ++  +
                                    Liftoff Mass    ++                                                                            + -                                                        ++  +




                                                                                                                                                                                                                                                              Do Not Delete
               Direction of improvement ( + or -) ê ê                                                                             ê é                                                        ê é ê




                                                                                                                                                                                                                                                          Do Not Delete
                                                         Launch Mission                                                                                                                     Payload
                            HOW




                                                                                                                                                                 Angular Momentum History
                                            IMPORTANCE
        WHAT




                                                                                                                                                                                                                             Power consumption
                                                                                                                                             Comm Architecture
                                                                                                               Loss of Velocity




                                                                                                                                                                                                            accelorometers


                                                                                                                                                                                                                                                 Ground Station
                                                                                                                                                                                            Fuel quantity
                                                                                    C.M. History
                                                         Liftoff Mass




                                                                                                   Spin Rate
                                                                        S/C Size




Export to Next Phase = *                                                                                                          Life
   Mission
       Burn Test                            20                                          9             9              9             9                                      9 9                                    9                 3
       Attitude Determination               20                                          9             9              9                                                     9 1                                                     3
       Command and Data Handling            20 3                                                                                                   9                                                             9                 9                  9
       De-Orbit after mission               10                                          3                            1             3                                                             9                                 3
   Cost
       Quick Assembly                        5 1                           3                                                                       1
       Launch Flexibility                    8 9                           9                          1                                                                                                                                               9
       Low Cost                             17 9                           9                                                       9               9                                             3               1                 9                  3
                                                           290.0
                                                                         240.0
                                                                                      390.0
                                                                                                     368.0
                                                                                                                  370.0
                                                                                                                                  363.0
                                                                                                                                                 338.0
                                                                                                                                                                      360.0
                                                                                                                                                                                               341.0
                                                                                                                                                                                                               377.0
                                                                                                                                                                                                                                 483.0
                                                                                                                                                                                                                                                    303.0



                    ABSOLUTE IMPORTANCE
                                                                                                                                                                                                                                 11%
                                                           7%
                                                                         6%
                                                                                      9%
                                                                                                     9%
                                                                                                                  9%
                                                                                                                                  9%
                                                                                                                                                 8%
                                                                                                                                                                      9%
                                                                                                                                                                                               8%
                                                                                                                                                                                                               9%


                                                                                                                                                                                                                                                    7%




                     RELATIVE IMPORTANCE
                                        RANK 11 12                                           2           5                 4          6                   9                        7                 8                3                   1 10
                                                                         30X30X35




                                                                                                                                                                                                               high accu
                                                                                                                                  3 months
                                                                                      constant




                                                                                                                                                 reliable
                                                                                                     20 rpm
                                                           40 kg




                                                                                                                                                                                               20 kg


                                                                                                                                                                                                                                 50 W




                             TARGET VALUE




                                                                                                                                                                                                                                                 58
Appendix B: ADCS

Disturbance Environment Calculations

1) Gravity Gradient:

Type of disturbance: Cyclic (since spacecraft is inertially fixed)
Influenced by: - spacecraft orientation
               - orbital altitude
Formula:
                         3µ
                  Tg =        I z − I y sin(2θ )                     (1.1)
                        2R3

where, Tg = maximum gravity torque,
       R       = orbit radius,
       Iz , Iy = spacecraft moment of inertias,
       µ       = gravitational constant for Earth,
       θ       = maximum deviation of the Z – axis from local vertical

Parameters are:
     Altitude = 350 km
   Þ R = 350 km + REarth
        = 350 km + 6378km = 6728 km Þ R = 6728 km                    (1.2)

   Spacecraft moments of inertia were first calculated using a cuboid model given below
for initial iterations. Later on the design process, using the actual size and the masses of
selected hardware, the moment of inertias were calculated using solid modeling in the
Unigraphics CAD Package. The moments of inertias were generated by the software,
based on the location and masses of the each component.




