Development of the Deorbitsail flight model

Olive R. Stohlman,∗ Mark Schenk,† and Vaios Lappas‡ University of Surrey, Guildford, GU2 7XH, United Kingdom

Deorbitsail is a collaborative project funded through the European Commission’s Sev- enth Framework Programme. A 5-by-5-metre sail will be deployed from the 10-by-10-by- 34-cm stowed satellite and demonstrate rapid deorbiting via atmospheric drag. Optimal pointing for drag will be accomplished with a compact three-axis-controlled attitude de- termination and control system. The project’s central goal is in-orbit technology demon- stration of a compact design for planned deorbiting of spacecraft. This paper presents two of the engineering considerations in the development of Deor- bitsail: a practical review of the sail manufacturing and packing, and a brief trade study on solar panel configuration. Deorbitsail’s deployable sail membrane is made of Kapton HN and packed into four rectangular packages using a double z-fold. Some of the challenges associated with the manufacture of this Kapton sail are discussed, including static cling and folding accuracy. The power study focuses on the limits common to the CubeSat form factor and the strict pointing requirements of the primary drag sailing mission.

I. Introduction

Deorbitsail is a nanosatellite technology demonstration mission, with the goal of deploying a 5-by-5-meter gossamer sail from a 3U CubeSat. Figure 1 shows the satellite in its deployed configuration.

Figure 1. Depiction of the deployed Deorbitsail satellite.

A promising application of large gossamer sails is to deorbit satellites from low earth orbit (LEO) by utilising atmospheric drag. Guidelines set out by international space agencies, including the European Code of Conduct for Space Debris Mitigation [1], propose a maximum deorbiting time of 25 years in order to mitigate the accumulation of space debris and ensure a sustainable orbit environment. Gossamer sails represent a low-cost and effective alternative to other deorbiting strategies, and the Deorbitsail mission is one of a competitive class of small satellites deploying multi-meter-wide drag sails in space. Deorbitsail also

∗Research fellow, Surrey Space Centre, University of Surrey, Guildford, UK, GU2 7XH, AIAA Member. †Research fellow, Surrey Space Centre, University of Surrey, Guildford, UK, GU2 7XH ‡Professor, Surrey Space Centre, University of Surrey, Guildford, UK, GU2 7XH, AIAA Member.

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American Institute of Aeronautics and Astronautics represents the limits of what can be achieved on a nanosatellite platform, by packaging a 3-axis ADCS, four 3.6m long deployable booms, and a 25 m2 sail membrane into a 3U CubeSat. Larger gossamer sails are being pursued by many organizations, primarily with the purpose of using the effect of solar radiation for solar sailing. Efficiency is judged by a measure similar to specific impulse: the sail’s area to mass ratio must be maximized. Launched in 2010, the JAXA IKAROS mission demonstrated the first successful deployment of a ; the 200 m2 sail was deployed and tensioned using centrifugal forces [2, 3]. Other large scale gossamer sail projects include the NASA/L’Garde [4] and the DLR Gossamer program [5]. On the scale of nanosatellites, another gossamer sail project under development at the Surrey Space Centre is CubeSail [6], which aims to demonstrate a combination of solar sailing and drag augmentation for deorbiting. A launch opportunity for Deorbitsail has been scheduled for Q3/Q4 of 2014, and manufacture of flight hardware has been initiated. Two of the engineering challenges encountered during the development process form the subject of this paper: the sail manufacturing and folding process, and the effect of the solar panel configuration on the satellite power budget. The analysis of the solar panel configuration was revisited relatively late in the design process, due to potential rescheduling of the available launch opportunity and the significant effect a specific orbit has on the Deorbitsail power budget.

Outline This paper is laid out as follows. In Section II a brief overview of the Deorbitsail mission and satellite is given; further detail is found in previous papers [7, 8]. This is followed by a description of the sail manufacturing and folding process in Section III.A and a summary of the solar panel configuration study in Section III.B. Finally, the paper is concluded with lessons learned.

