Virginia Tech



VASCAT

(Virginia Satellite for Carbon-monoxide Analysis and Tabulation)

MicroMAPS Host Satellite Design Proposal

|Michael P. Belcher |Ann W. Bergquist |

|Joseph G. Bidwell |Kevin D. Earle |

|Scott E. Lennox |Daniel Pedraza |

|Christine R. Rogers |Matthew C. VanDyke |

|Richard G. Winski |

August 27, 2002

Christopher D. Hall

Aerospace and Ocean Engineering Department

Virginia Polytechnic Institute and State University

215 Randolph Hall

Blacksburg, VA 24061

cdhall@vt.edu (540) 231-2314 fax (540) 231-9632

Table of Contents

List of Figures iii

List of Tables iv

List of Tables iv

List of Abbreviations v

List of Symbols vi

Chapter 1: Introduction and Problem Definition 8

1.1 Descriptive scenario 8

1.2 Scope 9

1.3 Needs, alterables, and constraints 9

1.4 Value system design 10

1.5 Summary and conclusions 12

Chapter 2: Satellite Configuration and Components 13

2.1 Configuration 13

2.2 Structure 15

2.2.1 Requirements 15

2.2.2 Launch vehicle selection 16

2.2.3 Bus structure 16

2.2.4 Structure configuration 19

2.2.5 Component layout 20

2.3 ADCS 21

2.3.1 Attitude control architecture 21

2.3.2 Attitude control modes 22

2.3.3 Disturbance torques 23

2.3.4 Hardware 25

2.4 Power 31

2.4.1 Power Requirements 32

2.4.2 Power Generation 33

2.4.3 Energy Storage 35

2.5 Thermal 36

2.6 Communication 42

2.6.1 Uplink 42

2.6.2 Downlink 43

2.6.3 AMSAT 44

2.7 Command and data handling 44

2.8 Summary 44

Chapter 3: Mission Operations 45

3.1 Orbits 45

3.1.1 Coverage 45

3.1.2 Orbit prediction 46

3.1.3 Orbit simulation 46

3.1.4 Orbit characteristics 46

3.1.5 Lifetime 47

3.2 Summary 50

Chapter 4: Cost Analysis 51

Chapter 5: Summary, Conclusions, and Remaining Work 53

References 54

Appendix A: MATLAB Power Code 56

Appendix B: HokieSat Loop Antenna 58

Appendix C: MATLAB Earth Ground Coverage Code 59

Appendix D: MATLAB Disturbance Torque and Attitude Actuator Sizing Code 62

List of Figures

Figure 1: Objective hierarchy chart 11

Figure 2: Internal configuration of HokieSat7 13

Figure 3: External configuration of HokieSat7 14

Figure 4: VASCAT external configuration 15

Figure 5: Illustration of isogrid construction15 20

Figure 6: Ithaco CES sensor head diagram11 26

Figure 7: An isometric diagram of the BEI Systron Donner QRS-11 rate gyro17 27

Figure 8: A three view drawing of the Ithaco IM-103 magnetometer11 28

Figure 9: A cut-away diagram showing the interior of an Ithaco Type A momentum wheel11 29

Figure 10: External configuration diagram of an Ithaco TR30CFR magnetic torque bar11 31

Figure 11: VASCAT power model 34

Figure 12: Cycle life versus DOD20 35

Figure 13: Uplink transceiver5 42

Figure 14: Downlink transmitter5 43

Figure 15: Lifetime plotted as a function of altitude 47

Figure 16: Lifetime plotted as a function of drag coefficient for a 400 km altitude orbit 48

Figure 17: Lifetime plotted as a function of drag coefficient for a 500 km altitude orbit 48

Figure 18: Lifetime plotted as a function of drag area for a 400 km altitude orbit 49

Figure 19: Lifetime plotted as a function of drag area for a 500 km altitude orbit 49

Figure 20: Lifetime plotted as a function of orbit inclination 50

Figure 21: Loop antenna assembly from HokieSat drawing package 58

Figure 22: Copper tube loop from HokieSat drawing package 58

List of Tables

Table 1: List of needs, alterables, and constraints for host satellite design 9

Table 2: List of objectives and their associated subsystem 10

Table 3: Mass budget by subsystem 15

Table 4: Structural requirements16 16

Table 5: Limiting loads on structure during launch 17

Table 6: Trade study of component mounting techniques 21

Table 7: MicroMAPS imposed attitude requirements19 22

Table 8: Estimated structural properties of the VASCAT 24

Table 9: Estimated orbital properties of the VASCAT 24

Table 10: Estimated disturbance torques 25

Table 11: Properties of the Ithaco CES11 26

Table 12: Properties of the Valley Forge Composite Technologies Sun Sensor18 27

Table 13: Properties of the BEI Systron Donner QRS-11 rate gyro17 27

Table 14: Properties of the Ithaco IM-103 magnetometer11 28

Table 15: VASCAT orbital and environmental properties 29

Table 16: Properties of the Ithaco TW-4A12 momentum wheel11 30

Table 17: Properties of the Ithaco TR30CFR magnetic torque bar11 31

Table 18: Component power requirements 32

Table 19: Daylight and eclipse power budget 33

Table 20: Design parameters for preliminary VASCAT thermal analysis 37

Table 21: VASCAT Temperature Limits (°C) 37

Table 22: Component internal power dissipations 39

Table 23: Environmental fluxes in space (W/m2) 39

Table 24: Surface properties 39

Table 25: Temperatures of the VASCAT components 41

Table 26: Uplink receiver specifications5 43

Table 27: Downlink transmitter specifications5 43

Table 28: The VASCAT cost estimate using PECM20 52

List of Abbreviations

|ADCS |Attitude determination and control system |

|AMSAT |Amateur Satellite |

|CER |Cost estimation relationships |

|CES |Conical Earth sensor |

|DOD |Depth of discharge |

|ECA |Earth center angle |

|GASCAN |Getaway special canister |

|GSFC |Goddard Space Flight Center |

|ICD |Interface control document |

|IR |Infrared |

|LaRC |Langley Research Center |

|LEO |Low-Earth orbit |

|MAPS |Measurement of Air Pollution from Satellites |

|(MAPS |MicroMAPS Gas Filter Correlation Radiometer |

|MTB |Magnetic torque bar |

|MOE |Measure of effectiveness |

|NASA |National Aeronautics and Space Administration |

|NiCd |Nickel cadmium |

|NiMH |Nickel metal-hydride |

|PECM |Parametric cost estimation method |

|RTG |Radio-isotope thermoelectric generator |

|SHELS |Shuttle Hitchhiker Experiment Launch System |

|SINDA |Systems Integrated Numerical Differential Analyzer |

|STK |Satellite Tool Kit |

|TCS |Thermal control system |

|UHF |Ultra-high frequency |

|VASCAT |Virginia Satellite for Carbon-monoxide Analysis and Tabulation |

List of Symbols

|( |View factor |

|A |Area |

|a |Semi-major axis |

|B |Magnetic field strength |

|b |Plate width |

|Cd |Drag coefficient |

|cg |Location of the center of gravity |

|Cp |Specific heat capacity |

|c |Speed of light |

|cpa |Location of the center of atmospheric pressure |

|cps |Location of the center of solar pressure |

|D |Magnetic dipole strength |

|E |Modulus of elasticity |

|Fcr |Critical load |

|fnat |Natural frequency |

|Fs |Solar constant |

|G |Conduction coupling value |

|g |Gravitational constant |

|h |Angular momentum |

|i |Inclination |

|Ix, Iy, Iz |Moments of inertia |

|k |Thermal conductivity |

|k’ |Boundary condition factor |

|l |Length |

|M |Bending moment |

|m |Mass |

|mc |Cell mass |

|Nc |Number of cells |

|P |Power |

|Paxial |Axial limit load |

|Peq |Equivalent axial load |

|Pult |Ultimate load |

|Q |Net heat flux |

|q |Reflectance factor |

|R |Moment arm, orbital radius |

|T |Temperature |

|Ta |Atmospheric pressure torque |

|Td |Total disturbance torque |

|Tg |Gravity gradient torque |

|Tm |Magnetic torque |

|Tsp |Solar pressure torque |

|t |Thickness |

|α |Absorptivity |

|Δt |Change in time |

|δ |Beam deflection |

|ε |Emissivity |

|( |Gravitational constant |

|ν |Poisson’s ratio |

|( |Atmospheric density |

|σ |Axial stress, Steffan-Boltzmann constant |

|( |Off-nadir angle |

|(a |Allowable angular error |

Chapter 1: Introduction and Problem Definition

1.1 Descriptive scenario

Scientists at the National Aeronautics and Space Administration’s (NASA) Langley Research Center (LaRC) developed an instrument to study pollution in the Earth’s atmosphere from space. This Earth-observing instrument, known as the MicroMAPS Gas Filter Correlation Radiometer ((MAPS), a smaller version of the original Measurement of Air Pollution from Satellites (MAPS) instrument, measures carbon monoxide levels in the troposphere. Researchers study the characteristics and movement of air pollution from data acquired. Following cancellation of the Clarke mission, upon which the (MAPS instrument was scheduled to ride, scientists at LaRC began to formulate new ideas for getting the instrument into space. One alternative mission requests that a single satellite be designed whose sole purpose is to house and support the (MAPS instrument. Virginia Tech is chosen to design this satellite, based on its existing nanosatellite design, HokieSat. This report describes the host satellite design for the (MAPS instrument.

The new host satellite will be designed, built and tested in Virginia through collaboration of Virginia Tech, the University of Virginia, Old Dominion University, the Virginia Space Grant Consortium, and LaRC. Virginia Tech is responsible for the design of the host satellite, including the structure and all internal subsystems. The host satellite design is based on Virginia Tech’s HokieSat, part of a project supported by NASA’s Goddard Space Flight Center (GSFC). The host satellite is designed to house and support the (MAPS instrument, and possibly a camera, with a three-year lifetime.

