Solar Sail Research Articles

Dynamics and control of a full-scale flexible electric solar wind sail spacecraft

The dynamics and control strategies of a full-scale flexible electric solar wind sail (E-sail) spacecraft are studied in this work. The configuration of the E-sail is an umbrella shape consisting of 100 main tethers of 20 km long, with a remote unit attached at the free end of each main tether; such remote units are also connected by an auxiliary tether with 100 separated segments; the electric voltages of each main or each segment of the auxiliary tether can be independently prescribed to control the orbit, orientation, and vibrations of the E-sail. Two computationally effective formulations, the reference nodal coordinate formulation (RNCF) and the nonlinear floating frame of reference method (FFRM) in a large deformed configuration, are developed to describe the dynamics of the E-sail spacecraft. The RNCF is accurate and comprehensive, but requires over 10000 degrees of freedom to describe the highly flexible and nonlinear dynamics of the E-sail. The FFRM requires only tens of degrees of freedom, and can be adopted for controller designs. The time scales of the orbit motions, the orientation motions and the structural vibrations of the E-sail are quite different. The modes in FFRM are categorized into three groups, such that the influences of the electric voltages on each category of modes are distinctively different, and the controllable properties of each category of modes are explored for controller designs. Although it is designed from the simplified FFRM approach, the resultant controller is implemented to the full-scale RNCF approach to verify its effectiveness, which validates that the E-sail spacecraft can be adopted for solar system exploration missions.

Inverse design of deployable origami structures that approximate a general surface

Shape-morphing finds widespread utility, from the deployment of small stents and large solar sails to actuation and propulsion in soft robotics. Origami structures provide a template for shape-morphing, but rules for designing and folding the structures are challenging to integrate into broad and versatile design tools. Here, we develop a sequential two-stage optimization framework to approximate a general surface by a deployable origami structure. The optimization is performed over the space of all possible rigidly and flat-foldable quadrilateral mesh origami. So, the origami structures produced by our framework come with desirable engineering properties: they can be easily manufactured on a flat reference sheet, deployed to their target state by a controlled folding motion, then to a compact folded state in applications involving storage and portability. The attainable surfaces demonstrated include those with modest but diverse curvatures and unprecedented ones with sharp ridges. The framework provides not only a tool to design various deployable and retractable surfaces in engineering and architecture, but also a route to optimizing other properties and functionality.

Coupled Orbit-attitude Saturated Control for Solar Sail in Earth-Moon 3-body System

Coupled Orbit-attitude Saturated Control for Solar Sail in Earth-Moon 3-body System

Active Shape Control of Membrane Structures Using Spin-Synchronous Vibrations

A novel approach for shape control of membrane structures is presented to realize their use in three-dimensional and variable configurations. The shape control is accomplished by exciting a spinning membrane. The membrane forms a shape consisting of several vibration modes, depending on the input frequency, and the wave surface stands still when its frequency is synchronized with the spin rate; that is, the wave propagation and the spin cancel each other, resulting in a static wave surface in the inertial frame. This idea enables control of continuous membrane structures with large deformation using fewer actuators than conventional methods. This paper describes the general theory of the static wave-based shape control. The mathematical model of membrane vibration, the classification of control input, and the control system for exciting a static wave are summarized. The proposed method is demonstrated through a ground experiment. A 1 m large polyimide film is rotated and vibrated in a vacuum chamber, and the output shape is measured using a real-time depth sensor. It is shown that the observed shapes agree with numerical simulation results. An additional simulation that models the Japanese solar sail Interplanetary Kite-craft Accelerated by Radiation Of the Sun (IKAROS) demonstrates that the proposed method also works with a practically large-scale membrane in the space environment.

On deployment of solar sail with superconducting current-carrying wire

We present a novel idea of the deployment of a circular solar sail consisting of superconducting wire attached to the thin circular membrane. Based on classical electrodynamics and theory of elasticity we predict that the superconducting current in the wire can deploy the large size circular solar sail.

