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ABSTRACT
Hundreds of space missions have been launched since the last lunar mission, including several deep space probes that have been sent to the edges of our solar system. However, our journeys to space have been limited by the power of chemical rocket engines and the amount of rocket fuel that a spacecraft can carry. Today, the weight of a space shuttle at launch is approximately 95 percent fuel. What could we accomplish if we could reduce our need for so much fuel and the tanks that hold it?
International space agencies and some private corporations have proposed many methods of transportation that would allow us to go farther, but a manned space mission has yet to go beyond the moon. The most realistic of these space transportation options calls for the elimination of both rocket fuel and rocket engines -- replacing them with sails. Yes, that's right, sails.
Solar-sail mission analysis and design is currently performed assuming constant optical and mechanical properties of the thin metalized polymer films that are projected for solar sails. More realistically, however, these properties are likely to be affected by the damaging effects of the space environment. The standard solar-sail force models can therefore not be used to investigate the consequences of these effects on mission performance. The aim of this paper is to propose a new parametric model for describing the sail film's optical degradation with time. In particular, the sail film's optical coefficients are assumed to depend on its environmental history, that is, the radiation dose. Using the proposed model, the optimal control laws for degrading solar sails are derived using an indirect method and the effects of different degradation behaviors are investigated for an example interplanetary mission.
INTRODUCTION
Hundreds of space missions have been launched since the last lunar mission, including several deep space probes that have been sent to the edges of our solar system. However, our journeys to space have been limited by the power of chemical rocket engines and the amount of rocket fuel that a spacecraft can carry. Today, the weight of a space shuttle at launch is approximately 95 percent fuel. What could we accomplish if we could reduce our need for so much fuel and the tanks that hold it?
International space agencies and some private corporations have proposed many methods of transportation that would allow us to go farther, but a manned space mission has yet to go beyond the moon. The most realistic of these space transportation options calls for the elimination of both rocket fuel and rocket engines -- replacing them with sails.
NASA is one of the organizations that has been studying this amazing technology called solar sails that will use the sun's power to send us into deep space.
SOLAR SAIL CONCEPT
Nearly 400 years ago, as much of Europe was still involved in naval exploration of the world, Johannes Kepler proposed the idea of exploring the galaxy using sails. Through his observation that comet tails were blown around by some kind of solar breeze, he believed sails could capture that wind to propel spacecraft the way winds moved ships on the oceans. While Kepler's idea of a solar wind has been disproven, scientists have since discovered that sunlight does exert enough force to move objects. To take advantage of this force, NASA has been experimenting with giant solar sails that could be pushed through the cosmos by light.
There are three components to a solar sail-powered spacecraft:
• Continuous force exerted by sunlight
• A large, ultrathin mirror
• A separate launch vehicle
A solar sail-powered spacecraft does not need traditional propellant for power, because its propellant is sunlight and the sun is its engine. Light is composed of electromagnetic radiation that exerts force on objects it comes in contact with. NASA researchers have found that at 1 astronomical unit (AU), which is the distance from the sun to Earth, equal to 93 million miles (150 million km), sunlight can produce about 1.4 kilowatts (kw) of power. If you take 1.4 kw and divide it by the speed of light, you would find that the force exerted by the sun is about 9 newtons (N)/square mile (i.e., 2 lb/km2 or .78 lb/mi2). In comparison, a space shuttle main engine can produce 1.67 million N of force during liftoff and 2.1 million N of thrust in a vacuum. Eventually, however, the continuous force of the sunlight on a solar sail could propel a spacecraft to speeds five times faster than traditional rockets.
SAIL CONSTRUCTION
The strategy for near-term sail construction is to make and assemble as much of the sail as possible on earth. Thus, while the delicate films of the sail must be made in space, all other components are made on earth. The sail construction system consists of the following elements: a scaffolding (to control the structure's deployment), the film fabrication device, a panel assembly device, and a "crane" for conveying panels to the installation sites.
