Solar Sail Research Articles

Nonlinear Deployment Dynamics and Wrinkling of a Membrane Attached to Two Axially Moving Beams

The out-of-plane and in-plane deployment dynamics of a flexible space structure, namely, a solar sail quadrant consisting of a membrane attached to two support booms, are considered. The equations of motion of the system are obtained using a time-varying generalization of the extended Hamilton’s principle. They are then discretized via quasi-modal expansion of the deflections as truncated series involving both time- and space-dependent basis functions. Because all directions are accounted for and plate strains are used to capture the potentially significant effect of even a small stiffness on the dynamics, nonlinear terms appear in the discretized equations. To increase computational efficiency, coordinate transformations and linear algebraic manipulations are performed to make all spatial integrals time invariant. In addition, attempts are made to predict wrinkling using the Miller–Hedgepeth model: a coarse mesh is defined, the instantaneous state of each region is determined using a wrinkling criterion and averaged principal stresses, and constitutive relation of each region is adjusted based on its wrinkling state. Numerical simulations provide basic validation, sample deployment results, and a comparison against the results of an earlier linear model with only out-of-plane deflections. The stress predictions are also partially validated using previous results based on constant-size loaded membrane experiments.

Correction to: End-of-life geostationary satellite removal using realistic flat solar sails

Correction to: End-of-life geostationary satellite removal using realistic flat solar sails

Realistic sunshade system at L1 for global temperature control

So far, space-based geoengineering has rarely been studied from a practical point of view, considered unrealistic as a near-future alternative to fight climate change. This paper evaluates the feasibility of implementing a space sunshade in the vicinity of the first Lagrange point of the Sun-Earth system by the middle of the century. The analysis considers the necessary technological development, the possible trajectories for the shades, and an approximation of the size and cost of the system. It is strongly dependent on the possible optical properties of future solar sails, so an optimal and a more conservative alternative have been studied. With the latter, the shade will be formed by 1.5 × 109 sailcraft with a sail area of 2500 m2 and a total mass of 8.3 × 1010 kg. In the optimal case, the total mass is 3.4 × 1010 kg. Each one of these sails will be launched to a 2000 km orbit, from where they will travel for about 600 days to the equilibrium point using solar radiation pressure. The total cost of the mission is estimated to be five to ten trillion dollars, based on a launch cost of US$50/kg. There are two main technological challenges for this to become a reality: the low TRL of the solar sails proposed and the necessary development in the launch vehicle industry given the dimensions of the mission.

Deployment strategy for satellite-sail transverse formation

In the general 2-satellite formation near Earth, the deputy satellite moves around the chief one, resulting that the relative baseline exhibits the periodical variations in the form of trigonometric functions. In such case, only the certain positions can be employed for interferometric imaging, and the high requirements of Earth observation and remote sensing can be barely satisfied. Therefore, a new tethered satellite-sail system, termed satellite-sail transverse formation, is proposed in this study. The chief satellite is in a sun-synchronous orbit and is connected to one deputy solar sail in a non-Keplerian displaced orbit. Given the continuous solar radiation pressure, the sail can move with the satellite side by side synchronously such that the relative baseline is always perpendicular to the subastral point tracks of the satellites. Our investigation mainly focuses on the relative dynamics and control of the proposed system during the deployment process that is divided into two stages: pop-up and steady release. Subsequently, the deployment dynamics are established considering the chief and deputy satellites as mass points connected by a rigid rod. To ensure a successful deployment, a sliding mode controller with a saturation function is adopted where the control force is provided by the solar radiation pressure and tether tension. The results show that the proposed deployment strategy is successful, and the transverse formation is eventually realized under the smooth rotation of the solar sail.

Photonic materials for interstellar solar sailing

Solar sails are of great promise for space exploration, affording missions that push the limits of the possible. They enable a variety of novel science missions ranging from ultrafast interstellar travel to imaging the poles of the sun—missions that are beyond the reach of current propulsion technology. Here, we describe requirements and challenges associated with optical materials and photonic designs facing the next generation of solar sails. A technology development roadmap is outlined to guide researchers in pioneering the space faring future.

