DESIGN, ANALYSIS, IMPLEMENTATION AND TESTING OF THE THERMAL CONTROL, AND ATTITUDE DETERMINATION AND CONTROL SYSTEMS FOR THE CANX-7 NANOSATELLITE MISSION by Bradley Scott Cotten A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Aerospace Science and Engineering University of Toronto Copyright © 2014 by Bradley Scott Cotten
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DESIGN, ANALYSIS, IMPLEMENTATION AND TESTING
OF THE THERMAL CONTROL, AND
ATTITUDE DETERMINATION AND CONTROL SYSTEMS
FOR THE CANX-7 NANOSATELLITE MISSION
by
Bradley Scott Cotten
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Aerospace Science and Engineering
University of Toronto
Copyright © 2014 by Bradley Scott Cotten
ii
Abstract
Design, Analysis, Implementation, and Testing of the Thermal Control, and
Attitude Determination and Control Systems for the CanX-7 Nanosatellite Mission
Bradley Scott Cotten
Master of Applied Science
Graduate Department of Aerospace Science and Engineering
University of Toronto
2014
In the context of space debris mitigation, a major challenge currently facing the space
community is the removal of nano and microsatellites from orbit following the completion of
their missions. To address this problem, the Space Flight Laboratory has developed the CanX-7
mission; a technology demonstration mission to validate the use of a mechanically deployed drag
sail for de-orbiting satellites from low-Earth orbit. This thesis report describes the design,
analysis, implementation, and testing of both the attitude determination and control system, and
thermal control system for the CanX-7 mission. The attitude determination and control system
uses an entirely magnetic solution to meet mission level pointing requirements with a limited set
of hardware, and the thermal control system relies primarily on passive control measures to
allow the spacecraft to survive the harsh thermal environment in space. Both subsystems are
essential to the success of the CanX-7 mission.
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Acknowledgements
I would like to thank my friends and colleagues at the Space Flight Laboratory for
providing an energetic and stimulating work environment. Over the past two years I have learned
more than I ever could have imagined. Thank you to Dr. Robert Zee for providing the rare
opportunity to work on actual space missions, something that has been a dream of mine for many
years. Thanks to CanX-7 project manager Grant Bonin for his guidance and support, and for
trusting me with a wide variety of challenging work. Grant, your unwavering confidence in my
abilities really allowed me to grow as an engineer. Thanks to Bryan, Daniel, Jenn, and Vince for
your mentorship and readiness to answer my exhausting amount of questions and queries. To
Jamie, John, Josh, and Thomas with whom I shared this experience, thank you for your
willingness to help me work out any problem academic or otherwise, and for adding humour to
every day.
I would like to thank my family for always encouraging me to follow my dreams, and for
teaching me the strong work ethic which I relied on heavily throughout my degree. Most
importantly I’d like to thank Jessamyn for her love and support, you are truly my greatest
inspiration.
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Table of Contents
Chapter 1 Introduction ................................................................................................................. 1
1.1 The CanX-7 Mission ................................................................................................... 2
The Space Debris Problem.......................................................................................... 3 1.1.1
Drag Sail Technology ................................................................................................. 4 1.1.2
Additional Scientific Value ......................................................................................... 6 1.1.3
1.2 The CanX-7 Satellite................................................................................................... 9
1.3 Launch and Orbital Parameters ................................................................................. 13
Chapter 2 Magnetic Attitude Control ........................................................................................ 15
2.1 Local Magnetic Field Tracking ................................................................................. 16
2.2 Attitude Control Hardware ....................................................................................... 18
Magnetometer ........................................................................................................... 18 2.2.1
Magnetorquers .......................................................................................................... 19 2.2.2
2.3 Magnetic Cleanliness ................................................................................................ 22
Tape Spring Booms – Parasitic Dipole Moment Contribution ................................. 24 2.3.1
Hall Effect Sensor Magnets – Parasitic Dipole Moment Contribution..................... 29 2.3.2
Overall Expected Spacecraft Parasitic Dipole Moment ............................................ 30 2.3.3
2.4 Attitude Control Algorithms ..................................................................................... 30
2.5 Expected On-Orbit Performance ............................................................................... 33
Model ........................................................................................................................ 34 2.5.1
Input Parameters ....................................................................................................... 36 2.5.2
Results ....................................................................................................................... 37 2.5.3
Pointing Budget ........................................................................................................ 43 2.5.4
2.6 Attitude Determination and Control System Software ............................................. 44
Ground Support Software ......................................................................................... 47 2.6.1
Chapter 3 Passive Thermal Control for Low-Earth Orbit Satellites .......................................... 50
3.1 Boundary Conditions for Thermal Analysis of Space Systems ................................ 51
Orbit .......................................................................................................................... 52 3.1.1
Attitude ..................................................................................................................... 54 3.1.2
Environmental Parameters ........................................................................................ 55 3.1.3
Internal Heat Dissipation .......................................................................................... 58 3.1.4
3.2 Modeling Heat Flow Paths........................................................................................ 58
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Internal Radiation Heat Transfer .............................................................................. 60 3.2.1
3.3 Thermal Control Materials ........................................................................................ 61
Chapter 4 CanX-7 Thermal Control System ............................................................................. 63
4.1 Temperature Requirements ....................................................................................... 64
4.2 Thermal Finite Difference Model ............................................................................. 65
4.3 Thermal Model Boundary Conditions ...................................................................... 67
Worst Case Attitudes ................................................................................................ 67 4.3.1
Internal Heat Dissipation .......................................................................................... 68 4.3.2
4.4 Thermal Control System Design ............................................................................... 70
Surface Properties ..................................................................................................... 70 4.4.1
Battery Heater ........................................................................................................... 72 4.4.2
Structural Design Modifications ............................................................................... 73 4.4.3
4.5 Results ....................................................................................................................... 73
4.6 Drag Sail Thermal Analysis ...................................................................................... 78
Drag Sail Design Evolution ...................................................................................... 81 4.6.1
4.7 Thermal Model Validation ........................................................................................ 83
Chapter 5 Conclusion ................................................................................................................ 84
Bibliography ................................................................................................................................. 85
Appendix A: Attitude Performance Sensitivity Study .................................................................. 88
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List of Tables
Table 1-1: Key CanX-7 Spacecraft Parameters ............................................................................ 13
Table 1-2: Range of Orbit Parameters used for Spacecraft Detailed Design ............................... 13
Table 2-1: Magnetorquer States .................................................................................................... 21
Table 2-2: Range of Expected Magnetorquer Magnetic Dipole Moments ................................... 22
Table 2-3: Magnetic Dipole Moment Measurements for Coiled Booms ..................................... 26
Table 2-4: Magnetic Dipole Moment Measurements for Coiled Booms following Magnetization
............................................................................................................................................... 29
Table 2-5: Input Parameters used for Attitude Simulations.......................................................... 36
Table 2-6: CanX-7 ADCS Pointing Budget [degrees (2σ)] .......................................................... 43
Table 2-7: List of ADCS Software Telemetry .............................................................................. 47
Table 3-1: Properties for Several Thermal Control Tapes [42]
[43] ............................................. 62
Table 4-1: CanX-7 Subsystem Assembly Operating Temperature Limits ................................... 64
Table 4-2: Summary of Boundary Conditions for the CanX-7 Thermal Model ........................... 67
Table 4-3: Worst Case Cold and Worst Case Hot Power Consumption Values .......................... 69
Table 4-4: Baseline and Desired Spacecraft Surface Thermo-Optical Properties ........................ 70
Table 4-5: Thermal Control Tapes by Spacecraft Face ................................................................ 71
Table 4-6: Thermal Analysis Results Summary – Cold Reference Orbit ..................................... 76
Table 4-7: Thermal Analysis Results Summary – Hot Reference Orbit ...................................... 76
Table A-1: Additional Attitude Simulations Results .................................................................... 88
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List of Figures
Figure 1-1: Images of a Single Drag Sail Module in Stowed (Left) and Deployed (Right)
Configurations......................................................................................................................... 5
Figure 1-2: Drag Sail Electronics – Hall Effect Sensor (Left), Cartridge Board (Middle), Main
Board (Right) .......................................................................................................................... 6
Figure 1-3: Operations Concept for the ADS-B Payload [2] .......................................................... 7
Figure 1-4: ADS-B Payload Hardware ........................................................................................... 8
Figure 1-5: mVIC Hardware (Left), mVIC Field-of-View Projections (Right) ............................. 9
Figure 1-6: CanX-7 Spacecraft Exterior Views (Stowed) ............................................................ 10
Figure 1-7: CanX-7 Spacecraft Exterior Views (Deployed) ......................................................... 10
Figure 1-8: CanX-7 Spacecraft with Deployed Drag Sail ............................................................ 11
Figure 1-9: CanX-7 Spacecraft Internal Layout: -Z Tray (Left), +Z Tray (Right) ....................... 12
Figure 1-10: CanX-7 XPOD ......................................................................................................... 14
Figure 2-1: Spacecraft Attitude Profile given Perfect LMF Tracking .......................................... 17
Figure 2-2: Top (Left) and Bottom (Right) Images of the Magnetometer ................................... 18
Figure 2-3: CanX-7 Smart Torquer............................................................................................... 19
Figure 2-4: Smart Torquer Electrical Schematic .......................................................................... 20
Figure 2-5: Magnetorquer Current and Dipole Directions by State ............................................. 21
Figure 2-6: Tape Spring Boom Samples (Left) and Cross Section Dimensions (Right) .............. 24
Figure 2-7: Parameters for Estimating Magnetic Dipole Moment of Boom Samples .................. 25
Figure 2-8: Magnetic Dipole Moment vs. Boom Length ............................................................. 25
Figure 2-9: A Pair of Tape Spring Booms in their Stowed Configuration ................................... 26
Figure 2-10: Helmholtz Coil Test Setup ....................................................................................... 27
Figure 2-11: Induced Magnetic Dipole Moment vs. Boom Length using a 2.5 mT Field ........... 28
Figure 2-12: Hall Effect Sensor with Magnet ............................................................................... 30
Figure 2-13: CanX-7 Attitude Model – Block Diagram ............................................................... 35
Figure 2-14: Spacecraft Angular Velocity during Detumbling (4°/s initial) ................................ 37
Figure 2-15: Spacecraft Angular Velocity during Detumbling (20°/s initial) .............................. 38
Figure 2-16: Magnetorquer Power Consumption during Detumbling (4°/s initial) ...................... 38
Figure 2-17: Magnetorquer Power Consumption during Detumbling (20°/s initial) .................... 39
Figure 2-18: Spacecraft Angular Velocity during LMF Tracking ................................................ 40
Figure 2-19: LMF Tracking Error................................................................................................. 40
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Figure 2-20: Steady State LMF Tracking Error ............................................................................ 41
Figure 2-21: Magnetorquer Power Consumption during LMF Tracking ..................................... 41
Figure 2-22: Nadir Tracking Error ................................................................................................ 42
Figure 2-23: ADS-B Payload Coverage (Shaded Red) for a Single Orbit ................................... 42
Figure 2-24: ADCS State Transition Diagram.............................................................................. 44
Figure 2-25: ADCS Software Architecture – Commands Diagram ............................................. 45
Figure 2-26: ADCS Software Architecture – Control Cycle ........................................................ 46
Figure 2-27: CanX-7 Control Ground Support Software – ACS Module .................................... 48
Figure 2-28: CanX-7 FlatSat ......................................................................................................... 49
Figure 3-1: Heat Transfer in Space ............................................................................................... 51
Figure 3-2: Orbit Average Heat Load vs. Beta Angle (Cold Reference Orbit - LTAN 11:47) .... 53
Figure 3-3: Orbit Average Heat Load vs. Beta Angle (Hot Reference Orbit - LTAN 7:32) ........ 53
Figure 3-4: Analysis for Determining WCH Spacecraft Attitudes ............................................... 55
Figure 3-5: Screenshot of the Thermal Environment and Orbital Parameter Selection Tool ....... 58
Figure 3-6: Thermal Circuit Representation for a Common Heat Flow Path ............................... 59
Figure 3-7: Interaction of Radiation with First and Second Surface Mirrors ............................... 61
Figure 4-1: CanX-7 Finite Difference Model: Exterior View ...................................................... 65
Figure 4-2: CanX-7 Finite Difference Model: +Z Interior View .................................................. 66
Figure 4-3: CanX-7 Finite Difference Model: -Z Interior View ................................................... 66
Figure 4-4: Stable WCC Attitudes (as viewed from the orbit normal direction).......................... 68
Figure 4-5: Battery Assembly ....................................................................................................... 72
Figure 4-6: Structural Design Modifications ................................................................................ 73
Figure 4-7: Cold Reference Orbit – WCC Boundary Conditions ................................................. 74
Figure 4-8: Cold Reference Orbit – WCH Boundary Conditions ................................................. 74
Figure 4-9: Hot Reference Orbit – WCC Boundary Conditions................................................... 75
Figure 4-10: Hot Reference Orbit – WCH Boundary Conditions ................................................ 75
Figure 4-11: Nominal Temperature Profiles – Cold Reference Orbit .......................................... 77
Figure 4-12: Nominal Temperature Profiles – Hot Reference Orbit ............................................ 78
Figure 4-13: Drag Sail Finite Difference Model........................................................................... 79
Figure 4-14: Drag Sail WCC Conditions ...................................................................................... 80
Figure 4-15: Drag Sail WCH Conditions...................................................................................... 80
Figure 4-16: Initial (Left) and Final (Right) Drag Sail Geometries .............................................. 81
Figure 4-17: Drag Sail Temperature Variation (in degrees Kelvin) ............................................. 82
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Figure 4-18: Thermal Vacuum Chamber Test Setup .................................................................... 83
x
List of Acronyms
3U Triple Cube
ADCS Attitude Determination and Control System
ADS-B Automatic Dependent Surveillance – Broadcast
CANOE Canadian Advanced Nanosatellite Operating Environment
CanX Canadian Advanced Nanospace eXperiment
C&DH Command and Data Handling
DC Direct Current
ECI Earth-Centered Inertial
ECSS European Cooperation on Space Standardization
ERBE Earth Radiation Budget Experiment
FEP Fluorinated Ethylene Propylene
GNB Generic Nanosatellite Bus
IADC Inter-Agency Space Debris Coordination Committee
IC Integrated Circuit
IGRF International Geomagnetic Reference Field
LMF Local Magnetic Field
LEO Low-Earth Orbit
LTAN Local Time of Ascending Node
MFC Microsoft Foundation Class
mVIC miniature Visual Inspection Camera
NSP Nano-Satellite Protocol
OBC On-Board Computer
PCB Printed Circuit Board
PDU Power Distribution Unit
PID Proportional, Integral, Derivative
PWM Pulsed Width Modulation
RGB Red, Green, Blue
SFL Space Flight Laboratory
SSO Sun-Synchronous Orbit
UHF Ultra-High Frequency
UI User Interface
UTIAS University of Toronto Institute for Aerospace Studies
xi
WCC Worst Case Cold
WCH Worst Case Hot
XPOD eXoadaptable PyrOless Deployer
xii
1
Chapter 1
Introduction
The CanX-7 mission is a technology demonstration mission to validate the use of a deployable
drag sail to assist in the de-orbiting of micro and nanosatellites. This technology will allow future
Space Flight Laboratory (SFL) missions to meet de-orbiting guidelines for Low-Earth Orbit
(LEO) satellites and help mitigate the problems associated with space debris. The CanX-7
mission employs a Triple Cube (3U) satellite bus, having dimensions 10 x 10 x 34 cm. The drag
sail and the associated deployment mechanisms make up the primary payload. The spacecraft
will also carry a secondary payload: an Automatic Dependent Surveillance - Broadcast (ADS-B)
receiver for the purpose of aircraft tracking provided by Royal Military College of Canada in
collaboration with COM DEV. The secondary payload will operate for approximately 6 months
prior to drag sail deployment. A tertiary payload is an imaging system located on a deployable
boom to evaluate the drag sail deployment. Once the drag sail has been deployed, the satellite
will de-orbit within 10 years. The CanX-7 satellite is currently in the final stages of assembly,
integration and testing, and the CanX-7 team is targeting flight readiness by Q2 2015.
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To support payload operations, the CanX-7 satellite is equipped with the following
subsystems: thermal control, attitude determination and control, power, structure, Command and
Data Handling (C&DH), and communications. The Attitude Determination and Control System
(ADCS) and the thermal control system are the focus of this thesis project, including all aspects
of design, analysis, implementation, and testing. These two subsystems represent a significant
contribution to the CanX-7 mission. The thermal control system will allow the satellite to survive
the harsh space environment, while the ADCS is designed to fulfill the pointing requirements for
secondary payload operations and to monitor drag sail performance post-deployment.
