Deployment System for the CubeSail nano-Solar Sail Mission

S. Nasir AdeliAdvisor: Vaios J. Lappas

Surrey Space Centre, University of Surrey, Guildford GU2 7XH, UK

Abstract

The CubeSail is a nano-Solar Sail based on the 3U CubeSat standard currently being built at theSurrey Space Centre. The CubeSail mission aims to demonstrate the concept of solar sailing and at itsend-of-life use the sail membrane for de-orbiting. One of the main challenges in the design of any SolarSail is the deployment mechanism. This paper proposes a deployment mechanism for the CubeSail.This mechanism consists of four booms and four quadrant sail membranes. The proposed booms aremade from tape-spring blades and will deploy a 5m × 5m sail membrane. The paper investigatesfour possible folding patters and proposes a Creasing Indicator to quantify the effects of folding onsail membrane efficiency. The testing of a 1.7-m engineering model of the deployment mechanism isdiscussed with data on angular rates experienced during deployment presented.

Keywords: CubeSail , Solar Sail, Deployment, Folding, Membrane, Creasing Indicator, De-orbiting

1 Introduction

Solar Sails are highly reflective spacecrafts that usethe photons from the sun to propel themselves.Their propellentless and low cost nature gives ac-cess to long-duration missions and new range of or-bits . Missions such as comet rendezvous, polar or-bits about the sun, the study of earth magneto-tailand station keeping at Lagrange points are oftenvery difficult to achieve with traditional chemicalpropulsion and Solar Sails give considerable prom-ise [7, 9].The momentum transfer of the photons impact-

ing on a reflective surface implies that Solar Sailsneed to have a large reflective area. This is whilea smaller mass is highly beneficial, resulting in ahigher accelerations.In the past few years there have been a few at-

tempts at launching a Solar Sail, the PlanetarySociety in 2005 launched Cosmos-1 and NASA in2008 launched the NanoSail-D[3]. Both missionsended prematurely when the launch vehicle failedto reach orbit. More recently JAXA is hopping tolaunch IKAROS [8] within this year. With currentavailable small satellite technologies and ultralightmembranes, building a Solar Sail has become overdue. That is why we are at the onset of world widerace to be the first to launch a sailcraft and provesolar sailing.At the Surrey Space Centre, Solar Sails have been

researched in the past, and currently a 5m × 5m,3kg nano-Solar Sail called CubeSail is being de-signed and constructed. This mission will utilise

the CubeSat structure and will attempt to be thefirst to launch, deploy, control and de-orbit a SolarSail.

There are two main challenges facing the con-struction of a Solar Sail. First is the deploymentof a large structure in space and second, the at-titude control of a spacecraft with very large mo-ments of inertia.This paper focuses on the former.The deployment subsystem usually has a high riskof failure due to its numerous moving components.

In the next section, an introduction is given tothe CubeSail mission and it’s objectives are dis-cussed. The paper will then move on to cover theCubeSail deployment mechanism, in section 3, con-sisting of tape-spring based booms. Four mem-brane folding patterns are then discussed in section4 and a comparison between them is provided.

In section 5 the Creasing Indicator (CI) is pro-posed. This indicator attempts to quantify andbridge the gap on the effects of folding on sail mem-brane efficiency. CI of all four patterns are calcu-lated and discussed. Section 6 presents a grounddeployment of a 1.7m × 1.7m CubeSail. The de-ployment takes place on a rotating platform en-abling experimental results on angular rates duringdeployment to be presented.