The scaffolding structure rotates at a rate within the operational envelope of the sail itself, to facilitate the sail's release. Six compression members define the vertical edges of the hexagonal prism. Many tension members parallel to the base link these compression members to support them against centrifugal loads. Ballast masses flung further from the axis provide additional radial tension and rigidity near the top of the scaffolding. Other tension members triangulate the structure for added rigidity. Tension members span the base of the prism, supporting a node at its center. The interior is left open, providing a volume for deploying and assembling the sail. The top space is left open, providing an opening for removing it. The face of the sail is near the top of the scaffolding, and the rigging below. If the scaffolding is oriented properly, the sun will shine on the usual side of the sail, making it pull up on its attachment point at the base of the prism. The total thrust of the said is then an upper bound on the axial load supported by the compression members. It is clearly desirable to make the scaffolding a deployable structure.
The sail's structure consists of a regular grid of tension members, springs, and dampers, and a less regular three-dimensional network of rigging. This is a very complex object to assemble in space. Fortunately, even the structure for a sail much larger than described herein can be deposited in the Shuttle payload bay in deployable form.
Since the sail is a pure tension structure, its structural elements can be wound up on reels. Conceptually, the grid structure can be shrunk into a regular array of reels and a plane. With each node in the lid represented by housings containing three reels. The rigging can be sunken into a less regular array, and the nodes containing its reels stacked on top of those of the grid.
The structure will be deployed by pulling on cords attached to certain nodes. Deployment may be controlled by a friction brake in the hubs of the reels. By setting the brakes properly, positive tension must be applied for deployment and certain members may be made to deploy before others. Further control of the deployment sequence, if needed, may be introduced by a mechanism which prevents some elements from beginning to deploy until selected adjacent elements have finished deploying. If detailed external intervention is deemed desirable, brakes could be rigged to release when a wire on the housing is severed by laser pulse.
The film fabrication device produces a steady stream of film triangles mounted to foil spring clusters at their corners. The panel fabrication device takes segments of the stream and conveys them along a track to assembly stations. Each segment is fastened to the previous segment and to the edge tension members that will frame the finished panel. This non-steady process of panel assembly requires a length of track to serve as a buffer with a steady film production process.
At the assembly station, the segments are transferred to fixtures with a lateral transport capability. During transfer, each segment is bonded to the one before along one edge. While the next segment is brought into position, the last segment is indexed over a one strip width, completing the cycle. Special devices bearing the edge tension members travel on tracts and place foil tabs on the panel structure. The foil tabs linking the segments may be bonded to one another in many ways, including ultrasonic welding, spot welding, and stapling. Attachment and conveyance may be integrated if the foil tabs are hooked over pins for conveyance. The panel assembly cycle ends with a pause, as the completed panels, now held only by their corners, are lured into a storage region and new edge members are loaded into position.
At this point the sail's structure is deployed within scaffolding, and panels are being produced and stored at a panel fabrication module. The stored panels are initially loaded at a node suspended on tension members above the center of the sail. A crane is likewise suspended, but from tension members terminated in actively controlled reels mounted on devices free to move around the top of the scaffolding. This makes it possible to position the crane over any aperture in the grid.
Once panel installation is complete and the operation of various reels has been checked, the sail is ready for release and use. It is already spinning at a rate within its operational envelope, and is already under thrust, hence, this task is not difficult. First, the sail's path must be cleared. To do this, the film fabrication device, its power supply, the panel assembly device, and the crane are conveyed to the sides of the scaffolding in a balanced fashion. The top face is cleared of objects and tension members. Then, the members holding the corners of the sail are released, and the remaining restraint points are brought forward to carry the sail out of the scaffolding. Finally, all restraints are released, and the sail rises free.
SOLAR SAIL DYNAMICS AND CONTROL
There are essentially two modes for operation and control of the solar sail.
In the first mode, the tilting of panels produces control forces. Each panel has a mass of some 0.3 to 1.1 kilograms.
This first mode is conceived of as a semi-passive control mode for interplanetary cruising (where only slow changes of attitude are needed). It is of importance to consider the stability of a passive sail set at various angles to the sun. In the ideal sail approximation (planar, perfectly reflecting), thrust will be normal to the sail and act through its center of area, that is, along the axis of symmetry. In an absorbing sail, its thrust is divided into purely reflective and purely absorptive components. The former produces no torque, while the latter produces a torque. To counter this torque, light pressure must be increased on the far side of the sail from the sun relative to that on the near side. Making the sail concave toward the payload accomplishes this purpose.
