(ed note: Icarus was to have a maximum velocity of 0.2 c)

A proposed means of decelerating from interstellar speeds is the magnetic-sail, which is a large loop of superconducting wire producing an artificial magnetosphere around the moving spacecraft. By deflecting interstellar ions, the magnetic field forms a semi-spherical zone forward of the vehicle where the magnetic pressure of the field and the pressure of colliding ions are evenly balanced. A magnetopause forms, in which ions are reversed in direction and their change in momentum produces an equal, but opposed, change in momentum in the magnetic-sail, and thus the spacecraft to which it is attached.

Interestingly the Sun’s magnetosphere already acts like a deflector shield, forcing the ions and small charged particles of dust to flow around the Sun as it moves against the average flow of the Galaxy. Exposed to energetic photons (ultraviolet and x-ray) and high-energy ions (cosmic rays) the interstellar dust is charged. The very smallest dust particles, up to a certain diameter, are completely excluded from the inner Solar System by the Sun’s magnetosphere, while particles a bit larger are significantly deflected. Only the high-end of the dust size range is able to penetrate.

In the case of a moving magnetic-sail, the atoms of the Interstellar Medium (about 90%-50% of the ISM) are actually ionized by its rapidly changing magnetic-field strength, in a process akin to that used to ionize gas in a Pulsed Inductive Thruster. If you imagine an atom drifting through space at typically 15 km/s, to then encounter a magnetic field approaching at 60,000 km/s is to experience a change in field sufficiently quick enough to ionize the atom. In effect the ship is creating a shock-wave in the ISM which is producing a lot of extra charge as atoms are ionized. All those suddenly energetic electrons could be sufficient to increase the charge on the ISM dust, thus increasing the deflector effect.

The question needing investigation is whether this is sufficient to provide protection against all the ISM dust, or whether some additional defences will be needed. Cosmic sand-grains, with the kinetic energy of 100 pound bombs, while rare, will perhaps still need some means of interception by “Icarus”. The original “Daedalus” study proposed an artificial dust cloud moving 200 kilometres ahead of the main vehicle and this might prove sufficiently effective.

Alternatively newer materials have become available which might provide multilayer protection – carbon allotropes, the most exciting of which is graphene. Graphene is basically a single sheet of graphite – a hexagonal grid form of carbon in the form of immensely strong sheets of covalently bonded carbon atoms, but held together between the sheets via via weak hydrogen bonds to make graphite. Peeling away single layers of graphene has now become possible and it has all sorts of surprising properties.

What I’m interested in for shielding is making a large, low-mass “bumper” which cosmic sand-grains run into before hitting the craft. After passing through several layers of graphene the offending mass is totally ionized and forms a high-energy spray of particles, but particles that can now be deflected by the vehicle’s cosmic-ray defences (akin to the mag-sail, but smaller with a higher current) and safely diverted away from sensitive parts. To put the bumper in place, perhaps 100 kilometres ahead, it can be deployed via a small sub-vehicle – sheets made from carbon fibre are surprisingly springy and can self-unfold from a small volume. Once in place it might be kept in place by firing lasers at super-reflective patches on the bumper. Via reflecting ~2,000 times the laser achieves far more push than a single pulse of energy can achieve.

Circuitry is being made from graphene in laboratories around the world, thus the bumper isn’t a passive mass. Multiple layers could work together to track any grains that pass through without being totally ionized. This causes a signal to be sent back to the vehicle which then activates its final layer of defence, high-powered lasers. In microseconds the lasers either utterly ionize the target or give it a sideways nudge via ablation – blowing it violently to the side via a blast of plasma. Such an active tracking bumper would need to be further away than 100 km to give the laser defence time to react, though 1/600th of a second can be a lot of computer cycles for a fast artificial intelligence. The lasers might use advanced metamaterials to focus the beam onto a speck at ~100 km, without needing to physically turn the laser itself in such a split-second. Highly directional, high-powered microwave phased arrays exist which already do so purely electronically and an optical phased-array isn’t a stretch beyond current technology.

• 

‘You’ll see that the ship is roughly cylindrical — length four kilometres, diameter one. Because our propulsion system taps the energies of space itself, there’s no theoretical limit to speed, up to the velocity of light. But in practice, we run into trouble at about a fifth of that speed (0.2 c), owing to interstellar dust and gas. Tenuous though that is, an object moving through it at sixty thousand kilometres a second or more hits a surprising amount of material — and at that velocity even a single hydrogen atom can do appreciable damage.

‘So Magellan, just like the first primitive spaceships, carries an ablation shield ahead of it. Almost any material would do, as long as we use enough of it. And at the near-zero temperature between the stars, it’s hard to find anything better than ice. Cheap, easily worked, and surprisingly strong! This blunt cone is what our little iceberg looked like when we left the solar system, two hundred years ago. And this is what it’s like now.’

The image flickered, then reappeared. The ship was unchanged, but the cone floating ahead of it had shrunk to a thin disc.

‘That’s the result of drilling a hole fifty light-years long, through this rather dusty sector of the galaxy. I’m pleased to say the rate of ablation is within five per cent of estimate, so we were never in any danger — though of course there was always the remote possibility that we might hit something really big. No shield could protect us against that — whether it was made of ice, or the best armour-plate steel.

‘We’re still good for another ten light-years, but that’s not enough. Our final destination is the planet Sagan 2 — seventy-five lights to go.

‘So now you understand, Mr. President, why we stopped at Thalassa. We would like to borrow — well, beg, since we can hardly promise to return it — a hundred or so thousand tons of water from you. We must build another iceberg, up there in orbit, to sweep the path ahead of us when we go on to the stars.’

---

‘But why is it that shape?’ the president asked.

Deputy Captain Malina sighed; he was quite sure that this had already been explained several times.

‘It’s the old problem of covering any surface with identical tiles,’ he said patiently. ‘You have only three choices — squares, triangles, or hexagons. In our case, the hex is slightly more efficient and easier to handle. The blocks — over two hundred of them, each weighing six hundred tons — will be keyed into each other to build up the shield. It will be a kind of ice-sandwich three layers thick. When we accelerate, all the blocks will fuse together to make a single huge disk. Or a blunt cone, to be precise.’

---

For that matter, they might never reach Sagan 2. Although the ship’s operational reliability was still estimated to be ninety-eight per cent, there were external hazards which no one could predict. Only a few of his most trusted officers knew about the section of the ice-shield that had been lost somewhere around light-year 48. If that interstellar meteoroid, or whatever it was, had been just a few metres closer …

• 

(ed note: GAILE colony starships spend much of their voyage traveling at relativisitic velocities. The "citadel" acts as the starship bumper. Granted that antigravity "g-fields" and disintegrator-ray "w-fields" are total handwavium. But their useage here is educational for starship design)

The citadel structure at the end of each force field wand houses three additional field generators that protect the ship and its passengers from collisions with foreign objects. At near light speeds, an impact between the ship and a particle no bigger than a grain of sand would melt a hole several inches in diameter in the strongest and most refractory of materials. Solid particles occur even less commonly in the interstellar void than they do in the space of our Solar system. Yet they do exist, ranging in size from fine dust to giant spheres several times the mass of the planet Jupiter! There is a slim but finite probability that a ship could collide with such a particle during the trillions of kilometers of an interstellar crossing, and just one such collision would be fatal.

Figure 4.7 above is a schematic profile of the ship’s defense fields. The familiar g-field offers the first line of defense. Physically identical to the anti-acceleration fields of the ship and the anti-gravity fields of levicars, the polarity of the citadel g-field is reversed so that it repels mass instead of attracting it. The field is focused into a beam which extends up to 100 million kilometers in front of the ship. When it encounters a particle at this range, it exerts just a slight force on both the ship and the particle. This gentle nudge is usually sufficient to deflect the particle from the ship’s path, just as the bow wave of a boat keeps floating debris from striking the hull.

The g-field grows stronger as the ship and the obstacle get closer until, within a certain critical range of the ship, sensors automatically activate the “weak field” generator, the ship’s second line of defense. The w-field neutralizes the weaker of the interatomic forces (I think the writers intended the Strong nuclear force, not the weak). This causes all matter within the field to break up into a cloud of free protons, neutrons, and electrons (i.e., it is a disintegrator ray). A magnetic field, emanating from the citadel, captures the protons and electrons, forming an artificial “Van Allen belt” about the ship. Just before arrival, the crew de-energizes the magnet to release the charged particles to space. The g-field and conventional neutron shielding protect the ship’s occupants from the w-field’s neutrons.

GAIL starship’s take special precautions to avoid energizing the w-field when another starship is in their path. All vessels carry wideband transponders which emit conventional EM radiation (radio) over a series of specific frequencies. Association ships also monitor an even wider range of frequencies and employ long-range sensors tuned to detect unnatural energy sources just in case alien ships of unknown origin should cross their path. Unprovoked firing of the w-field at such an alien might be misinterpreted as a hostile act. (Gee, you don't say?)

What mass ratio will the Peek-A-Boo need for a fly-by, and for a brachistochrone? For a fly-by T = 3.94 years, for a brachistochrone T = 6.58 years.

Fly-by

R = e^{(a * T / c)}
R = e^{(1.03 * 3.94 / 1.0)}
R = e^4.06
R = 57.97

Brachistochrone

R = e^{(1.03 * 6.58 / 1.0)}
R = e^6.78
R = 880.07

So for a brachistochrone the Peek-A-Boo will have to have 880.07 kilograms of propellant for every kilogram of ship that isn't propellant. Egad.

• 

In Stephen Baxter’s “Xeelee” tales the early days of human starflight (c.3600 AD), before the Squeem Invasion, FTL travel and the Qax Occupation, starships used “GUT-drives”. This presumably uses “Grand Unification Theory” physics to ‘create’ energy from the void, which allows a starship drive to by-pass the need to carry it’s own kinetic energy in its fuel. Charles Sheffield did something similar in his “MacAndrews” yarns (“All the Colors of the Vacuum”) and Arthur C. Clarke dubbed it the “quantum ramjet” in his 1985 novel-length reboot of his novella “The Songs of Distant Earth”.

