Introduction

So you give someone an inch and they want a yard. Given them a rocket ship and suddenly they want a star ship. SF writers want to use exotic settings on alien planets, but the real estate in our solar system mostly looks like a bunch of rocks. "That's OK," the writer thinks, "There are a million-jillion other solar systems in the galaxy, surely they are not all a bunch of rocks (I know they are there, I've got a map). I know that those spoil-sports at NASA have ruined our solar system for SF writers since their nosy space probes failed to find dinosaur-infested jungles of Venus and scantily-clad Martian princesses. But they haven't sent probes to other stars yet! Why not turn my rocket ship into a star ship?"

Unfortunately it isn't that easy. The basic problem is that interstellar distances are freaking huge.

The introduction begins like this: "Space," it says, "is big. Really big. You just won't believe how vastly hugely mindboggingly big it is. I mean you may think it's a long way down the road to the chemist, but that's just peanuts to space. Listen ..." and so on.

From The Hitchhiker's Guide to the Galaxy by Douglas Adams (1979)

Consider: a single light-year is an inconceivable abyss. Denumerable but inconceivable. At an ordinary speed — say, a reasonable pace for a car in a megalopolitan traffic, two kilometers per minute — you would consume almost nine million years in crossing it. And in Sol's neighborhood, the stars averaged some nine light-years apart. Beta Virginis was thirty-two distant.

From Tau Zero by Poul Anderson (1970)

Let's make a mental model. Say the scale is such that one astronomical unit is equal to one millimeter (1/25th inch). There is a glowing dot for the Sun, and one millimeter away is a microscopic speck representing the Earth. The edge of the solar system is about at Pluto's orbit, which varies from 30 mm to 50 mm from the Sun (about 1 and 3/16 inch to almost 2 inches). Imagine this ten-centimeter model floating above your palm.

This would put Proxima Centauri, the closest star to the Sun, at about 272 meters away. That's 892 feet, the length of about two and a half football fields or four and a half New York city blocks! Glance at the ten-centimeter solar system in your hand, then contemplate the nearest solar system four and a half city blocks away.

And the center of the galaxy would be about 1600 kilometers away (about 990 miles), which is a bit more than the distance from Chicago, Illinois to Houston, Texas.

"All right, all right!" the SF author grumbles, "So the distance is outrageous. What of it?"

This of it. How long do you think it is going to take to travel such distances? As an example, the Voyager 1 space probe is currently the fastest human made object with a rest mass, zipping along at a blazing 17.46 km/s. This means that in the space of an eyeblink the little speed demon travels a whopping eleven miles! That's smokin'. What if it was aimed at Proxima Centauri (it isn't), how long would it take to reach it?

About 74,000 years! Which means that if Neanderthal men had launched something as fast as Voyager 1 to Proxima, it would just barely be arriving right now. And the joke's on them. Neanderthals are extinct so not even their descendants would reap the benefit of any scientific broadcasts from the Proxima probe. A similar argument could be used against any interstellar probes we could launch.

This leaves us with two alternatives: deal with the fact that average human lifespan is 74 years, not 74,000; or make the starship go faster.

Well, three, if you count "faster than light", but that will be covered later.

As Gordon Woodcock put it, the three methods of travelling to other stars are "go slow", "go fast", and "go tricky." This means "deal with short human lifespan", "use relativistic speeds", and "go faster than light".

Go Slow

The first of Gordon Woodcock's methods of interstellar travel is "go slow".

Distance between stars is huge, traveling said distance slower-than-light will take a huge amount of time, human beings have a very limited lifespan. And it is much easier to travel at 10% the speed of light than it is to travel at 99.99999% the speed of light

"Go Slow" means to focus on the limited human lifespan problem, and be content to travel slowly ato 10% c or so.

Lifespan

There are several ways of dealing with the lifespan issue. Go to the Tough Guide to SF and read the entry "Slowboat".

Generation Ship

In the "Generation ship" concept, the starship is huge (typically a hollowed-out asteroid) and contains an entire community. As the ship crawls to its destination, generations of people are born, have children, and die of old age. Problems include the later generations refusing to cooperate with their forefather's vision, civil wars that wreck the ship, failure of the closed ecological life support system, and the later generations forgetting where they came from, forgetting where they are going, and forgetting the fact that they are on a starship. An interesting incremental approach is the Cross-generation ship.

In Larry Niven and Jerry Pournelle's FOOTFALL, the aliens deal with the "forgetful generation" problem by including a group of original crew frozen in suspended animation. Members of the original crew are periodically woken so they can ensure that the generational crew keeps the faith.

Seed Ship

A variation is the "Seed ship" concept. The starship is tiny, containing a payload of millions of frozen fertilized eggs, artificial wombs, robots, and a master computer. After traveling for thousands of years, the ship lands in a good spot for a colony. The master computer thaws out enough eggs for the available wombs, brings the babies to term, then tries to convince the babies that the robots are mommy and daddy. I don't know about you but I suspect that the first generation is going to grow up a little bit emotionally stunted.

Examples include The Song of Distant Earth by Sir. Arthur C. Clarke, and "Longshot" by Vernor Vinge.

Digital Crew

Still more extreme is the "digital crew" concept. Since every atom of mass is a penalty, the logical ship would just carry a master computer and no frozen fertilzed eggs and associated equipment. However, nobody wants wants to read about the adventures of a computer (yes, I know there have been some SF stories on this theme, but it requires extraordinary skill on the part of the author). Authors such as Sean Williams, Shane Dix, and Greg Egan have gotten around this by postulating technology capable of "uploading" human brain patterns into a computer. In essence, the ship's computer is running incredibly advanced simulations of the crew, creating a virtual reality much like that found in the movie The Matrix. This also allows the author to pontificate upon the nature of reality, ask if we are actually unaware virtual people in a virtual reality, and stuff like that. Sean Williams and Shane Dix handwave the end run around Burnside's Zeroth Law by stating that artificial intelligence proved to be an unexpectedly difficult challenge.

One could add equipmment capable of manufacturing artificial bodies for the crew from local materials. However, the advantage of a digital crew ship over a seed ship is the lower ship mass due to the absence of frozen embryos, artificial wombs, and robot mommies. Adding artifical body manufacturing facilites would reduce or remove the advantage. The only remaining advantage is that the new bodies inhabited by adults instead of babies.

Sleeper Ship

In the "Sleeper ship" concept, the crew is frozen into suspended animation, so they do not age nor require food and oxygen during the thousand year journey. Poul Anderson warned that frozen crew have a limited shelf life. Naturally-occurring radioactive atoms in the human body will cause damage. Normally the body will repair such damage, but one in suspended animation cannot. After a few hundred years, enough damage will accumulate so that a corpse instead of a living person is thawed out at journey's end. This may force one to thaw each crew member every fifty years or so to allow them to heal the damage, then freezing them again.

Alter Metabolism

A variation of this was in Charles Sheffield's Between The Strokes Of Night. A technique was discovered that would allow human metabolism to enter the "S-state." In this state, humans age at a rate 1/1000th normal, and perceive things at the same rate. So with ships traveling at a slow 10% light speed, the trip to Proxima Centauri seems to take only a few weeks to an S-state person. But normal humans move so fast that S-state humans cannot see them, and normal humans will still perceive the trip taking about forty years.

Increase Lifespan

Finally there is the "Methuselah" concept. Advances in medical technology might increase human lifespan to thousands of years. So prolonged interstellar trips are more a problem of boredom instead of life-span.

Mechanical Reliability

A related issue is mechanical reliability. Currently the best space probe NASA can build cannot be guaranteed to properly function past about forty years. The starship will need an extensive self-repair capability or have some way of having humans periodically available to fix things.