The ADCS is capable of recovering the satellite from tumbling, and aligning the ADS-B
antenna boresight direction with the local magnetic field with an accuracy of ±3 degrees (2σ)
during secondary payload operations. The CanX-7 ADCS relies only on magnetic attitude
control. A three-axis magnetometer is used for attitude determination, and custom built
magnetorquers are used for attitude control. A Local Magnetic Field (LMF) tracking attitude
control algorithm has been developed for this mission. This algorithm has been evaluated
through computer simulation and has been implemented in flight software for the mission.
The thermal control system is designed to maintain all satellite components within their
operating temperature ranges during secondary payload operations. The thermal control system
is primarily passive and uses tapes applied to the exterior of the satellite in order to control
radiation heat exchange between the satellite and its environment. The selection of these tapes
relies on an iterative process using thermal finite difference analysis, and is the main aspect of
the thermal control system design.
1.1 The CanX-7 Mission
In recent years, orbital debris has been identified as a major risk to the future of space operations.
Every satellite on-orbit is susceptible to collision with orbital debris, which is likely to result in
loss of mission. Earth orbiting satellites provide the foundation for many communication and
navigation technologies, Earth observation techniques, and space science missions, making
Earth’s orbital environment a very valuable and limited resource that must be protected. If
satellites continue to be sent into orbit without implementing any means of space debris
mitigation, the probability of collisions will increase and eventually, carrying out useful space
operations will become impossible. In an effort to maintain current satellite operations, and
3
protect the future of space technology, the Inter-Agency Space Debris Coordination Committee
(IADC) has developed a guideline that all LEO satellites should have a means to de-orbit within
25 years of end-of-mission [1].
De-orbiting is particularly challenging for micro and nanosatellites, as they are limited in
terms of mass and volume. Consequently, there is currently no mature de-orbiting technology
targeted towards this class of satellite. In order for Canada to be a responsible partner in
maintaining a sustainable space environment for the future, it is essential that satellite de-orbiting
technology is made available for Canadian satellite missions. In order to meet this need, the
Space Flight Laboratory at the University of Toronto Institute for Aerospace Studies (UTIAS)
has investigated several possible de-orbiting technologies and has identified a mechanically
deployed drag sail to be the most advantageous technology for small satellite missions, which
predominately operate in LEO [2]. Upon end-of-mission, a satellite can deploy a drag sail to
interact with gaseous particles in the upper atmosphere to reduce the satellite’s orbital energy,
causing it to drop in altitude and eventually re-enter Earth’s atmosphere. Theoretical analysis has
concluded that a 4 m2 drag sail can successfully de-orbit satellites with mass up to 15 kg and
initial altitudes of up to 800 km in less than 25 years [3]. Before this technology can be
implemented on operational satellite missions, it must first be demonstrated on-orbit. The
CanX-7 (Canadian Advanced Nanospace Experiment-7) mission is designed to do exactly that.
The Space Debris Problem 1.1.1
Since the first satellite was launched in 1957, Earth’s orbital environment has been steadily
populated with man-made objects. Space debris is the compilation of rocket body upper stages,
retired satellites, and fragmented debris in orbit around Earth. As of 2010, there were
approximately 16000 items of space debris being tracked, primarily by ground-based radar, of
which 75% were in LEO [4]. Of major concern is a collision between two satellites. Not only
does a collision result in the loss of valuable satellite missions, it also leads to a large amount of
fragmented debris. In 2009, a collision occurred between the Kosmos 2251 and the Iridium 33
satellites that resulted in the creation of over 2300 pieces of fragmented space debris [5]. By
generating fragmented debris, satellite collisions increase the probability of more collisions
occurring in the future and therefore have an overall cascading effect. A study organized by
IADC concluded that without intervention, catastrophic collisions will occur between LEO
satellites every 5 to 9 years and this will drive the orbital debris population to increase steadily
4
over the next 200 years [6]. The study also advises that compliance with the 25 year de-orbit
guideline for LEO satellites is the first step in avoiding this trend. When the predicted natural
orbital decay for a future satellite is not sufficient to meet the 25 year de-orbit guideline,
equipping it with a de-orbit device is the proactive approach to space debris mitigation and can
involve one of several technologies including a mechanically deployed drag device, an inflatable
drag device, a solar sail, an electrodynamic tether, or a propulsion system.
Drag Sail Technology 1.1.2
Of all the de-orbit technologies, a mechanically deployed drag sail is well suited for nano and
microsatellite missions since it is relatively lightweight, compact, and simple in design. A drag
sail can be deployed upon end-of-mission to decrease the ballistic coefficient of the host
spacecraft. This results in an increased drag force due to interaction with Earth’s upper
atmosphere. The continuous drag force leads to a progressive decrease in orbit energy and
eventual de-orbiting of the satellite. The overall de-orbit device consists of the drag sail itself,
which is made of a thin film material such that it can be stowed tightly within the spacecraft
during the operational phase of its mission, and the mechanism used to deploy the sail. Once
deployed, a drag sail is completely passive and requires no operator intervention or support from
other satellite subsystems to ensure successful de-orbiting. When compared with propulsion or
an inflatable drag device, a drag sail requires no propellants or other pressurants which pose
issues for long term storage on-orbit as well as for safe storage and transport on Earth during
assembly, integration and testing of the spacecraft.
The CanX-7 mission aims to provide the first on-orbit demonstration of a drag sail
de-orbit device. Similar technologies have been demonstrated in the context of solar sails – a
device which aims to provide renewable propulsion for interplanetary missions. An example of
this is the NanoSail-D2 mission that demonstrated a 10 m2 solar sail that was deployed from a
3U satellite in 2011 [7] [8]. Several organizations are currently developing drag sail de-orbit
devices including the Space Glasgow Research Cluster at the University of Glasgow in
collaboration with small satellite systems provider Clyde Space, and Cranfield University in
collaboration with small satellite company Surrey Satellite Technologies Ltd. [9] [10]. What
makes the CanX-7 drag sail unique is that is follows a modular approach. The drag sail payload
is made up of four modules that each deploys a 1 m2 portion of the sail. Each sail module is
equipped with a deployment mechanism and electronics for command and telemetry gathering.
5
This allows the sail modules to be operated independently of one another to protect against a
single point of failure. In addition to redundancy, the modular design allows the de-orbit device
to be adapted for different spacecraft geometries and drag area requirements.
Figure 1-1: Images of a Single Drag Sail Module in Stowed (Left) and Deployed (Right) Configurations
The 1 m2 trapezoidal sail sections are folded and pre-packed into cartridges which are
then installed in the sail modules. The sail sections are mechanically deployed using a pair of
tape spring booms, which also maintain the sail geometry post-deployment. The booms are
manufactured at SFL from a copper beryllium alloy that is non-magnetic, as oppose to a more
traditional tape spring material such as carbon steel. The boom material selection was driven by a
magnetic cleanliness study for the spacecraft which is presented in Section 2.3.1. The sail
membrane is made from a thin film polyimide called Upilex with an aluminum coating deposited
on both sides via vapour-deposition. This material was selected to provide the desired
combination of mechanical and thermo-optical properties. The thermal analysis that contributed
to the drag sail material selection is presented in Section 4.6.1. The tape spring boom and sail
designs, along with their manufacturing processes are described in [11].
The sail module structures are primarily additively manufactured using a carbon fiber
reinforced polyamide composite material called Windform XT 2.0. This allows for a lightweight
product as well as intricate features that would be difficult or impossible to make using
traditional machining. A detailed description of the mechanical design for the drag sail modules
can be found in [12]. Prior to drag sail deployment, the sail membrane and the tape spring booms
remain stowed within the sail modules. Hinged doors on the sail cartridges restrain the coiled
tape spring booms, preventing them from unwinding, and are held closed by Vectran cords.
6
When a sail module is commanded to deploy, a nichrome wire heating element is used to melt
the Vectran cord thereby releasing the door and allowing the booms to unwind, which then pull
out the sail and cause it to unfurl.
The drag sail electronics, shown in Figure 1-2, are made up of two Printed Circuit Boards
(PCBs) referred to as the main board and the cartridge board. The main board which is mounted
in the module housing is responsible for decoding commands routed from the spacecraft’s radio
receiver, operating the sail deployment heater, and gathering deployment telemetry from a switch
on the cartridge door and a Hall effect sensor used to measure the deployment rate of the booms.
The cartridge board provides a convenient method for mounting the heating element and the door
switch.
Figure 1-2: Drag Sail Electronics – Hall Effect Sensor (Left), Cartridge Board (Middle), Main Board (Right)
Overall, the drag sail de-orbit device developed at SFL represents a proactive solution to
the space debris problem, allowing micro and nanosatellites to be de-orbited from LEO within
the IADC 25 year specification. The modular, lightweight, and compact design was the result of
various stages of prototyping and extensive testing, and now represents a robust product. Once
validated on-orbit during the CanX-7 mission, the drag sail de-orbit device can be easily
implemented on a wide variety of spacecraft platforms for future missions.
Additional Scientific Value 1.1.3
In addition to the primary drag sail payload, the CanX-7 mission offers additional scientific
value from each of the two remaining payloads. Operation of the ADS-B payload on-orbit will
validate and enable further improvements to this technology. Automatic dependant surveillance –
broadcast is a new aircraft surveillance technique that is well positioned to replace radar
7
surveillance. Aircraft equipped with this technology autonomously broadcast flight information
including aircraft ID, position, altitude, airspeed, and heading at regular intervals via radio
communications [13]. This information is provided to pilots and air traffic controllers to allow
for improved situational awareness and flight planning. This surveillance technique is already
used in several regions across North America, however, falls short in oceanic and remote regions
where ground stations that receive the ADS-B radio signals are out of range. With the use of
satellites to receive and relay ADS-B radio signals, ADS-B surveillance can be made available in
these regions. This will allow air traffic controllers to accurately monitor and coordinate aircraft
spacing which can reduce flight times and fuel consumption. This would lead to significant
environmental benefits, as well as financial benefits for the airline industry. The overall
operations concept for the ADS-B payload is shown in Figure 1-3 below.
Figure 1-3: Operations Concept for the ADS-B Payload [2]
In Canada, the main stakeholder is NAV CANADA. NAV CANADA is Canada’s civil air
navigation service provider. In 2009, NAV CANADA implemented ground based ADS-B
surveillance in the Hudson Bay region where surveillance was previously unavailable. They have
estimated an annual fuel savings of 195 million dollars as a result of this implementation [14].
The CanX-7 mission is a stepping stone towards a global infrastructure of on-orbit ADS-B relay
stations that will improve air travel for the future. Specifically, operation of the ADS-B receiver
on-orbit will validate signal propagation and system throughput models, characterize signal
8
collision in congested airspace, and allow evaluation of the data gathering process with
NAV CANADA in the loop. An image of the ADS-B payload hardware is shown in Figure 1-4
below.
Figure 1-4: ADS-B Payload Hardware
In order for the ADS-B antenna to receive radio transmissions from aircraft, the antenna
boresight must be roughly pointed in the nadir direction. To reduce mass, complexity and cost,
the CanX-7 satellite does not include a full suite of three-axis ADCS hardware, making it very
difficult to achieve nadir pointing. Therefore, it was determined that aligning the ADS-B antenna
boresight with the local magnetic field direction (with an accuracy of ±15 degrees 2σ) will be
adequate to receive ADS-B radio transmissions, and this became a design requirement for the
mission [15]. Antenna pattern analysis completed for the ADS-B payload shows that signals can
be received at incoming angles up to 65 degrees from the antenna boresight direction [16].
According to the antenna pattern and simulated spacecraft attitude profiles, ADS-B signals will
be received over a large geographic region in the northern hemisphere. The specific coverage
will be discussed in more detail in Section 2.5.
The miniature Visual Inspection Camera (mVIC) for imaging the drag sail acts as a
tertiary payload, and is the first imaging system developed at SFL for the purpose of spacecraft
visual inspection. For the CanX-7 mission, it will be used for evaluating drag sail deployment
and monitoring the drag sail for damage due to micrometeoroid and orbital debris impacts.
9
mVIC will be mounted on a deployable boom and uses three commercial off-the-shelf 0.3
megapixel resolution RGB (red, green, blue) image sensors optimally oriented in order to image
all four sail sections. This same technology can be implemented on future missions for
evaluating spacecraft health and providing deployment confirmation for drag sails, antennas, or
solar arrays. The mVIC hardware is shown in Figure 1-5 below, along with an illustration of the
field-of-view for each sensor when projected onto the sail sections to show the imaged areas.
Figure 1-5: mVIC Hardware (Left), mVIC Field-of-View Projections (Right)
1.2 The CanX-7 Satellite
In order to be demonstrated on-orbit, the payloads are integrated into a satellite bus, and together
form the CanX-7 spacecraft. As mentioned before, the satellite uses a 3U form factor with
dimensions 10 x 10 x 34 cm. Exterior views of the satellite in both the stowed and deployed
configurations are illustrated in Figure 1-6 and Figure 1-7 below. The coordinate system
provided in Figure 1-6 and Figure 1-7 will be referred to as the spacecraft body-fixed frame ( )
and will be used throughout this report. The origin of the spacecraft body-fixed frame is located
at the spacecraft’s center of mass, however, is often shown adjacent to the spacecraft for clarity.
The bus structure is made from aluminum panels and is designed to survive the mechanical loads
experienced during launch on board a chemical rocket. The bus structure provides mounting
locations for the payloads as well as all spacecraft electronics. The overall bus design along with
results from structural finite element analysis can be found in [17].
10
Figure 1-6: CanX-7 Spacecraft Exterior Views (Stowed)
Figure 1-7: CanX-7 Spacecraft Exterior Views (Deployed)
X
Y
Z
�� 𝑏
UHF Antennas
S-band Antennas
ADS-B Antenna
Y X
Z
�� 𝑏
Drag Sail
Modules
Inspection Camera/
Magnetometer Boom
Solar Cells
Y
Z
X
�� 𝑏
Z
Y X
�� 𝑏
11
Several components are mounted to the exterior surfaces of the spacecraft including solar
cells which provide electrical power generation, a deployable Ultra-High Frequency (UHF)
canted turnstile antenna which allows for radio uplink, S-Band patch antennas which allow for
radio downlink, and the ADS-B L-Band patch antenna used for receiving aircraft transmissions.
There is also a deployable boom which supports the inspection camera and the magnetometer.
By placing these components on a deployable boom, the inspection camera is able to image all
four drag sail sections, and the magnetometer measurements are less susceptible to magnetic
disturbances from the spacecraft electronics. The four drag sail modules are mounted near the
+Y satellite panel, and are arranged to deploy at right angles to one another. The post sail
deployment configuration of the CanX-7 spacecraft is illustrated in Figure 1-8 below.
Figure 1-8: CanX-7 Spacecraft with Deployed Drag Sail
12
The interior layout of the satellite is illustrated in Figure 1-9 below. The –Z tray
accommodates the Power Distribution Unit (PDU) and the On-Board Computer (OBC). The
PDU provides a regulated bus voltage that is used by the spacecraft payloads and subsystems,
and can vary between 3.8 and 5.5 V. The OBC is used for gathering telemetry from the various
spacecraft subsystems and payloads, routing communication packets, executing the attitude
control algorithms, and supports storage and compression of image data gathered by the
inspection camera. The +Z tray houses the radio electronics and the battery. A 5.0 A∙h battery
provides energy storage and eclipse power. A UHF receiver provides a 4 kbps command uplink,
while an S-Band transmitter provides downlink at 32 kbps minimum, 1 Mbps maximum. The
ADS-B payload is located in its own enclosure which is mounted to both the –Z and +Z trays.
Figure 1-9: CanX-7 Spacecraft Internal Layout: -Z Tray (Left), +Z Tray (Right)
The key spacecraft parameters are summarized in Table 1-1 below. Of these parameters,
the total spacecraft mass and the spacecraft inertia matrix are very important to the attitude
determination and control system design.
Y
X Z
�� 𝑏
Magnetorquers
OBC
PDU
X
Y
Z
�� 𝑏
Battery
ADS-B Payload
Enclosure
Drag Sail
Modules
UHF & S-Band
Radio Enclosures
13
Table 1-1: Key CanX-7 Spacecraft Parameters
Parameter Value
Spacecraft Geometry
Total Mass ( )
Center of Mass ( ) [ ]
Spacecraft Inertia Matrix ( ) [
]
Power Generation
Battery Capacity
Bus Voltage ( )
Attitude Solution Local Magnetic Field Tracking
Pointing Accuracy Command Uplink
Data/Telemetry Downlink
On-board Data Storage
1.3 Launch and Orbital Parameters
The CanX-7 team is targeting launch readiness by Q2 2015. However, at this time no launch
service has been arranged. It is certain that the spacecraft will travel to space aboard a chemically
propelled launch vehicle. The CanX-7 spacecraft will act as a secondary payload aboard the
launch vehicle and therefore will be inserted into the same orbit specified by the primary payload
provider. As a consequence, the CanX-7 team will not be able to choose the spacecraft’s orbit.