The resulting moments of inertias were found to be (in the principal directions shown
above)
       I x = 0.2995 kg ⋅ m2
        I y = 0.3488 kg ⋅ m2
        I z = 0.3890 kg ⋅ m 2



                                                                                         59
Since the spacecraft is a single spinner, as dynamics of the motion points out, spinning
about the maximum moment of inertia will be the only stable spinning motion. What’s
more, having the maximum moment of inertia as big as possible compared to inertias
about the other axes provides better stability. Our mass budget (most of the mass values
were calculated using the actual component masses) indicates that we have
approximately % 40 margin in our aimed mass budget. Thus in order to enhance the
stability properties of the spacecraft we are going to add additional masses to increase Iz
moment of inertia. Since we have a big margin, we can have as much as 0.4 kg.m2
increase in our Iz moment of inertia but to stay on the safe side we are going to assume a
smaller increase in Iz moment with added masses at the corners. This will account for
some uncertainties during actual manufacturing of the spacecraft. With the modifications,
the principal moment of inertia values used in calculation are as follows

          I x = 0.32 kg ⋅ m 2
          I y = 0.36 kg ⋅ m 2                        (1.3)
          I z = 0.50 kg ⋅ m 2

The other parameters in equation (1.1) are given next:

θ = 45o (worst case)                                 (1.4)
µ = 3.986 × 1014 m3/s2                               (1.5)

Thus having defined all the parameters in equation (1.1) we can compute Tg as follows:

       3 × (3.986 ×1014 m3 / s 2 )
Tg =                               0.5 − 0.32kg ⋅ m 2 × sin(90o )
          2 × (6728 ×103 m)3

Þ Tg = 3.5338 ×10−7 N ⋅ m                            (1.6)



2) Solar Radiation:

Type of disturbance: Cyclic (since spacecraft is inertially fixed)
Influenced by: - spacecraft geometry
               - spacecraft surface reflectivity
               - center of gravity location
Formula:
                  Tsp = F (C ps − C g )       (2.1)
                           Fs
           where,     F=      As (1 + q ) cos i      (2.2)
                           C

The parameters are defined below:



                                                                                        60
Tsp   = solar radiation pressure (torque),
Fs    = solar constant, (= 1367 W/m2)
C     = speed of light, (= 3 × 108 m/s)
As    = surface area,
Csp   = location of the center of solar pressure,
Cg    = center of gravity location,
q     = surface reflectance (ranges between 0~1),
i     = angle of incidence to the sun

We set these parameters as follows for the worst-case conditions:
As ≅ 0.14 m2 ( ≅ 0.3 2 × 0.35m2 - the worst possible case)
q = 0.6 (semi reflective)
cos i = 1 (i = 0 worst case)
Csp - Cg ≅ 0.075 m (this is an approximation based in the fact that the spacecraft is
highly symmetric and the color pattern and surface properties do not vary significantly)

Thus from equation (2.1) and (2.2) we calculate as follows:

      1367 W
F=                 (       )
              m 2 × 0.14m 2 × (1 + 0.6) × cos(0o )
      3 × 108 m                                               (2.3)
                s
Þ F = 1.0207 × 10−6 N

Thus,

Tsp = (1.0207 × 10−6 ) × (0.075m)
                                                              (2.4)
Þ Tsp = 7.65525 ×10−8 N ⋅ m


3) Magnetic Field:

Type of disturbance: Cyclic (since spacecraft is inertially fixed)
Influenced by: - orbit altitude
                - residual spacecraft magnetic dipole
                - orbit inclination
Formula:
        Tm = D ⋅ B                                             (3.1)
where, D is the residual dipole of the vehicle in amp ⋅ turn ⋅ m2   ( A ⋅ m ) and,
                                                                          2


           2M
         B=            (for polar orbit with i = 90o)
            R3
           M
         B= 3          (for equatorial orbit with i = 0o)
           R



                                                                                     61
Since our inclination is i = 40o, by linear interpolation we find the corresponding number
for our orbit:
             13M
        B=                                      (3.2)     (Exact using linear interpolation)
              9R3
In the above equation M is the magnetic moment of the Earth and measured as;
        M = 7.96 × 1015 [tesla ⋅ m2]
and, R is the radius from dipole (Earth) center to spacecraft in [m] . Thus we calculate
for R = 6728 km, and for D = 1 A ⋅ m2 (this is a common value for small-sized,
uncompensated vehicle);