Since torques can be balanced at all sail angles of interest, small perturbing torques can shift the sail from one attitude to another, or change its rotation rate. Since heliocentric orbit times are typically months, spin-up and spin-down times of ten days and precession rates of 0.1 radian/day seem reasonable targets. Tilting a panel by about twenty degrees changes the force on it--both normal to the sail and parallel to it--by about thirty percent of the panel's maximum thrust. Sail operation in this first mode configuration is characterized by torques that may be ballasted by a few statically positioned trim panels 100, permitting an entirely passive cruise mode. Slow changes in the sail's attitude and spin rate may be made, from time to time, by cyclic variation of panel tilt to produce perturbing torques. The passivity of cruise mode and the ease of providing redundant tiltable panels recommend this mode for reliable interplanetary transportation.
In the second mode of sail configuration, the payload mass is assumed to be large compared to the sail mass, and the sail is considered as a separate object linked to it by actively controlled shroud lines 202 and 204. In the second mode, the tilting of the panels 200 controls the spin rate. However, in this mode precession is effected by varying the tension exerted by the shrouds 202 and 204 on different parts of the sail. This is accomplished by reeling and unreeling the shrouds in a coordinated fashion as the sail turns. For the sail discussed above, and the probable range of sail performances, this arrangement implies precession rates of 13 to 26 rad/100 minutes, when the sail is flat with respect to the sun. This provides a generous margin in turn rate, even from maneuvers in low earth orbits. This active control permits damping of nutation. This is important, since nutation would otherwise be initiated by rapid changes in precession rate. It should be noted that during precession the payload is offset from the axis of rotation in a direction fixed in inertial space.
For missions involving both interplanetary cruise and circumplanetary maneuvering, a vehicle able to operate in both modes is desirable. The first mode has a decisive advantage near planets (because of its maneuverability), but cannot enter a passive cruise mode. The greater distance between the payload and sail in this mode precludes balancing the torque on the sail resulting from absorbed light with a reasonable amount of concavity, as is done in the first mode. Instead, the torque must be countered in the same manner as the sail is precessed: by active manipulation of shroud tension. While control of shroud tension might be made redundant by placing reels at both ends of the lines, reliability still favors a passive system on long missions. Fortunately, interconversion seems simple. The second mode control can be maintained as the shroud lines 202 and 204 are reeled in, so long as the sail is properly ballasted for mode one. While the payload reaches the mode one position, the reel can be locked and mode one control begun.
4.1 Cruising by Sunlight
Maneuvering a solar-sail spacecraft requires balancing two factors: the direction of the solar sail relative to the sun and the orbital speed of the spacecraft. By changing the angle of the sail with respect to the sun, you change the direction of the force exerted by sunlight.
When the spacecraft is in orbit around the Earth or sun, it is traveling in a circular or elliptical path at a given speed and distance. To go to a higher orbit (travel farther away from the object), you angle the solar sail with respect to the sun so that the pressure generated by sunlight is in the direction of your orbital motion. The force accelerates the spacecraft, increases the speed of its orbit and the spacecraft moves into a higher orbit. In contrast, if you want to go to a lower orbit (closer to the object), you angle the sail with respect to the sun so that the pressure generated by the sunlight is opposite the direction of your orbital motion. The force then decelerates the spacecraft, decreases the speed of its orbit and the spacecraft drops into a lower orbit.
The pressure of sunlight decreases with the square of the distance from the sun. Therefore, sunlight exerts greater pressure closer to the sun than farther away. Future solar-sail spacecraft may take advantage of this fact by first dropping to an orbit close to the sun -- a solar fly-by -- and using the greater sunlight pressure to get a bigger boost of acceleration at the start of the mission. This is called a powered perihelion maneuver.
SOLAR SAIL MATERIALS
While solar sails have been designed before (NASA's had a solar sail program back in the 1970s), materials available until the last decade or so were much too heavy to design a practical solar sailing vehicle. Besides being lightweight, the material must be highly reflective and able to tolerate extreme temperatures. The giant sails being tested by NASA today are made of very lightweight, reflective material that is upwards of 100 times thinner than an average sheet of stationery. This "aluminized, temperature-resistant material" is called CP-1. Another organization that is developing solar sail technology, the Planetary Society (a private, non-profit group based in Pasadena, California), supports the Cosmos 1, which boasts solar sails that are made of aluminum-reinforced Mylar and are approximately one fourth the thickness of a one-ply plastic trash bag.
