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Solar Sail. Department of Aerospace Engineering and Mechanics AEM 4332W – Spacecraft Design Spring 2007. Team Members. Solar Sailing:. Project Overview. Design Strategy. Trade Study Results. Orbit. Eric Blake Daniel Kaseforth Lucas Veverka. Eric Blake.

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solar sail

Solar Sail

Department of Aerospace Engineering and Mechanics

AEM 4332W – Spacecraft Design

Spring 2007



Eric Blake

Daniel Kaseforth

Lucas Veverka

eric blake

Eric Blake

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

recall orbital mechanics
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.
equations of motion
Equations of Motion

= Sail Lightness Number

= Gravitational Parameter

problem minimize transfer time
Problem: Minimize Transfer Time

By Inspection:


  • 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.
orbital equations of motion
Orbital Equations of Motion

= Sail Lightness Number

= Gravitational Parameter

maximizing solar force in an arbitrary direction
Maximizing solar force in an arbitrary direction


Sail pointing for maximum acceleration in the q direction:

locally optimal trajectories
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
Method of patched local steering laws (LSL’s)
  • Initial Conditions: Earth Orbit
  • Final Conditions: semi-major axis: 0.48 AU inclination of 60 degrees
global optimal solution
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.
  • 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

Lucas Veverka


Orbit Implementation

reflectivity approximation
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.
sail surface temperature
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.
transfer orbits
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
cold transfer orbit
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.
hot transfer orbit
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.
inclination first transfer orbit
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.
  • 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!
daniel kaseforth

Daniel Kaseforth

Control Law Inputs and Navigation System


Jon T Braam

Kory Jenkins

jon t braam
Jon T. Braam

Structures Group:

Primary Structural Materials

Design Layout

3-D Model


primary structural material
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
primary structural material1
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

primary structural material2
Primary Structural Material
  • Density
  • Mechanical Properties
    • Allowing unistrut design
      • Decreased volume
  • Thermal Properties
    • Capible of taking thermal loads
design layout
Design Layout
  • Constraints
    • Volume
    • Service task
    • Thermal consideration
    • Magnetic consideration
    • Vibration
    • G loading
design layout1
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
design layout2
Design Layout
  • Large Picture of expanded module
3 d model
3-D Model
  • Large picture
3 d model1
3-D Model
  • Blah blah blah (make something up)
  • Kick ass picture
  • Kick ass picture
trade studies
Trade Studies
  • Blah blah blah
why i deserve an a
Why I deserve an “A”
  • Not really any reason but when has that stopped anyone!
kory jenkins
Kory Jenkins

Sail Support Structure

Anticipated Loading

Stress Analysis


Sail Deployment

sail sizing
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.
sail support structure
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.
Step 5

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
Estimate Worst Case Loading

Solar Pressure


  • 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
Analysis of a Tapered Beam




Hoop stress

(inflation pressure)



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 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:

conclusions and future work
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

Attitude Determination and Control

Brian Miller

Alex Ordway

alex ordway 60 hours worked

Alex Ordway60 hours worked

Attitude Control Subsystem Component Selection and Analysis

design drivers
Design Drivers
  • Meeting mission pointing requirements
  • Meet power requirements
  • Meet mass requirements
  • Cost
  • Miscellaneous Factors
trade study
Trade Study
  • Sliding Mass vs. Tip Thruster Configuration
    • Idea behind sliding mass
trade study1
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
adcs system overview
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
  • 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
  • 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
  • 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
  • Gear matching- load inertia decreases by the gear ratio squared. Show that this system does not need to be geared.
  • 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
  • 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
Attitude Control
  • Conclusion
    • Robust ADCS
      • Meets and exceeds mission requirements
      • Marriage of simplicity and effectiveness
      • Redundancies against the unexpected
brian miller

Brian Miller

Tip Thrusters vs. Slidnig Mass

Attitude Control Simulation

attitude control1
Attitude Control
  • Conducted trade between tip thrusters and sliding mass as primary ACS
  • Considerations
    • Power required
    • Torque produced
    • Weight
    • Misc. Factors
attitude control2
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
attitude control3
Attitude Control
  • Attitude Control System Characteristics
    • Rotational Rate
    • Transfer Time
    • Required Torque
    • Accuracy
    • Disturbance compensation
attitude control4
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

attitude control5
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

Attitude Control

Torque Req.

Transfer Time

Slope = 0.00004 rad/s

attitude control6
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

Attitude Control

Torque Req.

Transfer Time

Slope = 0.00002 rad/s

power thermal and communications

Power, Thermal and Communications

Raymond Haremza

Michael HitiCasey Shockman

raymond haremza

Raymond Haremza

Thermal Analysis

Solar Intensity and Thermal Environment

Film material

Thermal Properties of Spacecraft Parts

Analysis of Payload Module

Future Work

decision to take cold orbit
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.

payload panel analysis
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

heat transfer analysis
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.

spacecraft component thermal management
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.

star tracker thermal analysis
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.

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
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…

thermal analysis of solar panels
Thermal Analysis of Solar Panels

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

casey shockman
Casey Shockman
  • Communications
  • Stephanie Thomas
  • Professor Joseph Mueller
  • Professor Jeff Hammer
  • Dr. Williams Garrard
  • Kit Ru….
  • ?? Who else??