II. Mission and Satellite Overview

The primary mission objectives for Deorbitsail are to demonstrate i) the controlled deployment of a large deployable structure from a CubeSat, ii) the deorbiting capability of a gossamer sail, and iii) the efficacy of a CubeSat ADCS (Attitude Determination and Control System) that incorporates sail-based attitude control using a translation stage. Verification of mission objective (i) will be achieved by transmitting pictures of the deployed sail taken with an on-board camera, and objectives (ii) and (iii) will be reported on using on-board attitude data as well as ground observations of the orbital decay. The satellite operations during the Deorbitsail mission can be summarised as follows. 1. Deploy antennas to establish communications

2. Enable ADCS to detumble spacecraft into a Y-Thompson spin [9, 10] (using the coarse sun sensors, magnetometer and 3 magnetorquers) 3. Deploy the 4 solar panels 4. Activate ADCS Y-Thompson despinning mode to stabilise and align the spacecraft (adding data from the sun and nadir sensors and actuation of the Y-momentum wheel)

5. Deploy the 5-by-5 m gossamer sail 6. Deorbiting phase, using the conventional and sail-based attitude control systems to maintain optimal orientation for drag deorbiting

A. Satellite Design In its launch configuration, the Deorbitsail design complies with the form factor of a 3U CubeSat. The tight volume constraints (a design envelope of 10×10×34 cm) have proven to be the primary design driver for the Deorbitsail subsystems. In order to achieve the mission objectives, the satellite also utilises the additional clearance provided by the ISIPOD CubeSat deployer [11] to accommodate deployable solar panels and an external magnetometer. After the satellite has detumbled into a Y-Thompson four, spin deployable solar panels are released to lie in a plane parallel to the deployed sail; see Figure 2. During the remainder of its mission the satellite orientation will be optimised to maximize aerodynamic drag, and for a given orbit the fixed configuration of

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American Institute of Aeronautics and Astronautics Figure 2. After ejection from the CubeSat deployer, the antennas are deployed to enable communications. After initial detumbling into a Y-Thompson spin, the four solar panels are released to expose the sail and boom deployment system, and provide a field of view for the cameras of the sun and nadir sensors. the solar panels will therefore strongly affect the satellite power budget. This trade-off will be described in further detail in Section III.B. Prior to their deployment, the four carbon fibre deployable solar panels (each with 6 solar cells) serve a further purpose as a hold-down mechanism for the primary mission payloads. This dual use of the solar panels is an unusual design element of the Deorbitsail satellite, and allows a single actuation to fulfill multiple structural control purposes. As shown in Figure 3, the satellite bus is separated from the sail deployment system by a translation stage. Once the sail is deployed, this system controls the XY offset between the satellite centre of mass (CoM) and centre of pressure (CoP) of the sail. The resulting torque is used as an additional means of attitude control during deorbiting. The use of a translation stage has important implications, as the relative motion between the two parts of the spacecraft must be constrained during launch. No space is available for a dedicated hold down system, and motion is therefore limited by the ISIPOD guide rails. The guide rails contact the boom deployment mechanism and the electronics bus along their longitudinal edges, forcing their alignment to within the margin of the ISIPOD. The solar panels have a limited ability to restrain this motion through contact with the top and bottom elements of the translation stage. What is more, the solar panels are used to contain the folded sail, and keep the doors of the boom deployment system closed (which in turn hold down the coiled booms). It is necessary to minimise bulging of the CFRP solar panels under these internal loads, to enable a smooth ejection from the CubeSat deployer. Lastly, an important consequence of this configuration is that three separate rail sections will engage with the deployment guides of the CubeSat deployer: along the bus, along the middle of the solar panels, and along the boom deployment mechanism.

1. Satellite Bus The electronic systems in the satellite bus manage electrical power, attitude control and communications. Most components are commercial off-the-shelf (COTS). The transceiver is the ISIS TRXUV VHF/UHF, used in combination with the ISIS deployable antenna; the EPS is GomSpace NanoPower P31u, and the ADCS stack is a sister model of the CubeAim used for the QB50 mission. The ADCS includes the CubeComputer OBC, CubeSense for attitude determination (coarse sun sensors, sun sensor, nadir sensor, magnetometer) and attitude control systems including three orthogonally placed magnetorquers and a Y-momentum wheel. In

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American Institute of Aeronautics and Astronautics Figure 3. The Deorbitsail stack.

addition, the ADCS incorporates the translation stage for CoM/CoP attitude control. The control objectives will change throughout the mission, and different control algorithms and actuators will be used.