The host satellite will be placed into a 400 km circular orbit with an inclination of 51.6o. The host satellite can launch on a shuttle hitchhiker system such as the Shuttle Hitchhiker Experiment Launch System (SHELS) or the getaway special canister (GASCAN), or as a secondary payload on an expendable launch vehicle. To relay data from the instrument to the ground, the host satellite uses Amateur Satellite (AMSAT) groundstations around the world to downlink data continuously.

1.2 Scope

The focus of this proposal is the design of a satellite that is capable of supporting the (MAPS instrument and mission. The structure of this satellite, as well as all internal and external subsystem components are designed and sized. The satellite must carry the necessary power generation and energy storage systems. The ADCS is designed to fulfill (MAPS orientation requirements. The method of ground communication is chosen for adequate transmission of necessary data.

The design process begins with an established nanosatellite design. This design is modified in all respects to fulfill our scope. The (MAPS host satellite design must be complete by the end of the current semester. HokieSat provides a first iteration on the desired satellite, therefore allowing for a complete design in the time allotted. Launch vehicle suggestions are included in the scope of the project; however, this design does not limit launch vehicle selection.

1.3 Needs, alterables, and constraints

This satellite needs to integrate the (MAPS instrument into a modified HokieSat design, which must perform all bus functions, access groundstations periodically, and maintain an orbit that allows fulfillment of the instrument’s science goals over a three year lifetime. The subsystems and operations are alterable within the limits set forth by the list of constraints. Other alterables include the launch vehicle selection, addition of a camera, the use of AMSAT broadcasting, and the solar array design. All needs, alterables, and constraints are listed in Table 1.

Table 1: List of needs, alterables, and constraints for host satellite design

|Category |Element |

|Needs: |Perform all bus functions |

| |Integrate (MAPS into a design similar to HokieSat |

| |Access necessary groundstations periodically |

| |Maintain an orbit to fulfill required science goals |

| |Three year lifetime |

|Alterables: |Camera |

| |Solar cell mounting |

| |AMSAT broadcasting |

| |Launch vehicle |

|Constraints: |Nadir pointing +/- 2.5o |

| |At least one year lifetime |

| |Orientation of instrument with respect to orbital reference frame |

1.4 Value system design

The value system design (VSD) is used to evaluate iterations on the HokieSat design. The VSD puts all mission objectives into a hierarchy beginning with the top-level objective: optimize the satellite design. Maximizing the performance objectives and minimizing the cost objectives optimizes the satellite design. The performance and cost objectives are described in this section.

The main objective of this satellite is to support the (MAPS instrument. Below the top-level objective are two second-level mission objectives: maximize performance and minimize cost. The performance objectives are gathered from the instrument requirements placed on each subsystem, found in the interface control document (ICD, Reference 20). Each subsystem achieves these objectives in different ways. Table 2 depicts the interactions between subsystems and mission objectives. Figure 1 illustrates the entire objective hierarchy.

Table 2: List of objectives and their associated subsystems

|Objective |Relevant subsystem |

|Maximize performance | |

| Minimize pointing error |ADCS |

| Maximize data to LaRC |COMM |

| Maximize quality of data to LaRC |All |

| Maximize power efficiency |Power |

| Maximize lifetime |All |

| Minimize excess strength/stiffness |Structures |

| Maximize external surface area |Structures |

| Maximize coverage |ADCS |

| Minimize radiation effects |ADCS |

| Maximize attitude stability |ADCS |

| Minimize position error |GN&C |

|Minimize cost | |

| Minimize launch cost |All |

| Minimize production cost |All |

| Minimize operational cost |All |

| Minimize mass |All |

[pic]

Figure 1: Objective hierarchy chart

This objective hierarchy is further divided into sub-levels of performance and cost that are associated with measures of effectiveness (MOEs). For example, a MOE for the ADCS is pointing error of the satellite. This MOE is minimized to achieve greater precision in attitude maneuvers. The communications subsystem maximizes data quality transferred to ground stations as one of its performance objectives. An objective of the structural engineers is to maximize the available surface area to allow for body mounted solar cells.

Several performance MOEs are comprised of separate quantities. The performance of the satellite structure accounts for material strength and stiffness. These quantities depend on material characteristics. Maximizing the efficiency of the power system depends on all internal components of the satellite such as the computer, ADCS components, and the (MAPS instrument. The communications system performance also depends upon factors, which affect the entire satellite, such as the radiation dose.

1.5 Summary and conclusions

Chapter 1 introduces the need for a satellite to house the (MAPS instrument. The problem definition identifies the scope, boundaries, and relevant elements of the problem. Students at Virginia Tech modify an existing nanosatellite design, HokieSat, to fit the needs of the (MAPS instrument. The following chapters outline the components pre-existing to HokieSat, and the detailed modifications made to each subsystem to arrive at a host satellite design.

Chapter 2: Satellite Configuration and Components

Chapter 2 presents the VASCAT configuration and subsystem components. The configuration and the subsystem components are based on the HokieSat design. This chapter defines the subsystem designs and presents the analyses leading up to these designs. The satellite subsystems include the structure, the attitude determination and control system, the power system, the thermal system and the communications system.

2.1 Configuration

The configuration of this satellite is based on an existing satellite design. HokieSat is a hexagonal nanosatellite with a major diameter of 18 inches and a height of 13.725 inches. It draws power from body-mounted solar cells covering approximately 80% of each side. HokieSat uses an electric propulsion system whose thrusters protrude from four sides of the structure. The HokieSat bus is made of a 6061-T6 aluminum alloy cut into an isogrid pattern. All eight sides are 0.23” thick isogrid. The six side panels are composite isogrid-skin. The 0.02” skin is bonded to the isogrid to form a 0.25” total thickness. All internal components are mounted to the interior of the six side panels and the two end panels. The external communications components are mounted to the exterior of the two end panels. Figure 2 and Figure 3 illustrate this configuration.8

[pic]

Figure 2: Internal configuration of HokieSat7

[pic]

Figure 3: External configuration of HokieSat7

The Virginia Satellite for Carbon-monoxide Analysis and Tabulation (VASCAT) is larger than HokieSat to accommodate added science instruments. Similarities between the two satellites’ components include the electronics box, the battery box, most communications equipment, and the magnetometer. This new satellite also houses the (MAPS instrument, a digital camera, and some additional ADCS components. The VASCAT satellite does not require a propulsion system, as does HokieSat. The structure of the VASCAT deviates substantially from that of HokieSat. These detailed variations of all subsystems are discussed in the following sections.

Using knowledge of configuration and component properties, a mass budget is created to approximate the mass allocated for the structure. Table 3 is a breakdown of each subsystem’s mass. The sum of the masses of all components must be lower than the mass limit of the chosen launch vehicle. The subsystem masses are taken from component specifications and the structure mass is taken from mass properties calculations done in AutoCAD™.

Table 3: Mass budget by subsystem

|Subsystem |Total mass, kg |

|Science |6.4 |

|ADCS |14.0 |

|C&DH |2.8 |

|Power |1.7 |

|Communications |0.4 |

|Structure |11.4 |

|TOTAL |36.7 |

2.2 Structure

The structure of VASCAT is designed with adequate surface area for body mounted solar cells and adequate volume to house all components including the (MAPS instrument. The structure of the VASCAT is 0.67 m in major diameter and 1 m high. Figure 4 is an illustration of the VASCAT. The satellite’s dimensions are small enough to allow for 0.85 m on each side in the payload fairing.

[pic]

Figure 4: VASCAT external configuration

2.2.1 Requirements

Design and analysis of primary structural components necessitates the derivation of structural requirements. Table 4 lists all requirements relevant to this preliminary design. Mass and size of the structure are limited by the launch vehicle selected, and the size and mass of the primary payload, should this satellite be a hitchhiker. The launch vehicle selected also sets requirements on the strength of the structure. The orbit altitude desired, and therefore the launch vehicle, restricts the mass of the structure. All primary and secondary structural components should meet the pre-determined mass allocation (see Table 3).16

Table 4: Structural requirements16

|Requirement |Description |Required information |

|General shape and |Provides load paths between supported components and |Configuration, spacecraft component level |

|purpose |launch vehicle; fits inside payload fairing |layout |

|Strength |Survives loads induced during launch; withstands |Load factors from launch vehicle; mass |

| |on-orbit loads, cyclic over lifetime |properties of spacecraft |

|Stiffness |Meets launch vehicle fundamental frequency requirement |Dynamic envelope of launch vehicle |

| | |environment; mass properties of spacecraft |

|Mechanical interface |Meets launch vehicle flatness requirements; adaptable |Interface requirements inside payload fairing|

| |to launch vehicle attachment interface | |

|Mass |Meets target mass allotment; meets launch vehicle mass |Allocated mass |

| |limitation | |

2.2.2 Launch vehicle selection

Since the launch of this satellite is uncertain, no launch vehicle is desired more than another. The VASCAT can either launch on the Space Shuttle as a hitchhiker payload, or as a secondary payload on any other launch vehicle. The structure is designed based on a worst case launch environment scenario. The Athena I launch vehicle is therefore chosen for structural analysis due to its relatively high launch loads. The Athena I is produced by Lockheed Martin. It has a payload fairing diameter of 2.36 m and a height of 8.81 m, and is capable of carrying up to 794 kg to LEO.10

2.2.3 Bus structure

Configuration and component layout guides the sizing of all primary structures. However, these dimensions change with strength requirements placed on the satellite. The challenge is to design a system to house all components, survive the launch environment, and withstand cyclic on-orbit loads.15 This section describes the process used to define dimensions of the VASCAT’s primary structure.

