Solar Sail Department of Aerospace Engineering and Mechanics AEM 4332W – Spacecraft Design Spring 2007

2 Solar Sailing:

3 Project Overview –Motivation –Scope –Organization (tasks [%complete], groups, [who?]) –Present the scope of your design work. What are you setting out to do? –Explain how you have organized the work. What are the major tasks? What groups have you organized your team into, and who is in each group?

4 Team Members Orbit: Eric Blake, Daniel Kaseforth, Lucas Veverka Structure: Jon Braam, Kory Jenkins ADC: Brian Miller, Alex Ordway Power, Thermal and Communication: Raymond Haremza, Michael Hiti, Casey Shockman System Integration: Megan Williams

5 Design Strategy –Describe all of the trade studies you are considering in this project –Describe the trade study conclusions and any other design decisions that you have already made –Discuss the unfinished trade studies and what effect they will have on your design –Summarize the key properties of the mission (orbit, anticipated lifetime, candidate launch vehicles) –Summarize the key properties of the spacecraft (mass, dimensions, peak and average power requirements, ADCS configuration, type of propulsion system, list of any moving parts, other important info as you see fit) –Show a 3D diagram of the spacecraft (use a CAD package, ie Solid Works or Pro-E)

6 Trade Study Results

7 Cost Estimate Delta II Launch: $42,000, Navigation System: Carbon fiber booms: $ 250, Aluminum Bus: $ 1, stepper motors (sail deployment): $ 80, Heater: Helium Tank: Star Tracker: $ 1,000, Step Motors (sliding masses): $ 160, Reaction Wheels: $ Thrusters: Antenna Horn: Thermal Coating: Sail material: Solar Panels: Total: $43,491, Before Launch $ 1,491,800.00

Orbit Eric Blake Daniel Kaseforth Lucas Veverka

Eric Blake Optimal Trajectory of a Solar Sail: Derivation of Feedback Control Laws

10 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.

11 Orbital Elements

12 Equations of Motion = Sail Lightness Number= Gravitational Parameter

13 Problem: Minimize Transfer Time By Inspection: Transversality :

14 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.

15 Orbital Equations of Motion = Sail Lightness Number= Gravitational Parameter

16 Maximizing solar force in an arbitrary direction Maximize:Sail pointing for maximum acceleration in the q direction:

17 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

18 Method of patched local steering laws (LSL’s) Initial Conditions: Earth Orbit Final Conditions: semi-major axis: 0.48 AU inclination of 60 degrees

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

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21 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.

22 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

25 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. –u i is the incident vector. –n is the vector normal to the sail. Emissivity and specular reflection neglected. Assumed a Lambertian surface.

26 Sail Surface Temperature F solar is the solar flux. α is the absorptance. ε is the emittance. σ is the Stefan-Boltzman constant. d sun is the distance from the sun.

27 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

28 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.

29 Cold Transfer Orbit

30 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.

31 Hot Transfer Orbit

32 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.

33 Inclination First Transfer Orbit

34 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!

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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

40 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

41 Primary Structural Material Aluminum Alloy Unistrut –7075 T6 Aluminum Alloy Density –2700 kg/m 3 – lb/ft^3 Melting Point –? Kelvin Picture of Unistrut

42 Primary Structural Material Density Mechanical Properties –Allowing unistrut design Decreased volume Thermal Properties –Capible of taking thermal loads

43 Design Layout Constraints –Volume –Service task –Thermal consideration –Magnetic consideration –Vibration –G loading

44 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

45 Design Layout Large Picture of expanded module

46 3-D Model Large picture

47 3-D Model Blah blah blah (make something up)

48 Graphics Kick ass picture

49 Graphics Kick ass picture

50 The blanks will be filled in soon

51 Trade Studies Blah blah blah

52 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

54 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.

55 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.

56 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

57 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

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

59 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.

60 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:

61 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

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

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

66 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

67 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

68 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

69 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

70 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

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

72 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

73 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

74 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

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

77 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

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

79 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

80 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

81 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

85 Design Approach Strategy

86 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.

87 Solar Sail Material and Thermal Analysis

88 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

89 Spacecraft Heat Transfer Analysis

90 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.

91 Thermal Analysis of Payload Module

92 Thermal Analysis of Payload Module

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95 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.

96 Thermal Analysis of Antenna

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98 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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100 Using the amount of heat needed to be radiated from star tracker, the additional area required to dissipate heat can be calculated and chosen.

101 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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103 Thermal Analysis of Solar Panels Need to radiate heat away from solar sail, any ideas, stephanie, group?

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105 Casey Shockman Communications

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Michael Hiti Power

108 Objectives Determine the amount of power required to support the payload instruments, and all other components of the spacecraft Perform a trade study to determine whether to use a normal-pointing or conformal solar array Determine appropriate solar array materials Determine appropriate solar array size

109 Objectives (continued) Determine appropriate battery type to be used in mission Determine appropriate battery size

110 Power Requirements All power requirements for solar sail Peak Power (W) Remote Sensing Instruments Coronograph4 All Sky Camera3 EUV Imager5 Magnetograph - Helioseismograph5 IN-SITU Instrument Package Magnetometer2 Solar Wind Ion Composition and Electron Spectrometer3.5 Energetic Particle (20keV - 2MeV)2 Attitude Control Small Reaction Wheels70 Large Reaction Wheel70 Sliding Mass40 Structure Heat Curing Elements335 Communications Antenna Gimbal8 Antenna36 Misc/Thermal Thermal Management50 TOTAL633.5

111 Power Requirements (continued) Anticipated beginning- of-life (BOL) power load Peak Power (W) Structure Heat Curing Elements335 Communications Antenna36 Attitude Control Large Reaction Wheel70 Misc/Thermal Thermal Management50 TOTAL491