                          æ 13 × (7.96 ×1015 tesla ⋅ m3 ) ö
       TM = (1A ⋅ m 2 ) × ç                               ÷
                          è     9 × (6728 ×103 m)3        ø
        Þ TM = 3.77534 ×10−5 N ⋅ m                  (3.3)


4) Aerodynamic Disturbance:

Type of disturbance: Variable (since spacecraft is inertially fixed)
Influenced by: - orbit altitude
               - spacecraft geometry
               - center of gravity location
Formula:
                  Ta = F ⋅ (C pa − Cg ) = F ⋅ L      (4.1)
         where,    F = 0.5 ⋅ é ρ ⋅ Cd ⋅ A ⋅ V 2 ù
                             ë                  û             (4.2)

The parameters are defined below:
Ta = aerodynamic torque,
F    = aerodynamic force,
ρ    = atmospheric density
Cd = drag coefficient (usually between 2 ~ 2.5),
A = exposed surface area,
V = spacecraft velocity,
Cpa = center of aerodynamic pressure,
Cg = center of gravity

We assign the following numbers to these parameters;
ρ ≅ 6.98 × 10-12 kg/m3 (mean density at 350 km altitude),
Cd ≅ 2.25 (usually between 2 and 2.5 – we take it to be constant at 2.25)
A ≅ 0.14 m2 (worst possible case)
Vmax ≅ 8000 m/s (this is calculated from the circular velocity at 700km altitude in
                                            µ    3.986 ×1014 m3 / s 2
                       orbit where Vcirc =    =                       ≅ 7697m / s
                                            R       6728 ×103 m
                       Since the spacecraft may not be in the circular orbit during the


                                                                                          62
                   experiments, we can take V ≅ 8000 m/s to compensate higher speeds
                   of an elliptic orbit at perigee. )
Cpa-Cg ≅ 0.1 m (this is an approximation based in the fact that the spacecraft is
geometrically symmetric)

Thus from equations (4.4.1) and (4.4.2) we calculate as follows;

        F = 0.5 ⋅ é(6.98 ×10−12 kg / m3 ) ⋅ (2.25) ⋅ (0.14m 2 ) ⋅ (8000m / s)2 ù
                  ë                                                            û
        Þ F = 7.03584 ×10−5 N

Thus Ta=( 7.03584 × 10−5 N ) × (0.1m)
        Þ Ta = 7.03584 ×10−6 N ⋅ m                          (4.3)

    This concludes the calculation of major disturbances in the LEO orbit. Next we will
try to give the idea of how significant are the disturbance torques on the motion and the
attitude of the spacecraft in orbit. We are going to assume that spacecraft is spinning with
25 rpm about the maximum moment of inertia axis, and all the disturbance torques are
acting on the same direction! (This is a much exaggerated assumption but this will give a
fairly good idea how effective these torques are). Thus we sum all the disturbing torques;
        Tdisturbance = Tg + Tsp + TM + Ta
        Tdisturbance = 3.5338 × 10−7 + 7.65525 × 10−8 + 3.77534 × 10 −5 + 7.03584 × 10−6
        Þ Tdisturbance ≅ 4.52192 × 10−5 N ⋅ m

Thus we conclude that even if the torques were exaggerated greatly and assumed to be all
in the same direction, the net effect is not very significant. Therefore, for the length of the
mission and the possible disturbance environment we do not need to have an active
attitude control & compensation system since our experiments do not require an active
control other than the initial spin-up.
    As the last step in our calculations we are going to calculate the nutation frequency of
the spacecraft. The relation between the inertial nutation frequency (wni) and the
spacecraft rotation frequency is:

                Is
        ωni =      ωs                                       (4.4)
                IT

where ws is the spin frequency and Is and IT are moments of inertia about the spin axis and
transverse axis, respectively. Thus setting Is=Iz nutation frequencies for the transverse
axes x and y are;

                  Iz       0.5kg ⋅ m2
        ωni | =      ωz =              × 25rpm = 39.0625rpm
            x
                  Ix      0.32kg ⋅ m 2



                                                                                            63
                  Iz       0.5kg ⋅ m 2
        ωni | =      ωz =              × 25rpm = 34.7222rpm
            y
                  Iy      0.36kg ⋅ m 2
Thus,
        ωni | = 39.0625rpm
                                                      (4.5)
            x


        ωni | = 34.7222rpm
            y




We must make sure that the nutation damper to be selected is capable of eliminating
nutation within the range of above numbers.