And a common science fiction gag is the "jumping the gun" plot. A slower than light ship departs on a 500 year journey to Alpha Centauri. About 100 years after launch, some joker on Terra invents a faster-than-light starship. Fleets of FTL ships fly to Alpha Centauri and colonize the place. The slower than light ship arrives to find not the virgin planets they were expecting, but instead 400 year old colonies. Har, har.

Go Fast

The second of Gordon Woodcock's methods of interstellar travel is "go fast".

Distance between stars is huge, traveling said distance slower-than-light will take a huge amount of time, human beings have a very limited lifespan. And it is much easier to travel at 10% the speed of light than it is to travel at 99.99999% the speed of light

"Go Fast" means to focus on traveling near the speed of light so that relativity will partially fix things. Time dialiation will allow the crew to experience only a few months passing while traveling to a star 50 light years away. Travleing back home to Terra will add a few more months to the crew's experience. Unfortunately they will discover that 50+50 = 100 years have passed n Terra during their round trip. But you can't have everything.

Naturally to the SF author, the more attractive option is to increase the speed of the starship. But this too has several serious problems.

First off, the equation for deltaV coupled with the huge velocities required imply some truly ugly mass ratios. We are talking about a crew cabin the size of a coffin strapped to the nose of a rocket ten times the size of the Empire State building. Or worse.

Secondly, that party-pooper Albert Einstein's theory of relativity more or less ruled out faster than light travel. And it inflicted extra difficulties for near-light travel.

And thirdly is the fact that space is not 100% empty. Remember Rick Robinson's First Law of Space Combat. At near light speeds hitting a dust speck will be like a contact explosion from a thermonuclear bomb. Indeed, individual protons will be transformed into deadly cosmic rays.

Relativity

V/cγ
0.00011.0000000
0.0011.0000005
0.011.000050
0.021.000200
0.051.001252
0.11.005038
0.21.020621
0.31.048285
0.41.091089
0.51.154701
0.61.250000
0.71.400280
0.81.666667
0.92.294157
0.922.551552
0.953.202563
0.985.025189
0.997.088812
0.99922.366272
0.999970.712446

Einstein's theory of Special Relativity is an incredibly complicated topic, and I don't pretend to understand it all. Certainly I don't understand it enough to try and teach it. I'd advise you to go study the Wikipedia Special relativity for beginners or Jason Hinson's tutorial. If you want an intuitive feel for this: run, don't walk and get a copy of Poul Anderson's classic novel TAU ZERO.

But there are only a few implications of relativity that we have to worry about. First is of course the well-known fact that Special Relativity forbids any object possessing a rest mass from traveling at the speed of light in a vacuum (Which boils down to no FTL travel for you. Science fiction authors have been cursing Einstein for decades over that one). The second concern is "time dilation", crew members on a starship moving relativistically (i.e., faster than about 14% c) will age and experience time at a slower rate than people who stayed at home on Terra. Thirdly it makes calculating transit times and mass ratios much more difficult.

In relativistic equations, a common factor called gamma (γ) appears often. Its value depends on the velocity of the starship.

γ = 1 / Sqrt[ 1 - (v2 / c2) ]

where

  • γ = gamma, the time dilation factor (dimensionless number)
  • Sqrt[x] = square root of x
  • v = current ship's velocity as measured in Terra's frame of reference (m/s)
  • c = speed of light in a vacuum = 3e8 m/s

Or more conveniently, you can make c = 1.0 and v the percentage of c, e.g., a starship moving at three-quarters light-speed would have v = 0.75. The ship's γ would be about 1.51.

If a starship is moving at 0.99c relative to Terra, it's γ = 7.09. When the crew mark off one day passing inside the ship (the so-called "proper time"), 1 day * 7.09 = 7.09 days will pass on Terra. From the view point of people on Terra, the starship crew will be living and moving in slow motion, experiencing time at about 1/7th the rate on Terra (Due to the weird non-intuitive implications of relativity, from the viewpoint of the crew it will be the inhabitants of Terra who are moving in slow motion, but if you are not going to take the time to learn more about relativity you'd best ignore this).

With respects to a viewer on Terra, the starship's mass will increase by a factor of γ (which makes relativistic kinetic weapons quite deadly). The ship's length in the direction of travel will decreased by a factor of 1/γ, but nobody cares since this has little practical effect.

In the following equations, note that a*T/c = (Ve / c) * ln(R)

Time elapsed (in Terra's frame of reference)

t = (c/a) * Sinh[a*T/c] (given acceleration and proper time)

t = (c/a) * Sinh[(Ve / c) * ln(R)] (to expend all propellant, given exhaust velocity and mass ratio)

t = sqrt[(d/c)2 + (2*d/a)] (given acceleration and distance)

Distanced traveled (in Terra's frame of reference)

d = (c2/a) * (Cosh[a*T/c] - 1) (given acceleration and proper time)

d = (c2/a) * (Cosh[(Ve / c) * ln(R)] - 1) (when all propellant is expended, given exhaust velocity and mass ratio)

d = (c2/a) (Sqrt[1 + (a*t/c)2] - 1) (given acceleration and Terra time)

Final Velocity (in Terra's frame of reference)

v = c * Tanh[a*T/c] (given acceleration and proper time)

Δv = c * Tanh[(Ve / c) * ln(R)] (given exhaust velocity and mass ratio)

v = (a*t) / Sqrt[1 + (a*t/c)2] (given acceleration and Terra time)

Time elapsed (in starship's frame of reference, "Proper time")

T = (c/a) * ArcSinh[a*t/c] (given acceleration and Terra time)

T = (c/a) * ArcCosh[a*d/(c2) + 1] (given acceleration and distance)

Gamma factor

γ = Cosh[a*T/c] (given acceleration and proper time)

γ = Cosh[(Ve / c) * ln(R)] (given exhaust velocity and mass ratio)

γ = Sqrt[1 + (a*t/c)2] (given acceleration and Terra time)

γ = a*d/(c2) + 1 (given acceleration and distance)

where

  • a = acceleration (m/s2) remember that 1 g = 9.81 m/s2
  • T = Proper Time, the slowed down time experienced by the crew of the rocket (s)
  • t = time experienced non-accelerating frame of reference in which they started (e.g., Terra) (s)
  • d = distance covered as measured in Terra's frame of reference (m)
  • v = final speed as measured in Terra's frame of reference (m/s)
  • c = speed of light in a vacuum = 3e8 m/s
  • Δv = rocket's total deltaV (m/s)
  • Ve = propulsion system's exhaust velocity (m/s)
  • R = rocket's mass ratio (dimensionless number)
  • γ = gamma, the time dilation factor (dimensionless number)
  • Sqrt[x] = square root of x
  • ln[x] = natural logarithm of x
  • Sinh[x] = hyperbolic Sine of x
  • Cosh[x] = hyperbolic Cosine of x
  • Tanh[x] = hyperbolic Tangent of x

The hyperbolic trigonometric functions should be present on a scientific calculator and available as functions in a spreadsheet.

In many cases it will be more convenient to have T and t in years, distance in light-years, c = 1 lyr/yr, and 1 g = 1.03 lyr/yr2.

Here are some typical results with a starship accelerating at one gravity.

