This page is for starships that travel at relativistic speeds. Starships that can travel near the speed of light laugh at the huge distance between stars. Relativistic time-dilation will drastically reduce the elapsed time on board the ship, depending upon how close they can crowd the speed of light. The starships can reach their destinations long before the astronauts die of old age or the ship exceeds its warranty time limit.

The first problem is that achieving relativistic velocities is very hard to do. The delta-V required will be monstrously huge.

The second problem is that the time reduction only applies on board the ship. The ship may be capable of traveling to the Pleiades and back home in a few months of ship time. But they will discover that about 800 years have passed by on Terra and everybody they knew has died of old age. Including the nation that sent them.

The starships in this page come under the headings of "Go Fast", "AAFAL" (almost as fast as light) and "Pericee" (near to c).

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 specific implications of relativity that we have to worry about. Unless you are writing Gregory Benford style novels, in which case you know about the extra implications already.

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. Not yours. 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 will age and experience time at a slower rate compared to people who stayed at home on Terra. The crew won't notice anything odd, until they return home to the Rip Van Winkle Experience. As a general rule, you can figure the start of "moving relativistically" is arbitrarily when the the dilation effect gets bigger than 1/100th. This is when γ equals 1.01, which happens at about 14% c.

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. In other words

γ = 1 / Sqrt[ 1 - (vpercent2) ]

vpercent = Sqrt[ 1 - (1 / γ)2 ]


  • vpercent = current ship's velocity as measured in Terra's frame of reference (percentage of c)

How do you use gamma?

  • Time : A viewer on Terra will observe the crew of a starship moving relativistically relative to Terra living in slow motion. One unit of crew time will pass during one unit times gamma of Terra time

  • Mass : A viewer on Terra will observe a starship moving relativistically relative to Terra having an increased mass. The mass will be multiplied by gamma.

  • Length : A viewer on Terra will observe a starship moving relativistically relative to Terra having its length in the direction of motion shortened. The width and height will be the same, but the length will appear flattened. The length will be divided by gamma.

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 other than making the ship look funny.


As a side note, at around 0.7 c the starship will be at Functional Lightspeed. This is because 0.7 c has a gamma of 1.4, and 1/1.4 is about 0.7 (unlike all the other values on the table). Well, actually after playing around on a spreadsheet it looks like it is closer to 0.707 c with a gamma of 1.414. But anyway:

What does this mean?

Say the good starship Breakaway is traveling to Alpha Centauri (distance 4.4 light-years) and is cruising at the Functional Lightspeed velocity of 0.7 c. The gamma is 1.4 and 1/γ = 0.7. From the viewpoint of the crew, the 4.4 light year distance appears to be only 3.1 light years (4.4×0.7=3.1 where 0.7 is 1/γ). The speed is still 0.7 c.

So for the crew, the trip will appear to take 4.4 years (3.1/0.7 where 0.7 is percent of lightspeed), where 4.4 is the quote "real" unquote distance to Alpha C in light-years. The crew will conclude they are traveling at one light-year per year, the speed of light, even though they are not. "Functional Lightspeed."


As another side note, the equation for gamma demonstrates how things go haywire when you calculate speed faster than light. Look at the formula for gamma above. If c = 1.0 and v = 2.0 (that is, a velocity of twice light speed), what is gamma?

Well, there is a problem there:

γ = 1 / Sqrt[1 - (v2 / c2)]
γ = 1 / Sqrt[1 - (2.02 / 1.02)]
γ = 1 / Sqrt[1 - (4 / 1)]
γ = 1 / Sqrt[1 - 4]
γ = 1 / Sqrt[-3]

The problem is when you try to take the square root of -3. If you try it on your calculator it will flash you INVALID INPUT! This is because there ain't no number you can multiply by itself to get a negative number (because a positive times a postive is a positive number, and a negative times a negative is also a positive). The only way you can get a negative number is by multiplying a negative by a postive, but by definition squaring a number means multiplying the same number together.

So if you try to calculate the gamma of a velocity faster than light, the equation blows up in your face.

Mathematicians have constructed towers of bizarre theories by saying "let's wave our hands and say there is weird number called i, such that i2 = -1." These are called, appropriately enough, imaginary numbers. The practical point is these numbers have been around since the 17th century, but they haven't helped much making a faster than light starship.


About now somebody has a question about adding velocity. If a starship is moving at half lightspeed, and somebody shoots their laser laser pistol in the direction of starship motion, how fast does the laser beam travel? Since the beam travels at 100% lightspeed and the starship is moving at 50% lightspeed, then the combined velocity should be 100 + 50 = 150% the speed of light, right?

Not so fast, it don't work like that, nohow. As it turns out, velocities do not add. Instead rapidities add. You have to use the relativistic velocity addition formula. Which is so constructed that no matter what the two velocities are or in which direction, adding them will never ever make a velocity faster than lightspeed. That noise you hear is the shade of Albert Einstein, snickering in the background. Curse you, Albert!

Note that in special relativity, velocities do not add. Instead, rapidities add. The velocity is the speed of light times the hyperbolic tangent of the rapidity. At low rapidities, the rapidity times the speed of light is almost the same as the velocity. However, no matter how high your rapidity gets, the hyperbolic tangent maxes out at 1 for very large rapidities so that your velocity can never be higher than the speed of light.

So imagine someone in a starship. As he burns propellant, the (delta-V) / (c) consumed adds to his rapidity. If he has a lot of delta-V, he can get a very high rapidity, but when you look at the velocity, it is always less than the speed of light.

Interestingly, the time dilation and length contraction factor is the hyperbolic cosine of the rapidity.

Luke Campbell


As a third side note, a kinetic energy weapon whose projectiles travel at 0.866 c the amount of kinetic energy is equal to the rest mass. Which means the projectiles contain the same amount of energy as if they were made out of pure antimatter.


From The Relativistic Rocket in the Usenet Physics FAQ

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

  • 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.

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)

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

Proper time elapsed
Terra time elapsed
Final velocity
1 year1.19 years0.56 lyrs0.77c1.58


Relativistic rocket refers to any spacecraft that travels at a velocity close enough to light speed for relativistic effects to become significant. The meaning of "significant" is a matter of context, but often a threshold velocity of 30% to 50% of the speed of light (0.3c to 0.5c) is used. At 30% of c, the difference between relativistic mass and rest mass is only about 5%, while at 50% it is 15%, (at 0.75c the difference is over 50%) so that above this range of speeds special relativity is required to accurately describe motion, whereas below this range sufficient accuracy is usually provided by Newtonian physics and the Tsiolkovsky rocket equation.

In this context, a rocket is defined as an object carrying all of its reaction mass, energy, and engines with it.

There is no known technology capable of accelerating a rocket to relativistic velocities. Relativistic rockets require enormous advances in spacecraft propulsion, energy storage, and engine efficiency which may or may not ever be possible. Nuclear pulse propulsion could theoretically achieve 0.1c using current known technologies, but would still require many engineering advances to achieve this. The relativistic gamma factor (γ) at 10% of light velocity is 1.005. The time dilation factor of 1.005 which occurs at 10% of light velocity is too small to be of major significance. A 0.1c velocity interstellar rocket is thus considered to be a non-relativistic rocket because its motion is quite accurately described by Newtonian physics alone.

Relativistic rockets are usually seen discussed in the context of interstellar travel, since most would require a great deal of space to accelerate up to those velocities. They are also found in some thought experiments such as the twin paradox.

Relativistic rocket equation

As with the classical rocket equation, one wants to calculate the velocity change Δv that a rocket can achieve depending on the exhaust velocity ve and the mass ratio, i. e. the ratio of starting rest mass m0 and rest mass at the end of the acceleration phase (dry mass) m1.

In order to make the calculations simpler, we assume that the acceleration is constant (in the rocket's reference frame) during the acceleration phase; however, the result is nonetheless valid if the acceleration varies, as long as exhaust velocity ve is constant.

In the nonrelativistic case, one knows from the (classical) Tsiolkovsky rocket equation that

Assuming constant acceleration a, the time span t during which the acceleration takes place is

In the relativistic case, the equation is still valid if a is the acceleration in the rocket's reference frame and t is the rocket's proper time because at velocity 0 the relationship between force and acceleration is the same as in the classical case. Solving this equation for the ratio of initial mass to final mass gives

where "exp" is the exponential function. Another related equation gives the mass ratio in terms of the end velocity Δv relative to the rest frame (i. e. the frame of the rocket before the acceleration phase):

For constant acceleration, (with a and t again measured on board the rocket), so substituting this equation into the previous one and using the hyperbolic function identity returns the earlier equation .

By applying the Lorentz transformation, one can calculate the end velocity Δv as a function of the rocket frame acceleration and the rest frame time t'; the result is

The time in the rest frame relates to the proper time by the hyperbolic motion equation:

Substituting the proper time from the Tsiolkovsky equation and substituting the resulting rest frame time in the expression for Δv, one gets the desired formula:

The formula for the corresponding rapidity (the inverse hyperbolic tangent of the velocity divided by the speed of light) is simpler:

Since rapidities, contrary to velocities, are additive, they are useful for computing the total Δv of a multistage rocket.

From the Wikipedia entry for RELATIVISTIC ROCKET

      “The latest development is the mass-conversion ship, such as the Mayflower, and it may be the final development—a mass-conversion ship is theoretically capable of approaching the speed of light. Take this trip: we accelerated at one gravity for about four hours and twenty minutes which brought us up to more than ninety miles a second. If we had held that drive for a trifle less than a year, we would approach the speed of light.
     “A mass-conversion ship has plenty of power to do just that. At one hundred per cent efficiency, it would use up about one per cent of her mass as energy and another one per cent as reaction mass. That’s what the Star Rover is going to do when it is finished.”

     One of the younger kids was waving his hand. “Mister Chief Engineer?”
     “Yes, son?”
     “Suppose it goes on a few weeks longer and passes the speed of light?”
     Mr. Ortega shook his head. “It can’t.”
     “Why not, sir?”
     “Eh, how far have you gone in mathematics, sonny?”
     “Just through grammer school calculus,” the kid answered. (ed note: egads!)
     ‘Tm afraid there is no use in trying to explain it, then. Just take it from me that the big brains are sure it can’t be done.”

     I had worried about that very point more than once. Why can’t you go faster than light? I know all that old double-talk about how the Einstein equations show that a speed faster than light is a meaningless quantity, like the weight of a song or the color of a sound, because it involves the square root of minus one—but all of that is just theory and if the course we had in history of science means anything at all, it means that scientists change their theories about as often as a snake changes his skin. I stuck up my hand.
     “Okay,” he says. “You with the cowlick. Speak up.”
     “Mr. Ortega, admitting that you can’t pass the speed of light, what would happen if the Star Rover got up close to the speed of light—and then the Captain suddenly stepped the drive up to about six g and held it there?”
     “Why, it would—No, let’s put it this way—” He broke off and grinned; it made him look real young. “See here, kid, don’t ask me questions like that. I’m an engineer with hairy ears, not a mathematical physicist.” He looked thoughtful and added, “Truthfully, I don’t know what would happen, but I would sure give a pretty to find out. Maybe we would find out what the square root of minus one looks like—from the inside.”

(ed note: in the real world what would happen is you'd continue to add more decimal 9s to your V/c, and your gamma would keep rising.)

From FARMER IN THE SKY by Robert Heinlein (1950)


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.


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…


Starship Bumpers

The principle of relativity implies the Einstein equivalence principle. In Einstein-talk there are no Preferred frames.

In plain English, it means you cannot figure out which of two objects are moving. For example: according to the equivalence principle, you cannot tell if you are standing stationary while a .22 caliber bullet travels at 340 meter per second and embeds itself in your ass OR if the .22 caliber bullet is hovering stationary while your ass travels backwards at 340 m/s and impales itself on the bullet. Well, ignoring things like the entire world and the atmosphere traveling backward along with you, but you see the principle.

"Who gives a rat's heinie?", I hear you exclaim. "What of it?"

This of it: there is no difference between a starship traveling at 0.01 c plowing through a stationary cloud of protons AND a stationary starship being hit by a lethal solar proton storm with radiation particles moving at 3,000 kilometers per second..

For all intents and purposes: a starship moving relativistically will find that the interstellar medium has been transformed into deadly radiation. Curse you, Einstein!

