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IAC-18-D4.4 Page 1 of 9
IAC-18-D4.4
CHARACTERIZATION OF A NON-STATIONARY SPHERICAL INFLATED
LIGHT SAIL FOR ULTRA-FAST INTERSTELLAR TRAVEL
BY USING COMMERCIAL 3D CODES
Gianmario De Blasio*
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy
E-mail: gianmario.deblasio@polito.it
Dario Riccobono*
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy
E-mail: dario.riccobono@polito.it
Giancarlo Genta
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Italy
E-mail: giancarlo.genta@polito.it
*Indicates equal contribution to the manuscript, co-first authorship.
Abstract: Spherical inflated light sails have been considered to push ultra-light nanocrafts at a significant fraction
of the light speed. The light sail, which is essentially an extremely thin shell, would be subjected to extremely high
accelerations and deformations. The purpose of this research is to perform a non-stationary 3D numerical analysis
to study the deformed shape of a spherical inflated light sail riding on a laser beam. Common commercial codes are
not specifically designed to deal with this phenomenon. A similar physical context can be found in crash events,
which can be analyzed by using commercial codes. Since the development of a dedicated numerical code would
require a remarkable effort, an attempt of using such commercial codes has been conducted. Moreover, the effect
of changing the sail’s shell features, such as its thickness, as well as the inflating pressure have been considered.
The model is close to a potential real case application in terms of both the acceleration given to the light sail (20000
g) and the sail’s diameter-to-thickness ratio (2 m / 0.1 μm). Particular attention has been paid to the simulation of
the dynamics of the inflating gas and its effect on sail’s deformation. The inflating gas was introduced with the aim
of providing a stabilizing effect on sail’s shape. Contrary to expectations, the results have shown a counterintuitive,
destabilizing effect. Significant changes in the deformation mechanisms at different pressure regimes were
observed, all showing the active role of the inflating gas in the destructive failure of the sail. A solution without
inflating gas has been simulated showing significant benefits. The results of this study provide significant guidelines
to drive the future developments of light sails, as well as a useful input for further analysis on beam’s riding stability.
Keywords: Light sail, Interstellar space travel, Ultra-fast space travel, Nanocraft
Symbols
Speed of light in vacuum.
Nodal mass.
Element stiffness.
Interface stiffness.
Acronyms/Abbreviations
CAD
Computer Aided Design
CNT
Carbon Nano-Tube
FEM
Finite Element Method
IKAROS
Interplanetary Kite-craft Accelerated
by Radiation Of the Sun
JAXA
Japanese Aerospace Exploration
Agency
NASA
National Aeronautics and Space
Administration
NEA
Near Earth Asteroid
SPH
Smoothed Particle Hydrodynamics
SRP
Solar Radiation Pressure
2D
Two-dimensional
3D
Three-dimensional
69th International Astronautical Congress, Bremen, Germany. Copyright ©2018 by the International Astronautical Federation. All rights reserved.
IAC-18-D4.4 Page 2 of 9
I INTRODUCTION
Space propulsion systems adopted in the past
nearly 60 years of spaceflight are unable to provide the
required energy to accelerate a space probe at a
reasonable speed for interstellar travel. Only the
Voyager 1 spacecraft, launched in 1977, has barely left
the Solar System after 37 years of flight at a speed of
17 km/s, or less than 0.006% of the speed of light. To
pave the way to interstellar travel it is necessary to
change our thinking about the idea of both propulsion
and spacecraft [1].
A number of different propulsion concepts have
been proposed to allow reaching the nearest stars.
Some of those proposals include advanced electric
propulsion, nuclear (fission, fusion, antimatter)
propulsion, electromagnetic catapults, in-situ
propellant production (e.g. the interstellar ramjet) and
hybrid systems (e.g. antimatter-catalyzed
fission/fusion). Those technologies range from
relatively feasible long slow missions to high risk fast
missions. Among those proposals, a light sail riding on
a laser beam (i.e. the beamed energy propulsion
technology) represents a promising candidate being
able to push gram-scale spacecraft at a significant
fraction of the speed of light and reach the nearest star
in few decades [2] [3].