T Proper time elapsedt Terra time elapsedd Distancev Final velocityγ Gamma
1 year1.19 years0.56 lyrs0.77c1.58
23.752.900.973.99
583.782.70.9999386.2
81,8401,8390.99999981,895
12113,243113,2420.99999999996116,641

Of course, as a general rule starships want to slow down and stop at their destinations, not zip past them at 0.9999 of the speed of light. You need a standard torchship brachistochrone flight plan: accelerate to halfway, skew flip, then decelerate to the destination (which makes sense, since such starships will have to be torchships). To use the above equations, instead of using the full distance for d, divide the distance in half and use that instead. Run that through the equations, then take the resulting T or t and double it.

Example

The good scout starship Peek-A-Boo is doing a 1 g brachistochrone for Vega, which is 27 light-years away. Half of that is 13.5 light-years. How long will the journey be from the crew's standpoint (the proper time)?

T = (c/a) * ArcCosh[a * d / (c2) + 1]
T = (1/1.03) * ArcCosh[1.03 * 13.5 / (12) + 1]
T = 0.971 * ArcCosh[13.9 / 1 + 1]
T = 0.971 * ArcCosh[13.9 + 1]
T = 0.971 * ArcCosh[14.9]
T = 0.971 * 3.39
T = 3.29 years
That's the crew time to the skew flip. The total time is twice this
T = 3.29 * 2
T = 6.58 years

But if you have more mathematical skills than I have, you could easily derive this short cut:

Tt = 1.94 * ArcCosh[dly/1.94 + 1]

where

  • Tt = Proper Time experienced during a brachistochrone flight (years)
  • dly = total distance to destination(light-years)

Remember this equation assumes a constant 1 g acceleration.

Mass Ratio

As you may expect, the mass ratio for such rockets are generally absolutely outrageous. The "Relativistic Rocket" website made some estimates on the best possible mass ratios, assuming a 100% efficient photon rocket using constant acceleration.

Mass Ratio

R = (Mpt / Me) + 1, (1)

Mpt/Me = e(aT/c) - 1, (2)

Substituting (2) into (1):

R = e(a * T / c)

where

  • R = mass ratio (dimensionless number)
  • Mpt = Spacecraft's total propellant mass(kg)
  • Me = Spacecraft's empty (dry) mass (kg)
  • e = base of natural logarithms = 2.71828...(most calculators have an ex key, and spreadsheets have the exp() function)
Example

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 = e4.06
R = 57.97

Brachistochrone

R = e(1.03 * 6.58 / 1.0)
R = e6.78
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.

Why are these mass ratios absolutely outrageous? Because it is probably impossible to make a single-stage spacecraft with a mass ratio over about 20. And because the mass ratios that come out of the equation are the theoretical maximums of a 100% efficient photon drive. Since a real rocket is not going to be 100% efficient, and may not be a photon drive, the mass ratio will probably be much worse than what the equation suggests. It is also important to keep in mind that one g of constant acceleration is pretty huge. If the Peek-A-Boo only does 1/10th g, it will take 30 years of proper time to get to Vega, but it will only need a mass ratio of 21.

Other Relativistic Effects

The crew of a ship moving at relativistic velocities will notice some weird effects. The view of the sky will be distorted both fore and aft by relativistic aberration. Doppler shift will make the stars ahead look more blue, and the stars behind will appear more red. Back in the 1970's it was thought that the two effects would combine to make a sort of a rainbow of stars around the ship's destination. Alas, in 1980 a study published in the Journal of the British Interplanetary Society did the math and proved that it just wasn't going to happen.

Valkyrie Antimatter Starship

Noted polymath Charles Pellegrino and Brookhaven physicist Jim Powell have an innovative antimatter powered starship design called a Valkyrie. They say that current designs are guilty of "putting the cart before the horse", which create ships that are much more massive than they need be. Their "spaceship-on-a-string" starship is capable of accelerating up to ninety-two percent the speed of light and decelerating back down to stationary. At this velocity, relativity mandates that time on board the ship will travel at one-third the rate of the stay at home people on Terra (actually it's closer to 1/2.55). They figure this will be adequate for visiting stars up to about twelve light-years from Terra, without using up excessive amounts of the crew's lifespan.

Dr. Pellegrino served as a scientific consultant on James Cameron's Avatar movie. The interstellar vehicles seen in the film are based on the designs of Pellegrino and Powell's Valkyrie rockets, fused with Robert L. Forward's designs. I figured this out when I noticed that the Avatar starship had the engine in the front, which is a unique feature of the Valkyrie.

...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).

From Flying To Valhalla by Charles Pellegrino (1993)

If I am reading this correctly, this is a mass ratio of 1.5, which I find a little difficult to believe. The equations above seem to say that accelerating up to 92%c and back down to zero will require a mass ratio around 22.

Adam Crowl got in touch with Mr. Pellegrino on this matter. As it turns out, the mass ratio of 1.5 only applies to a Valkyrie capable of approaching ten percent lightspeed.

Mr. Pellegrino's response to Adam Crowl:

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.

Charles Pellegrino

Anyway, back to the main description:

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.

(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.

From Flying To Valhalla by Charles Pellegrino (1993)

Bussard Ramjet

So, there is the obscenely-huge-mass-ratio problem, and the deadly-space-junk problem. SF authors were depressed. Then in 1960, a brilliant physicist named Robert W. Bussard proposed to use these two problems to solve each other.

If your starship is moving fast enough, the widely scattered hydrogen atoms will hit your hull like cosmic rays, and damage both the ship and the crew. One can theoretically use magnetic or electrostatic fields to sweep the hydrogen atoms out of the way so the ship doesn't hit them.

But wait a minute. Hydrogen is propellant, and could also be fusion fuel. Instead of sweeping it away, how about gathering it?

And if you are gathering your propellant instead of carrying it along with you, your mass ratio becomes infinity. This means you could theoretically accelerate forever.

This is the legendary "Bussard Interstellar Ramjet." No mass ratio problems, and no space junk problems. Pretty slick, eh? Accelerating at 1 g a Bussard ramjet could reach the center of the galaxy in a mere twenty years of proper time, and could theoretically circumnavigate the entire visible universe in less than a hundred years.

(Keep in mind that twenty years to the galactic core is in terms of "proper time", that is, the time as experienced by the crew. The people who stay at home on Earth will still see the Bussard ramjet taking the better part of 25,000 years to make the trip.)

Of course there are some other problems.

The density of the vacuum of space is about 10e-21 kg/m3. This means you have to scoop a gargantuan 10e18 cubic meters in order to harvest a single gram of hydrogen. Bussard, working with an estimate of one hydrogen atom per cubic centimeter, and desiring a 1,000-ton spacecraft with an acceleration of 1 g, figured that the scoop mouth will need a frontal collecting area of nearly 10,000 km2. Assuming the scoop mouth is circular, I figure the mouth will have to be about 56 kilometers radius or 112 kilometers diameter. Other estimates have the scoop orders of magnitude larger. It is probably out of the question to build a physical scoop of such size, so it will have to be an immaterial scoop composed of magnetic or electrostatic fields.

Hydrogen ignores magnetic and electrostatic fields unless it is ionized. This means you will need a powerful ultraviolet beam or strong laser to ionize the hydrogen heading for the scoop.

A Bussard ramjet has to be boosted to a certain minimum speed before the scoop can operate. Estimates range from 1% to 6% of c, which is pretty awful.

The Sun has the misfortune to be located near the center of a huge region about 330 to 490 light-years in diameter called "The Local Bubble". The interstellar medium within the Local Bubble has a density of about 0.07 atoms/cm3, which is about ten times lower than in the rest of the galaxy. This makes a thin fuel source for a Bussard ramjet. The Local Bubble is thought to have been caused when the star Geminga went supernova about 300,000 years ago.