ADCS Cost Estimation:

The following table represent the actual and estimated component costs

                 Unit
                Price                       Number
  Component       ($)                       of parts
Sun Sensor      20000          (estimated)      2
Gyroscope        2450          (actual)         1
Accelerometer    1100          (actual)         1
Nutation Damper 1000           (estimated)      2
                                    Total = 44550 $




                                                                                64
Appendix C: Power

        In order to accurately compare the solar panels to the batteries, there are rough
calculations to determine the mass and cost of solar panels. The equations are from
reference three.

Pe       = power during eclipse
Pd       = power during daylight
Psa      = power provided by solar array
PBOL = beginning of life power
PEOL = end of life power
Psun = 1367 W / m2
Po       = ideal solar output per area
Te       = time in eclipse
Td       = time in daylight
Xe       = efficiency
Xd       = efficiency
Msa = mass of panels
Mcontrol = mass of power control unit
Mreg = mass of regulator and converters
Mwiring = mass of wiring
Mtot = total mass of subsystem
Msecondary = mass of rechargeable batteries
Mdry = dry mass of the spacecraft = 40 kg
C        = capacity in W hrs
Ld       = life degradation
Eff      = solar conversion efficiency = 22% for Multijunction GaInP / GaAs
Asa = area of solar array
θ        = angle of sun striking solar array

        For short mission, it is assumed that there is no degradation and that PBOL = PEOL.
Equation 1 calculates the power the solar panel must provide. Equation 12 gives and total
mass of a solar panel system and equation 13 gives an estimated cost of the system. The
important results are shown in table C-1. It is important to note that the maximum
production efficiency of the solar panels was used, which does not account for the losses
due to thruster’s exhaust.

                      Psa = [(Pe Te / Xe) + (Pd Td / Xd)] / Td                     (1)

                      Po = Psun * Eff                                              (2)

                      PBOL = Po Id cos θ                                           (3)

                      Ld = (1 – degradation / yr)^satellite life                   (4)

                      PEOL = PBOL Ld                                               (5)



                                                                                         65
                      Asa = Psa / PEOL                                             (6)

                      Msa = 0.04 * Psa x 4                                         (7)

                      Mcontrol = 0.02 * Psa                                        (8)

                      Mreg = 0.025 * Psa                                           (9)

                      Mwiring = 0.04 * Mdry                                        (10)

                      Msecondary = C / 45 (for NiH2)                               (11)

                      Mtot = Msa + Mcontrol + Mreg +M wiring + Msecondary          (12)

                      Costsa = $800 - $3000 / watt                                 (13)


                    Psa                                          37 Watts

                   Mtotal                                         12.3 kg

          Asa (outer surface area)                                 0.6 m2

                   Costsa                                  $29,600 – $111,000

Table C-1: Important results for solar cell comparison.

       For the calculations of the primary batteries exact figured were found using
available devices. The important results are shown in Table C-2: After comparing Table
C-2 with C-1, primary cells are the better option for this particular mission. Also, in the
generation of table VII -2, power losses were calculated with equations 14 and 15.

                      Preg = 0.2 P                                                 (14)

                      Pwiring = 0.02 P                                             (15)

              Energy Density                                    0.4 W / cm3

         Energy Specific Density                                250 W / kg

    Cost regulator/converter and wiring                            $ 300

               Cost per cell                                        $ 17




                                                                                          66
           Mtotal                                       8.3 kg

          Costtotal                                     $ 2000

Table C-2: Important results for primary cell comparison.