Granting this possibility, what does this enable a starship to do? First, we need to look at the limitations of a standard rocket.

In Newton’s Universe, energy is ‘massless’ and doesn’t add to the mass carried by a rocket. Thanks to Einstein that changes – the energy of the propellant has a mass too, as spelled out by that famous equation:

For chemical propellants the energy comes from chemical potentials and is an almost immeasurably tiny fraction of their mass-energy. Even for nuclear fuels, like uranium or hydrogen, the fraction that can be converted into energy is less than 1%. Such rockets have particle speeds that max out at less than 12% of lightspeed – 36,000 km/s in everyday units. Once we start throwing antimatter into the propellant, then the fraction converted into energy goes up, all the way to 100%.

But… that means the fraction of reaction mass, propellant, that is just inert mass must go down, reaching zero at 100% conversion of mass into energy. The ‘particle velocity’ is lightspeed and a ‘perfect’ matter-antimatter starship is pushing itself with pure ‘light’ (uber energetic gamma-rays.)

For real rockets the particle velocity is always greater than the ‘effective exhaust velocity’ – the equivalent average velocity of the exhaust that is pushing the rocket forward. If a rocket energy converts mass into 100% energy perfectly, but 99% of that energy radiates away in all directions evenly, then the effective exhaust velocity is much less than lightspeed. Most matter-antimatter rockets are almost that ineffectual, with only the charged-pion fraction of the annihilation-reaction’s products producing useful thrust, and then with an efficiency of ~80% or so. Their effective exhaust velocity drops to ~0.33 c or so.

Friedwardt Winterberg has suggested that a gamma-ray laser than be created from a matter-antimatter reaction, with an almost perfect effective exhaust velocity of lightspeed. If so we then bump up against the ultimate limit – when the energy mass is the mass doing all the pushing. Being a rocket, the burn-out speed is limited by the Tsiolkovsky Equation:

(ed note: keeping in mind that such a gamma-ray laser plugged into the infinite power of the universe if used as a weapon would make the primary weapon of the Death Star look like a flashlight)

However we have to understand, in Einstein’s Relativity, that we’re looking at the rocket’s accelerating reference frame. From the perspective of the wider Universe the rocket’s clocks are moving slower and slower as it approaches lightspeed, c. Thus, in the rocket frame, a constant acceleration is, in the Universe frame, declining as the rocket approaches c.

To convert from one frame to the other also requires a different measurement for speed. On board a rocket an integrating accelerometer adds up measured increments of acceleration per unit time and it’s perfectly fine in the rocket’s frame for such a device to meter a speed faster-than-light. However, in the Universe frame, the speed is always less than c. If we designate the ship’s self-measured speed as V’_ƒ and the Universe measured version of the same, V_ƒ, then we get the following:

[Note: the exhaust velocity, V_e, is measured the same in both frames]

and…

To give the above equations some meaning, let’s throw some numbers in. For a mass-ratio, of 10, exhaust velocity of c, the final velocities are V’_ƒ = 2.3 c and V_ƒ = 0.98 c. What that means for a rocket with a constant acceleration, in its reference frame, is that it starts with a thrust 10 times higher than what it finishes with. To slow down again, the mass-ratio must be squared – thus it becomes 10² = 100. Clearly the numbers rapidly go up as lightspeed is approached ever closer.

A related question is how this translates into time and distances. In Newtonian mechanics constant acceleration (g) over a given displacement (motion from A to B, denoted as S) is related to the total travel time as follows, assuming no periods of coasting at a constant speed, while starting and finishing at zero velocity:

this can be solved for time quite simply as:

In the relativistic version of this equation we have to include the ‘time dimension’ of the displacement as well:

This is from the reference frame of the wider Universe. From the rocket-frame, we’ll use the convention that the total time is τ, and we get the following:

where arcosh(…) is the so-called inverse hyperbolic cosine.

Converting between the two differing time-frames is the Lorentz-factor or gamma, which relates the two time-flows – primed because they’re not the total trip-times used in the equation above, but the ‘instantaneous’ flow of time in the two frames – like so:

For a constant acceleration rocket, its gamma is related to displacement by:

For very large γ factors, the rocket-frame total-time τ simplifies to:

The relationship between the Lorentz factor and distance has the interesting approximation that γ increases by ~1 for every light-year travelled at 1 gee. To see the answer why lies in the factors involved – gee = 9.80665 m/s², light-year = (c) x 31,557,600 seconds (= 1 year), and c = 299,792,458 m/s. If we divide c by a year we get the ‘acceleration’ ~9.5 m/s², which is very close to 1 gee.

This also highlights the dilemma faced by travellers wanting to decrease their apparent travel time by using relativistic time-contraction – they have to accelerate at bone-crushing gee-levels to do so. For example, if we travel to Alpha Centauri at 1 gee the apparent travel-time in the rocket-frame is 3.5 years. Increasing that acceleration to a punishing 10 gee means a travel-time of 0.75 years, or 39 weeks. Pushing to 20 gee means a 23 week trip, while 50 gee gets it down to 11 weeks. Being crushed by 50 times your own body-weight works for ants, but causes bones to break and internal organs to tear loose in humans and is generally a health-hazard. Yet theoretically much higher accelerations can be endured by equalising the body’s internal environment with an incompressible external environment. Gas is too compressible – instead the body needs to be filled with liquid at high pressure, inside and out, “stiffening” it against its own weight.

Once that biomedical wonder is achieved – and it has been for axolotls bred in centrifuges – we run up against the propulsion issue. A perfect matter-antimatter rocket might achieve a 1 gee flight to Alpha Centauri starts with a mass-ratio of 41.

How does a GUT-drive change that picture? As the energy of the propellant is no longer coming from the propellant mass itself, the propellant can provide much more “specific impulse”, I_sp, which can be greater than c. Specific Impulse is a rocketry concept – it’s the impulse (momentum x time) a unit mass of the propellant can produce. The units can be in seconds or in metres per second, depending on choice of conversion factors. For rockets carrying their own energy it’s equivalent to the effective exhaust velocity, but when the energy is piped in or ‘made fresh’ via GUT-physics, then the Specific Impulse can be significantly different. For example, if we expel the propellant carried at 0.995 c, relative to the rocket, then the Specific Impulse is ~10 c.

…where γ_e and V_e are the propellant gamma-factor and its effective exhaust velocity respectively.

This modifies the Rocket Equation to:

Remember this is in the rocket’s frame of reference, where the speed can be measured, by internal integrating accelerometers, as greater than c. Stationary observers will see neither the rocket or its exhaust exceeding the speed of light.

To see what this means for a high-gee flight to Alpha Centauri, we need a way of converting between the displacement and the ship’s self-measured speed. We already have that in the equation:

which becomes:

For the 4.37 light year trip to Alpha Centauri at 50 gee and an I_sp of 10 c, then the mass-ratio is ~3. To travel the 2.5 million light years to Andromeda’s M31 Galaxy, the mass-ratio is just 42 for an I_sp of 10c.

Of course the trick is creating energy via GUT physics…

• 

(ed note: in this science fiction story, Arthur C. Clarke gets around the mass ratio problem by frantically waving his hands and postulating that the Overlords's Stardrive can tap the energy fields around a nearby sun. Which means the ship can only accelerate and decelerate at the start and end of the mission. And if you miss your destination you'll go sailing off into intergalactic space and a lonely death. But you have to admit that any sun creates astronomical amounts of energy. Obtaining energy from an external source is the classic way for a rocket to avoid the mass ratio problem.)

The rising moon was beginning to paint the eastern sky with a pale milky glow. Up there, Jan knew, was the main base of the Overlords, lying within the ramparts of Plato. Though the supply ships must have been coming and going for more than seventy years, it was only in Jan's lifetime that all concealment had been dropped and they had made their departure in clear sight of Earth. In the two-hundred-inch telescope, the shadows of the great ships could be dearly seen when the morning or evening sun cast them for miles across the lunar plains. Since everything that the Overlords did was of immense interest to mankind, a careful watch was kept of their comings and goings, and the pattern of their behaviour (though not the reason for it) was beginning to emerge. One of those great shadows had vanished a few hours ago. That meant, Jan knew, that somewhere off the moon an Overlord ship was lying in space, carrying out whatever routine was necessary before it began its journey to its distant, unknown home.

He had never seen one of those returning ships launch itself towards the stars. If conditions were good the sight was visible over half the world, but Jan had always been unlucky. One could never tell exactly when the take-off would be—and the Overlords did not advertise the fact. He decided he would wait another ten minutes, then rejoin the party.

What was that? Only a meteor sliding down through Eridanus. Jan relaxed, discovered his cigarette had gone out, and lit another.

He was half-way through it when, half a million kilometres away (x1.4 lunar orbit radius), the Stardrive went on. Up from the heart of the spreading moonglow a tiny spark began to climb towards the zenith. At first its movement was so slow that it could hardly be perceived, but second by second it was gaining speed. As it climbed it increased in brilliance, then suddenly faded from sight. A moment later it had reappeared, gaining speed and brightness. Waxing and waning with a peculiar rhythm, it ascended ever more swiftly into the sky, drawing a fluctuating line of light across the stars. Even if one did not know its real distance, the impression of speed was breathtaking; when one knew that the departing ship was somewhere beyond the moon, the mind reeled at the speeds and energies involved.

It was an unimportant by-product of those energies, Jan knew, that he was seeing now. The ship itself was invisible, already far ahead of that ascending light. As a high-flying jet may leave a vapour trail behind it, so the outward-bound vessel of the Overlords left its own peculiar wake. The generally accepted theory—and there seemed little doubt of its truth—was that the immense accelerations of the Stardrive caused a local distortion of space. What Jan was seeing, he knew, was nothing less than the light of distant stars, collected and focused into his eye wherever conditions were favourable along the track of the ship. It was a visible proof of relativity—the bending of light in the presence of a colossal gravitational field.