Oh, it gets worse. If you had ever studied kinetic energy weapons, you'd be aware that their destructive energy is equal to ½v2m, that is, 0.5 times the square of the velocity v times the mass m. This means if you get hit in the head by a 1 kilogram brick traveling at 1 meter per second; if the brick was reduced to 0.1 kilograms, to get the same sized headache you'd only have to increase the velocity to 3 m/s. Not to 10 m/s like you'd expect, because just a little bit of velocity increase makes a big difference in the destructive energy. You might have noticed in the equation that while the mass is just in there plain, the velocity is squared.

Getting back to starships: first off if the starship is moving at relativistic velocities (above 0.1 c), squaring that velocity is going to make a huge number. And secondly, space ain't 100% empty. Yes, the interstellar medium is pretty darn close to being a perfect vacuum, but that is not the same as zero atoms. When you are multiplying this by a relativistic velocity squared, every atom counts.

In other words, a starship traveling relativistically will suffer as if it was under bombardment by a particle beam weapon. Over every square centimeter of frontal surface area. For decades.

And if you hit something larger than an atom, like for instance a microscopic grain of interstellar dust, it will be like a shell from a naval 16-inch gun.

Within about 200 light-years of Sol the density is around 7×10-2 atoms/cm3, because Sol in inside a bubble. Elsewhere it varies from 10-4 to 106 atoms/cm3 depending upon what sort of space you are in.

Remember, this was one of the problems a Bussard Ramjet was designed to solve.

While the bombardment will erode away the solid metal of the leading edge of the starship, the main threat is the radiation. The bombardment will be functional equivalent of you basking your unprotected body in the radioactive glow of twenty unshielded nuclear reactors. According to Dr. Oleg Semyonov, the estimated radiation dose is about:

D = 1.67×10-8 × Q × n × S × β × c × H(β) × d(β) / M


D = radiation dose (rem/s)
Q = radiation quality factor (for protons Q = 10)
n = concentration of interstellar gas (cm-3) varies from 104 cm-3 om galactic clouds to less than 1 cm-3 between clouds. Around Sol 0.2 cm-3
S = cross-section of a human body (cm2) ≈ 104 was used in the paper
H = stopping power of particles in human tissue (MeV cm2/g)
d = EITHER penetration depth of particles in human tissue OR thickness of human body in direction of motion (35 cm), whatever is less (g/cm2)
M = mass of individual (g)
c = speed of light in a vacuum (cm/s) = 29,979,245,800 cm/s
β = percentage of the speed of light, v/c

Paper says The data for H and d as functions of energies of nucleons are taken from the NIST (National Institute of Standards and Technology) online database.

A safe dose is about 3×10-7 rem/s or about 10 rems/year.

The paper estimates that up to 0.3 c the radiation can be controlled with a titanium radiation shield about 2 cm thick. Above 0.3 c the thickness increases "dramatically". Around 0.8 c the titanium shield will have to be several meters thick.

You can find details and other equations in Radiation Hazard of Relativistic Interstellar Flight by Oleg Semyonov. Also fun reading is The Interaction Of Relativistic Spacecrafts With The Interstellar Medium.


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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

From THE SONGS OF DISTANT EARTH by Arthur C. Clarke (1985)

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

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

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

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

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

From HANDBOOK FOR SPACE PIONEERS by L. Stephen Wolfe and Roy L. Wysack (1977)

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.


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

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

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

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

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

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

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

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

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

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

[Note: the exhaust velocity, Ve, 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 V’ƒ = 2.3 c and Vƒ = 0.98 c. What that means for a rocket with a constant acceleration, in its reference frame, is that it starts with a thrust 10 times higher than what it finishes with. To slow down again, the mass-ratio must be squared – thus it becomes 102 = 100. Clearly the numbers rapidly go up as lightspeed is approached ever closer.

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

this can be solved for time quite simply as:

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

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

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

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

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

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

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

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

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

How does a GUT-drive change that picture? As the energy of the propellant is no longer coming from the propellant mass itself, the propellant can provide much more “specific impulse”, Isp, 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 γe and Ve are the propellant gamma-factor and its effective exhaust velocity respectively.

This modifies the Rocket Equation to:

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

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

which becomes:

For the 4.37 light year trip to Alpha Centauri at 50 gee and an 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…


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

From CHILDHOOD'S END by Arthur C. Clarke (1953)

Other Relativistic Effects


A common feature of fantasy tales about the mystical land of Fairie is that time is weird there. Typically the protagonists will stumble into the Fairy Dimension, stay for what seems to be a few days, return to our mundane reality, and be shocked to discover that while they were in Fairie a century or two elapsed at home. Nobody recognizes the protagonist, any of their small children have since died of old age, that sort of thing. TV Tropes calls it Year Outside, Hour Inside. Older readers will recognize the concept from Brigadoon. Slightly less older readers read about this in Andre Norton's Dread Companion and Here Abide Monsters.

Science fiction authors writing about relativistic starships take great delight in transposing this concept into a future key. Starship crews leave Terra on a relativistic round-trip that takes a few months subjective time, then the author can write chapters and chapters about the bizarre Terran cultural changes and the cultural shock experienced by the "Rip Van Winkle" starship travelers. James Nicoll calls it the The Urashima effect of NAFAL travel. One-way time travel into the future, yes-siree-bob!

Science fiction that uses this theme include The Forever War by Joe Haldeman, Time For The Stars by Robert Heinlein, A World Out Of Time by Larry Niven, The Pusher by John Varley and the movie Interstellar.

Note that in The Forever War, Joe Haldeman cleverly uses the cultural shock experienced by the relativistic army troops as a metaphor for the cultural shock experienced by the US soldiers returning from Vietnam. As a side note: yes, the troops in The Forever War travel faster-than-light by collapsar jump. But to safely enter a collapsar the starship must move at relativistic speeds.


The crew and passengers on a relativistic starship will notice a peculiar optical illusion. The view of the sky will be distorted both fore and aft by relativistic aberration.

The starship at rest will see all the stars in the galaxy in their normal positions. The yellow lines show where stars located 90° from the ship's nose (pointed straight up). The green lines are for stars at 60°, the blue for 120° and so on.

But once the starship reaches a velocity larger than about 25% the speed of light in a vacuum (v/c = 0.25), the stars in the ship's "sky" won't be in their proper positions. The sky will warp so the stars will start to crowd towards that point where the ship's nose is pointing.

The stars with real positions closest to 90° are distorted the most, the stars fore and aft are distorted to a lesser degree. The stars at angle yellow should appear at 90°, but they have been distorted so they look like they are 75° away from the nose. The blue angle stars should be at 120°, but they appear at 105°. The red and light blue angle stars are at slightly different positions.

At 50% lightspeed (v/c = 0.50), yellow angle stars that should be 120° away from the nose point will have their positions distorted so they will appear to be at 90° i.e., around the ship's equator.

At 99.99% lightspeed (v/c = 0.9999), violet angle stars that should be 175° from the nose (i.e., 5° away from the stern) are distorted so much they look like they are only 15° from the nose. Only the stars that are almost exactly aft will appear there, almost all the other stars will be crammed straight ahead.

This will make navigation a bit of a challenge.


Doppler shift will make the stars ahead look more blue, and the stars behind will appear more red. The effect isn't really noticeable until the starship gets above 10% c or so. The effect is strongest directly ahead and behind, fading in strength the closer you get to the starship's "celestial equator" (i.e., at 90° to the ship's line of flight).

In 1961 Ing E. Sänger did some calculations that he published in a paper entitled "Some Optical and Kinematical Effects in Interstellar Astronautics", which appeared in the Journal of the British Interplanetary Society. He was trying to figure out what the sky would actually look like to a traveler in a starship moving at relativistic velocities.

He did make a simplifying assumption: all stars are monochromatic yellow.

Relativistic doppler shift would make most of the stars ahead invisible because their yellow light had been doppler blue-shifted into ultraviolet and x-rays. Most of the stars to the rear are invisible because they had been doppler red-shifted into infrared and microwaves.

Around the celestial equator the stars would still be yellow, shading to violet toward the zenith (in the direction of flight) and shading to red toward nadir. A rainbow in other words.

He calculated the addition of aberration would cram the rainbow ring toward zenith, while simultaneously making it narrower. The starship would appear to be flying in the direction of a rainbow ring.

Sänger called it a Starbow.

In 1972 noted science fiction author Frederik Pohl was reading a current issue of Spaceflight (published by the British Interplanetary Society) and came across a popularization of Sänger starbow concept. Mr. Pohl was thunderstruck at what a fantastically vivid metaphor the starbow was. He simply had to use it in his next science fiction story.

Said story was started almost as soon has he had finished the article. Do you know how large crystals are grown? You start with a jar filled with a supersaturated solution of whatever chemical the crystal is made of. Then you drop in a tiny seed crystal. In the solution the seed crystal rapidly grows into a larger one, incorporating the chemical molecules floating in the solution.

In this case, Mr. Pohl mind was full of random facts and half-baked ideas that could be used in future stories (I am given to understand this is common among many authors). That was the functional equivalent of a supersaturated solution. And the starbow concept was the seed crystal. A couple of his more interesting random facts suddenly attached themselves to the seed crystal and the story rapidly grew. It was called The Gold at the Starbow's End.

The story was well received, but more importantly it popularized the starbow concept. It became a standard part of any science fiction story featuring relativistic starships. It even made an appearance in Star Trek: The Motion Picture in 1979.

Unfortunately in 1979 the story caught the attention of two science fiction fans named John M. McKinley and Paul Doherty. "Unfortunate" because they were also physicists at Oakland University in Rochester, Michigan. They were inspired to examine the starbow concept more closely, and even do some computer simulations.

And they killed it. According to their simulations the starbow does not exist.

They reported their party-pooping results in a paper called “In search of the 'starbow': The appearance of the starfield from a relativistic spaceship.(behind a paywall). As it turns out, stars do not emit only yellow monochromatic light. Instead they emit blackbody-like spectra and a distribution of temperatures. They integrated the transformed spectrum of a star, over the response function of the human eye. They also took into account relativistic beaming.

The computer simulations showed no starbow. You can see their disappointing images here.

McKinley and Doherty were apologetic about it, they didn't want to destroy such a memorable image. But physicists have to deal with reality, not fantasy.

Be that as it may there are still science fiction stories using the starbow because the word has not gotten around everywhere yet.


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

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

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

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

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

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

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

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

Table 17.5 Wavelength of 5000 Angstrom Laser Light Communication Signals
Received by a Relativistic Starship
Starship Velocity
Redshifted Signal
Starship Receding
Blueshifted Signal
Starship Approaching
0%c5000 (green)5000 (green)
10%c5500 (green)4500 (blue)
50%c8500 (Near Infared)2900 (Ultraviolet B)
90%c22,000 (Near Infared)1150 (Ultraviolet C)
99%c70,500 (Mid Infrared)355 (Extreme Ultraviolet)
99.9%c223,500 (Mid Infrared)110.0 (Extreme Ultraviolet)
99.99%c707,000 (Far Infrared)35.5 (Soft X-ray)
99.999%c2,235,000 (Far Infrared)11.0 (Soft X-ray)
99.9999%c7,070,000 (Far Infrared)3.55 (Soft X-ray)
99.99999%c22,350,000 (Microwave)1.10 (Hard X-ray)

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

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

From THE GOLD AT THE STARBOW'S END by Frederik Pohl (1972)

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

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

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

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

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

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

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

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

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

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

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

From LOOKING FOR THE STARBOW by Frederik Pohl (1980)

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

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

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

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

From TAU ZERO by Poul Anderson (1970)

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.)


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)

Writers of science fiction prose noticed the difference between interplanetary flight and interstellar flight earlier than anyone. Various fictional methods of faster-than-light (FTL) were invented in the 1930s, John Campbell even inventing the term ‘warp drive’. Asimov’s Galactic Empire is only facilitated by FTL ‘jump-drives’. Slower than light interstellar travel made an appearance in Goddard and Tsiolkovsky’s writings in the form of ‘generation ships’, usually called ‘worldships’ now.

As far as I know, the first engineer to look at the very basic physics — quantitative calculations — of relativistic interstellar flight was Robert Esnault-Pelterie; he made relativistic calculations before 1920 that were published in his book L’Astronautique (1930). The first derivation of the relativistic rocket equation occurs in Esnault-Pelterie’s writings. This was long before Ackeret (J. Ackeret, “Zur Theorie der Raketen,” Helvetica Physica Acta 19, p.103, 1946). The classical mass ratio rocket equation of Tsiolkovsky showed the difficulty of space travel. The relativistic rocket equation showed that interstellar flight was even more difficult.

