CubeSat Based Solar Sail Testing Platform Final Design Review

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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 h
ave 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 b
y
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 Desi
gn 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 Ov
erview
................................
.............................

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

New
ton’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
ii
i

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 Sched
ule

................................
................................
................................
......................

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 Sustainab
ility
................................
................................
................................
...............

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

F
igure 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
So
lar 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

Fig
ure 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



Page
1

1.0 Introduction


PaperSat Engineering has designed a picosate
llite 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 picosatellit
e 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 Prob
lem 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 f
rom
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
-
processin
g 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
configura
tion, 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
sola
r 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


Page
2

certain materials reflect light, how that property can be used to navigate a sp
acecraft, 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 import
ant 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, Pap
erSat 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 accel
eration provided by energy transferred from
light striking the surface of the sail to the spacecraft can be measured.





Page
3

2.0 Design Factors



To achieve the goals outlined in the previous section, it was necessary to adopt
several design constraints. The r
estrictions 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 satelli
te 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.



Page
4



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 Comp
onent 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 evaluatio
n 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 s
ail 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 mus
t 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.



Page
5



Cos
t
. 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.




Page
6


3.0 Sat
ellite 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 s
ystems 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

-

Sat
ellite Systems




Page
7


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 hard
ware 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 ge
ometrically
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 t
ravel 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


Page
8

satellite in three
-
dimensional space can be determined. This technique requires that the
satellite position be known approximately be
fore 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 ea
sy 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 a
board 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 sa
tellite 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 ear
th, 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 recei
ved 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 ax
is 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


Page
9

sail is facing the su
n. 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. Optica
l 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 m
easurements 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 satelli
te 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 gr
ound station should be adequate for these


Page
10

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 th
e 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


Page
11

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 time
s be exposed to direct sunlight.
Banner Engineering has one design of reflector array that can operate at 900
o
F.
Unfortunately corner cube reflector models with high operational temperatures have
lower reflectivity. For final determination of the corner cu
be 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.



Page
12


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 specifica
tions. 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 approxim
ately 44 grams, require a total of approximately 77
cm
3

and will be 41 mm in diameter. The estimated total price for the corner cube
reflectors through Banner Engineering is $6000.




Page
13

3.2 Electrical System


As previously stated, the necessary electrical sys
tems 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 v
oltages 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 mm
2

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.



Page
14

Ult
rallife polymer lithium ion batteries were selected for powering the timing
system
. Figure 5 sh
ows 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
-
20
o

C and +60
o

C. Three of these batteries will require roughly
35x62mm
2

x 12mm of volume and weight roughly 45 grams.





Page
15





3.3 Mechanical Systems and Deployment


The satellite structural d
esign 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.

Th
e 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
compress
ed 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 necess
ary 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 satell
ite 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 weig
ht
budget. This section ends with a walk
-
through of the entire installation and deployment
process.




Page
16

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 Univers
ity. 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 s
witch will be placed in a corner of the satellite and,
including wires, should consume 2cm
3

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 s
witch 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 swi
tch 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 deploy
ment. The timing system will be as described in S
ection 3.2
. Since the
final timing system has not been selected, the current estimate for the space and weight of


Page
17

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 Cube
Sat 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 cm
3

of space.


Frame

The frame of PaperSat is wh
at 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 c
ross
-
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 cm
3
. The frame is also the
base upon which the corner cube reflector panels are to be placed.




Page
18


Corner
-
Cube Reflector Panels

The corner cube reflector panels are the basis for the ground
-
based tracking
system that will be em
ployed 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
cm
3
. 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. Th
e 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
m
2

(5.64 m radius), and will have a final weight of approximately 720 grams. For
packing into the satellite, the
so
l
ar 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


Page
19

to the ends of the sail. Employing this folding method, the packed solar sail should take
u
p 700 cm
3
.




Capillaries


The capillaries being used for this project are responsible for c
ontaining 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 tub
es 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 releas
ed, the sail will first separate
the two arms of the sail folded into the center, followed by the full expansion of the solar
sail utilizing capillaries place
d

in the middle and along the edges of the sail. The
capillaries will be inflated with the Nitrog
en at a rate of 3.5 cm
3

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 Nitrog
en 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
cm
3
. The volume used to specify internal satellite arrangement

will be 90 cm
3

and the


Page
20

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 rel
eased from the canister at 3.5 cm
3

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


Page
21

for the PaperSat program. Hardening strips must be add
ed 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 subs
tance 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. Th
e 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 ha
s 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 bat
teries 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 fold
s coming away from the canister. Using the
components discussed above, the satellite will have used 958 of the available 1000 cm
3
.
This leaves an available 42
cm
3

that can be used to maximize the size of our solar sail or
space
-
harden some of the compone
nts. The total weight of the components is 968 grams


Page
22

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 th
e 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
s
atellite will not become active until after the CubeSat has been released in the designated
orbit.




Page
23

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 counti
ng 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 b
e 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

Weigh
t 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 cm
3
. In ord
er 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 th
at 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


Page
24

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 cm
3
. 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
reasonab
le since the sail is the most important component in the satellite. The frame,


Page
25

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 cm
3

remaining emp
ty 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







Page
26


3.4 Propulsion S
ystems


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 modeli
ng 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 attem
pt 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 unp
roven nature of solar
sails, this proposal was rejected [7].