2 The CubeSail Mission

The CubeSail is a three axis stabilised nano-SolarSail, that will be inserted into an 800-km sun-synchronous orbit. It will demonstrate solar sailing

1

5m CubeSail

1.7m Ground Demo

6.25m2 Sail Quadrent

Tape spring Booms

CubeSat Bus 10!10cm

Figure 1: CubeSail deployment concept - deployed

by changing its orbital inclination by 2 deg overa one year period. The CubeSail utilises a 3-axisattitude control system based on the change in thecentre of mass verses the centre of pressure togetherwith magnetic torque rods[6].In its stowed configuration it occupies a 3 unit

(3U) CubeSat standard structure. Figure 4 showshow the CubeSail structure is divided into differentsection. The avionics, sensors and attitude determ-ination system will occupy 1U (100x100x100 mm)of this structure. The remaining 2U will be usedto house the Solar Sail deployment mechanism. Tohold the 4 quadrants of the sail, four booms made oftape-spring are utilised. These booms extend froma 0.4U compartment and simultaneously unfurl thesail membrane wrapped around a central spindle.In terms of volume this limited space provides achallenge for stowage of such a large structure.

2.1 Mission Objectives

The CubeSail’s primary mission objective are asfollows:

− Demonstrate Deployment of a 25m2 Solar Sail

− Demonstrate Solar Sailing over a year.

− Demonstrate a 3-axis active ADCS

− Self de-orbiting.

2.2 Mission Orbit

The CubeSail will demonstrate solar sailing bychanging the inclination of its orbit. To keep theeffects of drag low the CubeSail will face towards

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97

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98.5

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inat

ion

i (de

g)

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CubSat, no Sail CubeSail, with Sail

Figure 2: Changes in orbital inclination and sunangle of the CubeSail vs a 3U CubeSat

the normal of the orbital plain, flying on its edgeinto the velocity vector. Figure 2 compares thechange in inclination and sun angle of a CubeSatwith no Sail and the CubeSail in an 800-km sun-synchronous orbit. The inclination stays roughlythe same throughout the 360 days of the simulationfor the CubeSat while the CubeSail achieves a 2-degchange in inclination. As the sail normal is boundto the normal of the orbit, the sun angle (α) willbe affected by the right ascension of ascending node(RAAN). The changes seen in the sun angle(α) area result of the changes of RAAN with respect tothe position of the sun.

2.3 De-orbiting

At the end of its life time the CubeSail will changeorientation and point its Sail along the velocity vec-tor. The increased cross sectional area will causerapid descent. Figure 3(a) shows the life time ofa normal 3U CubeSat to be more than a 100 yrs.In comparison Figure 3(b) shows when the Cube-Sail is in de-orbiting mode it will de-orbit in lessthan a year. To this effect the CubeSail could beused as a de-orbiting device and be attached to anyspacecraft [5]. It will be able to effect the ballisticcoefficient of the spacecraft after deployment, caus-ing rapid de-orbiting.

3 Deployment Mechanism

The deployment mechanism of a Solar Sail is a crit-ical subsystem which usually has a high risk asso-ciated with it. The deployment mechanism of theCubeSail consists of two main section (see Figure4).

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10003U CubeSat

Hei

ght A

poge

e (k

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Heig

ht A

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(b) CubeSail - deorbit

Figure 3: Lifetime comparison of a CubeSat withand without 25m2 sail

The first is concerned with boom stowage and de-ployment and the second with membrane stowageand deployment.

!"#"#$%

#%

5m CubeSail

1.7m Ground Demo

6.25m2 Sail Quadrent

Spring-steel Booms

CubeSat Bus 10!10cm

3U 3

40m

m

1U 1

00m

m

Cube

Sat B

us

0.4U

40m

m

Attit

ude

Actu

ator

2U

200

mm

De

ploy

men

t

1.6U 160mm Membrane Stowage

0.4U 400mm Boom Stowage

Figure 4: CubeSail deployment concept

3.1 Booms

The booms have to occupy a small volume duringstowage which is confined to a 100mm × 100mmbase area and leave a reasonable amount of spacefor the folded sail. This is on top of the fact thatthey have to extend to about 3.6 meters in length.