Eugen Sänger, who had been interested in interstellar flight in the 1930s, addressed the interstellar mass ratio problem in 1953 with a paper on photon rockets, “Zur Theorie der Photonenraketen” (Vortrag auf dem 4. Internationalen Astronautischen Kongreß in Zürich 1953). Sänger, more than almost anyone before him, studied the hard physics of antimatter rockets and relativistic rocket mechanics. Using the most energetic energy source, antimatter, would require tons of it in a conventional rocket. There was sore need of a better method.


Robert W Bussard was a rangy man who looked like he walked the halls of power. I had dinner with him at a San Francisco section of the American Institute of Aeronautics and Astronautics meeting in 1979. We had invited Poul Anderson, author of Tau Zero; Anderson and Bussard had never met. Over dinner Bussard told me he started working on nuclear propulsion at Los Alamos in 1955, and that he and R. DeLauer wrote the first monograph on atomic powered rockets in 1959 [1]. He also said he had been looking at work at Lawrence Radiation Laboratory in 1959.

Bussard told me he had always been interested in interstellar flight. One day at breakfast at Los Alamos he got a tortilla rolled up with scrambled egg in it. That cylinder made him think of a fusion ram starship! I have to wonder if that story is true, for had he been looking at Livermore’s lab papers he probably saw Project Pluto, the nuclear powered atmospheric ramjet.

Bussard sat down in 1959 and wrote the paper “Galactic matter and interstellar flight,” published in Astronautica Acta in 1960. This paper is thoroughly technical; Bussard summarizes Ackeret, Sänger and Les Shepherd’s studies of interstellar flight [2]. Sänger had shown that even using antimatter one still had a mass ratio problem with a conventional rocket. Bussard then presents an amazing new concept that solved the mass ratio problem [3]. He notes that one can scoop interstellar hydrogen and fuse it to produce a propulsion system.

The treatment is rigorously special relativistic; using conservation of energy and momentum he derives the equations of motion of an interstellar ramjet. He accounts for the energy production and propulsion efficiency of the vehicle in general terms. He uses the most energetic fusion mechanism, the proton-proton fusion reaction which converts .0071 of the rest mass of collected protons to energy. Bussard derives the property that the ramjet will need to be boosted to an initial speed.

Bussard discusses the engineering physics problems; the difficulty of using the p-p chain is enormous. He notes that interstellar hydrogen can be unevenly distributed, there being rich and rarefied regions. He gives a simplified model for scooping and sometimes it is missed that he mentions magnetic fields as a ‘collector’. Bussard also notes both radiation losses and radiation hazards during the operation of the ramjet.


The Bussard Ramjet got a boost in 1963 when Carl Sagan noted that there was a solution to the mass ratio problem for interstellar flight [4]. Sagan summarized this paper in Intelligent Life in the Universe in 1966 [5], probably the best popularization of the Ramjet. Sagan also noted that ships accelerating at one gravity could circumnavigate the universe, ship proper time, in about 50 years. He references Sänger in the paper version [4] and the calculation of the mechanics of a 1g starship. As far as I know, the 1957 paper of Sänger [6] is the first exposition of a constant acceleration starship and the consequences of time dilation when extreme interstellar distances are traveled. Bussard mentioned, very briefly, a magnetic field as a scoop, but Sagan describes such a collector in a more elaborated though qualitative way.


John Ford Fishback published his MIT bachelor’s thesis in Astronautica Acta in 1969 [7]; this was supervised by Philip Morrison. Morrison and Cocconi were the fathers of radio SETI. Morrison seems to have taken an interest in Sagan’s mention of Bussard’s ramjet — I’m not sure if it was Morrison or Fishback who suggested the study. The paper is a remarkable marshalling of electrodynamics, charged particle motion, plasma physics, the physics of materials and special relativity.

Fishback constructs a model for the magnetic scoop field taking into account the fraction of hydrogen ingested and reflected. Using conservation laws, he derives the most detailed equations of motion accounting for mass and radiation losses that had been published anywhere. In the scooping process, Fishback examines the statistical distribution of gas in the galaxy and derives a relativistic expression for ship proper acceleration with ‘drag’. An important consequence, expressed for the first time, is the mechanical stress on the scoop field magnets. He derived an upper limit on the maximum Lorentz factor that can be obtained as a ramjet accelerates at 1 g for a long time due to stress on the source of the scoop field.

[For more on Fishback, see Al’s John Ford Fishback and the Leonora Christine from 2016, with further thoughts by Greg Benford.]


In 1971 [8] and 1973 [9] Tony Martin reviewed Fishback’s paper, making useful clarifying observations. Martin provides details of calculation that Fishback leaves to the reader on the relation of the fraction of particles that are magnetically confined to the reactor intake as a function of the confining field and the starship’s speed. In his second paper, Martin corrects a numerical error by Fishback showing that the cutoff speed due to the stress properties of the magnetic source is 10 times larger than was calculated. Martin also gives a nice calculation of the size of the magnetic scoop field. Fishback and Martin’s papers account for the ‘drag’ due to reflected particles; this result seems unknown to later critics of the ramjet.


I met Dan Whitmire in 1973, when we were both working on doctorates in physics at the University of Texas at Austin. Dan and I were talking about interstellar flight one day and I showed him Bussard’s paper. Dan was in the nuclear physics group at Texas and took an immediate interest in the problem with proton-proton fusion as had been pointed out by Bussard and Martin. Then he came up with an ingenious solution: Carry carbon on board the starship and use it as a catalyst to implement the CNO fusion cycle [10]. The CNO process is 1018 times faster than the PP chain at the fusion reactor temperatures under consideration. This reduces the fusion reactor size to 10s (and more) of meters in dimension. Since carbon cycles in the process, in theory one would only need to carry a small amount; however it is not clear how under dynamic conditions one would recover all the catalysis needed.

Later Developments

The above are the core studies of the interstellar ramjet. Hybrid methods occurred to several researchers. Alan Bond [11] proposed a vehicle that carried a separate energy source yet scooped-up interstellar hydrogen not as fuel but simply as reaction mass, this is known as the augmented interstellar ramjet. Conley Powell [12] presented a refined analysis of this system. The author [13] presented a study using antimatter added to the scooped reaction mass for propulsion as an augmented method. Relevant to the augmented ramjet is antimatter combined with matter for propulsion as studied by Forward and Kammash [14, 15].

T. A. Heppenheimer published a paper in the Journal of the British Interplanetary Society [16] noting the problems with the p-p chain for fusion without citing Dan Whitmire’s solution. Heppenheimer notes radiation losses but does not cite Whitmire and Fishback, who addressed the problems of bremsstrahlung and synchrotron radiation in the reactor and the scoop field.

Matloff and Fennelly [17] have interesting papers on charged particle scooping with superconducting coils. Cassenti looked at several modifications and aspects of the ramjet [18].

Recently Semay and Silvestre-Brac [21, 22] re-derived the equations of motion of the interstellar ramjet, first done by Bussard and Fishback. They find some new extensions with solutions of the relativistic equations for distance and time.

Dan Whitmire and the author [23] removed the fusion reactor by taking the energy source out of the ship and placing it in the Solar System. If one scoops hydrogen but energizes it with a laser system it is possible to make a ramjet that is smaller and less massive. Such a system probably has a limited range similar to laser pushed sails.

An excellent survey of interstellar ramjets and hybrid ram systems can be found in the books by Mallove and Matloff [24] and a recent monograph by Matloff [25], see these books and the references listed in them. See also Ian Crawford’s paper [26].

The Interstellar Ramjet in Science Fiction

It seems the Bussard Ramjet first appeared in a Larry Niven short story called “The Warriors” (1966). Later Niven used the Ramjet in his other fiction, inventing, I think, the term Ram Scoop. However I think the best known use of the Ramjet is Poul Anderson’s Tau Zero [26]. The core story in Tau Zero is not the Interstellar Ramjet but the constant acceleration circumnavigate-the-universe calculation first done by Eugen Sänger.

My guess is that Anderson only saw Carl Sagan’s exposition on this in Intelligent Life in the Universe. The Greek letter ‘Tau’ was introduced by Hermann Minkowski in 1908; it is the time measured by the travelers in the starship Leonora Christine, while the time measured by people back on earth is t. Special relativistic time dilation leads to (ship time)/(Earth Time) going to almost zero. Accelerate at one g for 50 years and one covers a distance of about 93 billion light years that is roughly the size of the universe.

The Bussard Ramjet Leonora Christine sets out for Beta Virginis, approximately 36 light years away. A mid-trip mishap robs the ship of its ability to slow down. Repairs are impossible unless they shut down the ramjet, but if the crew did that, they would instantly be exposed to lethal radiation. There’s no choice but to keep accelerating and hope that the ship will eventually encounter a region in the intergalactic depths with a sufficiently hard vacuum so that the ramjet could be safely shut down. They do find such a region and repair the ship.

Anderson then introduces the mother of all twists. The Leonora Christine has accelerated for so long that the crew discover relative to the universe a cosmological amount of time has elapsed. The universe is not ‘open’ but fits the re-collapse model, it is going for the big crunch. I know of no other science fiction novel with more extreme problem solving that this hard SF story.

Anderson’s cosmology for Tau Zero seems to come totally from George Gamow [28]. Gamow and his students did pioneering work on early time cosmology, an elaboration of earlier work done by Georges Lemaître. When Poul Anderson wrote the novel, he may have been aware that Big Bang cosmology had evolved beyond Gamow’s models …. However, having his starship eventually orbit the ‘Cosmic Egg’ or Ylem was a solution to the crew’s problem. Alas, even in Gamow’s cosmology the ‘Ylem’ is the universe, so no way to ‘orbit’ it. Poetic license for the sake of a Ripping Yarn! (An intersecting exercise is to see what the trajectory of the Leonora Christine’s plot problem is in current accelerating universe cosmology.)

After Niven and Anderson, the Bussard Ramjet became common currency in science fiction, although it has faded somewhat in recent times. Recently a fusion ramjet, SunSeeker, appears as an integral part of the Bowl of Heaven series by Greg Benford and Larry Niven [29].

Final Thoughts

There seems to be a thread of pessimism about the Bussard Ramjet centered around drag on the ramjet due to interaction with the scoop field. This is an issue that Fishback deals with in his analysis; he shows one cannot just use a dipole magnetic field. A more complex collector field is needed. Fishback and Martin do show there is a fundamental physics limitation. Even using the strongest material theoretically possible, there is an upper limit to a mission Lorentz factor, probably equal to 10,000. Above this one will bust the scoop coil due to magnetic stress. The cosmological peril of the Leonora Christine depicted in Tau Zero is not physically possible.

The main show stopper for the ramjet is the engineering. There is no way with foreseeable technology to build all the components of an interstellar ram scoop starship. Several aspects should be revisited. (1) The source of the magnetic scoop field, Fishback [7] derived one, Cassenti elaborated another [20]; (2) the fusion reactor — the aneutronic fusion concept is direct conversion of fusion to energy [30]; (3) hybrid systems, especially laser-boosted ramjets.

Since basic physics does not rule a ramjet out, it is possible that an advanced civilization might build one. Freeman Dyson [31] pointed out many times that what we could not do might be done by some advanced civilization as long as the fundamental physics allows it. An interesting consequence of this is that interstellar ramjets may have been built and might have observable properties. Doppler-boosted waste heat from such ships might be observable. Plowing into HII regions in the galaxy, a starship’s magnetic scoop field might produce a bow-shock which could be observable. Isolated objects in this galaxy with Lorentz factors in the thousands would be unusual and if they are accelerating even more unusual.

The idea of picking up your fuel along the way in your journey across interstellar space may be the optimal solution to the mass ratio problem in interstellar flight. The interstellar ramjet warrants more technical study.


Because Robert Bussard sketched a ramjet with a physical ‘funnel’ …all the many illustrations I have seen since seem to have some kind of ‘cow catcher’ on the front. Though it is reasonable that such a structure is the source of an electromagnetic device, I think it more likely that the ‘scoop’ field will be produced by a magnetic configuration that directs the incoming stream into the mouth of the reactor without any extra funnel-like forward structure. Here is a rough schematic done for me by artist Doug Potter. There is a ‘bulb’ representing the magnetic source field (maybe the parabolic magnetic field calculated by Fishback), a reactor section and an exhaust. Not a very elegant representation of the ramjet but a suggested configuration.


