1. 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

7. Orbit Eric Blake Daniel Kaseforth Lucas Veverka

8. 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)

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.

22. Lucas Veverka Temperature Orbit Implementation

24. Daniel Kaseforth Control Law Inputs and Navigation System

26. Structure Jon T Braam Kory Jenkins

27. 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: 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!

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

43. Attitude Determination and Control Brian Miller Alex Ordway

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

45. Alex Ordway60 hours worked Attitude Control Subsystem Component Selection and Analysis

46. Design Drivers • Meeting mission pointing requirements • Meet power requirements • Meet mass requirements • Cost • Miscellaneous Factors

47. Trade Study • Sliding Mass vs. Tip Thruster Configuration • Idea behind sliding mass

48. 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

49. 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

50. 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