The CubeSail booms are made of tape-springblades, similar to the ones used in tape measures orcarpenter’s tape (See Figure 5). Due to it’s flexiblenature a long blade is able to roll around a spindleand still roll back out and hold its original shape.These blades show a very good stiffness when held

(a) Stowed & extended

(b) Cross section

Figure 5: 1.7m CubeSail ground demonstrationboom

curve down. Some tape measures are claimed tostand horizontally up to 4 meters. This kind ofbending stiffness is more than sufficient in a verylow gravity environment to extend the sail film andmake it taught while enduring the Solar RadiationPressure. But when blades are flipped upside down(curve up) they quickly buckle under gravity andbend under the smallest of forces.

To strengthen the blade, two of the blades are at-tached to each other front to front. This solves thebuckling problem and increases the stiffness of thebooms, see the boom cross section in Figure 5. Thetwo blades are also wrapped in Kapton Film. TheKapton film not only holds the two blades togetherbut also acts as a thermal barrier and stops atomicoxygen at low earth orbit from reacting with theblades and degrading them.

3.2 Boom Sizing

The CubeSat structure has a limited bus area of100mm×100mm, limiting the length of the boomsthat can be wrapped around a given size spindle.Boom stowed thickness plays an important factorin the maximum possible boom length. To ana-lyse this, Figure 6 shows the total diameter vs. thespindle diameter for the different thickness booms.A 0.32mm thick boom with an 11mm spindle dia-meter will result in a total stowed diameter of about80mm. A 0.4mm thickness with a spindle diameterof 20mm will result in a total diameter of about90mm, well within the 100mm limit.

Figure 6 also shows the absolute maximum thick-

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110

120

Spindle diameter (mm)

Tota

l dia

met

er (m

m)

0.32mm0.4mm0.5mm

Figure 6: Sizing of the 3.7m booms for differentspindle thickness

ness that will result in a total diameter of 95mmleaving only 0.25mm clearance on each side. Anyboom above 0.5mm in thickness would have to beshorter in length to be fitted inside the 100mm ×100mm area, resulting in a smaller Solar Sail. Butthis in not considering the amount of space requiredfor the deployable solar panels, and the structure.In comparison the 0.32mm and 0.4mm leave 10mmand 5mm of clearance respectively on each side forthe structure walls and/or deployable solar pan-els. Note that the 0.32mm, 0.4mm thick boomshave cross sectional heights of 19mm, and 25mmrespectively.Alternately one could divide the booms into two

sets and wrap each around a separate spindle moun-ted on top of each other. This enables longer boomsand the possibility of a larger Sail. But the boomswill ocupy twice the foreseen volume, ultimately re-ducing the volume available for the sail membranestowage. In effect the longer booms will be useless.

3.2.1 Boom mass-loading

The boom mass loading is a crucial characteristicin the design of a Solar Sail. The smaller the mass-loading the larger a solar sail can become with asmall mass penalty. In McInnes [7] the Solar Sailcharacteristic acceleration (a0) is a direct functionof the sail mass-loading (σ). Table 7 shows themass-loading of each set of booms and possiblemasses for four 3.6m booms. Figure 7 shows theboom mass-loading vs. the boom width for thethree different boom sizes.

Thickness mass-loading 4 x 3.6m Boom(mm) (g/m) total mass (g)0.32 29.60 426.240.4 40.38 581.530.5 64.61 930.46

Table 1: Tape-spring boom mass-loading

0.35 0.4 0.45 0.520

40

60

80

Boom

mas

s−lo

adin

g (g

/m)

Boom thickness(mm)

Figure 7: Tape-spring boom mass-loading

3.3 Boom Summary

Comparing the different size booms, indicates thatthe stiffness and strength of the booms is a func-tion of tape-spring blade width and thickness. The0.5mm booms because of their thickness and widthhave a high mass-loading. The mass of four 3.6mbooms is about 930g (see Table 7), too large fora CubeSail with a mass limit of 3kg. Thus thisboom size is discarded. Between the 0.32mm and0.4mm, it is evident that the 0.4mm will have ahigher stiffness, even though it has a mass-loadingslightly higher than that of the 0.32mm boom. Us-ing these characteristics the 0.4mm booms are agood choice for the CubeSail.