1. Bussard, R. W., and R. D. DeLauer. Nuclear Rocket Propulsion, McGraw-Hill, New York, 1958

2. L. R. Shepherd, “Interstellar Flight,” Journal of the British Interplanetary Society, 11, 4, July 1952

3. R.W. Bussard, “Galactic matter and interstellar flight,” Astronautica Acta 6 (1960) 179–195

4. C. Sagan, “Direct contact among galactic civilizations by relativistic interstellar spaceflight,” Planet. Space Sci. 11 (1963) 485–498

5. Sagan, Carl; Shklovskii, I. S. (1966). Intelligent Life in the Universe. Random House

6. Sänger, E., “Zur Flugmechanik der Photonenraketen.” Astronautica Acta 3 (1957), S. 89-99

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

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

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

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

11. Bond, Alan, “An Analysis of the Potential Performance of the Ram Augmented Interstellar Rocket,” Journal of the British Interplanetary Society, Vol. 27, p.674,1974

12. Powell, Conley, “Flight Dynamics of the Ram-Augmented Interstellar Rocket,” Journal of the British Interplanetary Society, Vol. 28, p.553, 1975

13. Jackson, A. A., “Some Considerations on the Antimatter and Fusion Ram Augmented Interstellar Rocket,” Journal of the British Interplanetary Society, v33, 117, 1980.

14. R.L. Forward, “Antimatter Propulsion”, Journal of the British Interplanetary Society, 35, pp. 391–395, 1982

15. Kammash, T., and Galbraith, D. L., “Antimatter-Driven-Fusion Propulsion for Solar System Exploration,” Journal of Propulsion and Power, Vol. 8, No. 3, 1992, pp. 644 – 649

16. Heppenheimer, T.A. (1978). “On the Infeasibility of Interstellar Ramjets”. Journal of the British Interplanetary Society 31: 222

17. Matloff, G.L., and A.J. Fennelly, “A Superconducting Ion Scoop and Its Application to Interstellar Flight”, Journal of the British Interplanetary Society, Vol. 27, pp. 663-673, 1974

18. Matloff, G.L., and A.J. Fennelly, “Interstellar Applications and Limitations of Several Electrostatic/Electromagnetic Ion Collection Techniques”, Journal of the British Interplanetary Society, Vol. 30, pp. 213-222, 1980

19. Matloff, G.L., and A.J. Fennelly , B. N , “Design Considerations for the Interstellar Ramjet,” 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2008

20. Cassenti, B. N , “The Interstellar Ramjet,” 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2004

21. Claude Semay and Bernard Silvestre-Brac, “The equation of motion of an interstellar Bussard ramjet,” European Journal of Physics 26(1):75, 2004

22. Claude Semay and Bernard Silvestre-Brac, “Equation of motion of an interstellar Bussard ramjet with radiation loss,” Acta Astronautica 61(10):817-822, 2007

23. Whitmire, D. and Jackson, A, “Laser Powered Interstellar Ramjet,” Journal of the British Interplanetary Society Vol. 30pp. 223-226, 1977

24. Mallove, E. F., and G.L. Matloff, The Starflight Handbook, Wiley, New York, 1989

25. Matloff, G., Deep-Space Probes, Praxis Publishing, Chichester, UK, 2000

26. Ian A Crawford, “Direct Exoplanet Investigation Using Interstellar Space Probes.” In Handbook of Exoplanets Springer 2017

27. Anderson, Poul. Tau Zero. New York: Lancer Books (1970)

28. George Gamow, The Creation of the Universe (1952)

29. Benford, G. and Niven, L., Bowl of Heaven series, Macmillan.

30. Benford, G., Private communication.

31. Dyson, F. J., “The search for extraterrestrial technology,” in Marshak, R.E. (ed), Perspectives in Modern Physics, Interscience Publishers, New York, pp. 641–655

From THE INTERSTELLAR RAMJET AT 60 by A. A. Jackson (2020)

Ramjet Problems

Of course not everything is rainbows and unicorns, there are a few 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. There is an equation here but it depends upon other assumptions about the minimum mass-collection rate.

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.

Ramjet Show Stopper

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?


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

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

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


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

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

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

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

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

Robert Zubrin (1994)

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

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

Now let us look at the "engineering details."

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

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

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

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

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

From BORDERLANDS OF SCIENCE by Charles Sheffield (1999)

Ramjet Show Starter

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.

Then Daniel Whitmire found that you could avoid the problems of trying to ignite a proton-proton fusion reaction by carrying a supply of carbon and using it with the protons scooped up by the ramjet to ignite a catalytic CNO cycle. You need carbon to start off the reaction, but you get it all back at the end of the reaction.

Bussard Scramjet

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.

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thread Bussard Ramjet woes on (2001)
Toroidal-Field Ramscoop

The information here is mostly from Deep Space Probes: To the Outer Solar System and Beyond by Dr. Gregory Matloff.

In the late 1990s Brice Cassenti tried to salvage the Bussard Ramjet concept.

The good news is that he managed to drastically reduce the drag.

The bad news is it uses an array of flimsy superconducting wires in front of the spacecraft. Which means only accelerations on the order of 0.04g are possible. That is about 50 snails worth of acceleration, which is pathetic.

Earlier attempts to stop drag used electrostatic fields for the scoop. But the Debye-Hückel screening effect raised its ugly head. The interstellar ions are charged (otherwise they wouldn't be ions), so are attracted to the electrostatic scoop. The trouble is the charge on the ions is also an electrostatic field. The huge cloud of attracted ions that gather in front of the scoop make a huge electrostatic field of their own (of opposite polarity), perfectly positioned to totally mask the scoop field. This screening ensures that ions further away do not even see the scoop field, forget about them actually being scooped up.

Others tried to eliminate the drag with standard Bussard electromagnetic fields by playing around with the geometry. Alas, most of the designs were better at reflecting away the ions instead of gathering them. Talk about counter-productive.

Cassenti's design was electromagnetic not electrostatic. Thus avoiding the heartbreak of Debye-Hückel screening.

And Cassenti's design did not affect the ions until they are actually inside the scoop, so there would be little or no ion reflection.

The scoop is a torus (donut shape) with a superconducting wire wound around the circumference. Depending upon the current direction and ion charge, an ion entering the torus will either be deflected to the center or the circumference. The idea is to deflect to center, so eventually they will enter the engine intake. Deflect to the cirumference would also be counter-productive.

So an ion in the interstellar media is just sitting around, minding its own business. Here comes the ramjet starship traveling at a sizable fraction of c. As the ion passes through the torus, it gets an electromagnetic shove to the center. As the ion passes further on, it gets closer and closer to the thrust axis. Using this information one can calculate the point where the ion hits the axis. This is where you put the engine fuel intake.

Cassenti analyzed a sample design of a ramjet with a scoop radius of 400 kilometers (800 km diameter), a supercurrent of 3×105 amps, twelve wire turns, traveling through the interstellar medium at 0.1 c. Using some hideous equations that I won't scare you with, Cassenti calculated that an ion entering the torus 200 kilometers from torus center would travel about 170 kilometers parallel to the thrust axis before it moved laterally enough to hit it.

Translation: the scoop torus will have to be held 170 kilometers in front of the engine fuel intake or the ions will miss the intake.

Since every gram counts and the freaking scoop is too huge to fit between New York and Cleveland the wire structure will have to be dangerously flimsy. Cassenti's design uses rotation produced centripetal force and minimal supporting structure, but still would collapse if the acceleration got above a measly 0.04 g.

His design had a featherweight mass of a few hundred thousand kilograms, making it very un-dense. This is about the mass of the International Space Station. But the scoop is more than seven thousand times as wide. Same mass but bigger means the torus is less dense than the ISS. And the station wasn't that dense to start with. Unfortunately very low density usually means flimsy, weak, and vulnerable to strong acceleration.

Cassenti looked into supporting the scoop with ion drive thrusters and/or laser beam radiation pressure (where part of the support structure is composed of beams of radiation with zero or almost zero mass), but one rapidly gets to the point of diminishing returns with that sort of thing.

A helpful reader named Yoel Mizrahi (יואל מזרחי) contacted me explaining that I had the design incorrect. Not surprising considering the sparse details I had. Mr. Mizrahi said Dr. Cassenti's design did not use fusion for propulsion. Instead it utilized beamed power. A large power plant back home at Sol energized a free-electron x-ray laser whose beam was sent to the light-years distant toroidal-field ramscoop. But instead of the laser beam pushing a laser sail, it is turned into electricity and used to accelerate the hydrogen scooped up.

So it is like a beam-powered RAIR with a no-drag scoop. The advantage of the toroidal scoop is that a conventional RAIR requires mass for fusion fuel and mass for the fusion reactor. In addition the conventional RAIR scoop suffers from drag. Beamed power is a good way to drastically reduced the mass of the propulsion system. The main drawback is that the starship is at the mercy of whoever back home controls the x-ray laser.

Advantages of toroidal scoop: does not waste mass on carrying propellant or energy. And the scoop is drag free.

Disadvantage: the acceleration of a toroidal scoop will be limited to about 0.4 m/s2 (0.04 g). The scoop does not gather a lot of hydrogen propellant due to the thinness of the interstellar medium, and due to the relatively small scoop radius. The exhaust consists of only light ions. More importantly, if the acceleration climbs above 0.4 m/s2 the flimsy scoop will buckle and collapse.

Technical challenges: designing a high-efficiency low mass x-ray power system. Figuring out how to use electricity to efficiently accelerate the scooped propellant.

Dr. Cassenti is going to send a copy of the scientific paper to Mr. Mizrahi, so stay tuned for more details. In the meanwhile, Mr. Mizrahi gave me these images:

I made some quick images with Blender 3D to figure out how the rigging worked:

Schattschneider Ramjet

The Bussard ramjet is an idea whose attractions do not fade, especially given stunning science fiction treatments like Poul Anderson’s novel Tau Zero. Not long ago I heard from Peter Schattschneider, a physicist and writer who has been exploring the Bussard concept in a soon to be published novel. In the article below, Dr. Schattschneider explains the complications involved in designing a realistic ramjet for his novel, with an interesting nod to a follow-up piece I’ll publish as soon as it is available on the work of John Ford Fishback, whose ideas on magnetic field configurations we have discussed in these pages before.

The author is professor emeritus in solid state physics at Technische Universität Wien, but he has also worked for a private engineering company as well as the French CNRS, and has been director of the Vienna University Service Center for Electron Microscopy. With more than 300 research articles in peer-reviewed journals and several monographs on electron-matter interaction, Dr. Schattschneider’s current research focuses on electron vortex beams, which are exotic probes for solid state spectroscopy. He tells me that his interest in physics emerged from an early fascination with science fiction, leading to the publication of several SF novels in German and many short stories in SF anthologies, some of them translated into English and French. As we see below, so-called ‘hard’ science fiction, scrupulously faithful to physics, demands attention to detail while pushing into fruitful speculation about future discovery.

When the news about the BLC1 signal from Proxima Centauri came in, I was just finishing a scientific novel about an expedition to our neighbour star. Good news, I thought – the hype would spur interest in space travel. Disappointment set in immediately: Should the signal turn out to be real, this kind of science fiction would land in the dustbin.

The space ship in the novel is a Bussard ramjet. Collecting interstellar hydrogen with some kind of electrostatic or magnetic funnel that would operate like a giant vacuum cleaner is a great idea promoted by Robert W. Bussard in 1960 [1]. Interstellar protons (and some other stuff) enter the funnel at the ship‘s speed without further ado. Fusion to helium will not pose a problem in a century or so (ITER is almost working), conversion of the energy gain into thrust would work as in existing thrusters, and there you go!

Some order-of-magnitude calculations show that it isn‘t as simple as that. But more on that later. Let us first look at the more mundane problems occuring on a journey to our neighbour. The values given below were taken from my upcoming The EXODUS Incident [2], calculated for a ship mass of 1500 tons, an efficiency of 85% of the fusion energy going into thrust, an interstellar medium of density 1 hydrogen atom/cm3, completely ionized by means of electron strippers.

