The University of Texas at Austin

Department of Aerospace Engineering and Engineering Mechanics

CubeSat Based Solar Sail Testing Platform Preliminary Design Review

Submitted to: Dr. Wallace Fowler

for the purpose of partial fulfillment of the requirements for ASE 274L/174M

Submitted by: Phillip Hempel Daniel Parcher Paul Mears Taffy Tingley

November 12, 2001

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Executive Summary

Objectives

To design a 10cm sided cubic picosatellite for the purposes of solar sail testing while maintaining compliance with the Stanford sponsored CubeSat program. This objective will be carried out in the following manner:

?? Determine the size and material of the solar sail to be used. ?? Design a picosatellite capable of housing the solar sail. ?? Determine necessary packing configuration of the sail. ?? Determine the impact that the packing configuration has on the sail’s efficiency. ?? Design the necessary deployment apparatus ?? Design apparatus for identifying the orientation and position of the satellite. ?? Create an orbital trajectory simulation for the satellite design

Design Restrictions Adopted ?? The satellite will have no attitude control ?? The satellite will have no communication systems ?? The satellite will require no power in addition to the power requirements prescribed by

the CubeSat program ?? Position, velocity and orientation will be performed from ground stations by analyzing

light reflected from corner cube reflectors on the solar sail. Status

?? Completed Tasks o Satellite system and mission conceptual design o Preliminary satellite system integration

?? Remaining Tasks o Finalization of satellite system integration o Analysis of failure modes and reliability

Proposed Budget Expense Item Predicted Expense (dollars) Expenses to Date Personnel (based on an estimated 150 hrs. worked, 14 hrs. for consultants)

15,653

Materials / Electronics 5,000 Testing 2,000 Launch 50,000 Total 72,653

Team Members Phillip Hempel – Mechanical Specialist Paul Mears – Orbit Trajectory Specialist Daniel Parcher – Team Leader Taffy Tingley – Solar Sail Specialist

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Table of Contents

Executive Summary............................................................................................................... i Table of Contents................................................................................................................. ii Table of Figures.................................................................................................................. iv Table of Tables................................................................................................................... iv 1.0 Introduction...................................................................................................................1

1.1 Problem Statement.....................................................................................................1 1.2 Purpose .....................................................................................................................2

2.0 Design Factors...............................................................................................................3 2.1 Satellite Component Evaluation Criteria ......................................................................3 2.2 Design Restrictions.....................................................................................................5

3.0 Satellite Systems ............................................................................................................7 3.1 Satellite Tracking Systems ..........................................................................................8

3.1.1 Optical Ranging Principles...................................................................................8 3.1.2 Design Impact...................................................................................................11 3.1.3 Optical Tracking Hardware Specifications .........................................................12

3.2 Electrical System......................................................................................................13 3.3 Structural Systems....................................................................................................14

3.3.1 Kill Switch........................................................................................................14 3.3.2 Timer................................................................................................................15 3.3.3 Frame...............................................................................................................16 3.3.4 Corner Cube Reflector Panels ...........................................................................16 3.3.5 Solar Sail ..........................................................................................................17 3.3.6 Nitrogen Capillaries...........................................................................................18 3.3.7 Compressed Nitrogen Canister..........................................................................18 3.3.8 Hardening Strips ...............................................................................................19 3.3.9 Component Placement and Overview...............................................................20 3.3.10 Satellite Construction Summary.......................................................................21 3.3.11 Solar Sail Deployment Summary......................................................................21

3.4 Propulsion Systems ..................................................................................................23 3.4.1 Solar Sail Material Selection Criteria and Design Constraints..............................23 3.4.2 Solar Sail Material Structure..............................................................................24 3.4.3 Solar Sail Historical Survey...............................................................................26 3.4.4 Aluminized Mylar..............................................................................................29 3.4.5 Finite Element Analysis......................................................................................30 3.4.6 Finite Element Analysis Results..........................................................................32 3.4.7 Finite Element Test Plan and Future Work.........................................................33

4.0 Orbital Trajectory Analysis ...........................................................................................35

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4.1 Background and Motivation.....................................................................................35 4.2 Theory.....................................................................................................................35

4.2.1 Orbital Mechanics.............................................................................................36 4.2.2 Newton’s Law of Gravitation.............................................................................39

4.3 Solar Radiation Pressure ..........................................................................................41 4.3.1 How Solar Radiation Pressure Creates Force ....................................................41

4.4 Orbital Initial Conditions...........................................................................................43 4.5 Matlab Technique for Orbit Simulation......................................................................44 4.6 Simulation Results ....................................................................................................46 4.7 Future Simulations and Applications..........................................................................48

5.0 Schedule......................................................................................................................51 6.0 Management Organization............................................................................................53

6.1 Company Management Structure..............................................................................53 6.2 Design Conflict Resolution Procedure.......................................................................55

7.0 Proposed Budget .........................................................................................................56 7.1 Budget Item Description...........................................................................................56

7.1.1 Personnel Budget Description............................................................................56 7.1.2 Material and Electronics Budget Description......................................................56 7.1.3 Testing Budget Description................................................................................56 7.1.4 Launch Budget Description................................................................................57

7.2 Budget Summary......................................................................................................58 8.0 Future Work................................................................................................................59 9.0 Conclusion...................................................................................................................60 10.0 References................................................................................................................61 Appendix A –PaperSat Team Appendix B – CubeSat Frame Appendix B – ABAQUS Input Appendix C – ABAQUS Output Appendix D – Orbital Simulation Code Appendix E – PaperSat Schedule

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Table of Figures

Figure 1 - Satellite Systems Outline.......................................................................................7 Figure 2 - Corner Cube Reflector Array…………………………………………………12 Figure 1 - RDAS Compact Timer / Accelerometer……………………………………...13 Figure 4 - Compressed Nitrogen Canister……………………………………………….18 Figure 5 - Satellite Cut-Away……………………………………………………………20 Figure 6 - Solar Sail Material Layers…………………………………………………….25 Figure 7 - Haley's Comet Solar Sail Design Concept [3]…..……………………………26 Figure 8 - Current Solar Sail Projects……………………………………………………28 Figure 9 - Solar Sail Finite Element Mesh……………………………………………….31 Figure 10 - ABAQUS Output for First Solar Sail Rendering……………………………32 Figure 11 - Position Vector Schematic…………………………………………………..37 Figure 12 - Sail Normal Orientation in the ECI Coordinate System [12]………………..38 Figure 13 - Incidental and Reflected Light and Force Vectors Acting on the Sail……....41 Figure 14 - Two Body Orbit……………………………………………………………..46 Figure 15 - Close-up of Two-Body Orbit at Apogee…………………………………….46 Figure 16 - Four-Body Problem without Thrust……………………..…………………..47 Figure 17 - Close-up of the Four-Body Problem at Apogee……………………………..47 Figure 18 - Four-Body Problem with Magnified Thrust…………………………………48 Figure 19 - PaperSat Engineering Management Structure……………………………….51 Figure 20 - Analysis of Proposed Budget………………………………………………..56

Table of Tables Table 1 - Contract Deliverables..........................................................................................51 Table 2 - PaperSat Personnel Responsibilities.....................................................................54 Table 3 - Proposed Budget ................................................................................................58

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1.0 Introduction

PaperSat Engineering proposes to design a picosatellite in accordance with the

regulations of the CubeSat program hosted by Stanford University. The CubeSat program

offers educational institutions the opportunity to design a cubic satellite with 10 cm sides and, for

a relatively low cost, the CubeSat program will arrange for the launch of the satellite. The

proposed picosatellite’s mission is entirely at the discretion of the educational institution

sponsoring the satellite. This scenario offers the students working on each satellite design a large

amount of control over the satellite’s mission and design. Because of the CubeSat program's

freedom with design criteria and mission objectives, educational institutions and students

involved in the program have an excellent opportunity to develop a satellite for actual

application.

1.1 Problem Statement

The PaperSat Engineering CubeSat design will fulfill two objectives: an educational

objective and a scientific objective. The educational objective is simply to give students the

opportunity to design the systems and mission of a satellite from concept to creation by

providing a "real world" application in which the students can apply their design. Students will

have the opportunity to aide in the design process of this satellite and, once the satellite is

launched, perform the post-processing tasks necessary to obtain scientific data from this

propulsion system test.