In general, it is advantageous to design a spacecraft that is compatible with a large range
of possible orbits such to not exclude possible launch services. With this in mind, during the
detailed design phase, the ADCS and thermal control system were designed for a Sun-
Synchronous Orbit (SSO) with an altitude between 600 and 800 km, and an unconstrained Local
Time of Ascending Node (LTAN). Table 1-2 below summarizes the relevant parameters for this
range of orbits.
Table 1-2: Range of Orbit Parameters used for Spacecraft Detailed Design
Parameter Value
Orbit Type SSO
Orbit Altitude 600 – 800 km
Inclination 97.8° – 98.6° Orbit LTAN Any
Orbital Period 5792 – 6044 s
Eclipse Period 0 – 2103 s
14
Once the launch vehicle has achieved the target orbit, the CanX-7 satellite will be ejected
from the launch vehicle by an eXoadaptable PyrOless Deployer (XPOD). The SFL developed
XPOD system consists of an aluminum shell which houses the spacecraft during launch, a large
compression spring to push the spacecraft away from the launch vehicle, and a mechanism to
release the door which holds the spacecraft in place. Figure 1-10 below provides an illustration
of the XPOD that will be used for the CanX-7 mission. On command, the door is released and
the potential energy stored in the spring causes the spacecraft to be pushed-out away from the
launch vehicle. The XPOD design and operation is fully documented in [18]. The XPOD
interfaces with four launch rails that are part of the bus structure to hold it securely during launch
and to guide the spacecraft as it is ejected. During ejection, the XPOD will impart some angular
velocity on the CanX-7 spacecraft. The ADCS will have to eliminate this angular velocity during
the commissioning phase of the mission through a process called detumbling. Traditionally at
SFL, spacecraft attitude analysis has been completed to validate detumbling from initial angular
velocities up to 20°/s. More recently, theoretical analysis of the ejection dynamics has shown this
value to be very conservative [19]. Based on the CanX-7 geometry and mass properties, the
analysis predicts an initial spacecraft angular velocity of 4.0°/s. ADCS simulation results for
detumbling are provided later in Section 2.5 for initial angular velocities of both 4.0 and 20 °/s.
Figure 1-10: CanX-7 XPOD
15
Chapter 2
Magnetic Attitude Control
Magnetic attitude control relies on interactions between on-board magnetic actuators and Earth’s
magnetic field to apply control torques on a spacecraft. This attitude control technique is used
extensively for nano and microsatellite missions where physical space and power are limited.
Magnetic attitude control is most commonly used for a process known as detumbling that
involves eliminating spacecraft angular velocity which results from the satellite being ejected
from the launch vehicle. The control algorithm used for this procedure is known as the B-dot
control law because it relies on the change in local magnetic field relative the spacecraft, which
is commonly denoted with the symbol [20]. Magnetic attitude control has been implemented
on all past SFL missions for detumbling including the most recently launched CanX-4 and
CanX-5 satellites [21]. CanX-7 will be the first SFL mission to utilize active magnetic attitude
control alone to fulfill mission level pointing requirements.
The CanX-7 attitude determination and control system uses a magnetometer to measure
the local magnetic field with respect to the spacecraft body-fixed frame, and a set of three
16
orthogonally mounted magnetorquers to induce torques on the spacecraft by interacting with
Earth’s magnetic field based on the following equation [20]:
(2-1)
where is the induced control torque, is the local magnetic field strength, and is the sum
of the magnetic dipole moments created by each of the magnetorquers ( ∑ ), all
expressed in the spacecraft body-fixed frame.
As mentioned before, ADS-B payload operations require the ADS-B antenna boresight
direction to be aligned with the local magnetic field with an accuracy of ±15 degrees (2σ) [15]. A
first cut of the attitude control algorithm for the mission was developed by Tarantini [22], and
preliminary computer simulations indicated that this pointing accuracy can be achieved. As part
of this thesis project, the magnetorquer attitude actuators for the mission were designed and
tested, the control algorithm and attitude simulations were refined, and the ADCS software was
designed and implemented. Also, a magnetic cleanliness study for the CanX-7 satellite was
completed to determine input parameters for the attitude simulations.
2.1 Local Magnetic Field Tracking
Earth’s magnetic field is complex; however, its main component is that of a perfect
dipole located at the center of Earth and tilted approximately 11.5 degrees from Earth’s
geometric north pole. A simplified illustration of Earth’s magnetic field is provided in Figure 2-1
below. Figure 2-1 also shows the CanX-7 spacecraft attitude if the antenna boresight was able to
perfectly track the local magnetic field direction. Given perfect LMF tracking the satellite would
rotate 720 degrees per orbit. For evaluation of the CanX-7 attitude control algorithms, the
International Geomagnetic Reference Field (IGRF) model is used. IGRF is a numerical model
for calculating Earth’s magnetic field at a given location on or above Earth’s surface at a given
time [23]. The IGRF model has been developed through the collaboration of scientists and
engineers from around the world using data gathered from satellites and ground based magnetic
observatories.
17
Figure 2-1: Spacecraft Attitude Profile given Perfect LMF Tracking
To facilitate discussion later in this report regarding attitude simulations and performance
of the ADCS, important reference frames are illustrated in Figure 2-1. The Earth-Centered
Inertial (ECI) frame ( ) is located at the center of Earth with the Z axis pointed towards the
geometric north pole, and the X axis pointed in the direction of the vernal equinox. For
simplicity, Figure 2-1 shows the direction of the vernal equinox to lie in the orbital plane; for a
SSO this condition cannot persist, however, will occur twice per year. As previously defined, the
spacecraft body-fixed frame ( ) is located at the spacecraft’s center of mass and is fixed
relative to the spacecraft. The ADS-B antenna boresight is aligned with the –X direction in the
spacecraft body-fixed frame and is shown by the blue arrows.
Antenna
Boresight
Magnetic
North Pole
Geometric
North Pole
Z
Y
X
�� 𝒊
Y
Z
X
�� 𝑏
18
2.2 Attitude Control Hardware
In this section, the magnetic sensors and actuators for the CanX-7 attitude determination and
control system will be described in greater detail. The magnetometer sensor follows a generic
design and is used for many SFL missions, whereas the magnetorquer actuators have been
custom designed for the CanX-7 mission.
Magnetometer 2.2.1
The magnetometer that is being used for attitude determination has been manufactured in-house
at SFL and was designed by Fournier [24]. The magnetometer uses three orthogonally mounted
magneto-inductive sensors to provide 3-axis magnetic field measurements. The magnetometer
has a measurement range of -1100 to +1100 μT, and a resolution of +/- 20 nT. The
magnetometer board also includes power conditioning components and a microcontroller to
support polling software for the magneto-inductive sensors and to support communications with
the on-board computer. The whole package takes up a 42 22 mm dimensioned board and can
be seen in Figure 2-2 below.
Figure 2-2: Top (Left) and Bottom (Right) Images of the Magnetometer
In order to prepare the magnetometer for flight, a standard SFL magnetometer acceptance
test was completed [25]. This involved testing the magnetometer’s functionality over its
operational temperature range using a thermal chamber. In addition, the magnetometer was sent
to the Institute for Geophysics and Extraterrestrial Physics at TU Braunschweig where it was
calibrated in a three-axis Helmholtz coil facility [26]. The coil facility is used to produce a
known magnetic field, which is then compared against the magnetometer readings. The
differences are recorded and are then accounted for by the ADCS software.
19
Magnetorquers 2.2.2
A magnetorquer is a set of coiled wires, and when current is passed through the coil a magnetic
field is generated. With three magnetorquers mounted orthogonally, a net magnetic dipole
moment can be created in any direction. Magnetorquers have been designed and implemented for
past SFL missions; however, they have always relied on external electronics to control the
current flow through the magnetorquers coils [27]. For the CanX-7 mission, there was a desire to
have the control circuit built into the magnetorquers themselves to reduce cost and complexity.
This desire has been fulfilled through the design of new magnetorquers that include a built-in
logic circuit. Fittingly, this new hardware has been dubbed the “Smart Torquer”. To enable
reliable and repeatable manufacturing and performance, the Smart Torquers were designed using
printed circuit board technology. An image of the final product can be seen in Figure 2-3 below.
Figure 2-3: CanX-7 Smart Torquer
The design for the magnetorquers involves two main aspects, the logic circuit for
controlling the current flow through the coils and the coils themselves. In order to create a
magnetic dipole moment in any direction, the three magnetorquers must be capable of passing
current in both directions. To allow this functionality, an H-bridge Integrated Circuit (IC) is
20
used. Figure 2-4 below provides a schematic of the overall electrical circuit for the Smart
Torquers.
Figure 2-4: Smart Torquer Electrical Schematic
Two control lines are used to set the state of the H-bridge; this controls the direction of
current passing through the coils. The transistors (Q) act as intermediate switches to provide the
H-bridge inputs with the correct voltage. Pull-up resistors (Rpull-up) are included to ensure
H-bridge inputs settle quickly when the control line voltages are switched, and the bypass
capacitor (Cbypass) dampens noise on the input bus voltage (Vbus). A selectable trim resistor (Rtrim)
allows the total magnetorquer resistance to be fine-tuned after the hardware is tested. The two
control lines are designed to be connected to general purpose inputs/outputs on the OBC which
are controlled by the ADCS software. These control lines may be set to a low logic voltage (0 V)
or a high logic voltage (3 V). As a result, there are four possible magnetorquers output states.
The output states will be referred to as Forward, Reverse, Brake, and Idle. Table 2-1 below
summarizes the possible inputs, and the corresponding output states. Figure 2-5 below illustrates
the current and magnetic dipole moment directions which are expected in both the Forward and
Reverse states. When braked, the H-Bridge outputs are both connected to Vbus, therefore
stopping the flow of current through the coils. When idling, the H-Bridge outputs are connected
with high impedance. The electrical circuit does not allow the current magnitude to be
controlled; this is accomplished through pulsed width modulation of the control lines.
Specifically, the ADCS software sets the amount time each magnetorquer is to be actuated and in
H-Bridge
GndQControl Line 1
Cbypass
Q
Rpull-up
Rpull-up
Gnd
IN1
IN2
OUT1
OUT2
Control Line 2
Vbus
Vbus
Magnetorquer
Coil
Rtrim
21
which direction during each control cycle. The operation of the magnetorquers will be discussed
in more detail in Section 2.4.
Table 2-1: Magnetorquer States
Inputs Output State Current Direction
Magnetic Dipole
Direction Control Line 1 Control Line 2
Low Low Brake N/A N/A
High Low Forward Clockwise South
Low High Reverse Counter-Clockwise North
High High Idle N/A N/A
Forward State Reverse State
Figure 2-5: Magnetorquer Current and Dipole Directions by State
The end goal of the magnetorquers is to induce torques on the spacecraft based on the
relationship given in (2-1). Therefore, the most important design metric for the magnetorquers is
the magnetic dipole moment which they generate. The magnetic dipole moment for each
magnetorquer is given by the following equation:
(2-2)
where is the current passing through the coil, is the area vector encompassed by the coil, and
is the number of coil windings. The current depends on the bus voltage and the total resistance
of the coil. Based on the power system design, the bus voltage is predefined and can vary
between 3.8 and 5.5 V. The total coil resistance, however, can be adjusted based on the coil
geometry and number of coil windings.
Current
Direction
Magnetic Dipole
Moment Direction Current
Direction
Magnetic Dipole
Moment Direction
22
The magnetorquers were designed to produce a nominal magnetic dipole moment of
0.2 A∙m2. The coil geometry is constrained by the spacecraft mechanical design, and is allowed
maximum dimensions of 76 mm by 65 mm. To achieve the desired magnetic dipole moment
within the size constraints, each magnetorquer is made up of two PCBs stacked on top of each
other, each with 11 layers and 7 windings on each layer. In total, the magnetorquers have 154
windings with an average area of 3.67 cm2. The total resistance of each magnetorquer varies with
temperature since the resistivity of the copper coil is temperature dependent. To avoid placing
demanding requirements on the thermal control system for the CanX-7 mission, as well as to
remain compatible with future missions, the magnetorquers are design and tested for an
operating temperature range from -30 to 70°C. Table 2-2 below summarizes the expected
magnetorquer magnetic dipole moments across the full range of temperatures and supply
voltages. The range of expected magnetic dipoles moments is considered when predicting
on-orbit performance in Section 2.5.
Table 2-2: Range of Expected Magnetorquer Magnetic Dipole Moments
Case Bus Voltage
[V]
Temperature
[°C]
Overall Resistance
[Ω]
Magnetic Dipole Moment
[A∙m2]
Minimum Dipole Moment 3.8 70 13.9 0.154
Nominal Dipole Moment 4.2 20 11.7 0.200
Maximum Dipole Moment 5.5 -30 9.61 0.281
To ensure functionality of the magnetorquers across their required operating temperature
range, an acceptance test procedure has been developed and carried out [28]. The test involved
placing the magnetorquers in a thermal chamber and testing their functionality at several key
temperature levels. The Smart Torquers functioned as expected throughout all testing and are
now ready for spacecraft integration.
The Smart Torquer design represents a substantial improvement over previous designs
and this hardware is now being incorporated into other SFL missions including GHGSat-D and
NORSAT-1.
2.3 Magnetic Cleanliness
By the same principal that the magnetorquers apply control torques to the spacecraft, any
magnetic field generated by ferromagnetic materials or current loops also induces a torque on the
spacecraft. The net torque induced on the spacecraft by magnetic fields other than those created
23
by the magnetorquers is known as the magnetic disturbance torque ( ) and is given by the
following equation:
(2-3)
where is the local magnetic field strength, and is the net magnetic dipole moment created
by all sources other than the magnetorquers, which will be referred to as the parasitic dipole
moment of the spacecraft. All parameters in (2-3) are expressed in the spacecraft body-fixed
frame. The overall torque on the spacecraft ( due to the magnetorquers and the spacecraft
parasitic dipole moment is given by (2-4) below. Again, all parameters are expressed in the
spacecraft body-fixed frame.
(2-4)
In order to maintain control of the spacecraft’s attitude, the parasitic dipole moment must
be less than the magnetic dipole moment created by the magnetorquers. Based on the minimum
magnetic dipole moment that is available from the magnetorquers (see Table 2-2), the parasitic
dipole moment must be less than 0.154 A∙m2. In addition, with a smaller parasitic dipole
moment, less magnetorquer actuation will be required to control the spacecraft’s attitude and will
result in lower power consumption. Overall, it is important to predict the parasitic dipole moment
for the spacecraft, and reduce its magnitude when possible.
In order to estimate the parasitic dipole moment of the spacecraft, a magnetic cleanliness
study was completed. Since it was not possible to measure the magnetic field generated by the
fully assembled CanX-7 satellite, the study involved making estimates based on past SFL
satellites and investigating certain components that are likely to cause problems for CanX-7. The
main contributors to the spacecraft parasitic dipole moment are expected to be steel fasteners,
current loops in the wire harness, the solar cells, the tape spring booms which are used to deploy
the drag sails, and the magnets used by the Hall effect sensors which measure the deployment
velocity of the tape spring booms. Since the bus structure and layout is similar to that used for
the CanX-2 mission, the dipole contribution from the fasteners, wire harness and solar cells is
estimated based on the total parasitic dipole moment determined for CanX-2. The total parasitic
dipole moment for CanX-2 was never measured precisely using a coil facility; however, attitude
telemetry from orbit suggests that the spacecraft has a total parasitic dipole moment of
0.007 A∙m2 [22].
24
Tape Spring Booms – Parasitic Dipole Moment Contribution 2.3.1
Due to low cost and availability, early prototypes of the drag sail payload used tape spring
booms made with AISI 1050 medium carbon steel. In total, the payload uses 8 of these tape
spring booms, each 1.6 m in length. AISI 1050 steel is ferromagnetic, and therefore the impact of
the tape spring booms on the magnetic cleanliness of the spacecraft was investigated. Since the
magnetic properties of steel are highly dependent on the manufacturing process and final part
geometry, the magnetic dipole moment of the booms was determined through experimentation.
An image of the boom samples used for experimentation as well as an illustration of the cross
sectional profile of the tape spring booms are provided in Figure 2-6 below.
Figure 2-6: Tape Spring Boom Samples (Left) and Cross Section Dimensions (Right)
The magnetic dipole moment of the boom samples cannot be measured directly;
however, it can be estimated based on magnetic field measurements taken in the vicinity of the
samples with a calibrated magnetometer. Experimentation revealed that the magnetic dipole
moment for all samples is roughly aligned with the boom longitudinal direction. Using this
information, the magnetic dipole moment for each sample can be predicted with a single
magnetic field measurement using (2-5) below:
∑
⁄ (2-5)
where is the magnetic dipole moment of the boom sample in the x direction (see Figure 2-7),
is the magnetic permeability of free space, is the magnetic field measured by the
magnetometer in the x direction, is the distance between each discretized boom element and
magnetometer, and is the number of boom elements. All of the variables are illustrated in
Figure 2-7 below. In order to account for other sources of magnetic field in the lab environment
18.15 mm
2.71 mm
0.12 mm
25
where the testing was completed, a background field measurement without the boom sample in
position was taken and subtracted from that measured when the boom sample was present.
