cubesat based solar sail testing platform final design...

The University of Texas at Austin

Department of Aerospace Engineering and Engineering Mechanics

CubeSat Based Solar Sail Testing Platform Final 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

December 7, 2001

Page i

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 Satellite system integration

??Weight / Volume Budget Analysis ??Component Configuration

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 14,080

Materials / Electronics 5,000 7,050 Testing 2,000 2,000 Launch 50,000 50,000 Total 72,653 73,130

Team Members

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

Page ii

Table of Contents

Executive Summary..............................................................................................................i Table of Tables.....................................................................................................................v 1.0 Introduction................................................................................................................... 1

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

2.0 Design Factors............................................................................................................... 3 2.1 Design Restrictions ................................................................................................... 3 2.2 Satellite Component Evaluation Criteria .................................................................. 4

3.0 Satellite Systems ........................................................................................................... 6 3.1 Satellite Tracking Systems........................................................................................ 7

3.1.1 Optical Ranging Principles ................................................................................ 7 3.1.2 Design Impact .................................................................................................. 10 3.1.3 Optical Tracking Hardware Specifications ...................................................... 11

3.2 Electrical System..................................................................................................... 13 3.3 Mechanical Systems and Deployment .................................................................... 15

3.3.1 Satellite Components ....................................................................................... 16 3.3.2 Component Placement and Overview............................................................. 21 3.3.3 Satellite Construction Summary ...................................................................... 22 3.3.4 Solar Sail Deployment Summary..................................................................... 23

3.4 Propulsion Systems ................................................................................................. 26 3.4.1 Solar Sail Historical Survey............................................................................. 26 3.4.2 Solar Sail Material Structure............................................................................ 29 3.4.3 Solar Sail Material Selection Criteria and Design Constraints ........................ 30 3.4.4 Aluminized Mylar............................................................................................ 32 3.4.5 Finite Element Analysis – Model Description................................................. 33 3.4.6 Finite Element Analysis Results ...................................................................... 35 3.4.7 Propulsion Analysis Conclusions .................................................................... 41

4.0 Orbital Trajectory Analysis......................................................................................... 43 4.1 Background and Motivation ................................................................................... 43 4.2 Physics Models and Simulation Techniques........................................................... 44

4.2.1 Orbital Mechanics............................................................................................ 44 4.2.2 Newton’s Law of Gravitation........................................................................... 48

4.3 Solar Radiation Pressure ......................................................................................... 50 4.3.1 How Solar Radiation Pressure Creates Thrust ................................................. 50

4.4 Orbital Initial Conditions ........................................................................................ 52 4.5 Umbra and Penumbra Effects ................................................................................. 53 4.5 Matlab Technique for Orbit Simulation.................................................................. 54 4.6 Simulation Results .................................................................................................. 55

4.6.1 Introduction to Plot Information: Two-Body Problem .................................... 55 4.6.2 Sun and Moon Perturbations: Four-Body Problem ......................................... 56

Page iii

4.6.3 Thrust as a Perturbing Force: Four-Body Problem with Thrust ...................... 58 4.6.4 Displaying Thrust: Non-Rotating Thrust Vectors............................................ 59 4.6.5 Dynamic Thrust: Rotating Thrust Vectors....................................................... 60 4.6.6 How Thrust Can Change an Orbit: Magnified Thrust Vectors ........................ 61

4.7 Measuring Thrust .................................................................................................... 64 5.0 Schedule ...................................................................................................................... 65 6.0 Management Organization.......................................................................................... 66

6.1 Company Management Structure ........................................................................... 66 6.2 Design Conflict Resolution Procedure.................................................................... 68

7.0 Project Budget............................................................................................................. 69 7.1 Budget Item Description......................................................................................... 69

7.1.1 Personnel Budget Description.......................................................................... 69 7.1.2 Materials and Electronics Budget Description ................................................ 69 7.1.3 Testing Budget Description ............................................................................. 69 7.1.4 Launch Budget Description ............................................................................. 70 7.1.5 Implementation Costs / Manufacturability ...................................................... 70

7.2 Budget Summary .................................................................................................... 72 7.3 Cost Overrun Analysis ............................................................................................ 73

8.0 Sustainability............................................................................................................... 74 8.1 Environmental impact............................................................................................. 75 8.2 Ethics, Health and Safety........................................................................................ 75

9.0 Future Work ................................................................................................................ 77 10.0 Conclusion ................................................................................................................ 79 11.0 References ................................................................................................................ 80 Appendix A – PaperSat Team Appendix B – CubeSat Frame Appendix C – PaperSat Schedule Appendix D – Orbital Simulation Code

Page iv

Table of Figures

Figure 1 - Satellite Systems ................................................................................................ 6 Figure 2 - Corner Cube Reflector Concept ......................................................................... 7 Figure 3 – Sample Corner Cube Reflector Array from Banner Engineering [2] .............. 12 Figure 4 - RDAS Compact Timer / Accelerometer Board [3] ......................................... 13 Figure 5 - Ultralife Lithium Ion Battery Schematic [4].................................................... 14 Figure 6 - Compressed Nitrogen Canister ........................................................................ 20 Figure 7 - Satellte Cut-Away............................................................................................ 22 Figure 8 - Weight Budget for the Satellite ........................................................................ 24 Figure 9 - Volume Budget for the Satellite....................................................................... 25 Figure 10 - Halley’s Comet Solar Sail Design Concept [7].............................................. 27 Figure 11 - Current Solar Sail Projects. (a) Encounter Satellite [9] (b) Solar Blade

Solar Sail [8] (c) Star of Tollerance [10] (d) Cosmos I [11].................................... 28 Figure 12 - Solar Sail Material Layers: (a) Layers of Conventional Solar Sail Material

