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

23

Daniel Kaseforth

Control Law Inputs and Navigation System

25

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

29

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

30

Primary Structural Material

• Density

• Mechanical Properties– Allowing unistrut design

• Decreased volume

• Thermal Properties– Capible of taking thermal loads

31

Design Layout

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

32

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

33

Design Layout

• Large Picture of expanded module

34

3-D Model

• Large picture

35

3-D Model

• Blah blah blah (make something up)

36

Graphics

• Kick ass picture

37

Graphics

• Kick ass picture

38

• The blanks will be filled in soon

39

Trade Studies

• Blah blah blah

40

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

Alex Ordway

•Sliding Mass vs. Tip Thrusters

•Component Selection

45

Brian Miller

•Tip Thrusters vs. Slidnig Mass

•Attitude Control Simulation

47

Attitude Control

• Conducted trade between tip thrusters and sliding mass as primary ACS

• Considerations– Power required– Torque produced– Weight– Misc. Factors

48

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

49

Attitude Control

• Attitude Control System Characteristics– Rotational Rate– Transfer Time– Required Torque– Accuracy– Disturbance compensation

50

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

51

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

52

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

53

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

56

Casey ShockmanCommunications

58

Michael HitiPower

60

61

Demonstration of Success

62

Future Work

63

Acknowledgements

• Stephanie Thomas

• Professor Joseph Mueller

• Professor Jeff Hammer

• Dr. Williams Garrard

• Kit Ru….

• ?? Who else??