The scientific objective is specific to the particular organization developing any particular

CubeSat design. PaperSat Engineering will be focusing on the problem of understanding solar

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sail propulsion capability. PaperSat will be exploring a satellite testing platform to test solar sail

configuration, materials, and efficiency. This project would allow any interested company to test

their solar sail design on a picosatellite before investing their resources into an expensive full

sized satellite. Companies wishing to develop solar sail technology can protect their investment.

The academic community will benefit from solar sail research. As tests are performed, the

results will show the scientific community how certain materials reflect light, how that property

can be used to navigate a spacecraft, and how to implement that technology. Solar sails have

not been used as a major propulsion system by any spacecraft to date. The technology is largely

untested and theoretical. Testing of this technology may prove to be an important step in space

flight, and small satellites are an excellent testing platform for this technology.

1.2 Purpose

The purpose of the solar sail CubeSat design will be to test solar sail capabilities in an

inexpensive manner. To achieve that purpose, PaperSat will design a small satellite that complies

with CubeSat regulations and that can deploy a solar sail to achieve thrust. Once deployment is

achieved the spacecraft's position, velocity and attitude will be monitored from the ground so

that the acceleration provided by energy transferred from light striking the surface of the sail to

the spacecraft can be measured.

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2.0 Design Factors

2.1 Satellite Component Evaluation Criteria

The following list summarizes the constraints used to aid in evaluating all candidate

solutions:

?? Weight. Pursuant to the CubeSat regulations, a single CubeSat must weigh no more

than 1 kg. This restriction causes lighter weight components to be more attractive.

?? Volume . The pods that deploy the CubeSat can fit three 10 cm cubes per pod.

Preliminary estimations of an Aluminized Mylar solar sail with 100 m2 surface area

predicts that the solar sail will be within 75% of the total CubeSat volume. Preliminary

estimates show that volume will be the most stringent constraint, so low volume

components will be considered carefully.

?? Rigidity. The thrust a solar sail produces is a function of its surface area exposed to

direct sunlight. To ensure that the maximum surface area is exposed to the sun, it is

important that the sail not fold and flex, thereby covering part of its surface. To this end,

the solar sail must be kept as rigid as possible. In addition, data reduction and orbital

trajectory calculations are greatly simplified under a rigid sail assumption.

?? Number of Folds . Minimizing the number of folds required to pack the solar sail in the

CubeSat will both maximize reflectivity and limit the areas of thermal stress.

?? Cost. The major cost for this project is in the actual launch of the satellite, if PaperSat

is to design a satellite for use with the CubeSat program, the cost for launch is outside of

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the control of this company. Material costs for the systems aboard the satellite will be

considered, but reliability will not be greatly sacrificed to spare materials costs.

?? Reliability. It is key to this project that all of the internal components aboard the

satellite be very reliable. To that end, many of the components we have chosen for this

design are simple and require few moving parts. In addition, we have take measures to

ensure that if the solar sail is damaged, the sail can continue to function.

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2.2 Design Restrictions

The PaperSat team (Appendix A) has developed several design concepts to serve as

possible solutions for the project. All design solutions must contain the following components,

which are required by the CubeSat project:

?? Weight – As previously stated, the satellite must weigh less than a total of 1 kg.

?? Volume – The satellite must be no larger than a 10 cm sided cube.

?? Shell – A shell design made of 7075 aluminum is available on the CubeSat Internet

site, and will be adopted for this satellite design.

?? Timer/Kill Switch – In effort to assure that the solar sail does not deploy during the

injection phase of the picosatellite orbit, a timing mechanism is required. The kill switch

will activate the timer upon release from the pod. The timer will then send a deployment

command after a specified time has passed. A previous CubeSat team has already

investigated different timers. PaperSat is still evaluating the timers.

?? Power Sources - A battery is required for powering the timer. The battery will not be

rechargeable as it will only need to function until the solar sail is deployed. Aside from

timer requirements, no additional power requirements or systems are needed.

In addition, the PaperSat team placed other base requirements on the CubeSat design:

?? Attitude Control - There will be no independent attitude control system. PaperSat will

not make special provisions to control attitude. However, limited efforts may be taken

to stabilize the rotations, such as geometry modifications.

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?? Tracking - Corner cube reflectors will be used to aid in orbit and attitude

determination. Further, ground stations will send signals to these reflectors.

Bearing the above restrictions in mind, PaperSat is developing designs for all of the

necessary satellite systems.

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3.0 Satellite Systems

In light of the design constrictions outlined in the previous section, this CubeSat design will

require the following systems:

?? Tracking – Consisting of hardware used for tracking of the satellite.

?? Electrical – Composed of the required timer and battery.

?? Structural – Including the satellite frame, the walls enclosing the interior satellite

components, the solar sail deployment mechanism, and solar sail hardening strips.

?? Propulsion – Consisting of a solar sail.

The satellite systems have been kept to a minimum for this project to facilitate compliance with

the design constraints for weight and volume. The satellite systems and how they interact with

each other are displayed in Figure 1.

Figure 2 - Satellite Systems Outline

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3.1 Satellite Tracking Systems So that the thrust produced by the solar sail can be measured, the satellite’s position

must be tracked over time. The tracking system must have be able to determine the satellite’s

orientation and position at a given time.

3.1.1 Optical Ranging Principles

Optical ranging is currently used in satellite applications for a solution to satellite position

determination. The technique is passive, using only electric resources on ground stations, and

requires only that the satellite have small hardware devices known as corner cube reflectors

mounted in such a way that they maintain line-of-sight with the earth.

A corner cube reflector is a set of three orthogonal mirrors that are geometrically

arranged such that they reflect light from any source location directly back to that location.

Because of this property, if a laser were directed toward a corner cube reflector it would be

reflected directly back to the source. If the time of travel of the laser light is recorded, the

distance between the source and the reflector can be determined. If the position of the laser light

source is known in three dimensions and the azimuth and elevation of the laser light pulse are

known with respect to that source location, then once the distance between the source and the

satellite is determined, the orientation of the satellite in three-dimensional space can be

determined. This technique requires that the satellite position be known approximately before

the optical ranging can be performed. Since laser light can be sent in pulses that have set widths,

laser pulses from ground stations can effectively search a range of sky for a satellite. Knowledge

of the satellite's approximate location should be easy to obtain, since the CubeSat program will

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provide the initial conditions of launch. In addition, the size of the solar sail involved with this

project will allow the satellite to be observed from the earth and easily identified.

If there are several corner cube reflectors aboard the satellite and the geometry of these

corner cube reflectors is known, then with the information received from optical ranging, the

orientation of the satellite can be determined. Since the corner cube reflectors will only reflect

the laser pulses from the earth, they cannot be distinguished from each other. Because of this the

corner cube reflector geometry that will be implemented for this project requires a minimum

three corner cube reflectors oriented in the plane of the solar sail. Each the reflector coordinates

are received by the ground station will define the plane of the solar sail. Since the reflectors

cannot be distinguished from each other they will not contain any information about the rotation

of the solar sail about the axis perpendicular to the solar sail, an axis of rotation that is not of any

particular interest to this project. The only other piece of satellite orientation information that

cannot be determined from the corner cube reflector orientation described is which side of the

solar sail is facing the sun. Since the solar sail is doubly reflective, the sides will be identical and

therefore will not need to be determined.

If several measurements of the satellite position are recorded, the satellites rotation rate

and orbit can be determined. If the orbit is then analyzed, the accelerations acting on the satellite

can be determined (for more details see Section 4). The result is knowledge of the forces acting

on the satellite, when applied to this project, the ranging technique allows the satellite's thrust to

be calculated.

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Optical ranging offers a post-processing intensive solution to satellite position and

orientation determination. The solution is particularly attractive for CubeSat implementation due

to the size and weight restrictions on the satellite. Optical ranging allows for the lack of any

communications systems, power systems (in excess of the timer battery), and micro processing

systems aboard the satellite. The result is a substantial size and weight savings. The ranging

technique also has the benefit of requiring no moving parts or electrical systems, making the

implementation of the technique a much more sound choice from the perspective of reliability.