The International Reference Guide to Space Launch Systems states that the Athena I environment’s limit load factors are 8.1-g’s axially and 1.8-g’s laterally. A factor of safety of 2 is used during static calculations to ensure that the structure withstands these loads during launch. 20 The fundamental frequency of the VASCAT must be above 15 Hz laterally and 30 Hz longitudinally. The type of structure is chosen during dynamic calculations to ensure that the natural frequency of the satellite meets this stiffness requirement.

The mechanical interface is chosen for integration with the launch vehicle such that it meets the payload fairing’s flatness requirement and coincides with its bolt hole patterns and other attachment restrictions. 20 The VASCAT mass budget (Table 3) allows for the structure to be approximately 30% of the total mass of the satellite.

2.2.3.1 Ultimate loads

An ultimate load for the bus structure is calculated for tensile strength sizing.

Table 5: Limiting loads on structure during launch

|Type of Load |Weight, N |Distance, m |Load factor |Limit load, N |

|Axial |359 |-- |8.1 |2908 |

|Lateral |359 |-- |1.8 |646 |

|Moment |359 |0.45 |1.8 |291 |

The equivalent axial load, Peq, is calculated by:

|[pic] |2-1 |

In Equation 2-1 Paxial is the axial limit load taken from Table 5: Limiting loads on structure during launch, M is the bending moment limit load taken from the same table, and R is the moment arm taken as half the length of the structure. The ultimate load for the structure, Pult, is then found by multiplying Peq by the factor of safety. 20 The equivalent axial load on the structure is 4,201 N, giving an ultimate load of 8,403 N.

2.2.3.2 Tensile strength

Axial stress is used to size the structures for tensile strength, and is given by:

|[pic] |2-2 |

In Equation 2-2 σ is the axial stress and A is the necessary cross-sectional area. By solving for A from Equation 2-2, an adequate thickness to maintain tensile strength during launch is t = 0.01 mm. 20

2.2.3.3 Buckling analysis

To further define the cross-sectional thickness of the bus structure, some buckling analysis is performed. The critical load, or buckling load, Fcr, is approximated to find a thickness to withstand buckling under the axial loading of the launch environment. For this analysis, the buckling load is approximated as the ultimate load.

|[pic] |2-3 |

|[pic] |2-4 |

In Equation 2-3 t is the thickness of the plate, b is the width of the plate, and E is Young’s Modulus of the material. In Equation 2-4 k is a constant corresponding to the boundary conditions imposed on the plate and ν is Poisson’s ratio for the material. To model the buckling of the flat side panels that make up each structure, the fixed-fixed configuration is assumed, corresponding to a value of k’ = 6.42.15 Thickness to withstand buckling during launch is t = 0.046 mm.

2.2.3.4 Dynamic analysis

In addition to static survival, the bus structure is sized to survive dynamic loading and meet the launch vehicle minimum natural frequency requirements. The following cases are considered to estimate the natural frequencies and deflections for the uniform beam in both lateral and axial dynamic loading.

Case A, lateral:

|[pic] |2-5 |

|[pic] |2-6 |

Case B, axial:

|[pic] |2-7 |

|[pic] |2-8 |

In Equations 2-5 through 2-8, δ is beam deflection, m = 36.7 kg uniformly distributed mass, l = 1 m is the length of the beam, and fnat is the natural frequency requirement from the launch vehicle. Solving for A from Equation 2-8, a thickness of t = 0.004 mm satisfies axial natural frequency requirements and gives δ = 0.0026 m at the minimum frequency of 30 Hz. This thickness gives a moment of inertia, Ix, for the cross-section of 3.06 × 10-4 m4. Substituting this value into Equation 2-6 gives a lateral natural frequency of 428 Hz, which is above the minimum allowed value of 15 Hz.20

2.2.4 Structure configuration

After all necessary structural analysis is performed to determine dimensions of the structure, the type of structural configuration is chosen. Typically, increasing thickness increases buckling strength of a structure. However, this directly conflicts with minimizing mass. A more effective way to strengthen and stiffen a bus structure is to use isogrid construction. Isogrid consists of machining a plate of material into a triangular pattern, as shown in Figure 5. This option is lighter than pure aluminum for smaller bus structures, with identical strength properties in all load directions. 15 Because isogrid is the proposed structure type, wall thickness must be increased to 3 mm to allow for ease in machining the isogrid, adequate web strength, and a skin thick enough to support solar cells.

[pic]

Figure 5: Illustration of isogrid construction15

2.2.5 Component layout

The VASCAT design varies from the HokieSat design by volume due to added components. The (MAPS instrument is 0.007 m3 and occupies as much space inside the new satellite. Other added components include the communications hardware required to use the AMSAT frequency and the addition of a camera for high quality photos. The VASCAT grows with the added components.

In addition to increased volume constraints, mounting constraints accompany the instrument. The instrument’s lens must be nadir pointing at all times, and its feet are located on an adjacent side to its lens. Therefore, the (MAPS instrument must be mounted to a vertical interface and look through a hole in the bottom panel. Isogrid modification or addition of a vertical shelf is considered as component mounting solutions in the following trade study. The following lists the parameters used in the trade study:

1. Mass: This represents the mass added to the satellite due to the configuration change. This parameter is weighted on a scale of 1 to 10, with 10 representing negligible added mass

2. Manufacturing cost: This represents how much the production of this configuration addition costs. This parameter is weighted on a scale of 1 to 10, with 10 being no added cost

3. Ease in mounting: This represents a measure of how trivial attachment of components to the structure will be. For example, threaded inserts are complicated while fasteners are fairly simple. This parameter is weighted on a scale of 1 to 10, with 10 being the easiest to mount.

Weights are assigned to each parameter to signify its level of importance. Table 6 shows the results of this trade study. The option with the highest weight score is desired. Modified isogrid is chosen for component mounting.

Table 6: Trade study of component mounting techniques

|Selection parameter |Weight |Modified isogrid |Center component shelf |

| | |Rating |Weighted score |Rating |Weighted score |

|Mass |20 |9 |180 |5 |100 |

|Cost |40 |5 |200 |7 |280 |

|Simplicity |10 |7 |70 |1 |10 |

|Totals | | |450 | |390 |

2.3 ADCS

The ADCS stabilizes and maintains the attitude of the VASCAT. An ADCS consists of sensors and actuators. The sensor measurements are used to calculate the attitude of the satellite. The calculated attitude is compared to a desired attitude and the proper inputs are given to the attitude actuators. The actuators apply a torque to the satellite to reach the desired attitude.

2.3.1 Attitude control architecture

The VASCAT uses a single wheel momentum-bias attitude control system. The momentum wheel’s spin axis is aligned normal to the orbital plane. It controls the attitude about the satellite’s pitch axis and stabilizes the attitude about the yaw and roll axes. Three magnetic torque bars (MTB) are used to perform momentum-dumping maneuvers when the momentum wheel reaches its momentum storage limit. The MTBs are arranged in a triad to create a magnetic torque in any direction, except the direction of the magnetic field.

Attitude knowledge is required to be accurate within (0.5 degrees by the (MAPS instrument.19 Attitude determination is performed using two Earth sensors, two sun sensors, three rate gyros, and a magnetometer. The attitude requirements imposed by the (MAPS instrument are summarized in Table 7.

Table 7: MicroMAPS imposed attitude requirements19

|Requirement |Value |

|Pointing Direction |Nadir pointing |

|Control accuracy (3() |( 2.5( |

|Knowledge accuracy (3() |( 0.5( |

2.3.2 Attitude control modes

The VASCAT uses three modes of attitude control. The satellite operates in normal mode during the majority of its mission. A momentum-dump mode is entered whenever the momentum wheel reaches its upper limit of momentum storage. The satellite’s computer initiates safe mode should it experience system level error.

2.3.2.1 Normal

The ADCS of the satellite operates in normal mode during the majority of its mission. The attitude of the satellite is determined every ten seconds and transmitted to a ground station. All available sensor data is used to determine attitude to ensure that the attitude knowledge is accurate to (0.5 degrees. Attitude knowledge is compared with the desired attitude and a control torque is applied using the momentum wheel or magnetic torque bars accordingly. This ensures that the pointing error is kept below (2.5 degrees.

2.3.2.2 Momentum-dump

The satellite uses a momentum wheel for attitude control and stabilization. Over time secular attitude disturbances build up momentum in the wheel. When the build up of momentum reaches the storage limit of the momentum wheel, a momentum-dumping maneuver is performed. The three MTBs are used to apply an external torque to the satellite so that the momentum wheel applies an equal and opposite torque to lower its spin rate. The attitude determination system performs as it does in normal mode, but the magnetometer readings are not used for attitude determination while the MTBs are active.

2.3.2.3 Safe

The satellite enters safe mode if an error occurs during operation. The satellite’s computer determines the entry and exit of this mode. During this mode the ADCS is passive. The momentum stored in the momentum wheel and the gravity-gradient stabilize the satellite.

2.3.3 Disturbance torques

The VASCAT encounters disturbance torques on orbit. It is subjected to solar pressure, gravity-gradient, atmospheric drag, and magnetic torques. A significant torque is due to the gravity-gradient. The force of gravity varies with an object’s distance from the center of the Earth. The lower sections of the satellite feel a greater gravitational force compared to the upper sections. The result is a torque exerted on the satellite if it is not directly nadir pointing.

|[pic] |2-920 |

The moments of inertia, Iz and Iy, of the satellite as well as its radius, R, and the angle off nadir, (, determine the magnitude of the torque.