2. Sail Payload The primary payload for the Deorbitsail mission is the 5 × 5 m sail, which consists of 4 quadrants which are deployed and tensioned by 4 diagonal deployable masts or booms. As the booms deploy, they unfold the packaged sail and draw it taut in its fully deployed configuration. The booms are part of the DLR family of deployable carbon fibre deployable booms [12, 13], which also feature on the Gossamer-1 spacecraft. The four closed-section booms are flattened before being coiled around a central hub. The deployment is controlled using a motor, which winds up thin metal strips that are co-coiled with the booms, thereby rotating the boom coil and extending the booms; see Figure 4. Further details of the deployment system can be found in [14]. The sail is made of a 12.5 µm thick membrane. A semi-translucent Kapton HN membrane was selected, as it reduces occlusion of the solar panels and attitude determination systems, and minimises interference with the RF system compared to aluminised membranes. For other gossamer sail missions, an identical system could deploy a reflective membrane and make use of the solar radiation pressure to change orbit, accomplish- ing solar sailing[6]. In the deployed configuration, the sail quadrants are tensioned using a constant-force spring attached at the central connection point. The sails were folded using a double Z-fold, with a first set of fold lines parallel to the hypotenuse of the quadrant at a spacing of 88 mm, and the second perpendicular set of folds at 49 mm intervals. This allows the sail quadrants to be packaged into bundles approximately 93 × 50 × 37 mm in size. Further details of the sail folding procedure are provided in Section III.A.

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American Institute of Aeronautics and Astronautics (a) (b)

Figure 4. The Deorbitsail boom deployment system (courtesy DLR).

(a) (b)

Figure 5. A sail quadrant during manufacture (a) and in its storage box after packing (b).

III. Engineering Challenges

A. Sail Manufacture and Folding The flight sail membrane was manufactured by project staff on a 2.5 × 18 m vacuum table at the Contender UK facility in Fareham, UK. This facility is more commonly used for the manufacture of sails for boats and ships. Manufacturing consisted of marking, assembling, and folding the sail. The procedure was as follows. 1. Mark the fold lines The marking was done using the facility’s computer-controlled marking and cutting head. Different colors were used for peaks and valleys of the primary z-folds. Alignment marks were also included for the glue lines. 2. Cut the sail segments Cutting was done with a computer-controlled laser cutter. It was noted that the laser-cut edge was slightly jagged and tore more easily than an edge cut with scissors or a sharp blade; this effect was present at the lowest laser power setting that produced a successful cut and grew more severe with increasing power. 3. Assemble the sail quadrant Each quadrant is assembled from two pieces along a line approximately 2.3 metres long. The two pieces

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American Institute of Aeronautics and Astronautics of the segment were primed and aligned along the glue line, before the top layer was peeled back so that glue could be applied to the bottom layer while maintaining alignment.

Figure 6. Glue application.

Primer and glue (Nusil CV1142) were applied by hand with a glue gun, as shown in Figure 6, to the glue line that joins the two pieces of each segment. Glue was applied to one piece, the pre-aligned second piece was then flipped on top of the glue, and the line was manually pressed flat with a roller, removing excess glue. A very small amount of adjustment was possible for a limited period of time after glue application.

4. Tape the edges Earlier specifications for the sail did not call for edge reinforcement. However, as the laser-cut edge was more fragile than anticipated, and because the sails will be handled and stressed during testing, a line of Kapton tape was applied along each edge.

5. Fold the primary Z-folds Creasing the primary Z-folds was the most time and labor-intensive part of the sail manufacturing process. While Deorbitsail uses one of the simplest possible folding patterns, a double Z-fold, folding two complete sets of sail segments took approximately three days’ work for four people. The primary Z-folds were applied by aligning the fold markings and creasing the folds with a rubber roller (a hard rubber brayer, rather than a soft foam paint roller). The folds were spaced at 88 mm intervals, and the total height of the folded strip was less than 93 mm in all places. A folded strip is shown in Figure 7. Despite very accurate fold placement, to within 0.5 mm, the stacked folds generally did not align with the precision of the individual creases. This may be because Kapton is a relatively resilient material and layers were adhered very strongly with static electricity.

Figure 7. A sail segment after primary Z-folds have been introduced.

6. Fold the secondary Z-folds The secondary Z-folds could be applied by a single person, and the

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American Institute of Aeronautics and Astronautics process does not require a large flat surface. It was noted that the secondary fold lines were positioned less accurately than for the primary folds, as a result of folding a large number of layers simultaneously.

