1

Experimental Research on Roll-up Storage Method for a Large Solar Sail

By Kazuya SAITO1), Nobukatsu OKUIZUMI2) , Hiraku SAKAMOTO3), Junji KIKUCHI2)

, Jun MATSUMOTO2), Hiroshi FURUYA3) , Osamu MORI2)

1)Institute of Industrial Science, The University of Tokyo, Tokyo, Japan 2)The Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan

3) Tokyo Institute of Technology, School of Engineering, Tokyo, Japan

(Received 1st Dec, 2016)

Large membranes used as solar sails should be stored compactly to reduce launch volume. In addition, their stored

configuration should be sufficiently predictable to guarantee reliable deployment in orbit. The roll-up method is a workable

option for storage of large solar sails, as demonstrated in IKAROS. However, with this method, it is difficult to predict the

roll-up position because the membrane’s thickness causes deviation from the ideal position. In this presentation, these

deviations are evaluated in an experiment involving storage of a 50-m solar sail, and a position control method for roll-up

storage of a large solar sail is proposed. These techniques contribute strongly to the repeatability of storage configurations

of large solar sails.

Key Words: Deployable Structure, Storage Method, Solar Sail

1. Introduction

An efficient method for storing a large membrane in a

compact space is essential for the solar sail systems1-4.

Therefore, researchers have proposed various types of solar sail

folding methods. In the case of IKAROS3, 4, one of the

successful solar sail missions operated by JAXA, the roll-up

storage method and centrifugal-force deployment were

demonstrated (Fig. 1). These storage and development systems

are also planned to be used in JAXA’s next-generation solar sail

missions5. Figure 1 shows a schematic of the roll-up storage

method discussed in this paper. A square-shaped solar sail is

divided into four trapezoidal membranes (Fig. 2(a)), and each

membrane is folded into a belt-shaped “petal” by z-folding (Fig.

2(b), (c)). Each petal is fixed to the center of the satellite body

(dram) (Fig. 2(d)). As indicated by the red circle in Fig. 2, each

petal is connected half-and-half to the next petal by the harness

and reeled on the dram together.

Z-folding and the roll-up process were executed by hand in

IKAROS, and similar manual techniques are planned to be used

in next-generation solar sail projects. However, with the

manual roll-up method, it is difficult to ensure repeatability of

storage shape because it is difficult for workers to maintain

constant tension during the roll-up process. This inconsistency

in roll-up forces causes misalignment in the fixed position of

the petals each time the storage process is executed. To cope

with this difficulty, we analyzed the roll-up position control

method. Before roll-up, equally spaced markers are placed on

each petal. By using these markers and the scale on the dram,

workers can roll up the petals to predetermined positions on the

dram without having to maintain constant tension. If the target

positions of all markers are given properly, that is, the roll-

upped petals have no biased tension that may slide the rolled-

up shape, so it is possible to maintain a consistent storage

configuration.

The purpose of this research is to develop a procedure for

determining the target positions in the above-mentioned manual

roll-up process. In a previous study, a few of the authors of the

present study performed a roll-up experiment by using a dram

with a radius of 150 mm and 10-m class solar sail membranes,

and investigated the relation between the

Fig. 1 Deployment sequence and mechanism of IKAROS8.

Fig. 2 Schematic of the roll-up storage method.

(a)

(b) (c) (d)

2

petal thickness and misalignment in a roll-up position6, 7. On the

basis these results, we conducted additional roll-up experiments

using a dram with a radius of 1500 mm and an 18-m-class solar

sail, which is intended for use as the next-generation large-sized

solar sail. First, we present the basic idea of the proposed roll-

up position control method and explain how to calculate the

target position. Second, we describe the roll-up experiments

and discuss the validity of the proposed method. This method

enables us to guarantee repeatability of the storage

configuration, even in the case of manual roll-up storage.

2. Roll-up Position Control Method

Consider an L-long petal reeled on a dram of radius R, as shown

in Fig. 3. The petal has marks (A1, A2, ….) at intervals of l. Phase

angles (1,2,…) express the rolled-up position of each mark on the

dram. For a zero-thickness petal, the phase angle of An can be

calculated as

n = nl/R. (1)

In a real roll-up process, the marks’ position slide from above the

ideal phase angles. Owing to the thickness of the petal, the actual

roll-up radius is larger than the dram radius. To express this slide

value quantitatively, we use deviation dn defined as follows. For a

petal with uniform thickness tc, assuming that the actual roll-up

radius is (R+ tc) (see Fig. 4(b), deviation dn is given as

dn R{nl/R–nl/ (R + tc)} ≒ n tcl/R = tcn. (2)

Here, we assume that the dram radius R is much greater than the

petal thickness tc. In fact, the actual petals are not uniform in

thickness but have a complex profile because of the shape of the

original (unfolded) membrane and owing to the presence of many

equipped devices such as solar panels and harnesses. Expressing

this thickness profile by the function t(), deviation d() at point

in the petal is given by the following equation:

𝑑(𝜙) = ∫ 𝑡(𝜃)𝑑𝜃𝜙

0 (3)

For simplicity of calculation, petal length is expressed by the form

of the phase angle . (Using x, the distance from the roll-up starting

point, = x / R[rad]). From eq. (3), deviation d equals the area of

thickness profile t().