(ed note: mathematical details can be found here)

On the Way

Like existing ramjets the Bussard ramjet is an assisted take-off engine. In order to harvest fuel it needs a take-off speed, here 42 km/s, the escape velocity from the solar system. The faster a Bussard ramjet goes, the higher is the thrust, which means that one cannot assume a constant acceleration but must solve the dynamic rocket equation. The following table shows acceleration, speed and duration of the journey for different scoop radii.

At the midway point, the thrust is inverted to slow the ship down for arrival. To achieve an acceleration of the order of 1 g (as for instance in Poul Anderson’s celebrated novel Tau Zero [3]), the fusion drive must produce a thrust of 18 million Newton, about half the thrust of the Saturn-V. That doesn’t seem tremendous, but a short calculation reveals that one needs a scoop radius of about 3500 km to harvest enough fuel because the density of the interstellar medium is so low. Realizing magnetic or electric fields of this dimension is hardly imaginable, even for an advanced technology.

A perhaps more realistic funnel entrance of 200 km results in a time of flight of almost 500 years. Such a scenario would call for a generation starship. I thought that an acceleration of 0.1 g was perhaps a good compromise, avoiding both technical and social fantasizing. It stipulates a scoop radius of 1000 km, still enormous, but let us play the “what-if“ game: The journey would last 17.3 years, quite reasonable with future cryo-hibernation. The acceleration increases slowly, reaching a maximum of 0.1 g after 4 years. Interestingly, after that the acceleration decreases, although the speed and therefore the proton influx increases. This is because the relativistic mass of the ship increases with speed.

Fusion Drive

It has been pointed out by several authors that the “standard“ operation of a fusion reactor, burning Deuterium 2D into Helium 3He cannot work because the amount of 2D in interstellar space is too low. The proton-proton burning that would render p+p → 2D for the 2D → 3He reaction is 24 orders of magnitude (!) slower.

The interstellar ramjet seemed impossible until in 1975 Daniel Whitmire [4] proposed the Bethe-Weizsäcker or CNO cycle that operates in hot stars. Here, carbon, nitrogen and oxygen serve as catalysts. The reaction is fast enough for thrust production. The drawback is that it needs a very high core temperature of the plasma of several hundred million Kelvin. Reaction kinetics, cross sections and other gadgets stipulate a plasma volume of at least 6000 m3 which makes a spherical chamber of 11 m radius (for design aficionados a torus or – who knows? – a linear chamber of the same order of magnitude).

At this point, it should be noted that the results shown above were obtained without taking account of many limiting conditions (radiation losses, efficiency of the fusion process, drag, etc.) The numerical values are at best accurate to the first decimal. They should be understood as optimistic estimates, and not as input for the engineer.

Waste Heat

Radioactive high-energy by-products of the fusion process are blocked by a massive wall between the engine and the habitable section, made up of heavy elements. This is not the biggest problem because we already handle it in the experimental ITER design. The main problem is waste heat. The reactor produces 0.3 million GW. Assuming an efficiency of 85% going into thrust, the waste energy is still 47,000 GW in the form of neutrinos, high energy particles and thermal radiation. The habitable section should be at a considerable distance from the engine in order not to roast the crew. An optimistic estimate renders a distance of about 800 m, with several stacks of cooling fins in between. The surface temperature of the sternside hull would be at a comfortable 20-60 degrees Celsius. Without the shields, the hull would receive waste heat at a rate of 6 GW/m2, 5 million times more than the solar constant on earth.

Radiation shielding

An important aspect of the Bussard ramjet design is shielding from cosmic rays. At the maximum speed of 60% of light speed, interstellar hydrogen hits the bow with a kinetic energy of 200 MeV, dangerous for the crew. A.C. Clarke has proposed a protecting ice sheet at the bow of a starship in his novel The Songs of Distant Earth [5]. A similar solution is also known from modern proton cancer therapy. The penetration depth of such protons in tissue (or water, for that matter) is 26 cm. So it suffices to put a 26 cm thick water tank at the bow.

Artificial gravity

It is known that long periods of zero gravity are disastrous to the human body. It is therefore advised to have the ship rotate in order to create artificial gravity. In such an environment there are unusual phenomena, e.g. a different barometric height equation, or atmospheric turbulence caused by the Coriolis forces. Throwing an object in a rotating space ship has surprising consequences, exemplified in Fig. 1. Funny speculations about exquisite sporting activities are allowed.

Fig. 1: Freely falling objects in a rotating cylinder, thrown in different directions with the same starting speed. In this example, drawn from my novel, the cylinder has a radius of 45 m, rotating such that the artificial gravity on the inner hull is 0.3 g. The object is thrown with 40 km/h in different directions. Seen by an observer at rest, the cylinder rotates counterclockwise.


The central question for scooping hydrogen is this: Which electric or magnetic field configuration allows us to collect a sufficient amount of interstellar hydrogen? There are solutions for manipulating charged particles: colliders use magnetic quadrupoles to keep the beam on track. The symmetry of the problem stipulates a cylindrical field configuration, such as ring coils or round electrostatic or magnetic lenses which are routinely used in electron microscopy. Such lenses are annular ferromagnetic yokes with a round bore hole of the order of a millimeter. They focus an incoming electron beam from a diameter of some microns to a nanometer spot.

Scaling the numbers up, one could dream of collecting incoming protons over tens of kilometers into a spot of less than 10 meters, good enough as input to a fusion chamber. This task is a formidable technological challenge. Anyway, it is prohibitive by the mere question of mass. Apart from that, one is still far away from the needed scoop radius of 1000 km.

The next best idea relates to the earth’s magnetic dipole field. It is known that charged particles follow the field lines over long distances, for instance causing aurora phenomena close to earth’s magnetic poles. So it seems that a simple ring coil producing a magnetic dipole is a promising device. Let’s have a closer look at the physics. In a magnetic field, charged particles obey the Lorentz force. Calculating the paths of the interstellar protons is then a simple matter of plugging the field into the force equation. The result for a dipole field is shown in Fig. 2.

An important fact is seen here: the scoop radius is smaller than the coil radius. It turns out that it diminishes further when the starting point of the protons is set at higher z values. This starting point is defined where the coil field is as low as the galactic magnetic field (~1 nT). Taking a maximum field of a few Tesla at the origin and the 1/(z/R)3 decay of the dipole field, where R is the coil radius (10 m in the example), the charged particles begin to sense the scooping field at a distance of 10 km. The scoop radius at this distance is a ridiculously small – 2 cm. All particles outside this radius are deflected, producing drag.

That said, loop coils are hopelessly inefficient for hydrogen scooping, but they are ideal braking devices for future deep space probes, and interestingly they may also serve as protection shields against cosmic radiation. On Proxima b, strong flares of the star create particle showers, largely protons of 10 to 50 MeV energy. A loop coil protects the crew as shown in Fig. 3.

After all this paraphernalia the central question remains: Can a sufficient amount of hydrogen be harvested? From the above it seems that magnetic dipole fields, or even a superposition of several dipole fields, cannot do the job. Surprisingly, this is not quite true. For it turns out that an arcane article from 1969 by a certain John Ford Fishback [6] gives us hope, but this is another story and will be narrated at a later time.


1. Robert W. Bussard: Galactic Matter and Interstellar Flight. Astronautica Acta 6 (1960), 1-14.

2. P. Schattschneider: The EXODUS Incident – A Scientific Novel. Springer Nature, Science and Fiction Series. May 2021, DOI: 10.1007/978-3-030-70019-5.

3. Poul Anderson: Tau Zero (1970).

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

5. Arthur C. Clarke: Songs of distant Earth (1986).

6. John F. Fishback: Relativistic Interstellar Space Flight. Astronautica Acta 15 (1969), 25-35.

From CRAFTING THE BUSSARD RAMJET by Peter Schattschneider (2021)

Building a Bussard ramjet isn’t easy, but the idea has a life of its own and continues to be discussed in the technical literature, in addition to its long history in science fiction. Peter Schattschneider, who explored the concept in Crafting the Bussard Ramjet last February, has just published an SF novel of his own called The EXODUS Incident (Springer, 2021), where the Bussard concept plays a key role. But given the huge technical problems of such a craft, can one ever be engineered? In this second part of his analysis, Dr. Schattschneider digs into the question of hydrogen harvesting and the magnetic fields the ramjet would demand. The little known work of John Ford Fishback offers a unique approach, one that the author has recently explored with Centauri Dreams regular A. A. Jackson in a paper for Acta Astronautica. The essay below explains Fishback’s ideas and the options they offer in the analysis of this extraordinary propulsion concept. The author is professor emeritus in solid state physics at Technische Universität Wien, but he has also worked for a private engineering company as well as the French CNRS, and has been director of the Vienna University Service Center for Electron Microscopy.

As I mentioned in a recent contribution to Centauri Dreams, the BLC1 signal that flooded the press in January motivated me to check the science of a novel that I was finishing at the time – an interstellar expedition to Proxima Centauri on board a Bussard ramjet. Robert W. Bussard’s ingenious interstellar ramjet concept [1], published in 1960, inspired a generation of science fiction authors; the most celebrated is probably Poul Anderson with the novel Tau Zero [2]. The plot is supposedly based on an article by Carl Sagan [3] who references an early publication of Eugen Sänger where it is stated that due to time dilation and constant acceleration at 1 g „[…] the human lifespan would be sufficient to circumnavigate an entire static universe“ [4].

Bussard suggested using magnetic fields to scoop interstellar hydrogen as a fuel for a fusion reactor, but he did not discuss a particular field configuration. He left the supposedly simple problem to others as Newton did with the 3-body problem, or Fermat with his celebrated theorem. Humankind had to wait 225 years for an analytic solution of Newton‘s problem, and 350 years for Fermat’s. It took only 9 years for John Ford Fishback to propose a physically sound solution for the magnetic ramjet [5].

The paper is elusive and demanding. This might explain why adepts of interstellar flight are still discussing ramjets with who-knows-how-working superconducting coils that generate magnetic scoop fields reaching hundreds or thousands of kilometres out into space. Alas, it is much more technically complicated.

Fishback’s solution is amazingly simple. He starts from the well known fact that charged particles spiral along magnetic field lines. So, the task is to design a field the lines of which come together at the entrance of the fusion reactor. A magnetic dipole field as on Earth where all field lines focus on the poles would do the job. Indeed, the fast protons from the solar wind are guided towards the poles along the field lines, creating auroras. But they are trapped, bouncing between north and south, never reaching the magnetic poles. The reason is rather technical: Dipole fields change too rapidly along the path of a proton in order to keep it on track.

Fishback simply assumed a sufficiently slow field variation along the flight direction, Bz=B0/(1+ ε z) with a „very small“ ε. Everything else derives from there, in particular the parabolic shape of the magnetic field lines. Interestingly, throughout the text one looks in vain for field strengths, let alone a blueprint of the apparatus. The only hint to the visual appearance of the device is a drawing of a long, narrow paraboloid that would suck the protons into the fusion chamber. As a shortcut to what the author called the region dominated by the ramjet field I use here the term „Fishback solenoid“.

Fig. 1 is adapted from the original [5]. I added the coils that would create the appropriate field. Their distance along the axis indicates the decreasing current as the funnel widens. Protons come in from the right. Particles outside the scooping area As are rejected by the field. The mechanical support of the coils is indicated in blue. It constitutes a considerable portion of the ship’s mass, as we shall see below.

Fig. 1: Fishback solenoid with parabolic field lines. The current carrying coils are symbolized in red. The mechanical support is in blue. The strong fields exert hoop stress on the support that contributes considerably to the ship’s mass. Adapted from [5].

Searching for scientific publications that build upon Fishback’s proposal, Scopus renders 6 citations up to this date (April 2021). Some of them deal with the mechanical stress of the magnetic field, another aspect of Fishback’s paper that I discuss in the following, but as far as I could see the paraboloidal field was not studied in the 50 years since. This is surprising because normally authors continue research when they have a promising idea, and others jump on the subject, from which follow-up publications arise, but J. F. Fishback published only this one paper in his lifetime. [On Fishback and his tragic destiny, see John Ford Fishback and the Leonora Christine, by A. A. Jackson].

Solving the dynamic equation for protons in the Fishback field proves that the concept works. The particles are guided along the parabolic field lines toward the reactor as shown in the numerical simulation Fig. 2.