The reflective nature of the sails is the key. As photons (light particles) bounce off the reflective material, they gently push the sail along by transferring momentum to the sail. Because there are so many photons from sunlight, and because they are constantly hitting the sail, there is a constant pressure (force per unit area) exerted on the sail that produces a constant acceleration of the spacecraft. Although the force on a solar-sail spacecraft is less than a conventional chemical rocket, such as the space shuttle, the solar-sail spacecraft constantly accelerates over time and achieves a greater velocity.
5.1 Aluminum as Solar Sail Material
The thin metal film, according to the preferred embodiment of this invention, is an aluminum film. Aluminum films have high reflectivity, low density, a reasonable melting point, and a very low vapor pressure. The reflectivity and transmissivity of aluminum film is a function of its thickness. Generally, reflectivity for short wave lengths falls off faster with decreasing film thickness than for longer wave lengths. Consequently, any aluminum film thick enough to reflect well in the visible wave lengths should reflect even better in the infrared, where roughly half the sun's power output lies. Even in the visible wave length, aluminum's reflectivity remains near its bulk value down to a thickness of 30 nm, and remains above 0.8down to about 15 nm. The reflectivity of aluminum films varies with the deposition conditions. Over a range of at least 300 degrees to 473 degrees Kelvin, reflectivity increases with decreasing substrate temperatures. High deposition rates, near-normal vapor incidence, and a good vacuum favor high reflectivity. In general, poor deposition conditions reduce reflectivity with a shorter wave length more than for a longer wave length, and thicker films are more sensitive to vapor incidence angle than are thin films. Since most of the sun's power output is at comparatively long wave lengths, and since the films are to be quite thin, poor deposition conditions should not greatly affect sail performance.
Above some temperature, thin metal films fail by agglomeration. This occurs because thin films have an enormous ratio of surface to volume, permitting them to substantially reduce the surface energy by forming droplets. Above the melting point, the material rearranges swiftly, like a soap bubble bursting. At temperatures somewhat below the melting point, agglomeration into droplets occurs far more slowly, through surface diffusion. Thin films made from silver, with a melting point of 1235degrees Kelvin agglomerate at less than 500 degrees Kelvin. However, the analogous temperature for aluminum is a mere 378 degrees Kelvin. Nevertheless, aluminum films have survived fifteen minute anneals at 673 degrees Kelvin, and two hour anneals at700 degrees Kelvin. The reason for this discrepancy is the presence of an oxide layer on the aluminum, which armors the surface with a rigid, refractory skin, thereby inhibiting surface diffusion and preventing changes of shape.
Since the film is to be hot and mounted under tension, creep is of concern. The interior of a small droplet will be in compression, because of its surface energy and resulting force of surface tension. In like fashion, the interior of a thin film will be in compression, unless the mounting tension exceeds its surface tension. Considering the oxide-coated film, elongation not only breaks the oxide skin (which may be very strong), but also creates a fresh, uncoated aluminum surface. To shrink, on the other hand, it must somehow crush or destroy the outside surface, which it clearly cannot do. In fact, shrinkage would manifest itself as agglomeration, as discussed above.
The strength of a variety of thin metal films and thicker vapor deposited sheets has been measured experimentally. Metals in thin films have mechanical properties differing from those of the bulk material, because of the close proximity of all parts of the film to the surface. The yield and fracture stresses of aluminum film increase as the film gets thinner. Aluminum films show substantial ductility, and a variable degree of deformation before failure.
Aluminum films of the minimum thickness required for reflectivity may prove too weak to support the stresses imposed upon them during fabrication and operation, or may creep under load at elevated temperatures. If so, it is possible to strengthen them, not by adding further aluminum, but by adding a reinforcing film of a stronger, more refractory material. A good reinforcing film should be strong, light, and easy to deposit. It need not be chemically compatible with aluminum, since a few nanometers of some other material can serve as a barrier to diffusion. A reinforcing film is apt to have a high modulus such that it will act as the sole load bearing element in the composite film. The aluminum film could help contribute tear resistance, however. The use of a metal as a reinforcing film could reduce the amount of aluminum needed to give good reflectance. Some metals, such as nickel, may reflect well enough to be of interest by themselves.