Modal Analysis of Electric sail

The electric solar wind sail (E-sail) has been proposed as a novel propulsion system that, if successful, promises to facilitate missions that would be inconvenient or impractical with traditional chemical propellants. The most common E-sail concept includes a central hub with several long positively charged tethers extending radially outward that harvest momentum from protons in the solar wind. Before the technology is ready for a demonstration mission, we must prove E-sail dynamics can be controlled throughout all phases of the mission. The objective of this paper is to present an analytical model for the linear vibrations of hub and spoke E-sails to facilitate the development of necessary control schemes. Although there is no limit to the number of spokes in our model, we demonstrate its capability by representing a system with 3 spokes. The resultant natural frequencies and mode shapes provide insight into the dynamics and stability of E-sails and lay the foundation for development of control schemes. In addition, our work reveals several simple calculations that accurately estimate many of the natural frequencies and could be used to facilitate the design of future E-sails.

‘Oumuamua as a light sail: Evidence against artificial origin

‘Oumuamua, the first detected interstellar visitor to the Solar System, exhibits non-gravitational acceleration in its trajectory. In ruling out other means of propulsion, such as the evaporation of material via a cometary tail, it has been argued that radiation pressure is responsible for this acceleration. From this (a = 5 × 10−6 m s−2), the mass of the object must be approximately 4 × 104 kg, and given its dimensions, ‘Oumuamua must have a thickness of ≲1 mm if of a similar rock and iron composition as the Earth. This raises the much publicised possibility that ‘Oumuamua is artificial in origin and intentionally sent across interstellar space by an alien civilisation. This conclusion, however, relies upon the common misapprehension that light (solar) sails can accelerate to a considerable fraction of the speed of light, permitting rapid interstellar travel. We show that such speeds are unattainable for conceptual man-made sails and that, based upon its observed parameters, ‘Oumuamua would require half a billion years just to travel to our Solar System from its closest likely system of origin. These cosmological timescales make it very unlikely that this is a probe sent by an alien civilisation.

Light sail boosted by instantaneous radiation pressure

Light sail acceleration by ultrashort, superintense laser pulses is presently investigated as an approach to compact accelerators of matter. The usual light sail equation assumes a cycle-averaged light pressure, which becomes questionable for ultrashort pulse drivers or in the highly relativistic regime. Here, we remove such assumption and compute solutions of the light sail equations which show oscillations of the sail acceleration. The dependence of the final sail velocity on the temporal profile of extremely short pulses is discussed.

Inverse Design of Diffractive Relativistic Meta‐Sails via Multi‐Objective Optimization

AbstractPhotonic propulsion of light sails using the radiation pressure of an intense laser beam is a promising route to achieve relativistic velocities for deep space exploration. A successful photonic design of such relativistic sails requires efficient acceleration and maintaining stability of the beam‐riding across a Doppler‐broadened propulsion band due to considerable red‐shift of the wavelength in the frame of the moving sail. While efficient acceleration of the sail requires maximizing the optical force along the beam propagation direction, the stability degree of the sail depends on the magnitude of lateral forces in the transverse plane of the beam. This establishes a trade‐off between these two requirements which calls for their synergistic engineering. In this work, an evolutionary multi‐objective optimization technique for the inverse design of diffractive relativistic meta‐sails with a genetic pixelated geometry is adopted. The goal is to identify a set of Pareto optimal solutions which provides the designer with an intuitive understanding of the ultimate trade‐off between acceleration and stability degree of the sail in a vast design space, and allows for a well‐informed decision on the best design given the requirements for the acceleration time and distance as well as the tolerance with respect to mispointings and misalignments.

Multistable inflatable origami structures at the metre scale.