The reactor intake is centered at (r,z)=(0,0). In the ship’s rest frame the protons arrive from top – here with 56 % of light speed, the maximum speed of the EXODUS in my novel [8]. Some example trajectories are drawn. Protons spiral down the magnetic field lines as is known from earth’s magnetic field and enter the fusion chamber (red lines). The scooping is well visible. The reactor mouth has an assumed radius of 10 m. A closer look into the first 100 m (right figure) reveals an interesting detail: Only the first two trajectories enter the reactor. Protons travelling beyond the bold grey line are reflected before they reach the entrance, just as charged particles are bouncing back in the earth’s field before they reach the poles. From the Figure it is evident that at an axial length of 200 km of the Fishback solenoid the scoop radius is disappointingly low – only 2 km. Nevertheless, the compression factor (focussing ions from this radius to 10 m) of 1:40.000 is quite remarkable.

The adiabatic condition mentioned above allows a simple expression for the area from which protons can be collected. The outer rim of this area is indicated by the thick grey line in Fig. 2. The supraconducting coils of the solenoid should ideally be built following this paraboloid, as sketched in Fig. 1. Tuning the ring current density to

yields a result that approximates Fishback‘s field closely.

What does it mean in technical terms? Let me discuss an idealized example, having in mind Poul Anderson’s novel. The starship Leonora Christina accelerates at 1 g, imposing artificial earth gravity on the crew. Let us assume that the ship‘s mass is a moderate 1100 tons (slightly less than 3 International Space Stations). For 1 g acceleration on board, we need a peak thrust of ~11 million Newton, about 1/3 of the first stage of the Saturn V rocket. The ship must be launched with fuel on stock because the ramjet operates only beyond a given speed, often taken as 42 km/s, the escape velocity from the solar system. In the beginning, the thrust is low. It increases with the ship’s speed because the proton throughput increases, asymptotically approaching the peak thrust.

Assuming complete conversion of fusion energy into thrust, total ionisation of hydrogen atoms, and neglecting drag from deviation of protons in the magnetic field, at an interstellar density of 106 protons/m3, the „fuel“ collected over one square kilometer yields a peak thrust of 1,05 Newton, a good number for order-of-magnitude estimates. That makes a scooping area of ~10 million square km, which corresponds to an entrance radius of about 1800 km of the Fishback solenoid. From Fig. 2, it is straightforward to extrapolate the bold grey parabola to the necessary length of the funnel – one ends up with fantastic 160 million km, more than the distance earth – sun. (At this point it is perhaps worth mentioning that this contribution is a physicist’s treatise and not that of an engineer.)

Plugging the scooping area into the relativistic rocket equation tells us which peak acceleration is possible. The results are summarised in Table 1. For convenience, speed is given in units of the light speed, ß=v/c. Additionally, the specific momentum ßγ is given where

is the famous relativistic factor. (Note: The linear momentum of 1 kg of matter would be ßγ c.) Acceleration is in units of the earth gravity acceleration, g=9.81 m/s2.

Under continuous acceleration such a starship would pass Proxima Centauri after 2.3 years, arrive at the galactic center after 11 years, and at the Andromeda galaxy after less than 16 years. Obviously, this is not earth time but the time elapsed for the crew who profit from time dilation. There is one problem: the absurdly long Fishback solenoid. Even going down to a scooping radius of 18 km, the supraconducting coils would reach out 16,000 km into flight direction. In this case the flight to our neighbour star would last almost 300 years.

Fishback pointed out another problem of Bussard ramjets [5]. The magnetic field exerts strong outward Lorentz forces on the supraconducting coils. They must be balanced by some rigid support, otherwise the coils would break apart. When the ship gains speed, the magnetic field must be increased in order to keep the protons on track. Consequently, for any given mechanical support there is a cut-off speed beyond which the coils would break. For the Leonora Christina a coil support made of a high-strength „patented“ steel must have a mass of 1100 tons in order to sustain the magnetic forces that occur at β=0,74.

But we assumed above that this is the ship‘s entire mass. That said, the acceleration must drop long before speeding at 0,74 c. The cut-off speed βc=0,74 is an upper bound (for mathematicians: not necessarily the supremum) for the speed at which 1 g acceleration can be maintained. Lighter materials for the coil support would save mass. Fishback [5] calculated upper bounds for the speed at which an acceleration of 1 g is still possible for several materials such as aluminium or diamond (at that time the strongest lightweight material known). Values are shown in Table 2 together with (ßγ)c.

Martin [7] found some numerical errors in [5]. Apart from that, Fishback used an optimistically biased (ßγ)c. Closer scrutiny, in particular the use of a more realistic rocket equation [6], results in more realistic upper bounds. Using graphene, the strongest material known, the specific cut-off momentum is 11,41. This value would be achieved after a flight of three years at a distance of 10 light years. After that point, the acceleration would rapidly drop to values making it hopeless to reach the galatic center in a lifetime.

In conclusion, the interstellar magnetic ramjet has severe construction problems. Some future civilization may have the knowhow to construct fantastically long Fishback solenoids and to overcome the minimum mass condition. We should send a query to the guys who flashed the BLC1 signal from Proxima Centauri. The response is expected in 8.5 years at the earliest. In the meantime the educated reader may consult a tongue-in-cheek solution that can be found in my recent scientific novel [8].


Many thanks to Al Jackson for useful comments and for pointing out the source from which Poul Anderson got the idea for Tau Zero, and to Paul Gilster for referring me to the seminal paper of John Ford Fishback.


[1] Robert W. Bussard: Galactic Matter and Interstellar Flight. Astronautica Acta 6 (1960), 1-14.

[2] Poul Anderson: Tau Zero. Doubleday 1970.

[3] Carl Sagan: Direct contact among galactic civilizations by relativistic inter-stellar space flight, Planetary and Space Science 11 (1963) 485-498.

[4] Eugen Sänger: Zur Mechanik der Photonen-Strahlantriebe. Oldenbourg 1956.

[5] John F. Fishback: Relativistic Interstellar Space Flight. Astronautica Acta 15 (1969), 25-35.

[6] Claude Semay, Bernard Silvestre-Brac: The equation of motion of an interstellar Bussard ramjet. European Journal of Physics 26 (1) (2005) 75-83.

[7] Anthony R. Martin: Structural limitations on interstellar space flight. Astronautica Acta 16 (6) (1971) 353-357.

[8] Peter Schattschneider: The EXODUS Incident. Springer 2021,
ISBN: 978-3-030-70018-8.

From NOTES ON THE MAGNETIC RAMJET II by Peter Schattschneider (2021)

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.


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.

Black Hole Starships

Thanks to Evan Rinehart for reminding me about this. It is from Are Black Hole Starships Possible. The basic idea is to see if the laws of physics will allow a practical starship using Hawking radiation of an artificial black hole as a power source.

The study authors saw the obvious fact that slower-than-light starships are going to need outrageous amounts of energy, and the two major theoretical possibilities were [a] antimatter and [b] primordial black holes.

They were looking into black holes because antimatter has lots of problems: manufacturing antimatter is outrageously inefficient, and if any of the fuel touches the fuel tank the entire starship blows up. Tiny black holes touching the fuel tank will just gobble big holes in the tank, and manufacturing black holes is mostly a matter of shoveling in enough matter into its bottomless gullet until it is the size you want (meaning it will require about a million times less energy than making antimatter).

However, astronomers have not noticed any of these primordial black holes lurking in our solar system. Believe me, they would have quickly spotted anything that gave off energy like detonating one W87 thermonuclear warhead every second. Which is most inconvenient, meaning if there are no primordial black holes nearby to scoop up and use, we'll have to manufacture one.

To simplify the math the study authors decided to just deal with Schwarzschild type black holes (with no spin or charge). Other people suggest that Kerr-Newman black holes give you more control, but I digress.

Primordial black holes

In 1975 legendary physicist Stephen Hawking discovered the shocking truth that black holes are not black (well, actually the initial suggestion was from Dr. Jacob Bekenstein). They emit Hawking radiation, for complicated reasons that are so complicated I'm not going to even try and explain them to you (go ask Google). The bottom line is that the smaller the mass of the black hole, the more energy and deadly radiation it emits.

Black holes with a mass of your average star or larger emit practically no energy. But you will get plenty of energy from naturally occurring small black holes are called "Primordial black holes."

The radiation will be the same as a "black body" with a temperature of:

6 × 10-8 / M kelvins

where "M" is the mass of the black hole where the mass of the Sun equals one. The Sun has a mass of about 1.9891 × 1030 kilograms or .

Jim Wisniewski created an online Hawking Radiation Calculator to do the math for you.

In the table:

  • R is the black hole's radius in attometers (units of one-quintillionth or 10-18 of a meter). A proton has a diameter of 1000 attometers.
  • M is the mass in millions of metric tons. One million metric tons is about the mass of three Empire State buildings.
  • kT is the Hawking temperature in GeV (units of one-billion Electron Volts).
  • P is the estimated total radiation output power in petawatts (units of one-quadrillion watts). 1—100 petawatts is the estimated total power output of a Kardashev type 1 civilization.
  • P/c2 is the estimated mass-leakage rate in grams per second.
  • L is the estimated life expectancy of the black hole in years. 0.04 years is about 15 days. 0.12 years is about 44 days.

"Lifespan?" I hear you ask. "What do you mean by Lifespan?". Well, as the small black holes emit energy, their mass also grows smaller. They gradually move up the table until their mass becomes zero. According to semi-classic physics, when the mass becomes zero the black hole explodes. So the ship will have to jettison the hole before that happens.

The black hole can be fed more mass, in theory, but that has problems. Trying to shove multiple kilograms of mass per second down a black hole with a mouth only a couple of attometers wide is almost impossible. Besides, the entire point of using a black hole was to avoid the entire mass-ratio problem. Feeding the hole with matter you carry along just puts you back at square one. The study authors assumed that the hole would not be fed during the journey.

Black Hole Generator

The black hole is artificially created by firing a huge number of gamma rays from a spherically converging laser. The principle is to pack enough energy into a small enough space to create the conditions of a black hole. Photons instead of particles are used to avoid the inconvenient Pauli exclusion principle.

The report talks vaguely about using "nuclear lasers" mentioned also vaguely in this report. They estimate that the laser and the lasing mass will have to be about 1010 tonnes, the size of a small asteroid.

Black Hole Drive

Proper Black Hole Size?

Now, the study authors figured that a black hole suitable to power an STL starship need the following:

  • has a long enough lifespan to be useful
  • is powerful enough to accelerate itself up to a reasonable fraction of the speed of light in a reasonable amount of time
  • is small enough that we can access the energy to make it
  • is large enough that we can focus the energy to make it
  • has mass comparable to a starship

Luckily, it turns out that there are some sizes of black holes which fit all the parameters. It was not impossible that there existed no size that would fit them all simultaneously.

Long enough lifespan to be useful and powerful enough to accelerate itself up to a reasonable fraction of the speed of light in a reasonable amount of time?

For an upper limit on the most energy intensive trip, the authors used a starship on a one-way trip from Terra to Alpha Centauri with a 1 g acceleration/deceleration Brachistochrone trajectory. Proper time duration of the trip will be 3.5 years, so that sets the minimum black hole lifespan to 3.5 years, which corresponds to a minimum radius of 0.9 attometers.

A black hole with a radius of 0.9 attometers will have a mass of 606,000 metric tons and a power output of 160 petawatts. 20 days worth of output is enough energy to delta-V the 606,000 tonne black hole up to about 10% the speed of light, assuming 100% efficiency converting emitted energy to kinetic energy (the mass of the starship is probably negligible compared to the black hole). Increase the time to make up for the inefficiency, e.g., if the efficiency is only 10% then the output time becomes 200 days.

A trip proper time of 100 years requires a black hole with a radius over 2.7 attometers. This has a mass of 1,820,000 metric tons and radiates 17 petawatts. 1.5 years to delta-V up to 10% c at 100% efficiency.

The report makes a wild guess that an upper limit on starship trip proper time would be 1,000 years. This requires a black hole with a radius over 5.9 attometers. A black hole with a radius of 10 attometers has a lifespan of 5,000-odd years, mass of about 6,730,000 tonnes, and the radiated power drops to 1 petawatt. But there is a problem. At 100% efficiency this would take one hundred freaking years to delta-V up to 10% c.

Bottom line: a black hole with a long enough lifespan to be useful and is powerful enough to accelerate itself up to a reasonable fraction of the speed of light in a reasonable amount of time will have a radius between 1 and 6 attometers.

Small enough that we can access the energy to make it?

