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.


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

Digital Crew

Since every atom of mass is a penalty, the logical starship would just carry a master computer and no human crew. This avoids the payload mass of the crew, the habitat module, the life support system, food, water, and everything. The starship might be under a meter long, which would make this concept the lowest mass of all the slowboat starships.

However, nobody wants wants to read about the adventures of a computer (yes, I know there have been a couple of SF stories on this theme, but it requires extraordinary skill on the part of the author, and the stories are not wildly popular).

Enter the "digital crew" concept. You postulate 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. Authors who have used this concept include Sean Williams, Shane Dix, and Greg Egan.

The point is the author is allowed to write stories about human beings, but the digital humans and their digital environment take up zero mass.

One could add equipmment capable of manufacturing artificial bodies for the crew from local materials upon arrival at the destination. 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.

You could regain the advantage if the manufacturing equipment is really tiny. Say a couple of grams worth of nanotechnology self-replicating machines, intended to work on handy asteroids or other free materials lying around the destination solar system. The nanotechnology bootstraps itself by replicating using in-situ resources as feedstocks until it has mass of a few tons, then shifts gears to start manufacturing artificial bodies.

Seed Ship

The next higher mass class of slowboat is the Seed ship. It will tend to have more mass than a Digital Crew ship and less than a Sleeper Ship.

The starship is tiny, containing a payload of millions of frozen fertilized eggs, artificial wombs, robots, and a master computer. No mass is needed for life-support, habitat modules, or any human crew.

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.

Sleeper Ship

Sleeper ship tend to have more mass than a Seed Ship and less than a Generation Ship.

The crew is frozen into suspended animation, so they do not age nor require food and oxygen during the thousand year journey. Or spacious living accomodations. The Sleeper Ship does require the mass of the crew, enough mass for a spartan habitat module, and only enough consumables for the time the crew will be awake.

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.

Generation Ship

The highest mass type of slowboat tends to be the Generation ship. This is because it has to carry the mass of an entire community as crew, a habitat module at the minimum the size of a small town, and enough life support for the people for however many hundreds of years the journey takes. 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 indeed forgetting the fact that they are in 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.

If the generation ship is escaping from some Terra-destroying catastrophe; carrying Terra's scientific and cultural heritage, a representative sample of animal species, colony equipment and supplies, and a fertile representative sample of humanity, the craft is termed an Interstellar Ark.

Alter Metabolism

A variation of the "Increase Lifespan" technique 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.



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) ]


  • 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)


  • 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

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.


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]


  • 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.

Extreme Relativistic Rocketry

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

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

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

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

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

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

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

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

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

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

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


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

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

this can be solved for time quite simply as:

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

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

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

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

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

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

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

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

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

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

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

This modifies the Rocket Equation to:

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

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

which becomes:

As and , then we have

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

Of course the trick is creating energy via GUT physics…

From Extreme Relativistic Rocketry by Adam Crowl (2015)

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)


  • 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)

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.


R = e(a * T / c)
R = e(1.03 * 3.94 / 1.0)
R = e4.06
R = 57.97


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.

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?