Indirect Estimation Based Active Disturbance Rejection Control for Solar Sail Station-Keeping

Indirect Estimation Based Active Disturbance Rejection Control for Solar Sail Station-Keeping

Panel flutter mechanism of rectangular solar sails based on traveling mode analysis

The solar radiation pressure acting on the sail surface provides a force, which depends on the deformation of the surface itself, and thus the coupling between the force and the deformation may lead to flutter. The panel flutter mechanism of two-dimensional solar sail subjected to solar radiation pressure is investigated in this study based on the traveling mode analysis. The partial differential equations governing the panel vibrations are truncated into a set of ordinary differential equations. Two types of flutter have been detected, namely, traditional coupled-mode flutter and novel coupled-direction flutter especially existing in two-dimensional cases. Varying mode shapes with solar radiation pressure and critical values have been studied by considering the eigenvalue problem. By studying the mode shapes in standing wave contour or traveling wave contour, the flutter phenomena have been described based on the mechanism of energy accumulation.

Experiments on the symmetry-breaking effect of orientation on a pair of connected cantilevers

It is well established that axial loads tend to influence lateral stiffness and hence natural frequencies of slender structural components. For very slender structures, the axial loading can be caused by self-weight (in a gravitational field), and these effects influence equilibrium configurations and dynamic behavior. In some applications, for example solar sails, attached cables provide an additional complication. This paper will focus attention on a specific form of double cantilever beam system, i.e., two cantilevers sharing a common hub. Two specific cases are considered, in which the two ends of the cantilevers are connected by a cable under a given tensile load. The key observation is the effect that orientation (with respect to gravity) has on breaking the inherent symmetry in the vibration modes shapes of the systems studied. Although theoretical results are available for both a single cantilever pulled by a cable attached to its tip, together with results on the effect of gravity, the focus of the current paper is on the natural frequencies and mode shapes of two-beam systems from an experimental modal analysis perspective.

Effect of Laser Pulse Profile on Energy of the Accelerated Ions in the Light Sail Regime

In laser acceleration of ions by the radiation pressure acceleration (RPA) mechanism, the efficiency of energy and momentum transfer to ions increases if the shape of the laser pulse is suitably tailored. Numerical results are presented for the Gaussian, Lorentzian, and hyperbolic secant pulse shapes of the incident laser interacting with an ultrathin, ultra-dense plasma foil. The numerical results show that the energy and momentum imparted to the ions by the hyperbolic laser pulse are 1.17 and 1.11 times more compared to the Lorentzian shaped pulse of approximately the same intensity.

Pedal coordinates, solar sail orbits, Dipole drive and other force problems

Pedal coordinates provide a natural framework for studying force problems of classical mechanics in the plane. The trajectory of a test particle under the influence of central and Lorentz-like forces can be translated into pedal coordinates at once without the need of solving any differential equation. We generalize this result to cover more general force laws and also show the advantage of pedal coordinates in certain variational problems. These enable us to link together many dynamical systems as well as problems of the calculus of variation. Finally, we apply these results to compute orbits of Solar sail and Dipole drive.

Solar sail heliocentric transfers with a Q-law

The propellantless working principle of a solar sail requires the total flight time to be minimized when looking for the optimal trajectory to reach a given target state. In this work the solar sail steering law is found by applying a Q-law algorithm, which aims at driving the spacecraft toward the final (target) orbit by decreasing the distance between actual and desired states or by increasing the rate of change of the state variables. A formulation of the Q-law algorithm for a solar sail-based mission is given, which accounts for the constraints along the transfer trajectory imposed by the sail thrust model. The performance of the proposed procedure, which represents the novelty of this work, is checked in some potential solar sail mission scenarios, including coplanar interplanetary transfers and the exploration of outer Solar System regions.

Three-Axes Attitude Control of Solar Sail Based on Shape Variation of Booms

Actively controlling the attitude of the solar sail is necessary to adjust the solar radiation pressure force for trajectory transfer and orbit control. The special configuration of the solar sail makes it very important to develop a unique attitude control strategy that differs from traditional methods. An attitude control method, based on shape variation of booms, is proposed in this manuscript. Firstly, we derive the equations to calculate the solar radiation pressure force and torque of the deformed solar sail. Then, the factors affecting forces and torques are analyzed. Finally, PD control law is applied to realize the three-axis attitude control for the solar sail.

