Solar Sail
Department of Aerospace Engineering and Mechanics
AEM 4332W – Spacecraft Design
Spring 2007
2
Team Members
3
Solar Sailing:
4
Project Overview
5
Design Strategy
6
Trade Study Results
Orbit
Eric Blake
Daniel Kaseforth
Lucas Veverka
Eric Blake
Optimal Trajectory of a Solar Sail: Derivation of Feedback Control Laws
9
Recall Orbital Mechanics
• The state of a spacecraft can be described by a vector of 6 orbital elements.– Semi-major axis, a– Eccentricity, e– Inclination, i– Right ascension of the ascending node, Ω– Argument of perihelion, ω– True anomaly, f
• Equivalent to 6 Cartesian position and velocity components.
10
Orbital Elements
11
Equations of Motion
vr
nnrr
rr
v2^
2
^
2
^^^^
sinsincossincos rpprn
^
r
^
p
^^
rp
n
linesun
sail
= Sail Lightness Number = Gravitational Parameter
12
Problem: Minimize Transfer Time
1),,(2^
2
^
2
nnr
rr
rvuxH vvr
^
r
^
p
^^
rp
n
linesun
sail
^^^
353)(2))((2)(3 rnrnnnr
rrr
rr vrvr rv
^^
}max{ vv nn
By Inspection:
Transversality:
fttv
ttv npnr
rnpnr
r
2
^
22
^
2)()(
0
13
Solution
• Iterative methods are needed to calculate co-state boundary conditions.
• Initial guess of the co-states must be close to the true value, otherwise the solution will not converge.
• Difficult• Alternative: Parameter Optimization.
– For given state boundary conditions, maximize each element of the orbital state by an appropriate feedback law.
14
Orbital Equations of Motion
r
pTfSe
e
pr
df
dasin
)1(
222
2
e
p
rTf
p
rTfS
r
df
decos1sin
2
Wfp
r
df
di)cos(
3
Wfip
r
df
d)sin(
sin
3
f
p
rTfS
e
ri
df
d
df
dsin1coscos
2
12
2sin1cos1
f
p
rTfS
e
r
r
p
dt
df
)1( 2eap fe
pr
cos1
32
cosr
S sinsincos22r
T cossincos22r
W
),,( xgx
= Sail Lightness Number = Gravitational Parameter
15
Maximizing solar force in an arbitrary direction
^^^^
sinsincossincos rpprn ^^~~^~~^~
sinsincossincos rpprq
^
r
^
p
^^
rp
n
linesun
sail
Maximize:
qnnr
raq
2^
2
~
~
~2
tan4
tan893tan
Sail pointing for maximum acceleration in the q direction:
16
Locally Optimal Trajectories• Example: Use parameter optimization method to derive
feedback controller for semi-major axis reduction.
• Equations of motion for a:
r
pTfSe
e
pr
df
dasin
)1(
222
2
3
2cos
rS
sinsincos22r
T
fe
fe
cos1
sintan
~
fe
pr
cos1 )1( 2eap
2
~
~2
tan4
tan893tan
Feedback Law:
Use this procedure for all orbital elements
17
Method of patched local steering laws (LSL’s)
• Initial Conditions: Earth Orbit
• Final Conditions: semi-major axis: 0.48 AU inclination of 60 degrees
0
0
0
0
0
1
0tt
i
e
a
free
free
free
AU
i
e
a
tft
60
0~
48.0
18
Trajectory of SPI using LSL’s
Time (years)
19
20
Global Optimal Solution– Although the method of patched LSL’s is not ideal, it is a solution that is
close to the optimal solution.
– Example: SPI Comparison of LSL’s and Optimal control.
21
Conclusion
• Continuous thrust problems are common in spacecraft trajectory planning.
• True global optimal solutions are difficult to calculate.
• Local steering laws can be used effectively to provide a transfer time near that of the global solution.
Lucas Veverka
•Temperature
•Orbit Implementation
Optimal Trajectory of a Solar Sail: Orbit determination and
Material properties.
Lucas Veverka
24
Reflectivity Approximation• Reflectivity constant, r, negatively affects the
solar radiation pressure force.