Page
27



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
in
expensive 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 e
merging. 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 satellit
e 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


Page
28

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 differ
ent 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


Page
29

at only 5 grams per square meter. Th
e 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 conve
ntional 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 t
ypically 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 laye
r, another reflective layer will be inserted. The primary purpose for this
modification is to remedy modeling and trajectory problems associated with having no


Page
30

attitude control system. This satellite will be unable to control whether or not the
reflectiv
e 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
-
refle
ctive 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 wil
l 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 s
olar
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 f
acing 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.



Page
31



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 sa
il
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 sa
il 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 minimizin
g 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. Spec
ific costs were unavailable during the selection process.
However, including this criterion eliminates inherently expensive material
candidates such as gold or silver.





Page
32


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 refl
ective
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 requ
ire 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 resp
ect 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 sa
mple to be used by PaperSat will have a thickness of 6
microns and a weight per area of 1.38 g/m
2
, which is the lowest weight per area of
all solar sail materials in the database.



Page
33



Strength
. The yield stress of the AM to be used in PaperSat is 172 GPa, w
hich 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 f
ollowing 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 integrat
ion


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 h
ardening 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


Page
34

corner cube reflectors and the middle componen
ts 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



Page
35

Since the hardening strips are made of such an exotic material, PaperSat was
unable to locate a complete set of material properties. Since the hard
ening 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 El
ement 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 ca
n 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 t
ime 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 obse
rvations will be included in this report. The full


Page
36

time history of this simulation fully animated plots is located the CD included in the
PaperSat design package.


Design Results


Figure 1
3

shows a schematic of the final solar sail in the fully deploye
d mode.
The finite element simulation served as a tool for determining the final configuration.
Through runn
ing 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 Sa
il Configuration




Page
37


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 ma
gnitude 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 dia
meter 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/m
2

flux on the sail [7]. The flux is allowed to heat th
e sail for 1 second before the
distributed load acts on the sail.
Figure 1
4

shows the final time step of this simulation,
showing a maximum
deformation
of approximately 1.5 mm.



Page
38


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 sa
me.
Figure 1
5

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


Page
39

hours. Consid
ering 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
p
arallel 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.



Page
40


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 1/8
th

p
ortion of the solar sail,
as shown
in Figure 1
8
.

The resulting deflection plot maintains a reasonable amount of
rigidity, with a maximum deflection of 5.3 mm.



Page
41


Figure
18

-

Unevenly Distributed Load of Solar Sail



Test 5: Enteri
ng 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 ha
lf 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 elem
ent modeling:



Page
42



Thickness:



6 μm



Solar sail area:



100 m
2



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 b
e 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 an
alysis 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.



Page
43


4.0 Orbital Trajectory Analysis


4.1 Background and Motivation


An accurate model of a satellite in orbit around the Earth is a useful too
l 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 thrus
t, 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 m
2
) 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 meas
ured.

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 s
atellite
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 sh
ape 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.


Page
44


4.2 Physics Models and Simulation Techniques

The theory behind the simulation is based on the prin
ciples 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 Su
n, 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 simu
lation 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 effect
s will also be considered. Refer to
Figures
19

and
2
0

(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 th
e 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
t
he
North Pole. The coordinate system isn’t rotating

with respect to the earth
, and the Earth’s
rotation is not considered in the
simulation.



Page
45

Position Vectors


To account for the gravitational forces of the major gravitational bodies acting on
the satell
ite, it is necessary to know where these bodies are with respect to the satellite
.
Figure 1
9

shows the position vectors between each body.




Figure
19

-

Position Vector Schematic

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



-

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.



-

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 1
5
. The algorithm can
also be found in the Matlab code SPV in
Appendix D
.



-

Position vector from Earth to Moon.




Page
46

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
.



-

Position vector from Sun to satellite.





This vector is used to calculate the direction and magnitude of the gravitational
force between the Sun and the satellite. Ve
ctor

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.



-

Position vector from Moon to sa
tellite.




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.



-

unit vector from c
enter 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 a
tmospheric drag forces.





Page
47



Figure
20

-

Sail Normal Orientation in the ECI Coordinate System [1
6
]


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
and
. Definitions of
,
, and
follow:






where



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




= angular velocity of the sail normal.


= initial angle from the xy
-
plane to the sail normal vector a
t time t
0.



= angular velocity of the sail normal.





Page
48




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 1
9

shows the Earth, the satellite, their masses, and the vector from
the Earth to the satellite (
). Newton’s Law of Gravitation for the two
-
body problem
takes

the form:










(1)


where



km
3
/kg
-
s
2


The equation is negative because the force acts in the direction opposite to
. To
simulate the orbit, acceleration vectors are used instead of
forces. The acceleration due to
the force of Earth’s gravity is:










(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 grav
itational constant:




km
3
/s
2



(3)


Equation (2) now becomes:











(4)



Page
49


Equation (4) is the equation of Newton’s Law of Gravitation for the two
-
body problem in
terms of acceleration. This is the form use
d to calculate the position vector

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