(b) Layers of Solar Sail Material for this project...................................................... 29 Figure 13 - Solar Sail Finite Element Mesh...................................................................... 34 Figure 14 - Final Deployed Solar Sail Configuration....................................................... 36 Figure 15 - Thermally Coupled Loading on the Solar Sail............................................... 38 Figure 16 - Non-Thermally Loaded Solar Sail ................................................................. 39 Figure 17 - Parallel Loading on Solar Sail........................................................................ 40 Figure 18 - Unevenly Distributed Load of Solar Sail ....................................................... 41 Figure 19 - Position Vector Schematic ............................................................................. 45 Figure 20 - Sail Normal Orientation in the ECI Coordinate System [16] ........................ 47 Figure 21 - Incidental and Reflected Light and Force Vectors Acting on the Sail........... 50 Figure 22 - Obit Diagram.................................................................................................. 52 Figure 23 - Earth's Shadow............................................................................................... 53 Figure 24 -Two Body Orbit .............................................................................................. 55 Figure 25 - Close up of Two-Body Orbit at Apogee ........................................................ 56 Figure 26 - Four-Body Problem without Thrust ............................................................... 57 Figure 27 - Close Up of Four Body Problem without Thrust ........................................... 58 Figure 28 - Four Body Problem with Magnified Thrust ................................................... 59 Figure 29 - Orbit with Thrust Vector for a Constant Sail Attitude ................................... 60 Figure 30 - Rotating Thrust Vector................................................................................... 61 Figure 31 - Magnified Thrust Vector ................................................................................ 62 Figure 32 - Magnified Thrust Vector Side View .............................................................. 62 Figure 33 - Magnified Thrust Vector with 3D Rotation................................................... 63 Figure 34 - Magnified Thrust Vector with 3D Rotation (side view) ................................ 63 Figure 35 - PaperSat Engineering Management Structure ............................................... 66 Figure 36 - Analysis of Proposed Budget ......................................................................... 72

Page v

Table of Tables Table 1 - Summary of Elements Used .............................................................................. 33 Table 2 - Contract Deliverables ........................................................................................ 65 Table 3 - PaperSat Personnel Responsibilities.................................................................. 67 Table 4 - Proposed Budget................................................................................................ 72

1.0 Introduction

PaperSat Engineering has designed a picosatellite in accordance with the

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

offers educational institutions the opportunity to, for a relatively low cost, launch a 10cm

sided cubic satellite. The proposed picosatellite mission is entirely at the discretion of the

educational institution sponsoring the satellite. The CubeSat program therefore offers the

students working on each satellite design a large amount of control over the satellite’s

mission and design.

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 for this project is to retrieve empirical thrust data for solar

sail propulsion. PaperSat will be exploring a test design to analyze 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. With this option, companies wishing to develop

solar sail technology can protect their investment. The academic community will benefit

from this solar sail research as well. As tests are performed, the results will show the 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 successfully used as a major

propulsion system by any spacecraft to date and, as a result, the technology is largely

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 this 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.

2.0 Design Factors

To achieve the goals outlined in the previous section, it was necessary to adopt

several design constraints. The restrictions listed below allow this satellite design to

maintain accordance with CubeSat regulations and maintain simplicity reliability.

2.1 Design Restrictions

The PaperSat team (Appendix A) has adopted the following design restrictions for

this satellite design. Some design restrictions are imposed by the CubeSat program,

others were imposed by the design team.

?? Weight – The satellite must weigh less than a total of 1 kg. (CubeSat Restriction)

?? Volume – The satellite must be a cube with sides 10cm or less. (CubeSat Restriction)

?? Shell – A shell similar to the CubeSat recommended shell design made of 7075

aluminum was adopted for this satellite design and will house the satellite

components.

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

the injection phase of the satellite 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. Their recommendation has been

adopted for this project.

?? 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.

?? 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.

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

determination. Laser ranging will be performed by ground stations.

2.2 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. Weight is therefore a crucial evaluation criteria for each candidate

satellite component.

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

This stringent restriction ensures that component volume is also a crucial

evaluation criteria.

?? 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. This criteria is applied to deployment components such as solar

sail capillaries and hardening strips.

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

Component costs therefore do not effect the overall budget for this project greatly.

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. Reliability is therefore also

an important evaluation criteria for all components.

Each of the components selected for the design of this satellite were selected bearing

the above restrictions and evaluation criteria in mind.

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 batteries.

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

components, the solar sail deployment components, and solar sail hardening and

tear strips.

?? Propulsion – Consists only of the 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 1 - Satellite Systems

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 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 position

determination. The technique is passive, using only 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.

Figure 2 - Corner Cube Reflector Concept

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 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.

Measuring small thrust aboard this satellite requires that the satellite’s position in its orbit

be known very accurately. Laser ranging has the capability to determine satellite position

to an accuracy of up to 1 cm [1].

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. 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 will not need to be distinguished.

If several measurements of the satellite position are recorded, the satellite’s

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.

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, offering a very reliable solution to

satellite position determination.

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

position fixes is required. Five to ten position measurements 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

five to ten bursts of five measurements per orbital period would provide sufficient

information about the spacecraft. One ground station should be adequate for these

purposes. It will be sufficient to track the satellite for the times that it has a positive

elevation with respect to the McDonald Observatory laser ranging facility in west Texas.

For a four day propagation of the predicted orbit, the satellite maintained a positive

elevation over west Texas for up to almost half a day, corresponding to a full orbital

period of the satellite. Positioning over a full orbital period will not be required, however,

as the portion of the orbit that is of most interest is the portion farthest from the earth

because there will be fewer perturbations. Measurements will also 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 also be obtained.

3.1.2 Design Impact

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

is minimal. Small lightweight panel corner cube reflector arrays will be used as walls for

the CubeSat while it is in its launch configuration. The corner cube reflectors will

therefore provide service as walls and laser ranging devices. 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. The reflectors do take up a substantial amount

of space and weight, but when compared to an electronic ranging solution, the weight and

volume requirements are reasonable.