Solar pressure is exerted on the satellite by photons, emitted from the Sun, that strike the satellite. The force is exerted at the center of solar pressure of the satellite. If the center of solar pressure and center of gravity do not coincide then a torque is created.

|[pic] |2-1020 |

The surface area exposed to the sun, Asp, the center of solar pressure, cps, the center of gravity, cg, and the reflectance factor, q, are the satellite properties that determine the torque. The solar constant, Fs, and the speed of light, c, are the constants that influence the magnitude of the torque.

The electronics on-board the VASCAT induce a magnetic dipole during operation. The magnetic dipole interacts with the geomagnetic field to produce a torque. The maximum torque occurs when the magnetic dipole direction is perpendicular to the geomagnetic field.

|[pic] |2-1120 |

The worst case magnitude of the torque is calculated using Equation 2-11, where D is the strength of the magnetic dipole and B is the magnitude of the local geomagnetic field.

Although the atmosphere in Low-Earth Orbit (LEO) is sparse, the high velocity of a satellite creates some drag. The drag force acts at the center of pressure of the satellite. If the center of pressure does not coincide with the center of gravity, the drag creates a torque.

|[pic] |2-1220 |

The torque is equal to the drag force times the length of the moment arm, or the distance between the center of atmospheric pressure, cpa, and the cg. Equation 2-12 is used to calculate the magnitude of the torque, where ( is the atmospheric density, Cd is the drag coefficient, A is the projected area, and V is the velocity of the satellite.

Preliminary estimates of the structural properties and orbital parameters of the satellite are used to estimate these torques. Table 8 summarizes the structural properties used in the calculations.

Table 8: Estimated structural properties of the VASCAT

|Description |Value |

|Ix |4.4 kg/m2 |

|Iy |4.4 kg/m2 |

|Iz |1.9 kg/m2 |

|As |0.18 m2 |

|cg |0.10 m |

|c.p. |0.17 m |

|Cd |2.5 |

The estimated orbital parameters used in the calculations for disturbance torques are summarized in Table 9.

Table 9: Estimated orbital properties of the VASCAT

|Description |Value |

|R |6778 km |

|( |2.72 ( 10-12 kg/m2 |

The disturbance torques are estimated using equations 2-9 through 2-12 above. A simple Matlab code is used to perform the calculations, and is presented in Appendix D. Table 10 summarizes the results of the calculations.

Table 10: Estimated disturbance torques

|Disturbance |Torque (N-m) |

|Gravity gradient |4.8 × 10-6 |

|Solar pressure |8.5 × 10-8 |

|Magnetic |5.1 × 10-5 |

|Atmospheric drag |2.3 × 10-12 |

The magnitude of the total disturbance torque is estimated to be 56 (N-m. The majority of the disturbance torque is due to the magnetic torque created by the interaction of the satellite’s electronics with the geomagnetic field. A magnetic dipole of 1 A-m2 was assumed for the magnetic disturbance torque calculation. The second largest component is due to the gravity-gradient. The VASCAT is nadir pointing. In this orientation the torque due to the gravity-gradient is zero and acts as a restoring torque in case of deviation from nadir.

2.3.4 Hardware

The ADCS consist of two types of hardware: attitude sensors and attitude actuators. Attitude sensors take measurements that determine the orientation of the satellite. Attitude actuators apply a torque to the satellite to control its orientation.

2.3.4.1 Determination

The attitude determination hardware used by the VASCAT includes two Earth sensors, two sun sensors, three rate gyros, and a magnetometer. Earth sensors are chosen as attitude sensors for the VASCAT because it is an Earth-referenced satellite, and the sensors meet accuracy requirements. The Earth sensors are Ithaco Conical Earth Sensors (CES). Figure 6 is a diagram of the sensor head of the CES with dimensions.

[pic]

Figure 6: Ithaco CES sensor head diagram11

The CESs use a rotating scanner that sweeps out a 45 degree half-angle cone.11 A measurement is taken to determine where in that cone the scanner crosses Earth’s horizon. This knowledge, combined with the known curvature of the Earth, is used to determine the pitch and roll of the satellite. The VASCAT uses two CESs mounted along the roll axis of the satellite. They are angled down 45 degrees towards the Earth. The structural and power requirements as well as the performance characteristics are presented in Table 11.

Table 11: Properties of the Ithaco CES11

|Description |Value |

|Mass |3 kg |

| |Sensor Head: 1.1 kg |

| |Electronics: 1.9 kg |

|Peak Power |8 W |

|Voltage |22 to 36 V or 31 to 52 V |

|Dimensions |Sensor Head: 9.9 ( 11.8 cm |

| |Electronics: 16.8 ( 17.0 ( 8.3 cm |

|Accuracy |0.1( (3(), 1’ (avg.) |

|Scan Cone Half-Angle |45( |

The VASCAT uses two sun sensors manufactured by Valley Forge Composite Technologies. The sun sensors measure the direction of the sun vector in the body-fixed reference frame. This measurement is compared with the inertial sun vector direction to perform single axis attitude determination. Table 12 summarizes the requirements imposed by the sun sensors and their performance characteristics.

Table 12: Properties of the Valley Forge Composite Technologies Sun Sensor18

|Description |Value |

|Mass |350 grams |

|Peak Power |2.5 W |

|Accuracy |1 arc second |

|Measurement Frequency |10 Hertz |

|Field of View |100( ( 50( |

Rate gyros measure the angular rate of the satellite in the body-fixed reference frame. BEI Systron Donner manufactures the rate gyros used on the VASCAT. They measure the angular rate about one axis. Figure 7 is an isometric view of the rate gyro with dimensions and shows about which axis the angular rate is measured.

[pic]

Figure 7: An isometric diagram of the BEI Systron Donner QRS-11 rate gyro17

Three rate gyros mounted orthogonally determine the satellite’s angular velocity vector. The physical and electrical requirements of the rate gyros and performance characteristics are shown in Table 13.

Table 13: Properties of the BEI Systron Donner QRS-11 rate gyro17

|Description |Value |

|Mass |60 grams |

|Peak Power |2.1 W |

|Voltage |(5 V |

|Dimensions |38.1 ( 16.38 mm |

|Accuracy |3(/second |

|Bandwidth |60 Hertz |

An Ithaco IM-103 three-axis magnetometer is one of the sensors in the VASCAT attitude determination system. A three view drawing of the magnetometer is shown in Figure 8.

[pic]

Figure 8: A three view drawing of the Ithaco IM-103 magnetometer11

A magnetometer measures the direction and magnitude of the local geomagnetic field. The measurement is compared to the same vector in the inertial frame for single-axis attitude determination. The measurement is used to determine the magnetic dipoles required to create a desired control torque using the magnetic torque bars. Table 14 summarizes the characteristics of the Ithaco IM-103 magnetometer.

Table 14: Properties of the Ithaco IM-103 magnetometer11

|Description |Value |

|Mass |227 grams |

|Peak Power |1 mW |

|Voltage |(15 V |

|Dimensions |5.5 ( 4.2 ( 3.6 cm |

|Accuracy |0.5( |

|Frequency Response |3 dB @ >100 Hz |

|Field Measurement Range |(600 mG |

2.3.4.2 Control

The attitude control system of the VASCAT is a single-wheel momentum bias system with magnetic torque bars for momentum dumping. The momentum wheel is mounted so that its spin axis is along the pitch axis of the satellite. The purpose of the momentum wheel is to control the attitude about the pitch axis and stabilize the attitude about the roll and yaw axes.

The sizing of the momentum wheel is based on the maximum disturbance torque applied to the satellite, and the accuracy requirement of (2.5 degrees. The reaction torque capability must cope with the maximum total disturbance torque, estimated to be 56 (N-m. The amount of stability required by the satellite and the maximum disturbance torque determines the momentum capacity of the momentum wheel.

|[pic] |2-1320 |

The disturbance torque, TD, the semi-major axis of the orbit, a, and the allowable angular deviation, (a, affect the required momentum storage capability. 20 The calculations are performed using the values shown in Table 15. The momentum wheel is required to maintain 1.78 N-m-s of momentum.

Table 15: VASCAT orbital and environmental properties

|Description |Symbol |Value |

|Semi-major axis |a |6778 km |

|Disturbance torque |TD |56 (N-m |

|Allowable angular deviation |(a |(2.5( |

The momentum wheel used in the VASCAT is an Ithaco TW-4A12 momentum wheel. Figure 9 is a cut-away diagram depicting the internal configuration of this momentum wheel.

[pic]

Figure 9: A cut-away diagram showing the interior of an Ithaco Type A momentum wheel11

This momentum wheel is capable of 12 mN-m of torque, which exceeds the maximum disturbance torque of 56 (N-m. The maximum momentum capacity of the wheel is 4 N-m-s.11 The momentum wheel operates with at least 2 N-m-s of momentum stored at all times to satisfy the stability requirement. The mass and power properties and performance characteristics of the momentum wheel are summarized in Table 16.

Table 16: Properties of the Ithaco TW-4A12 momentum wheel11

|Description |Value |

|Mass |3.46 kg |

| |Motor Drive: 2.55 kg |

| |Wheel: 0.91 kg |

|Peak Power |25 W |

|Dimensions |Motor Drive: 15 ( 19 ( 32 cm |

| |Wheel: 20.5 ( 6.4 cm |

|Momentum Capacity |4 N-m-s |

|Reaction Torque |12 mN-m |

|Steady State Power |Max. Speed: 9 W |

| |@ 1000 rpm: 5 W |

|Speed Range |(5100 rpm |

Momentum dumping is performed using magnetic torque bars (MTBs). Magnetic torque bars induce a magnetic dipole that interacts with the geomagnetic field to create a torque on the satellite. 20 The MTBs are mounted orthogonally. This arrangement allows greater flexibility in inducing the direction of the magnetic dipole.