Now the end of that vast, pencil-shaped lens seemed to be moving more slowly, but that was only due to perspective. In reality the ship was still gaining speed; its path was merely being foreshortened as it hurled itself outwards to the stars. There would be many telescopes following it, Jan knew, as Earth's scientists tried to uncover the secrets of the Drive. Dozens of papers had already been published on the subject; no doubt the Overlords had read them with the greatest interest.

The phantom light was beginning to wane. Now it was a fading streak, pointing to the heart of the constellation Carina, as Jan had known that it would. The home of the Overlords was somewhere out there, but it might circle any one of a thousand stars in that sector of space. There was no way of telling its distance from the Solar System.

It was all over. Though the ship had scarcely begun its journey, there was nothing more that human eyes could see. But in Jan's mind the memory of that shining path still burned, a beacon that would never fade as long as he possessed ambition and desire.

---

"We know a lot now, through our observation of their departure, about the speed of the Overlord ships. They leave the Solar System under such tremendous accelerations that they approach the velocity of light in less than an hour. That means that the Overlords must possess some kind of propulsive system that acts equally on every atom of their ships, so that anything aboard won't be crushed instantly. I wonder why they employ such colossal accelerations, when they've got all space to play with and could take their time picking up speed?

My theory is that they can somehow tap the energy fields round the stars, and so have to do their starting and stopping while they're fairly close to a sun. But that's all by the way…

"The important fact was that I knew how far they had to travel, and therefore how long the journey took. NGS 549672 is forty light-years from Earth. The Overlords ships reach more than ninety-nine percent of the speed of light, so the trip must last forty years of our time. Our time; that's the crux of the matter.

"Now as you may have beard, strange things happen as one approaches the speed of light. Time itself begins to flow at a different rate—to pass more slowly, so that what would be months on Earth would be no more than days on the ships of the Overlords. The effect is quite fundamental; it was discovered by the great Einstein more than a hundred years ago.

"I have made calculations based on what we know about the Stardrive, and using the firmly-established results of Relativity theory. From the viewpoint of the passengers on one of the Overlord ships, the journey to NGS 549672 will last not more than two months—even though by Earth's reckoning forty years will have passed. (99.999% speed of light) I know this seems a paradox, and if it's any consolation it's puzzled the world's best brains ever since Einstein announced it.

"Perhaps this example will show you the sort of thing that can happen, and will give you a clearer picture of the situation. If the Overlords send me straight back to Earth, I shall arrive home having aged only four months. But on Earth itself; eighty years will have passed. So you understand, Maia, that whatever happens, this is goodbye.

---

The ship of the Overlords came sliding in along its glowing meteor-trail through the heart of Carina. It had begun its mad deceleration among the outer planets, but even while passing Mars it had still possessed an appreciable fraction of the velocity of light. Slowly the immense fields surrounding the Sun were absorbing its momentum, while for a million kilometres behind, the stray energies of the Stardrive were painting the heavens with fire.

Jan Rodricks was coming home, six months older, to the world he had left eighty years before.

(ed note: 40 year = 480 months. If proper time is only 2 months, then gamma is 240.0. This means a velocity of about 0.99999 c {99.999% c} or 299,789,460 m/s.

If getting to that velocity takes 1 hour (3,600 seconds), the acceleration is 299,789,460 / 3,600 = 83,275 m/s² or about 8,500 gravities of acceleration.

Say the Overlord's spacecraft has a mass of a Russian Oscar submarine: 15,000,000 kilograms. To get it up to that speed will require about 6.7×10²³ Joules. This is about 160,000,000 megatons of nuclear weapons, the energy released by the Dinosaur Killer asteroid, or five times the total energy output of Wolf 359 each second )

Without some means of navigational control, any interstellar transport system is useless. As we shall see presently, relativistic starship navigation is hardly a trivial affair.

At only 1-10%c there are few problems. Just set the crosshairs on the target star, the home star, and three reference stars to either side, and the ship’s navigator can calculate velocity and heading fairly exactly. Problems begin to crop up at higher speeds, however. Two distorting effects begin to dominate: Aberration and Doppler Shift.

Aberration causes stars to appear to be displaced forward into the direction of flight. The situation is analogous to raindrops streaking the windows of a speeding train. Although we know the rain is falling straight down, the streaks on the window run diagonally, slanting downward from the front as if the source was ahead rather than above. Aberration of starlight, similarly, causes stars to appear farther forward than they really are. At relativistic velocities the effect can be extreme. As the speed of light is approached, stars will appear to move to the front and huddle together in a small patch directly in the line of flight. The rest of the sky is black.

Doppler Shift applies to light as well as sound. The changing pitch of a moving siren as it passes the listener is an example of this effect. On board a starship, Doppler Shift will blue-shift light from approaching stars (looking forward) and red-shift light from receding stars (looking astern). So suns ahead of the vessel in the line of flight will become bluer in color; those behind will become redder.

At 37%c, a starship leaving Sol would no longer be able to see it. Sol’s light, severely red-shifted, would have moved into the infrared and would be invisible to human eyes. If the destination is Alpha Centauri that star would also be invisible, having been blue-shifted up into the ultraviolet range.

As velocity increases still more, a growing zone of darkness appears directly sternward. It grows larger as the ship picks up speed. A similar patch of starless blackness develops toward the bow. At 50%c, the cone of invisibility distends an angle of 30° forward and more than 60° astern. The only stars that are still visible are crammed into a "barrel" surrounding the starcraft. The forward rim of the Star Barrel is seemingly dominated by brilliant blue-white stars. Sweeping the eye upwards and rearward, the hue of star light changes from blue to green to yellow to orange to red, then to blackness. All the familiar constellations are compressed and distorted beyond recognition.

Mounting speed forces the Barrel slightly backwards, then forward again, compacting still narrower with even more vivid coloration. The Barrel has now become what Eugene Sänger once called the Starbow. At 99%c the Starbow, now an annular rainbow-hued ribbon of color leading the spacecraft, is 12° wide with its forward edge raised up 23° from the line of flight. The rest of the sky it jet black. Precise navigation by external fixes has become utterly impossible, and the starship pilot must rely on a system of dead reckoning or inertial guidance.

Communications between starship and home planet become problemmatical as the vessel moves off at relativistic speeds. Not only will there be a growing time delay due to rapidly increasing distance, but the frequency of the signals received will be altered. If the communication system uses laser transmitters tuned, say, to monochromatic green light at exactly 5000 Angstroms, then the changes in frequency at the receiver are as shown in Table 17.5. A receding starship sees the green light as infrared for speeds above 50%c, and at excessive suboptic velocities as microwaves. Conversely, an approaching vessel sees ultraviolet signals above 50%c and x-rays above 99.9%c.

Table 17.5 Wavelength of 5000 Angstrom Laser Light Communication Signals
Received by a Relativistic Starship

Starship Velocity (psol)	Redshifted Signal Starship Receding (Angstroms)	Blueshifted Signal Starship Approaching (Angstroms)
0%c	5000 (green)	5000 (green)
10%c	5500 (green)	4500 (blue)
50%c	8500 (Near Infared)	2900 (Ultraviolet B)
90%c	22,000 (Near Infared)	1150 (Ultraviolet C)
99%c	70,500 (Mid Infrared)	355 (Extreme Ultraviolet)
99.9%c	223,500 (Mid Infrared)	110.0 (Extreme Ultraviolet)
99.99%c	707,000 (Far Infrared)	35.5 (Soft X-ray)
99.999%c	2,235,000 (Far Infrared)	11.0 (Soft X-ray)
99.9999%c	7,070,000 (Far Infrared)	3.55 (Soft X-ray)
99.99999%c	22,350,000 (Microwave)	1.10 (Hard X-ray)

Even the stars off to one side are showing relativistic color shifts. It’s almost like a rainbow, one of those full-circle rainbows that you see on the clouds beneath you from an airplane sometimes. Only this circle is all around us. Nearest the black hole in front the stars have frequency-shifted to a dull reddish color. They go through orange and yellow and a sort of leaf green to the band nearest the back hole in black, which are bright blue shading to purple…But the starbow itself is beautiful. It’s worth the trip.

(ed note: actually he got the order of the colors mistakenly reversed, but he fixed it in later editions)

• 

• 

Seven or eight years ago (starting at 1980) I read an article in the British Interplanetary Society's magazine, Spaceflight. Before I had even finished it I sat up in bed, crying, “Eureka!” It was a great article. It talked about how the stars would look from an interstellar spaceship in nearly relativistic flight, say, traveling upwards of 60,000 miles a second. The colors of the stars would shift. Stars ahead would change color toward the blue end of the spectrum, stars behind toward the red. And after the color shifts had gone as far as they could go in the visible bands of the rainbow, the stars would go off the end and could be seen no more.

So what you would have, at about a third of the speed of light, would be a ring of stars visible out of your window. They would vary in color from blue to red fore and aft, and would leave only expanding areas of blackness both where you were going and where you had come from. You could call it a “starbow.”

It made a pretty picture. The Eureka syndrome occurred as I was thinking about that, and wondering absentmindedly if I could ever use it in a story—and then realized that two or three other ideas that I had had wandering around homeless in my mind for some time, looking for a story to come to rest in, would fit nicely into just such a story. Edward de Bono’s conjecture that too many resources hinder problem-solving rather than helping. Gödel's discovery that any written message (even the Encyclopedia Britannica) can be expressed as a single, if very large, number—just by assigning the position of each letter in the message to an ascending series of prime numbers, and expressing which number it was by an exponent from 1 to 26.

You've wondered where we sf writers get our ideas? Well, that's the usual place where I get mine. It isn't a single event. It's a sort of catalysis. An intriguing idea comes along—a bit of scientific lore, or a situation, or a character—and matches up with some other half-baked notions already floating around in my head. And when they collide, they attain critical mass. I then perceive that, put together, they make an interesting situation that can be carried out to, hopefully, interesting conclusions. That's enough. Then I start typing.