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.

Unfortunately corner cube reflector models with high operational temperatures have

lower reflectivity. For final determination of the corner cube reflector to be designed, a

mission submission to the International Laser Ranging Service (ILRS), of which

McDonald observatory in west Texas is a part, should be completed. The ILRS can then

supply detailed information with regards to cost of operation and reflectivity

requirements of the corner cube reflectors. A “middle ground” must be reached with

respect to operational temperature, cost, and ILRS capabilities. For the purposes of this

design, a custom glass corner cube reflector array will be used.

Figure 3 – Sample Corner Cube Reflector Array from Banner Engineering [2]

Banner Engineering merchandise similar to that shown in Figure 3 was used as a

template for the corner cube reflector specifications. The reflector shown in Figure 3 is

made of Acrylic, which will most likely not be able to handle the operating temperatures

required for space. Banner has glass corner cube reflectors which do not require the

backing plate seen in Figure 3, allowing them to be thinner. The glass retroreflector will

be 7mm in thickness, accounting for a 3mm thickness reflector array on both sides of

component and 1mm of glass in between. The four double-sided reflectors for the

satellite will weigh a total of approximately 44 grams, require a total of approximately 77

cm3 and will be 41 mm in diameter. The estimated total price for the corner cube

reflectors through Banner Engineering is $6000.

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 batteries for the timer. 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.

Figure 4 - RDAS Compact Timer / Accelerometer Board [3]

The RDAS Compact timer model shown in the above figure, provided by

Aerocon Systems will cost $211. The timer is capable of supplying voltages at different

times to trigger events during deployment. The timer requires 9-11 V of power to operate

and draws 70-90 mA of current. The board requires a volume of 90x36 mm2 x 17 mm

and weights 31 grams. To ensure that the board capable recording time for the 5 hours

between kill switch activation and satellite system deployment, the board requires

roughly 500 mAh of current. Three lithium Ion batteries will be stacked within the

satellite to provide the timer’s power and current requirements.

Ultrallife polymer lithium ion batteries were selected for powering the timing

system. Figure 5 shows the battery model to be used.

Figure 5 - Ultralife Lithium Ion Battery Schematic [4] Three of these batteries at 3.8 Volts each will provide 530 mAh of current. The batteries

operate between -20o C and +60o C. Three of these batteries will require roughly

35x62mm2 x 12mm of volume and weight roughly 45 grams.

3.3 Mechanical Systems and Deployment

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 the component’s weight, volume, and

attachment needs.

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

components of our satellite design. Other components specific to this satellite design

include the corner cube reflector panels, the solar sail, nitrogen capillaries, the

compressed nitrogen canister, and the 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 vital component in the satellite, it is also necessary to

have each of these components placed strategically to maximize the working volume. 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 volume each component

occupies along with what portion of the weight each component composes, the volume

and weight of each component will be mentioned and discussed in a volume and weight

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

process.

3.3.1 Satellite Components

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 kill switch performs this

operation. 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 2cm3 and weigh 10 grams. Upon placement of the

CubeSat into the main satellite before launch, the button on the kill switch is pushed in

and held in by the rails on the deployment device. The kill 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.

Timer

The timer is the brain of the satellite 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 solar sail

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 45.9 cm3, weigh 32 grams, 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 nitrogen from the onboard capsule, set for 5 hours 2 minutes after the

timer activation at deployment.

Batteries

The batteries in the CubeSat will be used to power both the timer and the servos

that release the side panels. The batteries used will be three Lithium Ion batteries placed

directly next to the timer. They occupy 45 grams and 31.5 cm3 of space.

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 and sheets attached together. Each beam will be

approximately 10 cm in length with a square cross-section 0.2 cm on a side. The sheet

sections on the ends will be 10 cm square and will be .5 mm thick. In combination with

the attached side panel parts not associated with the corner cube reflectors, this brings the

total weight of the frame to 43.43 grams and the volume to 16 cm3. The frame is also the

base upon which the corner cube reflector panels are to be placed.

Corner-Cube Reflector Panels

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

system that will be employed to track the CubeSat. The corner cube reflector panels

being used are 6 cm in diameter circular reflector panels mounted in the center of the side

walls. The total weight of the panels will be 43.39 grams and the volume will be 75.6

cm3. Each of these corner cube reflector panels is double sided, allowing reflectivity on

both sides of the panel with the mounting of only one reflector. The four panels will be

placed on the four of the sides of the CubeSat. Prior to the inflation of the solar sail, the

four side panels with the reflectors will be released. 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 released panels will be rigidly attached to the solar sail in the plane of the sail.

Solar Sail

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

important component of the program. The solar sail will be constructed of 6 micron thick

Aluminized Mylar. The solar sail will be circular in shape, will have a total area of 100

m2 (5.64 m radius), and will have a final weight of approximately 720 grams. For

packing into the satellite, the solar 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 700 cm3.

Capillaries

The capillaries being used for this project are responsible for containing 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 placed in the middle and along the edges of the sail. The

capillaries will be inflated with the Nitrogen at a rate of 3.5 cm3 per second. This will

make the total inflation time three minutes and will leave a final pressure in the

capillaries of 0.5 psi.

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 6, will be 7.6 cm long, 3.8 cm in diameter, and have a volume of 86

cm3. The volume used to specify internal satellite arrangement will be 90 cm3 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 75 grams. The Nitrogen in the canister will

be stored at 60.5 psi. Once the Nitrogen is released from the canister at 3.5 cm3 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. The papersat

development team was unable to find a CubeSat program regulation prohibiting the use

of compressed gasses. However, if CubeSat does have such a regulation, we are confident

that through testing we can convince them that use of this canister will be safe for our

satellite and satellites to be deployed nearby.

Figure 6 - Compressed Nitrogen Canister

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. Hardening strips must be added to the sail due to the fact that

over the time span the CubeSat would be in orbit, the Nitrogen will 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.