– P is the solar pressure as a function of distance. – A is the sail area being struck by the solar radiation.– ui is the incident vector.– n is the vector normal to the sail.
• Emissivity and specular reflection neglected.• Assumed a Lambertian surface.
nnuPArf i22
25
Sail Surface Temperature
4
1
24
sun
solarsurface d
FT
• Fsolar is the solar flux.• α is the absorptance.• ε is the emittance.• σ is the Stefan-Boltzman constant.• dsun is the distance from the sun.
26
Transfer Orbits
• Objective:-Reach an orbit with semi-major axis of 0.48 AU and inclination of 60 degrees as quickly as possible.
• Investigated four possible orbits-Cold transfer orbit-Hot transfer orbit-Inclination first transfer orbit-Simultaneous orbit
27
Cold Transfer Orbit
• Advantages:– Very simple two-stage transfer.– Goes no closer to sun than necessary to avoid
radiation damage.
• Disadvantages:– Is not the quickest orbit available.
• Order of operations:– Changes semi-major axis to 0.48 AU.– Cranks inclination to 60 degrees.
• Time taken:– 10.1 years.
28
Cold Transfer Orbit
29
Hot Transfer Orbit
• Advantages:– Still simple with three-stages.– Is a much quicker transfer.
• Disadvantages:– Radiation is very intense at 0.3 AU.
• Order of operations:– Changes semi-major axis to 0.3 AU.– Cranks inclination to 60 degrees.– Changes semi-major axis to 0.48 AU.
• Time taken:– 7.45 years.
30
Hot Transfer Orbit
31
Inclination First Transfer Orbit
• Advantages:– Very simple two-stage transfer.– Avoids as much radiation damage as possible.
• Disadvantages:– Takes an extremely long time.
• Order of operations:– Cranks inclination to 60 degrees.– Changes semi-major axis to 0.48 AU.
• Time taken:– 20.15 years.
32
Inclination First Transfer Orbit
33
Conclusion
• Simultaneous transfer is too complicated with little or no real benefit.
• Inclination first transfer takes too long.• Hot transfer orbit is much quicker but submits
materials to too much radiation.• Cold transfer orbit is slower than the hot but
gets the equipment to the desired location safely.
• Choice: Cold transfer orbit!
34
Daniel Kaseforth
Control Law Inputs and Navigation System
36
Structure
Jon T Braam
Kory Jenkins
Jon T. BraamStructures Group:
• Primary Structural Materials
• Design Layout
•3-D Model
• Graphics
39
Primary Structural Material
Weight and Volume Constraints• Delta II : 7400 Series • Launch into GEO
– 3.0 m Ferring» Maximum payload mass: 1073 kg» Maximum payload volume: 22.65 m3
– 2.9 m Ferring» Maximum payload mass: 1110 kg» Maximum payload volume: 16.14 m3
40
Primary Structural Material
Aluminum Alloy Unistrut– 7075 T6 Aluminum
Alloy• Density
– 2700 kg/m3
– 168.55 lb/ft^3
• Melting Point– ? Kelvin
Picture of Unistrut
41
Primary Structural Material
• Density
• Mechanical Properties– Allowing unistrut design
• Decreased volume
• Thermal Properties– Capible of taking thermal loads
42
Design Layout
• Constraints– Volume– Service task– Thermal consideration– Magnetic consideration– Vibration– G loading
43
Design Layout
• Unistrut Design– Allowing all inside surfaces to be bonded to
• Titanium hardware
– Organization• Allowing all the pointing requirements to be met with
minimal attitude adjustment
44
Design Layout
• Large Picture of expanded module
45
3-D Model
• Large picture
46
3-D Model
• Blah blah blah (make something up)
47
Graphics
• Kick ass picture
48
Graphics
• Kick ass picture
49
• The blanks will be filled in soon
50
Trade Studies
• Blah blah blah
51
Why I deserve an “A”
• Not really any reason but when has that stopped anyone!
Kory Jenkins• Sail Support Structure• Anticipated Loading•Stress Analysis• Materials•Sail Deployment
53
Sail Sizing• Characteristic acceleration is a measure of
sail performance.
• Characteristic acceleration increased with sail size.
• Higher acceleration results in shorter transfer time.