From stadium covers to solar sails, we rely on deployability for the design of large-scale structures that can quickly compress to a fraction of their size1-4. Historically, two main strategies have been used to design deployable systems. The first and most frequently used approach involves mechanisms comprising interconnected bar elements, which can synchronously expand and retract5-7, occasionally locking in place through bistable elements8,9. The second strategy makes use of inflatable membranes that morph into target shapes by means of a single pressure input10-12. Neither strategy, however, can be readily used to provide an enclosed domain that is able to lock in place after deployment: the integration of a protective covering in linkage-based constructions is challenging and pneumatic systems require a constant applied pressure to keep their expanded shape13-15. Here we draw inspiration from origami-the Japanese art of paper folding-to design rigid-walled deployable structures that are multistable and inflatable. Guided by geometric analyses and experiments, we create a library of bistable origami shapes that can be deployed through a single fluidic pressure input. We then combine these units to build functional structures at the metre scale, such as arches and emergency shelters, providing a direct route for building large-scale inflatable systems that lock in place after deployment and offer a robust enclosure through their stiff faces.

Event-triggered coordinated control for multiple solar sail formation flying around planetary displaced orbits

This paper presents a planetary elliptic displaced orbit (PEDO) for a solar sail with reflectivity control devices (RCDs). The problem of multiple solar sail formation flying in which the leader follows the PEDO is investigated. The trajectory of the leader is not affected by that of the followers, whereas each follower needs to know the state information of the leader to achieve formation configuration. An undirected and connected graph is used to describe the communication topology among the followers, and an event-triggered coordinated control algorithm is proposed. With this algorithm, each follower does not need to maintain continuous communication with other followers, reducing communication burden. Additionally, the existence of Zeno behavior is excluded by theoretical analysis. Finally, numerical simulations are performed to verify the effectiveness of the proposed algorithm.

CONFIGURATION SELECTION AND ANALYSIS OF A SUPERSTRUCTURE SOLAR SAIL

Solar sail propulsion is one of the most innovative spaceship propulsion system which make use of the radiation pressure in space. The continuous supply of radiation pressure means the ship has infinite propellant reserve. Theoretically, the solar sail keeps accelerating to gain high velocities due to this continuous supply of radiation pressure, therefore this system is ideal for interstellar exploration. As there are numerous developments going on this field of study, it is important to have a generalized sail design that can be used for further developments. This paper gives the configuration selection of the sail along with calculations and analysis to develop a superstructure solar sail, which is theoretically ideal for interstellar exploration and for future engineering

Characterizing Minimum-Time Solar Sail Geostationary Orbit Transfers Using Pseudospectral Optimal Control

This work examines the problem of planet-centered orbit transfers using solar sail propulsion. Though solar sails offer unlimited , they place coupled time-dependent restrictions on thrust magnitude and direction, and the multiple objectives of an orbit transfer can make locally optimal approaches inefficient; it is therefore advantageous to use optimal control to design such trajectories. This paper presents orbit-averaged equinoctial-element equations of motion for a solar sail under a discretized and interpolated control law. These equations are used to study transfer from a geostationary transfer orbit to geostationary orbit; a locally optimal control law is used to generate initial trajectories, and Gaussian pseudospectral optimal control is applied to yield minimum-time transfers. In the default case, with sail area–mass ratio of , optimization reduces the transfer time from 1222 to 293 days. Finally, sail area per mass, sail reflectivity, and initial sun–Earth orientation are varied to explore their effects, and to provide general design guidelines for planet-centered solar sail transfers. Distinct performance regimes are observed for transfers taking longer or shorter than one year, and for reflectivities greater or less than 0.4. Additionally, initial solar position was found to drastically affect the behavior of transfers in the fast regime.

Electromagnetic and Mechanical Analysis of a Modular Outer Rotor Synchronous Reluctance Machine for Light Propulsion Vehicles

This article presents the optimal design from the electromagnetic and structural point of view of a fault-tolerant modular outer rotor synchronous reluctance machine, a not previously constructed topology. Two new topologies with the rotor in modular construction, one with each pole of the rotor considered as a separate module and a segmented one where each rib of a module can be considered as independent, are compared with a classic structure. The electromagnetic analysis is carried out using FLUX 2D software. The main studied parameters are electromagnetic torque, torque ripple content, saliency ratio, and power factor. In order to optimize the power factor of the machine, a cosimulation procedure is carried out for each structure, by employing a MATLAB and FLUX 2D coupling. Based on the obtained performances, the best topology is selected. Furthermore, a mechanical analysis is performed to determine if the new proposed rotor meets the structural integrity at rated speed and to establish the maximum speed value that can be attained such that the structural failure of the rotor is prevented. A modular outer rotor synchronous reluctance machine is designed and built. Experimental results of testing the prototype are given to confirm the validity of the proposed machine.