5.1.1 Titanium as reinforcing material
Films of pure titanium from 150 to 2,000 nanometers thick were found to have strengths of 460 to 620 NPa, while vapor deposited foils of Pi-6Al-4V from 40,000 to 2,000,000 nanometers thick had tensile strengths of 970 to 1200 NPa. Titanium has enough strength and temperature tolerance to make it an attractive choice as a reinforcing film.
5.1.2 Nickel as reinforcing material
The strength of nickel film exceeds 2,000 NPa at a thickness of 70 nanometers or less, dropping to 1500 NPa on annealing. Nickel’s density is a disadvantage for use in sails of the highest performance, which should prove acceptable for bulk transport sails.
5.1.3 Silicon Monoxide as reinforcing material
Silicon monoxide is a popular thin film material with many uses. On aluminum, these films have found extensive use as satellite thermal control coatings, and have demonstrated their stability in the space environment. Mounted on fine metal meshes, unbacked SiO films as thin as 2.5 nanometers have found use as specimen supports in electron microscopy; such films are described as having "great strength," and are so stable at high temperatures that they may be cleaned by passing them rapidly through a flame. Since silicon monoxide is easy to evaporate, is refractory, has a low density, is apparently of high strength in extremely thin film form, and is of known space compatibility, silicon monoxide shows promise as a reinforcing film material.
Boron as reinforcing material
Vapor deposited boron film has a strength of 620 MPa. Since it is light and refractory, boron may prove desirable as a reinforcing material. Carbon forms amorphous films of "exceptional strength;" those used in electron microscopy are made as thin as 4 nanometers. Since carbon is strong, light, refractory, and easy to deposit, it is a promising material for reinforcing film. For a wide variety of reasons, the sail surface will not be one big piece of film, but rather many smaller sheets mounted on a structure. Since the fabrication device, as described hereinafter, will produce strips, natural choices for the shapes of the sheet include long strips, shorter rectangles or squares cut from strips, and triangles cut from the strips. The sheets must be tensioned, and should be planar. Since a triangular sheet will be planed if tensioned at its corners, and since triangular sheets will fit well into a fully triangulated structure, they will be used as a basis for further design.
In 2000, Energy Science Laboratories developed a new carbon fiber material which might be useful for solar sails. The material is over 200 times thicker than conventional solar sail designs, but it is so porous that it has the same weight. The rigidity and durability of this material could make solar sails that are significantly sturdier than plastic films. The material could self-deploy and should withstand higher temperatures.
Tears are a critical concern in the use of thin films for solar sails. While even sheets of extremely thin material have adequate strength to support the load expected during fabrication and operation in the absence of stress concentrations, the inevitability of manufacturing flaws and micrometeoroid damage makes this a small comfort. A means of limiting the spread of tears would be desirable, as it would allow a thinner sheet to tolerate greater damage without failure.
The most obvious method of limiting tears is to mount the film on a supporting mesh. However, differing coefficients of thermal expansion and differing temperature between the mesh and the film are apt to make the film become slack and lose its flatness, or become taut and possibly tear. Further, the mesh adds mass to the sail and, because it must be fabricated, transported into space and attached to the film, adds cost as well.
A more natural approach to tear-stopping is to subdivide the film, convert it from a continuous sheet to a redundant network of small, load-bearing elements. In such a structure, a large manufacturing flow or a grazing micrometeoroid impact is free to initiate a tear--but the tear will cause the failure, not of an entire sheet, but of a small piece of film, perhaps 25 square millimeters in area. Patterns of cuts and wrinkles can de-tension areas of film to isolate stress to smaller regions. Each wrinkled region is fabricated with enough extra material to avoid being stretched flat as the film is tensioned. Stress isolation is aided by slits extending perpendicular to the boundary. The slits are terminated at their stress bearing ends in a way that avoids initiation of tears. This approach to tear resistance appears superior to that of mounting the films on a metal mesh. It involves the fabrication of no additional elements and the addition of no extra mass. By taking advantage of the natural strength of the films, it avoids slackness due to differential expansion and yields a flatter sail.