In the case of multiple roll-ups with more than one petal,

overlaps on other petals occur, accompanied by an additional

increase in the actual roll-up radius, leading to further deviation. If

the petal length exceeds the dram perimeter, a self-overlap would

occur as well. For calculating deviation, these overlap effects can

be considered in the thickness profile’s function. Figure 5 shows

an overlap case; petal-A with a thickness profile t1() overlaps

petal-B with a thickness profile t2() at the point In this

situation, the deviation can be calculated from the practical profile

T(), which is obtained by summing the two profile functions as

T() = t1() + t2() (4)

In the case of three or more petals self-overlapping, deviation d()

can be calculated in a similar manner using the practical profile

T().

The phase angle n of rolled-up position An can be predicted as

follows:

n = n–dn/R (4)

dn = ∫ 𝑇(𝜃)𝑑𝜃(𝜃𝑛)

0 (5)

To determine n, the practical thickness profile T() is required.

This function must include not only the thickness of the membrane

but also that of the equipped devices. In addition, the roll-up

tension force in the outer petal imposes a pressing force on the

inner petal. Therefore, the roll-upped thickness is thinner than that

of an un-rolled petal. The previous study also reported bulging

between inner and outer petals6 ,7. For these reasons, it is difficult

to measure the practical thickness profile T() directly. As

discussed in the following sections, we therefore use an indirect

method to determine T(). Before determining the target phase

angle, the first part of petal was rolled up preliminarily. By

investigating the trend in deviation on each mark, the practical

profile T() can be approximately calculated.

Fig. 3 Relationship between dram radius R and phase angle

Fig. 4 Ideal (zero-thickness) petal model and uniform thickness petal model.

Fig. 5 Schematic of calculation of the practical profile T() in overlap

case.

l

A0

A1

A2 L

A1

A2

1 2

・・・

・・・

R

l

A0

A0

R

R

nl

A0

n

R

Antc

dAn

n nl

R tc

T

t1

t2

+

t2

t1

3

3. Single Roll-up Experiment

3.1. Setup

To investigate the practical thickness profile T, the petal was

reeled one round on the dram and the deviation of each mark

was measured. Figure 6 shows the schematics of the dram and

the petal used. The dram radius R is 1,328 mm with petal

holders at 1/8th point of each round. The petal is made from

trapezoidal solar sail membranes having dummy solar cell

devices. The membrane is folded into a belt-shaped petal with

a length of 17,472 mm and width of 450 mm through Z-folding

and is held by clips to maintain the folded shape. The petal has

marks at intervals of 1,048 mm as targets of the roll-up

positions. At the start of the experiment, the petal was housed

in another small dram for easy handling. During the roll-up

process, a worker tried to maintain constant tension on the petal.

Two types of roll-up configurations, one-fold roll up and

twofold layer roll-up, are examined, as shown in Fig. 7.

3.2. Result

The experimental results are summarized in Figs. 8 and 9.

The points in Fig. 8 show the deviation of each marker in the

one-fold roll-up experiment. The deviation increases

approximately linearly, which indicates a uniform-thickness

model, as shown in Fig. 4(b). Eq. (2) can be used for calculation.

The gradient of the approximate line that corresponds to the petal

thickness tc is 38 mm. Figure 9 shows the results of the two-fold

roll-up experiment. As indicated by the dotted line in Fig. 9 (a), the

change in the deviation can be approximated by a parabolic curve.

This means that the thickness profile T() can be considered to

follow the tapered-thickness model, in which thickness decreases

linearly. The practical thickness profile T() can be calculated from

the approximate curve in Fig. 9(a), and it is shown in Fig. 9(b).

Fig. 6 Schematics of dram and petal used in the experiment.

Fig. 7 Schematics of one-fold roll-up (upper) and two-fold roll-up

experiments (lower).

Fig. 8 Deviation of each marker in one-fold roll-up experiment.