Preliminary trajectory design for NASA’s Solar Cruiser: A technology demonstration mission

This investigation outlines preliminary trajectory design for NASA’s sail-based Solar Cruiser spacecraft, selected on December 3, 2020, to be a secondary payload launched with the Interstellar Mapping and Acceleration Probe (IMAP) in 2025. Trajectory optimization is carried out to ensure that Solar Cruiser can successfully reach a halo orbit about a Sun–Earth sub-L1 Lagrange point in under one year using only solar sail propulsion. Trade studies are performed to identify optimal trajectories subject to restrictions on sail incidence angles and deployment times, and off nominal initial-conditions are examined to determine the feasibility of the baseline mission profile. Results, thus far, show that Solar Cruiser can be incorporated as a secondary payload on IMAP while satisfying tight operational restrictions. However, additional work must be done to mitigate risks from large launch vehicle injection errors.

Experimental investigation of Mach-Effect thrusters on torsion balances

Successful interstellar venture depends on the development of propellantless propulsion with a thrust-to-power ratio much greater than a photon rocket and without the limitations of solar sails. Claims of μN thrust for Woodward's MEGA Drive, along with predicted mass fluctuations as a consequence of the Mach-Effect have initiated a few decades of table-top experiments seeking to observe variable mass and using it to generate significant propellantless thrust efficiency. However, using different thrust balances with increasing measurement sensitivity to characterize these effects resulted in a decrease in the claimed effect's magnitude. Large second harmonics begin to appear in the pre-stressed piezoelectric stack's integrated strain gauge signal, showing the vibration present at system resonances, as well as significant nonlinearity. Observation of the balance beam's oscillations reveal sub-harmonic vibration coupling and amplified vibration around electromechanical resonances of the system that can explain the transients observed in the force trace. Different piezo-actuator driving conditions are explored and an account for the different behaviors observed is made. The varying driving conditions do not significantly affect the forces observed, contrary to the theory. It is concluded that the observed effect is a result of coupled vibrations on the torsion balance.

Analytical Investigation of Global Deployed Shape of a Spinning Solar Sail Membrane

In this paper, the deployed shape of spinning square solar sails was investigated through dynamic nonlinear finite element analysis of the full model of the solar power sail of the world’s first solar sail: Interplanetary Kite-craft Accelerated by Radiation of the Sun (IKAROS). The on-orbit photographs of IKAROS revealed that the sail membrane was deformed toward the sun and the membrane maintained its deployed shape during very low-spin-rate operations. To clarify the mechanism of the deformation and high stiffness, the authors of the present study previously performed deployed shape analyses of one-quarter of one square sail by employing Abaqus and reported that the phenomenon was probably caused by curvatures of thin-film devices attached to the membrane. In this study, a finite element model of the entire square sail of IKAROS was created. Furthermore, deployed shape analysis under several combinations of curvatures and spin rates was conducted by employing the dynamic solver “Abaqus/Explicit.” The results indicated that the sail deformations were induced by the curvatures of thin-film devices and that umbrella and saddle shapes appeared owing to the curvatures. The results also indicated that the electric harnesses between the sail and spacecraft supported the sail shape when the spin rate was low.

The sun diver: Combining solar sails with the Oberth effect

A highly reflective sail provides a way to propel a spacecraft out of the solar system using solar radiation pressure. The closer the spacecraft is to the Sun when it starts its outward journey, the larger the radiation pressure and so the larger the final velocity. For a spacecraft starting on the Earth's orbit, closer proximity can be achieved via a retrograde impulse from a rocket engine. The sail is then deployed at the closest approach to the Sun. Employing the so-called Oberth effect, a second, prograde, impulse at closest approach will raise the final velocity further. Here, I investigate how a fixed total impulse (Δv) can best be distributed in this procedure to maximize the sail's velocity at infinity. Once Δv exceeds a threshold that depends on the lightness number of the sail (a measure of its sun-induced acceleration), the best strategy is to use all of the Δv in the retrograde impulse to dive as close as possible to the Sun. Below the threshold, the best strategy is to use all of the Δv in the prograde impulse and thus not to dive at all. Although larger velocities can be achieved with multi-stage impulsive transfers, this study shows some interesting and perhaps counter-intuitive consequences of combining impulses with solar sails.