• Sail size is limited by launch vehicle size and deployment power requirements.
Am
Pa
pso /
2
Amss /
54
Sail Support Structure
• Challenge: Design a robust, easy to deploy structure that will maintain sail shape.
• A 150 x 150 meter sail covers the same area as 5 football fields. (22,500 square meters)
• Solution: An inflatable boom structure based on the L’Garde design supports 4 triangular sail quadrants.
• Booms are deployed in pairs to minimize power consumption.
55
Heater: Raises boom temperature above glass transition temperature to 75 C.
Inflation gas inlet: booms are inflated to 120 KPa for deployment.
Cables attached to stepper motors maintain deployment rate of ~ 3 cm/s.
Once deployed, booms cool below glass transition temperature and rigidize.
Deployment cables retract to pull the sail quadrants out of their storage compartments.
To sail quadrant
To deployment motor
Step 1 Step 5
Step 4
Step 3
Step 2
56
Estimate Worst Case Loading
Assumptions:• Solar Pressure at 0.48 AU
= 19.8 µN/m^2.• Thin wall tube.• Sail quadrant loading is
evenly distributed between 3 attachment points.
• Isotropic material properties.
• Safety factor of 3.
Solar Pressure
P = 2/3 P_quadrant
57
Analysis of a Tapered Beam
Bending
Buckling
Shear
Hoop stress
(inflation pressure)
Section
Modulus
I
My
2
2
4L
EIPcr
Iy
VQmax
r
tP hoop
max
2
)(4
)(
L
xdAdBdA
txS
58
• Expected deployment loads of 20 N in compression dictate boom sizing.• Booms sized to meet this requirement easily meet other criteria.• Verified using laminate code that accounts for anisotropy of composite materials.
59
Boom Specifications
• Cross-ply carbon fiber laminate.• IM7 carbon fiber• TP407 polyurethane matrix, Tg = 55 deg C• Major Radius = 18 cm, minor radius = 10 cm.• Length = 106 meters.
Analysis of a Composite Laminate:
mmffL EVEVE 1
m
m
f
fT E
V
E
VE
][][ TzQ K
oK
60
Conclusions and Future Work
• Sail support structure can be reliably deployed and is adequately designed for all anticipated loading conditions.
• Future Work– Reduce deployment power requirement.– Reduce weight of support structure.– Determine optimal sail tension.
Attitude Determination and Control
Brian Miller
Alex Ordway
Alex Ordway60 hours worked
Attitude Control Subsystem Component Selection and
Analysis
63
Design Drivers
• Meeting mission pointing requirements
• Meet power requirements
• Meet mass requirements
• Cost
• Miscellaneous Factors
64
Trade Study
• Sliding Mass vs. Tip Thruster Configuration– Idea behind sliding mass
65
Trade Study
• Sliding mass ACS offers– Low power consumption (24 W)– Reasonable mass (40 kg)– Low complexity– Limitations
• Unknown torque provided until calculations are made• No roll capability
• Initially decided to use combination of sliding mass and tip thrusters
66
ADCS System Overview
• ADS– Goodrich HD1003 Star Tracker primary– Bradford Aerospace Sun Sensor secondary
• ACS– Four 10 kg sliding masses primary
• Driven by four Empire Magnetics CYVX-U21 motors
– Three Honeywell HR14 reaction wheels secondary
– Six Bradford Aero micro thrusters secondary• Dissipate residual momentum after sail release
67
ADS
• Primary– Decision to use star tracker
• Accuracy• Do not need slew rate afforded by other systems
– Goodrich HD1003 star tracker• 2 arc-sec pitch/yaw accuracy• 3.85 kg• 10 W power draw• -30°C - + 65 °C operational temp. range• $1M
– Not Chosen: Terma Space HE-5AS star tracker
68
ADS
• Secondary– Two Bradford Aerospace sun sensors
• Backup system; performance not as crucial• Sensor located on opposite sides of craft• 0.365 kg each• 0.2 W each• -80°C - +90°C
69
ACS
• Sliding mass system– Why four masses?– Four Empire Magnetics CYVX-U21 Step Motors
• Cryo/space rated• 1.5 kg each• 28 W power draw each 200 °C
• $55 K each• 42.4 N-cm torque
70
ACS
• Gear matching- load inertia decreases by the gear ratio squared. Show that this system does not need to be geared.