                                                                 67
      Appendix D: Communications and Data Handling
The Earth angular radius, ρ is calculated as follows,

                æ RE ö            ο
      ρ = arcsinç
                ç R + h ÷ = 71.44
                        ÷                                                                      (1)
                è E     ø

where RE is the radius of the Earth. Also, the period, P, of the orbit is,

      P = 1.658669 × 10 −4 ⋅ (RE + h ) = 91.54 min                                             (2)

The maximum nadir angle, ηmax, is calculated from the following equation

     η max = arcsin (sin ρ cos ε min ) = 56.2 o                                                (3)

where εmin = minimum elevation that the ground station can view the satellite =

5deg. Next, the maximum Earth central angle, λmax, is

      λ max = 90 o − ε min − η max = 28.8 o                                                    (4)

From this, the maximum range is defined as

                æ sin λ max         ö
      Dmax = RE ç
                ç sin η             ÷ = 1656.76km
                                    ÷                                                          (5)
                è       max         ø

Next, the minimum Earth central angle, λmin, is

      λ min = arcsin(sin lat pole sin lat gs + cos lat pole cos lat gs cos(∆long )) = 14.2 o   (6)

where latpole = 90º – inclination, and latgs = 40 deg. for the Purdue ground station.

The mean motion, n, is

                           −3
      n ≅ 8681660.4 ⋅ a         2
                                    = 15.73 rev                                                (7)
                                                  day

where, a is the semi-major axis defined by,

                           2
      a ≅ 331.24915 ⋅ P        3
                                                                                               (8)

The total time in view, T, is calculated from,




                                                                                                     68
        æ P ö         æ cos λ max   ö
     T =ç     ÷ arccosç
                      ç cos λ       ÷ = 13.0 min
                                    ÷                                      (9)
        è 180 ø       è       min   ø

The received energy-per-bit to noise-density (Eb/N0) was calculated from

     Eb
        = 10 log( Pt ) + L + Ll + Gt + Gr + 228.6 − 10 log Ts − 10 log R   (10)
     N0

And the effective isotropic radiated power, EIRP, was calculated from

     EIRP = 10 log(Pt ) + Gt + Ll                                          (11)

Space losses, Ls, was calculated from the following equation

                 (       )
     Ls = 20 log 3 × 10 8 − 20 log(4π ) − 20 log(S ) − 20 log( f )         (12)

where S = 350,000meters, and f is the frequency in Hz.




                                                                                  69
Appendix E: Thermal


E.1 Equations for Table X-2:

      D, diameter of sphere which has equal surface area

                       D=     Aπ                                                     (E-1)

      ρ, angular radius of the Earth

                                   RE
                       sin ρ =                                                       (E-2)
                                 H + RE

      Ka, albedo correction factor

                       K a = 0.644 + 0.521ρ − 0.203 ρ 2                              (E-3)




E.2 Energy Balance and Required Emissivity Calculations

 It must first be determined how much energy needs to be dissipated, using the
 equilibrium energy balance equation:

                                 Qout = Qin + Qdis                                   (E-6)

 Qout is the equilibrium energy, or the heat generated by the satellite, which is given in
 Table X-2 as 9W. During eclipse, the only heat input will be from the Earth infrared,
 which emits at 216 W/m2. This gives Qin = 129.6 W, where A = 0.6m2. Solving the
 energy balance for heat dissipated yields:

                               Qdis = −120.6 W
 The positive value of Qdis   confirms that the satellite is too cold and heat must be added.

 Consider a satellite which must dissipate heat. Qdis can be broken down as follows:

                                 Qdis = Qins + Q prad                                (E-7)

              where,
                        Qins = Heat radiated into space by insulation coating


                                                                                          70
                                       Qins = εAσT 4                               (E-8)
                     Q prad = Heat radiated into space by passive radiators
                                    Q prad = εAσηT 4                               (E-9)
 It will first be determined whether or not the proper insulation will suffice to dissipate
 the required energy (Assume no radiator: Q prad = 0). Therefore,

                               Qdis = Qins                                         (E-10)

  Substituting Eq.(E-8) into Eq.(E-10) and rearranging to solve for ε, gives:

                                     Qdis
                               ε=                                                  (E-11)
                                    AσT 4

     where,
              ε   = emissivity

              A   = surface area of spacecraft = 0.6 m2
                                                               W
              σ   = Stefan-Boltzmann constant = 5.67 × 10 −8
                                                             m2K 4
              T   = min. absolute temperature of spacecraft = 12°C = 285.15 K

              Qdis = 120.6 W


Eq.(E-11) yields a required emissivity of,

                               ε = 0.55

     in order to maintain the satellite within its lower temperature limit.