To maintain knowledge of how the satellite's orbit is being perturbed, a series of

position fixes is required. Three or four position per orbit period should be sufficient to

determine how the satellite’s orbit is changing over time. If several measurements of the satellite

are taken over a small time interval for each of those position fixes, the rotation rate of the

satellite can be determined. In total, if five measurements are taken for the purpose of

determining rotation rates of the satellite, then 3 or 4 bursts of five measurements per orbital

period would provide sufficient information about the spacecraft. One ground station should be

adequate for these purposes. Measurements would not be required during the short time each

period that the satellite is in the earth's shadow as the thrust would not be acting on the satellite

during that time. The satellite will likely be at its closest approach to the earth while the satellite

is out of the sunlight. If the position, velocity and orientation of the satellite were measured as the

satellite entered the earth's shadow and as the satellite exited the earth's shadow, information

regarding the drag on the satellite from the earth's atmosphere could be obtained.

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3.1.2 Design Impact

The impact of implementation of laser ranging hardware for this CubeSat project is

positive. Small lightweight panel corner cube reflector arrays will be used as walls for the

CubeSat while it is in its launch configuration. In this way, the corner cube reflectors take up

room only as walls for the CubeSat, walls that are required for the project. The corner cube

reflectors will therefore provide two services. When the solar sail is deployed (for more details

see Section 3.3), the corner cube reflector panels will be detached from the sides of the satellite

and will deploy with the sails until they reach their final configuration at the edges of the sail.

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3.1.3 Optical Tracking Hardware Specifications

The optical tracking hardware will consist of four corner cube reflector arrays

purchased from an optical ranging equipment vendor such as the Banner Engineering

Corporation. The reflector arrays will

need to have a large operational

temperature range, as they will be in

shadows at times, and at other times

be exposed to direct sunlight. Banner

Engineering has one design of reflector

array that can operate at 900oF, so the

temperature restrictions should not be a substantial obstacle. Banner Engineering is also capable

of making these reflector arrays at custom sizes, allowing PaperSat to select the maximum area

of reflector array while maintaining CubeSat size restrictions. Figure 2 is one of the reflector

panels Banner Engineering offers. Notice that the width dimension is just less than 1 centimeter.

If four of these reflector panels are placed on the satellite, the volume will be reduced to that of

a 10x8 cm sided cube.

Figure 3 - Corner Cube Reflector Array

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3.2 Electrical System

As previously stated, the necessary electrical systems for this satellite only include a

timer to delay deployment of the satellite systems and a battery. A kill switch must activate the

timer so that the timing system becomes active once the satellite has been launched from the

CubeSat pod launcher.

PaperSat is currently investigating the compact Rocket Data Acquisition System

accelerometer and timer supplied by Aerocon Systems for potential

application to this project. The timer is shown in Figure 3. This timer

model is capable of supplying voltages to different outputs at specified

times. This feature is intended to be used to trigger events and will be

used to orchestrate the solar sail deployment. Petek timer models are

also being considered for use with this project. Both timers require a

battery that can last long enough for the satellites to disperse. Soyo

battery products are being evaluated to determine which model is best

suited for this mission. The RDAS compact timer can take a watch sized battery, whether that

battery will be able to supply enough power has not been determined. The RDAS timer is

125x45mm in size, while the Petek timer models are too large to be applied to CubeSat

application. A custom sized Petek timer may prove more suitable for this project than the

RDAS compact board. Neither timer model will be capable of operation at the temperatures

required. However, the timer models are indicative of the type of hardware needed for this

mission. PaperSat is still investigating temperature solutions for these electronics.

Figure 4 - RDAS Compact Timer / Accelerometer

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3.3 Structural Systems

The satellite structural design must support and house all of the satellite’s internal

components as well as providing for deployment of the solar sail. To accomplish this, it is

necessary to define each component and discuss each component’s weight, volume, and

attachment needs.

The kill switch, timer and frame are the CubeSat program required components of the

satellite design. Components specific to this satellite design include, corner cube reflector

panels, the solar sail, nitrogen capillaries, the compressed nitrogen canister, and hardening strips.

Each of these components play a vital role in the sequence required for a successful deployment

and will be discussed in detail. In addition to having each component fit in the satellite, it is also

necessary to have each of these components placed strategically in the satellite in order to

maximize the working volume inside the satellite. To aide in understanding where each satellite

component will be placed, placement will be mentioned for each component along with a cut-

away view of the final satellite and placement description in this section. To understand how

much room each component takes up, the volume of each component will also be discussed.

This section ends with a walk-through of the entire installation and deployment process.

3.3.1 Kill Switch

The kill switch is a required item for PaperSat, as set up in the CubeSat requirements

provided by Stanford University. According to Stanford, every CubeSat must be in an “off”

mode before actual deployment. The installation of a kill switch is the easiest way to ensure this

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is actually occurs. The kill switch consists of a simple spring-loaded button that is mounted to

the exterior of the satellite. The kill switch will be placed in a corner of the satellite and,

including wires, should consume 3 cubic centimeters and weight 50 grams. Upon placement of

PaperSat into the main satellite before launch, this button is pushed in and held in by the rails on

the Stanford deployment device. The kills switch will not allow power to travel from onboard

batteries to the timer while it is in a depressed state. As the satellite is released from the

deployment device, the button is allowed to spring out, deactivating the kill switch and allowing

electricity to get to the timer, which will then start a countdown for the deployment of the solar

sail.

3.3.2 Timer

The timer is the main brains of PaperSat and controls the timing and sequencing of all

onboard activities. Once the kill switch is deactivated, the timer begins to count towards the

time at which the deployment of the solar sail will begin. Once the time for deployment has

arrived, the timer will coordinate each of the individual tasks required for successful deployment.

The timing system will be as described in Section 3.2. Since the final timing system has not been

selected, the current estimate for the space and weight of the timer is for the R-DAS compact

model timer. The timer, with timing board, should occupy 50 cubic centimeters, weigh 100

grams (including a watch sized battery) and will be placed on a timing board mounted parallel

and directly next to one of the permanent sides of the satellite. The tasks the timer will be given

will be to control the time for the release of the satellite side panels, set for 5 hours after the

timer activation at deployment, and to control the time for the release of the compressed

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nitrogen from the onboard capsule, set for 5 hours 2 minutes after the timer activation at

deployment.

3.3.3 Frame

The frame of PaperSat is what all the other components of the program are to be

mounted on. The frame will appear as the one seen in Appendix B and will be composed of

7075 Aluminum beams attached to each other at the ends. Each beam will be approximately

10 cm in length with a square cross-section 0.5 cm on a side. This will make the total weight of

the frame approximately 81 grams. The total volume of the frame is 30 cubic centimeters. The

panel that holds the timer will be mounted to the inside of this frame, as will be the compressed

Nitrogen canister. The frame is also the base upon which the corner cube reflector panels are

to be placed.

3.3.4 Corner Cube Reflector Panels

The corner cube reflector panels are the basis for the ground-based tracking system that

will be employed to track PaperSat. The corner cube reflector panels being used are square in

shape, 10 cm on a side, and have a depth of .6cm. The total volume of the panels will be 360

cubic centimeters and the approximated weight will be 162 grams. Four of these panels will be

placed on four of the sides of the satellite. Two panels on the ends of the CubeSat will be

attached in a permanent fashion while the other four panels will be attached in a manner so that

they can be released from the frame allowing the solar sail to deploy. The material for the two

walls that are not corner cube reflectors has not been determined, but will be as thin and

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lightweight a material as possible. The four corner cube reflector panels that will be released

from the frame will also be attached to the edge of the solar sail and will expand outward with

the sail as it deploys. When the solar sail is in its final rigid form, the corner cube reflector

panels still attached to the frame will remain there while the released panels will be rigidly

attached to the solar sail in the plane of the sail, the method of attachment for the reflectors to

the sail is still under consideration. The issue of attachment involves how rigid the sail will be and

how the inertia of the reflector panels will affect the sail during deployment. The analysis of this

issue is being performed in ABAQUS as a dynamic deployment simulation. The result of that

analysis will prescribe whether we can simply attach the panels to the solar sail material itself

through some adhesive, or if we need to attach the panels to a small beam attached to the

remaining frame at the center of the sail.

3.3.5 Solar Sail

The solar sail is the where PaperSat derives all of its propulsion and is most important

component of the program. The solar sail will be constructed of 12 micron thick Aluminized

Mylar. The solar sail will be circular in shape, will have a total area of 100 m^2 (5.64 m

radius), and will have a final weight of approximately 20 grams. For packing into the satellite,

the soar sail will be folded in an accordion manner from the ends towards the center utilizing 7.5

cm folds. Once the two sides meet in the middle, the two remaining lengths of the sail will be

folded into the satellite using similar 7.5 cm folds, beginning at the center around the compressed

Nitrogen canister, and working out to the ends of the sail. Employing this folding method, the

packed solar sail should take up 421 cubic centimeters.