Deployment simulation of a scalable planar gossamer space structure based on Miura-ori pattern

Miura-ori is a rigid origami structure utilized in the packaging of deployable solar panels for use in space or in the folding of maps. It's pattern can largely reduce the membrane stress and improve the work efficiency. Inspired by origami structures, we numerically and experimentally studied a scalable solar sail structure. As an improvement of the existing membrane simulations, a variable Poisson's ratio model considering the wrinkling effect of the membrane was introduced. We focused on a quadrant shape and studied how its geometry parameters and initial imperfections affect the membrane mechanical behavior. We also designed and fabricated a pantographic mechanism as an origami membrane actuator. In addition, design protocols of deployment applied to a scalable gossamer structure were proposed.

Paths not taken – The Gossamer roadmap’s other options

Highly efficient low-thrust propulsion is increasingly applied beyond commercial use, also in mainstream and flagship science missions, in combination with gravity assist propulsion. Another recent development is the growth of small spacecraft solutions, not in size but in numbers and individual capabilities.Just over ten years ago, the DLR-ESTEC Gossamer Roadmap to Solar Sailing was set up to guide technology developments towards a propellant-less and highly efficient class of spacecraft for solar system exploration and applications missions: small spacecraft solar sails designed for carefree handling and equipped with carried application modules.Soon, in three dedicated Gossamer Roadmap Science Working Groups it initiated studies of missions uniquely feasible with solar sails such as Displaced L1 (DL1) space weather advance warning and monitoring, Solar Polar Orbiter (SPO) delivery to very high inclination heliocentric orbit, and multiple Near-Earth Asteroid (NEA) rendezvous (MNR). Together, they demonstrate the capability of near-term solar sails to achieve at least in the inner solar system almost any kind of heliocentric orbit within 10 years, from the Earth-co-orbital to the extremely inclined, eccentric and even retrograde. Noted as part of the MNR study, sail-propelled head-on retrograde kinetic impactors (RKI) go to this extreme to achieve the highest possible specific kinetic energy for the deflection of hazardous asteroids.At DLR, the experience gained in the development of deployable membrane structures leading up to the successful ground deployment test of a (20 m)2, i.e., 20 m by 20 m square solar sail at DLR Cologne in 1999 was revitalized and directed towards a 3-step small spacecraft development line from as-soon-as-possible sail deployment demonstration (Gossamer-1) via in-flight evaluation of sail attitude control actuators (Gossamer-2) to an envisaged proving-the-principle flight in the Earth-Moon system (Gossamer-3). First, it turned the concept of solar sail deployment on its head by introducing four separable Boom Sail Deployment Units (BSDU) to be discarded after deployment, enabling lightweight 3-axis stabilized sailcraft. By 2015, this effort culminated in the ground-qualified technology of the DLR Gossamer-1 deployment demonstrator Engineering Qualification Model (EQM). For mission types using separable payloads, such as SPO, MNR and RKI, design concepts can be derived from the BSDU characteristic of DLR Gossamer solar sail technology which share elements with the separation systems of asteroid nanolanders like MASCOT. These nano-spacecraft are an ideal match for solar sails in micro-spacecraft format whose launch configurations are compatible with ESPA and ASAP secondary payload platforms.Like any roadmap, this one contained much more than the planned route from departure to destination and the much shorter distance actually travelled. It is full of lanes, narrow and wide, detours and shortcuts, options and decision branches. Some became the path taken on which we previously reported. More were explored along the originally planned path or as new sidings in search of better options when circumstance changed and the project had to take another turn. But none were dead ends, they just faced the inevitable changes when roadmaps face realities and they were no longer part of the road ahead. To us, they were valuable lessons learned or options up our sleeves. But for future sailors they may be on their road ahead.