2
2
2170 (600sec)
20.00389
(10 )(0.00389 )
0.0389
ms
ms
m a
a
F ma kg
F N
71
ACS
• Three Honeywell HR14 reaction wheels– Mission application– Specifications
• 7.5 kg each• 66 W power draw each (at full speed)• -30ºC - +70ºC• 0.2 N-m torque• $200K each• Not selected
– Honeywell HR04– Bradford Aerospace W18
72
ACS
• Six Bradford micro thrusters– 0.4 kg each– 4.5 W power draw each– -30ºC - + 60ºC– 2000 N thrust
– Supplied through N2 tank
73
Attitude Control
• Conclusion– Robust ADCS
• Meets and exceeds mission requirements• Marriage of simplicity and effectiveness• Redundancies against the unexpected
Brian Miller
•Tip Thrusters vs. Slidnig Mass
•Attitude Control Simulation
75
Attitude Control
• Conducted trade between tip thrusters and sliding mass as primary ACS
• Considerations– Power required– Torque produced– Weight– Misc. Factors
76
Attitude Control
• Tip Thrusters (spt-50)– Pros
• High Torque Produced ~ 1.83 N-m• Low weight ~ 0.8 kg/thruster
– Cons• Large Power Requirement ~ 310 Watts• Lifetime of 2000 hrs• Requires a fuel, either a solid or gas
77
Attitude Control
• Attitude Control System Characteristics– Rotational Rate– Transfer Time– Required Torque– Accuracy– Disturbance compensation
78
Attitude Control
• Requirements– Orbit
• Make rotation rate as fast as possible
• Roll spacecraft as inclination changes
– Communications– Within Maximum Torque
• Pitch and Yaw Axis
~ 0.34 N-m
• Roll Axis
~ 0.2 N-m
M
mFzU
m – sliding massF – solar forcez – distance from cgM – spacecraft mass
79
Attitude Control
• Pitch and Yaw Axis • Rotation Rate = 0.144 rad/hr
~ 8.25 deg.
• Transfer Time = 5300s ~ 1.47 hrs
• Required Torque = 0.32 N-m
~ 98.8% of maximum produced
• Converges to desired angle
Slope = 0.00004 rad/s
Torque Req.
Transfer Time
80
Attitude Control
• Roll Axis • Rotation Rate = 0.072 rad/hr
~ 4.12 deg
• Transfer Time = 7000s ~ 1.94 hrs
• Required Torque = 0.15 N-m
~ 75% of maximum produced
• Converges to desired angle
Torque Req.
Slope = 0.00002 rad/s
Transfer Time
Power, Thermal and Communications
Raymond Haremza
Michael HitiCasey Shockman
Raymond HaremzaThermal Analysis
•Solar Intensity and Thermal Environment•Film material•Thermal Properties of Spacecraft Parts•Analysis of Payload Module•Future Work
Thermal Analysis and Design
-Raymond Haremza
84
Design Approach Strategy
85
Decision to take “cold” orbit
By taking longer to get to 0.48 AU, we in turn reduce the amount of design, analysis,
production time and weight.
86
Solar Sail Material and Thermal Analysis
87
Payload Panel Analysis
The Carbon-Carbon Radiator has aluminum honeycomb sandwiched between it, and
has thermal characteristics, Ky= Kx=230W/mK, and through the thickness Kz = 30W/mK which allows the craft to spread its heat to the cold side of the
spacecraft, but also keeping the heat flux to the electric parts to a minimum.
0.06
0.78
Material Properties
E 1.2e7psi
G 6.11e6psi
v 0.32
88
Spacecraft Heat Transfer Analysis
22
26
4
104
m
W
dflux
WattsAfluxQsun
KelvinA
QT
total
sunsurface
41
Solar Intensity vs Distance
0.00E+00
1.00E+03
2.00E+03
3.00E+03
4.00E+03
5.00E+03
6.00E+03
7.00E+03
4.80E-015.80E-016.80E-017.80E-018.80E-019.80E-01
Distance from Sun (AU)
So
lar
Inte
nsi
ty (
flu
x) (
W/m
^2)
89
Heat Transfer Analysis
A AfluxQsun
41
4
rad
sunsurf
surftotrad
Q
QT
TAQ
totA
Setting the heat fluxes together yields the surface temperature of the object based on
emmissivity, absorbitivity, size and geometry of the object.