Bussard Ramjet Equations

Acceleration of a Ramjet

Consider a ramjet moving through the interstellar medium at speed u. Translating to the ramjet's frame of reference, this is equivalent to the medium flowing past a stationary ramjet at speed u. Assume that whatever mass is collected in the intake funnel is ejected from the rear of the ramjet at speed v (relative to the ramjet), which is naturally greater than u. The change in momentum of a given mass m of interstellar medium on passing through the ramjet is:
Δ momentum = m (v - u)
By the conservation of momentum, this is equal to the change in momentum of the ramjet:
m (v - u) = M Δ V
M = the mass of the ramjet ship
Δ V = the change in velocity of the ramjet ship.
Note: This equation is an approximation which neglects the small amount of collected mass which is converted into energy by the nuclear fusion reaction. For hydrogen fusion, less than 1% of the mass is lost in this way, so any error is quite small. The acceleration of the ramjet a is then given by:
a = dV / dt = m (v - u) / M dt
dt = an "infinitesimal change in time" (I am not bothering with strict formalities of calculus here).
Now, the change in kinetic energy of the interstellar medium material Δ (m v2) / 2 is equal to the generated engine power P multiplied by the change in time:
P dt = Δ (m v2) / 2
      = m (v2 - u2) / 2
      = m (v - u) (v + u) / 2
But (v + u) / 2 is the average speed V of the ramjet relative to the interstellar medium over the time increment in question. Substituting this, and the acceleration formula above:
P dt = a M dt V
P = a M V
Now consider the volume of interstellar medium swept up by the ramjet funnel. If the effective funnel (including any electromagnetic attraction fields) is circular, with a radius r, then in a time dt it sweeps through a volume of:
π r2 V dt
If the density of hydrogen nuclei in the interstellar medium is ρ (in mass per unit volume units), then the mass of hydrogen nuclei swept up in time dt is:
π r2 V ρ dt
This mass is available for conversion into energy, with a nuclear fusion efficiency η (η is 0.753% for hydrogen fusion), so:
E = m c2
P dt = π r2 V ρ η c2 dt
c = the speed of light.
Substituting the formula for power above and rearranging:
a = π r2 ρ η c2 / M

This means the acceleration of a ramjet is dependent only on the size of the collecting funnel, density of the interstellar medium, efficiency of the nuclear fusion reaction, and mass of the ship, and is a constant over time. In other words, the ship's velocity will increase linearly with time.

The limit to this velocity increase is the speed of light, and close to the speed of light the equation derived above will break down due to the effects of special relativity.

Threshold Speed

Normally a Bussard ramjet needs to be moving at a certain threshold speed before the ramjet engine can begin operation. If the ship is moving too slowly, hydrogen may be swept up at too slow a rate to sustain the nuclear fusion reaction.

If we assume a threshold mass-collection rate dm/dt (the units are mass per unit time), then the rate of mass collection by the funnel π r2 ρ V needs to be greater than the threshold. This gives a threshold velocity:

Vt   >   (dm/dt) / ( π r2 ρ )
Below this velocity, the ramjet engine will not work.

In order to get up to the threshold velocity, a ramjet may be equipped with a reaction engine with its own power and reaction mass supply. This engine can be switched off once the ramjet begins to work.

Slowing Down

A ramjet which needs to slow down can utilise its mass collection system as a brake by simply collecting the incoming matter rather than fusing and ejecting it.

Consider a ramjet moving at speed V with respect to the interstellar medium. If matter collected by the funnel is stored in the ship, then in a time increment dt an amount of mass dm is given a change in momentum equal to the change in momentum of the ship, but in the opposite direction:

dm V = - M dV
But the mass collected in this time interval is as given under Acceleration of a Ramjet above, so:
π r2 ρ V2 dt = - M dV
dt / dV = - M / ( π r2 ρ V2 )
Integrating with respect to V from time to when speed is Vo to time t when speed is V:
t = [ M / ( π r2 ρ ) ] (1 / V - 1 / Vo)
Rearranging to make speed the subject as a function of time:
V = M Vo / (M + π r2 ρ Vo t )
Note that the drag generated on the ship by the incoming interstellar medium does not affect the acceleration calculated above, since only the total change of momentum is relevant (and is how the acceleration was calculated).
From Bussard Ramjets by David Morgan-Mar (2004)

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:

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:

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:

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

  • Subject: Re: Bussard Ramjet woes
  • From: schillin@xxxxxxxxxxxxx (John Schilling)
  • Date: 26 Nov 2001 11:02:35 -0800
  • Newsgroups:
  • 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 (2001)


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.



The URSS Alabama is a fictional Bussard Ramjet starship from Alan Steele's novel Coyote (2002). It was the first starship, build by the authoritarian conservative regime which took over after the fall of the United States. At its dedication ceremony, it is hijacked by the captain, and escapes the regime by travelling to 47 Ursae Majoris. The 46 light-year journey takes 230 years cruising at 0.2c, with the crew and colonists in biostasis.

Avatar ISV Venture Star

RocketCat sez

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

The good starship ISV Venture Star from the movie Avatar is one of the most scientifically accurate movie spaceships it has ever been my pleasure to see. When I read the description of the ship, I got a nagging feeling that something was familiar. A ship with the engines on the nose, towing the rest of the ship like a water-skier? Wait a minute, that sounds like Charles Pellegrino and Jim Powell's Valkyrie starship.