3.3.2 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 7. 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 and batteries are installed on the bottom of the satellite

as close as possible to each other on the permanently mounted base 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 958 of the available 1000 cm3.

This leaves an available 42 cm3 that can be used to maximize the size of our solar sail or

space-harden some of the components. The total weight of the components is 968 grams

out of our available 1000. This gives the current design an extra 32 grams that can be

used for increasing the size of the solar sail or space-hardening some of the components.

Figure 7 - Satellte Cut-Away

3.3.3 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 on the

sides of the satellite, completing the satellite housing. Once the satellite construction has

been completed, it will be placed in the CubeSat P-Pod deployment mechanism. The

satellite will not become active until after the CubeSat has been released in the designated

orbit.

3.3.4 Solar Sail Deployment Summary

Once the 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, the four side panels containing the doubly reflective corner cube reflectors

are released from the frame. At 5 hours, 2 minutes after the satellite was inserted into its

orbit, the nitrogen will be released from the canister and inflate capillaries. Once the

capillaries have fully inflated, the hardening strips will begin to cure, making the sail

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

3.3.5 Weight and Volume Budgets The two most important regulations to be met in the CubeSat program are to

ensure that the total weight and volume of the satellite and the internal components does

not exceed the respective limits of 1 kilogram and 1000 cm3. In order to see how each of

the components fits in the weight and volume budget for the CubeSat, the following

sections explain each topic in detail.

The total weight allowed in the CubeSat can not exceed one kilogram, or 1000

grams. Each of the components to be used for the CubeSat has been broken down to

show how much each of the components weighs. Each of these components is then

placed into the pie chart in Figure 8 in order to show how each of the components fits

into the whole picture.

Figure 8 shows that the sail comprises most of the weight budget for the satellite.

This is reasonable since the sail is the most important component of the satellite. The

frame, corner cube reflectors, timer, and other components don’t take up much of the

weight volume, but are still vital components for the successful deployment of the solar

sail.

There are 42 grams remaining in the weight budget of the CubeSat. This means

that there are still 42 grams that can be used for maintaining environmental conditions for

the internal components of the satellite if necessary or for increasing the size of the solar

sail.

Figure 8 - Weight Budget for the Satellite

The total volume allowed for the housing and components of the CubeSat can not

exceed the designated 1,000 cm3. Each of the components to be used in the CubeSat has

been broken down to show how much volume each of the components will use. Figure 9

shows that the sail comprises most of the volume budget for the satellite. This is

reasonable since the sail is the most important component in the satellite. The frame,

corner cube reflectors, timer, and other components necessary for the successful

deployment of the sail combined take up about 25% of the volume.

There are 42 cm3 remaining empty in the volume budget of the CubeSat. This

remaining space can be used for increasing the size of the solar sail or bulking up some of

the internal components.

Figure 9 - Volume Budget for the Satellite

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 including solar

sail material selection, and stress analysis. A finite element modeling program was used

to analysis the effects of predicted stresses on the solar sail and aid in optimizing solar

sail thickness specification and hardening strip placement while modeling the impact of

the corner cube reflector arrays and satellite shell.

3.4.1 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 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 [6]. 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 10 below. Due to the unproven nature of solar

sails, this proposal was rejected [7].

Figure 10 - Halley’s Comet Solar Sail Design Concept [7]

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 [7]. As time went by, the demand for

inexpensive propulsion methods increased. In addition, advancements in solar sail

material technology greatly reduced the weight of solar sail designs, 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 [8]. Figure 11 features a

few of these new concepts. The Encounter satellite is a privately funded project (a) [9].

The Solar Blade Solar Sail (b), with 30-meter blades, is being developed by Carnegie

Mellon University [8]. The European Space Agency and German Space Agency have

combined resources in the development of the Star of Tolerance (c) [10]. Figure 11 (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 [11].

(a) (b)

(c) (d)

Figure 11 - Current Solar Sail Projects. (a) Encounter Satellite [9] (b) Solar Blade Solar Sail [8] (c) Star of Tollerance [10] (d) Cosmos I [11]

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 11, 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 [12].

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.

Figure 12 (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) (b)

Figure 12 - Solar Sail Material Layers: (a) Layers of Conventional Solar Sail Material

(b) Layers of Solar Sail Material for this project

The solar sail that will be used for this project 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. This satellite will be 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 using double-reflective solar

sail material, because there is no need to differentiate which side is facing the Sun if

double reflectivity is assumed. To ensure that the missing thermal layer does not cause

thermal problems with this solar sail design, thermal stresses will be discussed in the

thermal loading portion of the finite element analysis section of this report.

3.4.3 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 is 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 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.

?? 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.

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

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

The following list describes the material evaluation 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.

3.4.4 Aluminized Mylar The criteria outlined in Section 3.4.3 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) [13, 14].

?? 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 [14].

?? UV Life. With respect to the other solar sails, AM has an average UV life [5].

The duration will be within the constraint limits.

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

section 3.4.3 for solar sails materials:

?? Density. The AM sample to be used by PaperSat will have a thickness of 6

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 – Model Description The completion of the material selection process marked the beginning of the

finite element analysis. ABAQUS Explicit was used to assist in the modeling. The

analysis was limited to the fully deployed satellite configuration. The following table

summarizes all components integrated into the finite element model:

Table 1 - Summary of Elements Used

Component Element Type Description

Solar Sail Material

m3d4r 3D four node membrane elements with reduced integration – 2D elements in 3 space

Corner Cubes *mass A rigid body point mass. Capillary elements close to the point were stiffened to simulate the connection

Capillaries b31 3D 2 node beam elements – one dimensional elements in 3 space

Hardening Strips

b31 Same as capillaries, but smaller cross sectional area and different stiffness

Middle Components

*mass A rigid body point mass.