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3.3.6 Nitrogen Capillaries

The Nitrogen capillaries being used for this project are responsible for carrying the

Nitrogen being used to inflate the solar sail throughout the surface of the sail to strategic

locations for maximum rigid deployment in the minimum deployment time. The capillaries that

will be used on the solar sail are 1.27 cm diameter tubes made of the same Aluminized Mylar

used to make the solar sail. The total volume of these tubes is negligible and is considered to be

a part of the volume of the solar sail. The tubes will be placed on the solar sail so that when the

Nitrogen is released, the sail will first separate the two arms of the sail folded into the center,

followed by the full expansion of the solar sail utilizing capillaries place in the middle and along

the edges of the sail. The capillaries will be inflated with the Nitrogen at a rate of 3.5 cubic

centimeters per second. This will make the total inflation time three minutes and will leave a final

pressure in the capillaries of 0.5 psi.

3.3.7 Compressed Nitrogen Canister

The compressed Nitrogen canister is what will

hold the compressed Nitrogen used to inflate the

capillaries, and thus inflate the solar sail. The canister

will be similar to the one seen in Figure 4, will be 7.6

cm long, 3.8 cm in diameter, have a volume of 86 cc’s. Figure 4 - Compressed Nitrogen Canister

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The volume used to specify internal satellite arrangement will be 90 cubic centimeters and the

canister will be placed in the very center of the satellite. The total weight of the canister,

containing the compressed Nitrogen, will be 200 grams. The Nitrogen in the canister will be

stored at 60.5 psi. Once the Nitrogen is released from the canister at 3.5 cubic centimeters per

second, it will take three minutes for the canister to extinguish the Nitrogen supply. This will

leave a final pressure in the canister, and in the capillaries, of 0.5 psi.

3.3.8 Hardening Strips

Hardening strips are a new technology that will be used to make the solar sail a permanently

rigid circle after the sail has been deployed. It is necessary to make sure that the sail remains a

perfect circle in order to have maximum correlation between the deployed solar sail and the

theoretical solar sail being used in the computer simulations for the PaperSat program. It was

decided that hardening strips must be added to the sail due to the fact that over the time span

PaperSat would be in orbit, the Nitrogen would easily leak from the thin capillary walls, leaving

the sail with no rigid internal structure. The hardening strips to be used will consist of a tape-like

substance that has the unique property that the tape will remain pliable and tape-like until it is

exposed to solar radiation. When the strips are exposed to solar radiation, they will begin to

harden and will permanently cure in approximately 15 minutes. The hardening strips will be

placed on the solar sail in a spider web pattern and along the outer rim to minimize any warping

or shape changing of the sail after deployment. There is a concern with the hardening strips that

there is no knowledge about the hardening rate of the strips once they are exposed to the solar

radiation. This could cause problems if most of the hardening is done in the first minute or so

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after exposure since it would hinder the further deployment of the solar sail. More investigation

is planned for this matter. If the hardening strips harden at a constant rate for the 15 minutes of

curing time, then they should not cause problems with the deployment system.

3.3.9 Component Placement and Overview

The placement of each of the components has been described above and will now be

shown pieced together in a cut-away

view in Figure 5. As can be seen in

the figure, the corner cube reflector

panels make up the exterior of the

satellite and are incorporated with the

frame. The timer board is installed on

the bottom of the satellite as close as

possible to the permanently mounted

reflector panel. The compressed

Nitrogen canister can be seen in the center of the satellite with a representation of the solar sail

shown in folds coming away from the canister. Using the components discussed above, the

satellite will have used 954 of the available 1000 cubic centimeters. The numbers used to

calculate the volumes were very conservative and will most likely be lowered with further

investigation. This will most likely result in more room available for a larger solar sail. The total

Figure 5 - Satellite Cut-Away

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weight of the components is 613 grams out of our available 1000. This low number is most

likely due to the extremely light nature of the solar sail material that makes up the majority of our

volume. With such a low number, certain onboard systems could possible be beefed up such as

the timer battery, which has not been finalized, or the attachment method of the corner cube

reflectors to the edges of the sail. Volume appears to be the major constraint with design.

However, the preliminary design has been, so far, very conservative. As the PaperSat team

enters its integration stage, these numbers will all become more concrete.

3.3.10 Satellite Construction Summary

Upon completion of the frame, the kill switch (activated), timer board, and nitrogen

canister will be installed. After the sail is folded, it too will be installed and attached to the

canister. Finally, the corner-cube-reflector panels will be installed completing the satellite

housing. Once the satellite has been configured in the manner prescribed in Figure 5, it will be

placed in the CubeSat P-Pod deployment mechanism. It will then activate once the kill switch is

released when the satellite has been inserted into its orbit.

3.3.11 Solar Sail Deployment Summary

Once satellite is deployed from the deployment mechanism, the kill switch is deactivated

and the timer begins counting toward the deployment time. Five hours from deployment, four of

the side panels are released from the frame. At 5 hours, 2 minutes after the satellite was

inserted into its orbit the nitrogen is released from the canister and used to inflate the solar sail

via the capillaries. Once the capillaries have fully inflated, the hardening strips will begin to cure,

22

making the sail permanently rigid. Each stage of this deployment will be triggered by the timing

system.

23

3.4 Propulsion Systems

The satellite design for this project will use only solar sail propulsion. As a result, this

section will concentrate only on an analysis of the solar sail design.

3.4.1 Solar Sail Material Selection Criteria and Design Constraints

In this section, the process of selecting a material that will be suitable for the solar sail

itself will be documented. A historical database of solar sail materials was developed to aid in

selection. The database was then tested under a set of criteria, and the best solar sail material

was extracted. At the end of this process, Aluminized Mylar was chosen as the PaperSat solar

sail material.

The following list summarizes the design constraints imposed on the material selection

process:

?? Double Reflectivity - Since PaperSat has no attitude control, the ability to produce

thrust if the satellite is facing toward or away from the sun increases the amount of thrust

produced. In addition, the orbital simulation is simplified by imposing this design

constraint, making completion of this project within one semester more feasible.

?? Space Flown - Pursuant to CubeSat requirements, the solar sail material should be

composed of materials that are approved for space flight.

?? Foldable - The material should not be brittle enough to tear when folded.

?? Temperature Resistance - The material selected must withstand both the heat of

direct Sun exposure and the extreme cold when in Earth’s umbra.

24

?? UV Life. Exposure to UV rays from the sun can be highly corrosive. The PaperSat

solar sail material must withstand UV light for a reasonable duration (1 year).

The following list describes the criteria used to select the solar sail materials:

?? Density. CubeSat program regulations state that the total satellite weight must be less

than 1 kg. In addition, the solar sail size depends on the sail weight. Since it is

desirable to construct the largest sail possible, minimizing the sail density optimizes sail

size.

?? Strength. Stresses are imposed on the sail due to solar pressure, deployment

mechanisms, and component attachments. A strong sail is essential to withstanding

these stresses. Also, minimizing the weight implies minimizing the sail thickness. At such

a thin dimension, the sail’s strength may be compromised. A balance between a light

and strong solar sail must be attained.

?? Cost. In all designs, cost is always a key limitation in the design process and

construction. Specific costs were unavailable during the selection process. However,

including this criterion eliminates inherently expensive material candidates such as gold

or silver.

3.4.2 Solar Sail Material Structure In an effort to gain further understanding behind solar sail material selection, a brief

description of conventional solar sail structure is necessary.

25

Figure 6 (a) shows a schematic of a typical solar sail. The reflective layer faces the Sun,

and is typically 1-2 microns thick. The structural layer bears stresses imposed on the solar sail

material and is typically the thickest layer. Since the presence of solar radiation dominates the

thermal activity of the sail, a conductive layer is usually implanted on the side facing away from

the Sun and is usually 2-5 microns thick [1].