Well, as it turns out, there was a good reason for that. James Cameron likes scientific accuracy in his movies. So he looked for a scientist who had experience with designing starships. Cameron didn't have to look far. As it turns out he already knew Dr. Pellegrino. This is because Dr. Pellegrino had worked with Cameron on a prior movie, since Dr. Pellegrino is one of the worlds greatest living experts on the Titanic.

After James Cameron had designed all the technical parameters of the Venture Star, master artist Ben Procter worked within those parameters to bring it to life.

Departing from Earth

In the upper diagram is a green arrow at the ship's nose, indicating the direction of flight. The ship is 1.5 kilometers long. In the Sol departure phase, a battery of orbital lasers illuminates a 16 kilometer diameter photon sail attached to the ship's nose (sail not shown). A mirror shield on the ship's rear prevents the laser beams from damaging the ship. The lasers accelerate the ship at 1.5 g for 0.46 year. At the end of this the ship is moving at 70% the speed of light (210,000 kilometers per second).

Keep in mind that battery of orbital lasers is going to have to be absolutely huge if it is going to push a lightsail at 1.5 g. This is not going to be a tiny satellite in LEO.

I cannot calculate the exact power rating since figures on the mass of the ISV Venture Star are conspicuous by their absence. The equation is Vs = (2 * Ev) / (Ms * c) where Vs is the starship acceleration, Eb is the energy of the beam, Ms is the mass of the starship, and c is the speed of light in a vacuum. Dr. Geoffrey Landis says is boils down to 6.7 newtons per gigawatt.

In Dr. Robert Forward's The Flight of the Dragonfly (aka Rocheworld), his starship's light sail is illuminated by a composite laser beam with a strength of 1500 terawatts. This pushes the starship with an acceleration of 0.01g (about 150 times as weak as the acceleration on the Venture Star). The beam is produced by one thousand laser stations in orbit around Mercury (where solar power is readily available in titanic amounts). Each station can produce a 1.5 terawatt beam, 1500 terawatts total. By way of comparison, in the year 2008, the entire Earth consumed electricity at a rate of about 15 terawatts. Since the Venture Star appears to be more massive than Forward's starship, and is accelerating 150 times as fast, presumably its battery of laser cannons is orders of magnitude larger.

As a side note, it is good to remember Jon's Law for SF authors. and The Kzinti Lesson. While technically this laser array is a component of a propulsion system, not a weapon; in practice it will have little difficulty vaporizing an invading alien battlefleet. Or hostile human battlefleet, for that matter (with the definition of "hostile" depending upon who actually controls the laser array). As Commander Susan Ivanova said in the Babylon 5 episode Deathwalker: "Our gun arrays are locked on to your ship, and will fire the instant you come into range. You will find their firepower most impressive ... for a few seconds."

Anyway, after the laser boost period is over, the sail is then collapsed along molecular fold lines by service bots, and stowed in the cargo area. The ship then coasts for the next 5.83 years to Alpha Centauri.

Braking at Alpha Centauri

There are no batteries of laser cannon at Alpha Centauri so the lightsail cannot be used to brake to a halt. Instead, the twin hybrid fusion/matter-antimatter engines are used. These engines are not used for the Sol departure phase because that would increase the propellant requirement by about four times with a corresponding decrease in cargo capacity. The engines burn for 0.46 year, producing 1.5 g of thrust, thus braking the ship from a velocity of 70% c to zero.

Matter and antimatter is annihilated, and the energy release is used both in the form of photons and to heat up hydrogen propellant for thrust. A series of thermal shields near the engines protect the ship's structure from the exhaust heat. The engines are angled outwards a few degrees so that the exhaust does not torch the rest of the ship (exhaust path indicated in diagram by red arrows). This does reduce the effective thrust by an amount proportional to the cosine of the angle but is acceptable.

Why is most of the ship behind the engine exhaust? Because this reduces the mass of the ship. And when you are delta-Ving a ship up to and down from 70% c, every single gram counts. Conventional spacecraft have the engines on the bottom and the rest of the ship build on top like a sky scraper. This design has the engines on the top and the rest of the ship is dragged behind on a long tether (the "tensile truss" on the diagram). The result is a massive reduction in structural mass.