And to top it off, trying to use hydrogen in a fusion reactor would require mastery of proton-proton fusion, which is so much more difficult than deuterium fusion that some scientist doubt that we will ever learn how to do it.

But none of these were show-stoppers. There was a Renaissance of science fiction novels written using Bussard ramjets. Arguably the best is the classic Tau Zero by Poul Anderson, which you absolutely must read if you haven't already. Other include Larry Niven's Protector and short stories set in his "Known Space" series, Footfall by Larry Niven and Jerry Pournelle, A Deepness in the Sky by Vernor Vinge, and The Outcasts of Heaven's Belt by Joan Vinge.

Things started to unravel in 1978. T. A. Heppenheimer wrote an article in Journal of the British Interplanetary Society entitled "On the Infeasibility of Interstellar Ramjets." Heppenheimer applies radiative gas dynamics to ramjet design and proves that radiative losses (via bremsstrahlung and other similar synchrotron radiation-type mechanisms) from attempting to compress the ram flow for a fusion burn would exceed the fusion energy generated by nine orders of magnitude, that is, one billion times. The energy losses will probably show up as drag. This was confirmed by Dana Andrews and Robert Zubrin in 1989.

The effect of drag? What it boiled down to was that the ramjet had a maximum speed, where the relative velocity of the incoming hydrogen equaled the drive's exhaust velocity. It has a "terminal velocity", in other words.

A proton-proton fusion drive has an exhaust velocity of 12% c, so a proton-proton fusion Bussard Ramjet would have a maximum speed of 12% c. You may remember that a spacecraft with a mass ratio that equals e (that is, 2.71828...) will have a total deltaV is exactly equal to the exhaust velocity. So if a conventional fusion rocket with a mass ratio of 3 or more has a better deltaV than a Bussard Ramjet, what's the point of using a ramjet?

Magnetic Sail

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.

Robert Zubrin (1994)

Bussard Scramjet

Things look bleak for the Bussard Ramjet, but it isn't quite dead yet. First off, Dr. Andrews and Dr. Zubrin's analysis depends upon certain assumptions. But even if the drag problem is as severe as calculated, there may be ways to avoid it. The drag is caused by bremstrahlung and synchrotron radiation produced by the motion of the charged particles as they spiral through your collector fields and into your fusion chamber. It is theoretically possible to recover energy instead of it being wasted as drag. Then the energy could be added to the fusion energy and used to accelerate the exhaust stream, thus defeating the drag.

It would be a Bussard Scramjet, in other words.

But only theoretically. It is incredibly difficult, as in "we might not manage to do it with five hundred years of research" level of difficult.

  • Subject: Bussard Ramjet woes
  • From: Nyrath the nearly wise
  • Date: Mon, 26 Nov 2001 02:41:46 GMT
  • Newsgroups: rec.arts.sf.science

According to my understanding of the legendary Bussard Ramjet, it has a terminal velocity. This is when the velocity of the incoming hydrogen relative to the scoop is equal to the exhaust velocity.

Assume that the ramjet has enough technomagic to manage real live proton-proton fusion.

The question is: does anybody have a ballpark estimate of what this terminal velocity is likely to be?

Extra credit question: I understand that the terminal velocity constraint can be by-passed if the ramjet can use even more technomagic to somehow gather and fuse the hydrogen without affecting the hydrogen's vector.

  • Is this:
  • [1] not even theoretically possible
  • [2] not impossible, given about ten thousand years of research
  • [3] possible with about 500 years of research

  • Subject: Re: Bussard Ramjet woes
  • From: "Ray Drouillard"
  • Date: Sun, 25 Nov 2001 23:20:26 -0500
  • Newsgroups: rec.arts.sf.science

I came up with about 12% of C. I forgot what I assumed as an efficiency.

The terminal velocity assumption is true IF the incoming hydrogen has to be stopped relative to the ship (IOW, sped up). If it is merely gathered, compressed, then shot out the back, I see no reason for a terminal velocity. of course, the exhaust speed will be very high relative to the ship. It will be 0.12C (or whatever) relative to the original "stationary" interstellar hydrogen. (Note the quotes around "stationary" and don't give me any grief about relativity).

Note 2: The engineering details will be pretty nasty :-)


  • Subject: Re: Bussard Ramjet woes
  • From: "Geoffrey A. Landis"
  • Date: Mon, 26 Nov 2001 11:05:19 -0500
  • Newsgroups: rec.arts.sf.science

This is *vastly* dependent on the assumptions you make.

Can you harvest the energy released by stopping the protons?

The primary energy loss mechanism seems to be bremstrahlung and synchrotron radiation produced by the motion of the charged particles as they spiral through your collector fields and into your fusion chamber.

In the worst case, all of the original energy of the particles (in your frame of reference) is lost; in the best case— well, how big do you want to assume your collector is?

  • Geoffrey A. Landis
  • http://www.sff.net/people/geoffrey.landis

  • Subject: Re: Bussard Ramjet woes
  • From: schillin@xxxxxxxxxxxxx (John Schilling)
  • Date: 26 Nov 2001 11:02:35 -0800
  • Newsgroups: rec.arts.sf.science
  • Organization: University of Southern California, Los Angeles, CA

Nyrath the nearly wise writes:

The question is: does anybody have a ballpark estimate of what this terminal velocity is likely to be?

I get 0.120c using a simple non-relativistic calculation, should be good to within a few percent. With such a limit, it is not worth the trouble of using a ramjet at all. A simple fusion rocket, with the fuel carried in tanks, can do the same job much easier.

Extra credit question: I understand that the terminal velocity constraint can be by-passed if the ramjet can use even more technomagic to somehow gather and fuse the hydrogen without affecting the hydrogen's vector.

Or if you can recover the energy associated with decelerating the incoming fuel, and pump it back into the exhaust stream.

For example, if one can collect the fuel without decelerating it, feeding the relativistic plasma jet through a suitable MHD generator would produce *enormous* ammounts of power. Add this to the power produced by fusing the hydrogen and use the combined total to accelerate the exhaust.

  • Is this:
  • [1] not even theoretically possible
  • [2] not impossible, given about ten thousand years of research
  • [3] possible with about 500 years of research

It is theoretically possible. Anyone who imagines they can predict the results of five hundred, much less ten thousand, years of research, is using a much higher grade of LSD than I have ever heard of. It would require an indeterminate ammount of research and an unknown number of theoretical breakthroughs, which means that it could take anywhere from ten years to forever.

	— 
	*John Schilling                    * "Anything worth doing,         *
	*Member:AIAA,NRA,ACLU,SAS,LP       *  is worth doing for money"     *
	*Chief Scientist & General Partner *    -13th Rule of Acquisition   *
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thread Bussard Ramjet woes on rec.arts.sf.science (2001)

Fictional Ramscoops

Tau Zero

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)

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.

From Tau Zero by Poul Anderson (1970)

Bussard Ramjet Combat

Orion Wargame

This Bussard ramjet is from a science fiction boardgame/wargame called ORION Combat Near the Speed of Light (1987) by Alan Sherwood and David Cohn (Monash Games).

...The large map ... is a 2-dimensional representation of the Great Nebula of Orion... Regions A to D are ionized gas (H-II regions), A being the Strömgren zone, and E and F are dusty molecular clouds...

...The ramships in this game are envisaged as vehicles of about 10,000 tonnes mass, with a magnetic field acting as the ramscoop extending out to about 1000 km radius. The field would be produced by magnetic coils of about 1 km radius. Protons (ionized hydrogen) collected by the field are fed into a nuclear fusion reactor, and the reactions products exhausted out the rear to produce thrust. Turning and braking are done by directing either this exhaust or the incoming stream of protons by magnetic fields (so the ramship can brake and turn without using the reactor). Induced drag results from this redirection of the gas stream. In low density gas, it must be redirected further, causing more drag. When traveling through un-ionized gas, the ramship shines an ultraviolet light ahead to ionize the gas in its path.

