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 = Sail Lightness Number= Gravitational Parameter

12 Problem: Minimize Transfer Time By Inspection: Transversality :

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 = Sail Lightness Number= Gravitational Parameter

15 Maximizing solar force in an arbitrary direction Maximize: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: 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

18 Trajectory of SPI using LSL’s Time (years)

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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

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Daniel Kaseforth Control Law Inputs and Navigation System

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Structure Jon T Braam Kory Jenkins

Jon T. Braam Structures 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: m 3 –2.9 m Ferring »Maximum payload mass: 1110 kg »Maximum payload volume: m 3

29 Primary Structural Material Aluminum Alloy Unistrut –7075 T6 Aluminum Alloy Density –2700 kg/m 3 – 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 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.

43 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.

44 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

45 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

46 Analysis of a Tapered Beam Bending Buckling Shear Hoop stress (inflation pressure) Section Modulus

47 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.

48 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:

49 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 Ordway 60 hours worked Attitude Control Subsystem Component Selection and Analysis

52 Design Drivers Meeting mission pointing requirements Meet power requirements Meet mass requirements Cost Miscellaneous Factors

53 Trade Study Sliding Mass vs. Tip Thruster Configuration –Idea behind sliding mass

54 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

55 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

56 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 °C operational temp. range $1M –Not Chosen: Terma Space HE-5AS star tracker

57 ADS Secondary –Two Bradford Aerospace sun sensors Backup system; performance not as crucial Sensor located on opposite sides of craft kg each 0.2 W each -80°C - +90°C

58 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

59 ACS Gear matching- load inertia decreases by the gear ratio squared. Show that this system does not need to be geared.

60 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

61 ACS Six Bradford micro thrusters –0.4 kg each –4.5 W power draw each –-30ºC ºC –2000  N thrust –Supplied through N 2 tank

62 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

64 Attitude Control Conducted trade between tip thrusters and sliding mass as primary ACS Considerations –Power required –Torque produced –Weight –Misc. Factors

65 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

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

67 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 – sliding mass F – solar force z – distance from cg M – spacecraft mass

68 Attitude Control Pitch and Yaw Axis Rotation Rate = 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 = rad/s Torque Req. Transfer Time

69 Attitude Control Roll Axis Rotation Rate = 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 = rad/s Transfer Time

Power, Thermal and Communications Raymond Haremza Michael Hiti Casey Shockman

Raymond Haremza Thermal 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

73 Design Approach Strategy

74 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.

75 Solar Sail Material and Thermal Analysis

76 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. Material Properties

77 Spacecraft Heat Transfer Analysis

78 Heat Transfer Analysis Setting the heat fluxes together yields the surface temperature of the object based on emmissivity, absorbitivity, size and geometry of the object.

79 Thermal Analysis of Payload Module

80 Thermal Analysis of Payload Module

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83 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.

84 Thermal Analysis of Antenna

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86 Star Tracker Thermal Analysis 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.

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88 Using the amount of heat needed to be radiated from star tracker, the additional area required to dissipate heat can be calculated and chosen.

89 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…

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91 Thermal Analysis of Solar Panels Need to radiate heat away from solar sail, any ideas, stephanie, group?

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93 Casey Shockman Communications

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Michael Hiti Power

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97 Demonstration of Success

98 Future Work

99 Acknowledgements Stephanie Thomas Professor Joseph Mueller Professor Jeff Hammer Dr. Williams Garrard Kit Ru…. ?? Who else??