Figure 2-7: Parameters for Estimating Magnetic Dipole Moment of Boom Samples
The results from this experiment are presented in Figure 2-8 below. It can be seen that the
measured magnetic dipole moment increases linearly with increasing boom length. Using linear
extrapolation, the overall magnetic dipole moment for a 1.6 m boom can be estimated at
0.24 A∙m2. Along with a large magnitude, the measured magnetic dipole moments exhibit a large
variation from sample to sample, as high as 171%. The error bars in Figure 2-8 indicate one
standard deviation of the estimated magnetic dipole moment across several samples.
Figure 2-8: Magnetic Dipole Moment vs. Boom Length
Compensating for parasitic dipole moments on the order of 0.24 A∙m2 is beyond the
capability of the magnetorquers. However, during ADS-B payload operations when the
X
Magnetometer
𝑟 𝑟 𝑟 𝑟4 𝑟5
𝐵𝑥 𝑚𝑥
Boom Sample
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0 5 10 15 20 25
Ma
gn
etic
Dip
ole
Mom
ent
[A∙m
2]
Boom Length [cm]
𝑦 𝑥
𝑅
26
magnetorquers are providing LMF tracking, the tape spring booms will be in their stowed
configuration. When stowed, the tape spring booms are coiled up inside the drag sail modules as
shown in Figure 2-9 below.
Figure 2-9: A Pair of Tape Spring Booms in their Stowed Configuration
To determine the magnetic dipole moment of the tape spring booms in their coiled
configuration, a similar experiment was performed. In this case, it was not possible to assume the
magnetic dipole moment direction; therefore, magnetic field measurements were taken with the
magnetometer at 11 locations in three dimensions around the set of coiled booms. Matlab was
then used to perform a least squares fit on the data in order to estimate the magnetic dipole
moment based on (2-6) below [29]:
(
5
) (2-6)
where is the magnetic field measured by the magnetometer, is the magnetic dipole moment
of the coiled booms, and gives the location of the magnetometer relative to the coiled booms,
all expressed in a common reference frame. The results from this experiment are summarized in
Table 2-3 below.
Table 2-3: Magnetic Dipole Moment Measurements for Coiled Booms
Sample 1 Sample 2 Sample 3 Sample 4 Average Standard
Deviation
0.0075 A∙m2 0.0060 A∙m2
0.0097 A∙m2 0.0078 A∙m2
0.0078 A∙m2 0.0015 A∙m2
The average magnetic dipole moment for a single set of coiled booms was measured to
be 0.008 A∙m2. Since the magnetic dipole moment for each boom section is in the longitudinal
27
direction, the vectors cancel out when the booms are coiled up and the total magnetic dipole
moment is small compared to that estimated for a deployed boom. Based on this data, the
absolute worst case dipole for all four sets of coiled booms would be 0.04 A∙m2.
The magnetic dipole moment of a ferromagnetic material is based on its residual
magnetism, and can be altered if the material is subjected to an external magnetic field. The
maximum expected magnetic flux density that the satellite may experience during transportation,
pre-launch activities, and launch is 2.5 mT based on a study by NASA [30]. To test this situation,
a Helmholtz coil was constructed in order to subject the tape spring booms to a 2.5 mT field. A
Helmholtz coil is made up of two identical current carrying coils which are separated by a
distance equal to the radius of the coils. Due to this geometry, a Helmholtz coil produces a
magnetic field that is uniform along the line that passes through the center of the two coils with a
magnetic flux density ( ) given by (2-7) below:
(
) ⁄
(2-7)
where is the number of loops in each coil, is the current passing through the coils, and is
the effective coil radius and spacing. The test setup is shown in Figure 2-10 below. The test
samples were placed on a pedestal at the center of the Helmholtz coil and a DC power supply
with variable current was used to produce the desired field strength of 2.5 mT.
Figure 2-10: Helmholtz Coil Test Setup
28
Magnetization experiments were conducted with booms of various lengths, and the
results are summarized in Figure 2-11 below. Again, the error bars indicate one standard
deviation of the estimated magnetic dipole moment across several samples. By extrapolating the
data, the maximum magnetic dipole moment expected for a 1.6 m boom after being exposed to a
2.5 mT field is 0.74 A∙m2. Compensating for this magnitude of magnetic dipole moment is far
beyond the capability of the magnetorquers. However, these experiments involved magnetizing
the booms in their longitudinal direction which will not be possible during transportation and
launch of the satellite, as the booms will be coiled up.
Figure 2-11: Induced Magnetic Dipole Moment vs. Boom Length using a 2.5 mT Field
Magnetization experiments were also conducted with pairs of coiled booms in their
stowed configuration. The results from these experiments are summarized in Table 2-4.
Following magnetization with a 2.5 mT field, the coiled booms showed an average magnetic
dipole moment of 0.018 A∙m2, an increase of about 0.01 A∙m2
when compared to the
unmagnetized booms. This is considerably less then was predicted for an uncoiled boom. It is
suspected that the outer layers of material act as magnetic shielding, which redirects the
magnetic fields lines and prevents the inner layers from being magnetized. Based on this result,
the maximum magnetic dipole moment for all 4 sets of coiled booms would be 0.072 A∙m2.
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 5 10 15 20 25
Maxim
um
Ch
an
ge
in
Magn
etic
Dip
ole
Mom
ent
[A∙m
2]
Boom Length [cm]
𝑦 𝑥
𝑅
29
Table 2-4: Magnetic Dipole Moment Measurements for Coiled Booms following Magnetization
Sample 1 Sample 2 Sample 3 Sample 4 Average Standard
Deviation
0.017 A∙m2 0.015 A∙m2
0.018 A∙m2 0.020 A∙m2
0.018 A∙m2 0.0021 A∙m2
Overall, the parasitic dipole moment contribution from AISI 1050 steel tape spring
booms could be significant. Given the worst case estimated magnetic dipole moment magnitude,
the worst case magnetic dipole moment direction, and nominal values for magnetorquer
resistance and bus voltage, an overall average magnetorquer power consumption of 1.13 W
would be required to overcome the magnetic disturbance torque. The CanX-7 power system
cannot support a load of this magnitude for the magnetorquers on a long-term basis [31]. To
mitigate the magnetic cleanliness issue associated with the tape spring booms, two solutions
were identified. The first solution involves degaussing the tape spring booms and transporting
the spacecraft in a magnetic shielding container. Degaussing is a process used to eliminate
residual magnetism in a material by exposing it to an alternating magnetic field of decreasing
strength [30]. Then, transporting the spacecraft in a magnetic shielding container ensures that the
tape spring booms would not be re-magnetized. The second option involves using a non-
magnetic material for the tape spring booms instead of steel. This option was chosen, and it was
decided to switch the boom material to a non-magnetic copper beryllium (CuBe) alloy. As a
result, the tape spring booms no longer contribute to the parasitic dipole moment of the
spacecraft. A manufacturing process for the CuBe tape spring booms was developed and carried
out in-house at SFL, and a full description of this process and the resultant boom properties can
be found in [11].
Hall Effect Sensor Magnets – Parasitic Dipole Moment Contribution 2.3.2
Operation of the Hall effect sensors that are used for measuring the extent of deployment for the
drag sails requires the use of small permanent magnets. In total there are 4 magnets, each with a
magnetic dipole moment of 0.005 A∙m2. The location of these magnets within the drag sail
modules is shown in Figure 2-12 below. Since the drag sail modules are mounted symmetrically,
the net magnetic dipole moment of the 4 magnets should be zero. If a conservative worst case
alignment of the magnets of 15 degrees is assumed, the total magnetic dipole moment would be
0.005 A∙m2.
30
Figure 2-12: Hall Effect Sensor with Magnet
Overall Expected Spacecraft Parasitic Dipole Moment 2.3.3
With non-magnetic tape spring booms for the drag sail payload, the worst case magnetic dipole
moment for the spacecraft can be taken as the sum of the contributions from the bus and the Hall
effect sensor magnets. Therefore, the expected worst case magnetic dipole moment for the
spacecraft is 0.012 A∙m2. This will be used as the parasitic dipole moment in the attitude
simulations presented in Section 2.5.
2.4 Attitude Control Algorithms
The CanX-7 attitude control algorithm uses a PID controller to eliminate error between the
spacecraft target vector and the LMF direction. Fittingly, this control algorithm has been dubbed
the “LMF Tracker”. Since magnetorquer currents are controlled via low frequency Pulsed Width
Modulation (PWM), the LMF Tracker calculates the duration each magnetorquer must be
actuated during the next control cycle based on the proportional, derivative and integral errors.
The first iteration of the control algorithm developed by Tarantini is given by (2-8)
below:
[
]
(2-8)
where is the control vector that specifies the actuation time for each of the three
magnetorquers ( ) during control cycle “ ”. , , and are the proportional, integral
and derivative gain matrices, and , , and are the proportional, integral and derivative
31
errors between the spacecraft target vector ( ) and the LMF direction ( ), both taken in the
spacecraft body-fixed frame. The proportional, integral and derivative errors are calculated using
the equations below:
(2-9)
(2-10)
(
)
(2-11)
where is the control cycle period.
The control algorithm has been refined and the final LMF Tracker control algorithm that
is implemented in the flight software is given by (2-12) below:
[
]
(
) (2-12)
Two main changes were implemented. First, a term ( ) has been added to scale the actuation
times based on the inertia matrix for the spacecraft. This change allows the algorithm to control
the angular acceleration that is imparted on the spacecraft as opposed to simply the torque which
acts on the spacecraft. This additional term significantly improves the performance of the control
algorithm, and reduces the steady state LMF tracking error from 11.4 to 3.0 degrees (2σ). The
second change is the addition of a bias term ( ) that is added to the final magnetorquer
actuation times. This term will allow the spacecraft operator to account for the spacecraft’s
parasitic dipole moment, which will not be accurately measured before launch but can be
determined based on on-orbit attitude performance. This will further improve pointing
performance and reduce the settling time when the spacecraft transitions from passive to active
attitude control states (see Section 2.6). Based on simulation results, a control cycle period of 1
second has been selected, and the proportional, integral, and derivative gains have been
optimized. The gain values implemented in the flight software are provided below:
[
] [
] [
]
Since the target vector is aligned with the -X axis in the spacecraft body-fixed frame, the X axis
integral error tends to infinity. This relationship arises because constantly actuating the X axis
32
magnetorquer, and hence constantly generating a magnetic dipole moment in the -X direction
leads to the best performance in terms of LMF tracking. However, it would also lead to a large
power consumption. Similar performance can be achieved at much lower power consumption if
the X axis integral error is ignored, therefore, the X axis integral gain is set to zero.
In addition to the LMF Tracker control algorithm, upper and lower limits are placed on
the magnetorquer actuation times. Since the ADCS software is run on the on-board computer and
must share processing time with other software threads, the timing of magnetorquer actuation has
an accuracy of +/-40 ms. Therefore, better LMF tracking is achieved if small actuation times
below a given threshold are not implemented. This threshold was determined through simulation
to be 20 ms. The equations below show how this rule is implemented for each of the
magnetorquers, and results in an updated control vector :
{
(2-13)
{
(2-14)
{
(2-15)
The upper limit for magnetorquer actuation times is driven by the power budget for the
mission, which restricts the magnetorquers to an average power consumption of 1W [31]. Since
the nominal power consumption for a single magnetorquer if actuated continuously is 1.51 W,
this leads to a maximum average actuation time for all three magnetorquers of 66% of the control
cycle. If this limit is exceeded, then the actuation times are scaled down by a factor . This
process is implemented using (2-16) and (2-17) below:
{
(| | | | | |)
( ( ) ) (| | | | | |)
(2-16)
(2-17)
where is the final control vector that specifies the actuation time for each magnetorquer
during the next control cycle.
33
The ADCS software also includes the option to run the classic B-dot control algorithm
given in equation (2-18) below [20]:
[
]
( ) (2-18)
The B-dot control algorithm will be used to detumble the spacecraft following ejection from the
launch vehicle, since it eliminates spacecraft angular velocity quicker than the LMF Tracker.
2.5 Expected On-Orbit Performance
The attitude control algorithms have been simulated in order to optimize control
parameters and predict on-orbit performance of the ADCS. Prior to deployment of the drag sails,
the CanX-7 satellite has no large appendages or flexible components, and therefore can be
approximated as a rigid body. Assuming rigid body dynamics, the spacecraft attitude can be
described by Euler’s equation [20]:
(2-19)
where is the spacecraft inertia matrix, is the angular velocity of the spacecraft body-fixed
frame ( ) with respect to the inertial frame ( ), is the control torque ( ), and
is the total disturbance torque, all expressed in the spacecraft body-fixed frame. The disturbance
torques that are considered are gravity gradient torque, aerodynamic drag torque, solar pressure
torque, and the magnetic disturbance torque which was discussed in Section 2.3.
Gravity gradient torque ( ) results due to nonsymmetric mass distribution of the
spacecraft, and is given by (2-20) below [20]:
5
(2-20)
where is the standard gravitational parameter for Earth, is the satellite’s distance from the
center of Earth, is the satellite’s position relative to the ECI frame expressed in the body-
fixed frame, and is the spacecraft inertia matrix.
Aerodynamic drag torque ( ) results due to an offset between the spacecraft center of
mass and the center of atmospheric drag pressure, and is given by (2-21) below [20]:
( ) (2-21)
34
where is the atmospheric density, is the spacecraft drag coefficient, is the ram area, is
the spacecraft orbital speed, is the spacecraft velocity direction, is the center of
aerodynamic pressure, and is the spacecraft center of mass, all expressed in the spacecraft
body-fixed frame.
Solar pressure torque ( ) results due to an offset between the spacecraft center of mass
and the center of solar radiation pressure, and is given by (2-22) below [20]:
( ) (2-22)
where is the solar flux, is the speed of light, is the sunlit surface area, is the spacecraft
solar absorptivity, is the Sun direction relative to the spacecraft, is the center of solar
radiation pressure, and is the spacecraft center of mass, all expressed in the spacecraft body-
fixed frame.
Model 2.5.1
The SFL developed attitude simulation software MIRAGE was used as the baseline for the
CanX-7 ADCS simulations. MIRAGE has been developed through the collaboration of students
and staff at SFL and represents a comprehensive and adaptable approach for emulating the
orbital environment and validating the performance of attitude sensors, actuators, and software.
MIRAGE is a Matlab and Simulink based software application whose operation is fully
documented by [32]. The overall Simulink model was customized to represent the CanX-7 ADCS
architecture, and sub-models were developed to simulate the magnetometer, attitude control
software, and the Smart Torquer attitude actuators.
Given initial conditions, numerical methods are used to integrate Euler’s equation to
solve for the spacecraft angular velocity. At each time step, the spacecraft angular velocity is
used to determine the new spacecraft attitude. In parallel, an orbit simulator provides the
spacecraft position and velocity based on the simulation time. This orbital information is
subsequently used to determine environmental parameters including solar flux, air density, and
the local magnetic field in the spacecraft body-fixed frame using the IGRF model. The LMF is
fed into a series of sub-blocks that simulate the attitude determination and control system. The
LMF along with the spacecraft orbital parameters are also fed into a sub-block which calculates
the disturbance torques acting on the spacecraft. A block diagram of the model is provided in
Figure 2-13 below.
35
Orbit
Simulator
Spacecraft
Position
Spacecraft
Velocity
Orbit
Environment
Simulator
Attitude Determination and
Control System Model
Magnetometer
Sensor Model
ADCS Software
Magnetorquer
Actuator Model
Solar Flux
Air Density
Local Magnetic Field
Disturbance
Torque
Model
Estimated LMF
Actuation Times
Control
Torques
Disturbance
Torques
Rigid Body
Dynamics
Model
Spacecraft
Attitude
Figure 2-13: CanX-7 Attitude Model – Block Diagram
The ADCS is modelled with a series of three sub-blocks that represent the magnetometer,
the ADCS software, and the magnetorquers. The magnetometer model takes in the actual LMF
and then adjusts it to account for the sensor frame relative to the spacecraft body-fixed frame, the
spacecraft’s residual magnetic field, and sensor misalignment, bias, scaling, noise and linearity.
Following these manipulations, the magnetometer model outputs the LMF value which is
representative of what will be provided by the actual magnetometer on-orbit. The ADCS
software model calculates the magnetorquer actuation times based on the LMF values provided
by the magnetometer model using either the LMF Tracker or B-dot control algorithm. The
magnetorquer model takes in the magnetorquer actuation times and outputs the control torque on
the spacecraft after including the effects of bus voltage, voltage noise, magnetorquer
temperature, software delays, and magnetorquer misalignment.
