by Eric Flint
Adham suspected it was enjoying the drama of the moment. "Actually, this is more for your benefit than mine. You see that chest by my mule? That's a goblin trap. It says so right on the front. Granted, it is a simple trap, but as they say, better safe than sorry. We should make sure that no goblin accidentally falls into it."
The goblin cupped its chin in its tiny hand and nodded sagely. "I see, I see. Not a bad idea. How do we do that?"
"In my coat pocket you'll find a padlock . . ."
* * *
NONFICTION
S.S. Sunbeam
Written by Iver P. Cooper
Illustrated by Laura Givens
A new Age of Sail is dawning. One in which the ships sail through outer space, not on water; and are propelled by the sunlight, not wind.
A conventional spacecraft burns fuel and discharges exhaust gases. The gases move backward and the spacecraft, in reaction, moves forward.
The great advantage possessed by "light sailers" is that they don't need to carry fuel. The force which is used to move these space clippers is supplied, free of charge, by the sun.
The exhaust of a rocket engine exerts a much greater force than that of sunlight. But once that fuel is used up, you're in trouble. The fuel-free solar sailer doesn't have that problem; it is the "Energizer Bunny" of space vehicles. So even though the rate of acceleration is slow, we can let the speed build up, day after day, week after week, month after month.
History of the Solar Sailing Concept
Johannes Kepler (1571-1630) was the first to propose that spaceships could use sails. He had noticed that comet tails point away from the sun. Of course, he thought this was the effect of a real wind, not of light.
In 1864, the great physicist James Clerk Maxwell (1831-1879) used his quantitative electromagnetic wave theory of light to predict the pressure that light would exert a pressure on objects.
Maxwell had speculated that light pressure might be observable in the laboratory if sunlight were directed onto a "thin metallic disk, delicately suspended in a vacuum." In 1901, Pyotr Lebedev experimentally measured the pressure of light (and it obeyed Maxwell's predictions).
* * *
Jules Verne's From Earth to the Moon (1865) is usually cited as the first science fiction story to postulate a sunlight-propelled spaceship. But all Verne did was to vaguely speculate that the speed of his cannon-fired craft would someday be surpassed by a vehicle using "light or electricity as the mechanical agent."
I would give more credit to an extraordinarily obscure novel by Georges Le Faure and Henri de Graffigny, Aventures Extraordinaires d'un Savant Russe (1889-91). According to Paul Gilster, their protagonists "travel in a hollow sphere pushed by the pressure of light from the sun. Launching the sphere is accomplished by concentrating sunlight from a huge reflecting dish onto a selenium disk."
The first serious proposal of solar sailing was by Soviet space enthusiasts Konstantin Tsiolkovsky and Friderikh Tsander, in the 1920s. A much more detailed analysis appeared in an article published in 1951 by Astounding Science Fiction. "Clipper Ships in Space" was written by engineer Carl Wiley, under the pseudonym "Russell Saunders." By the end of that decade, the subject was considered sufficiently respectable to be aired in the journal Jet Propulsion.
These articles inspired a new crop of science fiction writers. The earliest contributions were by Cordwainer Smith ("The Lady Who Sailed The Soul," 1960, and "Think Blue, Count Two," 1963), Jack Vance ("Sail 25," 1962), Pierre Boulle (Planet of the Apes, 1963), Poul Anderson ("Sunjammer," 1964), and Arthur C. Clarke ("Sunjammer," 1964, sometimes reprinted as "The Wind from the Sun").
Naturally, many of the readers of these stories were current or would-be scientists and engineers. Hence, solar sailing soon had its advocates within the space science community. In the late 1970s, NASA toyed with the idea of using a sunjammer to rendezvous with Halley's Comet. However, this never went past the study stage. Occasionally, ordinary spacecraft have used solar collectors and sun shades as makeshift solar sails, slowly adjusting their orbits.
