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.

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Orbital Elements

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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

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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

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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

23

Daniel Kaseforth

Control Law Inputs and Navigation System

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Structure

Jon T Braam

Kory Jenkins

Jon T. BraamStructures Group:

• Primary Structural Materials

• Design Layout

•3-D Model

• Graphics

28

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

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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

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Primary Structural Material

• Density

• Mechanical Properties– Allowing unistrut design

• Decreased volume

• Thermal Properties– Capible of taking thermal loads

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Design Layout

• Constraints– Volume– Service task– Thermal consideration– Magnetic consideration– Vibration– G loading

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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

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Design Layout

• Large Picture of expanded module

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3-D Model

• Large picture

35

3-D Model

• Blah blah blah (make something up)

36

Graphics

• Kick ass picture

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Graphics

• Kick ass picture

38

• The blanks will be filled in soon

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Trade Studies

• Blah blah blah

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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

42

Attitude Determination and Control

Brian Miller

Alex Ordway

Brian Miller

•Tip Thrusters vs. Slidnig Mass

•Attitude Control Simulation

Alex Ordway60 hours worked

Attitude Control Subsystem Component Selection and

Analysis

46

Design Drivers

• Meeting mission pointing requirements

• Meet power requirements

• Meet mass requirements

• Cost

• Miscellaneous Factors

47

Trade Study

• Sliding Mass vs. Tip Thruster Configuration– Idea behind sliding mass

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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

49

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

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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

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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

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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

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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

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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

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ACS

• Six Bradford micro thrusters– 0.4 kg each– 4.5 W power draw each– -30ºC - + 60ºC– 2000 N thrust

– Supplied through N2 tank

56

Attitude Control

• Conclusion– Robust ADCS

• Meets and exceeds mission requirements• Marriage of simplicity and effectiveness• Redundancies against the unexpected

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

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Casey ShockmanCommunications

61

Michael HitiPower

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Demonstration of Success

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Future Work

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Acknowledgements

• Stephanie Thomas

• Professor Joseph Mueller

• Professor Jeff Hammer

• Dr. Williams Garrard

• Kit Ru….

• ?? Who else??