The idea that light can push objects dates back to
17th century, when Johannes Kepler observed comets’
tails always point away from the Sun. In the 19th
century, James Clerk Maxwell’s equations gave
consistency to the hypothesis that electromagnetic
radiation has momentum and some experiments
performed in the early 20th century strengthened the
idea of harnessing photons pressure to propel a
spacecraft, a concept first proposed by Frederick
Tsander and Konstantin Tsiolkovsky in the 1920’s.
NASA’s Echo 1 balloon, launched in 1960, was the
first spacecraft designed to measure the effects of Solar
Radiation Pressure (SRP). The initial researches
focused on solar sails, a special class of light sails that
use the pressure of solar photons [4] [5]. In 2010, the
Japanese Aerospace Exploration Agency (JAXA)
launched the IKAROS (Interplanetary Kite-craft
Accelerated by Radiation Of the Sun) mission,
deploying a sail of about 200 m2 that demonstrated the
solar sail propulsion technology in deep-space for the
first time [6]. In the late 2010, NASA launched and
deployed in Earth orbit a sail of about 10 m2, called
NanoSail-D [7]. In 2015, Planetary Society’s funded
LightSail-1 mission successfully launched in Earth
orbit a three-units CubeSat with the aim to demonstrate
the deployment of a solar sail of about 30 m2 [8]. A
NASA mission currently under development, named
Near Earth Asteroid (NEA) Scout, will consist of a
controllable CubeSat spacecraft capable of
encountering a NEA by using a solar sail of about 85
m2 [9].
The technology advances that have followed the
invention of lasers have opened the possibility of light-
powered space travel at a significant fraction of light
speed, paving the way to potential future interstellar
probes [10] [11]. This technology would involve
ground or space-based laser beamers to accelerate
ultra-light nanocraft attached to light sails [12].
Recently, the Breakthrough Starshot Initiative was
funded with the intention of using high-power lasers to
propel miniature space probes attached to light sails to
a significant fraction of light speed, with the aim of
realizing the first interstellar mission to reach Alpha
Centauri in just few decades [13].
Several engineering challenges must be faced to
enable laser-propelled light sails. One of the most
important issues regards the sail’s stability with
respect to the laser beam, meaning that it is required
that disturbances, misalignments and manufacturing
imperfections do not influence sail’s centring on the
laser beam. Two main approaches are possible to
ensure such sail’s stability. The first one considers
active feedback controls but the need to use several
sensors and actuators would lead to a significantly
complex and massive spacecraft. The second approach
considers the possibility to design a light sail which is
passively stable. This approach would focus on sail’s
features (e.g. shape, material properties, etc.) and on
laser beam’s configuration to ensure stability. Previous
studies have shown that conical sails are unstable
without active control [14]. On the other hand,
spherical sails are passively stable because of their
intrinsically stable shape [15]. Therefore, the spherical
sail is one of the most suitable candidates to propel
ultra-light, ultra-fast nanocraft. A critical issue may be
related with the huge forces acting during the
acceleration phase, which may potentially deform the
sail and affect its stability with respect to the laser
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IAC-18-D4.4 Page 3 of 9
beam. This paper addresses the problem of the sail’s
stability with respect to its shape by performing a
preliminary analysis of the deformed shape and
evaluating the potential benefits of inflating the sail
with some gas. This solution may help keeping the
sail’s shape as spherical as possible and increase its
stability boundary with respect to the laser beam.
Two separate analysis were conducted in series.
The first analysis [16] involved a first approximation
2D model of the spherical sail and a not specialized
numerical code to quickly, still reliably test several
configurations and provide indications for the second
analysis. The latter analysis is described in this paper
and regards a more refined preliminary 3D analysis of
the spherical sail which involved the use of a
specialized commercial code to achieve better results.