The mesh of the finite element model is shown in Figure 13. The solar sail

membrane elements are visible, and a circular hardening strip can be seen between two of

the membrane element boundaries. The capillaries and the remaining hardening strips

are located along the membrane element boundaries and cannot be seen. Because the

corner cube reflectors and the middle components are points, they are not visually present

in the FE model.

Figure 13 - Solar Sail Finite Element Mesh

In addition to representing the geometry of the deployed solar sail, the finite

element representation also models the following properties:

?? Young’s modulus

?? Poisson’s ratio

?? Yield Strength

?? Ultimate Strength

?? Conductivity

?? Density

Since the hardening strips are made of such an exotic material, PaperSat was

unable to locate a complete set of material properties. Since the hardening strips were

developed for the purpose of reinforcing the solar sail structure, it was assumed that it

had higher stiffness than the solar sail material. The other material properties were

assigned default values by the ABAQUS program. However, the hardening strips are

structural components, and an adequate estimation of the stiffness is inputted. The

effects of the rest of the default values should be negligible the small volume with respect

to the solar sail is taken into account.

3.4.6 Finite Element Analysis Results

The resulting output produced a large amount of data including deformations 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. The initial goal of the finite element simulation was to

use the model as a design tool to aid in determining solar sail geometries. Since PaperSat

completed this project goal early, a limited preliminary structural analysis of the solar sail

was performed.

ABAQUS Explicit models structures in a dynamic environment. All tests were

conducted in only a .5 or 1 second time duration. Each successful ABAQUS rendering

generated between 10 to 20 megabytes of data and took up to 12 hours to render.

Because of the massive amount of data generated, there will be no raw data presented in

this report. Instead, results and observations will be included in this report. The full

time history of this simulation fully animated plots is located the CD included in the

PaperSat design package.

Design Results

Figure 13 shows a schematic of the final solar sail in the fully deployed mode.

The finite element simulation served as a tool for determining the final configuration.

Through running the FE model under several different thicknesses for the solar sail, a

minimal thickness of 6 µm was deduced. This thickness both conserves weight and

retains strength. In addition, several hardening strip configurations were tested in the FE

script. The configuration shown in Figure 10 shows the best solution, which produced

the least amount of deflection, minimized amount of material, and maintained simplicity

for ease of manufacturing.

Figure 14 - Final Deployed Solar Sail Configuration

The diameter of the circumferential capillary was also minimized with the aid of

finite element analysis. The CubeSat was subjected to a load parallel to the plane of the

solar sail along a concentrated area along the capillary. The magnitude of the load was

500000 times greater than the theoretical maximum thrust of the solar sail, or

approximately .5 Newtons. The diameter of the capillary was then incrementally

minimized until visible deflection was observed. The value for this diameter was then

rounded up to the nearest “convenient” number so that it is easier to manufacture.

Preliminary Analysis Results:

After the final solar sail configuration was determined, a limited preliminary

analysis was performed. All tests contain a 90 µN distributed load applied perpendicular

to the surface of the solar sail. Since the model simulates dynamic conditions, the load is

applied as a .1 second ramp function. The following pages describe the scenarios and

results of this analysis.

Test 1: Thermal Loading

In addition to stresses acting on the sail surface due to the light collisions, stresses

due to the increased temperature are acting on the sail. The first test imposes a 1400

w/m2 flux on the sail [7]. The flux is allowed to heat the sail for 1 second before the

distributed load acts on the sail. Figure 14 shows the final time step of this simulation,

showing a maximum deformation of approximately 1.5 mm.

Figure 15 - Thermally Coupled Loading on the Solar Sail

Test 2: No Thermal Loading

In order to isolate the effects of thermal stresses, another test was performed in

the finite element environment without a heat flux. With exception to the heat flux, the

conditions in the first test were exactly the same. Figure 15 shows the final time step for

this test. The maximum deflection for this test is of the same order of magnitude as the

thermally loaded test – 1.5 mm.

Data files were accessed to clarify the difference between the non-thermal and

thermal cases. The data shows a disparity of only 5 - 9% between the two cases

(depending on which node is measured). Additionally, the thermal case requires

approximately 6 hours to fully render, whereas the non-thermal case requires less than 2

hours. Considering that little accuracy is gained in the thermal case under a gross cost

penalty, further analysis will not include thermal effects.

Figure 16 - Non-Thermally Loaded Solar Sail

Test 3: Parallel Loading

A load applied on the edge of the solar sail directed parallel to the sail is a “worst

case scenario.” Although unlikely, this loading is applied in a direction that offers little

resistance to compression. A concentrated load over a finite area was applied to the sail

parallel to the solar sail in addition to the perpendicular load. The magnitude of the

parallel load is .5 Newtons. Figure 13 shows that the maximum deflection in this case is

about 2 mm. Most importantly, no dents can be seen on the figure.

Figure 17 - Parallel Loading on Solar Sail

Test 4: Unevenly Distributed Load

The purpose of this test is to illustrate the versatility of the finite element analysis.

In this test, an additional ramp load of 90 µN is applied on a 1/8th portion of the solar sail,

as shown in Figure 18. The resulting deflection plot maintains a reasonable amount of

rigidity, with a maximum deflection of 5.3 mm.

Figure 18 - Unevenly Distributed Load of Solar Sail

Test 5: Entering Direct Sunlight

The final test simulated the solar sail entering direct exposure to the Sun from the

penumbra of the Earth. An initial distributed load of 45 µN is applied to the entire sail.

After .5 seconds, a ramp load of an additional 90 µN is applied to the top half of the solar

sail. The maximum deflection observed in this simulation was approximately 7 mm.

3.4.7 Propulsion Analysis Conclusions

The following list summarizes the geometry of the solar sail, which was

determined with the assistance of finite element modeling:

?? Thickness: 6 µm

?? Solar sail area: 100 m2

?? Number of hardening strips: 7

?? Capillary diameter: .25 inches

The following list summarizes the results of the finite element analysis (using

ABAQUS Explicit) performed on the CubeSat in its fully deployed mode:

?? The finite element model successfully integrated all solar sail components.