The engines are topped by monumental heat radiators used to get rid of waste heat from the matter-antimatter reaction. According to the description, after the burn is finished, the radiators will glow dull red for a full two weeks.

Cargo Modules

Immediately stern ward of the engines is the cargo section. It is arranged in four ranks of four modules each. Each module contains 6 cargo pods. A mobile transporter with a long arm moves within the cargo section in order to load and unload the shuttles.

Interface Craft

Next comes Two Valkyrie trans-atmospheric vehicles, aka "surface to orbit shuttles." They are docked to pressurized tunnels connected to the habitation section. Each is capable of transporting either:

  1. the contents of two cargo pods and 100 passengers OR
  2. the contents of six cargo pods and no passengers
Habitation Modules

Next come the habitation module. This holds the passengers in suspended animation for the duration of the trip. This is constructed almost totally from non-metallic materials, to prevent secondary radiation from galactic cosmic radiation.

The habitation module's life support system can only support all the passengers being awake for a limited time. There is no problem for the short period when the passengers are woken up and shuttled to the planet's surface. However, if the suspended animation system malfunctioned half-way through the multi-year voyage, life support could not handle it. In theis case, the passengers would be "euthanized" instead of being awakened.

Crew Modules

Next is the two on-duty crew modules. These are spun on the ends of arms to provide artificial gravity. When the ship is under thrust, the spin is taken off, and the arms are folded down along their hinges so that the direction of gravity is in the proper direction.


Finally comes the shield. While the ship is being boosted by the laser batteries, the shield protect the ship (but not the sail) from the laser beams. After boost, while the ship is coasting at 70% c, the ship is rotated so that the shield is in the direction of travel. The shield is constructed as a Whipple shield, and protects the ship from being damage by grains of dust.

At 70% c relative, each dust grain would have 4,900,000,000 freaking Ricks of damage. This means a typical interstellar dust grain with a mass of 4 x 10-6 grams will hit with the force of 20 kilograms of TNT, or about the force of four anti-tank mines.

When the ship wants to depart Alpha Centauri and return to Sol, it re-fills its antimatter and propellant tanks from the local fueling stations, uses the matter-antimatter engines to boost up to 70% c again, coasts for five-odd years, and is decelerated to a halt by the laser batteries at Sol.

Egalitarian Republic

The fictious starship Egalitarian Republic is from from Buzz Aldrin and John Barnes' novel Encounter With Tiber (1996). 9,000 years ago aliens from Alpha Centauri visited Terra in the starship Wahkopem Zomos. When human archeologists discover the alien artifacts left behind, they create the Egalitarian Republic so as to return the favor.

Enzmann Starship

The Enzmann starship is a concept for a manned interstellar spacecraft proposed in 1964 (date is disputed) by Dr. Robert Enzmann. Over the years the basic design has evolved, and there were several types in the initial design. It was quite popular in the science fiction community. An analysis of the Enzmann starship can be found here.

In 1972 space artists Don Davis and Rick Sternbach worked with Dr. Enzmann to develop the idea. This refined the "lollypop" look of the ship. For some odd reason most paintings of the Enzmann starship show two of them in formation. The original design had a naked sphere of frozen deuterium as fuel. Calculations with Sternbach and Davis revealed that the deuterium could not be kept frozen and was too structurally weak to be accelerated. So the redesign encased the deuterium in a huge tank.

The Enzmann exploded into the science fiction community with the October 1973 issue of Analog magazine. G. Harry Stine wrote an extensive article about the concept, accompanied by a stunning piece of cover art by Rick Sternbach. Stine said the ships were 12 million tonnes, could reach 0.30 c (highly unlikely), had 8 engines, and used spinning habitats for artificial gravity.