The first true steps into the new Age of Sail were taken by Russia on February 4, 1993; in the Znamya-2 experiment, a small solar sail was deployed from an unmanned Progress M-15 supply ship after it was undocked from the Mir Space Station. More recently, on August 9, 2004, the Japanese Institute of Space and Aeronautical Science (ISAS) deployed "four-leaf clover" and "six-rayed fan" type test sails from an S-310 sounding rocket, at altitudes of 122 and 169 kilometers. Both Japanese sails were 7.5 microns thick. NASA has also gotten back into the act; on August 10, 2004, they ground-tested two 100 square meter solar sails in a vacuum chamber.
The Underlying Physics
In classical physics, light is characterized as an electromagnetic wave, composed of fluctuating electric and magnetic fields. However, it is more convenient to calculate light pressure if we, like Albert Einstein, visualize light as a stream of particle-like units (photons). The photons carry momentum, and one of the fundamental laws of physics is that momentum is conserved. When a photon strikes an object, it is absorbed, and delivers its momentum to the latter. The change in the target's momentum is felt as a force. If the object reflects light, it emits a photon in the opposite direction, and, to conserve momentum, the object recoils, as if it had felt a force. Thus, light delivers one "kick" per photon to a perfectly absorbing surface, and two "kicks" to a perfectly reflecting one.
* * *
The light exerts a force on the sail; this causes it to accelerate (increase speed). The force equals the light pressure times the reflective area of the sail. If the sailcraft is at Earth's distance from the sun (one Astronomical Unit, A.U.), and the sail directly faces the sun, the light pressure is 4.7 newtons per square kilometer on a perfectly absorbing surface, and twice that (9.4 newtons, or two pounds) on a perfectly reflecting one. (The pressure exerted by a 12 mph wind is about 50,000,000 times the latter.)
Light spreads as it moves away from the sun, and therefore weakens in intensity, according to the inverse square law first postulated by Johannes Kepler. So solar sailing is more efficient in the inner solar system, where the light pressure is stronger.
A common misconception is that solar sailing uses the "solar wind." The solar wind is the stream of ionized particles ejected by the sun. While it would produce a pressure on a spacecraft, that pressure is less than one-thousandth of the sunlight pressure. So it can safely be ignored.
* * *
The acceleration is the force divided by the total mass (sails, support and control structures, and payload). So the greater the mass, the more force is needed to achieve a particular acceleration (which in turn determines how soon you reach a desired speed).
Accelerations felt by space sailcraft are measured in millimeters (thousandths of a meter) per second, per second (mm/sec2 ). If your car accelerates from zero to 60 mph in ten seconds, it is increasing speed at a rate of 6 mph per second (about 2.68 meters per second, per second, "m/sec2 "). Newton's apocryphal apple fell toward the ground with an acceleration of 9.8 m/sec2 , or "one-gee," and jet aircraft feel accelerations of several "gees." If Earth were stopped in its orbit, it would fall toward the sun, its speed increasing at the rate of 5.9 mm/sec2 (half a gee).
Engineers find it convenient to define an "areal density," which is the reflective area divided by the mass. Then acceleration equals the light pressure divided by the areal density. The "characteristic acceleration" of a sailcraft is the acceleration it would feel from light if the sail faced the sun directly, and the sailcraft was one A.U. from the sun. If the areal density is 10 grams per square meter, and the sail is perfectly reflecting, then, at one A.U., the characteristic acceleration is 0.9 mm/sec2 (ten-thousandth of a gee). Halving the areal density doubles that limiting acceleration.
Maneuvering in Outer Space
There are two solar forces acting on the light sail: the force of gravity (pulling it sunward) and the photonic (electromagnetic) force (whose direction is determined by how the s
ail is oriented).
What is the best way to sail a sunjammer away from the sun? Surprisingly, it is not to aim the solar sail directly at the sun. Then the photonic force has to overcome the force of gravity. It is better to direct more of the force into the direction of travel.
If the sail is tilted so that the sunlight is reflected obliquely "backward," that is, away from the direction the spacecraft is orbiting the sun, it not only tries to push the spacecraft outward, but also pushes it "forward" in its orbit, speeding it up, and the orbit widens.