I started typing “The Gold at the Starbow's End" almost as soon as I put Spaceflight down. When I was finished with it, I liked it. It didn't win any awards, but it got nominated for most of them. I still do like it, only—

Only it begins to look as though there isn't any starbow.

The other day I opened my mail and saw to my pleasure that there was a letter from my good friend (every sf writer's good friend, because he shares and explains science with us so amiably), Robert L. Forward (this entire website is my poor attempt at being every SF writer's good friend). It contained a preprint from the American Journal of Physics. The paper is called “In search of the 'starbow': The appearance of the starfield from a relativistic spaceship.” (behind a paywall)

John M. McKinley and Paul Doherty, two meddling physicists from Oakland University in Michigan—not content to cure cancer or develop a cheap and harmless substitute for gasoline or do any of the other things scientists should do—read my story. They checked out the literature, rethought the question, programmed it all into a computer—and killed off the starbow forever. Or, anyway, until someone else finds a way of saving it. The original authors had, it seems, neglected some fine-detail effects, such as the fact that the stars start out with a variety of colors instead of one. When they instructed the computer to take that into account, it began to print out dull splotches of points in monochrome: "there is no starbow,” they conclude. True, they then go on to say, "we regret its demise. We have nothing so poetic to offer as its replacement, only better physics"—but what's the good of that?

Well, that doesn’t destroy the story, really. The starbow was only an image, a sort of metaphor, a poetic and colorful touch. But I do miss it.

Especially since, of all the stories I ever wrote, "The Gold at the Starbow’s End" has had the most questions raised about its content of factual science.

It is also high among the stories of mine whose science has been based most firmly on actual, if relatively unfamiliar, scientific reports. I don't think that's a coincidence.

• 

When Leonora Christine attained a substantial fraction of light speed, its optical effects became clear to the unaided sight. Her velocity and that of the rays from a star added vectorially; the result was aberration. Except for whatever lay dead aft or ahead, the apparent position changed. Constellations grew lopsided, grew grotesque, and melted, as their members crawled across the dark. More and more, the stars thinned out behind the ship and crowded before her. Doppler effect operated simultaneously. Because she was fleeing the light waves that overtook her from astern, to her their length was increased and their frequency lowered. In like manner, the waves into which her bow plunged were shortened and quickened. Thus, the suns aft looked ever redder, those forward bluer.

On the bridge stood a compensating viewscope: the single one aboard, elaborate as it was. A computer figured out continuously how the sky would appear if you were motionless at this point in space, and projected a simulacrum of it. The device was not for amusement or comfort; it was a valuable navigational aid. Clearly, though, the computer needed data on where the ship really was and how fast she was traveling with respect to objects in heaven. This was no simple thing to find out. Velocity — exact speed, exact direction — varied with variations in the interstellar medium and with the necessarily imperfect feedback to the Bussard controls, as well as with time under acceleration. The shifts from her calulated path were comparatively petty; but over astronomical distances, any imprecisions could add up to a fatal sum. They must be eliminated as they occurred.

Hence that neat, stocky, dark-bearded man, Navigation Officer Auguste Boudreau, was among the few who had a full-time job en route that was concerned with operating the ship. It did not quite require him to revolve in a logical circle — find your position and velocity so you can correct for optical phenomena so you can check your position and velocity. Distant galaxies were his primary beacons; statistical analysis of observations made on closer individual stars gave him further data; he used the mathematics of successive approximations.

This made him a collaborator of Captain Telander, who computed and ordered the needful course changes, and of Chief Engineer Fedoroff, who put them into execution. The task was smoothly handled. No one sensed the adjustments, except as an occasional minute temporary increase in the liminal throbbing of the ship, a similarly small and transitory change in the acceleration vector, which felt as if the decks had tilted a few degrees.

      The idea of collecting hydrogen is similar to the Bussard ramjet, which uses large electromagnetic fields to gather particles from kilometers around. While the design detailed in this work requires a similar number of particles to be collected, it is much more practical than the Bussard ramjet because it does not depend on proton-proton fusion (which has an extremely small cross-section), nor the collection of deuterium (which is tens of thousands of times less abundant than normal hydrogen).

     The catch is that getting the collected hydrogen into the breeding blanket would require it to be accelerated to the speed of the spacecraft. During the spacecraft's acceleration, any savings that were gained by not bringing the fuel would be entirely canceled by drag against the particles that must be gathered.

     However, during deceleration it could be doubly helpful — the drag would further decelerate the spacecraft, while the collected hydrogen could be used to breed deuterium.

The magsail was invented by Dana Andrews and I working in collaboration. What happened was this; Dana had an idea for a magnetic ramscoop that would gather interplanetary hydrogen and then feed it to a nuclear electric ion drive, thus avoiding the necessity of the p-p fusion reaction in the classic Bussard scoop. The problem was, according to Dana's rough back of the envelope calculations, he was getting more drag than thrust. Dana asked me to help him on it, hoping that a more expect calculation would give a more favorable result. I wrote a code and modeled the system as a Monte-Carlo problem, and discovered that Dana was wrong: he was not getting more drag than thrust, he was getting MUCH MUCH more drag than thrust. At that point I made the suggestion to Dana that we abandon the ion thruster and just use the collection device as a sail. He agreed. Based on the Monte Carlo results, we calculated total system drag and wrote a IAF paper in Oct. 1988 showing the value of the magsail as an interstellar drag device. Then, in early 1989 I derived a closed form analytic solution to the magsail drag problem, and also a set of equations governing magsail motion in the gravitational field of the Sun, and published this together with some mission analysis by Dana as a AIAA paper in July 1989 (republished in referred form in Journal of Spacecraft and Rockets, March-April 1991).

Up to this point (Dr. Robert) Forward had not been involved. However, after the presentation of the 1989 paper Forward suggested to me that I take a look at how the magsail would operate inside the Earth's magnetosphere — i.e. how it would interact with the Earth's magnetic poles — could this be used for orbit raising. I derived all the equations for this and published it as an AIAA paper AIAA-91-3352 in 1991, and republished it in JBIS later (in 1992, I think) Someone then sent me a letter pointing out that in 1963, Joe Engleberger had patented a concept for using a magnetic device to pump against the Earth's magnetic poles to raise orbits. I got hold of Engleberger's patent and sure enough, he had addressed that aspect of magsail capability. However Engleberger's equations in his patent are incorrect (get hold of his patent #3,504,868 — you can see that he's wrong by inspection) and of course, no one in 1963 had any viable technology to offer to allow such a propulsion system to be built — that was not made possible until 1987 when Chu introduced high T superconductivity. For these reasons, an USAF review of advanced propulsion systems done in 1972 rejected Engleberger's work. Interestingly, the attempt made in that USAF review (Meade et-al AFRPL-TR-72-31) to correct Engleberger's equations also resulted in a incorrect solution, although the error in the USAF derivation is harder to spot.

Around 1992, Dana did some further work on the Magsail together with Steve Love, and they showed that a magsail could be used to brake a spacecraft returning from the moon in the Earth's magnetosphere, i.e. a low stress alternative to aerobraking. Also in 1992, G.Vulpetti, of Italy, published some analysis of trajectory capabilities of spacecraft that combined magsails with light sails.Vulpetti's work was explicitly based upon the prior work by Dana and I, and referenced as such.

To my knowledge, which is based upon a pretty thorough literature search at this point, these are the only quantitative work done on magsails to date. People did know by the 1970's of course, that ramscoops would create some drag that would interfere with a Bussard scoop's performance, but no one had quantified this and thus the possibility of using a magnetic field as a propulsive sail was not seriously discussed .Occasionally I run into people who tell me that they "thought of" the magsail years ago, but they never published their "idea." I believe that without quantification and publication such intuitions, assuming they actually occurred, do not constitute invention. Invention requires real work, and real publication, and a real fight to prove the validly of an idea- not just idle musing within the confines of ones own daydreams.

For these reasons, I believe that the claim of Dana Andrews and I to be the co-inventors of the magsail are fully justified. Until someone can present a prior publication for a magsail, including a competent calculation of its performance, all claims to the contrary have to be regarded as nebulous.

8.15 The Bussard Ramjet. This is a concept introduced by Robert Bussard in 1960. It was employed in one of science fiction's classic tales of deep space and time, Poul Anderson's Tau Zero (Anderson, 1970).

In the Bussard ramjet, a "scoop" in front of the spaceship funnels interstellar matter into a long hollow cylinder that comprises a fusion reactor. The material collected by the scoop undergoes nuclear fusion, and the reaction products are emitted at high temperature and velocity from the end of the cylinder opposite to the scoop, to propel the spacecraft. The higher the ship's speed, the greater the rate of supply of fuel, and thus the greater the ship's acceleration. It is a wonderfully attractive idea, since it allows us to use reaction mass without carrying it with us. There is interstellar matter everywhere, even in the "emptiest" reaches of open space.

Now let us look at the "engineering details."

First, it will be necessary to fuse the fuel on the fly, rather than forcing it to accelerate until its speed matches the speed of the ship. Otherwise, the drag of the collected fuel will slow the ship's progress. Such a continuous fusion process calls for a very unusual reactor, long enough and operating at pressures and temperatures high enough to permit fusion while the collected interstellar matter is streaming through the chamber.

Second, interstellar matter is about two-thirds hydrogen, one-third helium, and negligible proportions of other elements. The fusion of helium is a complex process that calls for three helium nuclei to interact and form a carbon nucleus. Thus the principal fusion reaction of the Bussard ramjet will be proton-proton fusion. Such fusion is hindered by the charge of each proton, which repels them away from each other. Thus pressures and temperatures in the fusion chamber must be extremely high to overcome that mutual repulsion.