Performance is limited by the reactor power (which limits acceleration), structural g limits (limits turning and braking), and the gas density (which reduced all performance in low density regions)...

COMBAT Combat in interstellar space can occur between ramships that come within weapons range, which of course will be very small compared to interstellar distances, or even a single Mapsheet hex (1/6 light-year diameter). Range is envisaged to be limited by Beam weapons to about 100,000 km. Note this means that at closing speeds near to light, the battle may last less than a second, so there is no time for any manoeuvre in battle (although it would have been preceded by years of manoeuvring).

Once an encounter has been arranged, the most important parameter (apart from number of ramships involved) is the relative velocity, which is the closing speed of one ramship relative to the other. Except for its effect on manoeuvrability, the speed of each ramship through the nebula is not relevant; the two ramships are equivalent and neither has any advantage. This reflects the fundamental principle (in fact The Principle of Relativity) that all inertial (i.e., traveling at or approximately at constant velocity) observers are equivalent.

Before the encounter, a ramship would detach its Fighter, and then stand off from the battle while the Fighter pursued the enemy ramship. The Fighter is essentially a small ramscoop carrying only weapons and guidance systems that can manoeuvre much better than a ramship, without the extra weight of the reactor and life support systems. This necessity for a Fighter is a unique feature of interstellar combat. It results from the fact that when observing an enemy ramship from a great distance you are seeing it in the past, due to the finite speed of light. Thus, you do not see any of its evasive manoeuvres until some time later, and the counter-manoeuvres of your ramship will come too late to catch it. To catch an evading enemy, your ramship's manoeuvrability must be greater by the Pursuit Factor, which becomes quite large at even modest relative velocities. It is reasonable to assume that ramships would not differ much in their manoeuvrabilities, so if it was only ramship against ramship, an opponent who didn't want to fight would always escape. Thus, to be an effective fighting vehicle a ramship must carry a Fighter.

(ed. note: this means in at the start of a combat situation, all involved ramships must decide if they send their Fighters to attack enemy ramships or keep their Fighters with them to defend against enemy Fighters.)

The weapons envisaged to be carried by the Fighter are:

  1. Missiles: merely lumps of any matter thrown out in the path of the enemy. The kinetic energy released from an impact at such high speeds makes even nuclear warheads unnecessary. They would be thrown out in a large cloud of sand-sized particles to ensure a hit - this is how each missile can attack all opposing ramships. Missiles naturally do more damage at higher relative velocity due to their greater kinetic energy. The ramship would have frontal armor for protection, and only when missiles have enough energy to penetrate this do they become effective weapons.
  2. Beam weapons: Probably X- or Gamma-ray lasers - the shortest possible wavelength would be used to get the long range.
From ORION Combat Near the Speed of Light

Protector

The Flying Dutchman was a matrix of rock, mostly hollow. Three great hollows held the components of a Pak-style Bussard ramjet ship. Brennan called it Protector. Another had been enlarged to house Roy Truesdale's cargo ship. Other hollows were rooms.


The inside of the teardrop-shaped cargo pod was nothing like that of the alien ship that had come plowing into the solar system two centuries ago. Its cargo was death. It could sprout heavy attitude jets and fight itself. Its long axis was an X-ray laser. A thick tube parallel to the laser would generate a directed magnetic field. "It should foul up the fields in a monopole-based Bussard ramjet. Of course that might not hurt him enough unless your timing was right." When Roy had learned how to use it— and that took time; he knew little about field theory— Brennan started drilling him on when.


A directed magnetic field would churn the interstellar plasma as it was guided into a Bussard ramjet. As a weapon it might be made to guide the plasma flow across the ship itself. The gunner would have to vary his shots, or an enemy pilot could compensate for the weapon's effect. If the local hydrogen density were uneven, that would hurt him. If the plasma were dense enough locally, the enemy could not even turn off his drive without being cremated. Part of the purpose of the ram fields was to shield the ship from the gamma ray particles it was burning for fuel.

"Hit him near a star, if you get the choice," said Brennan. "And don't let him do that to you."

The laser was surer death, if it hit a ship. But an enemy ship would be at least light-seconds away at the start of a battle. It would make a small, elusive target, its image delayed seconds or minutes. The thousand mile wings of a ram field would be easier to hit.

The guided bombs were many and varied. Some were simple fusion bombs. Others would throw bursts of hot plasma through a ram field, or carbon vapor to produce sudden surges in the burn rate, or half a ton of pressurized radon gas in a stasis field. Simple death or complicated. Some were mere decoys, silvered balloons.


Lately he had come to enjoy these simulated battles, but he wasn't enjoying this one. Brennan was throwing everything at him. The Pak scouts had used a three gee drive until they crossed his wake, and then Wham! Six gees and closing. Some of his missiles were going wild; the scouts were doing something to the guidance. The pair dodged his laser with such ease that he'd turned the damn thing off. They'd used lasers on him, firing not only at his ship but at the field constriction behind him where hydrogen atoms met and fused, so that Protector surged unevenly and he had to worry for the generator mountings. They threw bombs at unreasonable velocities, probably through a linear accelerator. He had to dodge in slow random curves. Protector was not what you'd call maneuverable.


He tried some of his weaponry on the lone ship behind him.

Then half his weapons board was red, and he had to guess what had exploded in the trailing pod. Probably that idiot projector: he'd been trying to punch a hole in the lone ship's ram field. He bet his ship he was right, and gambled further that the explosion had wrecked his laser, which might otherwise have been of some use. He fired a flurry of bombs from the side of the cargo pod opposite the explosion. The lead ship of the remaining pair flared and died.

That left two, each the trailing ship of a pair, making less than his own acceleration. He dithered a bit, then ran for it. He continued to dodge missiles and laser beams.


He dropped two half-tons of radon with the drives disconnected.

Radon has a short half-life: it has to be kept in stasis. The generator was outside the bomb shell, and was partly soft iron. The enemy's ram field tore it apart. A minute later the radon was in the constriction, and incredible things were happening: radon fusing to transuranian elements, then fissioning immediately. The constriction exploded. The ram field sparkled like a department store Xmas tree gone manic. The Pak ship flared into a small white point, fading.


Brennan made pictures on the screen: ... He spread a wide cone before the lead ship, converging it almost to a point behind the ship. A needle shape with the ship in its point — the ship's protective shield — brought the incoming hydrogen into a ring shaped constriction.


"You depend too much on those long, slow turns," he said. "The way to dodge Pak weaponry is to vary your thrust. Keep opening and closing the constriction in the ram field. When they throw something like a laser pulse into the constriction, open it. Nothing's going to fuse if you don't squeeze the plasma tight enough."

Roy wasn't flustered. He was getting used to Brennan's habit of resuming a subject that may have been broken off days ago. He said, "That last ship could have done that when I threw radon at him."

"Sure, if he did it fast enough. At good ramscoop velocities the s**t should be in the constriction before he knows it's reached the ram field, especially as you didn't put any rocket thrust on it. That was good thinking, Roy. Memo for you: don't ever follow a ship that's running. There are too many things he can throw into your ram field. Hopefully we'll be doing the running in any battle."


"Then these scouts are tougher than what I fought."

"And there are three of them."

"Three."

