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??