Tilt the sail the other way, and the spacecraft slows down and its orbit shrinks. Thus, depending on the orientation of the sail, the solar sailer can move away from, or toward, the sun—even though the sunlight just moves outward.
It is only the thrust in the orbital direction(whether forward or backward) which is changing the size of the orbit. This thrust component is maximized when the angle of incidence of the sunlight on the sail (the angle between the sun and the perpendicular to the sail surface) is about 35.3 degrees.
However, tilting the sail reduces the total thrust (the sail captures less light, and the light is spread out), and only a portion of that thrust is in the orbital direction. The net result of these factors is that the effective orbital thrust at the optimum tilt angle is only 38% of the all-outward thrust obtained when the sail directly faces the sun.
* * *
An advanced maneuver is called "sun-diving" or, more prosaically, "fast solar sailing." While your ultimate goal is in the outer solar system, you sail sunward first. You slingshot around the sun, and head back out at a greatly increased speed.
Sun-diving is the extraterrestrial equivalent of an automobile driver taking a more roundabout route, using high speed expressways, to reduce the overall trip time. Sun-diving is very likely to be used for missions to Jupiter and beyond, but for a trip to Mars, a simple ballistic trajectory is about twice as fast.
All-Metal Sails
The simplest sail concept was an all-metal sail which was thick enough, by itself, to withstand the stresses of manufacture and use. If you're going to provide a metal sail which is several microns thick, you're going to favor a metal with a low density, such as lithium, sodium, potassium, beryllium, magnesium, calcium, or aluminum.
In 1929, Hermann Noordung suggested that an orbiting space station could be equipped with sodium mirrors. The great advantage of sodium is that it is of very low density (one-fifth that of aluminum, one-fifteenth that of iron). However, it is a very difficult metal to work with; it has to be handled in an inert atmosphere.
"Russell Saunders" favored lithium or magnesium sails for his "clipper ships of space." He pointed out that magnesium "has a fair strength mass ratio and is opaque for sheets 0.15 microns thick." Magnesium is about two-thirds as dense as aluminum (which is why magnesium is used in the bodies of professional cameras). Unfortunately, it is much more expensive. Also, if a magnesium sail strip somehow gets ignited during manufacture on Earth, you have a serious problem.
Composite Sails
An alternative to an all-metal mirror is one in which the metal is deposited as a very thin coating on a low-density substrate. Vance, in "Sail 25," favored a 2.5 micron thick "fluoro-siliconic film . . . fogged with lithium to the state of opacity." Clarke, in his 1962 story, envisioned sails made of "aluminized plastic," perhaps 50-100 microns thick.
NASA's Solar Sail Technology Development group considers a "conventional light sail" to be a 0.1 micron thick layer of aluminum, which reflects 90% of the sunlight, deposited on a five micron thick substrate made of Mylar polyester film. (Ordinary plastic wrap is about thirteen microns thick.)
Mylar is less dense than aluminum. Each square meter of five micron Mylar would have a mass of seven grams (as compared to sixteen for the plastic wrap), and so the characteristic acceleration would be ~1.3 mm/sec2 . The 0.1 micron aluminum coating adds ~0.3 g/m2 . In contrast, if NASA were to attempt to make the same sail entirely out of five micron thick aluminum foil (household aluminum foil is closer to thirty microns), its "areal density" would be almost twice that of the Mylar.
Mylar is now available commercially in films which are just 0.9 microns thick, and these are generally considered to be strong enough for use in solar sails. The new ultrathin films allow us to improve acceleration almost four fold (taking the aluminum coating into account).
* * *
The basic problem with Mylar is that it is susceptible to degradation by high-energy solar radiation. That, of course, is of particular concern if the solar sailer is going to be venturing sunward. An alternative to Mylar is Kapton polyimide film. Unfortunately, Kapton is only available now in a thickness of eight microns, so the areal density of a Kapton-based sail is high (12 g/m2 ).