Out-of-plane deflection of plate-like metastructures in tension due to corrugation asymmetry

Architected metastructures offer unprecedented mechanical characteristics due to particular design and assembly of engineered local structures. Here, we study the out-of-plane deflection of plate-like metastructures designed with hexagonal corrugation. Due to the out-of-plane asymmetry of the corrugation, our metaplates develop out-of-plane deflection when put under tension. A theoretical model is developed to analyze the tensile response of the corrugated metaplates, and experiments are conducted on the metaplates made of silicone rubber. The tensile modulus of the silicone rubber is calibrated and the rubber metaplates are then measured under tension. Numerical simulations validate the theoretical and experimental results, and satisfactory agreements are obtained for the force–displacement relations (i.e., effective tensile modulus) and out-of-plane deflection. Parametric studies are carried out to investigate the influences of the geometry (e.g., height h and thickness t) and the corrugation pattern (e.g., hexagonal diameter Dhex and rib width Wrib) on the tensile response of the metaplates. The presented corrugated metaplates are envisioned as a promising path to optimize structures for multifunctional applications (e.g., wings in flying robots or light sails for interstellar space travel).

Modified spiral folding pattern for deployable membranes

Solar sails which provide propellant free propulsion are quite effective for missions that utilize small spacecrafts. These structures require a larger surface area compared to launch vehicles, hence require adopting deployable concepts. Neglecting geometric effects of membrane thickness can result in plastic deformations and wrinkling of membranes. As the issues arise in the stored configuration, they can be overcome by certain modifications to the fold-line arrangement in the pattern. We have developed a modified fold-line arrangement for modules which utilizes the spiral folding pattern using the arrangement of nodes in the folded state. We provided an offset to the nodes along the vertices of the hubs to the folded configuration to let the folding pattern accommodate the thickness. The proposed modification rearranges the nodes in the folding pattern which overcomes the adverse effects caused by the membrane thickness while achieving a compact folding state. Modified folding pattern was verified using paper models for different thicknesses and different levels of complexity.

Study on the stability of artificial vibration points with internal resonance in solar sail dynamics

In this paper, the linear and stability of solar sail spacecraft at the libration point of artificial balance is studied. The stability has been analyzed for the linear cases and nonresonance cases. The changing law of artificial balance point is found when the attitude angle of solar sail is fixed. The linear stability region of the solar sail spacecraft at L4 was found. Based on the circular restricted three-body problem, the dynamic model of the continuous solar sail spacecraft is established. The variation law of the position of manual translational point with the β parameters is analyzed. The condition and existence range of linear stability of artificial translational point are given. The influence of thrust parameters on the system and manual translational point is analyzed. The dynamics equation of the solar sail spacecraft near the linearly stable artificial translational point and the nonlinear vibration theory, the range of the system mass parameters and thrust parameters when the system has 1:2 and 1:3 internal resonance is obtained. Using the multi-scale method, the stability of the long and short period motion of the detector is analyzed, and the boundedness of motion is proved.

Structural features of photogravitational celestial mechanics

The features of mathematical models of controlled motion of a spacecraft with a solar sail, which take into account the translational and rotational motion of all parts of the structure, are considered. Equations for motion in a photogravitational field are used on the basis of the two-body problem, taking into account perturbations, or a more general model of the bounded three-body problem. The gravitational field is supplemented by the field of light pressure forces, which makes it possible to simulate real dynamics processes. When approximating the system of equations of perturbed motion for different orbits and parameters of the main bodies, control capabilities and stability conditions of motion are obtained at the specified orbits, as well as in the vicinity of libration points. Stability of orientation or rotation relative to the center of mass is provided by the moment of light pressure forces on the elements of the sail system or additional actions of special engines.

Influence of electric charge on surface of a solar sail on dy-namics of the sail which moves along Tsander’s trajectories

The application of a solar sail spacecrafts for a realization of distant flights into a space is actively discussed. However, all bodies in space plasma get electric charge which depends on density and temperature of plasma, a stream of sunlight and electro-physical characteristics of a body. But till now not enough attention has been given a problem of influence of the charging of a solar sail on its dynamics and durability characteristics. The charging of thin films, such as a solar sail has a number of features. Most important of them are: 1) a surface is bilateral and not closed, 2) partial permeability of a film for the charged particles of a space environment. In this work there are the results of calculations of electric charge density on the surface of the solar sail in the space between orbits of the Earth and Jupiter and an estimate of influence of electric charge of a sail on dynamics of solar sail spacecrafts which moves along elliptic Tsander’s a trajectory. The problem about deflection determination is reduced to integration of one-dimensional problem of the motion of a body with variable acceleration. The obtained estimates of the influence of an electric charge induced on the surfaces of the solar sail on the motion of a space vehicle during interplanetary flights along the orbits mentioned above have shown that the influence is small.