?? Thermal coupled stresses were modeled in the ABAQUS finite element. The cost

of rendering a thermal model is far greater than the added accuracy. Thermal

modeling should only be used when accuracy is essential.

?? No yielding was observed on all tests conducted on the solar sail. All deflections

were less than 1 cm, which constitutes an adequately rigid solar sail.

?? The finite element model will serve as a good tool for future analysis of this

satellite design. One of ABAQUS Explicit’s strengths lies in its capability to

model crack propagation and imperfections. It is recommended that this analysis

be performed to determine how much collision damage the sail could endure.

?? More detailed material properties for the hardening strips is required to obtain a

more accurate model of the satellite.

4.0 Orbital Trajectory Analysis

4.1 Background and Motivation

An accurate model of a 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. From an

orbital mechanics standpoint, solar sail performance is measured by thrust, drag, and

stability. The purpose of this orbital trajectory analysis is to better understand how thrust

can influence solar sail performance. Drag would definitely effect the satellite due to its

huge frontal area (100 m2) and stability would also be a factor near the orbit perigee.

Since drag and stability are not major concerns for this project and can be greatly

influenced with the presence of an attitude control system, they will not be modeled in

this simulation. The purpose of this project is to measure the thrust produced by a solar

sail and the most import reason that the satellite’s orbit must be simulated is that the

comparison of the observed satellite’s orbit with the orbit simulation allows the thrust

generated by the solar sail to be measured.

Many forces act on a satellite that is in orbit around the Earth. To simulate an

orbit accurately, gravitational forces must be modeled as a foundation for applying other

perturbing forces. Newton’s Law of Gravitation for two bodies predicts how a satellite

would orbit if the gravitational attraction between the satellite and the Earth was the only

force to act on the satellite. 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 Physics Models and Simulation Techniques

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 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. Umbra and Penumbra effects will also be considered. Refer to Figures 19 and

20 (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 through the

North Pole. The coordinate system isn’t rotating with respect to the earth, and the Earth’s

rotation is not considered in the simulation.

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 19 shows the position vectors between each body.

Figure 19 - Position Vector Schematic

Including the Sun, Earth, Satellite and Moon Positions (left to right)

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 15. The algorithm can also be found in the Matlab code SPV in Appendix D.

m? - Position vector from Earth to Moon.

The Moon position vector describes where the Moon is relative to the earth at any time. It is calculated using an algorithm from Reference 15. The algorithm can also be found in the Matlab code SPV in Appendix D.

2r?

- Position vector from Sun to satellite. srr 12

?????

This 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.

Figure 20 - Sail Normal Orientation in the ECI Coordinate System [16]

Figure 20 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:

tt?

?? ??? 0)(

tt?

?? ??? 0)( 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(sin[

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

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

SN

?

4.2.2 Newton’s Law of Gravitation

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 19 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.

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 15 and 16)

4.3 Solar Radiation Pressure 4.3.1 How Solar Radiation Pressure Creates Thrust

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” [5].

Figure 21 - Incidental and Reflected Light and Force Vectors Acting on the Sail

Figure 21 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 [17].

)(cos2cos21(AcS

T 22r ???

???? ??????

? (7)

rS The first is the power output of the sun. The sun emits 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 c2, the speed of light squared.

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.

? = 2N

2N

rS

)rScos(a??

???

Figure 21 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

The CubeSat program is expected to launch a LEO to GEO, elliptic orbit mission

in the near future. The high altitude of the orbit will benefit observation, and tracking of

the satellite. The CubeSat 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 are listed below and are shown in Figure 22.

Also note that the simulated orbit has no inclination, argument of perigee, or right

ascension. These elements were reduced to zero for simplicity. The Matlab code for

calculating these initial conditions is in Appendix D.

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 i = 0° w = 0° ? ????°

Figure 22 - Obit Diagram

Sun Track

Moon Track

Apogee Ra – GEO circular Va – Lowest vel.

Perigee Rp – LEO circular Vp – Highest vel.

a

4.5 Umbra and Penumbra Effects The effects of the Earth blocking the Sun’s light from the satellite occurs in a

region called the umbra. This region behaves similarly to a lunar eclipse, when the moon

blocks the Sun’s light from striking certain parts of the earth. When the satellite passes

into the umbra, no sunlight can reach the sail to generate thrust. Therefore, it is necessary

to account for umbra effects to properly model sail thrust. The penumbra is a region

where the amount of sunlight is greatly reduced due to Earth’s atmosphere. Thrust would

be reduced from maximum in the penumbra, but it’s effects are neglected in this

simulation. Figure 23 shows the geometry of the umbra and penumbra. Calculation of

when the satellite is in the umbra requires using several vectors. The Matlab code for

determining umbra affects can be found in Appendix D.

Figure 23 - Earth's Shadow

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 program 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.

4.6 Simulation Results 4.6.1 Introduction to Plot Information: Two-Body Problem

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 24. 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

Figure 24 -Two Body Orbit

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 for the purpose display

within the figure. Figure 25 is a close-up of the orbit at apogee. It has a maximum radius

at apogee of 10.5?104 km.

Figure 25 - Close up of Two-Body Orbit at Apogee

4.6.2 Sun and Moon Perturbations: Four-Body Problem

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

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

body orbit. Figure 27 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 26 - Four-Body Problem without Thrust

Figure 27 - Close Up of Four Body Problem without Thrust

4.6.3 Thrust as a Perturbing Force: Four-Body Problem with Thrust

Figure 28 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.

Figure 28 - Four Body Problem with Magnified Thrust

4.6.4 Displaying Thrust: Non-Rotating Thrust Vectors Displaying the thrust vector that is applied to the satellite as it orbits was

accomplished using a Matlab command called quiver3.m. This command shows the

thrust vector (T?