"They're coming in a cone, through— you remember that map of the space around Sol? There's a region that's almost all red dwarfs, and they're coming through that. I think the idea is to map an escape route for the fleet, in case something goes wrong at Sol. Otherwise they'll see to it that Sol is clean, then go on to other yellow dwarf stars. At the moment they're all about a light year from Sol and about eight light-months apart."


In the 'scope screen the Pak scouts showed as tiny green lights, a good distance from each other, and measurably closer to Sol. Brennan seemed to know just where to find them, but then he'd been observing them for two months. "Still making three gravities," he said. "They'll be at rest when they reach Sol. I've been right about them so far. Let's see how far I can carry it."

"Isn't it about time you told me what you've got in mind?"

"Right. We're leaving the Flying Dutchman, now. The hell with convincing them I'm coming from Van Maanen's Star. They're seeing us from the wrong angle anyway. I'll take off for Wunderland at one point aught eight gee, hold for a month or so, then boost to two gee and start my turn away from them. If they spot me in that time, they'll turn after me, if I can make them think I'm dangerous enough."

"Why," he started to ask, before he remembered that one point aught eight was the surface gravity of Home.

"I don't want them to think I'm a Pak. Not now. They're more likely to chase an alien capable of building or stealing a Pak ship. And I don't want to use Earth gravity. It'd be a giveaway."

"Okay, but now they'll think you came from Home. Do you want that?"

"I think I do."

Home wasn't getting much choice about entering the war. Roy sighed. Who was? He said, "What if two of them go on to Sol and the other comes after us?"

"That's the beauty of it. They're still eight light-months apart. Each of them has to make his turn eight months before he sees the others make theirs. Turning back could cost them another year and a half. By then they may just decide I'm too dangerous to get away." Brennan looked up from the screen. "You don't share my enthusiasm."

"Brennan, it'll be two bloody years before you even know if they've turned after you. One year for them to spot you, one year before you see them make the turn."

"Not quite two years. Close enough." Brennan's eyes were dark beneath their shelf of bone. "Just how much boredom can you stand?"

From Protector by Larry Niven (1973)

Rec.Arts.SF.Science

This is from a discussion entitled Bussard Ramjet Evasion started at March 1st 2002.

Nyrath

A couple of acquaintances of mine have a disagreement. Perhaps the r.a.s.s. massmind can provide some input. Start off with the (implausible) postulate that Bussard Ramjets are practical.

Given two Bussard ramjets with identical propulsion performance, about one light year of separation, moving at relativistic velocities towards each other. Both ramjets armed to their cute little teeth.

Acquaintance #1 maintains that if one ramjet wished to avoid combat, it is impossible for the other ramjet to force combat. (combat being loosely defined as maneuvering such that the opposing ship is within one's weapons' footprint)

The argument is along the lines of the lightspeed delay in observing the position and vector of the enemy ramship coupled with relativistic velocity and parity in maneuverability will make it always possible for the enemy to dodge out of the way.

Acquaintance #2 argues that as a ship's speed increases, the maximum possible angular change in the ships vector decreases (given the same deltaV). So at relativistic velocities, any ship will have very limited maneuverability. Therefore they cannot avoid being caught.

My gut level feeling is that neither of my acquaintances are right or wrong, but that the answer depends upon the situation, e.g., ship's velocity compaired to ship's deltaV, size of weapon's footprint, etc.

Any thoughts?


JWMeritt

My thought: Sounds like the scenario in Niven's Ethics of Madness short story, though there it was one chasing the other. In your scenario much depends on what is meant by 'weapon footprint'.


Erik Max Francis

I think the answer really comes down to the actual maneuverability, velocities, and weapons ranges of the ships in question.


Mike Williams

I reckon that for relativistic velocities to be practical in your Bussard ramjet, then they should be capable of sustained accelerations of at least 0.1 g. If they can't do that, then it's going to take them over a decade to achieve relativistic speed, which I don't consider very practical.

The first ramjet starts to thrust sideways at a constant 0.1 g in a random direction. The second ship can't possibly observe which way they've gone for more than 6 months, by which time the first ship would have moved sideways by 125,000,000,000 km, and have accumulated a sideways velocity component of 15,800,000 m/s. That's only 0.013 of a light year off the original track, so the angular deflection is only about a degree and a half.

The second ship can't guarantee to come closer than about 5 light days from the first ship, so it's going to need an awfully big weapons footprint in order to engage it.


Hop David

The light year separation is observed from whose frame? What relativistic velocity are they moving towards each other?

Nyrath

I dunno, this exceeds my meager knowledge of relativity.

The key factor seems to be "relative velocity", that is, for each ramjet, the velocity of the enemy ramjet in the frame of reference of the friendly ramjet.

Hop David

By "what relativistic velocity" I meant whaf fraction of c. I believe observers on both ships would see an approach of the same velocity as the other, but a third observer might see something different.

If they are going a very good clip, the spatial distance could also be quite different depending on whose measuring. One observer's lightyear may be another observer's mile.


Serg

As far as I remember from huge Relativistic Kill Vehicles (RKV)/planet killers thread it's more or less consensus that maneuverable relativistic target could not be practically intersepted with single interceptor.

Nyrath

Oh, I agree that if the target is a planet, there is no way it is going to stop a relativistic weapon aimed at it.

However, is that true if the target is capable of the same propulsion performance as the weapon?

And is it true if the target's performance is an order of magnitude better than the weapon?

Serg

{ target propulsion the same } Target evades if it far enough from interceptor and have comparable fuel resource.

{ target propulsion order of magnitude superior} In this case target evades without any doubt.


Isaac Kuo

Actually, I calculated that a dumb brute force approach works really well if you know more or less the direction and time of the attack (i.e. seeing the incredibly bright launch signature of the multi-hour acceleration phase in the attacker's system).

The dumb brute force approach is to throw a planet-sized wall in the vague direction of the attack. This wall is actually a puff of gas generated by everything from particle beams to rocket exhausts—whatever creates gas (which will spread evenly without gaps) and can be directed more or less in the correct direction during the hours warning time.

This really really really thin spread wall looks like a dense disc moving at near-c velocities to the incoming munitions. It vaporizes the munitions instantly upon impact.

To a rough approximation, the amount of gaseous material the defenders need to throw up is about the same mass as the total mass of the incoming munitions. The fact that this mass is spread out over an area the size of a planet is roughly balanced out by the fact that the incoming munitions have the kinetic energy necessary to devastate and entire planet's surface.

Assuming the defenders have anything vaguely like the capabilities of the attackers, they could more plausibly throw up a planetary wall many orders of magnitude more massive than the incoming munitions.

{ However, is that true if the target is capable of the same propulsion performance as the weapon? } Umm...Serg is saying the opposite of what I think you think he's saying. He's saying that our conclusion was that a near-c interceptor probably could not intercept a maneuverable target. In other words, a near-c attacker could not intercept a near-c target (or any other target which was maneuverable).

I think you're going an extra unnecessary step, thinking that this means it's impossible for the defender to shoot down near-c missiles from the attacker. This is true...but it's a moot point since those missiles from the attacker can't hit the defender anyway.

Basically, it's the defender's game either way.

I haven't thought of a way to make near-c weaponry workable. They just give too much "free energy" to the defender to vaporize your munitions with their own incredible kinetic energy. Roughly, you stick to a munition velocity low enough so you can overwhelm defenses with sheer weight of fire.

Brian McGuinness

So instead of a missile you now have a gas with nearly the same momentum and kinetic energy approaching the planet. Why is this an improvement?

Isaac Kuo

Because it isn't nearly the same momentum and energy nor is it approaching the planet, except for a very tiny fraction of it.