36
Input Parameters 2.5.2
Given nominal operations, the spacecraft will first be detumbled using the B-dot control
algorithm and will then transition to LMF tracking. Both of these phases have been simulated
using the input parameters listed in Table 2-5. The input parameters are mainly based on the
spacecraft properties presented in Section 1.2 and a baseline orbit that falls within the range of
possible orbits presented in Section 1.3. Other important parameters include the initial attitude
quaternions (four parameters that describe the rotation between the ECI frame and the spacecraft
body-fixed frame), the initial spacecraft angular velocity (relative to the ECI frame), the
estimated spacecraft parasitic dipole moment from Section 2.3.3, the magnetorquer design
parameters from Section 2.2.2, and the expected magnetorquer temperatures based on thermal
analysis provided in Section 4.5.
Table 2-5: Input Parameters used for Attitude Simulations
Detumbling (B-dot control) LMF Tracking
Orbit Parameters
Orbit Type Sun-Synchronous
Orbit Altitude 650 km
LTAN 10:00 AM
Attitude Parameters
Initial Quaternions [ ] [ ]
Initial Angular Velocity [ ] [ ]
Spacecraft Parameters
Mass 3.65 kg
Inertia Matrix [
]
Bus Voltage 4.2 V
Parasitic Dipole Moment [ ]
Magnetorquer Parameters
Resistance at Room Temperature 11.7 Ω
Orbit Average Temperature 12.3°C
Temperature Amplitude 6.0°C
Additional attitude simulations were run to encompass all possible combinations of orbit
altitude, LTAN, initial attitude parameters, and parasitic dipole moment direction. The results for
37
these cases are presented in Appendix A, and show that the LMF tracking error varies no more
than 0.4 degrees from case to case. This variation arises due to differences in the disturbance
torques that are experienced. A variation of 0.4 degrees is small relative to the overall LMF
tracking error (see Figure 2-20); this indicates that the control algorithm is robust.
Results 2.5.3
In this section, the expected on-orbit performance of the attitude determination and control
system is presented based on the control algorithms provided in Section 2.4 and the nominal
input parameters provided in Section 2.5.2. The B-dot control algorithm is required to reduce the
spacecraft angular velocity to less than 0.2°/s [15]. Performance of the B-dot control algorithm
can be evaluated based on the time required to detumble the spacecraft after being ejected from
the launch vehicle. An initial angular velocity of 4°/s is expected; however, results are also
provided based on an initial angular velocity of 20°/s to illustrate the capability of the control
system. Simulation results presented in Figure 2-14 and Figure 2-15 show angular velocity
profiles over time as the spacecraft is detumbled from 4°/s and 20°/s respectively. Recall, that the
orbital period is approximately 98 minutes.
Figure 2-14: Spacecraft Angular Velocity during Detumbling (4°/s initial)
38
Figure 2-15: Spacecraft Angular Velocity during Detumbling (20°/s initial)
Results show that with an initial angular velocity of 4°/s, the velocity is reduced to less
than 2°/s within 0.14 orbits, and is reduced to less than 0.2°/s within 0.61 orbits. With an initial
angular velocity of 20°/s, the velocity is reduced to less than 2°/s within 1.2 orbits, and is reduced
to less than 0.2°/s within 1.6 orbits. Also of interest is the power consumed by each of the
magnetorquers during detumbling. Figure 2-16 and Figure 2-17 show the orbit average power
consumption of the magnetorquers given initial angular velocities of 4°/s and 20°/s respectively.
Figure 2-16: Magnetorquer Power Consumption during Detumbling (4°/s initial)
39
Figure 2-17: Magnetorquer Power Consumption during Detumbling (20°/s initial)
With an initial angular velocity of 4°/s, the orbit average power consumed by all three
magnetorquers begins at 0.18 W and decreases to 0.030 W as the spacecraft angular velocity is
eliminated. With an initial angular velocity of 20°/s, the orbit average power consumed by all
three magnetorquers is initially much higher at 0.84 W and again decreases to 0.030 W as the
spacecraft angular velocity is eliminated. Owing to disturbance torques acting on the spacecraft,
the power consumption for the magnetorquers never reaches zero. At all times, the magnetorquer
that is aligned with the Y axis consumes the most power. This occurs due to the spacecraft’s 3U
form factor, which results in a larger moment of inertia about the X and Z axes. According to
(2-1), the Y axis magnetorquer induces angular acceleration primarily about the X and Z axes.
Therefore, the Y axis magnetorquer must be actuated more to achieve the desired acceleration.
Overall, the B-dot control algorithm is effective in reducing the angular velocity of the spacecraft
to less than 0.2°/s. After the spacecraft has been detumbled, LMF tracking can begin.
Performance of the LMF Tracker is judged based on the LMF tracking error, or in other
words, the angle between the target axis (ADS-B antenna boresight direction) and the local
magnetic field direction. Figure 2-18 and Figure 2-19 show the spacecraft angular velocity and
the LMF tracking error over time after the control algorithm is initiated. After approximately half
an orbit, the integral term in the control algorithm reaches steady state, and LMF tracking error
settles at 3.0 degrees (2σ).
40
Figure 2-18: Spacecraft Angular Velocity during LMF Tracking
Figure 2-19: LMF Tracking Error
Figure 2-20 shows the steady state tracking error about the Y and Z spacecraft axes in
reference to the maximum required error of 15 degrees (2σ). Since the LMF Tracker will be
implemented on a continual basis for 6 months during ADS-B payload operations, the power
consumed by the magnetorquers in this control mode is very important. As illustrated in Figure
2-21, the average power consumption of all three magnetorquers settles after approximately 5
orbits. The long term average power consumption of the magnetorquers is 0.24 W.
41
Figure 2-20: Steady State LMF Tracking Error
Figure 2-21: Magnetorquer Power Consumption during LMF Tracking
The simulation results show that the mission requirement of tracking the LMF with an
accuracy of 15 degrees is easily met by the ADCS. Recall however, that ideally, the ADS-B
antenna boresight would be aligned with the nadir direction. Figure 2-22 provides the angle
between the antenna boresight direction and the nadir direction given both perfect LMF tracking
and the actual attitude achieved by the LMF Tracker control algorithm. At time zero the
42
spacecraft is ascending past the equator. Therefore, it can be seen that in the northern hemisphere
the nadir tracking error is always less than 90 degrees. Furthermore, based on the nadir tracking
error and the ADS-B antenna pattern analysis discussed in Section 1.1.3, the payload will be
capable of receiving signals from aircraft with latitudes above 22 degrees and within a 2800 km
cross-track. This result is important as it includes latitudes of 45 to 60 degrees, the range that
encompasses the majority of transatlantic air traffic routes. Figure 2-23 below illustrates the
ADS-B payload coverage for a single orbit that descends over the Atlantic Ocean.
Figure 2-22: Nadir Tracking Error
Figure 2-23: ADS-B Payload Coverage (Shaded Red) for a Single Orbit
43
Pointing Budget 2.5.4
A pointing budget is used to compare the estimated achievable pointing accuracy with the
required pointing accuracy. It also breaks down the estimated pointing accuracy based on sources
of error. The two main categories are determination error and control error. For the CanX-7
mission, determination error is the difference between the magnetometer’s predicted LMF
direction and the actual LMF direction. Determination error arises due to misalignment of the
magnetometer, measurement error due to the spacecraft’s residual magnetic field, error in the
magnetometer calibration model, and sensor noise. Control error arises due to the discretization
of magnetorquer actuation, variation in the generated magnetic dipole moments due to voltage
noise and magnetorquer temperature fluctuations, the timing accuracy of magnetorquer
actuation, and magnetorquer misalignment. The pointing budget for the CanX-7 ADCS is
provided in Table 2-6 below. All values presented in the pointing budget are 2σ LMF tracking
errors determined through attitude simulation. The main source of error is misalignment of the
magnetometer, which arises due to machining tolerances of the spacecraft structure and the
deployable boom. Overall, the total pointing error is estimated at 3.01 degrees, which gives a
healthy margin of 80% on the requirement.
Table 2-6: CanX-7 ADCS Pointing Budget [degrees (2σ)]
Determination Error
Magnetometer Misalignment 2.53
Spacecraft Residual Magnetic Field 0.892
Magnetometer Model Accuracy 0.451
Magnetometer Noise 0.0957
Total Determination Error: 2.84
Control Error
Controller Discretization 0.517
Magnetorquer Dipole Moment Variation 0.0986
OBC Timing Error 0.0562
Magnetorquer Misalignment 0.0273
Total Control Error: 0.504
Total Pointing Error: 3.01
Pointing Requirement: 15.0
Pointing Margin: 79.9%
44
2.6 Attitude Determination and Control System Software
The CanX-7 ADCS software is built upon the Canadian Advanced Nanosatellite Operating
Environment (CANOE), which is a software package developed in-house at SFL for the
spacecraft on-board computers. CANOE is a multi-threaded operating environment and provides
basic resources such as system clocks, an alarm handler, and a resource manager [33]. Several
standard software threads are used across missions and support communications, telemetry
gathering, and memory management. The ADCS software is also a thread managed by CANOE,
and was developed specifically for the CanX-7 mission. The ADCS software is written in C
programming language, and its main purpose is to implement the attitude control algorithms
presented in Section 2.4. In addition, the software accepts commands from ground support
software, and enables telemetry gathering. The software supports four control states: idle,
passive, active B-dot, and active LMF Tracking. The state transitions are illustrated in Figure
2-24 below.
Complication/Failure Complication/Failure
Nominal Path Nominal Path
Idle
Passive
Active LMF TrackingActive B-dot
Figure 2-24: ADCS State Transition Diagram
Given nominal satellite operations, the ADCS will start idle and will then be transitioned
into the passive state. In idle state, the ADCS software simply waits for commands. In passive
state, magnetic field data is polled at the control frequency but no actuation occurs. Once
magnetometer telemetry has been validated, the ADCS will be transitioned to B-dot control or
LMF tracking. In active B-dot, magnetic field data is polled, the B-dot control algorithm is used
to calculate actuation times, and the magnetorquers are actuated accordingly. In active LMF
Tracking, magnetic field data is polled, the LMF Tracker control algorithm is used to calculate
45
actuation times, and the magnetorquers are actuated accordingly. All transitions are made in
response to ground command. The software allows transitions between any of the four states, and
in the event of any complication – such as a system power reset, a deep discharge state for the
battery, or missing LMF measurements from the magnetometer – the system will return to idle.
The ADCS software is command driven and supports a total of nine commands for
setting the power state, setting the control state, gathering telemetry, updating control
parameters, and testing the magnetorquer actuators. A comprehensive diagram of the software
commands and the corresponding results is provided in Figure 2-25.
Command
Power State Commands
ADCS Hardware ON
ADCS Hardware OFF
Control State Commands
Go IDLE
Go PASSIVE
Go ACTIVE B-DOT
Go ACTIVE LMF TRACKER
Telemetry Commands
Get Telemetry
Update Control Parameters
Power
State?
Set Control
State flag
Start Control
Cycle
Stop Control
Cycle
Command magnetometer and
magnetorquers on via power system Set Power
State flag
Send error
message
Return telemetry
Update ACS Exchange structure
Magnetorquer TestActuate magnetorquers and set
alarms
Command magnetometer and
magnetorquers off via power system
ON
OFF
Figure 2-25: ADCS Software Architecture – Commands Diagram
In addition to responding to operator commands, the software executes an automated
control cycle based on the control state. Each control cycle involves gathering raw magnetometer
telemetry, processing the telemetry to determine the LMF, and potentially calculating
46
magnetorquer actuation times based on one of the control algorithms followed by actuating the
magnetorquers. When the magnetorquers are actuated, alarms are set within CANOE that are
monitored and compared against the system clock. When the alarms expire, functions within the
ADCS thread are called which return the magnetorquers to their brake state. A block diagram of
the ADCS control cycle is provided in Figure 2-26 below.
ADCS Control Cycle
Request Magnetometer
Telemetry
Process Magnetometer
Telemetry
Calculate actuation times
with B-dot algorithm
Control
State?
Calculate actuation times
with LMF Tracker
Actuate magnetorquers and
set alarms
Start
B-dot Passive
LMF Tracker
Figure 2-26: ADCS Software Architecture – Control Cycle
Certain control parameters can be set by the spacecraft operator to fine tune the
performance of the ADCS. These include the target vector, the controller gains, the bias term, the
minimum magnetorquer actuation time, and the maximum average magnetorquer actuation time
(see Section 2.4). The telemetry gathered by the ADCS software provides information regarding
the state of the software, the operation of the attitude hardware, and the overall detumbling or
LMF tracking performance. All of the telemetry values that are provided by the software are
listed in Table 2-7.
47
Table 2-7: List of ADCS Software Telemetry
Type of
Telemetry Value Units
General Control state Idle, Passive, B-Dot or LMF
Hardware power state ON, OFF
Magnetometer
Telemetry
Raw three-axis magnetometer readings
Three-axis LMF measurements in the
spacecraft body-fixed frame nT
Magnetometer temperature °C
Controller
Telemetry
Proportional, integral and derivative errors
Proportional, integral and derivative control
terms
Magnetorquer
Parameters
Actuation times for current control cycle s
Actuation polarities for current control cycle
Current state of all three magnetorquers Forward, Reverse or Brake
Overall
Performance
Spacecraft angular velocity degrees/s
LMF tracking error degrees
Ground Support Software 2.6.1
In addition to the ADCS flight software that has been implemented on the spacecraft’s on-board
computer, ground support software has been developed to aid an operator in sending ADCS
commands to the spacecraft. Ground support software for the CanX-7 mission dubbed “CanX-7
Control” was built from an existing platform named GNB Control that was developed at SFL to
support missions that use the generic nanosatellite bus [34]. GNB Control is a Win32 Windows
application that uses the Microsoft Foundation Class (MFC) framework. All spacecraft control is
achieved by sending commands via radio uplink expressed using the Nano-Satellite Protocol
(NSP) [33]. NSP is a communications protocol developed at SFL and specifies the data structure
used to convey information. According to the NSP, each communications packet contains a 16-
bit source address, a 16-bit destination address, a 5-bit command, and up to 256 bytes of data or
telemetry. GNB Control provides a User Interface (UI) that assists the spacecraft operator in
building NSP communication packets and queuing them to be uploaded to the spacecraft.
In order to support the CanX-7 mission, CanX-7 Control adds additional UI modules that
allow the operator to command and telemeter the power distribution unit, the drag sail payloads,
the inspection camera, and the ADCS software. The UI for commanding the ADCS software is
shown in Figure 2-27 below. With this UI, CanX-7 Control allows the spacecraft operator to
easily set the power state, set the control state, gather telemetry, and set control parameters. For
48
example, under the section titled “ACS State” the operator can select the desired state from the
drop-down menu and select “Set State”. This will call a function that generates a NSP
communications packet specifying the ground station as the source address, the ADCS software
thread as the destination address, and the control state command, and then adds it to the queue of
packets to be uploaded to the spacecraft.
Figure 2-27: CanX-7 Control Ground Support Software – ACS Module
The ADCS software and ground support software have both been tested using the
CanX-7 FlatSat. The FlatSat contains duplicates of all CanX-7 hardware, laid out on a flat plate
as opposed to packaged up in the 3U satellite bus. The FlatSat facilitates system level testing of
spacecraft hardware and debugging of spacecraft software. A photo of the CanX-7 FlatSat is
provided in Figure 2-28 below. Operation of the ADCS hardware and software at the system
level has been validated against the simulation results. Overall, a fully functional attitude
determination and control system for the CanX-7 mission is now complete.
49
Figure 2-28: CanX-7 FlatSat
50
Chapter 3
Passive Thermal Control
for Low-Earth Orbit
Satellites
Spacecraft thermal control is required to ensure that all satellite components remain within their
operational temperature range for the duration of the mission. Most satellite missions designed at
SFL rely on passive thermal control, and use thermal control tapes applied to the exterior of the
spacecraft to control radiation heat transfer between the spacecraft and its environment. The
overall methodology is to identify the operating temperature range for all spacecraft components,
then based on thermal finite difference simulation results adjust the spacecraft’s thermo-optical
properties in order to meet the required temperature ranges. The finite difference model
considers all heat flow paths through the spacecraft, and boundary conditions are applied based
on the Worst Case Cold (WCC) and Worst Case Hot (WCH) conditions expected during the
lifetime of the mission. Where, the WCC and WCH conditions are those which result in the
satellite getting the coldest and hottest respectively. These boundary conditions are comprised of
the spacecraft thermal environment, orbit parameters, attitude, and internal heat loads. The goal
51
is to design a thermal control system that can meet temperature requirements given both WCC
and WCH conditions.