The MTBs are sized to provide sufficient torque to dump enough of the momentum wheel’s momentum within a reasonable amount of time. The maximum storage capacity of the momentum wheel is 4 N-m-s, and the minimum storage capacity required for attitude stabilization is 2 N-m-s. Therefore, a momentum-dumping maneuver is required whenever 2 N-m-s of momentum is built up in the wheel. The amount of added momentum stored in the wheel during a single orbit is calculated using the following equation.

|[pic] |2-1420 |

The momentum stored per orbit is 0.22 N-m-s. Approximately every 9 orbits a momentum-dumping maneuver is required. The maneuver for the VASCAT takes approximately 22 minutes. The torque required to accomplish this is 1.52 mN-m. The magnetic dipole necessary to meet the torque requirement is the magnitude of the torque divided by the magnitude of local magnetic field.17 The magnitude of the local magnetic field is assumed to be 4.5 ( 10-5 Tesla in the worst case. Using the worst case results in a required magnetic dipole of 33.67 A-m2.

Ithaco TR30CFRs are the MTBs that are used by the VASCAT (shown above in Figure 10). These MTBs generate a 35 A-m2 magnetic dipole (Ithaco). This value meets the magnetic dipole requirement determined above. Other performance characteristics and physical and power requirements are presented in Table 17.

[pic]

Figure 10: External configuration diagram of an Ithaco TR30CFR magnetic torque bar11

Table 17: Properties of the Ithaco TR30CFR magnetic torque bar11

|Description |Value |

|Mass |1 kg |

|Peak Power |5.4 W |

|Voltage |26.2 W |

|Dimensions |49.6 ( 2.3 cm |

|Linear Moment |35 A-m2 |

|Saturation Moment |40 A-m2 |

2.4 Power

The power needs of every component on the satellite are supplied by the power system. The power system is comprised of the power generation system and the energy storage system. The power generation system collects and converts solar energy into electrical power. The energy storage system provides power to the satellite components during periods of eclipse. The power requirements of the satellite are used to design the power generation and energy storage systems.

2.4.1 Power Requirements

The components on the VASCAT require conditioned electrical power to function. Each component has a specific power and voltage requirement. The power system must meet the needs of all the satellite components. Table 18 is a list of all the satellite components and their power requirements.

Table 18: Component power requirements

|System |Device |Average power(W) |Peak power(W) |Voltages (V) |

|Comm: |Uplink |1.5 |3 |28 |

| |Downlink |3 |5 |28 |

| |AMSAT |1.8 |2 |28 |

|  |Dual single board computer |3.5 |4 |28 |

|ADCS: |Momentum Wheel |9 |25 |28 |

|  |Magnet Torque Bars |4.2 |5.4 |28 |

|  |Magnetometer |0.0008 |0.001 |28 |

|  |Magnetometer Board |0.036 |0.037 |28 |

|  |Earth Sensors |5 |8 |28 |

|  |Earth Sensor board |0.12 |0.6 |28 |

|  |Sun Sensor |2 |2.5 |28 |

|  |Rate Gyro |1.5 |2.1 |28 |

|  |MT and RG Board |0.5 |0.8 |28 |

|UMAPS: |Calibrate |27.2 |27.2 |28 |

|  |Normal Operation |16.2 |16.2 |28 |

|GN&C: |GPS |3 |5 |28 |

|Camera: |Camera |3 |3.5 |28 |

The power system is modeled from the peak power requirements to ensure that it supplies enough power to the satellite. A power budget quantifies the amount of power required for a single orbit, and it shows which components operate during daylight and eclipse. If the power system provides enough power to fulfill the budget for peak power needs, it is sufficient for all other cases. The VASCAT runs off of a 28 V bus voltage.

Table 19: Daylight and eclipse power budget

| | |Daylight |Eclipse |

|Operation: |Power (W) |Duration (s) |Energy (W-s) |Duration (s) |Energy (W-s) |

|Uplink |3 |600 |1,800 |0 |0 |

|Downlink |5 |600 |3,000 |0 |0 |

|AMSAT |2 |3,500 |7,000 |2,150 |4,300 |

|Dual single board computer |4 |3,500 |14,000 |2,150 |8,600 |

|Momentum Wheel |25 |3,500 |225 |2,150 |19,350 |

|Magnet Torque Bars |5.4 |3,500 |6,480 |0 |0 |

|Magnetometer |0.001 |3,500 |3.5 |2,150 |2 |

|Magnetometer Board |0.037 |3,500 |128 |2,150 |79 |

|Earth Sensors |8 |3,500 |28,000 |2,150 |17,200 |

|Earth Sensor board |0.6 |3,500 |2,100 |2,150 |1,290 |

|Sun Sensor |2.5 |3,500 |8,740 |2,150 |5,370 |

|Rate Gyro |2.1 |3,500 |7,340 |2,150 |4,510 |

|MT and RG Board |0.5 |3,500 |1,750 |2,150 |1,075 |

|Calibrate |27.2 |120 |3,260 |0 |0 |

|Normal Operation |16.2 |3,500 |56,600 |2,150 |34,820 |

|GPS |5 |3,500 |17,500 |2,150 |10,750 |

|Camera |3 |3,500 |10,500 |0 |0 |

Table 19 is a power budget of all the components showing the peak power, duration of operation, and energy during daylight and eclipse. These power requirements are used to design power generation and energy storage systems.

2.4.2 Power Generation

The power generation components fulfill the daylight power budget and adequately charge the energy storage system. Power generation system options include fuel cells, radio-isotope thermoelectric generators (RTG), and solar arrays. Fuel cells are not used for the VASCAT because of their relatively short lifetimes. Radio-isotope thermoelectric generators are too large and politically impractical because of their radioactive contents. VASCAT uses arrays of solar cells that convert solar energy from the sun into electrical energy. This method of power generation has extensive space heritage. Solar-to-electric energy conversion is a beneficial method of power generation for the VASCAT because solar energy is an inexhaustible resource and is easily harnessed. The amount of energy the VASCAT receives from the sun remains relatively constant over the 3 year lifetime.

The efficiency of solar cells degrades over time due to prolonged exposure to solar radiation. The severity of the lifetime degradation is different for each type of solar cell. These effects range from two to four percent of the power produced each year. The VASCAT uses a Gallium Arsenide, single-junction solar cell made by Spectrolab with low lifetime degradation of three percent. They convert solar energy into electrical energy at an electric potential of around 0.9 V.16

The VASCAT’s power requirements make body-mounted solar cells a feasible option. The solar cells are connected in series to produce the required 28 V bus voltage. There are 11 strings total on the side and top panels connected in parallel to provide the necessary power for the bus. The power generated by a solar cell, P, depends on the incident angle of the sun to the cell, (:

|[pic] |2-15 |

In this equation Po is the maximum power generated by a solar cell. Because the (MAPS instrument requires the satellite to point at the earth which defines the variation in (, we model the power generated over one orbit is created. Figure 11 is a plot of the power from each of the faces of VASCAT over one orbit.

[pic]

Figure 11: VASCAT power model

In this model, the satellite is in a circular orbit with altitude 500 km, and the body frame of the satellite is always aligned with the orbital frame. This assumption is accurate with the satellite pointing requirements. The model starts as the satellite is eclipsed and no power is generated. Ninety percent of the side panel area and 10% of the zenith and nadir area is covered with solar cells. This configuration accounts for the minimum power generated halfway through the orbit as the satellite eclipses Earth, and the zenith surface is facing the sun. The model runs for the maximum off-nadir attitude for the instrument to ensure that the power system meets the needs of the satellite in any normal operation orbit.

2.4.3 Energy Storage

The energy storage system must provide all the power needs of the satellite components during eclipse. The amount of power needed from this system is determined from the power budget and the orbit. The eclipse power budget, shown in Table 19, gives the power needs of the components. The orbit determines the duration that the energy storage system needs to provide that power.

The VASCAT uses batteries for energy storage. Batteries have high energy densities and extensive space heritage. Battery life decreases with the amount that the battery is discharged and is quantified by a value of depth of discharge (DOD). Long lifetime systems require a low DOD. Figure 12 shows the relationship between DOD and life cycles.14

[pic]

Figure 12: Cycle life versus DOD17

Nickel metal-hydride (NiMH) batteries have longer lifetimes than nickel cadmium (NiCd) batteries at the same DOD. They last the necessary 17,000 cycles for a DOD of 25%. Nickel cadmium batteries require a DOD of around 13% to last this lifetime and therefore, more battery mass. Nickel metal-hydride batteries are chosen for the VASCAT. The battery cells chosen are produced by Sanyo (HR-4/3FAU 4500).

Summing the energy column in Table 19 gives the total energy the VASCAT needs each eclipse period:

|[pic] |2-1620 |

Equation 2-16 calculates the number of cells needed in the battery box, where Nc is the number of cells, Ee is the eclipse energy, Ed is the energy density of the batteries, and mc is the mass of one battery. Calculations yield a NiMH cell that is approximately 62 g. The battery box holds 24 1.2V cells, connected in series and regulated by a control system to provide the 28 V bus voltage.

2.5 Thermal

The thermal subsystem of the VASCAT keeps all components within their operational temperature limits. A thermal control system (TCS) achieves this goal as efficiently as possible by minimizing power consumption, complexity, and mass. A passive TCS, which requires no power or control, is the best solution to minimize these criteria.

A preliminary thermal analysis determines the temperature variations the satellite experiences on orbit. This analysis is presented in Table 20. It assumes a spherical satellite with uniform surface properties. The minimum and maximum power dissipations are estimates from the preliminary power budget. The other values presented are discussed in more detail later in this section chapter.