A number of points are worthy of note for any future work. Aligning a transparent sail to be folded is much easier than aligning a reflective sail, because all the alignment marks are visible through both layers. Anti-static brushes, normally used for removing dust from static-prone surfaces, were very helpful while working with the film. Selective use of these brushes made it possible to reposition sections of the membrane while using static cling to fix others. The uncoated Kapton produces significant static cling forces against the metal table. It has been helpful to store the quadrants packed to their minimum folded size, as shown in 5(b). The force required to gradually compress a sail quadrant into its box, which had a minimum height of 37 mm, is graphed in Figure 8. When the lid is entirely closed, the volume fraction of the sail is approximately 80%. It is expected that 5 to 10 N of force from each of the four walls of the sail storage area will be required to pack the sail into the allocated storage area in the spacecraft, which is larger in absolute volume than the storage box but irregular in shape.

50 48 Quadrant 1 46 Quadrant 4 44 42 40 38 36

Stack height Stack (mm) height 34 32 30 0 5 10 15 20 Force (N)

Figure 8. The force required to pack sail segments in their storage boxes. Two sample quadrants are shown; behavior is similar between the two segments. The rectangular area available for sail packaging on the satellite is 35 mm deep, but an additional 10 mm of irregularly shaped space is also present.

As a final note, rapid decompression experiments demonstrated that the rate of decompression during launch will not be fast enough to damage the sail storage area or cause significant bulging of the stowed sail. The force required for packing is driven by the material properties of the sail, including contributions from the glue and tape, and not by trapped air.

B. Solar Panel Configuration and Power Budget While Deorbitsail is equipped with an attitude control system, it is limited to detumbling, stabilization, and pitch maneuvers. Since the purpose of the sail system is to deorbit the spacecraft, it always faces the direction of travel to present the maximum cross-sectional area. The orientation of the spacecraft is thus entirely determined by the deorbiting objective and the pointing requirements of the attitude determination system. As is the case with many , the solar panels do not have any sun-tracking capability; the me- chanical system would occupy too much volume and present an engineering challenge that is beyond the scope of Deorbitsail. The design for the panels must therefore provide adequate power both during tumbling and drag deorbiting, with only a single change in configuration. Before solar panel deployment the cells are on the four long sides of the spacecraft. This arrangement is acceptable for the power budget unless the satellite is perfectly pointed away from the sun. After deployment, however, the panels must meet a number of requirements at once: they must deploy via a simple mechanism; their final arrangement must not interfere with the sail deployment; they must not entirely occlude the field of view of the attitude determination cameras; and lastly, no cells can occupy the inner walls of the panels adjacent to the sail storage area or the boom deployer, which do not have any volume margin.

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American Institute of Aeronautics and Astronautics A number of panel and cell arrangements were considered. It was ultimately decided that no arrangement was suitable for all orbit cases, and the panel design would have to be particular to a given orbit (and thus to limited launch opportunities). This is not always the case for CubeSats: LightSail-1, for example, includes solar cells on the interior of its undeployed panels [15, 16], giving it a similar power profile in the deployed and undeployed states.

(A) (B)

(C) (D)

Figure 9. Four examples of solar panel configurations.

A selection of panel arrangements is presented in Figure 9 to illustrate the possibilities within the con- straints of Deorbitsail. Their performance is evaluated against two orbit cases, both of which are circular orbits at 650 km altitude and 98◦ inclination: a noon-midnight, and a dawn-dusk orbit. The evaluation method is a ray-tracing algorithm, applied to a simplified geometric model of the spacecraft. It is assumed that the spacecraft can carry 2 solar cells per 1U face, and that each cell produces 1150 mW of power at maximum illumination, a representative number for new CubeSat solar cells. The panel cases are as follows: (A) Four 3U panels deployed by 90◦ to lie in a plane. (B) Four 3U panels deployed by 180◦ with cells on the interior faces. This arrangement is not possible for Deorbitsail, but presented for reference.

(C) Four 2U panels deployed by 90◦ to lie in a plane, and additionally panels on two sides of the electronics bus (the sides not occupied by the ADCS cameras). This was considered in an earlier design iteration. (D) Two pairs of 3U panels connected along the long edge, deployed by 135◦. The two representative orbit cases are shown in Figure 10. The dawn-dusk orbit provides illumination from a near-constant angle in the satellite body frame, while the noon-midnight orbit sweeps across a range of angles in the body frame. Each case can be broken down to the contributions of the different panels. For example, Figure 11 shows the contributions of the four panels of configuration (D) in the dawn-dusk orbit. In this configuration, a single panel faces the sun directly for the entire orbit. Due to the slight inclination of the orbital plane, there is a phase where the panel is partially occluded by the sail membrane.