                                                                                        71
Appendix F: Structure




Appendix G: Propulsion

                                a. Cold Gas Thruster (CG)
The steps in developing the cold gas thruster were first determining gases to compare
against each other and finding the gas constant, R, ratio of specific heat, γ, and molecular
mass, m, of the gases. Then calculate the acoustic velocity, ao,
a o = γRTo                                                                           (G-1a)
where To is the stagnation temperature of the gas during operation assumed equal to
273.15 oK, because this is the average temperature the gas should be at during operation.
Next the characteristic velocity, c*, was calculated.
           ao
c∗ =           γ +1
                                                                                     (G-2a)
      æ 2 ö 2(γ −1)
      ç γ + 1÷
     γç      ÷
      è      ø
                •
The mass flow m was then calculated
                                    1
                         γ +1   −
         é                   ù      2
 •    F êæ 2 öæ 2 ö ú    γ −1
m= ∗ ç            ÷ç       ÷                                                   (G-3a)
     c γ êç γ − 1 ÷ç γ + 1 ÷ ú
          è       øè       ø ú
         ê
         ë                   û
where F is the thrust and equals 1.0 Newton from the SRD. The mass of propellant, mp,
was calculated.
       •
m p = m ∆T                                                                           (G-4a)
where ∆T is the burn time, which was assumed to be 300 seconds to provide a propellant
margin since for the two burn schemes on 240 seconds is needed. The volume of the
storage tank was then calculated
      m p RTo
 Vp =                                                                           (G-5a)
         Pc
and graphed for a range of pressures to determine what pressure would be needed in the
tank for using the gas.




                                                                                          72
As the figure illustrates the tank volume decreases and most of the gases begin to
converge as the tank pressure is increased. From graph values for the initial tank
pressure, Pti, were chosen that would give a low tank volume where any more increase in
pressure would provide negligible result in reducing the tank volume. Next expansion
ratios were determined by use of the expansion-mach number relation equation for a
range of mach numbers.
                                           γ +1
    A      1 éæ 2 öæ γ - 1 2 öù 2(γ -1)
ε= e =        êç     ÷ç1 +      M e ÷ú                                             (G-6a)
    A t M e ëç γ + 1 ÷è
               è     ø      2       øû
The pressure ratio was also determined by similar means
                        γ
Pe éæ γ - 1 2 ö ù (1-γ )
   = ç1 +      M e ÷ú                                                              (G-7a)
Pc êèë       2     øû
The specific impulse, Isp, was calculated
                                                  1

        ∗
           é                   γ +1
                                    ì   üù 2
                                          γ −1
       c γ êæ 2 öæ 2 ö γ −1 ï æ Pe   ö ïú   γ
I sp =      ç       ÷ç       ÷ í1 − ç÷ ý                                          (G-8a)
       g o êç γ − 1 ÷ç γ + 1 ÷ ï ç Pc÷   ú
           êè
           ë
                    øè       ø
                                    î
                                     ø ïú
                                      è
                                        þû
The specific impulse, equation (G-8a), was graphed against the expansion ration,
equation (G-6a), so a choice for exit Mach number, pressure ratio, and specific impulse
could be chosen.




Next a range of throat and exit areas was determined for a range of regulated pressures,
Pr.
       •
      m c∗
At =                                                                                (G-9a)
       Pr
A e = εA t                                                                          (G-
10a)
where ε is the chosen expansion ratio determined earlier for that specific gas. The
diameter of the throat and exit were determined and then graphed against the range of
regulated pressures