(a) Layers of Conventional Solar Sail Material (b) Layers of Solar Sail Material for this project

The solar sail that will be used is different. Instead of a conductive layer, another

reflective layer will be inserted. The primary purpose for this modification is to remedy

modeling and trajectory problems associated with having no attitude control system. The

PaperSat is unable to control whether or not the reflective side is facing the Sun. Creating a

double-reflective sail surface assures that there is continuous thrust regardless of the satellite’s

orientation. In addition, the corner-cube attitude/location determination system is simplified by

Reflective Structural Conductive

Figure 6 - Solar Sail Material Layers

Reflective Structural

26

using double-reflective solar sail material, because there is no need to differentiate which side is

facing the Sun if double reflectivity is assumed.

3.4.3 Solar Sail Historical Survey One of the most crucial steps in the design process is to research the previous work

conducted in the product’s field. From this research, a database of solar sail properties was

established, and served as a design aid. This section summarizes the research performed in the

area of previous solar sails for this project.

The concept of a solar sail, or a spacecraft that uses reflected light to provide

continuous thrust, was conceived in the 1920’s [2]. The first serious attempt to fabricate a solar

sail was in the 1970’s, when a proposal was developed by NASA to send a solar sail satellite

out to rendezvous with Halley’s Comet. A picture of one of the Halley’s Comet design

concepts is shown in Figure 7 below. Due to the unproven nature of solar sails, this proposal

was rejected [3].

Figure 7 - Halley’s Comet Solar Sail Design Concept [3]

27

In the 1980’s, an international solar sail race to the Moon in honor of Christopher

Columbus’s journeys sparked additional interest in the solar sail concept. However, this

competition faded due to lack of funding [3]. As time went by, the demand for inexpensive

propulsion methods increased. In addition, advancements in solar sail material technology

greatly reduced the weight of the solar sail, making the solar sail concept even more feasible.

At the present date, a new breed of solar sails is emerging. These concepts use current

material technologies to shrink the thickness of the solar sail down from the 80 micron thick

Halley’s Comet solar sail to a only few microns [4]. Figure 6 features a few of these new

concepts. The Encounter satellite is a privately funded project (a) [5]. The Solar Blade Solar

Sail (b), with 30-meter blades, is being developed by Carnegie Mellon University [4]. The

European Space Agency and German Space Agency have combined resources in the

development of the Star of Tolerance (c) [6]. Figure 6 (d) shows the infamous Cosmos I,

which was designed and constructed by the Planetary Society in conjunction with the Russian

space agency. The Cosmos I actually launched in July of 2001, but due to a software

malfunction, the sail never deployed. A relaunch is scheduled for early 2002 [7].

28

(a) (b)

(c) (d) Figure 8 - Current Solar Sail Projects. (a) Encounter Satellite [5] (b) Solar Blade Solar Sail [4] (c) Star

of Tollerance [6] (d) Cosmos I [7] Solar sail material technology is changing at a fast rate. Future solar sails are likely to

resemble a completely different form. For example NASA is currently investigating a new

material made of carbon fibers. This material is 200 times thicker than the solar sail materials

shown in Figure 8, but weighs about the same as these sails at only 5 grams per square meter.

The carbon fiber mesh, however, is many times tougher than the current materials and much

more rigid [8].

29

3.4.4 Aluminized Mylar The criteria outlined in section 3.1 were applied to the database of previous solar sail

materials. Aluminized Mylar (AM) was selected as the best PaperSat Material. Aluminized

Mylar has been used in a variety of products, including fire blankets, balloons, and photography.

In the space industry, AM is used as a reflective material in a variety of spacecraft, both solar

sail and non-solar sail related. The following list summarizes how well Aluminized Mylar meets

the design constraints:

?? Double Reflectivity. The structural layer for AM is Mylar, and the reflective layers

will be aluminum film.

?? Space Flown. AM is being used in several NASA projects, including the International

Space Station and Ariel 2 (which tested AM films in space) [9, 10].

?? Foldable. AM is used in other solar sail projects that require folding.

?? Temperature Resistance. Ariel 2 used AM films to measure micrometeoroids in a

near-earth environment. The temperatures AM was exposed to during this mission will

be comparable to the range required for this project [10].

?? UV Life. With respect to the other solar sails, AM has an average UV life [1]. The

duration will be within the constraint limits.

30

The following list describes how well AM meets the design criteria developed in section

3.4.1 for solar sails materials:

?? Density. The AM sample to be used by PaperSat will have a thickness of 5 microns

and a weight per area of 1.38 g/m2, which is the lowest weight per area of all solar sail

materials in the database.

?? Strength. The yield stress of the AM to be used in PaperSat is 172 GPa, which is an

average strength for solar sail materials.

?? Cost. With its widespread use, AM is not considered an exotic material. Aluminized

Mylar has a well-documented and researched material, which will further reduce cost.

3.4.5 Finite Element Analysis The completion of the material selection process marked the beginning of the finite

element analysis. As of the date of this report, the finite element phase of this project is still

progressing. The completion of the FE analysis is expected by the end of the semester.

A finite element model of the solar sail was developed using ABAQUS Explicit, which

is a computer program that is capable of dynamically modeling user supplied input files. The

input file for the current PaperSat model is located in Appendix C.

The base of the solar sail FE model is a circular disc with a hole in the center as shown

in Figure 9 (on the following page). This disc is composed of 4-node reduced integration

membrane elements, and represents a 100 m2 solar sail with a 10 cm diameter hole in the center

(for PaperSat instrumentation). The FE model of the solar sail also represents material

properties such as Young’s modus, Poisson’s ratio, thermal expansion coefficient, and density.

31

The model shown in Figure 9 has a total of 828 elements and 864 nodes, which took nearly 3

hours to render and occupied approximately 15 megabytes of space.

Figure 9 - Solar Sail Finite Element Mesh

For the first rendering, boundary conditions were imposed on the outer rim of the disc

such that the nodes cannot translate, but were free to rotate. In future models, the hardening

strips and deployment system will be integrated into the model, and such boundary conditions

will be unnecessary. A .1 second distributed ramp load was applied to the entire surface of

model, which simulates solar pressure. The maximum loading of the ramp function is 3 psi or

20.6 kPa, which is a realistic value for solar pressure. The total simulation lasts only .5 seconds,

with .05 seconds per time step (10 total time steps).

32

3.4.6 Finite Element Analysis Results The resulting output produced a large amount of data, including deformations,

directional stresses, and Mises Stresses at any node or section point in the model. This output

can be graphically represented using the ABAQUS Viewer program as series of animations.

The user can choose to model any data set as either a contour plot, mesh plot, or Cartesian plot

of various variables versus time or another variable.

Figure 10 shows a deformation contour plot of the solar sail at maximum deflection.

The full time history of this simulation with bigger, more readable plots is located in Appendix D.

The figure below shows the 4th time step, or .2 seconds after the ramp loading started. The

deformation scale factor for these plots are 1.0, so there is no distortion associated with

ABAQUS default settings.

Figure 10 - ABAQUS Output for First Solar Sail Rendering

Based on simple visual inspection, it is apparent that a great deal of curvature occurs at

this load setting. Pursuant to the rigid sail constraint, the current solar sail configuration is

33

unacceptable. Additional tension lines or hardening strips are required to attain a reasonable

amount of rigidity.

3.4.7 Finite Element Test Plan and Future Work As of the date of this report, the Finite Element analysis is incomplete. However, by the

end of the semester, the following objectives will be completed:

?? Integrate satellite Components. Inserting pipe elements for capillaries and composite-

type laminates for hardening strips will be sufficient for modeling the deployment system.

The corner cube reflectors can be modeled as lumped masses at the attachment points

on the solar sail.

?? Optimize Hardening Strip Placement. ABAQUS will serve as an aid for modeling the

stresses acting with different hardening strip configurations. The minimal amount of

strips may be easily deduced by experimenting with ABAQUS models.

?? Insert Thermal Stress Analysis. ABAQUS Explicit is capable of modeling radiation

from either a source or a direction. Inserting the code necessary to simulate heat from

the Sun will enable the PaperSat team to observe areas of heat or intense temperature

gradients.

?? Apply Different Initial Conditions. Once the systems integration is complete, a variety

of different initial conditions and loadings can be applied, and the resulting rigid body

modes and stresses can be observed. Different scenarios may include “gusts” caused

34

by the satellite entering the umbra or impulsive concentrated forces acting on one side of

the sail due to a piece of space debris hitting the surface.

?? Crack Imperfection Modeling. Holes due to space debris or tears can be inserted into

the finite element model to simulate damage. Additional tear strips or hardening strips

may be added if the introduction of such imperfections causes too much damage.