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American Institute of Aeronautics and Astronautics (a) (b)

Figure 10. The 98◦-inclination noon-midnight (a) and dawn-dusk (b) orbits, with the sun illuminating from the left. The spacecraft is shown here without the sail, but the booms and sail are modelled in their deployed states to assess blocking of the solar cells.

100

80 Panel 1 Panel 2 60 Panel 3 40 Panel 4

20

Percentage of maximum power 0 0 1000 2000 3000 4000 5000 Time in orbit (s)

Figure 11. The contributions of the four panels in configuration (D) during a dawn-dusk orbit cycle as a fraction of their maximum fully-illuminated power output.

With solar panel arrangement (A), the four panels all receive light at once, but only during part of the orbit. A comparison between these two arrangements, each in their preference orbit, is shown in Figure 12. These two very different orbits and configurations produce a similar amount of power, but configuration (A) in the noon-midnight orbit provides a large amount of power at once, while configuration (D) in a dawn- dusk orbit provides nearly constant input to the power system. Configuration (A) would therefore probably produce deeper battery discharges and more power storage losses. Depth of discharge is not a driving factor for Deorbitsail, which is a very short-term mission with an anticipated lifetime in the order of three months.

Panel Arrangement A B C D noon-midnight 6200 1700 3800 2300 dawn-dusk 1300 6700 2200 6300

Table 1. Mean power generation for different orbit and panel arrangement cases (in mW). The maximum power possible from 24 solar cells in this simulation is 27600 mW, and 6000 mW provides a good margin for the Deorbitsail mission.

In conclusion, no panel arrangements were found that provide a sufficient power margin across all possible orbits. In view of the potential launch opportunities, design (A) is the focus of development, but solutions exist for dawn-dusk orbits.

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American Institute of Aeronautics and Astronautics 30 Arrangement A in noon−midnight orbit 25 Arrangement D in dawn−dusk orbit 20

15

10

Power generation (W) 5

0 0 1000 2000 3000 4000 5000 6000 Time in orbit (s)

Figure 12. The preferred panel configuration (A) and noon-midnight orbit, compared with a valid panel configuration (D) for a dusk-dawn orbit.

IV. Conclusions

Deorbitsail is near the end of its design phase and many subsystems have entered flight production, with view of launch opportunities in Q3/Q4 2014. Two particular engineering challenges have been highlighted: the manufacture and folding of the sail quadrants, and the arrangement of solar panels. As the competing designs for 10-30m2 nanosatellite gossamer sails mature, several solutions to the same set of problems have arisen. Other common problems can be identified across designs, including sail containment, boom deployment and boom buckling failure modes, attitude control in the Cubesat form factor, and testing of the gossamer structure in what is often a low- cost setting. Future publications from the Deorbitsail project and the related work of project partners will contribute to the public knowledge on design principles and feasibility. Large-scale membrane manufacture is not a new topic in the space industry, with a history in inflatables [17] and sails [18, 19], particularly in singly Z-folded strips wrapped around a central hub [20, 21]. The Deorbitsail membrane enjoys the benefit of this heritage and modern materials, and uses one of the simplest possible designs. With specialist facilities, a 5-by-5-meter sail can be manufactured by three people in three days, with the majority of that time devoted to folding. Packing to a high volume fraction of 40% is possible, but requires relatively high constraint loads for a Cubesat structure. This has been and continues to be a significant design consideration in the project. While some Cubesats are able to optimize power generation by pointing the entire spacecraft, it is not common practice for the solar panels to have any independent pointing ability. Some commercially available panel systems with multiple deployable elements advertise power generation as high as 75 W [22]. Due to very tight volume and structural restrictions, Deorbitsail’s solar panel configuration is customized to a specific orbit. In 2014 functional testing of the refined sail deployment system will be carried out and the satellite will be assembled for flight.

A. Contributors Deorbitsail is an FP7 project funded by the European Commission. Deorbitsail is coordinated by the Surrey Space Centre at the University of Surrey (Guildford, UK) and the project partners are: • Athena SPU (Athens, Greece) • EADS Astrium SAS (Bordeaux, France) • Innovative Solutions in Space BV (Delft, The Netherlands) • Deutsches Zentrum f¨urLuft- und Raumfahrt e.V (Braunschweig, Germany) • Middle East Technical University (Ankara, Turkey) • Stellenbosch University (Stellenbosch, South Africa) • Surrey Satellite Technology, Ltd. (Guildford, UK) • University of Patras (Patras, Greece)

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American Institute of Aeronautics and Astronautics The California Institute of Technology (Pasadena, CA, USA) has also contributed to this project. The Deorbitsail website is located at http://www.deorbitsail.com.