112 Power Requirements (continued) Anticipated end- of-life (EOL) power load Remote Sensing Instruments Coronograph4 All Sky Camera3 EUV Imager5 Magnetograph - Helioseismograph5 IN-SITU Instrument Package Magnetometer2 Solar Wind Ion Composition and Electron Spectrometer3.5 Energetic Particle (20keV - 2MeV)2 Attitude Control Small Reaction Wheels70 Communications Antenna Gimbal8 Antenna36 Misc/Thermal Thermal Management50 TOTAL188.5

113 Array Sizing Key Equations V chg = (1.2) * V bus = 34.2 V C chg = (P L * t d ) / (V bus * DOD) = 52.9 Ah P chg = (V chg * C chg )/15h = W P EOL = (P L + P chg ) = 310 W V chg is the array voltage C chg is the total charge capacity of the battery P L is the required power load at EOL t d is the anticipated max load duration (2h) P chg is the power required to charge the batteries DOD is the depth of discharge (0.25)

114 Array Sizing (continued) The BOL power requirement is found by assessing the various efficiency factors that lead to the conditions at EOL Temperature efficiency = η temp = 1 - (0.005/K)*(T max – T nom ) Radiation efficiency = η rad = 1- R Cosine loss = η angle = cos(α) P EOL = η temp * η rad * η angle * P BOL T max is the maximum solar cell operating temperature T nom is the nominal solar cell operating temperature R is the percent loss due to radiaiation damage α is the maximum angle off-normal to the sun

115 Array Sizing (continued) Using a conformal solar array Assuming: η temp ≈ 0.51 η rad ≈ 0.3 η angle ≈ 0.81 P BOL = 1395 W

116 Array Sizing (continued) Array area equations A cell = P BOL / ( η GaAr * I s ) A array = A cell / η pack A cell is the area of the solar cells A array is the area of the array η GaAr is the efficiancy of the solar cells Η pack is the packing efficiency I s is the solar intensity

117 Array Sizing (continued) A cell = m^2 With a packing efficiency of 90% A array = m^2 These values reflect the sizes required to meet EOL power requirements at 0.48AU We must check to make sure this array area will generate enough power to support the BOL requirements at 1AU

118 Array Sizing (continued) Assuming that there is no radiation and cosine loss Assuming a η temp ≈ 0.90 I s = 1355W/m^2 at 1AUl The BOL load ≈ 546W This would require an A cell ≈ m^2 and an A array ≈ 1.57 m^2 This means that the array sizing based on the EOL requirements will not support the BOL load requirments. The BOL load requirements are the driving force behind the array sizing

119 Array Mass Gallium Arsenide cells weigh 84mg/cm Solar panels and coverslides weigh 2.06 kg/m^2 Aluminum honeycomb panel backing weighs 0.9 kg/m^2 The total mass of a conformal array will be kg

120 Solar Array Solar cells and panels made by Spectrolab –Ultra Triple Junction GaAs cells –28.5% efficiency –84 mg/cm^2 (cells) –2.06 kg/m^2 (panel)

121 Trade Study Advantages to using of a normal-point solar array –Able to collect maximum possible solar energy –Requires smaller solar array –Array could be positioned to minimize thermal and radiation damage Disadvantages to using of a normal-point solar array –Added mass of gimbal used for positional array –Added complexity to design –Creates problems regarding stowage in capsule

122 Trade Study (continued) The BOL power requirements have caused our solar array to be nearly twice area required to meet the EOL power requirements The reduction of mass is our highest priority The smallest gimbal used for array positioning alone weighs approximately 5kg –This is nearly equal to the entire mass of our array Since our array is already oversized for EOL requirements, an array with normal pointing capabilities will not be beneficial

123 Battery Sizing Key Equations C chg = (P L * t d ) / (V bus * DOD) = 52.9 Ah E bat = (V bus * C chg ) = 1508 W h m bat = E bat / e bat E bat is the battery energy capacity e bat is the energy density of the battery m bat is the mass of the battery m bat = 8.6 kg

124 Battery Batteries made by BST Systems –Silver-Zinc Battery –1.5 V/cell –175(W h) / kg

125 Demonstration of Success

126 Failure Modes and Effects Analysis Boom fails to fully inflate due to problem with tank, heater, etc. –Sail may still function, would apply different torques, difficult to control –One or more of the booms could fail to extend fully. i.e. the heaters don't work, or the inflation gas tank ruptures or it gets caught on something. If that were to happen, it might be possible to run up the sail part way, although there would be a lot of slack in it, and therefore a loss of propulsion efficiency. And the attitude control system might not be able to compensate for the asymmetric torque...assuming the sliding mass on the malfunctioning boom worked at all...I mean, um...yeah, it'll work perfectly... Failure of navigation system... sail fails to know it's location and can no longer implement control laws; will not reach desired orbit. Failure Modes and Efffects: 1. Module structure fails at 7.5 g's and breaks it shit off on exit. Effect: It will spread debris throughout LEO. Something like the Chinese did about 9 months ago. Oops. My Bad. 2. The Sail gets kinked inside the Bus module and is unable to deploy or rips on deployment. Effect: Huge embarrassing failure for the UofM design team. 3. The solar array is not able to pivot downward from its storage/capsule setup to its working format. Effect: Same as #2. FMEA Thermal can screw everything up. I don’t think I can narrow it down to one thing. If I have to I guess I will. Anyways, heres my FDR slides thus far, not done yet, but pretty much done calculating stuff. Now I have to explain things, add equations and graphics and explain what I would do if I had more time. I think stephanie will have plenty to say about what I have already. Thanks

127 Future Work

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