Third, there is only about one atom of interstellar matter in every cubic meter of space. Thus, the scoop will have to be many thousands of kilometers across if hydrogen is to be supplied in enough quantity to keep a fusion reaction going. It is impractical to construct a material scoop of such a size, so we will be looking at some form of magnetic fields.

Unfortunately, the hydrogen of interstellar space is mainly neutral hydrogen, i.e., a proton with an electron moving around it. Since we need a charged material in order to be able to collect it electromagnetically, some method must first be found to ionize the hydrogen. This can be done using lasers, beaming radiation at a carefully selected wavelength ahead of the ramjet. It is not clear that a laser can be built that requires less energy than is provided by the fusion process. It is also not clear that materials exist strong enough to permit construction of a magnetic scoop with the necessary field strengths.

The Bussard ramjet is a beautiful concept. Use it in stories by all means. However, I am skeptical that a working model will be built any time within the next couple of centuries, or perhaps ever.

Much as I hate to admit it, the Venture Star is arguably the most scientifically accurate spacecraft in the history of Hollywood. It is a beautiful piece of work, with all the major problems solved. And it has heat radiators!

Lighthuggers were spacecraft that traveled at just below the speed of light, taking months or years to accelerate to their cruising speed. Although capable of extremely powerful bursts of acceleration (At least 10 g without any inertial suppression), when in transit between stellar systems lighthuggers typically sustained an acceleration of 1 g which would enable them to reach 99% of the speed of light in about 1 earth year.

Generally 3–4 km long, they used Conjoiner drives for propulsion, and were also coated with a thick caul of ice that protected against minor impacts at relativistic velocities and acted as armour against the attacks of other ships. The great size of the lighthuggers enabled them to carry vast numbers of passengers and huge amounts of cargo.

Lighthuggers also possessed a limited repair and redesign capability. They were capable of moving rooms or machinery around within their hulls, or stripping material from one point to repair another. At least some were also equipped with "manufactories", which could build a considerable range of devices, given the relevant specifications.

Their small, point-defense weapons -- ostensibly defensive in nature -- were capable of blasting a 200 kilometre crater in a planet and disrupting weather formations in a fashion similar to a large geological event, such as an asteroid impact or volcanic eruption.

Most lighthuggers were owned or ruled by their crew of Ultranauts, who, because of their long stretches in reefersleep and constant hopping from one star system to another, were mostly divorced from baseline humanity. They were characterized by extreme modifications, often in the form of replacement or mechanical limbs or even holes right through them.

By the time of the Human-Inhibitor War, there existed a fleet of lighthuggers that had been upgraded or built from scratch by the human elements fighting the Inhibitors. These ships were far more advanced than the average lighthugger, and were equipped with dark drives that emitted nothing in any detectable spectrum, miniaturized cryo-arithmetic engines which cooled their hulls to make it nearly indistinguishable — in thermal terms — from empty space, inertia suppression machinery that allowed extremely fast acceleration and deceleration, free-force bubbles which absorbed enemy attacks, camouflage screens that aided concealment, and extremely heavy armaments, including bladder-mines and hypometric weaponry.

Notes

• At the end of Redemption Ark the vast carrying capacity of lighthuggers is demonstrated by Ana Khouri and Triumvir Ilia Volyova as they load approximately 160,000 of the almost 200,000 on the world Resurgam onto the Nostalgia for Infinity.
• The full extent of a lighthugger's manufacturing capabilities is unknown, as they are only ever used in the novels to produce weapons. However, it is implied in Absolution Gap that the shadows' mass-synthesizer technology operated on the same basic principle, and there was little it could not build (up-to and including near-immortal robotic bodies).
• Despite Skade mentioning to Clavain in Redemption Ark that Conjoiners sold their drives primarily to the Demarchists and never directly to the Ultras, Sajaki of the Nostalgia for Infinity claims to Dan that if he blackballed him among the Ultra community he would be stranded in the Epsilon Eridani system indefinitely -- a statement Dan doesn't dispute, despite Dan being an influential man among the Demarchists. This implies that sometime before 2460 Demarchist society either sold or re-purposed their lighthuggers en masse.

(ed note: obviously this is total technobabble)

Conjoiner drives were starship engines built by the Conjoiners that used quantum mechanics to propel starships up to relativistic speeds, giving such ships the name "lighthuggers". Conjoiner drives contained a small wormhole linked to the very deep past, through which they draw their propulsion energies from the Quark-gluon plasma created by the Big Bang. The drives had six manual control dials that allowed the power of the engines to be varied. Lighthuggers mounted a pair of Conjoiner drives, both of which were controlled by a disembodied Conjoiner brain that performed rapid calculations to control the internal drive reactions. It should be noted that the Conjoiners did not actually invent the drive themselves, but received the instructions for it via the Exordium Project.

As the drive power was increased, so did the risk of an uncontrolled, ship-destroying explosion. If the turbulence within the drive exceeded the ability of the brain to compensate for, the drive would explode. It would also explode if the gap between the two drives of any one ship grew too large; this occurred because the Conjoiner brain was housed within one of the engines and controlled the other remotely, and thus once the remotely controlled drive passed out of the brain's control, the internal reactions would quickly spiral out of control. The drive was also designed to explode if non-Conjoiners attempted to open it for reverse engineering purposes.

Demarchists were the primary buyers of Conjoiner Drives for centuries, with Ultras buying them second- or third-hand as the Conjoiners would not sell to them directly.

The emission of tau-neutrinos by the drives was eventually found to attract the Inhibitors, and, subsequent to a 100-year suspension of their production, successful experiments resulted in the "quiet" Conjoiner Drive.

(ed note: obviously this is total technobabble)

A cryo-arithmetic engine is a type of quantum computer employed by the Conjoiners. When certain algorithms are executed on processors of this architecture, it leads to a local violation of the Second law of thermodynamics -- the computer gets colder instead of hotter.

Such engines were utilized in Conjoiner asteroid factories as heat sinks, where their calculations drained away the excess heat produced. Cryo-arithmetic engines were also used by certain Conjoiner lighthuggers; they cooled the exterior of the ship to the temperature of space, making the vessels difficult to detect.

The technology was later successfully miniaturized with aid from Aura, Ana Khouri's daughter. The resulting device was the size of an apple.

• 

Seen from one of the shuttles that brought her crew to her, Leonora Christine resembled a dagger pointed at the stars.

Her hull was a conoid, tapering toward the bow. Its burnished smoothness seemed ornamented rather than broken by the exterior fittings. These were locks and hatches; sensors for instruments; housings for the two boats that would make the planetfalls for which she herself was not designed; and the web of the Bussard drive, now folded flat. The base of the conoid was quite broad, since it contained the reaction mass among other things; but the length was too great for this to be particularly noticeable.

At the top of the dagger blade, a structure fanned out which you might have imagined to be the guard of a basket hilt. Its rim supported eight skeletal cylinders pointing aft. These were the thrust tubes, that accelerated the reaction mass backward when the ship moved at merely interplanetary speeds. The "basket" enclosed their controls and power plant."

Beyond this, darker in hue, extended the haft of the dagger, ending finally in an intricate pommel. The latter was the Bussard engine; the rest was shielding against its radiation when it should be activated.

Thus Leonora Christine, seventh, and youngest of her class. Her outward simplicity was required by the nature of her mission and was as deceptive as a human skin; inside, she was very nearly as complex and subtle. The time since the basic idea of her was first conceived, in the middle twentieth century, had included perhaps a million man-years of thought and work directed toward achieving the reality; and some of those men had possessed intellects equal to any that had ever existed. Though practical experience and essential tools had already been gotten when construction was begun upon her, and though technological civilization had reached its fantastic flowering (and finally, for a while, was not burdened by war or the threat of war) —nevertheless, her cost was by no means negligible, had indeed provoked widespread complaint. All this, to send fifty people to one practically next-door star?

Right. That's the size of the universe...

• 

..." — zero!" The ion drive came to life. No man could have gone behind its thick shielding to watch it and survived. Nor could he listen to it, or feel any vibration of its power. It was too efficient for that. In the so-called engine room, which was actually an electronic nerve center, men did hear the faint throb of pumps feeding reaction mass from the tanks. They hardly noticed, being intent on the meters, displays, readouts, and code signals which monitored the system. Boris Fedoroff's hand was never distant from the primary cutoff switch. Between him and Captain Telander in the command bridge flowed a mutter of observations. It was not necessary to Leonora Christine. Far less sophisticated craft than she could operate themselves. And she was in fact doing so. Her intermeshing built-in robots worked with more speed and precision — more flexibility, even, within the limits of their programming — than mortal flesh could hope for. But to stand by was a necessity for the men themselves...

...Reaction mass entered the fire chamber. Thermonuclear generators energized the furious electric arcs that stripped those atoms down to ions; the magnetic fields that separated positive and negative particles; the forces that focused them into beams; the pulses that lashed them to ever higher velocities as they sped down the rings of the thrust tubes, until they emerged scarcely less fast than light itself. Their blast was invisible. No energy was wasted on flames. Instead, everything that the laws of physics permitted was spent on driving Leonora Christine outward...

(ed note: the ion drive is used to boost the ship up to the minimum velocity required for the Bussard ramjet to operate)

• 

...Practical problems arose. Where was the mass-energy to do this coming from? Even in a Newtonian universe, the thought of a rocket, carrying that much fuel along from the start, would be ludicrous. Still more so was it in the true, Einsteinian cosmos, where the mass of ship and payload increased with speed, climbing toward infinity as that speed approached light's.

But fuel and reaction mass were there in space! It was pervaded with hydrogen. Granted, the concentration was not great by terrestrial standards: about one atom per cubic centimeter in the galactic vicinity of Sol. Nevertheless, this made thirty billion atoms per second, striking every square centimeter of the ship's cross section, when she approximated light velocity. (The figure was comparable at earlier stages of her voyage, since the interstellar medium was denser close to a star.) The energies were appalling. Megaroentgens of hard radiation would be released by impact; and less than a thousand r within an hour are fatal. No material shielding would help. Even supposing it impossibly thick to start with, it would soon be eroded away.