Table 20: Design parameters for preliminary VASCAT thermal analysis

|Symbol |Value |Units |Description |

|A |1.1 |m2 |Surface area |

|D |0.593 |m |Diameter of sphere with equal surface area |

|AC |0.276 |m |Cross-sectional area of spherical satellite |

|σ |5.67 × 10-8 |W/m2K4 |Stefan-Boltzmann constant |

|Qw,max |88 |W |Max power dissipation |

|Qw,min |56 |W |Min power dissipation |

|H |400 |km |Altitude |

|RE |6378 |km |Radius of Earth |

|ρ |1.20 |rad |Angular radius of Earth |

|Ka |0.998 | |Albedo correction |

|ql,max |258 |W/m2 |Max Earth IR emission at surface |

|ql,min |216 |W/m2 |Min Earth IR emission at surface |

|GS |1420 |W/m2 |Direct solar flux |

|a |35% |- |Albedo |

|ε |0.8 |- |Emissivity |

|α |0.8 |- |Absorptivity |

|F |0.331 |- |View factor |

|Tmax |58 |°C |Worst case hot temperature |

|Tmin |-53 |°C |Worst case cold temperature |

Generalized component temperature limits are given in Table 21.

Table 21: VASCAT Temperature Limits (°C)

|Description |Cold Limit |Hot Limit |

|Structural members |-45 |65 |

|Batteries |0 |40 |

|Electronics |0 |50 |

|μMAPS |0 |25 |

A detailed thermal analysis is performed to better characterize the VASCAT. A thermal model provides information about specific components, such as the (MAPS instrument. The VASCAT thermal model is created by dividing the satellite into nodes. Analytically, every node obeys the basic heat transfer equation:

|[pic] |2-174 |

In this equation Q is the net heat flux into the node, Cp is the specific heat capacity, which is a measure of how the temperature of the node changes relative to energy input, T is the temperature of the node, and Δt is change in time. This equation is solved for the temperature of the node if the heat flux is known. Each pertinent component, as well as the bus structure side panels, is assigned to a node. The specific heat of each node is calculated by multiplying the component mass by the specific thermal capacitance of its primary material (typically aluminum).

Nodes transfer heat between themselves by conduction. Conduction couplings are a measure of how a node transfers heat to another node that is touching it. The following equation is the governing conduction heat transfer equation:

|[pic] |2-184 |

The kA/L term is the conduction coupling value, G, in W/K. As shown, G is a function of the contact area between nodes, A, the heat path length, l, and the material thermal conductivity, k. The conduction couplings are calculated using the geometry of the satellite and knowledge of the materials used.

Radiation heat exchange takes place between nodes and space. For the purposes of this analysis, internal radiation between components is neglected. The internal surfaces of the satellite are painted black, which minimizes internal radiative heat transfer. Only radiation from the bus external surfaces to space is considered. Radiation heat transfer is given by:

|[pic] |2-194 |

In this equation A is the surface area, σ is the Steffan-Boltzmann constant, and ε is the emissivity of the surface. The emissivity of the node is determined from the properties of its thermal coating, and the surface area is found from geometry.

Generation of a thermal model requires knowledge of the heat fluxes (see Equation 2-17) in addition to the heat transfer paths. Nodal heat fluxes are determined from the internal component dissipations and environmental inputs. Hot and cold cases are considered. The hot case includes the maximum or peak power dissipations from each of the components and the maximum orbit averaged fluxes on the satellite. Likewise, the cold case includes the minimum operational power dissipations and the minimum orbit averaged fluxes.

The internal dissipations are determined by the mission operation requirements and are obtained from the power subsystem. The component dissipations used for each of the cases are given in Table 22.

Table 22: Component internal power dissipations

| |Total power (W) |

|Description |Hot |Cold |

|(MAPS |27.2 |16.2 |

|Momentum Wheel |25 |7 |

|Magnetic Torque Bars |16.2 |12.6 |

|Magnetometer |0.001 |0.0008 |

|Earth Sensors |16 |16 |

|Sun Sensors |5 |5 |

|Rate Gyros |6.3 |6.3 |

The orbit averaged fluxes are calculated from information about the satellite’s orbit. The external heat sources are direct solar energy, Earth infrared (IR) and albedo. Albedo is a measure of how much of the sun’s energy is reflected from the Earth’s atmosphere and surface back into space, and is usually given as a percentage.6 The cold case analysis assumes the satellite is in eclipse and the only external heat source is from the Earth. The environmental fluxes are shown in Table 23.

Table 23: Environmental fluxes in space (W/m2)

|Source |Hot |Cold |

|Solar |1418 |0 |

|Earth IR |258 |216 |

|Albedo |35% |25% |

|Totals |2172.3 |216 |

The actual heat input depends on the surface properties of the satellite. Absorbtivity, α, is a measure of how much external radiation is absorbed by the surface in question and is dependant upon the thermal coating applied. Emissivity characterizes how much heat the surface radiates according to Equation 2-19.20 The surface properties of various VASCAT external components are given in Table 24.6

Table 24: Surface properties

|Component |Coating / Material |α |ε |

|Side Panels |Silicon |0.8 |0.8 |

|Nadir Panel |White Paint |0.3 |0.9 |

|Solar arrays |White Paint |0.3 |0.9 |

The total input power is determined by:

|[pic] |2-20 |

In this equation the term in parenthesis is the total orbit average flux in W/m2. View factor, (, describes how the surface is oriented relative to the flux vector.

View factor is a parameter that varies depending upon the position of the satellite relative to the orbital frame. For example, the nadir panel of the satellite is Earth-pointing, and therefore rarely has a full view of the sun. Therefore, the nadir panel view factor is approximately 0.2. The view factor is determined by the MATLAB code in Appendix A. This code determines the power output from body-mounted solar cells on a hexagonal cylinder at various positions in an orbit. It outputs the projected area that a surface will ‘see’ relative to the solar vector. This projected area is then used to determine the view factor for the external bus surfaces.

The thermal model is assembled after the heat transfer paths are identified and internal and external heat sources are considered. The thermal analysis requires simultaneous evaluation of Equations 2-17, 2-18, and 2-19 at each node. This evaluation is complex due to the nonlinear relationship between the temperature of a node and its resulting heat flux.9

The Systems Integrated Numerical Differential Analyzer (SINDA), a thermal analysis package commonly used in industry, analyzes the VASCAT thermal model.3 This software package calculates nodal temperatures based on user-generated conduction and radiation couplings and input fluxes. The program then uses an explicit forward solution method to evaluate the governing heat transfer equations. The explicit forward method uses the conditions at the current time step, or iterative loop, to calculate the temperature of each of the nodes in the system. It then performs an energy balance check on each of the nodes and varies the time step accordingly. The result is a steady state solution for nodal temperatures.

The (MAPS instrument is the mission driver for the VASCAT, so several steps are taken to thermally control it. The instrument is conductively coupled to the nadir and zenith panels of the satellite. Additionally, the nadir and zenith panels are coated with white paint to increase their dissipation to space and reduce their incident heat flux.

The hot and cold case temperatures of the VASCAT components are listed in Table 25. Almost all component temperatures are within their specified limits. The exception is the (MAPS instrument. In hot case conditions, (MAPS operates at about 0.5 degrees over its hot limit. The model has temperature accuracy limits of ±1 degrees. Therefore, a 0.5 degree temperature violation is deemed acceptable within the scope of this analysis. However, the analysis shows that (MAPS is a primary constraint driver for further design.

Table 25: Temperatures of the VASCAT components

| | |Hot Case Temps (°C) |Cold Case Temps (°C) |

|Description |ID |Predicted |Limit |Predicted |Limit |

|Side Panel 1 |1001 |42.6 |65 |-45 |-45 |

|Side Panel 2 |1002 |38.4 |65 |-45 |-45 |

|Side Panel 3 |1003 |31.2 |65 |-45 |-45 |

|Side Panel 4 |1004 |37.3 |65 |-45 |-45 |

|Side Panel 5 |1005 |35.7 |65 |-45 |-45 |

|Side Panel 6 |1006 |36.5 |65 |-45 |-45 |

|Nadir Panel |1007 |27.0 |65 |-45 |-45 |

|Top Panel |1008 |29.3 |65 |-45 |-45 |

|(MAPS |2001 |30.5 |30 |0 |-5 |

|Momentum Wheel |2101 |38.4 |50 |0 |0 |

|Magnetic Torque Bar |2102 |31.6 |50 |0 |0 |

|Magnetometer |2103 |37.2 |50 |0 |0 |

|Earth Sensor |2104 |35.2 |50 |0 |0 |

|Rate Gyro |2106 |42.6 |50 |0 |0 |

|Computer |2201 |36.2 |50 |-10 |-10 |

|Receiver |2202 |28.5 |65 |-20 |-20 |

|Transmitter |2203 |36.4 |70 |-20 |-20 |

|GPS |2204 |35.5 |65 |-20 |-20 |

|Battery Box |2301 |35.1 |65 |-45 |-45 |

|Batteries |2302 |34.6 |40 |0 |0 |

The exterior of the VASCAT is covered in solar cells. Therefore, it is not possible to incorporate a radiator into the design to help dissipate heat from (MAPS. However, it may be possible to use conductive straps or fasteners to better transfer heat from the instrument to the satellite. Additionally, a doubler or cold plate might be used to thermally isolate the (MAPS instrument from the rest of the satellite. These modifications are detailed design parameters and are therefore outside the scope of this analysis.

This analysis is preliminary and is based upon estimated values. A more in-depth analysis should be performed on the VASCAT to determine if a passive thermal control system is indeed accurate. No detailed internal structural configuration has yet been defined. Therefore, the conduction paths are estimated from HokieSat’s internal configuration. In addition, the thermal masses of each of the components are estimates. Finally, a transient analysis, which takes into account the change in variations in temperature of the satellite over the course of an orbit, should be performed to ensure that a passive TCS is adequate.