To achieve a robust and reliable thermal control system, care must be taken during the
design process to model the system accurately. This involves correctly identifying all boundary
conditions, properly evaluating all heat flow paths within the spacecraft, and fully understanding
the effect of different thermal control tapes. Each one of these concepts will be discussed in this
chapter as prerequisites to the CanX-7 thermal control system design, which is presented in
Chapter 4.
3.1 Boundary Conditions for Thermal Analysis of Space Systems
In space, the only mode of heat transfer between a spacecraft and its environment is radiation.
Satellites in low-Earth orbit experience incoming heat loads from three main sources: direct solar
radiation, indirect solar radiation reflected off Earth known as albedo, and infrared radiation
from Earth known as Earth IR. In addition, satellites lose heat through radiation heat transfer to
space. These heat loads and heat loss (illustrated in Figure 3-1), along with internal heat
dissipation determine the temperature of the satellite. Therefore, the boundary conditions must
completely describe these heat transfer processes. The boundary conditions are comprised of the
spacecraft’s orbit, attitude, thermal environment, and internal heat dissipation.
Figure 3-1: Heat Transfer in Space
Solar Radiation
QSolar
Albedo
QAlbedo
Earth IR
QEarth
IR
Radiation to Space
QLoss
52
Orbit 3.1.1
To validate the use of a passive thermal control solution, the thermal control system must often
be designed before a launch service has been arranged for the spacecraft. As a result, the actual
orbit for the mission is unknown. Given this situation, the conservative approach is to consider
the range of possible orbits for the mission, then identify two orbits within that range: one that
results in the lowest orbit average heat load, and one that results highest orbit average heat load.
These will be referred to as the Cold Reference Orbit and the Hot Reference Orbit. Then, for
each reference orbit, WCC and WCH conditions are identified. Next, a thermal control system is
designed for each of the reference orbits. If both thermal control system designs can successfully
meet the temperature requirements, then it is assured that an appropriate design exists to address
any possible orbit. Based on the orbit average heat load for the actual orbit relative to those for
the cold and hot reference orbits, the appropriate design can be thought of as an interpolation
between the cold and hot reference orbit designs.
The heat loads experienced by a satellite are best related to its orbit using the orbit beta
angle. Orbit beta angle is the angle between the solar vector and the orbit plane. Using CanX-7
as an example, Figure 3-2 and Figure 3-3 illustrate the relationship between beta angle and the
orbit average heat loads expected from each of the main heat sources: solar radiation, albedo and
Earth IR. In general, as beta angle increases, the fraction of the orbit during which the satellite is
in eclipse decreases, and as a result, the orbit average heat load from solar radiation increases.
With a beta angle above about 65 degrees, a satellite in low-Earth orbit will no longer pass into
eclipse, and further increase in beta angle will not result in additional heat load from solar
radiation. Also, as beta angle increases, there is a slight decrease in the heat load from albedo
that occurs due to the diffuse reflection of solar radiation from Earth. Since Figure 3-2 and
Figure 3-3 are based on the cold and hot reference orbits for CanX-7, specific orbit altitudes and
values for solar flux are used as inputs, and these values are listed in the figures. For the CanX-7
spacecraft, the total heat load decreases with increasing altitude due to a decrease in the heat
loads from albedo and Earth IR. Solar flux varies with time of year and the selection of this
parameter is discussed further in Section 3.1.3.
53
Figure 3-2: Orbit Average Heat Load vs. Beta Angle (Cold Reference Orbit - LTAN 11:47)
Figure 3-3: Orbit Average Heat Load vs. Beta Angle (Hot Reference Orbit - LTAN 7:32)
Beta angle is the most useful parameter when comparing heat loads; however, for a sun-
synchronous orbit, beta angle varies slightly throughout the year due to Earth’s axial tilt. One
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50 60 70 80 90
Orb
it A
ver
age
Heat
Load
[W
/m2]
Beta Angle [deg]
Solar Radiation
Earth IR
Albedo
Total Heat Load
Inputs
Orbit Type: SSO
Altitude: 800 km
Solar Flux: 1322 W/m2
L
TA
N:
11
:47
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50 60 70 80 90
Orb
it A
ver
age
Hea
t L
oad
[W
/m2]
Beta Angle [deg]
Solar Radiation
Earth IR
Albedo
Total Heat Load
Inputs
Orbit Type: SSO
Altitude: 600 km
Solar Flux: 1414 W/m2
LT
AN
: 7
:32
54
parameter that is always constant for a SSO is the local time of ascending node, and will
therefore be used to define the reference orbits. LTAN values are selected such that the cold
reference orbit includes the beta angle that results in the lowest orbit average heat load, and such
that the hot reference orbit includes the beta angle that results in the highest orbit average heat
load. LTAN values are also selected such that the reference orbits include the widest range of
beta angles. For the CanX-7 mission, the orbit is constrained to an altitude between 600 and
800 km with no restrictions on LTAN. The LTAN values that correspond to the cold and hot
reference orbits for CanX-7 are shown in Figure 3-2 and Figure 3-3, and the shaded blue and red
regions indicate the range of beta angles that are encompassed. The cold reference orbit has an
LTAN of 11:47 with the beta angle ranging from 0 to 6 degrees, and the hot reference orbit has a
LTAN of 7:32 with the beta angle ranging from 51 to 67 degrees.
Attitude 3.1.2
Heat loads experienced on-orbit are highly dependent on spacecraft attitude. This is particularly
true for satellites which are asymmetric such as the CanX-7 spacecraft with its 3U bus geometry.
Therefore, the attitudes which lead to the lowest and highest overall heat loads must be
identified, and will be referred to as WCC attitudes and WCH attitudes respectively. Since solar
radiation is the dominant heat load, attitudes are defined relative to the Sun. Depending on where
certain components are mounted within the spacecraft, their temperatures will vary based on
where heat loads are applied, and hence which spacecraft faces are directed towards the Sun. As
a result, several WCC and WCH attitudes must be considered.
WCC attitudes occur when spacecraft faces with low area absorptivity, which is the
product of surface area ( ) and surface solar absorptivity ( ), are perpendicular to the solar
vector. WCH attitudes occur roughly when a corner of the spacecraft is pointed towards the Sun,
such that the total exposed area absorptivity is high. WCH attitudes must be determined for each
corner of the spacecraft that can be directed towards the Sun, and can be described by two angles
with respect to the solar vector. Given and as illustrated in Figure 3-4 below, the overall area
absorptivity ( ) can be described as:
(3-1)
55
where , and are the area absorptivities for faces A, B and C respectively. The
angles and that give the maximum area absorptivity can then be found using (3-2) and (3-3)
below:
(
) (3-2)
(
) (3-3)
Figure 3-4: Analysis for Determining WCH Spacecraft Attitudes
Environmental Parameters 3.1.3
The environmental parameters help quantify the amount of heat energy arriving at the spacecraft
and include solar flux, albedo, and Earth IR. Solar flux is the heat flux incident on any surface
exposed to direct sunlight. Solar flux varies inversely and exponentially with increasing distance
from the Sun, however, at a given distance is almost constant. The solar constant ( ) represents
the solar flux at a distance of 1 AU (≈ 150 million km) from the Sun, and has a value of
1367 W/m2 [35]. Earth travels around the Sun in an elliptical orbit; therefore, the distance
between Earth and the Sun, and consequently the solar flux experienced by satellites in Earth
orbit is dependent on the time of year. The minimum and maximum values for solar flux at Earth
are calculated to be 1322 W/m2 and 1414 W/m
2 respectively.
Top
View
Solar Vector
Side
View
Solar Vector Solar
Vector 𝜑
𝜃
A
C B B A
56
A portion of all solar radiation that strikes Earth is reflected back to space. This process is
quantified by albedo, which is the fraction of solar radiation reflected by Earth at a given
location measured at the top-of-atmosphere (altitude of 30 km). Albedo varies significantly with
geographic location due to changes in Earth surface optical properties and atmospheric
conditions. As a result, the amount of reflected solar radiation that is incident on an Earth
orbiting satellite fluctuates continuously. Since the most extreme values for albedo only persist
for very short periods of time (tens of seconds), it would be overly conservative to assume these
extreme values occur continuously, and therefore, for thermal analysis an average value is used.
In selecting this value, one must consider the satellite’s orbit and thermal time constant. The
thermal time constant is a measure of how fast spacecraft temperatures fluctuation on-orbit, and
is a function satellite mass, specific heat, orbit average temperature, and orbit average heat load.
The temperatures experienced by a spacecraft with a low thermal time constant will change more
rapidly when exposed to fluctuating heat loads caused by changes in albedo. Consequently, one
must consider more extreme values for albedo when analyzing a spacecraft with a low thermal
time constant when compared to spacecraft that has a high thermal time constant.
Earth IR describes the heat transfer between a spacecraft and Earth. In general, any two
objects with a direct view of one another exchange heat via radiation, with the net heat transfer
being from the hotter object to the colder object. Therefore, a satellite in orbit around Earth will
both expel and absorb heat to/from Earth. To simplify the spacecraft thermal model, it is
assumed that the satellite will always absorb energy from Earth but will not expel energy to it.
This simplification is balanced by assuming that the satellite radiates to space with an
unobstructed view (i.e., ignoring the fact that Earth partially blocks the satellite’s view of space).
Specifically, Earth IR gives the heat flux expelled by Earth measured at the top-of-atmosphere,
and varies with satellite location due to variation in Earth’s surface temperature and emissivity.
Since the most extreme values for Earth IR only persist for very short periods of time (tens of
seconds), it would be overly conservative to assume these extreme values occur continuously,
and therefore, for thermal analysis an average value is used. Again, this average value is a
function of the satellite’s orbit and thermal time constant.
To further complicate the selection of environmental parameters, albedo and Earth IR
values have an inversely proportional relationship and need to be selected as a pair. Choosing
both the maximum albedo and Earth IR values for a WCH simulation or choosing both the
57
minimum albedo and Earth IR values for a WCC simulation would be overly conservative. This
occurs due to the fact that an Earth surface that is highly reflective will not absorb a lot of energy
from solar radiation, causing it to be relatively cold and consequently the Earth IR will be lower.
In order to select a pair of albedo and Earth IR values that are likely to occur simultaneously and
will result in the lowest or highest overall heat loads on the spacecraft, the spacecraft thermo-
optical properties must be considered in addition to the orbit and thermal time constant.
Prior to the availability of on-orbit experimental values for Earth IR and albedo, they
were estimated from Earth-based measurements. These estimates have been used for thermal
analysis in the past at SFL; however, they do not properly account for the satellite’s orbit, optical
properties, or thermal time constant. Overall, this results in poor estimation of worst case
spacecraft temperatures, especially for spacecraft appendages with small thermal time constants,
or components which are particularly sensitive to certain radiation wavelengths.
A new approach for selecting Earth IR and albedo values has been implemented and
relies on data collected as part of the Earth Radiation Budget Experiment (ERBE). The ERBE
consisted of three satellites that used on-board sensors to gather albedo and Earth IR
measurements over a period of 28 months [36]. The data gathered during the ERBE has been
tabulated based on orbit inclination, orbit beta angle, and spacecraft thermo-optical properties to
show the minimum and maximum values for average albedo and Earth IR that were observed for
a variety of time intervals [37].
A detailed procedure for selecting albedo and Earth IR values as boundary conditions for
spacecraft thermal analysis has been establish as part of this thesis project, and is documented in
[38]. In addition, an interactive tool was developed that automates this procedure. Figure 3-5
provides a screenshot of the user interface for the selection tool. Based on user inputs regarding
spacecraft properties and the range of orbits to be considered, the tool returns worst case
environmental and orbital parameters. This tool saves time and reduces the chance of
miscalculations when performing spacecraft thermal analysis. The results provided by the
selection tool have been verified for many combinations of spacecraft and orbit parameters, and
the tool has already been successfully used by thermal engineers at SFL for several missions.
58
Figure 3-5: Screenshot of the Thermal Environment and Orbital Parameter Selection Tool
Internal Heat Dissipation 3.1.4
Almost all power that is consumed by a spacecraft is eventually dissipated as heat. For example,
on-board CanX-7 the only exception is the power which is converted to radio energy by the
S-Band transmitter. As part of the power system analysis for a spacecraft mission, a power
budget is generated that defines all loads on board the spacecraft, and the amount of power
which they consume depending on the spacecraft mode. Using the power budget, internal heat
dissipation can be determined for all spacecraft components and implemented in the thermal
finite difference model.
3.2 Modeling Heat Flow Paths
When developing a thermal finite difference model, spacecraft components are generally
modelled as separate meshes. Heat flow paths between meshes are calculated separately and then
applied to the model. For each heat flow path, the total thermal conductance must be specified.
The thermal conductance values are calculated using the method of thermal circuits, which
assumes that each heat flow path is made up of a discrete number of thermal resistors in series
59
and/or parallel [39]. Equations were developed to find the thermal conductance for all frequently
occurring heat flow path geometries found within the CanX-7 spacecraft. A typical heat flow
path contains a combination of direct contacts, screws, washers, spacers, and bosses.
One common heat flow path geometry occurs when a circuit board is fastened to a
spacecraft structural panel via a screw, spacer and boss. This heat flow path can be represented
by the thermal circuit illustrated by Figure 3-6 below. The thermal circuit contains two paths in
parallel between the circuit board and the structural panel: one where heat travels through the
screw, and one where the heat travels through the spacer.
.
Path
1:
Board Mid-
Plane to Surface:
1D Conduction
Resistance
Board to Spacer:
Thermal Contact
Resistance
Spacer:
1D Conduction
Resistance
Spacer to Boss:
Thermal Contact
Resistance
Boss:
1D Conduction
Resistance
R1 R2 R3 R4 R5
Path
2:
Board Mid-
Plane to Surface:
1D Conduction
Resistance
Board to Screw:
Thermal Contact
Resistance
Screw:
1D Conduction
Resistance
Screw to Boss:
Thermal Contact
Resistance
R6 R7 R8 R9
Figure 3-6: Thermal Circuit Representation for a Common Heat Flow Path
R1
R2
R3
R4
R5
R6
R7
R8
R9
R1
R2
R3
R6
R7
R8
R9
R4
R5
Path
1
Path
2
Circuit Board
Mid-Plane
Structural Panel
Mid-Plane
60
The set of equations used to determine the total thermal conductance are provided below.
First, the resistance for Path 1 ( ) and Path 2 ( ) are determined by adding resistances in
series. The total resistance ( ) is found by adding the resistance for each of the paths in
parallel, and then the total conductance ( ) is simply the inverse of the total resistance. This
same methodology has been applied to determine the conductance for all heat flow paths found
in the CanX-7 spacecraft.
4 5 (3-4)
(3-5)
(
)
(3-6)
(3-7)
Internal Radiation Heat Transfer 3.2.1
In addition to the heat that is exchanged amongst the spacecraft components through conductive
heat transfer, there is also radiative heat transfer which occurs between all spacecraft components
that are in view of one another. To distinguish this radiation heat transfer from that which occurs
between the spacecraft and its environment, it is referred to as internal radiation heat transfer.
Internal radiation heat transfer between any two components can be approximated by [40]:
4
4 (3-8)
where is the heat transfer from component 1 to component 2, is the surface area of
component 1, is the view factor between component 1 and component 2, is the emissivity
of component 1, is the emissivity of component 2, is the Stefan–Boltzmann constant, is
the temperature of component 1, and is the temperature of component 2. Due to the large
amount of wire harnessing, fasteners, and spacers that are present in the small internal volume of
the CanX-7 satellite bus, the complex geometry of the spacecraft structural panels, and the
complex surface profile of circuit board assemblies, it is very difficult to accurately model the
view factors between components. Fortunately, the small bus size reduces the instantaneous
thermal gradients that occur among components, which causes radiation heat transfer to be
minimal. Consequently, internal radiation heat transfer can be neglected when analyzing
nanosatellite scale spacecraft, as was done in the case of CanX-7.
61
3.3 Thermal Control Materials
A variety of thermal control tapes designed specifically for spacecraft are commercially
available. These tapes are designed to have specific thermo-optical properties, and by applying
them to the exterior of a spacecraft, the radiation heat transfer between the spacecraft and its
environment can be controlled. The important properties are the tape’s solar absorptivity and IR
emissivity. The total heat energy absorbed by a spacecraft due to solar flux and albedo is directly
proportional to its solar absorptivity, and the total heat absorbed due to Earth IR as well as heat
loss to space are directly proportional to its emissivity. Thermal control tapes are available with
discrete values for absorptivity and emissivity; however, by applying multiple different tapes in a
pattern almost any combination of thermo-optical properties can be achieved.
A wide range of thermo-optical properties is made possible with the use of first surface
and second surface mirrors. A thermal control material is said to act as a first surface mirror if
incident light if reflected off of the outermost surface of the material. However, if incident light
passes through the outermost surface and is reflected off of a second surface within the material,
it is said to act as a second surface mirror. This concept is illustrated through Figure 3-7 below.