However, in the days of Leonora Christine non-material means were available: magnetohydrodynamic fields, whose pulses reached forth across millions of kilometers to seize atoms by their dipoles — no need for ionization — and control their streaming. These fields did not serve passively, as mere armor. They deflected dust, yes, and all gases except the dominant hydrogen. But this latter was forced aft — in long curves that avoided the hull by a safe margin — until it entered a vortex of compressing, kindling electromagnetism centered on the Bussard engine.

(ed note: seizing atoms by their dipoles is handwavium. Or maybe not.)

• 

The ship was not small. Yet she was the barest glint of metal in that vast web of forces which surrounded her. She herself no longer generated them. She had initiated the process when she attained minimum ramjet speed; but it became too huge, too swift, until it could only be created and sustained by itself. The primary thermonuclear reactors (a separate system would be used to decelerate), the venturi tubes, the entire complex which thrust her was not contained inboard. Most of it was not material at all, but a resultant of cosmic-scale vectors. The ship's control devices, under computer direction, were not remotely analogous to autopilots. They were like catalysts which, judiciously used, could affect the course of those monstrous reactions, could build them up, in time slow them down and snuff them out — but not fast.

Starlike burned the hydrogen fusion, aft of the Bussard module that focused the electromagnetism which contained it. A titanic gas-laser effect aimed photons themselves in a beam whose reaction pushed the ship forward — and which would have vaporized any solid body it struck. The process was not 100 per cent efficient. But most of the stray energy went to ionize the hydrogen which escaped nuclear combustion. These protons and electrons, together with the fusion products, were also hurled backward by the force fields, a gale of plasma adding its own increment of momentum.

The process was not steady. Rather, it shared the instability of living metabolism and danced always on the same edge of disaster. Unpredictable variations occurred in the matter content of space. The extent, intensity, and configuration of the force fields must be adjusted accordingly — a problem in? million factors which only a computer could solve fast enough. Incoming data and outgoing signals traveled at light speed: finite speed, requiring a whole three and a third seconds to cross a million kilometers. Response could be fatally slow. This danger would increase as Leonora Christine got so close to ultimate velocity that time rates began measurably changing.

• 

---

(ed note: I mentioned above that seizing atoms by their dipoles is handwavium. TallestSkil regretfully informs me that I am mistaken:)

TallestSkil: I was reading your Slower Than Light page and came upon the excerpt from Tau Zero in which the ship is stated to use a photon drive whose Bussard ramjet directs interstellar hydrogen through dipole manipulation. You added a footnote saying that dipole manipulation is handwavium, which you elsewhere define as a violation of the laws of physics — distinct from unobtainium (physically possible but either impossible now or unreasonably difficult).

Anyway, I looked into this a bit and found an experiment in 2006 wherein individual atoms (under lab conditions, sure) WERE manipulated by their dipoles. It’s aptly titled Dipole Trapping & Manipulation of Ultra-Cold Atoms.

So hey, one less for the handwavium pile, yeah? One day we might well use dipole ramscoops. Or maybe it’s impossible to do it to hydrogen, but not rubidium. I don’t know myself.

Like the Marie Celeste, the Leonora Christine is a storied vessel, at least among science fiction readers. In his 1967 story “To Outlive Eternity,” expanded into the novel Tau Zero in 1970, Poul Anderson described the starship Leonora Christine’s stunning journey as, unable to shut down its runaway engines, it moved ever closer to the speed of light. Just how a real Leonora Christine might cope with the stresses of a ramjet’s flight into the interstellar deep is the subject of Al Jackson’s latest, which draws on memories not only of Robert Bussard, who invented the interstellar ramscoop concept, but a young scientist named John Ford Fishback.

— Paul Glister

---

• 

by A. A. Jackson

Project Pluto – a program to develop nuclear-powered ramjet engines – must have been on Robert Bussard’s mind one morning at breakfast at Los Alamos. Bussard was a project scientist-engineer on the nuclear thermal rocket program Rover — Bussard and his coauthor DeLauer have the two definitive monographs on nuclear propulsion [1,2]. He said many times that the idea of the hydrogen scooping fusion ramjet came to him that morning. This was sometime in 1958 or 1959 and the SLAM (Supersonic Low Altitude Missile) would have been well known to him. SLAM was an nuclear ramjet, a fearsome thing, sometimes called the Flying Crowbar. Finding a solution to the mass ratio problem for interstellar flight was also something on Bussard’s mind. Thus was born the Interstellar Ramjet, published in 1960 [3].

Most here at Centauri Dreams know that the interstellar ramjet scoops hydrogen from the interstellar medium and uses this as both a fuel and energy source by way of fusion reactor. The sun does proton fusion using gravity as the agent of confinement and compressional heating. However, doing fusion in a ‘non-gravitational’ magnetic fusion reactor makes the process very difficult [3,4]. That is, the proton and Deuterium burning is quite severe to realize on a ‘small scale’. Dan Whitmire attacked this problem by proposing the use of a carbon catalyst using the CNO cycle [4]. The CNO cycle is about 9 orders of magnitude faster than proton-proton fusion. It would still require temperatures and number densities way beyond any technology known at this time.

• 

Bussard noted a number of problems such as losses from bremsstrahlung and synchrotron radiation. He also noted scooping with a material scoop would create a problem with erosion, hinting that magnetic fields might be used, and noting that drag would have to be accounted for.

About 8 years after Bussard’s paper, an undergraduate at MIT, John Ford Fishback, took up the problems Bussard had mentioned. He wrote this up for his Bachelor’s thesis under the supervision of Philip Morrison. The thesis was published in Astronautica Acta [5] in 1969.

Fishback did three remarkable things in his only journal paper: finding an expression for the ‘scoop’ magnetic field, computing the stress on the magnetic scoop sources, and working out the equations of motion of the ramjet with radiation losses. These calculations were done using a special relativistic formulation.

Fishback’s most important finding is noticing that when capturing ionized hydrogen to funnel into the fusion reactor, there is a large momentum flow of the interstellar medium which must be balanced by the scooping and confining magnetic fields. Using very general arguments, Fishback showed that sources (magnetic coils and their support) of the magnetic field determine an upper limit on how fast a ramjet can travel. The convenient measure of starship speed is the Lorentz factor

where v is the starship velocity and c the speed of light. It comes from the physical properties of the field sources, in particular the shear stress.

At the time, Fishback modeled the upper limit using diamond, because of its shear stress properties, and found that one could only accelerate until the Lorentz factor reaches about 2000 [5,6]. Tony Martin expanded on Fishback’s study [6, 7] in 1971, correcting some numbers and elaborating on Fishback’s modeling. Since that time, Graphene has been discovered and it has a shear stress that allows a limiting Lorentz factor of about 6000. This in turn implies a range of over 6000 light years when under 1 g acceleration. It does not mean the final range is 6000 light years, but one must travel at a reduced acceleration and then constant speed, which means a longer ship proper time.

This is bad news for the Leonora Christine of Poul Anderson’s Tau Zero [8].The range can probably be pushed to 10,000 light years, but accelerating at 1 g for 50 years would bust the Lenora Christine’s coils! That is, unless some magic material is found to take the stress loading at a Lorentz factor 10¹⁹, there is no way to circumnavigate the universe. And with the new accelerating universe, the story of Tau Zero becomes still more complicated.

What became of John Ford Fishback? I went to a lecture in California at Stanford in 1979 by Phillip Morrison. After the lecture I asked Morrison what had happened to Fishback. Morrison sadly told me that Fishback had gone to the University of California at Berkeley to work on his doctorate, but had committed suicide.

1. Bussard, R. W.; DeLauer, R.D. (1958). Nuclear Rocket Propulsion. McGraw-Hill.

2. Bussard, R.W.; DeLauer, R. D. (1965). Fundamentals of Nuclear Flight. McGraw-Hill.

3. Bussard, R.W., “Galactic Matter and Interstellar Flight”, Acta Astronatica, VI, pp. 179-195, 1960.

4. Whitmire, Daniel P. , “Relativistic Spaceflight and the Catalytic Nuclear Ramjet”, Acta Astronautica, 2 (5-6): 497–509, 1975.

5. Fishback, J. F., “Relativistic interstellar spaceflight,” Astronautica Acta, 15 25–35, 1969.

6. Anthony R. Martin; “Structural limitations on interstellar spaceflight,” Astronautica Acta, 16, 353-357 , 1971.

7. Anthony R. Martin, “Magnetic intake limitations on interstellar ramjets,” Astronautica Acta, 18, 1-10 , 1973

8. Anderson, Poul (2006), Tau Zero, Gollancz. ISBN 1407239139.

Table 1. Cut-Offs and Range for Ramjet accelerating at 1g. Interstellar medium 1/cm^-3 using the p-p fusion reaction.

Structural Material	σ/ρ dyn cm-2/gcm-3 1010	γβc Proton	Range LY
Aluminum	0.062	8.6	12.6
Stainless Steel	0.261	36.2	7.5
Silica	3.31	73.6	120
Copper	4.36	605	1000
Diamond	15.2	2110	3550
Graphene	600.0	6628.0	6418.0

Addendum: While he was working on this article and corresponding with me, Al shared the story with Greg Benford, who had further thoughts on John Ford Fishback, as below:

• 

Good article. I can add a touch: I was interested in this, after Edward Teller pointed out to me Fishback’s 1969 paper in Astronaut. Acta. I discussed it with Teller and did some calculations (just exploratory, never published). The idea seemed extreme but enlivened my discussions of the paper with Poul Anderson, who lived in Orinda near my Walnut Creek home and whom I saw often.

Someone told me Fishback was at Berkeley and I called him, agreed to meet. I had a one-day-per-week agreement with the Livermore Lab, where I was just turning from being a postdoc for Teller into a staff physicist — I spent Wednesdays at the Lab in Berkeley. So I met him at an Indian restaurant–a rail-thin smoker, nervous, ascerbic. “I wanted to show that we could reach the stars, really do it, with the right engineering,” he said, approximately. His anxiety was clear, but not its cause.