When the small mass of the incoming near-c munition hits the much larger mass of the nebulous defense cloud, it explodes more or less evenly in every direction. Actually, when it first hits the closest layers of the defense cloud, it merely expands into a narrow cone. However, this defense cloud is many planet diameters deep—the cone balloons out into a trumpet shape and then to a spherical expanding explosion quickly.

Very little of this explosion will impact the planet, depending upon how far away the defense cloud is from the planet. For example, if this defense cloud is being thrown from near the planet itself with crude chemical rocket exhausts, the cloud would plausibly be around 20+ planet diameters away. About 1% of the explosion would impact the planet. With more sophisticated plasma thrusters, the cloud could be 20 times further away—for 0.003% of the explosion impacting the planet.


Timothy Little

{ When the small mass of the incoming near-c munition hits the much larger mass of the nebulous defense cloud, it explodes more or less evenly in every direction. }

This does not at all square with your previous assertion that "the amount of gaseous material the defenders need to throw up is about the same mass as the total mass of the incoming munitions".

Furthermore, you are forgetting that relativistic collisions should be handled in the center-of-mass frame, which is still very highly relativistic.

Using your generous figures of (say) 2 Gm interception distance, an assumed incoming speed of 0.999c or more (based on the fact that the cloud "looks like a very dense disk"), an attack of 10 RKVs with an assumed mass of say 104 kg each with 0.1 m2 cross-section. I'll assume the defenders have the same energy budget and 100 hours warning, and hence can disperse about 1015 kg of gas and dust into the path with the same energy budget (assuming it doesn't have to be lifted off planet, but is available from some convenient moon).

The cloud is say 20 Mm wide (enough to shield the planet), and 100 Mm deep ("many planet diameters"). The cross-sectional density is thus 3 kg/m2. To model the interaction, it is best to consider the RKV to be a collection of independent nuclei; certainly its chemical binding energy is negligible. With this area density and these energies, the probability of significant interaction between RKV and cloud nuclei is somewhere around 0.03% to 1%, depending upon materials used, say 0.3%. Hence 99.7% of the RKV nuclei are affected only by mere chemical energies, say up to 1 keV per nucleon (to give a gross overestimate).

This imparts an average deflection of up to 400 km/s, so by the time it reaches the planet it misses its target by about 100 km. Hence with even 4 days to prepare, and the same energy availability as the attacker, the defender's 1015 kg cloud is grossly insufficient to prevent the RKV from hitting the planet.

With less time, quadratically more energy would be required to get the cloud into position. Furthermore, it is likely that the defender's available energy is somewhat proportional to how much time they have.

Hence, I conclude that for a 0.999c RKV, the defender needs at least 100 times the attacker's energy budget and/or at least a few weeks warning before they have a reasonable chance of protecting their planet.


Isaac Kuo

{ This does not *at all* square with your previous assertion that "the amount of gaseous material the defenders need to throw up is about the same mass as the total mass of the incoming munitions". }

That's the minimum amount of mass required to obliterate the incoming munitions. In reality, the defenders can afford to put up many orders of magnitude more mass—as I stated in the first posting.

{ Furthermore, you are forgetting that relativistic collisions should be handled in the center-of-mass frame, which is still very highly relativistic. Using your generous figures of (say) 2 Gm interception distance, an assumed incoming speed of 0.999c or more (based on the fact that the cloud "looks like a very dense disk"), }

Very dense disk is a relative term. Something a hundred kilometers deep by 10,000km in diameter is a thin dense disc compared to the same mass in 50,000km deep by 10,000km in diameter.

What launch mechanism do you have in mind with which to acheive 0.999c in an attacking munition across interstellar distances?

More or less, there are only three possibilities:

  1. A honking huge particle accelerator. This one won't work because it's not plausible to focus a particle beam over interplanetary distances, much less interstellar distances.
  2. An antimatter rocket. This can work, but the pathetically low acceleration implies launch acceleration runs on the order of centuries or much longer. This gives the defenders a very very long time to do something about it. Also, the minimum resources required to create this antimatter rocket are daunting, and the inefficiency in antimatter generation is a factor.
  3. Laser sail. This can work, with reasonably high accelerations, but once you get up to near-c velocities things become very problematic. With the sail travelling away from the beam, the beam is just barely able to keep up with the sail. The final hours or weeks of acceleration is provided by the beam generated in the final seconds or minutes of beam generation. What's worse, this beam is severely red-shifted, reducing its effectiveness. The effect is bad enough at 0.95c. I could see it going up to 0.99c, but not really further than that.

Note that whatever acceleration mechanism you use, it MUST accelerate the munitions without vaporizing them. If the munitions accept even the tiniest fraction of waste energy from the acceleration mechanism, it will melt and evaporate and disperse into a multi-AU conical beam by the time it reaches the target system.

Realistically, the only plausible way to deal with this problem is to accelerate the munitions slowly enough that they can radiate away what waste heat they do absorb. For interstellar laser sails, the numbers used seem to limit themselves to 1000m/s2 or lower. Realistically, even 1000m/s2 is highly optimistic for the sail not to instantly rip apart from slightly uneven acceleration.

If you've got a laser powerful enough to go the interstellar distances to accelerate a 0.999c sail, then it probably makes more sense to just use the laser itself as an interstellar weapon. Unlike the sail weapon, the victims will have NO preperation time—no brightly visible lengthy acceleration run is required.

{ I'll assume the defenders have the same energy budget and 100 hours warning, and hence can disperse about 10^15 kg of gas and dust into the path with the same energy budget (assuming it doesn't have to be lifted off planet, but is available from some convenient moon). }

What munition mass do you assume? What velocity of the defending gas cloud do you assume?

When calculating the energy budget, did you consider the inefficiencies in the launch mechanism vs the final warhead energy? Did you consider the budget required for the infrastructure? For example, laser launch requires a truly astronomically sized space laser to be built.

In contrast, the defenders can use existing rockets and their rocket nozzles, probably already in abundance for mundane purposes. At the low exhaust velocities ideal for interplanetary uses, rocket nozzles are pretty energy efficient (much better than 50%). OTOH, energy budget is not the limiting factor. Mass "budget" is.


Timothy Little

{ Very dense disk is a relative term. Something a hundred kilometers deep by 10,000km in diameter is a thin dense disc compared to the same mass in 50,000km deep by 10,000km in diameter. }

It is the latter case that you were proposing for the defending cloud, and I was basing my estimate of the speed on your post. To make the 50Mm deep cloud look like a "disc", you need a gamma of about 20 or so, hence 0.999c.

{ What launch mechanism do you have in mind with which to acheive .999c in an attacking munition across interstellar distances? }

I don't think it is feasible at all. I was simply countering your assertion that if one happened along, then you could easily defend against it, expending much less energy to do so.

{ If you've got a laser powerful enough to go the interstellar distances to accelerate a 0.999c sail, then it probably makes more sense to just use the laser itself as an interstellar weapon. }

I fully agree. I wasn't proposing that RKVs are useful weapons, just that defending against them involves a lot more than just blowing rocket exhaust at them. You need to intercept them with a few tonnes per square metre of something, or else a significant fraction of the nuclei pass straight through without interacting and hit the planet anyway. Note — this is just as true for 0.5c as for 0.999c. At GeV energies and above, nuclei have to get very close before they interact significantly.

{ What munition mass do you assume? What velocity of the defending gas cloud do you assume? }

Both were stated earlier in the post: munition mass 10 Mg (×10 munitions, total 100 Mg), defending gas cloud moving with the minimum speed needed to get it to the interception range in the time available. Neither are especially relevant.