  • Command center 30 meters in diameter
  • Central core load bearing struture 15 meters diameter
  • Frozen deuterium 300 meters diameter
  • Living modules 90 meters diameter × 90 meters long
  • Engineering compartments 70 meters diameter

In Science Digest, Rick Sternbach's 1972 piece depicts a pair of Enzmanns departing from an asteroid factory. The number of engines was increased from 8 in the original design to 24. Modular sections were created that can separate from the starship. Height of starship was 690 meters. 3 million tonnes of deuterium, with metal shell (doubling as a radiation shield). Magnetic confined fusion propulsion. 20 decks per habitat, 100 rooms per deck. Cruising speed 0.09c.

Thomas Schroeder wrote an article entitled "Slow Boat to Centauri" in Astronomy Magazine. Claimed a cruising speed of 0.1c, and an advanced design might reach 0.3c. 12 million tonnes deuterium. The outer layers of the habitats were composed of bulk material as radiation shielding for the inner layers. Bulk means nuclear reactor, store rooms, heat exchangers, airlocks, landing craft, observation areas, communication equipment. Eight Project Orion nuclear pulse units.

  • Frozen deuterium 305 meters diameter
  • Height 609.6 meters
  • Living modules 91.5 meters diameter × 91.5 meters long
  • From bottom of fuel sphere to top of Orion engines 305 meters

In the 1980's Dr. Enzmann started designing variants.

In 2011, K. F. Long, A. Crowl, and R. Obousy did a study on the Enzmann starship, and tried to rationalize it with recent developments in astronautics. First they took the historical concepts:

Historical Concepts
Length610 msamesame
Sphere Diameter305 msamesame
Total Habitat Length273 msamesame
Individual Habitat length91 msamesame
Habitat Diameter91 msamesame
Core Diameter15 msamesame
Num Habitats113
Num Engines8824
Exhaust VelocityUnspecifiedUnspecifiedUnspecified
Specific ImpulseUnspecifiedUnspecifiedUnspecified
Structural MassUnspecifiedUnspecifiedUnspecified
Propellant Mass3×106 metric tons12×106 metric tons3×106 metric tons
Cruise Speed27,000 km/s
90,000 km/s
27,000 km/s
Starting Colony200samesame
Final Colony2000samesame

Long et al created three variants. The primary difference is the size of the population carried. The rest of the design was re-sized to handled the population. As near as I can calculate, the cruise and mission times for all three are for a mission to Alpha Centauri.

Specific Power11.5 MW/kg
Thrust Power344 terawatts
Length620 m979 m1752 m
Dry Mass30,000 MT300,000 MT3,000,000 MT
Propellant Mass3 × 106 MT3 × 106 MT3 × 106 MT
Mass Ratio
Mass Ratio10.053.321.41
Exhaust Velocity11,700 km/s11,260 km/s12,119 km/s
ΔV54,000 km/s
27,000 km/s
8,400 km/s
Cruise Velocity27,000 km/s
13,500 km/s
4,200 km/s
Total Acceleration
18.95 yrs98.67 yrs84.9 yrs
Total Cruise
41.05 yrs51.33 yrs265.1 yrs
Total Mission
60 yrs150 yrs350 yrs
Mass Flow Rate5.02 kg/s0.96 kg/s1.12 kg/s
0.019 m/s2
0.003 m/s2
0.004 m/s2
Thrust58,730 kN10,810 kN13,573 kN

Firefly Starship

Firefly Starship
2013 design
ΔV2.698×107 m/s
Wet Mass17,800 metric tons
Dry Mass2,365 metric tons
Mass Ratio7.526
Payload150 metric tons
PropulsionZ-Pinch DD Fusion
Exhaust Velocity1.289×107 m/s
Thrust1.9×106 N
Acceleration0.11 m/s
(0.01 g)
Accel time4 years
Coast time93 years
Decel time1 years
Firefly Starship
2014 design
ΔV2.998×107 m/s
Wet Mass45,000 metric tons
Dry Mass3,000 metric tons
Mass Ratio15.0
Payload150 metric tons
PropulsionZ-Pinch DD Fusion
Specific Impulseone million seconds
Thrust855,000 N
Acceleration0.019 m/s
(0.002 g)
Accel time25 years
Coast time70 years
Decel time5 years
Length~1,0000 m

Icarus Interstellar has a project to design a fusion-rocket based interstellar spacecraft. They call it "Firefly". The technical lead director is Robert Freeland.