4 Membrane Folding

Correctly folding the sail membrane will effect howthe sail deploys and will impact the sail’s efficiency.Important factors to consider are not only the oc-cupied folded volume but also the folded dimen-sions. Another factor is how easily the membraneunfolds during deployment and weather there is po-tential for tarring. And finally the creases on themembrane must be kept to a minimum to have theleast amount of impact on sail performance and ef-ficiency.

The CubeSail is designed as a four quadrantsail with four booms, meaning four triangle shapedmembranes. Here four folding patterns that couldbe used to fold the sail membrane are presented.These four patterns will be discussed below, onewhich is a single sheet membrane and the rest arefour quadrant, triangular. The patterns are de-signed to wrap the membrane around a single cent-ral spindle. The patterns presented here are scal-able for larger Solar Sails.

4.1 Folding Pattern 1

The first folding pattern uses a single fold in themiddle as a guide for other subsequent folds. Fig-

4

ure 8 shows how the folding takes place. The num-ber of folds along the centre line must be an oddreal number (n), resulting in the end points of thecentre line to be folded in the same direction. Thisfacilitates connecting the right-angle corners of thesail to the spindle. When all four quadrants arefolded, they are wrapped around the spindle.To find out how many folds are required, the

height available to stow the membrane aroundthe spindle needs to be known. This is between150 − 160mm of the 3U height. So h in Figure 8is the maximum stowed height and will determinethe number of folds. Through some geometric cal-culations we have the following equation:

np1 =45

arctan 1l

h√

2+1

(1)Folding Problem

•  Our Folding Pattern!

Hill fold Valley fold

l

h

Figure 8: Folding pattern 1

The advantages with this folding pattern is thatit is easily stowed and is very compact. It will gen-erate a small h but larger stowed thickness aroundthe spindle per quadrant. It is also difficult to cre-ate the fold due to the existence of a central foldline and the convergence of other fold lines to thetriangle edges.Another major disadvantage is when the quad-

rants are deployed, the tension lines that will keepthe sail taught are along the crease lines. Hencea larger tension will be required to keep the sailtaught. Figure 9 shows how when 4 quadrants ofthe sail where deployed with an engineering modelof the CubSail (using the 0.32mm booms), therewhere not enough tension to keep the sail taught.

4.2 Folding Pattern 2

In pattern 1, a major issues was caused by thecrease lines being parallel to the tension lines, re-quiring extra force to tension the sail quadrants.Pattern 2 tries to resolve this. Here the creaselines begin at the right-angle corner of the triangleand spread out evenly (see Figure 10). The num-ber of folds (n) required to fit around the spindle

Figure 9: Deployed pattern 1

can be determined through the maximum spindleheight(h) in Equation 2. Given that the two cornersof the quadrant need to face the same direction(up/down), an odd value for the number of foldsis favorable.

np2 =90

arctan 1l

h√

2+1

(2)Folding Patterns To Try

•  Folding Pattern 2!

Hill fold Valley fold

l

h

(a) (b)

Figure 10: Folding pattern 2

There are two advantages in is folding pattern,first the crease lines are not parallel to the tensionlines and a smaller force is required to tighten thesail. Second, folding and stowage is much easierthan the previous pattern. But a disadvantage isthe convergence of the crease lines to a single pointat the right-angle corner of the quadrant. Thesecrease lines weaken the membrane, specially if it isa point of attachment to the bus, tearing might oc-cur and extra reinforcements are necessary. Theseextra reinforcements will thicken the membrane,adding mass and stowage volume and making thefolding even more difficult.