Finally, some potential future design solutions are
introduced.
II 3D ANALYSIS
The results of the 2D analyses previously
conducted have been affected by the strong
assumptions imposed to the model, limiting its
accuracy [16]. For this reason, a more refined 3D
model was developed to describe the light sail
behavior in a more accurate way, tearing down most of
the simplifications of the 2D model. A qualitative
representation of the phenomenon under investigation
is shown in Figure 1. To perform such kind of analysis,
it was necessary to adopt a more specialized
commercial suite performing FEM-based analyses, the
Altair HyperWorks suite. As a consequence, it was
possible to push the limits of the model to a higher
level of fidelity, closer to the real case, full exploiting
the capabilities of the simulation suite in providing
very stable and reliable numerical tools.
The axisymmetric assumption was removed,
making possible the evaluation of potential
non-axisymmetric loads/deformations.
The sail’s shell thickness was reduced of one
order of magnitude with respect to the 2D
model (from 5 μm to 0.1 ÷ 0.4 μm).
The sail’s diameter was doubled with respect to
the 2D model (from 1 m to 2 m).
The sail’s mass was reduced of one order of
magnitude with respect to the 2D model (from
21.3 grams to 1.7 ÷ 6.8 grams).
The sail’s acceleration was raised of three
orders of magnitude with respect to the 2D
model (from 30 g to 20000 g).
The internal properties of the gas were
modelled by using a particle method able to
reproduce both its internal behaviour and its
effect on the sail, especially concerning the
simulation of the impulsive dynamics related
with the ultra-high accelerations considered.
A dedicated explicit solver, named RADIOSS, was
used to simulate the high non-linearity related with the
super-impulsive phenomenology of the light sail
acceleration [17]. This solver is particularly suitable
since it is widely used to simulate strongly impulsive
events such as car crashes or airbags inflation, being
able to discretize the problem both in time and space.
Figure 1. Qualitative scheme showing the directions of
the external laser beam pressure which accelerates the
sail versus the internal pressure due to the gas inertial
effects.
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IAC-18-D4.4 Page 4 of 9
Even if this solver was never used for a specific
problem such as the one described in this study, it was
believed being one of the best options commercially
available.
Similarly to the 2D analysis previously performed,
the material used for the light sail is based on Carbon
Nano-Tubes (CNTs).
The suite has allowed to model the internal gas by
using the Smoothed Particle Hydrodynamics (SPH).
Such a method is generally used to simulate the
dynamics of continuum media. It is a mesh-free
Lagrangian method initially developed for
astrophysics but subsequently used in many other
fields [18]. The combination of using an explicit solver
and the SPH method to model the internal gas has
yielded a considerable higher computational cost and
time with respect to the 2D case. Such increases were
considered acceptable, being well within reasonable
margins and greatly balanced by the higher fidelity of
the model. The major limitation coming with the use
of the RADIOSS solver was the impossibility of
reproducing the 3D Gaussian distribution of the laser
beam, which for symmetry reasons would have been
made of four Gaussians instead of two such as in the
2D case. For this reason, a constant laser pressure was
applied to the light sail. The model used to reproduce
the shell of the sail is a sphere of 2 meters of diameter
whose surface was meshed with shell elements to
optimize the computational cost. In fact, a mesh with
tetrahedral elements in such a small thickness would
have led to huge computational cost, as well as poor
mesh and results quality. A total number of 14818
elements and 8321 nodes was obtained.
The internal volume of the spherical sail was
discretized with SPH entities (i.e. particles). A total
number of 3163 SPH entities was derived by selecting
some parameters defining this type of mesh.
Pitch. It is a dimensionless parameter that
determines the distances between each SPH
entity. A smaller value results in a higher
density of entities. This is not affecting the
mass or the density of the gas that the entities
represent. The choices for this field are:
o Simple cubic geometry, where the
SPH entities are arranged in groups of
8, with each entity placed in a corner
of a cube.
o Face centered cubic geometry, where
the SPH entities are arranged in
groups of 14, with the entities placed
in the center and the corners of each
face.