Another alternative is the carbon micro-truss, whose areal density is comparable to Mylar's.
Ultra-Thin All-Metal Sails
If we could manufacture the sail in space, we could dispense with the substrate. An all-aluminum sail, if just 0.1 microns thick, would have an areal density of 0.27 g/ m2 and allow an acceleration (at 1 A.U.) of 33 mm/sec2.
Why not make the sail even thinner? Even a 0.1 micron layer of aluminum is only a few hundred atoms thick. If the layer is made much thinner than that, reflecting power is lost. By way of analogy, if a forest is too thin, you will be able to see through the gaps between the trees.
But there is a trick which somewhat defies common sense. You can perforate the metal layer. If the holes are small enough (less than the wavelength of the light), the light waves have difficulty penetrating them.
Sail Metal: Silver vs. Aluminum
While thin films of silver are traditionally used in mirror-making, silver is expensive (~$1,300/kilogram), four times denser than aluminum, and easily oxidized (if manufactured on Earth). In thin films, it agglomerates (clumps) at high temperature. Also, it is fairly transparent to short wave ultraviolet, which allows that radiation to attack the Mylar or Kapton substrate beneath. Nowadays, most telescope mirrors are aluminized, and aluminum is the standard solar sail reflector.
Alternative Sail Metals
There are many metals, of course, and some have distinct advantages over silver and aluminum. But bear in mind that these metals can be expensive to obtain in high purity, and that there may be technological problems to overcome if they are to be formed into large, thin films.
Near-Earth, Mars, and Outer Planet Missions
For missions relatively far from the sun, it is critical to obtain the highest possible characteristic acceleration. This will be proportional to the ratio (1+R)/D, where R is the reflectivity, and D is the density. By this criterion, sodium, potassium, lithium, calcium, magnesium and beryllium are all superior to aluminum.
Because of its low density, beryllium was the material chosen for the James Webb Space telescope mirror. Unfortunately, it is rather pricey on Earth (~$5,000/kilogram). Magnesium and calcium are highly reactive, which makes them difficult to work with on Earth.
Lithium, sodium and potassium are even less dense, but they would melt if used in a sail unfurled at Earth's distance from the sun. Once we have manufacturing facilities in Mars orbit (1.5 A.U.), or on an asteroid (~2.8 A.U.), we can consider manufacturing such sails—assuming that the cost of shipping the metal, or extracting it locally, isn't prohibitive.
Inner Planet Missions
If the sailcraft is going to be entering the environs of Venus or Mercury, it will experience greater acceleration because of the increased solar pressure. However, the maximum acceleration achievable by heading sunward is limited by the melting point of the sail's metal veneer. The metal coating is thick enough so you can assume that whatever light isn't reflected is absorbed. The absorbed energy is then re-radiated as long infrared (heat) radiation. The rate of re-radiation by a square meter of surface is proportional to the fourth power of its temperature. Which means that the maximum acceleration is proportional to the fourth power of the melting point, divided by the density. NASA
scientist Geoffrey Landis suggested that this be used as a "figure of merit" for evaluating potential sail materials for an interstellar probe.
The metals with the highest scores are tungsten (33.5 times that of aluminum), tantalum (24.3), molybdenum (23.7), rhenium (23.6), and niobium (22.1).
Unfortunately, there is a general periodic correlation between melting point and density. So, the price of being able to descend deeper into the gravity well to increase the slingshot effect is poorer acceleration when far enough from the sun so that melting point is irrelevant.
It is therefore instructive to examine the metals in order of increasing density range. Of the metals lighter than aluminum, the one with the best score is beryllium (11.1), because it has a surprisingly high melting point of 1550o K. Beryllium's density is just 1.8 g/cm3.
Titanium is almost as good (11.0), but its density is a relatively painful 4.54. On the other hand, beryllium is also almost five times as expensive as titanium, so I am not prepared to rule the latter out.
To improve on beryllium's sundiving score, you have to switch to scandium (12.5), and accept a density of 2.99. However, scandium is an extremely expensive metal.