                                                                                           73
        A
D=2                                                                                (G-
        π
11a)

The graph was used to determine the best regulated pressure, exit diameter, and throat
diameter, which occurs when the throat and exit diameters are near each other and when
an increase in the regulated pressure does not affect the diameter difference greatly. Do
not want a large regulated pressure, because more residual propellant would be left in the
tank. Having determined the critical components of the design it is possible to calculate
the thrust of system.
       ì                                                1
                                                              ü
       ï         é                   γ +1
                                          ì    γ −1
                                                    ü ù2      ï
       ï         êæ 2 öæ 2 ö γ −1 ï1 − æ Pe ö γ ïú + (P A )ï
 F = λ íA t Pr γ êç                         ç ÷ ý
                  ç γ − 1 ÷ç γ + 1 ÷ í ç P ÷
                          ÷ç       ÷                  ú   e e ý                      (G-
       ï         êè       øè       ø ï è c ø ïú               ï
       ï         ë                        î         þû        ï
       î                                                      þ
12a)
where λ is the nozzle efficiency which is 99%, because the nozzle cone angle is so small.
The mass flow is again recalculated by rearranging equation (G-9a) for the mass flow and
solving. This is done so that a mass flow that is determined more from design
considerations is used. The propellant mass was recalculated using equation (G-4a) for
the same burn time. The volume of the tank taking in consideration for mass residue was
then calculated
      m p RTo
 V=                                                                                  (G-
     (Pti − Pr )
13a)
The mass residue, mr, was then calculated by
      PV
 mr = r                                                                              (G-
      RTo
14a)
The total propellant mass is the sum of the mass residue and propellant mass. A spherical
tank was chosen for the tank design due to its high strength capability and it is commonly
used. The inner radius of tank was determined
            1
      æ 3V ö 3
 ri = ç    ÷                                                                        (G-
      è 4π ø
15a)
The burst pressure was calculated
 Pb = f s (MEOP )                                                                   (G-
16a)
where fs is the factor of safety, which equals 2.25. MEOP is the maximum expected
operating pressure, which is calculated by using the ideal gas law and determining the
pressure for the tank filled at a temperature of 335.93 oK for the highest probable
temperature that the tank could while waiting for launch at the launch site. The thickness
of the case was then determined


                                                                                         74
         Pb ri
t cs =                                                                              (G-
         Ftu
17a)
where Ftu is the ultimate tensile strength of case material. Next the mass of the case was
determined
m cs = ρ cs π(rcs − ri3 )
      4        3
                                                                                     (G-
      3
18a)
where ρcs is the density of the case material and rcs is sum of tcs plus ri.


                              b. Solid Rocket Motor (SRM)
In calculating the amount of propellant required to achieve the ∆V an iterative approach
was used. The mass ratio, MR, was calculated
              ∆V
            g o I spv
 MR = e                                                                             (G-1b)
where ∆V is the change in velocity required, go equals 9.807 m/s2, and Ispv is the vacuum
specific impulse that solid rocket motors have historically. Assumed on the low end of
the range and chose Ispv = 200 sec. The mass of propellant was calculated
            λ p (MR − 1)
 m p = mi                                                                           (G-2b)
          1 − MR (1 − λ p )
where mi is the inert mass of the spacecraft and λp is the propellant mass fraction. The
propellant mass fraction is what is iterated on so it is initially guessed. Having a value
for the propellant mass and knowing the desired initial total mass of the spacecraft, mo,
calculated the propellant mass fraction
       mp
λp =                                                                                  (G-3b)
       mo
If the guessed propellant mass fraction is no more than 0.00001 different than the
propellant mass fraction calculated from equation (G-3b) then values are correct. If the
value is more than 0.00001 different then use the new propellant mass fraction in
equation (G-2b) and recalculate; continue this process till propellant mass fraction is
within the limit. Now knowing the mass of the propellant can calculate the volume of the
propellant.
Vp = m p /ρ p                                                                         (G-4b)
where ρp is the density of the propellant mixture. The average mass flow was calculated
by assuming steady state for the constant burn.
  •    F
 m = max                                                                         (G-5b)
     I spv g o
where Fmax is the maximum thrust, which occurs during the constant burn process of the
thrust scheme. The burn time was then calculated
      mp
 tb = •                                                                          (G-6b)
       m