Material Density/Filled Volume Mass. These
options allow to specify the quantity of gas
represented by SPH entities either by
specifying its total mass or its density. In the
latter case the total mass is determined by the
volume filled.
Partial Fill. This option is available to
simulate a fluid that does not completely fill
the selected volume, for example in case of a
liquid partially filling a tank.
Wall Clearance. This option allows to create
SPH entities from a specified distance. It is
used when avoiding contact between the SPH
entities and the walls of the container is
required at the first iteration of the simulation
run, helping the solver running smoothly.
For the purposes of this study, the number of SPH
entities was obtained by selecting a pitch of 0.1 and a
filled volume mass equal to the desired mass of gas and
by imposing a wall clearance of 0.1 in order to help the
solver running smoothly.
Once the SPH entities have been generated, a
contact interface between the sail’s inner shell and the
entities was defined. For this reason, a TYPE7 nodes-
to-surface contact was chosen, selecting the contact
surface containing all the elements belonging to the
sail’s shell as master surface and all the SPH entities
as slave. This interface contributes substantially to
decrease global time step. In fact, the interface time
step must be computed to ensure stability. The resistive
force is a function of the interface stiffness, and it is
strongly nonlinear with respect to the penetration of
the slave node into the gap, as shown in Figure 2,
where is the instantaneous stiffness and is the
initial stiffness value.
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IAC-18-D4.4 Page 5 of 9
It is crucial that the slave node does not cross the
master segment. This gives good accuracy for the node
location and means that the interface time step needs
to be evaluated during the solution. If there is large
penetration the interface stiffness becomes larger
leading to a time step reduction. The nodal time step
during contact can be expressed by using Eq. (1) [19].
(1)
Where is the nodal mass, and
are respectively the interface stiffness and the
element stiffness.
The contact interface in the gap can be schematized
as in Figure 3.
Figure 3. Contact interface scheme [19].
Once the contact was defined, a kinematic viscosity
similar to that of the air (7.71 ∙ 10-6 m2/s) was assigned
to the SPH entities.
Finally, in order to simulate the motion of the sail,
RADIOSS required to apply both the laser pressure
that pushes the sail and the respective acceleration
produced. Both the boundary conditions were applied
on the irradiated semi-sphere of the sail’s shell so that
the real conditions were faithfully represented.
III Numerical simulations and results
The explicit simulations focused on the steady-state
phase of the sail’s acceleration, meaning that the
starting point of the simulation considered the sail
already in motion at the desired acceleration. The idea
was to simulate the last milliseconds of the sail’s
motion from 19.999% (59957002 m/s) to 20% of the
speed of light (59960000 m/s). Considering an
acceleration in the order of 20000 g, the simulation
time was confined to the order of 15 milliseconds.
However, the limitations of the solver have imposed
the introduction of a substantial approximation.
Although the whole sail was subjected to an initial
velocity, the gas was instead at rest at the beginning of
the simulation, which is a condition substantially
different with respect to the real one. In fact, at the
beginning of the simulation, the gas should have been
already pushed against the irradiated semi-sphere of
the sail with a certain distribution. Unfortunately, such
distribution cannot be set as initial condition because
of the intrinsic limitations of the solver. Another
potential option could have been the simulation of the
sail’s motion from the real beginning. That means,
from the zero speed/zero acceleration condition (i.e.
sail at rest), through the transient phase (i.e.
acceleration raise) and the steady-state condition (i.e.
constant acceleration), up to the target speed (i.e. max
speed/zero acceleration). Even at very high
accelerations, such a simulation would have had a
duration of tens of seconds, if not even minutes, which
would have required an unacceptably high
computational cost and time, not in line with the
purposes of this preliminary study. For this reason, the
approximation introduced by the steady-state analysis
was considered acceptable.