Most of the other Icarus fusion designs use inertial confinement fusion. That's because IC fusion is easier to get halfway worthwhile power levels. Magnetic confinement fusion would be nicer but once you get enough nuclear fusion going to to be worthwhile, the magnetic bubble pops like a cheap balloon.

The drawback to IC fusion is that the confinement time is pathetic. The longer you confine the fusion reaction, the more of the fusion fuel actually burns and generates energy. But in IC fusion the first bit of fusion acts to blast the pellet apart, scattering the un-burnt fuel to the four winds.

Back in the olden days of fusion research, the darling was Z-Pinch fusion. You send a bolt of electricity (about 5 mega-amps) down the center of a long tube full of ionized plasma, creating magnetic field which compresses the plasma enough to ignite nuclear fusion. One of the big advantages with Z-Pinch was that the confinement time (and net energy output from the burn) can be increased by simply making the reaction chamber longer.

Unfortunatley, the disadvantage is that Z-Pinch fusion suffers from several hydrodynamic instabilities which disrupt the plasma. So researchers stopped working on it in.

But in 1998 Dr. Uri Shumlak discovered you could eliminate the instabilities if you made the plasma move at high velocities. Based on this work, Z-Pinch was selected for the Icarus design.

The Firefly's long thin tail is the Z-Pinch tube, frantically fusing and radiating x-rays like a supernova. So the starship was given its name for similar reasons as the one on the TV show: it is a flying thing whose tail lights up.

The spacecraft profile is long and skinny, for two reasons:

  • Its cruise velocity is a substantial fraction of the speed of light (4.5c for the 2013 version). This make interstellar dust grains impact with about 9.1×10-4 joules worth of damage, the equivalent of 46,000 cosmic ray photons. You want to reduce the ship's cross section as much as possible to minimize the number of grain impact events.
  • The longer the ship is, the farther the payload can be placed from the deadly radioactive Z-Pinch drive, taking advantage of distance shielding.

Many other starship designs use 3He-D fusion, because all the reaction products are charged particles that can be easily shieldied. The drawback is that 3He is rare, you'd have to harvest the atmosphere of Jupiter for twenty years in order to get enough.

Instead, Firefly uses D-D fusion, since deuterium can be easily found in common seawater. Of course then you have to deal with all the nasty neutrons and x-rays produced by that reaction. Firefly's approach is to forgo the use of massive radiation shields, and instead try to let as much of the radiation escape into space. The Z-Pinch core is almost totally open to space with only a triad of support rails connecting the aft electrode and magnetic nozzle to the rest of the vessel.

Even with that, the waste heat is going to be titanic. That's where the heat radiators come in. Notice how they are the bulk of the ship. Makes the thing look like a garantuan lawn-dart. The radiators use beryllium phase-change technology, and are positioned as close as possible to the heat loads on the tail.

A long conical shield forwards of the reactor core deflects x-rays away from the payload using shallow-angle effects. The electrodes, rails, and other structure near the core are constructed of zirconium carbide (which is capable of surviving the intensely radioactive environment.

The 2014 design had a total length of just under one kilometer, half of which is the fuel tanks. The forward part of the ship uses the old fuel tank in lieu of spine trick in an effort to save on ship mass.

A fission reactor provides secondary power.