The Sun has a luminosity of about 3.8427×1026 W. This boils down to the equivalent of two million tonnes of energy in less than half a second. A square solar cell array with 100% efficiency and an edge length of 370 kilometers, in circular orbit around the sun at a distance of 1,000,000 kilometer, would in one year accumulate enough energy to make a black hole with a radius of 2.2 attometers.

Even with much less efficiency in the moving parts, this seems reasonable. No show stoppers here.

Large enough that we can focus the energy to make it?

The proposed black hole generator makes the initial hole using gamma ray laser beams (see above). Then it is installed in the starship.

The spherically converging gamma ray laser beams will need to focus in a region with a radius between 1 and 6 attometers. This will require gamma ray photons with an energy between 210 and 1,240 GeV. These will be very difficult to make. But we might be able to get away with using gamma ray photons with energies roughly matching the Hawking temperature of the black hole to be synthesized. This would be gamma ray photons with a more modest energy of 3 to 16 GeV. These are comparable to wavelengths within the Compton radii of nucleii, so are technically possible.

Mass comparable to a starship?

Black holes with radii between 1 and 6 attometers have mass ranging from 673,000 to 4,040,000 tonnes. Starships of equal mass would be quite large. And if need be several black hole engines can be used if you wanted a larger starship.

So the answer to the four questions are all "Yes."


When he was considering white dwarfs and neutron stars in the context of what he called ‘gravitational machines,’ Freeman Dyson became intrigued by the fate of a neutron star binary. He calculated in his paper of the same name (citation below) that gradual loss of energy through gravitational radiation would bring the two neutron stars together, creating a gravitational wave event of the sort that has since been observed. Long before LIGO, Dyson was talking about gravitational wave detection instruments that could track the ‘gravitational flash.’

Observables of this kind, if we could figure out how to do it (and we subsequently have) fascinated Dyson, who was in this era (early 1960s) working out his ideas on Dyson spheres and the capabilities of advanced civilizations. As to the problematic merger of neutron stars in a ‘machine,’ he naturally wondered whether astrophysical evidence of manipulations of these would flag the presence of such cultures, noting that “…it would be surprising if a technologically advanced species could not find a way to design a nonradiating gravitational machine, and so to exploit the much higher velocities which neutron stars in principle make possible.”

He goes on in the conclusion to the “Gravitational Engines” paper to say this: “In any search for evidences of technologically advanced societies in the universe, an investigation of anomalously intense sources of gravitational radiation ought to be included.”

Searching for unusual astrophysical activity is part of what would emerge as ‘Dysonian SETI,’ or in our current parlance, the search for ‘technosignatures.’ It’s no surprise that since he discusses using binary black holes as the venue for his laser-based gravity assist, David Kipping should also be thinking along these lines. If the number of black holes in the galaxy were large enough to support a network of transportation hubs using binary black holes, what would be the telltale sign of its presence? Or would it be observable in the first place?

Remember the methodology: A spacecraft emits a beam of energy at a black hole that is moving towards it, choosing the angles so that the beam returns to the spacecraft (along the so-called ‘boomerang geodesic’). With the beam making the gravitational flyby rather than the spacecraft, the vehicle can nonetheless exploit the kinetic energy of the black hole for acceleration. Huge objects up to planetary size could be accelerated in such a way, assuming their mass is far smaller than the mass of the black hole. No fuel is spent aboard the spacecraft which, using stored energy from the beam, continues to accelerate up to terminal velocity.

Kipping likes to talk about the process in terms of a mirror. Because light loops around the approaching black hole and returns to the spacecraft, the black hole exhibits mirror-like behavior. Thus on Earth, if we bounce a ping-pong ball off a mirror, the ball returns to us. But if the mirror is moving towards us quickly, the ball returns faster because it has picked up momentum from the mirror. Light acts the same way, but light cannot return faster than the speed of light. Instead, in gaining momentum from the black hole, the light blueshifts.

We exploit the gain in energy, and we can envision a sufficiently advanced civilization doing the same. If it can reach a black hole binary, it has gained an essentially free source of energy for continued operations in moving objects to relativistic speeds. Operations like these at a black hole binary result in certain effects, so there is a whisper of an observable technosignature.

I discussed the question with Kipping in a recent email exchange. One problem emerges at the outset, for as he writes: “The halo drive is a very efficient system by design and that’s bad news for technosignatures: there’s zero leakage with an idealized system.” But he goes on:

The major effect I considered in the paper is the impact on the black hole binary itself. During departure, one is stealing energy from the black binary, which causes the separation between the two dead stars to shrink slightly via the loss of gravitational potential energy. However, an arriving ship would cancel out this effect by depositing approximately the same energy back into the system during a deceleration maneuver. Despite this averaging effect, there is presumably some time delay between departures and arrivals, and during this interval the black hole binary is forced into a temporarily contracted state. Since the rate of binary merger via gravitational radiation is very sensitive to the binary separation, these short intervals will experience enhanced infall rates. And thus, overall, the binary will merge faster than one should expect naturally. It may be possible to thus search for elevated merger rates than that expected to occur naturally. In addition, if the highway system is not isotropic, certain directions are preferred over others, then the binary will be forced into an eccentric orbit which may also lead to an observational signature.

Tricky business, this, for a black hole binary in this formulation can be used not only for acceleration but deceleration. The latter potentially undoes the distortions caused by the former, though Kipping believes elevated merger rates between the binary pair will persist. Our technosignature, then, could be an elevated binary merger rate and excess binary eccentricity.

I was also interested in directionality — was the spacecraft limited in where it could go? I learned that the halo drive would be most effective when moving in a direction that lies along the plane of the binary orbit. Traveling out of this plane is possible, though it would involve using onboard propellant to attain the correct trajectory. The potential of reaching the speed of the black hole itself remains, but excess stored energy would then need to be applied to an onboard thruster to make the course adjustment. Kipping says he has not run the numbers on this yet, but from the work so far be believes that a spacecraft could work with angles as high as 20 degrees out of the plane of the binary orbit and still reach an acceleration equal to that of the black hole.

For more on the halo drive, remember that Kipping has made available a video that you can access here. The other citations are Kipping, “The Halo Drive: Fuel-free Relativistic Propulsion of Large Masses via Recycled Boomerang Photons,” accepted at the Journal of the British Interplanetary Society (preprint); and Dyson, “Gravitational Machines,” in A.G.W. Cameron, ed., Interstellar Communication, New York: Benjamin Press, 1963, Chapter 12.


Quark Nuggets

A Quark Nugget is a chunk of "strange matter", which is composed of "strangelets", which are composed of roughly equal numbers of up, down, and strange quarks. In technical science speak it is described as Compact Composite Objects (CCOs) nuggets of dense Color-Flavor-Locked Superconducting quark matter created before or during the Quantum ChromoDynamics phase transition in the early universe. Now you know as much as I do.

Suffice to say that it is weird stuff.

Some scientist have become fascinated by the concept because:

  • It can explain Dark Matter (or why is there over five times as much gravity in the universe than can be accounted for with observed matter?)
  • It can explain the observed cosmological baryon asymmetry (that is, why isn't the universe half matter and half antimatter and thus suffering cosmic explosions every ten seconds?)
  • It can explain both of the above within exisiting physics, you do not need to postulate some bizarre new particle.

Thomas Marshall Eubanks examined the concept and wrote a scientific paper about them. You can tell it is relevant to our interests by the title: Powering Starships with Compact Condensed Quark Matter.

He calculates that this stuff is everywhere, left over from the Big Bang. There must be tons and tons of it, because it causes Dark Matter gravity. The point being it should be readily available in our own solar system. Now due to the incredible density of quark nuggets, it is all going to be at the core of various solar system objects. We won't be able to mine any at the core of Sol, the planets, or the moons, but asteroids are a different mattter. Eubanks notes there do exist so-called Very Fast Rotating asteroids, the little whirling dervishes have rotation periods measured in tens of seconds. This is consistent with strange matter asteroids with core masses between 1010 and 1011 kilograms (50 million metric tons). The cores can be extracted and used (but alas cannot be subdivided, the mutual attraction is too strong). The cores will typically be about one millimeter in radius.

Why do we care?

Because such quark nuggets can be used as SUPER-EFFICIENT ANTIMATTER FACTORIES, that's why.

Using Andreev reflection you could create about 109 kilograms (1 million metric tons) of antimatter before the nugget wore out. You bombard the nugget with a 100 MeV particle stream and some of the particles will transform into their antiparticle (it is actually more complicated than that, but who cares?). Each 1010 kg of quark nugget can produce 109 kg of antimatter.

One the one hand it is far easier to generate antimatter as you need it, instead of trying to carry a million tons of touchy antimatter. Especially since an antimatter containment failure would make an explosion big enough to obliterate an entire solar system.

On the other hand it will be a major engineering feat to drag along a quark nugget with a mass that is a substantial fraction of the weight of Mount Everest. That's why I filed this here in the "Starship" page instead of the "Engines You Can Use Within The Solar System" page.


Marshall Eubanks has posited the presence of million tonne masses of stable quark matter inside solar system objects – potentially both matter and antimatter forms of it, with the antimatter version protected from annihilation by a 100 MeV Colour-Force potential well.

Powering Starships with Compact Condensed Quark Matter

While pure antimatter/matter propulsion promises high exhaust velocities (~c) the difficulties of achieving that ultimate performance are considerable. But what if we use something else for reaction mass and use antimatter to energise that? And, instead of using it in a rocket, we use a magnetic scoop to draw in reaction mass from the interstellar medium? This is the Ram-Augmented Interstellar ‘Rocket’ – though technically a rocket carries all its reaction mass – and it promises high performance without all the disadvantages of exponentially rising mass-ratios. Mixing 1% antimatter into the matter flow could, in theory, produce an exhaust velocity of ~0.2 c. Scooping and energising the equivalent mass of ~100 times the mass of the starship would allow a top-speed of 0.999999996 c to be achieved, before braking to a halt using half that mass. This would allow, at 1 gee acceleration, a journey of ~20,000 light-years. The nearby stars would be accessible at a much lower antimatter budget.

Quark Matter in the Solar System : Evidence for a Game-Changing Space Resource

Very Rapid Rotating asteroids might be held together by the additional gravity of a mm-sized million tonne quark nugget.

Primordial Capture of Dark Matter in the Formation of Planetary Systems

Evidence for Condensed Quark Matter in the Solar System

Observational Constraints on Ultra-Dense Dark Matter

Such quark nuggets would be made in the Big Bang potentially, if antimatter is squirrelled away in such a form, the explanation of the observed lack of free-antimatter in the Universe. The abundance of such ultra-dense tiny specks, to be compatible with microlensing observations, would be in the ‘interesting’ mass-range suggested by the Solar System evidence.

From ANTIMATTER AT HAND? by Adam Crowl (2014)

Pondering Marshall Eubanks’s concept of quark nuggets for making antimatter and hunting for such inside NEOs and comets, I thought of what an antimatter starship would require. The difficulty of storing anti-hydrogen led to me reason that carrying an antimatter source, like a quark nugget, made more sense than refining the stuff, then trying to store it safely. Make it as you use it seems the best approach.

That does imply that starships will mass millions of tons, to match the quark nugget. Depending on how the antimatter is mixed into the propellant stream, I suspect an antimatter rocket will be a comet adapted to the purpose, blasting out a jet of energised water as the main reaction drive. I’d hazard to guess the efficiency of such a rocket, since mixing annihilation energy into a reaction stream is incredibly difficult. However an exhaust velocity of 0.1 to 0.2 c seems reasonable.

When drives are power limited, based on the endurance of the engine rather than the energy of the fuel, there’s a simple relationship between the mission velocity, exhaust velocity and cruise velocity, with an overall mass ratio of ~4.42. The cruise velocity – the speed at which the vehicle coasts – would be somewhere between 0.075 c to 0.15 c, while the mission velocity would be 0.05 c – 0.1 c.

In the Oort Cloud there’s about 100 billion comets in far-flung orbits. One for every star in the Galaxy. If each formed around a quark nugget, then that would be 100 billion potential starships. Launching forth to every star in the Milky Way at 0.1 c, they would take ~750,000 years to reach the stars on the opposite side of the Milky Way to us. To reach every Globular Cluster in the Milky Way’s vast halo might take 1.5 – 3 million years.