First surface mirrors use a shiny outer surface to provide low absorptivity and low emissivity.
Second surface mirrors use a shiny inner surface to provide low solar absorptivity, and an outer
surface that emits well in the IR range to provide high emissivity.
Figure 3-7: Interaction of Radiation with First and Second Surface Mirrors
Solar
Radiation
Infrared
Emission
First Surface Mirror
Second Surface Mirror
Solar
Radiation
Infrared
Emission
62
Table 3-1 below summarizes the thermo-optical properties for some of the thermal
control tapes commonly used at SFL. The provided thermo-optical properties are average values
based on in-house measurements performed using a calibrated reflectometer. When performing
thermal analysis, the variability in solar absorptivity and IR emissivity is also considered. All of
the thermal control materials have a pressure sensitive acrylic adhesive backing allowing them to
be easily applied to any spacecraft surface.
Table 3-1: Properties for Several Thermal Control Tapes [41]
[42]
Name/Part
Number
Solar
Absorptivity IR Emissivity Description
Acktar
Nano Black®
0.94 0.11
Selective black coating on an aluminum
substrate
ATU 2110 0.070 0.032 First surface aluminum coating on a polyimide
substrate
ATU 2510 0.19 0.023 First surface gold coating on a polyimide
substrate
ATU 4150 0.098 0.81 Second surface aluminum coating on an FEP
substrate
63
Chapter 4
CanX-7 Thermal Control
System
The CanX-7 spacecraft is equipped with a thermal control system to regulate heat exchange
between the satellite and the space environment, and to control heat transfer throughout the
satellite bus in order to maintain all spacecraft components within their operational temperature
ranges. To reduce cost and complexity of the spacecraft, a passive thermal control system is
used, with the exception of a small electric heater for the battery. The selection of thermal
control tapes is the main output of the design. In addition, certain structural aspects are tailored
in order to regulate conductive heat transfer throughout the satellite bus.
Thermal control system designs are presented to address both a cold reference orbit and a
hot reference orbit. For each reference orbit, WCC and WCH boundary conditions are
considered. Developing thermal control system designs that meet the temperature requirements
for each reference orbit affirms that a thermal control system can be designed to address any
potential orbit. The final thermal control system design will be developed once the orbit for the
mission has been identified, and can be thought of as an interpolation between the cold and hot
reference orbit designs.
64
As of the initiation of this thesis project, no work had been started on the thermal control
system for the CanX-7 spacecraft. Therefore, everything from requirement definitions through to
the thermal designs presented in Section 4.4 were completed as part of this thesis project.
4.1 Temperature Requirements
The thermal control system must maintain all spacecraft components within their
operational temperature ranges throughout the six month ADS-B payload campaign. Following
deployment of the drag sail, spacecraft operations are no longer necessary, and the only
temperature requirement is that imposed to ensure integrity of the drag sail for the duration of
de-orbiting. Table 4-1 below provides the operational temperature limits for all subsystem
assemblies.
Table 4-1: CanX-7 Subsystem Assembly Operating Temperature Limits
Temperature Limits [⁰C]
Subsystem Assembly Lower
Operating
Upper
Operating
C&DH On-Board Computer -20 60
Power
Solar Cell Arrays -50 70
Battery -20 60
Power Distribution Unit -30 60
ADCS Magnetorquers -30 70
Magnetometer -30 70
Comms
UHF Receiver -20 60
UHF Antennas -65 165
S-band Transmitter -30 60
S-band Patch Antennas -65 165
Payloads
Drag Sail Modules -30 70
Drag Sails (post-deployment) -269 270
ADS-B Receiver -20 60
Inspection Camera (mVIC) -30 70
Most temperature limits are driven by the electronic components used in the assembly.
Industrial grade electronics are used, and initially the temperature limits are determined based on
manufacturer’s recommendations and derating according to the ECSS Space Product Assurance
guidelines [43]. Derating is the intentional reduction of thermal stresses to levels below the
manufacturer specified ratings in order to increase reliability and extend the operational lifetime
of electronic components. After the circuit board assemblies have been manufactured, they are
65
functionally tested over a specified operational temperature range. The range across which the
hardware is tested defines the final temperature limits that must not be exceeded on-orbit, and
therefore the temperature requirements for the thermal control system. For the CanX-7 mission,
there are a few exceptions to this general approach. The upper operating temperature limit for the
solar cells is driven by power generation requirements, as solar cells are less efficient at high
temperatures. Also, the temperature limits for the drag sail are selected based on the datasheet for
Upilex to avoid excessive degradation of the sail’s mechanical properties.
4.2 Thermal Finite Difference Model
To accurately determine the spacecraft temperature on-orbit and the temperature distribution
throughout the satellite bus, a finite difference model of the spacecraft was created and is
illustrated in Figure 4-1 below.
Figure 4-1: CanX-7 Finite Difference Model: Exterior View
Finite difference modeling was completed using Siemens’ NX 8 software package. In
modeling the spacecraft, it has been divided into a series of meshes, where each mesh
corresponds to a single component such as a structural panel or a circuit board assembly. To
simplify the modeling process, fasteners and wire harnessing are not modelled explicitly.
66
Instead, the thermal conductance between meshes is calculated separately using the methods
described in Section 3.2 and applied to the model. In total, there are 103 thermal conductance
values that have been specified in the finite difference model.
In general, thermal finite difference analysis is not particularly sensitive to element size
and therefore to reduce computation time, elements were made only small enough to capture
component geometry. To reduce the complexity of the model, only 0D, 1D and 2D elements
were used. 0D elements were used to represent the battery and several components that make up
the drag sail modules including gears and axles, 1D elements were used to represent the launch
rails and structural stiffeners, and 2D elements were used to represent all structural panels and
circuit board assemblies. Figure 4-2 and Figure 4-3 illustrate internal views of the model.
Figure 4-2: CanX-7 Finite Difference Model: +Z Interior View
Figure 4-3: CanX-7 Finite Difference Model: -Z Interior View
X
Y
Z
�� 𝑏
Y
X Z
�� 𝑏
67
4.3 Thermal Model Boundary Conditions
The boundary conditions for the CanX-7 thermal analysis were selected through the methods
described in Section 3.1 and in particular using the interactive selection tool. One deviation from
these methods occurred when identifying the WCC spacecraft attitudes, and is discussed in the
following section. Table 4-2 below summarizes the orbit and environmental parameters used for
the analysis.
Table 4-2: Summary of Boundary Conditions for the CanX-7 Thermal Model
Orbit Parameters Environmental Parameters
Altitude
[km]
Beta Angle
[°] Solar Flux
[W/m2]
Earth IR
[W/m2]
Albedo
Cold Reference Orbit:
WCC Conditions 800
0 1322 231 0.20
Cold Reference Orbit:
WCH Conditions 6 1414 244 0.30
Hot Reference Orbit:
WCC Conditions 600
51 1322 231 0.25
Hot Reference Orbit:
WCH Conditions 67 1414 244 0.41
Worst Case Attitudes 4.3.1
As discussed in Section 3.1.2, the attitude that results in the lowest total heat load is a fixed
attitude where either of the small spacecraft faces (+Y or -Y) is perpendicular to the solar vector.
However, analysis conducted by Tarantini [22] concluded that these attitudes are unstable, and
cannot persist long enough to have significant impact on spacecraft temperatures. More realistic
attitudes that will result in low orbit average heat loads have been identified as gravity gradient
stabilized (Y axis aligned with the nadir direction), either of the X or Z satellite axes tracking the
local magnetic field, and a major axis spin with rates greater than 0.1°/s. Instead of having one of
the small spacecraft faces constantly fixed towards the sun, these dynamic attitudes have the
spacecraft rotating such that the small spacecraft faces are periodically directed towards the sun.
All three of these attitudes will be considered as WCC conditions in the analysis, and are
illustrated in Figure 4-4. WCH attitudes have been determined for each corner of the spacecraft
that can be pointed towards the sun based on the rationale and method discussed in Section 3.1.2.
All eight of these attitudes are considered as WCH conditions in the analysis.
68
Figure 4-4: Stable WCC Attitudes (as viewed from the orbit normal direction)
Internal Heat Dissipation 4.3.2
At all times during the mission, heat is dissipated by various electronics within the CanX-7
satellite bus. The amount of power that is dissipated depends on the spacecraft mode, which
designates the electronics that are operating and at what capacity. The estimated power
consumption for each of the operational modes can be found in the CanX-7 power budget [31].
Based on the power budget, the mode that results in the lowest power consumption is Safe-Hold,
and the mode that results in the highest power consumption is Secondary Payload Operations.
Safe-Hold is entered immediately after the spacecraft is ejected from the launch vehicle or in the
event of a spacecraft power reset. In this mode, only essential spacecraft systems are powered
including the PDU, and the UHF receiver. Within the Secondary Payload Operations mode, the
PDU, OBC, ADCS hardware, and UHF receiver are powered continuously, and the ADS-B
payload and S-band transmitter are powered for a portion of each orbit. The power consumption
values from these two cases were used to determine the WCC and WCH power consumption
values. Table 4-3 provides a breakdown of the power consumption values used to determine the
WCC and WCH internal heat dissipations. In all cases, the power consumption of spacecraft
components is determined through testing with the flight hardware.
In most cases, all of the consumed power is dissipated in the form of heat. The only
exception is the S-band transmitter, for which 0.5 W of the consumed power is converted to
radio energy. Based on the power consumption values listed above, heat loads are applied to the
appropriate elements in the finite difference model. The precise locations of applied heat loads
Gravity Gradient Stabilized Local Magnetic Field Tracking Major Axis Spin
Y Z
�� 𝑏
Y Z �� 𝑏
Y Z �� 𝑏
69
are determined through consideration of circuit board layouts and identification of resistors,
integrated circuits, or other components that dissipate the most heat. Additional heat loads are
also applied to account for losses in various power switches, current sensors, and wire harnessing
in the system. Most of the heat loads are applied continuously with exception of the S-band
transmitter and the ADS-B payload, since they will only be operated for a portion of each orbit.
The S-band transmitter may be operated for up to 17 minutes per orbit depending on ground
station communications windows, and the ADS-B payload may be operated for up to 26 minutes
per orbit according to the ADS-B payload operations plan. For each combination of reference
orbit and worst case attitude, the amount of power generated by the solar cells is also considered.
When the battery is fully charged and power generation exceeds power consumption, the extra
power is applied as heat loads on the solar cells that are illuminated. Transient heat dissipation
tables were developed for the S-band transmitter, ADS-B payload, and the solar cells as inputs to
the thermal finite difference model. When modeling the WCH conditions, it is assumed that the
ADS-B payload and S-band transmitter are operated consecutively while the spacecraft is in
sunlight.
Table 4-3: Worst Case Cold and Worst Case Hot Power Consumption Values
Worst Case Cold Worst Case Hot
Subsystem Component
Power
Consumption
[W]
Duty
Cycle
Average Power
Consumption
[W]
Duty
Cycle
Average Power
Consumption
[W]
C&DH On-Board Computer 0.189 0% 0.000 100% 0.189
Power
Power Distribution Unit 0.180 100% 0.180 100% 0.180
Battery Charge/
Discharge Regulator 0.070 100% 0.070 100% 0.070
Battery Heater 0.500 30% 0.150 0% 0.000
ADCS Magnetometer 0.016 0% 0.000 100% 0.016
Magnetorquers 4.410 0% 0.000 5% 0.240
Comms UHF Receiver 0.088 100% 0.088 100% 0.088
S-band Transmitter 4.820 0% 0.000 18% 0.849
Payloads
Drag Sail Electronics 0.192 0% 0.000 0% 0.000
ADS-B Receiver 3.000 0% 0.000 7% 0.218
Inspection Camera
(mVIC) 0.066 0% 0.000 0% 0.000
Total Power Consumption: 0.488 W 1.910 W
70
4.4 Thermal Control System Design
The thermal control system design for the CanX-7 satellite is made up of the thermal control
tapes applied to the exterior surfaces of the spacecraft, an electric heater for the battery, and
several modifications to the CanX-7 structural design. Each of these aspects is described in this
section of the report.
Surface Properties 4.4.1
As discussed in Section 3.2.1, tapes are used to control the radiation heat transfer between the
spacecraft and its environment. The selection of thermal control tapes is the most important
aspect of the thermal control system design and has the most influence on spacecraft
temperatures. Through an iterative process using thermal finite difference analysis, it was
determined that the CanX-7 spacecraft surfaces should have certain thermo-optical properties in
order to meet the temperature requirements. These properties are summarized in Table 4-4 for
both the cold and hot reference orbits. The baseline thermo-optical properties that occur without
applying any tapes are also provided for reference.
Table 4-4: Baseline and Desired Spacecraft Surface Thermo-Optical Properties
Baseline (No Tapes) Cold Reference Orbit Hot Reference Orbit
Spacecraft
Face Emissivity Absorptivity Emissivity Absorptivity Emissivity Absorptivity
+X 0.44 0.46 0.44 0.47 0.55 0.45
+Y 0.55 0.60 0.57 0.84 0.57 0.84
+Z 0.38 0.45 0.37 0.47 0.54 0.44
-X 0.41 0.34 0.41 0.36 0.46 0.43
-Y 0.55 0.60 0.57 0.84 0.57 0.84
-Z 0.22 0.31 0.22 0.34 0.39 0.44
Overall 0.39 0.42 0.39 0.47 0.50 0.50
The values listed in Table 4-4 are average values for the entire exposed area of each
spacecraft face and therefore must take into account all surface components including solar
panels and patch antennas in addition to the thermal control tapes. Surfaces that are free of
components and tapes are aluminum that has been subjected to an Iridite® chromate conversion
treatment and have the corresponding thermo-optical properties. For the cold reference orbit, an
increase in overall absorptivity is desired to allow the spacecraft to absorb a larger heat load from
solar radiation and albedo. For the hot reference orbit, an increase in overall emissivity is desired
71
to allow the spacecraft to radiate more heat away to space. In both cases, it is desired to have
high absorptivity on the –Y and +Y surfaces to compensate for their small surface areas.
A set of thermal control tapes was selected to achieve the desired thermo-optical
properties for each of the reference orbits. Table 4-5 below summarizes the combination of tapes
selected for each spacecraft face. The values listed indicate the percentage of exposed area that
the tapes will cover. Areas that are not available for taping include the solar panels, radio patch
antennas, mounting features for the deployables and the launch rails. The launch rails slide along
surfaces inside the XPOD during deployment and are not taped to avoid increased friction.
Table 4-5: Thermal Control Tapes by Spacecraft Face
Cold Reference Orbit
Tape 1 Tape 2
Spacecraft Face Description % Available Area Description % Available Area
+X ATU2510 100% - -
+Y Nano Black®
100% - -
+Z ATU2510 100% - -
-X ATU2510 100% - -
-Y Nano Black®
100% - -
-Z ATU2510 100% - -
Hot Reference Orbit
Tape 1 Tape 2
Spacecraft Face Description % Available Area Description % Available Area
+X ATU4150 93.3% ATU2510 6.7%
+Y Nano Black®
100% - -
+Z ATU4150 96.1% ATU2510 3.9%
-X Nano Black®
69.3% ATU4150 30.7%
-Y Nano Black®
100% - -
-Z ATU4150 56.1% Nano Black®
43.9%
The drag sail modules and the inspection camera/magnetometer boom assembly are very
much thermally isolated from the rest of the satellite bus; therefore, the selection of thermal
control tapes for these components is considered separately. The drag sail modules are mounted
through aluminum attachment plates to the launch rails. This provides a good heat flow path to
the rest of the spacecraft; however, the extremely low thermal conductivity of Windform XT 2.0
allows little conductive heat transfer throughout the drag sail modules themselves. To avoid large
temperature gradients within the modules, it is desirable to have very little heat exchange
between the drag sail modules and the space environment. To achieve this, ATU 2110 will be
72
applied to all exterior surfaces of the drag sail modules regardless of the orbit, as it is the thermal
control tape with the lowest absorptivity and emissivity values.
A similar approach is followed for both the enclosure that houses the inspection camera
and the magnetometer, and the boom that supports the enclosure. The majority of the surfaces
will be covered with ATU 2110 to provide low emissivity and absorptivity to reduce temperature
swings, with a small amount of ATU 4150 to increase the emissivity slightly and stop the
assembly from overheating. For the boom and enclosure, all surfaces are available for taping
except for the small apertures used by the inspection camera. As a percentage of the available
area, 95% will be covered with ATU 2110, and 5% will be covered with ATU 4150. This results
in an overall emissivity of 0.067 and an overall absorptivity of 0.071. The same combination of
tapes is suitable for both the boom and the enclosure, and both the cold and hot reference orbits.