) at different position vectors ( 1r?

) of the orbit. In Figure 29, you can see

the thrust vectors as blue arrows pointing to the right. The sail is given constant attitude

in the positive x-direction so that the thrust is always in the same direction. Umbra

effects are not included.

Figure 29 - Orbit with Thrust Vector for a Constant Sail Attitude

4.6.5 Dynamic Thrust: Rotating Thrust Vectors Figure 30 shows how the thrust vector changes direction with time. Since the

thrust vector is rotated in the xy-plane only (angle ? and rate?? ), the thrust vector is

always in the plane of the orbit.

Figure 30 - Rotating Thrust Vector

4.6.6 How Thrust Can Change an Orbit: Magnified Thrust Vectors Magnifying the thrust is accomplished by increasing the power output of the sun.

By doing this, it can be seen how thrust changes an orbit. Figure 31 shows a magnified

thrust vector. Thrust is always pointed along the positive x-axis. The effects of the thrust

are now obvious. Each elliptical orbit has rotated around the earth (clockwise due to the

pos. x-dir. of thrust). This is the equivalent of a changing argument of perigee (?? ).

Again, the thrust vector was rotated only in the xy-plane. Since the orbit is also in the xy-

plane, no out-of-plane forces occur. This is proven in Figure 32, a side view of the same

orbit. If out-of-plane forces were at work, an inclination change would be observed.

Figure 31 - Magnified Thrust Vector

Figure 32 - Magnified Thrust Vector Side View

Figure 33 shows a magnified thrust vector that is also being rotated in three

dimensions (? , ? , ?? ,

?? ). Here forces act very dynamically on the system. In-plane

forces change orbital elements such as argument of perigee and semi-major axis. Out-of-

plane forces change the inclination of the orbit, as can be seen in Figure 34.

Figure 33 - Magnified Thrust Vector with 3D Rotation

Figure 34 - Magnified Thrust Vector with 3D Rotation (side view)

4.7 Measuring Thrust

Once the solar-sail-propelled satellite has been tracked, 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.

5.0 Schedule

Table 2 outlines the deliverables the contractor will receive from PaperSat

engineering this semester. The completion dates associated with these items are also

indicated.

Table 2 - Contract Deliverables Item to be Delivered Date Delivered Status Proposal for Contract 10/03/01 Completed Presentation for the Departmental Visiting Committee 10/11/01 Completed First Preliminary Design Review Presentation 11/02/01 Completed First Preliminary Design Review Formal Report 11/12/01 Completed Second Preliminary Design Review Presentation 12/05/01 Completed Second Preliminary Design Review Formal Report 12/12/01 Completed Orbital Trajectory Simulation 12/12/01 Completed Picosatellite Model 12/12/01 Completed Project Poster 12/12/01 Completed Project Records 12/12/01 Completed

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

In addition to the deliverables listed in Table 2 PaperSat has established additional

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

chart included in the Appendix C 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 investigated the solar sail material,

solar sail deployment, and corner cube reflector integration. The project poser and

records have also been submitted with this final design review.

6.0 Management Organization

To ensure that engineering tasks were appropriately assigned, and design conflicts

and issues could be resolved efficiently PaperSat adopted a detailed management

structure.

6.1 Company Management Structure

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

systems integration branch. The Figure 35 shows how the branches are divided.

System Design Branch Systems Integration Branch

Figure 35 - 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 was only active

until PDR1 is submitted. After PDR1 was complete, the systems integration branch

became active so that the design could be further refined for construction purposes. Once

the systems integration branch produced PDR2, the contract requirements were fulfilled.

Table 3 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.

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.

Table 3 - 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.

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.

7.0 Project Budget 7.1 Budget Item Description 7.1.1 Personnel Budget Description

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

employee is listed below:

Team Member Rate Hours Daniel Parcher $26.0 / hr* 165.0 Taffy Tingley $24.5 / hr* 134.5 Paul Mears $24.5 / hr* 130.0 Phillip Hempel $24.5 / hr* 116.0 Dr. Cesar Ocampo (Orbital Simulation Consultant) $52.0 / hr* 009.0 *This number does not include withholdings for Tax Purposes 7.1.2 Materials 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 cost for the corner cube reflectors is

estimated at $6000, but the corner cube reflector arrays may be donated. The RDAS timer

will cost $250 and the batteries will cost $300. The cost for the frame and nitrogen

canister is estimated to be $500. The total estimated cost for materials and electronics is

$7050.

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 and will be conducted by CalPoly.

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.

7.1.5 Implementation Costs / Manufacturability

There will be little implementation cost for this project. A company wishing to

test their solar sail design will manufacture the sail. The only cost involved with

implementation of the sail will be the cost of folding it in the proper method for

deployment. The compressed nitrogen will be purchased and only requires fastening to

the satellite shell. The satellite timer, batteries and corner-cube reflectors will also be

purchased fully assembled and will need only to be fastened to the satellite shell. Break-

away joints for the shell walls, wiring for the timing system, and duct work for the

nitrogen canister will require a minimum of effort and cost to implement. The incidental

costs of manufacturing should stay below $1000.

Once the satellite is constructed, it will need to be tested for structural stability

under vibration. These tests will be conducted at Calpoly. The satellite will need to be

transported to the launch site. The cost of transportation should be minimal and will

possibly be donated by the University of Texas, especially if the launch site is within the

United States. The costs for launching the satellite are already incorporated into the

budget. Ground station time for laser ranging of the satellite will be required, that time

will be provided from the ILRS after the application for laser ranging support for this

project has been submitted. Finally, student volunteers will need to perform post-

processing of the data received from the ground station.

7.2 Budget Summary

The Table 4 contains a complete summary of the predicted expenses for the

PaperSat Engineering company’s work on this project.