4.3 Folding Pattern 3

Pattern 3 is an evolves from the two previous pat-terns and solves the convergence of the crease line

5

problem by making the crease lines parallel to eachother. Figure 11 shows the folding pattern in ques-tion. The number of crease lines can be calculatedusing Equation 3.

np3 = l/h (3)

Folding Patterns To Try

•  Folding Pattern 3!

Hill fold Valley fold

l h

(a) (b)

Figure 11: Folding pattern 3

Advantages of this folding pattern is that thereare no crease line convergence to weaken the sailmembrane and the crease lines are close to perpen-dicular with respect to the tension lines. Folding isalso fairly straight forward and any size membranecan easily be folded. A slight problem with this pat-tern arrises when the folded quadrants are wrappedaround the spindle. As seen in Figure 17 the mem-brane is quite loose around the spindle. This doesnot cause a problem as the membrane is inside thebus and covered by the bus side panels. Figure 12shows a deployed version of this Pattern.

Figure 12: Deployed pattern 3

4.4 Folding Pattern 4: single mem-

brane folding

Another way of stowing a 25m2 Solar Sail is by fold-ing a single sheet of 5m×5m membrane. This fold-ing technique was first proposed for a Solar Sail in atechnical report by Cambridge Consultants [1]. Butthe idea can be searched back to the 1960’s whereHuso [2] in a patent, proposed an early version ofa single sheet folding technique. In this approachthere is no need to divide the sail into 4 quadrants.A single sheet is folded with a series of hill and val-ley folds around a central spindle as shown in Figure13. To calculate the number of folds required for agiven size sail (l) and a given spindle height (h) wehave:

n =90

arctan 1l

h√

2+1

(4)

Folding Patterns To Try Pattern 3: single sheet using folding apparatus!

Valley fold

l

h

Hill fold

(a) (b)

Figure 13: Single membrane folding pattern

To fold such a pattern by hand could be possiblein smaller scale sheets but when the size increases,even a 5m × 5m sheet would cause a considerablechallenge. In 1961 Lanford in a patent proposeda folding apparatus to fold a circular shaped sheetsimilar to Figure 13 [4].

During our investigation a Folding Apparatus de-signed for a 1.7m × 1.7m square sail membranebased on Lanford’s original 1961 patent was con-structed. The folding apparatus works by creatingtension along points on the edges of the membraneusing strings and weights. The membrane is at-tached to a spindle at the centre of the apparatus.When the spindle is turned the tension caused bythe weights, force hill and valley folds along thesetension lines. Figure 14 shows time-lapsed imagesof the single sheet membrane being folded.

There are two major advantage to this type offolding. First is the lack of multiple quadrants, al-though this can be a disadvantage when one looksat tightening the sail. A single sheet enables a lar-ger sail area and causes a larger propulsion force.

6

(a) (b)

(c) (d)

(e) (f)

Figure 14: Time Lapse of folding a single 1.7m ×1.7m sheet of sail membrane

The second is that the membrane will be wrappedtightly around the spindle because of the tensionfrom the weights during folding. This folding pat-tern uses the available stowage volume efficiently.

5 Proposed Creasing Indic-

ator (CI)

It is known that creasing reduces the sail’s efficiencyand performance. Such a relation is difficult to un-derstand as it encompasses the tightness of the sailand its reflectivity, in addition to the number offold lines. But using the number of folds lines asa measurement of the effects on sail efficiency isunscientific and calls for a better understanding ofthe imapcts of each folding technique. To this ef-fect a creasing indicator (CI) has been developedto measure the amount of creases on the sail mem-brane. CI is a measure of the total length of creaselines on a sail membrane divided by the area of themembrane.

A =Total crease length(m)

Membrane area(m2)(5)

For each of the patterns the following equationsto calculate their creasing metric (CI) are derived.

Note that n is an odd real number representing thenumber of fold lines, l is the length of the side of thesail, and in pattern 4, r is the radius of the centralspindle.