References

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4 Sunjammer Mission, “First NASA solar sail mission to deep space, http://www.sunjammermission. com/,” December 2013. 5 Geppert, U., Biering, B., Lura, F., Block, J., Straubel, M., and Reinhard, R., “The 3-step DLR-ESA Gossamer road to solar sailing,” Advances in Space Research, Vol. 48, 2011, pp. 1695–1701. 6 Lappas, V., Adeli, N., Visagie, L., Fernandez, J. M., Theodorou, T., Steyn, W., and Perren, M., “Cube- Sail: A low cost CubeSat based solar sail demonstration mission,” Advances in Space Research, Vol. 48, No. 11, 2011, pp. 1890–1901. 7 Stohlman, O. R. and Lappas, V. J., “Deorbitsail: a deployable sail for de-orbiting,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, MA, 2013. 8 Lappas, V. J., Stohlman, O. R., Visagie, L., Theodorou, T., Fernandez, J. M., and Prassinos, G., “De- orbitsail: Flight-testing a deorbiting system,” 64th International Astronautical Congress, Beijing, MA, 2013. 9 Thompson, W. T., “Spin stabilization of attitude against gravity torque,” Journal of the Astronautical Sciences, Vol. 9, 1962, pp. 31–33. 10 Steyn, W. H., “Attitude control actuators, sensors and algorithms for a solar sail Cubesat,” 62nd Inter- national Astronautical Congress, Cape Town, South Africa, 2011. 11 ISIS, “ISIPOD CubeSat Deployer Brochure,” 2013. 12 Straubel, M., Block, J., Sinapius, M., and H¨uhne,C., “Deployable composite booms for various gossamer space structures,” 52th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, 2011. 13 Block, J., Straubel, M., and Wiedemann, M., “Ultralight deployable booms for solar sails and other large gossamer structures in space,” Acta Astronautica, Vol. 68, 2011, pp. 984–992. 14 Stohlman, O. R., Fernandez, J. M., Lappas, V. J., Hillebrandt, M., Straubel, M., and H¨uhne,C., “Test- ing of the Deorbitsail drag sail subsystem,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, MA, 2013.

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16 Planetary Society, “Lightsail-1 home page http://www.planetary.org/explore/projects/ -solar-sailing/,” September 2012. 17 Nakasuka, S., Senda, K., Watanabe, A., Yajima, T., and Sahara, H., “Simple and small de-orbiting package for nano-satellites using and inflatable balloon,” Trans. JSASS Space Tech. Japan, Vol. 7, No. 26, 2009.

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American Institute of Aeronautics and Astronautics 18 Lichodziejewski, D., West, J., Reinert, R., and Belvin, K. S. K., “Development and ground testing of a compactly stowed scalable inflatably deployed solar sail,” 45th AIAA/ASME/ASCE/AHS/ASC Struc- tures, Structural Dynamics, and Materials Conference, Palm Springs, CAA, 2004. 19 Leipold, M., Eiden, M., Garner, C. E., Herbeck, L., Kassing, D., Niederstadt, T., Kr¨uger,T., Pagel, G., Rezazad, M., Rozemeijer, H., Seboldt, W., Sch¨oppinger,C., Sickinger, C., and Unckenbold, W., “Solar sail technology development and demonstration,” Acta Astronautica, Vol. 52, 2003, pp. 317–326. 20 Sakamoto, H., Kadonishi, S., Satou, Y., Furuya, H., Shirasawa, Y., Okuizumi, N., Mori, O., Sawada, H., Matsumoto, J., Natori, M. C., Miyazaki, Y., and Okuma, M., “Repeatability of Stored Configuration of a Large Solar Sail with Non-negligible Thickness,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, MA, 2013.

21 Satou, Y. and Furuya, H., “Fold Line Based on Mechanical Properties of Crease in Wrapping Fold Membrane,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con- ference, Boston, MA, 2013.

22 Clyde Space, “Small Satellite Solar Panels Datasheet (PDF), via http://www.clyde-space.com/ products/solar_panels,” March 2012.

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