                                                                                          75
Once knowing the burn time it is possible to calculate the ramp up time, tr. The
limitations on the ramp up time so that it has some effect comes from Javorsek and
Longuski
     2nπ
 trñ                                                                                (G-7b)
      Ω
where Ω is the spin rate and n is some integer greater than zero. Knowing how long the
burns are can develop the propellant grain and thus the casing of the SRM. Using
information on propellant for typical chamber pressures set the throat radius. Since their
needs to be more propellant to ensure choked flow set the initial radius of propellant.
With the ramp up time the burn surface area was calculated
 A b = πr (t )                                                                      (G-8b)
where r(t) is the radius of the propellant as a function of time. Next the chamber pressure
is calculated
                   1
       æ aρ p A b c ∗ ö 1− n
 Pc = ç               ÷                                                                   (G-9b)
       ç At ÷
       è              ø
where a and n are constants determined by the propellant. Assumed St. Robert’s Law
was applicable so the rate of burn was calculated
 rb = aPcn                                                                                (G-10b)
The web distance burned was found
ω b = rb ∆T                                                                               (G-11b)
where ∆T is the step in time for the process. The height was calculated
 h new = h old + ω b                                                                      (G-
12b)
where hold was the height from the last time step; initial hold equals 0.0 cm. The new
propellant radius was then calculated for the burn in height
                       é æ      æ r − r ö öù
 rnew = rold + h new ê tanç atanç c i ÷ ÷ú
                             ç  ç r t ÷÷                                                  (G-
                       ê è
                       ë        è bi r ø ø ú
                                           û
13b)
where rc is the radius needed to obtain the constant thrust, ri is the initial propellant
radius, and rbi is the initial burn rate. This is continued till tb is reached with the few
minor changes. During the constant burn equation (G-13b) rnew = rold and during the
ramp down equation (G-13b) remains the same expect that the plus sign is negative. The
average volume of the tank was calculated from taking the burn surface area and height
half way through each burn time.
 Vt = A bru h ru + A bc h c + A brd h rd                                                  (G-
14b)
where the subscripts ru signify the ramp up phase and rd signify the ramp down phase.
Then compared the volume of the tank to the volume of propellant. If not in agreement
varied Fmax it till the tank volume converged with the propellant volume within 0.1
differences. The thrust coefficient was then found for the constant burn time, because
this when greatest thrust occurs.



                                                                                             76
          Fmax
Cf v =        •
                                                                                            (G-
          c∗ m
15b)
Using thrust coefficient tables determined the optimal expansion ratio by interpolation.
The thrust was determined
 Fv = Cf v At Pc                                                                   (G-
16b)
The thickness of casing used equation (G-17a) except burst pressure used a factor of
safety of 2.0 and MEOP equaled the chamber pressure at constant burn. The thickness of
insulation was determined by
              •
t insul = t b e f s                                                                         (G-
19b)
          •
where e is the insulations erosion rate, which is dependent on insulation material
selected. The mass of the casing was found by
 m cs = ρ cs π(rcs − ri2 )(h (t b − t r ))
                 2
                                                                                               (G-
17b)
where rcs equals rc plus tcs plus tinsul, ri equals rc plus tinsul, and h(tb-tr) is the height at the
time right after the constant burn occurs. The mass of insulation is calculated in the same
manner of equation (18.17b) except the density for case materials are the insulation
material’s density and rcs is replaced by rti (rti = rc + tinsul) and ri is replaced with rc. The
mass of the igniter was determined from an equation that correlates the propellant volume
and free space in SRM to the mass of the igniter using a number of SRMs that have been
actually used.
                                 0.571
              é æ 1     öù
                 ç η − 1÷ú
m ig = 0.0138êVp ç      ÷                                                          (G-
              ë è v     øû
18b)
where ηv is the volumetric loading efficiency, which is equal to 98% in this case. The
nozzle mass was determined by using a correlation equation
                           (       )
                                                  0.917
                    é    m p c ∗ ε 0.3 ù
                                1.2

m noz   = 0.0000256 ê 0.8 0.6                 ú                                             (G-
                    ê Pc t b (tan (θ cn )) ú
                                          0.4
                    ë                         û
19b)
where θcn is the nozzle cone angle, which equals 12 degrees so that a high nozzle
efficiency is possible. Finally the nozzle length was determined by
       D − Dt
Ln = e                                                                            (G-
       2tan (θ cn )
20b)
where De and Dt are the exit diameter and throat diameter, respectively.




                                                                                                  77
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