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

2. 2 Team Members

3. 3 Solar Sailing:

4. 4 Project Overview

5. 5 Design Strategy

6. 6 Trade Study Results

7. Orbit Eric Blake Daniel Kaseforth Lucas Veverka

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

9. 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. 10 Orbital Elements

11. 11 Equations of Motion = Sail Lightness Number= Gravitational Parameter

12. 12 Problem: Minimize Transfer Time By Inspection: Transversality :

13. 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. 14 Orbital Equations of Motion = Sail Lightness Number= Gravitational Parameter

15. 15 Maximizing solar force in an arbitrary direction Maximize:Sail pointing for maximum acceleration in the q direction:

16. 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. 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. 18 Trajectory of SPI using LSL’s Time (years)

19. 19

20. 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. 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.

22. Lucas Veverka Temperature Orbit Implementation

23. 23

24. Daniel Kaseforth Control Law Inputs and Navigation System

25. 25

26. Structure Jon T Braam Kory Jenkins

27. Jon T. Braam Structures Group: Primary Structural Materials Design Layout 3-D Model Graphics

28. 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 m 3 –2.9 m Ferring »Maximum payload mass: 1110 kg »Maximum payload volume: 16.14 m 3

29. 29 Primary Structural Material Aluminum Alloy Unistrut –7075 T6 Aluminum Alloy Density –2700 kg/m 3 –168.55 lb/ft^3 Melting Point –? Kelvin Picture of Unistrut

30. 30 Primary Structural Material Density Mechanical Properties –Allowing unistrut design Decreased volume Thermal Properties –Capible of taking thermal loads

31. 31 Design Layout Constraints –Volume –Service task –Thermal consideration –Magnetic consideration –Vibration –G loading

32. 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. 33 Design Layout Large Picture of expanded module

34. 34 3-D Model Large picture

35. 35 3-D Model Blah blah blah (make something up)

36. 36 Graphics Kick ass picture

37. 37 Graphics Kick ass picture

38. 38 The blanks will be filled in soon

39. 39 Trade Studies Blah blah blah

40. 40 Why I deserve an “A” Not really any reason but when has that stopped anyone!

41. Kory Jenkins Sail Support Structure Anticipated Loading Stress Analysis Materials Sail Deployment

42. 42

43. Attitude Determination and Control Brian Miller Alex Ordway

44. Sliding Mass vs. Tip Thrusters Component Selection

45. 45

46. Brian Miller Tip Thrusters vs. Slidnig Mass Attitude Control Simulation

47. 47 Attitude Control Conducted trade between tip thrusters and sliding mass as primary ACS Considerations –Power required –Torque produced –Weight –Misc. Factors

48. 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. 49 Attitude Control Attitude Control System Characteristics –Rotational Rate –Transfer Time –Required Torque –Accuracy –Disturbance compensation

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

51. 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. 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. 53

54. Power, Thermal and Communications Raymond Haremza Michael Hiti Casey Shockman

55. Raymond Haremza Thermal Analysis Solar Intensity and Thermal Environment Film material Thermal Properties of Spacecraft Parts Analysis of Payload Module Future Work

56. 56

57. Casey Shockman Communications

58. 58

59. Michael Hiti Power

60. 60

61. 61 Demonstration of Success

62. 62 Future Work

63. 63 Acknowledgements Stephanie Thomas Professor Joseph Mueller Professor Jeff Hammer Dr. Williams Garrard Kit Ru…. ?? Who else??