First evaluations have shown that increasing the
pressure of the gas (ranging from 0.1 Pa to 100 Pa)
with the aim to keep the sail’s shape as spherical as
possible, considerably amplifies the gas inertial forces
at very high accelerations (in the order of 20000 g),
because the mass of the gas increases accordingly with
its pressure (ranging from 0.0073 grams to 7.3 grams).
Figure 2. Resistive force of the contact interface with
respect to the penetration of the slave node into the
gap [19].
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IAC-18-D4.4 Page 6 of 9
The sail’s shell thickness has been also varied (ranging
from 0.1μm to 0.4 μm) to investigate its gas
containment capabilities. Results have shown that the
sail’s shell experiences remarkable stress due to the
inertial effects of the gas, which have represented also
the first cause of failure. The failure mode in presence
of a higher gas pressure is shown in Figure 4. This
figure highlights how the sail’s shell elongates
longitudinally along the direction of motion (i.e.
positive direction of the y-axis) due to the inertial
pressure of the gas, before breaking apart probably due
to the overpressure (i.e. the red spot) on the irradiated
surface. On the other hand, the failure mode in
presence of a lower gas pressure is shown in Figure 5,
where the failure seems still probably caused by an
overpressure on the irradiated surface but without
undergoing a massive deformation such as that shown
in Figure 4. What is more, a new phenomenon arises
on the non-irradiated surface where its inertia cannot
be balanced anymore because of the too low internal
pressure of the gas. This results in the crumpling of the
sail’s shell.
Figure 4. Failure mode at higher gas pressure. Stress
contour plot (upper figure, Pascal units) and SPH
entities distribution (bottom figure).
Figure 5. Failure mode at lower gas pressure. Stress
contour plot (upper figure, Pascal units) and SPH
entities distribution (bottom figure).
Therefore, the results have shown that, contrary to
expectations, the presence of the gas has a
destabilizing effect, reason why it was decided to
perform further simulations without the presence of the
gas. For these simulations, the effect of the sail’s shell
thickness was also evaluated.
The acceleration was imposed to 20000 g,
according to the previous simulations. The shell’s
thickness ranged from 0.1 μm to 0.4 μm, implying a
total sail’s mass ranging from 1.7 grams to 6.8 grams.
The simulations without gas have shown higher
stresses on the irradiated surface with respect to the
simulations with gas, probably due to the absence of
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IAC-18-D4.4 Page 7 of 9
the gas pressure balancing the laser pressure. On the
other hand, the non-irradiated surface has always
shown the crumpling of the sail’s shell, as expected.
Such phenomenon became more relevant as the shell’s
thickness has increased (Figure 6). This is probably
explainable by the rise of the shell’s inertia as the
thickness increases. One of the most relevant results is
that none of the simulations without gas has shown the
failure of the sail, representing a potential confirmation
of the destabilizing role of the gas.
Figure 6. Stress contour plots without gas (Pascal
units). 0.1 μm shell’s thickness (upper figure), 0.4 μm
shell’s thickness (bottom figure).
IV CONCLUSIONS
The simple 2D model adopted in the first phases of
the study has represented a good compromise between
computational time and cost, as well as an acceptable
first approximation to understand the physics of the
problem and the main issues at play. The simplified 2D
model has shown that no numerical issues were
encountered, mainly because of the low diameter-to-
thickness ratio of the sail, which was adequate for a
first approximation model but also quite far with
respect to the actual device. Such first evaluation was
used to outline the problem, identifying its main
features and providing useful information for the
further and more detailed 3D analysis. The successful
transition between the 2D model and the 3D model has
confirmed the goodness and the relevance of the use of
the first approximation model in the initial phases of
studying an unexplored problem.