Circumnavigating the sun with diffractive solar sails

A solar sail based on the physics of diffracted light provides a means of harnessing opto-mechanical momentum for in-space propulsion. As an example a heuristic roll maneuver of a diffractive sail is found to produce a spiral trajectory that provides a high orbital inclination angle at a close solar orbit. A comparison of five-year spiral trajectories of ideal diffractive and reflective sails reveals that the former achieves a higher solar inclination angle and a smaller orbital radius than the latter. We envision placing a constellation of diffractive solar sails around the sun to collect images and other data for space weather monitoring and heliophysics science. For illustration purposes we consider a series of 14 [kg], 400 [m2] lightsails at various inclination angles, all positioned at 0.32 [AU] within six years. This paper may inspire materials scientists to design and fabricate thin novel optical metamaterial films that efficiently diffract light at large angles across the solar spectrum for future solar sails. Mission designers may also be prompted to imagine alternatives beyond reflective sails.

Multi-faceted simulation of atomic oxygen erosion of deorbit sail for cleaning space debris

Deorbit sails are used in low earth orbit to reduce the growing amount of orbital debris by rapidly removing satellites at the end of their operational missions. However, in low earth orbit, atomic oxygen (AO) is a potential threat to long-duration exposure facilities. In this work, a multi-faceted simulation for the AO erosion of the Taurus Deorbit Sail was developed to calculate the erosion yield for the membrane material and the undercutting profile at the crease site. The disintegration and erosion detail for the deorbit sail membrane during AO impacts can be studied on an atomic scale. The ReaxFF reaction force field program is used to provide a large enough calculation speed in the size of the system to describe all the chemical reactions of the reaction. The on-orbit flight data from the Materials International Space Station Experiment 2 were used to validate the simulated erosion rate in this study. The defects on the deorbit sails were experimentally measured using a scanning electron microscope and then modeled by the Monte Carlo method. The computational predictions of AO undercutting at the defect sites were validated by experimental data from the NASA long-duration exposure facility. The disintegration of the membrane could be divided into two stages: the physical reaction stage and the chemical reaction stage, after 150 AO collisions the membrane becomes highly volatilized. The maximum undercutting depth for the deorbit drag sail within the predicted 37-month deorbit time was 5.5 μm and 7.5 μm for a defect width of 500 nm and 1 μm, respectively. The undercutting width for a deorbit sail with a width of 500 nm or 1 μm was predicted to be 1.6 μm and 2 μm, respectively, and the breaker was formed at the bottom of the undercutting profile. AO erosion has been studied by researchers in terms of evaluating the effectiveness of protective coatings. This current study, however, seeks to understand the fundamental interactions between AO and creases in the deorbit sail, which provides deeper knowledge than what has been developed so far. The multi-faceted simulation results can provide design references for engineering applications for the deorbit sail.

Study on the electro-optical properties of epoxy resin based polymer dispersed liquid crystal films

Abstrat Polymer dispersed liquid crystal (PDLC) films have been extensively studied for their ability to control the attitude of aircraft by varying the reflectivity of solar sails. However, most of the polymeric matrix of PDLC films are based on polyacrylates, which comprehensive properties such as thermal stability, chemical stability, mechanical strength and radiation resistance can not meet the requirements of the harsh environment in space. In order to improve the radiation resistance of PDLC films, polyimide-epoxy resin PDLC films were prepared by thermal polymerization using Kapton polyimide film as conductive film and two kinds of epoxy resin as monomer in this paper. The electro-optic properties of PDLC films prepared by flexible chain and rigid chain epoxy resin monomers in different ratios were studied and the microscopic morphology of the polymer network of the polyimide PDLC films was observed by scanning electron microscopy (SEM) and the relationship between them was studied.