I found him an odd duck but was shocked when a bit later I heard he had killed himself.

When I mentioned it to Poul, he found it contrasting that a man who wanted the stars would cut off his own personal hopes. We often discussed Tau Zero, Poul once remarking that he wished he had taken more time to polish and expand the novel, since it already looked as though it might be the most remembered of his works–and indeed, seems so. He said he had written it in a few months and needed the money–its 1967 serialization in Galaxy helped, but it was tough going as a full-time pro writer then. Plus he had a word limit on the hardcover.

Poul used his Nordic background in the novel, as he liked to do. From Wikipedia:

“Incidental to the main themes is the political situation on the Earth from which the protagonists set out: a future where the nations of the world entrusted Sweden with overseeing disarmament and found themselves living under the rule of the Swedish Empire. This sub-theme reflects the great interest which Anderson, an American of Danish origin, took in Scandinavian history and culture. In later parts of the book, characters compare their desperate situation to that of semi-mythical characters of Scandinavian legend, with the relevant poetry occasionally quoted.”

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(ed note: our heroes have traveled two light-years in a Bussard Ramjet starship called the Anna Lovinda. They have traveled to the Nemesis system. They were accompanied by an uncrewed robot-controlled cargo Bussard Ramjet named the Gertrud, carrying a load of space probes. The two ramjet starships have been linked by a long cable and spun for artificial gravity. Rudbeck is using a auxiliary boat named the Valkyrie to go retrieve a space probe named Osa.)

      As she drew away from the two large spacecraft, they became clear to her sight, starlit as heaven was. Gertrud (St. Gertrud, medieval patroness of wayfarers), the mother vessel of the un-manned pioneers, was a great metal mass from which instrument booms and transceiver dishes jutted. At the stem were simply linac thrusters, akin to those that drove Valkyrie; never being intended for retum, only for getting around in the neighborhood of Nemesis, the robot ship had discarded her Bussard system upon arrival.

(ed note: linac thrusters are apparently linear particle accelerators that have been engineered into electrostatic ion drives)

     From her bow extended two kilometers of cable, a bare glimmer in Rudbeck’s sight, no hint of the incredible tensile strength in precisely aligned atoms. The opposite end of the line anchored Anna Lovinda. That hull was lean, resembling the blade of a dagger whose basket-formed guard was the set of her own linacs. The haft beyond was mostly shielding against the Bussard engine, whose central systems formed a pommel at the top (when a knife is held point downward). The force-focusing lattice of that drive, extended while the vessel burned her way across deep space, had been folded back for safety, a cobweb around the knife. (very similar to the Leonora Christine)

     The linked vessels, bearer of probes and bearer of humans, tumed majestically about each other. Their spin provided interior weight without unduly inconveniencing auxiliarly craft; one rotation took nearly three hours. At her slight present acceleration, Rudbeck felt ghost-light (I'm not sure about this. With a spin radius of 1,000 meters {2 kilometer diameter}, and a rotation rate of 0.0055 rotations per minute {1 rotation per three hours}, my slide rule says the artificial gravity is a microscopic 0.00003 g).

     That soon ended. “Prepare for standard boost," came out of a speaker. The power-plant hummed, a low sound which bore no hint of the energies that burst from sundered nuclei (a nuclear fission reactor as power plant, using fission fuel), turned reaction mass into plasma, and hurled it down the linac until the jet emerged not very much less rapid than light. A full Earth gravity drew Rudbeck down into her chair. The boat could easily have exceeded that, but she herself needed to reach her goal unwearied and alert.

     In its present track, (the space probe) Osa had velocity of some 180 kilometers per second. That fluctuated, especially when rounding the equatorial bulge, and Valkyrie must match it exactly. Given timing and related factors, this meant rendezvous over the north pole, with Valkyrie’s path osculating Osa’s. The former would be a long ellipse, but come sufficiently close to the latter near that point that Rudbeck should have time to make the capture. Immediately thereafter she must use her jets, first to equalize velocities—at such speeds, a tiny percentage differential could rend hulls or start an irretrievable plunge—and then to begin escaping. The delta vee demanded was approximately seventy-five kilometers per second, and the deeper in the gravity well that thrust started, the less reaction mass need be expended.

     That was definitely a consideration. Given its exhaust velocity, a linac drive did not drain (reaction) mass tanks very fast, but it did draw upon them, and the expedition had no facilities for refining more material. This wasn’t a Bussard-drive situation, with a ship taking in interstellar hydrogen for fuel and boosterstuff (propellant) after she had reached minimum speed—no limit on how closely she could approach c, how far she could range. The auxiliary boats were meant merely to flit around among planets. When their tanks were dry, Anna Lovinda must go home. Economy could add an extra year or better to the nominal five she was to spend exploring—could add unbounded extra knowledge and glory.

     Rudbeck smiled and relaxed. She had about an hour of straight-line acceleration before the next change of vector. After that, maneuvers would become increasingly more varied, until in about four hours she was at Nemesis. There the equipment would cease carrying her as a passenger. She would be using it. Everything that happened would be in her hands.

...For propulsion purposes, microfusion bursts triggered by antihydrogen-hydrogen annihilation (possibly with a component of lithium added) will prove efficient up to ship-cruising speeds approaching twelve percent the speed of light, owing to jets of relatively slow, massive particles. Above twelve percent lightspeed, propulsion shifts from antimatter-triggered fusion jets to straightforward matter-antimatter annihilation, which produces a lower mass thrust than fusion, but provides particles with the high-exhaust velocities necessary to push the ship to a high fraction of lightspeed.

How much antimatter might be needed for a trip to Alpha Centauri — assuming that Asimov Arrays or something very much like them will eventually provide humanity with the excess energy required for its large-scale production? We have estimated that the fuel stores (both antimatter and matter combined) might be equal to roughly half the mass of the rest of the spacecraft, or about one hundred tons (to assure "burning" of all available antimatter, an as-yet-undetermined excess of matter will be required).

On Valkyrie, the lower mass of material you were quoting was for up to 10%c - much lower than the mass for giants like Daedalus, and other such nonsense. The mass of propellant is kept low because up to about 10% c you can go with the lower exhaust velocities of antiproton-triggered fusion. (As an aside, during a bowling game with Engineer Ed Bishop and my kids, last winter, I suddenly got a warning alarm screaming up from my subconscious - in 3-D with the berilium windows failing terribly. That's all I could think of as I bowled [I'm usually lousey at the game], and I have still not adequately solved the problem - - but for the only time in my life, and with my mind not at all in the game, I hit series of perfect strikes after series of perfect strikes.

In any case, the antiproton triggered fusion system, scaled down to Valkyrie Mark II, is wonderfully practical for getting around the solar system at a mere 750 km/sec. (this velocity would eventually be practical for Project Spaceguard: the kinetic force of merely ten Toyota masses impacting a comet or asteroid at this velocity (diameter 1/4 mile) would completely "dust" the object.

In answer to original question, for a true, Valkyrie Mark III (requiring direct proton-antiproton annihilation after 15%c), interstellar crewed mission, the propellant mass would of course exceed the ship mass. After 92%c, the excess becomes too extreme - which is a main reason that, although we could deal with particle collisions (dust) at 95%c (halving apparent travel time at this cruise velocity), that 92% becomes close to being a pretty solid speed limit. The time dialation effect gain is simply not worth the mass-energy cost.

Others have been more pessimistic, including an earlier study by space scientists Donald Goldsmith and Tobias Owen which yielded an estimate that a journey to Alpha Centauri would require four hundred million tons of matter-antimatter fuel. Such estimates arise from assumptions that the spacecraft will be huge, with powerful engines mounted in the rear. Everything forwards of the engines becomes, in essence, a massive, rocketlike tower, requiring enormous amounts of shielding from the rocket's gamma ray shine, supplemented by complex (and massive) cooling systems to shed intercepted engine heat (and a traditional rocket configuration must absorb most of the head-depositing gamma rays, even if they do, like X rays, have a tendency to pass through things). The addition of each layer of shielding and cooling equipment placed on top of the engine becomes increasingly prohibitive as ship mass increases, requiring higher burn rates, which in turn requires more cooling and shielding, which increases ship mass and burn rates, and so on.

With our elongated, two-crew-member ship on a string, gamma shine and heat are spilled directly into the unfillable sink of outer space. A pulling rather than a pushing engine eliminates most of the structural girders that would not only, by their mere existence, add unwarranted mass, but would multiply that mass many times over by their need for shields and coolers. Valkyrie, in effect, is a fuel-efficient, twenty-first-century version of today's "ultralight" aircraft...

...Since antimatter and matter annihilate each other on contact, releasing enormous bursts of energy from literally microscopic amounts of propellant, you cannot simply fill a shuttle tank with liquid antihydrogen and let it slosh around inside.

The only storage method that has a hope of working is solid antihydrogen, supercooled within one degree of absolute zero (within one Kelvin of -273 degrees C). At this temperature, antihydrogen condenses into "white flake," with an extremely low evaporation rate.

Particles of solid antihydrogen will be suspended and held away from the "pod" walls, probably by electrostatic forces and/or magnetism. According to our latest models, near 0.0005° K, antihydrogen should be sufficiently stable as to allow, in the form of matter-antimatter micropellets or wafers (we are presently working to determine which design, layered pellets or wafers, will provide optimal thrust). With one-fifty thousandth of a degree Kelvin, matter-antimatter storage becomes thinkable because wave functions do not overlap enough to produce an appreciable reaction, at least in principle.

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(And in practice?)

