Solar Sail

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

23. 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.

25. Sail Surface Temperature • Fsolar is the solar flux. • αis the absorptance. • εis the emittance. • σ is the Stefan-Boltzman constant. • dsunis 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!

35. Daniel Kaseforth Control Law Inputs and Navigation System

37. Structure Jon T Braam Kory Jenkins

38. Jon T. Braam Structures 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