Pattern 1

CI =2

l2

�l

2+ l

�1

cos( 452 )+ S

��(6a)

S =

(n−1)/2�

i=1

�1

cos( 452 − α)+

1

cos( 452 + α)

�(6b)

α =2

n+ 1

45

2i (6c)

Pattern 2

CI =2

l2

l

2+ 2l

(n−1)/2�

i=1

1

sin(90− α)

(7a)

α =90

n+ 1i (7b)

Pattern 3

CI =2

l2

l

2+ l

(n−1)/2�

i=1

1

n+ 1i

(8a)

(8b)

Pattern 4

CI =2

l2

x0 + xn/2 + 2

(n−1)/2�

i=1

xi

(9a)

xi =

��l

sin(90− α)

�2

+ r2 (9b)

α =90

n+ 1i (9c)

To better understand what the creasing indicatorrepresents and how it changes, it is plotted againstthe number of folds (see Figure 15). Note that thesail size is fixed to 5m, so as the number of foldsincreases the spindle length (h) will decrease. Thisplot shows CI is a linear function of the numberof folds, an expected result given the equations forCI. An interesting fact is the slope each patternmakes, showing the effect of the number of foldsfor a given pattern. As an example, pattern 1’sCI increases at a much faster pace as the numberof folds increase with respect to the other foldingpatterns.

Figure 16 better illustrates how CI changes asa function of sail size(l). In this plot the spindleheight (h) is set fixed to 0.15m and the optimum

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Figure 15: CI with fixed sail length of 5m

number of folds is calculated for each sail size to fith. Here pattern 3 is again at a major lead and hasa very low CI throughout the different sail lengths.What is also interesting is how patterns 1,2 and 4are much more scattered at small sail sizes for thegiven h, while pattern 3 keeps at a steady level.This is because the optimum number of folds forsmall sails to fit around a 0.15m spindle, results ina CI that is close between the different patterns.But to really understand how a required spindle

length (h) for a sail size (l) effects CI, a temperat-ure plot for each of the patterns is construct. (seeFigure 20). Again the number of folds has been cal-culated as a function of spindle length(h). In theseplots, pattern 3 has only a maximum CI of 20 whilepattern 2 and 4 are more close to 35 and pattern 1,the largest, is about 50. Using these plots one canalso find the spindle size and number of folds for agiven sail length (l) for an optimum CI. Lookingclosely at the plots shows diagonal shadows thatstart at the bottom-left corner and go up to thetop-right. Each of these different band of shadesrepresent a fixed-real number of folds.

0 1 2 3 4 5 6 7 8 9 100

2

4

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8

10

12

14

16

18

Sail length (m)

A m

etric

Pattern 1Pattern 2Pattern 3Pattern 4

Figure 16: CI with fixed spindle length (h) (chan-ging n folds)

The creasing indicator (CI) can not only be usedto analyse the effect of folding patterns on the effi-

ciency of the sail but also as a tool for optimisingthe number of folds(n) and spindle length(l). CIcan also be used to analyse different folding pat-terns and compare them with each other. To datethere have been no relationship between the effi-ciency of the sail and creasing. But CI has at-tempted to bridge this gap. As CI increases, thesail’s efficiency should decrease. But the amount itdecreases depends on how taught the sail is, whichintern depends on the sail material and size. Find-ing this relationship mathematically will prove dif-ficult, but experimental analysis could assist in de-termining the nature of this relationship.

5.1 Folding Summary

Folding the sail membrane is important in guaran-teeing reliable deployment of the Solar Sail. Fourfolding patterns where presented, of which threewhere implemented on a 1.7m×1.7m model. Table7 shows a trade-off of the different patterns. It alsopresents the number of optimum folds required fora 25m2 sail to fit around a 15−16mm long spindle.From this the thickness of each folded quadrantis derived, given an indication of the amount ofvolume each folding technique could potentially oc-cupy about the spindle.