Frisbee Antimatter Starship

Antimatter Starship
(one stage)
Beam Core
ΔV7.5×107 m/s
Exhaust Velocity9.99×107 m/s
Thrust1.174×107 N
Thrust Power587.4 TW
Average Accel0.098 m/s
(0.01 g)
Gamma radiation996.3 TW
Mass Ratio5.45
Dry Mass
Dust Shield6,530 MT
Power Systems1,064.6 MT
Payload100 MT
Misc.100 MT
Propellant tanks,
feed system
26,698.8 MT
Propellant tank
104.7 MT
Payload Rad Shield
w/ radiator
361.6 MT
Radiator Rad Shield6.4 MT
Magnet Rad Shield103.3 MT
R. R. +
Magnet Shield
15,533.7 MT
Magnet, structure,
282.3 MT
3,707.4 MT
30% Contingency
16,347.8 MT
Total Dry Mass70,940.6 MT
Propellant Mass
Propellant Total
matter LH2
159,450 MT
boiloff loss
matter LH2
1,579 MT
Propellant Usable
matter LH2
157,872 MT
Propellant Total
antimatter LH2
165,765 MT
boiloff loss
antimatter LH2
7,894 MT
Propellant Usable
antimatter LH2
157,872 MT
Engine Magnet Radiation Shield
mass103 MT
volume5.337 m3
thickness0.173 m
cross-section area0.088 m2
minimum distance
to ignition point
10.639 m
center distance
to ignition point
11.038 m
fraction of gamma
flux intercepted
gamma power
1.455×104 GW
Radiator Radiation Shield
mass6.434 MT
volume0.332 m3
diameter19.9 m
height0.125 m
cross-section area2.488 m2
minimum distance
to ignition point
along hypotenuse
11.455 m
minimum distance
to ignition point
along x-axis
5.123 m
fraction of gamma
flux intercepted
gamma power
1.503×103 GW
System & Payload
Radiation Shield
mass361.09 MT
volume18.661 m3
diameter19.9 m
height0.064 m
cross-section area311.026 m2
minimum distance
to ignition point
along hypotenuse
5.152×105 m
fraction of gamma
flux intercepted
gamma power
9.29×10-5 GW
Shield Radiator
gamma power
to radiate
16,052 GW
2-sided area1.025×107 m2
width19.9 m
height515,189 m
(515 kilometers)
mass15,533.7 MT

This is from AIAA 2003-4676 How To Build an Antimatter Rocket For Interstellar Missions by Robert H. Frisbee. The basic spacecraft has a delta V of one-quarter the speed of light and an acceleration of 0.01 g. The freaking thing is about 700 kilometers long (about the distance between Washington DC and Montpelier Vermont), due to the off-the-chart levels of gamma radiation and the 500 kilometers of heat radiators required to keep the ship from vaporizing.

Most of the 500 km of heat radiators is to reject the gamma-ray heat absorbed by the radiation shields.

The superconducting magnet in the engine proper is kept cool to 100 Kelvin, the liquid hydrogen is cooled to 20 K, and the solid anti-hydrogen pellets are cooled to 1 K.

On the nose is the dust impact shield, which protects against interstellar dust impacts. Because at 0.25 c even a speck of dust is going to hurt.

Everything you hit will have about 625 mega-Ricks worth of damage. This means if you hit a grain of sand that had a mass of one milligram (10-3 kg), it would explode with about the force of 625 metric tons of TNT. Now your average interstellar dust grain has only a mass of 10-17 kg which makes the boom much smaller. Unfortunately the interstellar medium has a dust density of 10−6 × dust grain/m3, and there are a lot of meters in a light year.

My slide rule says a cylinder with a diameter of 19.9 meters and a length of one light-year will contain about 2.94×1018 m3. This is the volume the nose of the starship will plow through per one light-year of travel. At a dust density of 10−6 grain/m3 means the nose will hit 2.94×1012 dust grains. 10-17 kg per grain means total mass impacting the shield per light year is 2.94×10-5 kg. At 625 mega-Ricks this means it will only subject the dust shield to the equvalent of an explosion of 18.4 metric tons of TNT. Per light year.

The design specs called for a cruising velocity of 0.5 c, which means you'd need four stages, that is, a stack of four of these monsters. One stage to boost up to the coasting speed of 0.5 c, second stage to brake from 0.5 c to halt at the destination, third stage to boost to 0.5 c for the trip home, and 0.5 c to brake to a halt at Terra. The four stage vehicle will have a length between 1,900 and 7400 kilometers, depending upon the technology assumptions. Egads.

As it turns out the starship needs a minimum acceleration or it will take a century to get up to speed. Dr. Frisbee drew up the above chart and figured if you wanted to maximize the mission time spent at peak velocity the starship would have to be capable of accelerating and decelerating at about 0.01 gee minimum. The trouble is that beam core antimatter drives are classic high specific impulse/low thrust rockets. This means you have to really crank up the propellant mass flow if you want to get 0.01 g. Which means the engine mass will skyrocket.