Fig. 9 Deviation of each marker in two-fold roll-up experiment (a) and

calculated thickness profile T() (b).

y = -3.1899x2 + 40.558x

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0.000 0.785 1.571 2.356 3.142 3.927 4.712 5.498 6.283

d [

mm

]

[rad]

y = 38.125x - 23.574

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0 0.78541.57082.35623.1416 3.927 4.71245.49786.2832

d [

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]

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T[mm]

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(b) 17,472mm

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4. Multi Roll-up Experiment

In the next-generation solar sail system, the satellite is

equipped with petals measuring 25 m in length, and these petals

would be rolled-up more than three times on the dram. To

validate the effects of multi roll-up and self-overlapping, we

conducted two- and three-Lap roll-up experiments after the

one-fold roll-up experiment described in the previous section.

Figure 10 shows the experimental result of the first roll-up. In

each lap, if the deviation increases linearly, it can be considered

that the process follows the uniform thickness model. In the

second and third laps, overlap occurs on the previously rolled-

up parts. As discussed in the section 2, these overlaps are

predicted to increase the practical thickness profile T; therefore,

the gradients of the deviation should increase with increasing

number of laps. However, such an increase in the gradient

because of the overlap effect was not observed in the second

and third laps, as shown in Fig. 10. The gradient of the second

lap is 0.5 times that of the first lap. The deviation in the third

lap shows the same gradient as that in the second lap.

5. Discussion

The petal used in this study is made from a Z-folded

trapezoidal membrane (Fig. 1), so the cross-section of the petal

is trapezoidal. However, the practical profile, T, calculated

from the single roll-up results is different from the predicted

shape. These differences are thought to be caused by

Fig. 10 Experimental result of 3-Lap roll-up experiment.

Fig. 11 Experimentally determined thickness profile T and calculated target

position.

deformation because of the roll-up tension force and additional

thicknesses of the harnesses and equipped devices.

As a result, simple models such as the uniform-thickness model

or linearly tapering model are effective for predicting the

deviation.

In the multi roll-up experiments, we confirmed that the

practical thickness profile decreases as the number of roll-up

laps increases. This decrease is considered to be caused by

deformation of the rolled-up part. In the cases of second and

third roll-ups, the petal is pressed on the previously rolled-up

part. Then, the roll-up tension force may cause the actual rolled-

up radius to decrease. In Fig. 10, the gradient of the third lap

shows no increase from that in the second lap; therefore, the

decrease in roll-up radius is larger than the increase in petal

overlap.

The results indicate that the following method is effective for

predicting the rolled-up target position. Firstly, an approximate

model of the practical thickness profile T is determined from

the result of the single roll-up experiment. The uniform

thickness model or linearly tapering model can be selected

according to the tendency of deviation. The target positions of

the second and third laps are calculated by these results in the

first lap. For simplifying discussion, we employed the uniform

thickness model. If deformation of the pressed petal is not

considered, the practical petal thickness in n-laps is given as tcn

= ntc1. Considering the decrease in the roll-up radius, the

proposed method uses an adjusted value for calculating (tc2, tc3).

tc2 = 2 tc1 (6)

tc3 = 3tc1 (7)

In the case of the experiment in the previous section, 2 = 0.5

and 3 = 0.0.

Using the proposed method, the multi roll-up experiment was

conducted again. In this experiment, the roll-up target positions

of the second and the third laps were calculated from the results

of the first lap. The results are summarized in Fig. 11. From the

deviations of the first lap, the thickness profile can be

approximated using the uniform thickness model and tc1 = 32.7

mm. Using the abovementioned adjusted value, tc2 and tc3 are

calculated to be 16.4 mm and 0.0 mm, respectively, and the

practical thickness profile T is shown in Fig. 11 (a). The red line

in Fig. 11(b) indicates the target position of each marker

calculated from Fig. 11(a) and Eqs. 4 and 5. The points in Fig.

11(b) show the results of the roll-up experiment conducted

using these target positions. It is confirmed that each marker is

positioned at the proper target phase in the storage shape. The

marker positions did not change after the experiment; therefore,

tension force is thought to be maintained properly in the stored

shape.

6. Conclusion

Roll-up storage experiments were conducted on next-

generation large-size solar sails, and deviation in the stored

position of the petals was investigated. Using the experimental

results, a method to calculate the proper target position for the

roll-up process was proposed. These techniques strongly

contribute to the repeatability of the storage configurations of

large solar sails in manual roll-up storage.

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0 1 2 2 3 4 5 5 6 7 8 9 9 10 11 12 13 13 14 15 16 16 17 18 19

d[m

m]

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y = 32.684x + 3.4741

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[rad]

tc1= 32.68mm tc2= 16.34mm tc3= 0.0mm

T

1-Lap 2-Lap 3-Lap

5

Acknowledgments

The experiments described in this study were conducted

with the support of students at Kawaguchi Lab. At

ISAS/JAXA, Sakamoto Lab. and Furuya Lab. at Tokyo

Institute of Technology. The authors thank the Solar Sail

Working Group members at ISAS/JAXA for meaningful

discussions.

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