Most of the above mentioned tests involve adding only a few lines of code, which is why it

is believed that the testing phase can be completed within one semester. Unfortunately, this

particular finite element analysis is limited to dynamic modeling in the elastic range. It is

recommended that future teams who wish to perform a more rigorous analysis consider the

plastic deformations of the solar sail in the ABAQUS input file.

35

4.0 Orbital Trajectory Analysis

4.1 Background and Motivation

An accurate model of the satellite in orbit around the Earth is a useful tool for

understanding solar sail performance. Analysis of sail performance in a simulated space

environment will inform sail designers about what sail properties to focus on. For instance, the

attitude of the sail with respect to the Sun may prove to be the most important design concern,

perhaps even more crucial than reflectivity or size. Perhaps the most important reason that the

satellite’s orbit must be simulated is that the comparison of the actual satellite’s orbit with the

orbit prediction allows the thrust of the solar sail to be measured. These are the design issues

that motivate the development of an accurate model of the satellite’s environment.

Many forces act on a satellite that is in orbit around the Earth. Newton’s Law of

Gravitation predicts how a satellite would orbit if the gravitational attraction between the satellite

and the Earth was the only force to act on the two-body system. This two-body system does

not exist in space. There are always more forces acting on an orbiting body that perturb the

shape of the orbit from its two-body version. The perturbing forces must be included in an orbit

simulation to give a more accurate model of the system.

4.2 Theory

The theory behind the simulation is based on the principles of orbital mechanics,

Newton’s Law of Gravitation, and solar radiation pressure. These principles will be combined

to develop a physics model of the four-body problem with thrust. The four bodies to be

included are the satellite, the Earth, the Sun, and the Moon. Thrust is generated by solar

36

radiation pressure. The physical model will then be coded into Matlab software to produce a

working simulation based on initial conditions such as initial position, velocity, and the period for

which the simulation will be evaluated.

4.2.1 Orbital Mechanics

The orbital mechanics of the model consist of the coordinate system, the planets, the

satellite, and how the body’s positions and velocities are defined relative to one another. Refer

to Figures 11 and 12 (on the following pages) for better understanding of the vectors to be

defined.

Coordinate System The model uses an Earth Centered Inertial (ECI) coordinate system. The origin is at the center

of the earth. The fundamental plane is the equatorial plane, and the x-axis points constantly to

the vernal equinox, which is a fixed point in space for this application. The y-axis points 90° to

the East in the equatorial plane. The z-axis extends to the North Pole. The coordinate system

isn’t rotating, and the Earth’s rotation is not considered in the simulation.

37

Position Vectors

To account for the gravitational forces of the major gravitational bodies acting on the

satellite, it is necessary to know where these bodies are with respect to the satellite. Figure 11

shows the position vectors between each body.

1r?

- Position vector from Earth to satellite.

The plot of this position vector with time traces the three-dimensional orbit of the satellite in the ECI coordinate system. This time dependent vector is used to define all other vectors relative to the satellite. The force of Earth’s gravity acts along this vector. Since the Earth’s gravity is considered the largest and most important force on the satellite, no perturbing forces act along this vector.

s?

- Position vector from Earth to Sun.

The Sun position vector describes where the Sun is relative to the earth at any time. It is calculated using an algorithm from Reference 11. The algorithm can also be found in the Matlab code SPV in Appendix D.

m? - Position vector from Earth to Moon.

1r?

Z

Y

XMMPV?

?

3r?

2r?

TSN

?,ˆ

SSPV?

?

Figure 11 - Position Vector Schematic Including the Sun, Earth, Satellite and Moon Positions (left to right)

38

The Moon position vector describes where the Moon is relative to the earth at any time. It is calculated using an algorithm from Reference 11. The algorithm can also be found in the Matlab code SPV in Appendix D.

2r?

- Position vector from Sun to satellite. srr 12

?????

The vector is used to calculate the direction and magnitude of the gravitational force between the Sun and the satellite. Vector 2r

? is also used to calculate the magnitude of

the thrust on the satellite due to solar radiation pressure. These forces are considered perturbing forces on the satellite.

3r?

- Position vector from Moon to satellite.

mrr 13???

?? This vector is used to calculate the direction and magnitude of the gravitational force between the Moon and the satellite. This force is also considered a perturbing force.

NS?

- unit vector from center of mass of the satellite, normal to the plane of the sail.

The sail normal vector is used to define the attitude of the sail. The sail has the geometry of a thin disk, and attitude is vital for calculating thrust from solar radiation pressure and atmospheric drag forces.

39

Figure 12 - Sail Normal Orientation in the ECI Coordinate System [12]

Figure 12 shows how the sail normal is oriented in the ECI coordinate system. The sail

normal can be in a constant direction, or it can be rotating in a manner defined by a(t) and ß(t) .

Definitions of NS?

, a(t) , and ß(t) follow:

?????? 0)t(

?????? 0)t(

where 0? = initial angle from the x-axis, in the xy-plane at time t0.

?? = angular velocity of the sail normal.

0? = initial angle from the xy-plane to the sail normal vector at time t0.

?? = angular velocity of the sail normal.

???

?

?

???

?

?

???

??

?)]t(cos[

)]t(cos[)]t(sin[

)]t(cos[]t(cos[

SN

?

4.2.2 Newton’s Law of Gravitation

40

Newton’s Law of Gravitation describes the force vector between two bodies. To

illustrate the law, a simple two-body system consisting of the Earth and the satellite will be

analyzed. Figure 11 shows the Earth, the satellite, their masses, and the vector from the Earth

to the satellite ( 1r?

). Newton’s Law of Gravitation for the two-body problem takes the form:

131

SE1 r

r

mGmF

??

??? (1)

where 2010673.6G ??? km3/kg-s2 The equation is negative because the force acts in the direction opposite to 1r

?. To simulate the

orbit, acceleration vectors are used instead of forces. The acceleration due to the force of

Earth’s gravity is:

131

SE1 r

r

)mm(Gr

??

? ???

??

(2)

By assuming that the mass of the satellite is small in comparison to the mass of the Earth, the

following equation can be made to obtain the Earth’s gravitational constant:

5

EESE 10986004.3Gm)mm(G ?????? km3/s2 (3) Equation (2) now becomes:

131

E1 r

rr

??

? ???

??

(4)

Equation (4) is the equation of Newton’s Law of Gravitation for the two-body problem in terms

of acceleration. This is the form used to calculate the position vector 1r?

in Matlab.

41

The four-body problem is similar to the two-body problem. The gravitational forces of

the Earth, Sun, and Moon all act on the satellite in the same way. The acceleration experienced

by the satellite (relative to ECI) is the sum of the three gravitational forces:

333

M23

2

S13

1

E1 r

rr

rr

rr

??

??

??

? ??

??

???

??

(5)

where 11

S 10327124.1 ??? km3/s2 799.4902M ?? km3/s2 This concludes the derivation of Newton’s Law of Gravitation for the four-body problem. (note: Derivation developed from several equations located in References 12 and 11)

4.3 Solar Radiation Pressure 4.3.1 How Solar Radiation Pressure Creates Force

The Sun’s light is electromagnetic energy that carries linear momentum in the form of

high-energy photons. These photons are reflected off the surface of the solar sail. “Since

photons carry momentum, the reflection of the photons changes their momentum and a resultant

force is exerted against the reflecting surface” [1].

Figure 13 - Incidental and Reflected Light and Force Vectors Acting on the Sail

42

Figure13 shows a useful diagram how the photons strike the sail surface. The surface

experiences incidental light and reflected light. Momentum is exchanged under both conditions

just as a ball bouncing elastically off of a wall. The millions of photons bouncing off the surface

at the same angle ? exert uniform pressure over the sail area. The force exerted on the sail

surface is the vector sum of both incidental and reflective forces.

RIT FFF

????? (6)

The magnitude of the thrust produced by a solar sail depends on many variables [13].

)(cos2cos21(Ac

ST 2r ???

????

???????

(7)

rS The first is the power output of the sun. The sun lets out an equal amount of photons at

all times. (For analysis purposes only. The Sun generates large energy fluctuations and so does the solar wind that our ship would sail on.) The power output of the Sun is a function of 2r

? (the vector from the Sun to the satellite). In equation (7), the power has

been scaled by c, the speed of light.