Another problem with using proton-antiproton antimatter rockets is that only 22% of the propellant mass actually propels the starship. The rest is wasted. This means that the standard delta V equation has to be modified to take this into account. It needs to be modified further for relativity if the delta V is substantial fractions of the speed of light. The equation was use to draw the graph above. The equation itself is below.

So a normal rocket that does not annihilate its reaction mass so that 100% of it propels the starship uses the standard delta V equation. This says if the specific impulse is 0.33 c and the delta V is 0.25 c, the mass ratio would be a modest 2.15. But for this antimatter rocket with only 22% of the propellant working (a=0.22), the mass ratio climbs to 5.45. By doing some estimates on the minimum tankage masses, Dr. Frisbee concludes that 0.25 c is the maximum delta V per stage of the starship. You can read his reasoning in the report.

It is bad that only 22% of the propellant is doing its job. What is worse, 38% of the propellant mass is turned into deadly gamma rays that will fry anything unprotected from their deadly shine. This means heavy radiation shields, which need 500 kilometers of heat radiators to keep the gamma-ray heat from vaporizing them. This also forces the vehicle to be long and narrow to minimize the solid angle of intercepted gamma radiation from the engine.

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)

Wahkopem Zomos

The fictious starship Wahkopem Zomos is from from Buzz Aldrin and John Barnes' novel Encounter With Tiber (1996). 9,000 years ago aliens from Alpha Centauri visited Terra using the starship, since an impending asteroid bombardment was about to drastically lower the property values of their home planet.

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 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

Winchell Chung: If you have two bussard ramjet ships with nearly identical propulsion performance, moving at relativistic velocities, and seeing only where the enemy was but not where it is now (due to lightspeed lag), well, if one of the ships wants to evade, there is no way the other can catch it.

David Iwancio: It seems like your evading would be more difficult to pull off in Einsteinian space than Newtonian. If the ability to evade relies on how far away from your present course you can "jink," your energy/thrust reqirements go up exponentially with the size of your "jink" (what with the increase in your mass and all).

Where your target might be after time T can be expressed as a sphere of a certain radius, and the radius increases with T. In Newtonian space, the radius increases linearly with T, so you can kind of visualize a cone centered about the target's current path of travel. However, in Einsteinian space the radius of the sphere increases only logarithmicly, giving you a smaller (usually much smaller) sphere radius than Newtonian space.

Wouldn't this kinda counteract the problems of light/sensor lag a bit?

Ken Burnside: I call this the trumpet bell effect, and it becomes much more noticeable when slinging ballistic weapons in 3-D play.

Provided your ballistic weapon's rate of closure is greater than the lateral velocity of the target, you get a trumpet bell, or manifold shape. As the projectile's velocity increases, the skinny part of the trumpet bell elongates — but it also thins out. The volume described by the surface of the trumpet and the centerline of the trumpet remains constant along the time axis, provided the ability to laterally accelerate remains constant.

In short, if you've GOT a good shot lined up, it's harder to dodge it by "jinking". If you've got a fuzzy shot that gets refined as you approach (which is roughly how Attack Vector: Tactical does it, because it's easier than having people pretend to be targeting computers in 3-D vector space), higher speeds on the shells can reach a threshold effect, where a small error that could be corrected for at a low closing velocity can't be corrected for at a high closing velocity.

A bit of practice renders this moot, but without that practice in the mechanics of doing vector ballistics (let alone 3-D vector ballistics), they can get very frustrating to use.

(somebody asks if sensor lag will prevent the trumpet bell effect)

My suspicion is that it's still going to be a trumpet bell effect. While there's sensor lag, if they're moving at 0.92 c (about where relativity becomes noticeable), the "trumpet bell" of the target's possible positions is also very long and skinny.

One thing you learn in Attack Vector: Tactical is that velocities past about 30 hexes/turn (300 km/64 seconds) actually make you EASIER to hit with ballistic weapons, because your ability to change your vector is so dramatically reduced. What you want for dodging missiles is a low enough velocity that you can swing around and thrust in an unanticipated direction and throw off the ballistic weapon's accuracy.

From thread on sfconsim-l (2002)


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."


"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)


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


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?


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?


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.


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.


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?


{ 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.


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.

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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