The more advanced 3D model has addressed the
main weaknesses outlined by the 2D model, such as
the bi-dimensionality, the low diameter-to-thickness
ratio of the sail, the absence of a model for the gas
behavior and the low acceleration imposed to the light
sail. The powerful specialized tools adopted for
creating the model and performing the simulations
have greatly helped to push the limits of the model to
a close-to-reality level, confirming that also some
commercial tools can be successfully used to address
uncommon problems with a good level of both
reliability and detail, providing very useful
information for further and more specific analysis. On
the other hand, the used tools have shown some
intrinsic features that have partially limited the range
of the analysis, still providing a very useful insight on
the most relevant phenomenon at play.
The major contribution given by this study
concerns the understanding of the actual effect that the
inflating gas would have on the light sail. The inflating
gas was in fact initially introduced with the aim of
providing a stabilizing effect, helping to keep the shape
of the light sail as spherical as possible. Conversely,
the results of this study have shown a completely
counterintuitive, destabilizing effect of introducing the
inflating gas. Very useful information on the sail’s
response to a wide range of inflating gas pressures
were also derived. In fact, the simulations were able to
accurately catch the changes in the deformation
mechanisms at different regimes. Disruptive
longitudinal elongations were seen at higher inflating
gas pressures, showing that the dominant effect of the
gas inertia at very high acceleration regimes brings to
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IAC-18-D4.4 Page 8 of 9
the destructive failure of the sail. On the other hand,
some sort of crumpling was seen involving the non-
irradiated surface of the sail as the gas pressure
decreases, showing the rise of the inertia of the sail’s
shell. The identification of a such disrupting,
unpredictable effect, together with the understanding
of the main mechanisms at play that contribute to drive
it, would not have been possible without a proper
modeling of both the gas behavior and its contact
interactions with the sail. Therefore, the results have
suggested to shift towards a design without the
presence of the inflating gas. Such a solution was
simulated and the results have shown the goodness of
the approach. In fact, the sail was for the first time able
to successfully sustain the very high loads of the
acceleration phase. Moreover, the typical disruptive
deformation mechanisms and the failure modes seen in
presence of the inflating gas have disappeared,
showing instead the expected crumpling phenomenon
already seen arising at lower inflating gas pressures.
The evidence of such expected transition also in the
simulations in absence of inflating gas has confirmed
the goodness of both the analysis and the interpretation
of the deformation mechanisms across different
regimes. The effect of the thickness of the sail’s shell
was also investigated in absence of inflating gas. The
results have shown that the crumpling effect becomes
stronger as the thickness increases, confirming that the
inertia of the sail’s shell is the dominant effect at those
regimes. In any case, the results show that the light sail
does not maintain a spherical shape during the
acceleration phase. For this reason, a dedicated
analysis would be needed to assess the stability
features of a such deformed shape with respect to the
laser beam. Ultimately, the simulations have shown
that a delicate equilibrium exists among main
parameters at play (acceleration, sail’s shell thickness,
forces distribution, etc.) and a careful trade-off study
is needed to identify the most appropriate
configuration of the light sail.
The results of this study provide crucial indication
to drive the design of the light sail. The benefits
initially attributed to the presence of the inflating gas
were found to be inconsistent, showing that a careful
analysis were needed to better understand the physics
of the problem. The results of such analysis have
shown that a light sail without any inflating gas is the
most promising direction to follow for the future
designs.
Some interesting solutions may involve the use of
some gas only for the deployment of the sail once in
space. Some sort of radiation sensitive patch applied
on the irradiated surface of the sail could then be
vaporized by the laser hitting the sail’s surface, letting
the inflating gas to escape outwards. On the other hand,
such expendable patch may be placed on the non-
irradiated surface of the sail and actively removed once
in space by using some sort of ejection system. This
solution would have also a benefit in terms of reducing
the mass of the non-irradiated surface, helping
containing also its inertia and the related crumpling
effects at very high acceleration. Finally, a pre-loaded
sail would be able to self-deploy in space once the
stowing load is removed.
ACKNOWLEDGMENTS
This research did not receive any specific grant
from funding agencies in the public, commercial, or
not-for-profit sectors and it was supported by the
Politecnico di Torino and the ANKERS Juss – Amg
company.
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