The best option in terms of ease and efficiencyof stowage is the single membrane folding. Whilebased on our proposed Creasing Indicator, pattern3 least effects the sail’s performance, trailing by thesingle sheet technique. Pattern 3 is the CubeSail’schoice of folding as it’s crease lines are close to right-anlge with respect to the tension lines, enabling ataught sail with a minimum force.

6 Sail Deployment

For ground demonstration and testing proposes, asmaller scaled sail membrane (1.7m × 1.7m) wasutilised on the CubeSail engineering model.

6.1 Test Setup

The deployment mechanism was mounted on a ro-tating platform constructed to enable the mechan-ism to rotate freely about its roll axis with as low afriction as possible. This enables observation of thechange in the roll angle as well as roll rate duringdeployment. Underneath the platform was coveredwith non-stick baking sheets to provide a smoothlow-friction surface for the booms to glide over.

To take measurements, two devices where used,a motion capture system and a video camera. The

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Sail membrane

25mm boom Spindle release

Batteries

Control electronics

Active IR markers

Central Shaft

Rotating Platform

Figure 17: Deployment setup on a Low friction ro-tating platform

motion capture system uses multiple infrared cam-eras to construct a 3D representation of the positionof an object. The cameras emit an IR pulse which isreflected by small spherical IR-markers and recap-tured by the cameras, the position of these markersare then accurately calculated.

6.2 Results

6.2.1 Uncontrolled Deployment

Figure 21 shows time-lapsed images and Figure 18shows the angular position and velocity data fromthe motion capture system of an uncontrolled de-ployment. Observation from the time-lapsed im-ages suggest that, from point (a) through to point(e) the booms do not contact the ground. Atpoint (e) the booms have extended to about 1mwith a change in angular position of 75.7deg, Theyhave started contacting the ground. At this pointthe angular position reverses until point (g) whenthe booms are fully extended, the angular positionsettles down to 72.2deg. Also the deployment speedis about 0.7s with a peak in angular velocity (ω) ofabout 438deg/s.Several oscillations are seen before and after full

extension at (g). Through careful observations ofthe video, it is thought that these are caused byvibrations in the booms. The booms extend so vi-olently that they vibrate. Even if the booms didnot contact the ground, it is thought that the vi-brations would feedback into the bus, this is visiblein the oscillations seen before (g) when the boomsare still airborne.When deployment porcess is uncontrolled as in

the above case, the instantaneous angular acceler-ations are too high. The attitude determinationsensors considered for the mission would not be able

to keep track of the attitude during this time. Thisshows that the booms would need to be deployedin a controlled manner.

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Figure 18: Uncontrolled deployment

6.2.2 Controlled Deployment

To control the deployment, a motor is added tothe system. This motor drives the booms out ofthe mechanism at a slow speed. Figure 22 showstime-lapsed images and Figure 19 shows the angu-lar position and velocity data from the motion cap-ture system of a controlled deployment. By point(c) most of the changes in angular position hasbeen completed, 3.8s into deployment and 38.3degchange in position. Between point (c) and (d) thechange in position remains somewhat constant withsmall back and forth motions cause by vibrationsin the boom. After point (d) and up to (f) thisvibration intensifies and causes large momentumson the system. It is only after point (e) when thebooms contact the ground that these vibrations aredamped. Point (f) is full deployment occurring at18.3s. The sources of these vibrations are causedby an opening in the mechanism for the booms toextend from. In the engineering model this openingis designed much larger than required to test differ-ent size booms, hence the boom is free to move andflex about.

When comparing the two above cases, a longerdeployment time is seen in the controlled system.Also in the controlled case the angular rate caused

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eg)

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time (sec)

Figure 19: Uncontrolled deployment

during deployment is an order of magnitude smal-ler than the uncontrolled case. It is concluded thatmost of the momentum transfered to the spacecraftoccurs at the initial stages of deployment. This iswhen the spacecraft inertia is small and the boomand membrane spindles are large. In effect an idealsystem will start with a slow boom extension tocause a small momentum transfer onto the space-craft and end with a faster more forceful extensionof the booms to achieve a tight sail membrane.

