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### Solar Sail

### Eric Blake

### Optimal Trajectory of a Solar Sail: Orbit determination and Material properties.

### Daniel Kaseforth Material properties.

### Alex Ordway boom sizing.60 hours worked

### Raymond Haremza boom sizing.

### Thermal Analysis and Design boom sizing.

### Michael Hiti tracker, the additional area required to dissipate heat can be calculated and chosen.

Department of Aerospace Engineering and Mechanics

AEM 4332W – Spacecraft Design

Spring 2007

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

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.

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.

Maximizing solar force in an arbitrary direction

Maximize:

Sail pointing for maximum acceleration in the q direction:

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

Method of patched local steering laws (LSL’s)

- Initial Conditions: Earth Orbit
- Final Conditions: semi-major axis: 0.48 AU inclination of 60 degrees

Trajectory of SPI using LSL’s

Time (years)

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.

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

Reflectivity Approximation Material properties.

- 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.

Sail Surface Temperature Material properties.

- Fsolar is the solar flux.
- αis the absorptance.
- εis the emittance.
- σ is the Stefan-Boltzman constant.
- dsunis the distance from the sun.

Transfer Orbits Material properties.

- 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

Cold Transfer Orbit Material properties.

- 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.

Cold Transfer Orbit Material properties.

Hot Transfer Orbit Material properties.

- 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.

Hot Transfer Orbit Material properties.

Inclination First Transfer Orbit Material properties.

- 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.

Inclination First Transfer Orbit Material properties.

Conclusion Material properties.

- 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!

Control Law Inputs and Navigation System

Jon T. Braam Material properties.

Structures Group:

Primary Structural Materials

Design Layout

3-D Model

Graphics

Primary Structural Material Material properties.

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

- 3.0 m Ferring

Primary Structural Material Material properties.

Aluminum Alloy Unistrut

- 7075 T6 Aluminum Alloy
- Density
- 2700 kg/m3
- 168.55 lb/ft^3

- Melting Point
- ? Kelvin

- Density

Picture of Unistrut

Primary Structural Material Material properties.

- Density
- Mechanical Properties
- Allowing unistrut design
- Decreased volume

- Allowing unistrut design
- Thermal Properties
- Capible of taking thermal loads

Design Layout Material properties.

- Constraints
- Volume
- Service task
- Thermal consideration
- Magnetic consideration
- Vibration
- G loading

Design Layout Material properties.

- 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

- Allowing all inside surfaces to be bonded to

Design Layout Material properties.

- Large Picture of expanded module

3-D Model Material properties.

- Large picture

3-D Model Material properties.

- Blah blah blah (make something up)

Graphics Material properties.

- Kick ass picture

Graphics Material properties.

- Kick ass picture

- The blanks will be filled in soon Material properties.

Trade Studies Material properties.

- Blah blah blah

Why I deserve an “A” Material properties.

- Not really any reason but when has that stopped anyone!

Kory Jenkins Material properties.

Sail Support Structure

Anticipated Loading

Stress Analysis

Materials

Sail Deployment

Sail Sizing Material properties.

- 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.

Sail Support Structure Material properties.

- 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.

Step 5 Material properties.

Step 1

Deployment cables retract to pull the sail quadrants out of their storage compartments.

Heater: Raises boom temperature above glass transition temperature to 75 C.

To sail quadrant

Step 4

Once deployed, booms cool below glass transition temperature and rigidize.

Step 2

Inflation gas inlet: booms are inflated to 120 KPa for deployment.

To deployment motor

Step 3

Cables attached to stepper motors maintain deployment rate of ~ 3 cm/s.

Estimate Worst Case Loading Material properties.

Solar Pressure

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.

P = 2/3 P_quadrant

Analysis of a Tapered Beam Material properties.

Bending

Buckling

Shear

Hoop stress

(inflation pressure)

Section

Modulus

- 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.

Boom Specifications boom sizing.

- 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:

Conclusions and Future Work boom sizing.

- 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 Control Subsystem Component Selection and Analysis

Design Drivers boom sizing.

- Meeting mission pointing requirements
- Meet power requirements
- Meet mass requirements
- Cost
- Miscellaneous Factors

Trade Study boom sizing.

- Sliding Mass vs. Tip Thruster Configuration
- Idea behind sliding mass

Trade Study boom sizing.

- 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

ADCS System Overview boom sizing.

- 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

- Four 10 kg sliding masses primary

ADS boom sizing.

- 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

- Decision to use star tracker

ADS boom sizing.

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

- Two Bradford Aerospace sun sensors

ACS boom sizing.

- 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

ACS boom sizing.

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

ACS boom sizing.

- 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

ACS boom sizing.

- Six Bradford micro thrusters
- 0.4 kg each
- 4.5 W power draw each
- -30ºC - + 60ºC
- 2000 N thrust
- Supplied through N2 tank

Attitude Control boom sizing.

- Conclusion
- Robust ADCS
- Meets and exceeds mission requirements
- Marriage of simplicity and effectiveness
- Redundancies against the unexpected

- Robust ADCS

Attitude Control boom sizing.

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

Attitude Control boom sizing.

- 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

- Pros

Attitude Control boom sizing.

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

Attitude Control boom sizing.

- 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

- Pitch and Yaw Axis

- Orbit

m – sliding mass

F – solar force

z – distance from cg

M – spacecraft mass

Pitch and Yaw Axis boom sizing.

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

Attitude ControlTorque Req.

Transfer Time

Slope = 0.00004 rad/s

Roll Axis boom sizing.

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

Attitude ControlTorque Req.

Transfer Time

Slope = 0.00002 rad/s

Thermal Analysis

Solar Intensity and Thermal Environment

Film material

Thermal Properties of Spacecraft Parts

Analysis of Payload Module

Future Work

-Raymond Haremza

Design Approach Strategy boom sizing.

Decision to take “cold” orbit boom sizing.

By taking longer to get to 0.48 AU, we in turn reduce the amount of design, analysis, production time and weight.

Solar Sail Material and Thermal Analysis boom sizing.

Payload Panel Analysis boom sizing.

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

Spacecraft Heat Transfer Analysis boom sizing.

Heat Transfer Analysis boom sizing.

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

Thermal Analysis of Payload Module boom sizing.

Thermal Analysis of Payload Module boom sizing.

Spacecraft Component Thermal Management boom sizing.

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.

Thermal Analysis of Antenna boom sizing.

Star Tracker Thermal Analysis boom sizing.

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.

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

Thermal Analysis of Microthruster tracker, the additional area required to dissipate heat can be calculated and chosen.

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…

Thermal Analysis of Solar Panels tracker, the additional area required to dissipate heat can be calculated and chosen.

Need to radiate heat away from solar sail, any ideas, stephanie, group?

Casey Shockman tracker, the additional area required to dissipate heat can be calculated and chosen.

- Communications

Power

Demonstration of Success tracker, the additional area required to dissipate heat can be calculated and chosen.

Future Work tracker, the additional area required to dissipate heat can be calculated and chosen.

Acknowledgements tracker, the additional area required to dissipate heat can be calculated and chosen.

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

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