Battery Heater 4.4.2
In order to meet the temperature requirements, an electric heater is used to regulate the battery
temperature. Using the 0.5 W heater that is integrated with the Battery Charge/Discharge
Regulator (BCDR) is adequate for the job. The heater is made up of three resistive heating
elements as shown in Figure 4-5 below, and is operated using a thermostat style control loop.
Figure 4-5: Battery Assembly
Resistive heating
elements
Thermal gap
filler
Battery
73
Structural Design Modifications 4.4.3
By modifying the heat flow paths within the satellite bus, the temperatures that certain
components experience can be controlled. In general, by isolating a component (decreasing the
thermal conductivity between that component and the rest of the satellite bus) the temperature
range that the component experiences can be decreased, as it will respond more slowly to
changes in average satellite temperature, which varies substantially as the satellite travels into
and out of eclipse. Several changes have been made to the structural design to help meet the
temperature requirements. All of the changes are illustrated in Figure 4-6 below (highlighted in
red). The spacers for the on-board computer and power distribution unit circuit board assemblies
have been changed from aluminum to stainless steel to help isolate them. Also, to increase
isolation, the spacers for the UHF radio board have been changed from aluminum to Delrin®
.
Figure 4-6: Structural Design Modifications
4.5 Results
In this section, the results from the thermal finite difference analysis are provided. The results are
based on the model provided in Section 4.2, the boundary conditions presented in Section 4.3,
and the thermal control system designs described in Section 4.4. Simulations were performed for
each set of boundary conditions as laid out in Table 4-2 as well as all of the worst case attitudes;
however, only the WCC and WCH temperature results for the cold and hot reference orbit will
be presented. Figure 4-7 through Figure 4-10 illustrate the orbit and attitude combinations that
lead to the WCC and WCH temperatures. Boundary conditions for each case are summarized in
the top left corner of the figures.
On-board
computer
Power distribution
unit
UHF
receiver
74
Figure 4-7: Cold Reference Orbit – WCC Boundary Conditions
Figure 4-8: Cold Reference Orbit – WCH Boundary Conditions
Earth’s Shadow Cone
Solar Vector
Sun Synchronous Orbit Altitude: 800 km LTAN: 11:47 Day Number: 275 Beta Angle: 0° Eclipse Fraction: 0.35 X-axis Spin: 0.1°/s Solar Flux: 1322 W/m2
Albedo: 0.2 Earth IR: 231 W/m2
Earth’s Shadow Cone
Solar Vector
Sun Synchronous Orbit Altitude: 800 km LTAN: 11:47 Day Number: 198 Beta Angle: 6° Eclipse Fraction: 0.35 +X –Y +Z Corner to Sun Solar Flux: 1414 W/m2
Albedo: 0.3 Earth IR: 244 W/m2
X
Y Z
�� 𝑏
X
Y
Z �� 𝑏
75
Figure 4-9: Hot Reference Orbit – WCC Boundary Conditions
Figure 4-10: Hot Reference Orbit – WCH Boundary Conditions
In all cases, transient simulations were performed to capture temperature variations
throughout the orbit. For simulations involving WCC conditions, the lowest temperature
experienced by each component was recorded, and for simulations involving WCH conditions,
Earth’s Shadow Cone
Solar Vector
Sun Synchronous Orbit Altitude: 600 km LTAN: 7:33 Day Number: 344 Beta Angle: 51° Eclipse Fraction: 0.28 X-axis Spin: 0.1°/s Solar Flux: 1322 W/m2
Albedo: 0.25 Earth IR: 231 W/m2
Earth’s Shadow Cone
Solar Vector
Sun Synchronous Orbit Altitude: 600 km LTAN: 7:33 Day Number: 96 Beta Angle: 67° Eclipse Fraction: 0 +X –Y –Z Corner to Sun Solar Flux: 1414 W/m2
Albedo: 0.41 Earth IR: 244 W/m2
X
Y
Z �� 𝑏
X
Y
Z �� 𝑏
76
the highest temperature experienced by each component was recorded. The temperature results
are summarized in Table 4-6 and Table 4-7 for the cold and hot reference orbits respectively.
Table 4-6: Thermal Analysis Results Summary – Cold Reference Orbit
Expected Temperatures [°C] Temperature Requirements [°C]
WCC Nominal WCH
Minimum Maximum
C&DH On-Board Computer -19.7 17.7 44.8
-20 60
Power
Solar Cell Arrays -24.7 0.90 44.3
-50 70
Battery 4.94 16.4 58.4
-20 60
Power Distribution
Unit -16.3 3.81 47.2
-30 60
ADCS Magnetorquers -22.2 4.00 44.1
-30 70
Magnetometer -29.5 9.06 65.8
-30 70
Comms
UHF Receiver -14.0 4.30 45.5
-20 60
UHF Antennas -24.2 1.60 43.9
-65 165
S-band Transmitter -22.9 1.90 44.0 -30 60
S-band Antennas -24.4 1.40 44.0
-65 165
Payloads
Drag Sail Modules -25.4 -1.10 56.5 -30 70
ADS-B Receiver -18.4 0.53 44.5 -20 60
Inspection Camera
(mVIC) -29.9 8.56 65.0 -30 70
Table 4-7: Thermal Analysis Results Summary – Hot Reference Orbit
Expected Temperatures [°C] Temperature Requirements [°C]
WCC Nominal WCH
Minimum Maximum
C&DH On-Board Computer -19.8 25.8 52.4
-20 60
Power
Solar Cell Arrays -25.2 9.80 46.0
-50 70
Battery 3.95 24.0 58.1
-20 60
Power Distribution
Unit -18.1 12.0 54.1
-30 60
ADCS Magnetorquers -23.0 12.3 48.7
-30 70
Magnetometer -29.3 19.1 66.0
-30 70
Comms
UHF Receiver -14.7 14.4 49.6
-20 60
UHF Antennas -24.9 10.2 45.1
-65 165
S-band Transmitter -17.5 9.80 42.7 -30 60
S-band Antennas -25.0 12.0 44.8
-65 165
Payloads
Drag Sail Modules -25.0 13.0 68.0 -30 70
ADS-B Receiver -14.4 9.69 59.4 -20 60
Inspection Camera
(mVIC) -28.8 18.8 65.2 -30 70
77
The expected WCC and WCH temperature results provided in Table 4-6 and Table 4-7
include a margin of 5°C (applied by subtracting 5°C from the WCC temperature results and
adding 5°C to the WCH temperature results) to account for uncertainty in the modelling process.
For all WCC results, a duty cycle of 30% is assumed for the battery heater. The nominal
temperature results are based on the attitude for secondary payload operations, where the satellite
–X axis is tracking the local magnetic field, and average values for the remaining boundary
conditions. Overall, all components remain within their operational temperature ranges in both
the cold and hot reference orbits.
Component temperatures vary throughout each orbit as the spacecraft passes into and out
of eclipse. Depending on thermal mass and thermal coupling to the rest of the satellite bus, the
temperature variation that certain components experience can differ. To illustrate this, Figure
4-11 and Figure 4-12 provide the nominal temperature profiles of various spacecraft components
as a function of time for both the cold and hot reference orbits. Again, the attitude for secondary
payload operations is assumed, with average values for the remaining boundary conditions. The
orbital period is about 99 minutes and the eclipse portions are indicated in the figures. Notice
that the battery experiences minimal temperature variation due to its large thermal mass.
Figure 4-11: Nominal Temperature Profiles – Cold Reference Orbit
-10
-5
0
5
10
15
20
0 50 100 150 200
Tem
per
atu
re [⁰C
]
Time [min]
On-Board Computer
Battery
Power Distribution Unit
Magnetorquers
UHF Receiver
S-band Transmitter
Drag Sail Payload
ADS-B Receiver
Eclipse Eclipse
78
Figure 4-12: Nominal Temperature Profiles – Hot Reference Orbit
4.6 Drag Sail Thermal Analysis
Post-deployment of the passive drag sail de-orbiting device, it is not required that the satellite
remains operational; however, it is important that the drag sail remains intact. Therefore, thermal
finite difference analysis was also conducted for the drag sail in its deployed configuration. The
drag sail thermal model is illustrated in Figure 4-13. 2D meshes were used to represent the sail
sections, with finer elements in the corners of the sail where it is attached to the tape spring
booms and drag sail module.
0
5
10
15
20
25
30
35
0 50 100 150 200
Tem
per
atu
re [⁰C
]
Time [min]
On-Board Computer
Battery
Power Distribution Unit
Magnetorquers
UHF Receiver
S-band Transmitter
Drag Sail Payload
ADS-B Receiver
Eclipse Eclipse
79
Figure 4-13: Drag Sail Finite Difference Model
As discussed in Section 1.1.2, the final drag sail design uses 12.7 µm thick aluminized
Upilex® as the sail membrane material. At this thickness, the drag sail has a very low thermal
time constant. If exposed to direct sunlight, the sail will go from 0 to 100°C in just 8 seconds.
Due to the low thermal time constant of the drag sail, instead of considering boundary conditions
that result in the highest and lowest orbit average heat loads, the boundary conditions that result
in the highest and lowest heat loads at a specific orbital location need to be considered. The
minimum heat loads occur when the satellite is fully eclipsed by Earth, and the sail plane is
parallel to the nadir direction. The highest heat loads occur when the spacecraft is directly
between the Sun and Earth with the sail plane perpendicular to the solar vector, as this
maximizes solar and albedo heat loads. The worst case boundary conditions for the drag sail
analysis were determined using the methods discussed in Section 3.1, and are summarized in
Figure 4-14 and Figure 4-15.
80
Figure 4-14: Drag Sail WCC Conditions
Figure 4-15: Drag Sail WCH Conditions
Given these boundary conditions, thermal analysis shows that the drag sail may
experience temperatures of -142.1°C to 189.2°C on-orbit. These results fall within the
temperature requirements for the drag sail and are based on the final design for the drag sail
Earth’s Shadow Cone
Solar Vector
Sun Synchronous Orbit Altitude: 800 km Beta Angle: 0° Point: Descending Node Earth IR: 108 W/m2
CanX-7 Spacecraft
Earth’s Shadow Cone
Solar Vector
Sun Synchronous Orbit Altitude: 600 km Beta Angle: 0° Point: Ascending Node Solar Flux: 1414 W/m2
Albedo: 0.42 Earth IR: 197 W/m2
CanX-7 Spacecraft
81
payload; however, thermal considerations actually played a major role in selecting the final
shape and material for the drag sail, and this will be discussed in the next section.
Drag Sail Design Evolution 4.6.1
Originally, the drag sail was going to be made from 12.7 μm aluminized Kapton™ and the sail
membrane was going to extend right to the edge of the spacecraft bus. The initial and final
geometries for the drag sail are illustrated in Figure 4-16 below.
Figure 4-16: Initial (Left) and Final (Right) Drag Sail Geometries
Initial thermal analysis indicated that given WCH conditions the sail would experience
significant hotspots in sections of the sail near the spacecraft bus. This effect is illustrated by
Figure 4-17, where it can be seen that the temperature near the base of the sail is about 35°C
hotter than the average sail temperature. The temperature variation is due to the proximity of the
satellite bus. Portions of the drag sail closer to the satellite bus have an obstructed view of space
or Earth, which causes their heat loads to differ from the rest of the sail. Given WCH conditions,
the portion of the sail close to the satellite bus is hotter due to a reduction in the amount of heat
energy that can be radiated away to space. With a modification to the sail geometry this situation
was averted and the maximum temperature that the sail membrane will experience is
significantly reduced.
82
Figure 4-17: Drag Sail Temperature Variation (in degrees Kelvin)
Kapton™ is rated for temperatures of -250°C to 290°C, and following the change in sail
geometry the resulting sail temperatures fell within this range. Unfortunately, the temperatures
are very sensitive to the thermo-optical properties of the material, which can vary due to the
manufacturing process and deposition of the aluminum coating. In addition, due to
contamination, the absorptivity of exposed materials in space tends to increase over time.
Overall, there is some uncertainty in the thermo-optical properties for the drag sail material that
could cause it to get hotter than predicted. Furthermore, the rated temperature range does not
represent a hard limit as Kapton™ experiences degradation of its mechanical properties over
time when held above temperatures of about 240°C. Thermal degradation is irreversible and
cumulative, and since the sail is designed to be exposed on-orbit for many years, this poses an
issue. A major concern is that the material could become brittle. Embrittlement is a particular
concern because the sail will inevitably be struck with micrometeorites or small pieces of orbital
debris which could cause the sail to shatter. Following identification of this issue, Sears [11]
completed a detailed trade study to select a more suitable material for the drag sail membrane.
Ultimately, aluminized Upilex® was chosen for its improved thermo-optical and mechanical
properties.
83
4.7 Thermal Model Validation
The thermal finite difference analysis concludes that all temperature requirements for the
CanX-7 spacecraft can be satisfied given either the cold or hot reference orbit. Once a launch
service for the spacecraft has been arranged and the orbit is known, the selection of thermal
control tapes will be updated to create the final thermal control system design. In order to
validate the finite difference analysis, thermal vacuum testing will be completed. Using the
thermal vacuum chamber at SFL, the fully assembled CanX-7 spacecraft will be exposed to a
simulated space environment. The test setup for a similar spacecraft is shown in Figure 4-18
below. The thermal vacuum chamber uses a series of positive displacement and entrapment
based vacuum pumps to provide a low pressure environment, while liquid nitrogen cooled
exterior walls and infrared lamps are used to simulate deep space and the Sun. It is not possible
to simulate the exact heat loads that are expected on-orbit. However, by monitoring spacecraft
temperatures throughout the test, the modelled thermal capacitance and conductance paths can be
verified, thereby providing confidence in the thermal finite difference analysis results.
Figure 4-18: Thermal Vacuum Chamber Test Setup
84
Chapter 5
Conclusion
The CanX-7 nanosatellite mission developed at the Space Flight Laboratory will demonstrate the
use of a mechanically deployed drag sail as a preventative approach to the space debris problem,
as well as an ADS-B receiver for aircraft tracking. As part of this thesis project, the attitude
determination and control system has been designed, analyzed, implemented with custom
magnetic actuators and control software, and tested with the CanX-7 FlatSat. Analysis shows
that LMF tracking will be achieved with an accuracy of ±3 degrees (2σ) and that the pointing
requirements for the ADS-B payload will be fulfilled. In addition, a primarily passive thermal
control system has been designed and analyzed. Results show that all spacecraft components can
be kept within their operational temperature ranges for the duration of the mission. The work
completed on these two spacecraft subsystems represents a major contribution the CanX-7
mission.
The CanX-7 spacecraft awaits final assembly, and system level vibration and thermal
vacuum testing, but is well positioned to meet the target for launch readiness of Q2 2015. Once
the drag sail technology is demonstrated on-orbit it can be implemented on future missions,
thereby allowing the Space Flight Laboratory to contribute to a sustainable space environment
for the future.
85
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88
Appendix A: Attitude Performance Sensitivity Study
In this section, additional attitude simulation results are provided based on a sensitivity study that
investigates the impact of initial/boundary conditions on detumbling and pointing performance.
The study considers all possible combinations of orbit altitude, orbit LTAN, and parasitic dipole
moment direction. Variation in these parameters causes small changes in the disturbance torques
that act on the spacecraft. The results are summarized in Table A-1 below. Note that the
spacecraft is considered to be detumbled when the angular rate has been reduced below 0.2 °/s.
Overall, the detumbling time varies no more than 0.39 orbits (~23 minutes) from case to case and
the steady state LMF tracking error varies no more than 0.4 degrees from case to case.
Table A-1: Additional Attitude Simulations Results
Orbit
Altitude
Orbit
LTAN
Parasitic Dipole
Moment
[A∙m2]
Number of Orbits
to Detumble
(Initial Angular
Velocity: 20 °/s)
Number of Orbits
to Detumble
(Initial Angular
Velocity: 4 °/s)
Steady State LMF
Tracking Error (2σ)
600 km
6:00
[ ] 1.65 0.59 2.89°
[ ] 1.33 0.41 3.06°
[ ] 1.67 0.61 2.87°
9:00
[ ] 1.65 0.59 2.93°
[ ] 1.33 0.41 3.08°
[ ] 1.67 0.61 2.92°
12:00
[ ] 1.63 0.58 2.97°
[ ] 1.31 0.39 3.12°
[ ] 1.65 0.60 2.95°
800 km
6:00
[ ] 1.66 0.60 3.08°
[ ] 1.34 0.40 3.20°
[ ] 1.69 0.62 3.07°
9:00
[ ] 1.66 0.60 3.07°
[ ] 1.34 0.40 3.25°
[ ] 1.69 0.62 3.05°
12:00
[ ] 1.64 0.59 3.06°
[ ] 1.30 0.39 3.28°
[ ] 1.68 0.61 3.05°
Maximum: 1.69 0.62 3.28°
Average: 1.55 0.53 3.05°
Standard Deviation: 0.16 0.10 0.12°
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