A The second is the area exposed to photons. Although the surface area of the sail is constant, the area exposed to light depends on the angle ? between 2r

? (position vector

from Sun to satellite) and the sail normal. When ? = 0? or 180???the area exposed to pressure will be zero.

? The reflectivity effects how much momentum is exchanged during photon collision. It is

similar to the elasticity of the ball hitting the wall analogy. ? = )rScos(a 2N

???

43

Figure 13 shows that TF

?begins at the center of mass, and it is always pointing in the direction of

NS?

at any angle ? . It follows that all thrust created by solar radiation pressure is always

directed along the sail normal such that:

NSTT

????? (8)

4.4 Orbital Initial Conditions

Due to the size of the solar sail, and the resulting drag force on the satellite when the sail

passes near the earth, the analysis of the thrust from the solar sail would be most easily

observed at a high altitude orbit. The CubeSat program, however, is limited to launching

satellites at low altitude orbit. To best study the amount of thrust generated by the solar sail, this

project will require a CubeSat launch that offers a high velocity at launch, allowing our satellite

to travel along a LEO to GEO orbit. The CubeSat release, and insertion velocity was assumed

to be at perigee of the LEO to GEO orbit. Using basic orbital mechanics, the initial conditions

and some of the orbital elements for a sample LEO to GEO orbit follow:

Rp = 7178.14 km Vp = 10.19 km/s2

Ra = 48619.23 km Va = 3.04 km/s2 a = 55797.37 km e = 0.743

44

The Matlab code for calculating these initial conditions is in Appendix D. 4.5 Matlab Technique for Orbit Simulation

The Matlab simulation consisted of several m-files working together. Each file will be

briefly described.

n_bodyproblem.m – This file facilitates user input, initial conditions, and plotting commands

for the satellite position vector. Also contained is the Matlab command ode45. This command executes a fourth order Runge-Kutta numerical integration. This command produces two vectors, t and x, with the same number of rows. At every row, x is defined for that t. For example, at time t=0, x=[xo; yo; zo; xdo; zdo]. As time is incremented, a new x vector is defined by the function n_bodyorbit.m. The time limit is defined by the statement [0:500:T]; where 0 is the starting time, 500 is the time step, and T is the ending time.

n_bodyorbit.m – This function is called every time new t and x vectors are needed.

Vectors t and x are sent into the file. Next, the Sun position vector, the Moon position vector, the sail normal, and the thrust vector are calculated. Using definitions in the theory section, the accelerations in the x, y, and z direction that the satellite experiences are calculated. Ode45 then uses the accelerations to calculate the position vector and sends it back to the file n_bodyproblem.m.

JD.m - The Julian Date is calculated at every time t. The Julian Date is used to

calculate the Sun position vector and the Moon position vector. SPV.m, MPV.m, and Plot_SMPV.m –

These files calculate where the Sun and Moon are relative to earth at every time t. The position of the Sun and the Moon is then plotted in Plot_SMPV.m.

Sail_Normal.m and Thrust Vector.m – The sail normal is generated from the sail’s initial conditions for attitude.

The magnitude of the thrust is calculated based on the distance between the Sun and the satellite and the angle theta between the sail normal and the sun position vector. The Thrust is then pointed along the sail normal and included in the equations of motion for the satellite in n_bodyorbit.

45

46

4.6 Simulation Results

The results of the orbit simulation are in graphical form. The analysis of the plots

obtained will show how perturbing gravitational forces and thrust can change the orbit’s shape.

The first plot of the orbit can be found in Figure 19. This orbit was simulated using only the

force of Earth’s gravity. This two-body simulation is how the satellite would fly without any

perturbing forces or thrust. Other important elements in the plot include the Moons orbit and

the Sun’s Orbit. The long, dark blue arc around the Earth indicates where the Moon would be

relative to the Earth during the four-day integration period. The magnitude of the Moon position

vector has been scaled down by 10-1 so that it would fit on the plot and give a basic

understanding of the Moons position. The shorter, light blue arc is a scaled down version of the

Sun’s orbit over the four-day integration period. The Sun Position vector was scaled by 10-4.

Figure 20 is a close-up of the orbit at apogee. It has a maximum radius at apogee of 10.5?104

km.

The four-body problem without thrust is plotted over a four-day period in Figure 21.

The changes are subtle, so it is best to examine the close-up of apogee of the four-body orbit.

Figure 22 shows the close-up of apogee. Here the maximum radius at apogee is 10.6?104 km:

1,000 km more than the two-body orbit.

Figure 23 shows a highly perturbed orbit. This is due to the application of a constant

direction thrust vector. The direction is held constant for simplicity, and the magnitude of the

thrust has been magnified 100 times to better display its perturbing effects.

47

Figure 14 - Two Body Orbit

Figure 15 - Close-up of Two-Body Orbit at Apogee

48

Figure 16 - Four-Body Problem Without Thrust

Figure 17 - Close-up of the Four-Body Problem at Apogee.

49

Figure 18 - Four-Body Problem with Magnified Thrust

50

4.7 Future Simulations and Applications

Future simulations will include the rotating, variable thrust vector. When the sail is

rotating, the thrust generated by the sail will change in direction and magnitude. As the orbit

propagates, the distance from the Sun to the satellite will change, causing a change in the

magnitude of the thrust. A rotating, variable thrust satellite should produce interesting orbits.

Once a rotating thrust vector is simulated, the initial conditions of the orbit will be optimized for

deployment systems and tracking missions.

Once the solar-sail-propelled satellite has been tracked over several orbital periods, the

difference between the orbit observed and the orbit predicted should be almost entirely due to

variations in the thrust acting on the solar sail. Since attitude and rotation information about the

satellite will be obtained through observation, the magnitude of the thrust vector is the only

unknown left and can be solved for via a reversal of the process used here to predict the

satellite motion. That reversal process, however, should not be necessary as the solar sail

manufacturer should have theoretical thrust predictions for the solar sail. If those predictions are

accurate, the observed orbit of the satellite will be very close to the predicted orbit. It is in this

manner that this project provides testing capability for solar sail manufacturers and the capability

to provide some empirical data for solar sail propulsion technology.

51

5.0 Schedule

Table 1 outlines the deliverables the contractor will receive from PaperSat engineering

this semester. The completion dates associated with these items are also indicated in the table.

Table 1 - Contract Deliverables

Item to be Delivered Date Delivered Status Proposal for Contract 10/03/01 Submitted Presentation for the Departmental Visiting Committee 10/11/01 Submitted First Preliminary Design Review Presentation 11/02/01 Submitted First Preliminary Design Review Formal Report 11/12/01 Submitted Second Preliminary Design Review Presentation 11/26/01* Pending Second Preliminary Design Review Formal Report 12/03/01* Pending Orbital Trajectory Simulation 12/03/01* Pending Picosatellite Model 12/03/01* Pending Project Poster 12/03/01* Pending Project Records 12/03/01* Pending

(* indicates that the date is subject to change by the contractor)

In addition to the deliverables listed in Table 1 PaperSat has established additional

requirements with respect to the content of the preliminary design reviews. The schedule chart

included in the Appendix E indicates that the solar sail material would be selected and sized and

the thrust analysis would be computed. The schedule also indicates that that the solar sail

deployment apparatus would be selected and sized and that the required CubeSat systems

would be selected and integrated. These tasks have been accomplished. In addition, the

PaperSat development teams have already begun investigating the solar sail material, solar sail

deployment, and corner cube reflector integration. At the end of PaperSat’s design phase for

this project, a record of all work done on this project will be supplied to the contractor in the

form of compact disk.

52

53

6.0 Management Organization 6.1 Company Management Structure

The PaperSat Engineering Company consists of a system design branch and a systems

integration branch. The Figure 14 shows how the branches are divided.

System Design Branch Systems Integration Branch

Figure 19 – PaperSat Engineering Management Structure

With the exception of the orbital trajectory department, which will remain active throughout the

contract, the two branches are not scheduled to be active simultaneously. The project schedule

(Appendix E) shows how the system design branch will only be active until PDR1 is submitted.

After PDR1 is complete, the systems integration branch will become active so that the design

can be further refined for construction purposes. Once the systems integration branch produces

PDR2, the contract requirements will have been fulfilled. Table 1 shows each of the team

members’ responsibilities and the corresponding branch.

Project Manager

Propulsion Integration Dept. Mngr.