90
Thermal Analysis of Payload Module
91
Thermal Analysis of Payload Module
92
Temperature vs Distance (Side of Payload Module)
100
120
140
160
180
200
220
240
260
280
300
4.80E-01 5.80E-01 6.80E-01 7.80E-01 8.80E-01 9.80E-01
Distance from Sun (AU)
Tem
pe
ratu
re (
K) 85 deg
80 deg75 deg70 deg65 deg60 deg55 deg
93
Temperature vs Distance (Top of Payload Module)
150
200
250
300
350
400
450
4.80E-01 5.80E-01 6.80E-01 7.80E-01 8.80E-01 9.80E-01
Distance from Sun (AU)
Tem
per
atu
re (
K)
0 incidence5 deg10 deg15 deg20 deg25 deg30 deg35 deg
94
Spacecraft Component Thermal Management
Notes: By using thermodynamics the amount of heat needed to be dissipated from the component taking into account its heat generation,
shape, size, etcetera. If the component is found to be within its operating range, the analysis is done, if not a new thermal control must be added or
changed.
95
Thermal Analysis of Antenna
96
Antennae Operating Temp (-373 to 373K) vs Distance With White Paint Reflector
250
270
290
310
330
350
370
390
4.80E-01 5.80E-01 6.80E-01 7.80E-01 8.80E-01 9.80E-01
Distance From Sun (AU)
Tem
pera
ture
(K
)
97
Star Tracker Thermal Analysis
Arad Qsun Qgenerated
Ts4
Atotal
Using the heat generated (10W), and using common coating material ( ); the required to maintain the star tracker’s temperature
to 30 K can be found by.
Knowing the heat needed to dissipate, a radiator size can be calculated, or other thermal control methods (MLI) can
be used to maintain temperature.
Qdiss Qtot Ts4Atotal
98
Heat Needed to Radiate Away From Star Tracker to Keep Temp 303K
-2.00E+02
0.00E+00
2.00E+02
4.00E+02
6.00E+02
8.00E+02
1.00E+03
1.20E+03
1.40E+03
1.60E+03
4.80E-01 5.80E-01 6.80E-01 7.80E-01 8.80E-01 9.80E-01
Distance (AU)
Heat
(W)
99
Area of Radiator Needed to Keep Star Tracker Surface Temp at 303K
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
4.50E-01 5.00E-01 5.50E-01 6.00E-01 6.50E-01 7.00E-01
Distance (AU)
Are
a o
f R
adia
tor
(m^
2)Using the amount of heat needed to be radiated from star tracker, the
additional area required to dissipate heat can be calculated and chosen.
100
Thermal Analysis of Microthruster
Notes: Since Microthrusters need to be within 247 to 333 K, will have to add MLI to stay
within thermal constraints.
Analysis of Multilayer insulation…
101
Microthruster and Sun Senser Temperature vs Distance
200
250
300
350
400
450
500
550
600
650
700
4.80E-01
5.80E-01
6.80E-01
7.80E-01
8.80E-01
9.80E-01
Distance (AU)
Tem
pera
ture
(K
)
Microthruster SideMicrothruster TopSun Sensor
102
Thermal Analysis of Solar Panels
Need to radiate heat away from solar sail, any ideas, stephanie, group?
103
Solar Panel Temp (Operating temp 123 to 400K) vs Distance from Sun
300320340360380400420440460480500520540560580
4.80E-01 5.80E-01 6.80E-01 7.80E-01 8.80E-01 9.80E-01
Distance from sun (AU)
Tem
pu
ratu
re (
K)
104
Casey Shockman• Communications
105
Michael HitiPower
107
108
Demonstration of Success
109
Future Work
110
Acknowledgements
• Stephanie Thomas
• Professor Joseph Mueller
• Professor Jeff Hammer
• Dr. Williams Garrard
• Kit Ru….
• ?? Who else??