We do not know. It has not been practiced yet, and can only be verified by experimentation. Personally, carrying matter-antimatter pellets already assembled, even at 0.0005° K, gives me nightmares. I keep seeing a cosmic ray particle stopping at the matter-antimatter interface, giving off its heat, and triggering a horrible chain reaction... Jim says we can prevent that, but I am still opting for storing our antihydrogen in complete isolation from matter until virtually the moment it is needed. I am reminded of that scene from the movie version of 2010, in which Roy Scheider describes the aerobraking maneuver his ship is about to make through Jupiter's atmosphere. "It's dynamite on paper," he says. "Of course, the people who came up with the numbers on paper aren't here."...

...Upon warming, electrons and positrons self-annihilate to produce small bursts of gamma rays which, in terms of thrust, can be totally ignored. The positrons are there simply for stability's sake. The proton-antiproton pair, however, produce three varieties of elementary particles called pi-mesons...

...The charged pions and muons are the particles we want and when not being used below twelve percent lightspeed to immediately trigger fusion explosions (a matter of simply modifying the type of pellet or flake used), we want to simply bounce the pions off the outermost fringes of the engine's magnetic field, and thus steal whatever thrust they have to contribute, before a significant fraction of them have traveled twenty-one meters and shed part of their energy as useless neutrinos. The engine we have designed ejects pions and muons (and, at lower velocities, pion- and muon-triggered fusion products) along a diverging magnetic field nozzle to produce thrust, in much the same fashion as hot, expanding gases in a conventional rocket impact against the solid wall or pusher plate at the back of the ship, propelling the entire assembly forwards. Since the pions and muons are acting only against a magnetic field, they can propel the Valkyrie without ablating or wearing down the engine walls (as does space shuttle propellant, with the result that the engines must be rebuilt after every flight, and eventually thrown away). However, gamma rays emitted by the decay of neutral pions will knock atoms out of position in structures near the antimatter reaction zones, making the material stronger, yet brittle. One solution is to add structures called shadow shields wherever practical. (Shadow shields are nifty little devices already being used in certain very advanced nuclear reactors. They are a major component of Valkyrie, so stay with me and I will get around to describing them in just a few moments.) Another, supplemental solution is to weave most structures residing within four kilometers of the reaction zone from hundreds of filaments, and to send electric currents through the filaments, heating them, one at a time, to several hundred degrees below their melting point. Gamma ray displacements in the wires are thus rearranged, and the atoms can reestablish their normal positions. (ed. note: this is called "In-Site Annealing")

There appears to be nothing we can do to prevent the occasional transmutation of atoms into other elements. Fly far enough with your engines burning at full throttle, and your ship will turn slowly into gold, plus lithium arsenic, chlorine, and a lot of other elements that were not aboard when you left. These new substances will be concentrated around the antimatter reaction zone, and it is important to note that advanced composite materials already coming into existence dictate that our Valkyrie, even at this early design stage, will be built mostly from organic and ceramic materials, rather than from metals. It is conceivable that expanding knowledge of composites can be taken into account by the time relativistic flight becomes a reality, so that the ship actually incorporates the transmuted elements into its filaments in a manner that ultimately results in structural improvements for a ship designed to essentially rebuild itself as it flies. Exploiting what at first glance seems to be a disadvantage (transmutation) is simply a matter of anticipating the "disadvantage" before you begin to build. It's the disadvantages unforeseen or unaddressed that will get you in the end.

The gamma ray flare from the engine dictates other major features of ship design. In particular, it has caused us to turn rocketry literally inside out.

Riding an antimatter rocket is like riding a giant death-ray bomb. An unshielded man standing a hundred kilometers away from the engine will receive a lethal dose of gamma radiation within microseconds. In designing spacecraft, even when considering propellant as efficient as antimatter, RULE NUMBER ONE is to keep the mass of the ship as low as possible. Even an added gram means extra fuel.

Here's how we can shave off many tons of shielding.

Put the engine up front and carry the crew compartment ten kilometers behind the engine, on the end of a tether. Let the engine pull the ship along, much like a motorboat pulling a water skier, and let the distance between the gamma ray source and the crew compartment, as the rays stream out in every direction, provide part of the gamma ray protection - with almost no weight penalty at all. (ed. note: this should remind you of "Helios") We can easily direct the pion/muon thrust around the tether and its supporting structures, and we can strap a tiny block of (let's say) tungsten to the tether, about one hundred meters behind the engine. Gamma rays are attenuated by a factor of ten for every two centimeters of tungsten they pass through. Therefore, a block of tungsten twenty centimeters deep will reduce the gamma dose to anything behind it by a factor of ten to the tenth power (10¹⁰). An important shielding advantage provided by a ten-kilometer-long tether is that, by locating the tungsten shield one hundred times closer to the engine than the crew, the diameter of the shield need be only one-hundredth the diameter of the gamma ray shadow you want to cast over and around the crew compartment. The weight of the shielding system then becomes trivial.

(ed note: This is the Waterskiing school of spacecraft design)

The tether system requires that the elements of the ship must be designed to climb "up" and "down" the lines, somewhat like elevators on tracks.

We can even locate the hydrogen between the tungsten shadow shield and the antihydrogen, to provide even more shielding for both the crew and the antihydrogen.

There is an irony involved in this configuration. Our "inside-out" rocket, the most highly evolved rocket yet conceived, is nothing new. We have simply come full circle and rediscovered Robert Goddard's original rocket configuration: with engines ahead of the fuel tanks and the fuel tanks ahead of the payload. Nor is the engine itself an entirely new creation. It guides and focuses jets of subatomic particles the same way the tool of choice among most microbiologists guides streams of electrons through magnetic lenses. Valkyrie, in essence, is little more than a glorified electron microscope.

In addition to shielding against gamma shine and avoiding the absorption of engine heat, another major design consideration is shielding against interstellar dust grains. Flying through space at significant fractions of lightspeed is like looking through the barrel of a super particle collider. Even an isolated proton has a sting, and grains of sand begin to look like torpedoes. Judging from what is presently known about the nature of interstellar space, such torpedoes will certainly be encountered, perhaps as frequently as once a day. Add to this the fact that as energy from the matter-antimatter reaction zone (particularly gamma radiation) shines through the tungsten shields and other ship components, the heat it deposits must be ejected.

Jim Powell and I have a system that can perform both services (particle shielding and heat shedding), at least during the acceleration and coast phases of flight. We can dump intercepted engine heat into a fluid (chiefly organic material with metallic inclusions) and throw streams of hot droplets out ahead of the ship. The droplets radiate their heat load into space before the ship accelerates into and recaptures them in magnetic funnels for eventual reuse. These same heat-shedding droplets can ionize most of the atoms they encounter by stripping off their electrons. The rocket itself then shuts the resulting shower of charged particles - protons and electrons - off to either side of its magnetic field, much the same as when a boat's prow pushes aside water.

The power generated by occasional dust grains should range from the equivalent of rifle shots to (rarely) small bombs. These detonate in the shield, harmlessly, far ahead of the ship. Fortunately, almost all of the interstellar particles likely to be encountered are fewer than 20 microns across (10,000 microns = 1 centimeter), and we should expect no more than one impact per day per square meter of Valkyrie's flight path profile...

...One of the great advantages of a droplet shield is that it is constantly renewing itself. Put a dent in it, and the cavity is immediately filled by outrushing spray.

If a dust grain passes into the shield, many of the shield's droplets are bound to be exploded. Some of the scattered droplet fluid will be absorbed and recovered by surrounding droplets, but some fluid is bound to be hurled out of the droplet stream, which means that we must add the weight of droplets to be replaced to the ship's initial mass.

In addition to spare droplet fluid, our preliminary design calls for a spare engine. Both engines will be located at opposite ends of the tether. The forward engine pulls the ship along during the acceleration phase of flight. It also fires during the cruise phase, but only at one-hundredth thousandth of a gravity, keeping the tether taut and permitting recapture of forward flying droplets. At the end of the cruise phase, the rear engine kicks in for deceleration (as we cannot simply swing a ten-kilometer-long ship broadside to relativistic bombardment in order to turn the engine around and fire in reverse).

In normal use, the rear engine is turned on only to decelerate the ship, or to maneuver the crew compartment into the center of the forward engine's gamma ray shadow. Nudging the crew compartment, from behind, to one side or the other will be necessary during major course changes, because the crew compartment, much like a water skier, cannot turn simultaneously with the motor that pulls it and might otherwise drift out of the protective shadow. A spare engine also provides some insurance against the chilling possibility of irreparable damage to the leading engine or, worse, a break in the tether. In the former case, identical engine parts could be ferried up and down the tether and exchanged as necessary. In the latter, depending upon where the break occurs, with careful rearrangement of the ship's components along the tether, the remaining coil can be safely used to finish the outbound leg of the mission.

At the end of the cruise phase, with nearly half of the ship's fuel exhausted, empty fuel tanks can be ground up into ultrafine dust, for dumping overboard (we see no reason to expend extra energy decelerating tons of equipment, no longer in use, which can easily be remanufactured and replaced at the destination solar system). At up to ninety-two percent the speed of light, the dust will fly ahead of the decelerating ship, exploding interstellar particles and clearing a temporary path (trajectories must be such that the relativistic dust will fly out of the galaxy without passing near stars and detonating in the atmospheres of planets). This fist of relativistic dust is the first line of defense against particles encountered during final approach. With the rear engine firing into the direction of flight, droplet shields will be come useful only for expelling heat from the rear engine, for along the tether, "up" has now become "down," and droplets can only be sprayed "up" behind the engine, where, traveling at uniform speed, they will fall back upon the decelerating ship. To shield against particles ahead of the ship, ultrathin "umbrellas" made of organic polymers similar to Mylar and stacked thousands of layers deep are lowered into the direction of flight. This is the second line of defense - against particles moving into the ever-lengthening space between the ship and the fist. The umbrellas will behave much like the droplet shield and, in like fashion, they will be designed with rapid self-repair in mind. Throughout the ship, repair and restructuring will be assisted (where such repair abilities as self-annealing filaments are not already built into ship components) by small, mouselike robots capable of climbing up and down tethers and rigging.