7 Conclusion

The deployment of a Solar Sail in space is a challen-ging problem and this paper addressed it by propos-ing a deployment system for the CubeSail mission.The deployment system consists of four booms andfour triangular quadrant sail membranes. Thebooms are made of tape-spring blades, put frontto front. Membrane folding and the importanceof efficient wrapping was discussed. Four foldingpatterns where presented and compared. A Creas-ing Indictor was proposed that aimed to bridge thegap between the effects of folding on sail efficiency.It also provided a means for calculating the effi-cient number of folds for a set size sail and set sizespindle. Finally, the deployment of a 1.7m engin-eering model was shown and test results of the an-gular rates during controlled and uncontrolled de-

ployment were discussed.

Acknowledgements

This work was carried our as a part of funding byEADS Astrium at the Surrey Space Centre and incollaboration with Stellenbosch University. The au-thors would like to specially thank Johnny Fernan-dez, Theodorous Theodorou and Lourens Visagiefor their assistance.

References

[1] Cambridge Consultants. Design study for a marsspacecraft. Technical report, Cambridge Consult-ants, 1989.

[2] M. A. Huso. Sheet reel, 1960. U.S. Patent no2942794.

[3] L. Johnson, M. Whorton, A. Heaton, R. Pinson,G. Laue, and C. Adams. Nanosail-d: A solar saildemonstration mission. Acta Astronautica, 2010.

[4] W.E. Lanford. Folding apparatus, 1961. US Patent3,010,372.

[5] V. Lappas, N. Adeli, J. Fernandez, T. Theodorou,Visagie. L., H. Steyn, O. Le Couls, and M. Perren.Cubesail: A low cost small cubesat mission for de-orbiting leo objects. In Small Satellites Systems andServices, June 2010.

[6] V. Lappas, H. Steyn, S.N. Adeli, L. Visagie,T. Theodorou, and J. Fernandez. Design of a cube-sat solar sail attitude determination and control sys-tem. In AIAA Guidance, Navigation, and ControlConference and Exhibit, 2010.

[7] Colin R. McInnes. Solar Sailing: technology, dy-namics and mission applications. Springer Praxis,2004.

[8] M. Osamu, H. Sawada, R. Funase, M. Mor-imoto, E. Tatsuya, T. Yamamoto, Y. Tsuda,Y. Kawakatsu, and J. Kawaguchi. First solar powersail demonstration by ikaros. JAXA, 2009.

[9] J.L. Wright. Space sailing. Routledge, 1992.

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Figure 20: Creasing indicator (CI) vs. sail size and spindle length

Pattern

CI Advantages Disadvantages25m2, 12µm sail membrane

Total no. Min spindle Quadrentfolds (per Q) height thickness

1 15.71 easy stowagedifficult folding

72 (17+1) 15.62cm 384µmcrease line convergencecrease � tension line

2 11.11easy stowage difficult folding

100 (25) 15.12cm 384µmcrease ⊥ tension line crease line convergence

36.8

easy foldingloose stowage 132 (33) 15.62cm 384µmcrease ⊥ tension line

no crease line convergence

4 12.57easy & compact stowage difficult folding

104 (25+1) 15.12cm 312µmcrease ⊥ tension line crease line convergencelarger sail area

Table 2: Sail membrane folding comparison

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(a) 0.00 s (b) 0.17 s (c) 0.27 s

(d) 0.37 s (e) 0.47 s (f) 0.57 s

(g) 0.67 s (h) 0.77 s (i) 0.87 s

Figure 21: CubeSail engineering model uncontrolled deployment

(a) 1.2 s (b) 2.6 s (c) 3.8 s

(d) 7.3 s (e) 11.25 s (f) 18.3 s

Figure 22: CubeSail engineering model controlled deployment

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