Mechanical Integration Dept. Mngr.

Comm. and Tracking Implementation Dept. Mngr.

Electronics Integration Dept. Mngr.

Propulsion Systems R&D Dept. Mngr.

Mechanical Systems R&D Dept. Mngr.

Tracking Systems Dept. Mngr.

Electrical Systems Dept. Mngr.

Orbital Trajectory Dept. Mngr.

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Table 2 - PaperSat Personnel Responsibilities

PaperSat Personnel

System Design Branch Titles Systems Integration Branch Titles

Phillip Hempel Mechanical Systems R&D Dept. Mngr. Mechanical Integration Dept. Mngr.

Paul Mears Orbital Trajectory Dept. Mngr.

Daniel Parcher Project Manager Electronic Systems Dept. Mngr. Tracking Systems Dept. Mngr.

Project Manager Electronics Integration Dept. Mngr. Comm. and Tracking Implementation Dept. Mngr.

Taffy Tingly Propulsion Systems R&D Dept. Mngr. Orbital Trajectory Dept. Engineer

Propulsion Integration Dept. Mngr.

The project manager will serve as a point of contact for each of the other managers.

The project manager is responsible for maintaining the group notebook, moderating evaluation

of design conflict solutions, and maintaining the project schedule. Each of the other managers is

responsible for ensuring that the work their department is responsible for is completed by the

appropriate deadline.

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6.2 Design Conflict Resolution Procedure

The managers of each department of PaperSat Engineering will caucus on Monday,

Wednesday and Friday of each workweek while under contract. At each Monday caucus, the

managers of each department must present a summary of their objectives for the coming week,

completed tasks for the previous week, and any concerns or issues they have with their

department’s progress and tasks. The Wednesday and Friday caucuses will be reserved for

troubleshooting of issues and concerns. (Note: Summaries do not need to be provided by

managers of inactive departments). Once issues are presented, each department manager will

present at least one potential solution to the conflict. The candidate solutions will be discussed

and an agreement of all departments must be reached before the candidate solution is adopted

by department raising the issue. Each department must agree on the proposed solution to the

conflict, as many conflicts may impact portions of the project for which other departments are

responsible. In this manner, engineering conflicts will be quickly identified and resolved. Weekly

reports submitted by the department managers and a log of issues and concerns will be

maintained and filed by the project manager in the PaperSat engineering notebook.

In the event of an emergency conflict requiring immediate solution, the project manager

will decide a course of action until the next management caucus. In the event of gridlock as

candidate solutions are being evaluated, the project manager may override one vote other than

his/her own. Poor use of override power may result in the dismissal of the project manager.

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7.0 Proposed Budget 7.1 Budget Item Description 7.1.1 Personnel Budget Description

The cost for personnel will be totaled per hour worked. The salary basis for each

employee for a full work year is listed below:

Daniel Parcher $26.0 / hr* Taffy Tingley $24.5 / hr* Paul Mears $24.5 / hr* Phillip Hempel $24.5 / hr* Dr. Cesar Ocampo (Orbital Determination Consultant) $52.0 / hr* *This number does not include withholdings for Tax Purposes 7.1.2 Material and Electronics Budget Description

The materials and electronic costs are not yet fully known. A company wishing to test

their material will provide the solar sail. The deployment hardware, shell casing, and electronics

will total approximately $5000.

7.1.3 Testing Budget Description

One of the things that makes a small satellite a good test platform for solar sail

technology is that solar sails cannot be tested on earth. The sail will not need to endure the air

pressure or gravitational force that it would on earth. The result is that the deployment

mechanism, being designed for a micro-gravity environment, will be difficult if not impossible to

test on earth. Because of this only vibration testing will be performed. After vibration testing, the

systems will be inspected for damage. The estimate for vibration testing cost is roughly $2000.

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7.1.4 Launch Budget Description

The CubeSat launch costs are roughly $50,000 per satellite launched. That cost is

expected to increase in the future, but PaperSat will estimate its final budget for one CubeSat

launched for the current cost.

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7.2 Budget Summary

The Table 3 contains a complete summary of the predicted expenses for the PaperSat

Engineering company’s work on this project.

Table 3 - Proposed Budget

Expense Item Predicted Expenses (dollars)

Expenses Realized (dollars)

Personnel (based on an estimated 150 hrs. worked, 14 hrs. for consultants) 15,653 9,000 Materials / Electronics 5,000 10 Testing 2,000 0 Launch 50,000 0 Total 72,653 9,010

It is easy to see from the Figure 25 below, that the majority of the expense for this

project lies with the launch cost.

Analysis of Proposed Budget

22%

7%

3%

68%

Personnel

Materials/ Electronics

Testing

Launch

Figure 20 – Analysis of Proposed Budget

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8.0 Future Work

The satellite design has not yet been completed and there are still several systems that

have components with specifications left to be determined. One of the required components left

to be determined is the timing board and the power required to time it. Another area to be

determined is the corner cube reflector attachment to the solar sail, the method has not yet been

finalized. Also, all of the components must have their final weight and volume determined.

In addition to the systems that have yet to be finalized, we will also be contacting the

CubeSat program for the purpose of determining the ground station resources available to us,

and completing the development of the rotating thrust vector orbital simulation. If time permits a

reliability analysis of each of the components for the satellite will also be preformed.

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9.0 Conclusion

PaperSat Engineering is in the process of designing a CubeSat based solar sail testing

platform. The satellite design will incorporate a compressed gas deployment system for the

Aluminized Mylar double reflective solar sail, corner cube reflector based optical tracking, and

an electronic timer that can supply triggers for events coordinated at specific times. The satellite

will deploy its solar sail after the nearby CubeSats have had an opportunity to disperse. The

orbital perturbations of the satellite will be measured periodically from laser positioning from

ground stations. The magnitude of the solar sail thrust will be obtained from analysis of those

perturbing forces.

Companies wishing to test their solar sail design can employ PaperSat to integrate their

sail design into a picosatellite. The solar sail design will give education institutions and their

students the opportunity to participate in a complete satellite development project, and the

academic community can benefit from research of the cutting edge propulsion technology.

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10.0 References 1. Wright, Jerome. Space Sailing. Gordon and Breach Science Publishers, Langehorne,

Pennsylvania 1992., pp. 2 2. Faust, Jeff. “Solar Sail Scheduled to Launch Early Next Year.” Spaceflight Now. 23

August 2001. http://www.spaceflightnow.com/news/n0108/23cosmos/ site accessed 1 Nov 2001.

3. Diedrich, Benjamin. “3 Axis Stabilized Solar Sails.” http://www.ugcs.caltech.edu/~diedrich/solarsails/types/3-axis.html. Site accessed 14 October 2001.

4. Solar Blade Solar Sail. http://www.frc.ri.cmu.edu/projects/blade/index2.html. Site accessed 14 October 2001.

5. Team Encounter Site. http://www.encounter2001.com/index.html. Site accessed 14 October 2001.

6. The Star of Tolerance. http://www.star-tolerance.com/english/index.htm. Site accessed 14 October 2001.

7. The Planetary Society: Cosmos I: The First Solar Sail. http://www.planetary.org/solarsail/index2.html. Site Accessed 6 November 2001.

8. Clark, Greg. Space.com Exclusive: Breakthrough in Solar Sail Technology.” http://www.space.com/businesstechnology/technology/carbonsail_000302.html. Site accessed 14 October 2001.

9. “Staying Cool on the ISS.” http://www.geocities.com/beyondearth2001/view15.htm. Site accessed 6 November 2001.

10. “Ariel 2.” Space Science. http://www.nasm.edu/nasm/dsh/artifacts/SS-ariel2.htm. Site accessed 6 November 2001.

11. Vallado, David A. Fundamentals of Astrodynamics and Applications. McGraw-Hill 1997 pp. 7,38,101-105

12. Dr. Ocampo, Cesar. Supplemental Instruction and Lectures, Weekly Mtgs. September though November 2001.

13. Polyakhova, Yalena Nikolayevna. Space Flight Using a Solar Sail: The Problems and Prospects. Leningrad State U, Department of Celestial Mechanics, July 1986

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Appendix A – PaperSat Team Appendix B – CubeSat Frame Appendix B – ABAQUS Input Appendix C – ABAQUS Output Appendix D – Orbital Simulation Code Appendix E – PaperSat Schedule