2.6 Communication

The communications system of the VASCAT transmits telemetry and health information to a ground station and receives commands from a ground station. The VASCAT communications system is based on HokieSat’s communications system with the addition of an AMSAT link.

2.6.1 Uplink

The uplink portion of the communications system operates at approximately 450 MHz using a loop antenna with a 100KHz bandwidth. The loop antenna is a HokieSat custom design, as shown in Appendix B. The loop antenna is mounted on the nadir panel of the satellite and is connected to an ultra-high frequency (UHF) receiver. The uplink system receives commands from ground stations.5

The UHF receiver used on HokieSat is a modified Tekk model 960LUHF data transceiver as shown in Figure 13. Table 26 gives the receiver specifications.

[pic]

Figure 13: Uplink transceiver5

Table 26: Uplink receiver specifications5

|Type |Value |

|FCC ID |GOXKS-900/15.22.90 |

|Frequency |430-450MHz |

|Operating Temperature |-30 to +60(C |

|Voltage |9.6 V |

|Dimensions |3.4” ( 2.1” ( 0.9” |

|Weight |5.2 ounces |

2.6.2 Downlink

The communications downlink operates using the S-Band. The downlink system is comprised of a patch antenna and a L3 communications model DST802 transmitter (Figure 14). The frequency of the downlink is between 2,200 and 2,290 MHz while the required bandwidth is approximately 200 kHz. The downlink system transmits telemetry and health information to ground stations at approximately 100 bps. Table 27 shows the specifications on the L3 communications transmitter. 5

[pic]

Figure 14: Downlink transmitter5

Table 27: Downlink transmitter specifications5

|Type |Value |

|Frequency |2.2 –2.3 GHz |

|Power Output |2 W |

|Voltage |28 ( 4 V, 0.8 W |

|Dimensions |2” x 3” x 0.80” |

|Mass |200 g |

2.6.3 AMSAT

The AMSAT link of the communications system transmits the data produced by the (MAPS instrument. The (MAPS instrument produces 40 bps of data. Every ten seconds the (MAPS instrument requires a time stamp, attitude, position, and velocity of the VASCAT added to the data to be downloaded. Assuming that the satellite data is available as floats, a total of 35.2 bps is added to the link budget. With the addition of the satellite data, the AMSAT link needs to transmit a total of 75.2 bps.19

The UoSAT-OSCAR 22 and the Malaysian-OSCAR 46 spacecraft use the AMSAT as their primary downlink to ground stations. These spacecraft have the capability of a 9,600 bps download rate using a transmitter at 435.12 MHz. The UoSAT-OSCAR 22 spacecraft uses the AMSAT to send grayscale pictures of the earth down to the ground stations. The size of the OSCAR 22 pictures is approximately 109 bytes.2 If VASCAT uses the same method and size for pictures of the Earth's atmosphere, a picture could be downloaded in 10 seconds using the maximum 9,600 bps download rate. The requirements on the AMSAT portion of the communications system needs to be defined further before the specific hardware is selected for use in the VASCAT satellite.

2.7 Command and data handling

The command and data handling system of the VASCAT satellite is identical to the HokieSat system. The computer is centered on a Hitachi SuperH RISC Processor, with a 16 MB telemetry buffer, a digital and analog interface subsystem, and a DMA-oriented CMOS camera frame buffer. The orbit average power is 3 W for the computer which. The computer can handle approximately 20 million instructions per second and is radiation hardened to 5 krads. The computer uses VxWorks as a real-time operating system.12

2.8 Summary

Chapter two presents the preliminary subsystem designs and configuration for the VASCAT. The systems defined in this chapter include the structure, the ADCS, the power system, the thermal system and the communications system. Each system is developed based on the HokieSat design. The designs presented in Chapter 2 serve as a starting point for further research and development.

Chapter 3: Mission Operations

3.1 Orbits

The main parameters considered in choosing the VASCAT orbit include the amount of Earth coverage the orbit pattern can provide and the lifetime of the satellite in its given orbit. The sensitivity of the (MAPS instrument requires a satellite without a propulsion system. The lack of a propulsion system also reduces the complexity of the satellite and reduces operations costs. The success of the mission depends heavily on the satellite’s ability to sustain a three-year lifetime without propulsion. This chapter presents analysis done to determine Earth ground coverage and lifetime predictions.

3.1.1 Coverage

The objective of the µMAPS instrument is to perform analysis on samples of the Earth’s atmosphere. Using the maximum amount of points possible in the Earth’s atmosphere is important to the success of the mission. Each one of these points corresponds to a point on the Earth’s surface. Using MATLAB, a coverage analysis is designed to determine the amount of time the µMAPS instrument sees each of these points over a given satellite lifetime. This code is shown in Appendix C.

The MATLAB code uses inputs of the five main orbital parameters: semi-major axis, eccentricity, inclination, argument of perigee, and right ascension of ascending node. It begins by defining a 91 × 361 coverage matrix whose components are all initially zero. The components of this matrix correspond to each point of latitude and longitude on the Earth’s surface. Based on the assumption that the northern and southern hemispheres have symmetrical coverage patterns, only 90 degrees of latitude are used. The program first propagates the input orbit over a given lifetime, in steps of mean motion, to determine the position and velocity of the satellite at any given time during the precession. For each point in time, the code then iterates through a series of targets, each corresponding to one point on the Earth’s surface. These targets cover each point over 90º of latitude and 360º of longitude. The Earth center angle (ECA) is calculated between the satellite and the target and is compared with the angle associated with the field of view of the instrument. The field of view of the instrument is 3º, or approximately 25 km2 on the surface of the Earth.19 If the ECA is greater than the field of view, the satellite is not in view of its target. If the ECA is less than the field of view, then the target is in view and that element of the coverage matrix is incremented by one to show that the target has been viewed for one second. This code iterates over a period of 100 orbits. After 100 orbits, the orbit pattern repeats. Therefore, the coverage over the entire lifetime of the satellite is determined. Parameters such as orbit inclination and altitude alter the range and frequency of coverage. This code is used to compare the coverage of a series of orbits. This orbit property is considered along with other factors to determine the optimal orbit for the VASCAT. This type of data is also used as a concrete model illustrating the capabilities of the mission.

3.1.2 Orbit prediction

Lifetime calculations predict the amount of time a LEO satellite remains in orbit before atmospheric drag causes re-entry. The lifetime of a satellite is calculated to decide if the mission goals are fulfilled before end-of-life, and determine optimal orbit parameters. Sources of uncertainty in satellite orbital lifetime prediction are estimated future solar radio flux and geomagnetic activity, modeled atmospheric density, and ballistic factor. The main source of uncertainty in models estimating future atmospheric density at orbital altitude is the solar extreme ultraviolet heat input values. An important problem in mission planning and satellite command & control is accurate prediction of orbital motion.

3.1.3 Orbit simulation

An orbit propagator is a mathematical algorithm for predicting the future position and velocity (or orbital elements) of an orbit given some initial conditions and assumptions. There are a wide variety of orbit propagation techniques available with different accuracy and applications. All built-in assumptions must be known before deciding on a propagation scheme.

An accurate atmospheric model computes drag effects using Satellite Tool Kit’s (STK) lifetime prediction feature.1 The gravitational model for the Earth is significantly simplified since the inclusion of the higher order terms does not impact orbit decay estimates.

3.1.4 Orbit characteristics

The VASCAT launches into a circular orbit with an initial altitude of 450 km and an inclination of 57 degrees. The desired design lifetime of the satellite is initially three years. A circular orbit obtains homogeneous and complete global coverage of the Earth. An initial altitude of 450 km guarantees a multi-year mission duration even under severe solar activity conditions. The altitude decreases over the mission lifetime due to atmospheric drag. The VASCAT may pass through the solar activity maximum, depending on launch. The predicted natural decay depends on the magnitude of the actual solar activity cycle.

3.1.5 Lifetime

The lifetime tool, available in STK, is used to estimate the amount of time the VASCAT remains in orbit. Lifetime computations are based on complex orbital theory and an accurate environment model. The results are only an estimate. Due to variations in atmospheric density and irregular solar activity, satellite lifetimes are determined with accuracy no better than ±10 %.1 To implement a practical computer lifetime program, some assumptions and simplifications are made that add additional degrees of uncertainty to the final result. Various parameters that effect lifetime include mass, altitude, satellite drag coefficient, satellite drag area, and orbit inclination. Because the VASCAT’s mass is fixed at approximately the 35-50 kg margin, all calculations are performed with the satellite’s mass fixed at 50 kg.

The most important parameter in determining the lifetime of the VASCAT is initial altitude. Figure 15 shows the complete trend from which an initial orbit altitude is determined to fulfill the mission lifetime.

[pic]

Figure 15: Lifetime as a function of altitude

The satellite’s drag coefficient, Cd is between 2.0 and 2.2. However, in calculating the effects of Cd, values are varied from 1 to 3 to more clearly see the trend that Cd has on lifetime. The results are plotted in Figure 16 and Figure 17 for two altitudes.

[pic]

Figure 16: Lifetime as a function of drag coefficient for a 400 km altitude orbit

[pic]

Figure 17: Lifetime as a function of drag coefficient for a 500 km altitude orbit

The drag area of the satellite is the mean cross-sectional area of the satellite perpendicular to its direction of travel. The effects of altitude are examined at two altitudes; the results can be seen in Figure 18 and Figure 19.

[pic]

Figure 18: Lifetime as a function of drag area for a 400 km altitude orbit

[pic]

Figure 19: Lifetime as a function of drag area for a 500 km altitude orbit

Inclination of the orbit effects the coverage of a satellite. Inclination analysis is performed and displayed in Figure 20.

[pic]

Figure 20: Lifetime as a function of orbit inclination

For all calculations the decay altitude is 300 km. The decay altitude is the altitude at which the satellite’s orbit is determined to be decayed. This is the altitude at which lifetime calculations stop.