{ When calculating the energy budget, did you consider the inefficiencies in the launch mechanism vs the final warhead energy? }

So long as the efficiency is more than about 1%, it doesn't much matter. I can't think of any that are that poor. For example, even the lightsail approach should be at least 10% efficient, and there is no theoretical reason why it couldn't approach 100%. Light reflecting from even a greatly red-shifted object still delivers its full momentum (and then some). In fact, energy efficiency of lightsails increases with speed.

{ Did you consider the budget required for the infrastructure? For example, laser launch requires a truly astronomically sized space laser to be built. }

So long as the equipment can deliver at least a significant fraction of the energy required for its assembly to projectiles over its working lifetime, I don't care. e.g., if a single 1 MW laser launcher module with associated power production and distribution costs 1 TJ in energy (or equivalent) to assemble, then its assembly cost becomes relatively insignificant in about 2 weeks of operation as far as energy budget goes.


Pervect

Thank you for a fascinating post — I've been trying to think of some intelligent questions to ask.

How do you calculate or estimate the cross-sections for the interactions? Is the columb force law good enough at these energies? If not, what do you do?

I suppose the real trick is to figure out how many ev you have to impart to the nucleus to have it miss the planet, then estimate the cross section for that interaction.

Is the direct nucleon-nucleon interaction really going to be the dominant way that deflection happens? (As opposed to some indirect mechanism, in which generated particles or radiation produce the deflection indirectly, rather than it being produced directly by a nucleon-nucleon interaction).


Timothy Little

{ How do you calculate or estimate the cross-sections for the interactions? Is the columb force law good enough at these energies? If not, what do you do? }

What I personally do is look at experiments and read papers by people closer to the source than I :)

A nucleon travelling at 0.999c has an energy of about 20 GeV. There are plenty of experiments probing this energy region, so you can usually find some relevant data, including collisions with heavy nuclei. Often, such papers determine empirical formulae for cross-section based on various properties, and propose theoretical models to explain them. Even if not demonstrated to be correct, it is usually a fair bet that some professional nuclear physicists have put a fair bit of brainpower into these models and they probably aren't grossly wrong. That suffices for Usenet :)

{ I suppose the real trick is to figure out how many ev you have to impart to the nucleus to have it miss the planet, then estimate the cross section for that interaction. }

That would work in a more general case, yes. I was more interested in the specific case of trying to hit a target region on the planet.

{ Is the direct nucleon-nucleon interaction really going to be the dominant way that deflection happens? (As opposed to some indirect mechanism, in which generated particles or radiation produce the deflection indirectly, rather than it being produced directly by a nucleon-nucleon interaction). }

I think so. Obviously there isn't any data on relativistic interactions between macroscopic objects, so I can't be sure :)

It seems to me that indirect interactions might initially play a part, but by the time the projectile matter has spread to even a few tens of metres across (i.e. to a millionth of the density), any such secondary processes become completely negligible.

My only remaining concern is that maybe the electrons, despite making up less than 0.05% of the overall energy, could interact orders of magnitude more strongly and transfer their momentum to the nucleons via electromagnetic coupling. In relativistic ion experiements they contribute pretty much negligible energy, but Coulomb energies go with the square of the number of separated charges. This might be a case where particle accelerator results can't simply be scaled up. A 10-tonne projectile has a hell of a lot of electrons that might try to separate...

It's an interesting problem, and one that may well affect my answer to Isaac's post. I'm more interested in finding out the correct answer than appearing to be correct, so I may have to post a retraction :)

{ My only remaining concern is that maybe the electrons, despite making up less than 0.05% of the overall energy, could interact orders of magnitude more strongly and transfer their momentum to the nucleons via electromagnetic coupling. }

This appears to be the case.

In my quantification of Isaac's scenario, on average the electrons pick up deflection energies of about 100 keV each just by electromagnetic interactions. Now obviously the electrons can't just nick off and leave the nucleons behind due to electromagnetic forces. So the RKV rapidly (on the order of microseconds) thermalizes into a plasma which is only partly constrained by its own magnetic fields. Using a reference for high energy plasmas that I don't fully understand [:(], it looks like the mean dispersion will be on the order of 400 km/sec for a single-layer impact.

In the the diffuse cloud case, it initially expands more slowly, with the rate increasing as it encounters more total mass. However, as it becomes more diffuse it does interact more weakly (the plasma is still moving at negligibly diminished relativistic speeds). The dispersion rate appears to approach a maximum around 2-3 Mm/s, independent of depth of the defending cloud but merely dependent upon its area density. In this scenario, the RKV plasma cloud impacts upon the planet across a region about 1500 km in diameter (instead of 100 km). The next 9 RKVs will do likewise.

So I conclude that the RKV does still deposit its total energy upon a region of the planet's surface and vaporize surface features down to bedrock, but with this dispersion it may be insufficient to guarantee destruction of a particular hardened target within the region. This may mean that the defender has acheived some benefit from throwing the shield cloud into place.

The energy requirements on both sides are rather staggering however: I've allocated both sides 2×1023 joules each. That's something like a few thousand years of energy at our civilization's current rate of production. Any civilization capable of mustering such energies within weeks or months no doubt has much better ways of using it than either RKVs or rocket exhaust.

Bussard Ramjet Derivatives

The lure of infinite fuel is too big a prize to let go without a fight. The Bussard ramjet concept has gotten a lot of scrutiny, trying to derive a spin-off concept without the crippling flaws but with most of the benefits.

In 1974, Alan Bond proposed the Ram-Augmented Interstellar Rocket (RAIR). RAIR attempts to deal with the drag problem and the difficulty of sustaining a proton-proton fusion reaction.

Basically, a RAIR carries its own fuel, but does not carry its own reaction mass.

Remember that fuel and reaction mass are generally not the same thing (unless you are dealing with a chemical rocket). For instance, in a nuclear thermal rocket, the fuel is the uranium or plutonium rods, and the reaction mass is the hydrogen propellant.

So the RAIR carries fusion fuel, feeding it to a fusion reactor in order to generate energy used to accelerate hydrogen gathered by the scoopfield. Since the RAIR carries its own fuel, it is not required to do proton-proton fusion, it is free to use whatever fusion fuel it wants.

The drag problem does not go away, but it is reduced. In a pure Bussard ramjet, the hydrogen scooped up has to be braked to a stop, creating drag (unless you can manage to make the hydrogen fuse while it is still travelling at whatever percentage of lightspeed the starship is travelling, which is pretty darn close to being impossible). In a RAIR, you do not have to slow the propellant down. You are left with the lesser problem of dealing with the braking effect of bremstrahlung and synchrotron radiation.

A related concept is the "Catalyzed RAIR." You still use a fusion rocket with internal fuel to get up to speed. But instead of heating the gathered hydrogen with the internal fusion reactor, you get it to do a low-grade reaction by itself.

You stick a target made of lithium or boron into the scooped hydrogen stream, as if it were the beam from a particle reactor. This will initiate a low-level lithium-hydrogen fusion reaction which will heat up and accelerate the rest of the stream. Lithium or boron fusion has the advantage of being almost totally without pesky neutron radiation.

Or if you want the ultimate Catalyzed RAIR, you just inject a steady flow of antimatter into the hydrogen stream. That will heat it up without requiring it to be braked to a stop first.

The draw-back to the RAIR is the fact that while the supply of propellant is infinite, the supply of fuel is not.

Go Tricky

The third of Gordon Woodcock's methods of interstellar travel is "go tricky".

This means to cheat and find a way to travel to the stars faster than light.

This is such can of worms that it has an entire page to itself.

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