Table 4 - Proposed Budget Expense Item Predicted

Expenses (dollars)

Expenses Realized (dollars)

Personnel (based on an estimated 150 hrs. worked, 14 hrs. for consultants) 15,653 14,080 Materials / Electronics 5,000 7,050 Testing 2,000 2,000 Launch 50,000 50,000 Total 72,653 73,130

It is easy to see from the Figure 36 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/ ElectronicsTesting

Launch

Figure 36 - Analysis of Proposed Budget

7.3 Cost Overrun Analysis

The corner-cube reflector arrays will be of custom design. The estimated price for

the reflectors is $6000, based partially on the glass reflector design in the Banner

Engineering products catalog. The estimate is conservative for this design, but hidden

costs of construction of these arrays may cause the price of the reflectors to increase

above the estimated value.

The launch cost is subject to change for the CubeSat program. This not something

that PaperSat can control and could increase the cost of this project substantially. The

launch cost has the capability to change the cost of this project far more easily than any

other expense.

8.0 Sustainability

There are no recourses aboard the spacecraft that must be replenished. The

spacecraft design relies on nitrogen and electricity for deployment, these resources will

not be replenished during the mission, but the satellite should not need these resources

once deployment has been completed. These non-replenishable resources need to last for

five hours after the satellite is inserted into its LEO to GEO orbit.

Once the satellite is deployed it needs only to stay in its deployed configuration to

provide empirical solar sail thrust data. However, the satellite needs only to remain in this

configuration for a few orbital periods so that thrust can be measured, if it is damaged

after that time, or re-enters the earth’s atmosphere, it will have already fulfilled its

mission.

8.0 Social and Political Issues

This space mission will has several social and political issues associated with it.

This satellite design will test an untested type of space propulsion, a type of space

propulsion that has the capability to change the possibilities of spacecrafts travel. The

mission will enhance the United States’ presence at the forefront of space propulsion

technology.

8.1 Environmental impact

The environmental impact of a satellite operating a solar sail is almost non-

existent. The satellite will require a rocket to launch it to orbit. The launch does have the

potential to impact the environment, but not significantly. This project should be

considered environmentally safe.

The project does, however have the potential to impact the environment of the

University of Texas substantially. Should this project be implemented, the university will

receive attention from the media. Since no previous spacecraft have relied on solar

power, the university would very likely receive a substantial amount of publicity.

8.2 Ethics, Health and Safety There is one ethical, health and safety issue concerning this project. This satellite

could remain in orbit for an extended period of time. If the satellite continues to orbit the

earth for a long time after it has completed its mission, it will pose a collision threat to

other orbiting spacecraft. The solar sail should be very easy to see and track, so it is likely

that other spacecraft will be launched in such a way that they will not come into contact

with this satellite. It is possible, however, that the solar sail, effectively space debris after

it has completed its mission, will collide with another satellite.

The solution to this issue is to ensure that other space missions are aware of this

satellite and can avoid it until the solar sail powered craft has the opportunity to re-enter

the earth’s atmosphere.

9.0 Future Work The corner cube reflector specifications must still be determined. The glass corner

cube reflectors designed for this satellite are most likely within specifications and can be

used as designed. However, the reflectivity and target area requirements of the ILRS are

not yet known as they require a laser ranging support application which must be

reviewed. The ILRS offered by McDonald observatory is funded by NASA and must

evaluate each mission to be supported on a case by case basis. If the project, though the

University of Texas, is determined to be of worthy scientific value, then the laser ranging

services available for use on this particular project can be discussed. For example,

McDonald observatory my have the means to perform laser ranging with satellites that

have relatively low reflectivity corner cube reflector arrays, but not consider the project

of significant scientific value to spend a significant portion of their budget on laser

ranging for this mission. The amount of compensation they will require, if any and the

specifications of the corner cube reflectors they require can therefore not be completely

determined until a mission application has been submitted and reviewed. The glass corner

cube reflector designs will, however, most likely be sufficient for use with the ILRS

system.

A detailed thermal analysis of the satellite must also be preformed so that the

internal component specifications prescribed. If the internal components currently

selected do not meet the thermal requirements then environmental conditioning can be

added to the satellite design, or new components should be selected.

Finally, an analysis of crack propagation for the solar sail, in the event that the

sail is damaged, would be useful for determining how well the solar sail can handle small

particles it may encounter.

10.0 Conclusion

PaperSat Engineering has designed a CubeSat based solar sail testing platform.

The satellite design incorporates 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 orbital perturbations of the satellite will be measured periodically

from laser positioning supplied by the International Laser Ranging Service. 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.

11.0 References 1. The University of Texas, “McDonald Laser Ranging Station”,

http://almagest.as.utexas.edu/~rlr/mlrs.html Site Accessed November 26, 2001 2. Banner Engineering Corp., “Retroreflector Products”

http://www.bannerengineering.com/products/accessories/retroreflectors/ Site Accessed September 17, 2001

3. Aerocon Systems Co. “RDAS Flight Electronics” http://www.fortunepaint.com/aerocon_interim/rdas.htm/ Site Accessed September 17, 2001

4. Ultralife Batteries, “Lithium Ion Polymer Batteries” http://www.ultralifebatteries.com/product-display.asp?ID=39 Site Accessed November 7, 2001

5. [1] Wright, Jerome. Space Sailing. Gordon and Breach Science Publishers, Langehorne, Pennsylvania 1992., pp. 2

6. Faust, Jeff. “Solar Sail Scheduled to Launch Early Next Year.” Spaceflight Now. August 23, 2001. http://www.spaceflightnow.com/news/n0108/23cosmos/ site accessed 1 Nov 2001.

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

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

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

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

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

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

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

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

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

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

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

Appendix A – PaperSat Team Appendix B – CubeSat Frame Appendix C – Orbital Simulation Code Appendix D – PaperSat Schedule

cubesat based solar sail testing platform final design...

Documents