3.2 Summary

Chapter three introduces the two main parameters in choosing an orbit for the VASCAT. A method for predicting Earth ground coverage is presented which is useful in choosing an orbit or predicting mission capabilities. Also, the variations of lifetime with orbit altitude, drag area, drag coefficient, and inclination are presented in chapter three. These variations provide the minimum orbital parameters for the VASCAT. The lifetime information can be combined with the coverage information to determine the optimal orbit for the VASCAT.

Chapter 4: Cost Analysis

A cost model predicts the overall cost of a project, from initial research and testing to its final end-of-life costs. Cost modeling is used as a method of maximizing performance while remaining within budgetary constraints, rather than estimating the cost of a project with given performance parameters.20

The parametric cost estimation method (PECM) uses mathematical relationships to relate input parameters directly to the cost of the project. The equations used are known as the cost estimation relationships (CER) and are expressed as a function of the cost drivers. Several assumptions are made when using a PECM. The most predominant assumption is that the PECM is based on historical spacecraft mission costs. A specific PECM is limited on the type and size of spacecraft for which it is effective. 20

The PECM used for the VASCAT is similar to an example for scientific small LEO satellites found in the Space Mission Analysis and Design reference. 20 The VASCAT fits into this description for the PECM. Table 28 shows the output of the PECM using parameters from the VASCAT. The total cost of producing the VASCAT is found by summing the values in the right hand column of Table 28. The cost to produce the VASCAT is approximately $16 million to $49 million. This cost is greater than HokieSat's budget of $1.5 million, which does not include testing costs or student labor costs.

NASA's Johnson Space Center provides the public with an online cost estimator for different types of spacecraft. One of the spacecraft options is a scientific satellite with mass as the only input. The mass of the VASCAT is assumed to be 40 kg. The NASA calculator outputs a development and production cost of approximately $15 million and an operations cost of approximately $0.5 million per year.13

Table 28: The VASCAT cost estimate using PECM20

|Cost component |Parameter x (unit) |Input value |Subsystem cost (FY00$K) |

|1. Payload |Satellite total cost (FY00$K) |33,000 |13,100 |

|2. Satellite |Satellite bus dry mass (kg) |40 |3,510 |

|2.1 Structure |Structures mass (kg) |12 |722 |

|2.2 Thermal |Thermal control mass (kg) |5 |351 |

|2.3 Electrical power |Average power (W) |100 |315 |

|system | | | |

| |Power system mass (kg) |7 |1,590 |

| |Solar array area (m2) |1.3 |3,260 |

| |Battery capacity (A-hr) |5 |2,030 |

| |BOL power (W) |130 |3,750 |

| |EOL power (W) |110 |3,480 |

|2.4a Telemetry tracking &|TT&C/DH mass (kg) |3 |536 |

|command | | | |

| |Downlink data rate (Kbps) |100 |2,570 |

|2.4b Command & data |TT&C + DH mass (kg) |3 |726 |

|handling | | | |

| |Data storage capacity (MB) |16 |2,800 |

|2.5 ADCS |ADCS dry mass (kg) |14 |3,040 |

| |Pointing accuracy (deg) |5 |1,520 |

| |Pointing knowledge (deg) |1 |2,640 |

|2.6 Propulsion |Satellite bus dry mass (kg) |N/A |0 |

| |Satellite volume (m3) |N/A |0 |

| |Number of thrusters |N/A |0 |

|3. Integration, assembly,|Satellite total cost (FY00$K) |33,000 |4,570 |

|& test | | | |

|4. Program Level |Satellite total cost (FY00$K) |33,000 |7,530 |

|5. Ground support |Satellite total cost (FY00$K) |33,000 |2,170 |

|equipment | | | |

|6. Launch & orbital |Satellite total cost (FY00$K) |33,000 |2,010 |

|operations support | | | |

The total cost of the VASCAT ranges from $16 million to $49 million. Each of these estimates is examined, to find the areas that disagree with one another, to determine which of these cost estimates is more accurate. This comparison is difficult to complete because the details of the NASA cost estimator are proprietary and not available for public use.

Chapter 5: Summary, Conclusions, and Remaining Work

The satellite design VASCAT detailed in this paper is a preliminary design incorporating the μMAPS instrument into a host spacecraft. The VASCAT design, based on Virginia Tech’s existing nanosatellite HokieSat, supports the μMAPS instrument with a minimum mission lifetime of one year.

The preliminary design of the required subsystems is described in this report. Component level definitions are given for the ADCS, thermal, and power subsystems. The VASCAT is configured for body-mounted solar cells and room to house the instrument and all other subsystem components. The structure design incorporates the (MAPS instrument’s existing mounting feet. Preliminary structural analysis is used to size the primary structure. The orbital analysis presented lays the groundwork for determining a more definite orbit to adequately complete the mission. The satellite is designed to meet the desired lifetime requirements of one year without propulsion. The addition of a digital camera is not discussed in detail, but it has been considered by all subsystems and can fit into the VASCAT design.

The AMSAT frequency is proposed to allow high school students to participate in the VASCAT mission. This frequency downloads data from both the μMAPS instrument and the proposed digital camera. The camera takes pictures during data collection. The AMSAT downlink needs to be further defined to accomplish the download of atmospheric pictures and the secondary educational requirements.

All subsystem designs are incomplete. Further knowledge of the AMSAT hardware is required to fully define its use. The interior of the VASCAT, including component placement and wiring paths, must be configured. A launch vehicle must be chosen for further structural analysis and design. Most importantly, a design and fabrication budget is required to continue high level subsystem design.

References

1. Analytical Graphics, Inc. “Analytical Graphics, Inc.” 2002. (24 March, 2002)

2. AMSAT. "AMSAT From A to Z." 2002. (4 May, 2002)

3. C&R Technologies, Inc. "SINDA/FLUINT 4.4 manual." 2002. (2 May, 2002)

4. Cengel, Y.A. Introduction to Thermodynamics and Heat Transfer. Irwin/Mcgraw-Hill. Botson, Massachusetts. 1997.

5. Findlay, S. ION-F Flight Communications Design Specification. University of Washington, Seattle, Washington. Issue date: 14 September, 2000.

6. Gilmore, D.G. and Bello, M. (editors). Satellite Thermal Control Handbook. The Aerospace Corporation Press. El Segundo California. 1994.

7. Harvey, A.C. HokieSat Interface Control Document, Revision VT ICD C-2. Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Issue date: 2 November, 2000.

8. HokieSat webpage, webmaster Jana L. Schwartz. Updated 14 March, 2002.

9. Incropera, F.P. and DeWitt, D.P. Fundamentals of heat and mass transfer, fourth edition. School of Mechanical Engineering, Purdue Univ. John Wiley and Sons. New York. 1996.

10. Isakowitz, S.J., Hopkins, J.P. and Hopkins, J.B. International Reference Guide to Space Launch Systems: Third Edition. AIAA Publishing. Reston, Virginia. 1999.

11. Ithaco. “Ithaco Home Page.” 1997. (28 April, 2002)

12. Jensen, J.D. and Swenson C.M. Command and Data Handling Subsystem Design for the Ionospheric Observation Nanosatellite Formation. Utah State University, Logan, Utah. Issue date: 28 June, 2000.

13. Johnston Space Center. “JSC Homepage.” 2002. (20 April, 2002)

14. Sanyo North America Corporation. “Nickel-Metal Hydride Battery HR-4/3 FAU 4500.” 2001. (26 April, 2002)

15. Sarafin, T. Spacecraft Structures and Mechanisms from Concept to Launch.

Torrance: Microcosm Press. 1995.

16. Spectrolab. "Spectrolab Products." 2000. (21 March, 2002)

17. Systron Donner. “Systron Donner Inertial Division.” 1998. (20 April, 2002)

18. Valley Forge Composite Technologies. “VFCF: Valley Forge Composite Technologies.” 2001. (20 April, 2002)

19. Walberg, G., Reichle, H.G. and Morrow, W.H. Design and Testing of MicroMAPS Gas Filter Correlation Radiometer. 21 January 1999.

20. Wertz, J.R. and Larson, W.J. (editors). Space Mission Analysis and Design 3rd Edition. Microcosm Inc. El Segundo, California. 1999.

Appendix A: MATLAB Power Code

% This function takes the height and major diameter of a hexagonal prism

% and returns the projected area of the eight faces.

% This function returns a matrix eight by N (time step) with projected areas

% for the faces in the rows

% and the columns are different instances in the orbit.

function pete = bidwell(height,diameter)

W = 0*pi/180;

inc = 50*pi/180;

si = [1 0 0]';

a = 6778;

mu = 3.986*10^14;

Gs = 1358;

sce = 0.20;

Ld = 0.02;

life = 1;

Id = 0.88;

n = sqrt(3.986*10^5 / a^3);

Period = 2*pi/n;

Npoints = 900;

tspan = linspace(0,Period,Npoints);

facesb = faces(height,diameter);

R13 = R1(inc)*R3(W);

Roop = [0 1 0; 0 0 -1; -1 0 0];

for ti = 1:1:Npoints

% Calculation of True Anomaly

u = n * (tspan(ti) - 0);

% Rotations

Roi = Roop*R3(u)*R13;

Rbo = eye(3,3); %Orbital frame aligned with body frame

Rbi = Rbo * Roi;

sb = Rbi * si;

rper = [a*cos(u) a*sin(u) 0]';

ri = Roi*rper;

alpha = atan(6378/norm(ri));

%Eclipse angle

if u = 2*pi-alpha

eclipse=0;

else

eclipse=1;

end

for i = 1:8

costheta(i) = sb' * facesb(1:3,i);

if costheta(i) ................
................

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