Not every star has an Oort Cloud, ours being one of the few to keep its Cloud, as passages through Molecular Clouds and tight star clusters can lure the far-flung comets away with their gravity. Yet there are enough Oort Clouds that Others might have done the same before us. If Other Civilizations came to the same conclusion, as my musings above, and launched forth thus-like, what would a Galaxy in the throes of such a “Life Burst” look like from far away? Would we see the unique signs of antimatter annihilation spraying forth from that Galaxy? Could we see it with the right gamma-ray telescopes?


Q-Balls are a form of exotic shadow matter, used in many hi-tech applications, particularly the manufacture of antimatter from matter.
(an extract from a partially translated transap physics module follows, with references):
beginitem: Editors Note
Author: Verified, NodeE4568/EGEB DateTime4.154E3/10499

Q-balls have been known since antiquity, as non-topological soliton solutions with a conserved quantum number. Q-balls are a form of shadow matter, participating only in gravitational interactions.

"Supersymmetric dark matter Q-balls and their interactions with matter", A. Kusenko, L. Loveridge, M. Shaposhnikov <Link>

Detailed study into basic minimal supersymmetric model (MSSM) theory, however, has been suppressed since the Dark Ages. When one studies the mathematics of even basic applications for Q-balls, one comes quickly to the realization that this field of study has been memegineered for very good reasons -- MSSM engineering has the ability to throw off the shackles the Archai have placed, by provided limitless fuel and energy to even basic modosophonts, as well as containing the seeds to a weapon so powerful even the Archai tremble in <3.6M deleted>


Q-balls have several properties of interest for engineering applications:

1. Q-balls reflect incident fermions as anti-fermions with a cross-section of unity.

"Interactions of Q-balls and matter", S. Clark <Link>

Antimatter production is greatly simplified by taking advantage of massive Q-ball kernel structures. A hypothetical Q-factory would be a simple disk of Q-balls; incident protons and electrons (such as from neutral hydrogen) would be reflected as antiprotons orbited by positrons. Heavier materials would be similarly replaced with their antimatter analogues with extreme ease.

Such interactions would be of only academic interest if not for the next two properties:

2. Q-balls make up a portion of the dark matter of the universe, and are more common than natural cosmic monopoles. Some emissions from the core of the Milky Way have been traced back to positronic annihilations generated from electron flux on primordial Q-balls.

"511 keV line from Q balls in the Galactic Center", S. Kasuyaa and F. Takahashi <Link>

3. Q-balls of sufficient mass are metastable, evaporating on timescales longer than the current age of the universe.

"Particle Creation from Q-Balls", S. Clark <Link>

Taken together, these properties indicate that Q-balls should be relatively plentiful for a civilization with proper resources to look in likely places. Once gathered (or manufactured), Q-material can be composed into structures ranging from primitive pits in the cores of asteroids, to complex free form structures shaped by metric engineering.

Such structures have the ability to create antimatter from matter (or matter from antimatter) for as long as a suitable supply can be maintained.

Indeed, it is hypothesized that several natural Q-forges exist in neutron stars that have captured relic Q-balls, which are naturally formed during the supersymmetric phase transitions that occurred as the universe cooled. In such systems, a single heavy Q-ball is calculated to be able to "eat" a neutron star in a few Gigayears, until the neutron star density becomes insufficient to maintain Fermi degeneracy. At this point, the neutrons revert to protons and electrons, and the neutron star explodes.

Q-Forge: See Q-Ball
Q-Ball: See Q-Forge

Recursion warning!, Node45E21/MGMU DateTime2.345E6/10499, stack truncated

From Q-BALLS by Adam Getchell (2007)

Nearlight Starships


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.

Colonized Interstellar Vessel

This section has been moved here

Encounter With Tiber

There is not one, not two, but three different slower-than-light starships in Encounter With Tiber by Buzz Aldrin and John Barnes.

9,000 years ago, the aliens ("Tiberans") living around Alpha Centauri A become aware of a rogue planet that is going to drastically lower the property values of their home planet. They need to migrate their civilization to another planet, and their is not any suitable candidates in the Alpha Centauri star system. So they take a look at our Solar System.

In the 73rd century BCE they mount an interstellar scouting mission to Terra, using the starship Wahkopem Zomos. The mission mysteriously fails. In the 72nd century BCE a follow-up mission is sent, using the starship Egalitarian Republic. It fails as well.

Around 2030 we humans discover artifacts from the two alien mission on Luna's south pole and on Mars. In 2069 a mission is sent to Alpha Centauri to make first contact, using the starship Tenacity.

Wahkopem Zomos

A plasma-core antimatter booster section sends the starship Wahkopen Zomos into a close perihelion approach to the primary star (Alpha Centauri A). A 1000 kilometer diameter solar sail is unfurled. This accelerates the ship to a close approach to Alpha Centauri B for a second perihelion manoeuvre. It is then further accelerated by lasers until it reaches a velocity of 0.4c. It then cruises to Sol for about 18 (alien) years.

Approaching Sol, it deploys a "brakeloop" of superconducting wire 100 kilometers in diameter. This converts the ship's kinetic energy into heat in the interstellar medium. Two years of braking is enough to slow the starship into the solar system.

The plan was for the homeworld to launch a 5000 kilometer laser sail and guide it into the solar system. Then it could reflect laser beams on to the Wahkopen Zomos' sail and return it to Alpha Centauri A. Unfortunately politics at home led to abandoning this plan, thus stranding the Wahkopen Zomos. This is an occupational hazard for laser lightsail starships. The advantage is you leave at home your engine and its inconvenient mass. The disadvantage is you are at the mercy of the people at home (and their political parties) who control the engine.

Wahkopem Zomos was a stubby cylinder, wider than it I was long and about as tall as a four-story building, inside a wide ring that surrounded its base and extended about one-fourth as high as the cylinder. We lived in the ring—once we were on our way, the ship would be spun along its axis, so that the outer edge of the ring formed the outer deck, with the gravity we were used to, and an interior deck formed the inner deck, with about four-fifths of Nisuan (Tiberian Homeworld) gravity, a little less than the gravity would be on Setepos (Terra) when we got there.

Yet despite the apparent size from the outside, quarters were fairly cramped inside. The entire central cylinder was devoted to the ship's farm, sail room, power plant, and lander storage; life support, waste recycling, general storage, and everything else took up more than half of the ring. So we actually only lived in the outermost part of the ring, on a double deck that barely had head clearance for Poiparesis. And many parts of the living space were things like the cockpit and the biological laboratory that couldn't be used for much of anything else and weren't used most of the time. Even with all that space in the ship, at the time, as a child, I could already span my compartment with my outstretched hands.

Inside the central cylinder were the power plant, the reaction engines, the recycling system, the ship's farm, and the squat, dark forms of the two landers, Gurix and Rutnaz. Though it would be almost twenty-four years until we used them, they were always there, reminding us of what we were intending to do. The forward third of the cylinder was taken up with the sail, brakeloop, shrouds, and winches to operate them.

"Boost imminent," Osepok's voice said from the intercom.

We turned to look out the big view port. Behind the ship, connected by a long, thin pole, was a big structure of struts and tanks, a third as wide as the ship and five times as long: the booster. It filled most of the window, shining silver in the harsh light of space. For a long breath or two nothing happened. Then a glow appeared behind the booster and spread to fill the rest of the window.

There was no sound, of course, with no air to carry it; just the purplish-white glow. We sank into the webbing, and the hammocks swung around so that our faces were pointed down toward the view port as the ship began to accelerate. Moment by moment, we felt ourselves gaining weight, sinking deeper into the hammocks.

Ordinary spacecraft had to take off from Nisu's surface, starting with no velocity and fighting directly against gravity; they had to accelerate at about one and a half times the acceleration of gravity, increasing to three gravities, for periods of a thirty-second of a day (45 minutes) or more, to leap up to orbit. But Wahkopen Zomos was already in orbit around Nisu, and Nisu was orbiting Sosahy; we could begin with a gentler thrust and let it run for a third of a day (8 hours).

At first the thrust was pushing Wahkopen Zomos, plus all those tanks and struts in the booster, plus the immense weight of fuel, thirteen times the weight of the ship itself (mass ratio of 14, which is a little excessive). The ship and booster sped up very slowly. But with each passing instant, more of the fuel was gone, and yet the engines pushed just as hard. Acceleration increased, and the webs pressed harder against our faces.

The glare we saw was hydrogen plasma, heated far beyond the point where its electrons and protons stayed together, so that it was a mere thin wisp of atomic particles. By weight the booster was almost all liquid hydrogen, and the rest was the assembly of girders, tanks, and pipes that held it together—but a tiny fraction of the total mass, held in one small compartment that any of us could have picked up and carried with one hand, was the key to the whole thing: antimatter. Mix liquid hydrogen just above absolute zero with one millionth of its weight in antimatter, and it became hydrogen plasma hotter than the core of the sun (plasma-core antimatter rocket).

Had we been outside, looking directly at the glow instead of seeing it through a shielded viewport, we would have been blinded; on Nisu below us, people had to be warned not to look directly at our boost out of orbit, and we briefly lit up the sky ss brightly that night animals went back to their dens and plants opened their leaves to what they thought was sunrise.

(they make a close perihelion approach to Alpha Centauri A, deploying a photon sail)

Long ages crept by and I watched my screen. I itched in a couple of places and quickly scratched those, always watching the clock on the screen to make sure that it wasn't too close to sail deployment. Poiparesis had told us that if we got a hand trapped under ourselves, very likely we would break every bone in that hand and in our wrists, and give ourselves deep bruises in whatever flesh lay across the hand.

Time crawled by slowly. The screen showed the sun bloated and swollen, almost as large as Sosahy seen from Nisu's surface; the filters over the cameras meant we were seeing less tan one ten-millionth of the actual brightness outside, and yet the screen was becoming uncomfortably bright to look at.

If we had tried to use a rocket, to have made the trip to Setepos and returned within our lifetime would have taken a vastly larger ship that would have had to be almost all antimatter. As it was we had burned virtually all the antimatter of Nisu, nine years of production, in our booster at takeoff, and the speed it had gotten us up to would have taken tens of thousands of years to get us to Setepos. We needed more power than all of Nisu produced in a year, and we needed it early in the trip so that we could travel as much of it as possible at high speed.

From ENCOUNTER WITH TIBER by Buzz Aldrin and John Barnes (1996)
Egalitarian Republic

Photon drive powered by vacuum energy. At top speed of 0.99 c, one day of shipboard time equals eight days back home.

During acceleration the ship emits a spray of antiprotons as a starship bumper to ward off relativistic dust particles in the interstellar medium. Since the antiproton energy release will be on the side of the dust particle facing the ship, the energy will propel the dust out of the ship's path. This does cause a bath of gamma rays over the ship's nose so there is extra shielding there.

During deceleration the fury of the photon drive will vaporize and ionize any dust particles that get in the way.

The ship can hover in a pseudo-orbit over a given spot on a planet, boosted by the photon drive. However if the spot was on dry land, it would rapidly turn into a gigantic volcano.


The Tenacity gets its initial impetus from a ring of antimatter-powered booster rockets around its tail. The main propulsion is a battery of Casimir-effect lasers, thirty zero-point-energy lasers (photon drive). The acceleration is 0.06 g. On the trip to Alpha Centauri it will accelerate for several years to a speed of 0.75 c. Once the ship enters the Alpha C system and comes within 35 AU of the primary star, it will deploy a magnetic loop brake to decelerate. That will take about two years.

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.


Lighthuggers are fictitious (but famous) almost-as-fast-as-light starships invented by sci-fi writer and scientist Alastair Reynolds for his Revelation Space series.

Lighthuggers are huge torchships, i.e., they have unreasonably powerful propulsion systems with unreasonably tiny mass ratios. They can accelerate at 1 g for the better part of a year, reaching a velocity of about 99% c. And they still have enough delta-V to brake to a halt at the destination. The boost and deceleration phase is 1 g, but under combat conditions they are capable of 10 g bursts. Not bad for a ship several kilometers long. And composed of pure-quill handwavium. Their engines break a scientific law or two.

The propulsion system for lighthuggers were invented and constructed by a faction of humanity called the Conjoiners. They use intelligence-amplifying methods so their technology level is quite a bit higher than the other humanity factions.

I mention lighthuggers because people interested in AAFAL starships will eventually stumble over the blasted things, and I don't want anybody being confused.

Mr. Reynolds says that the name "lighthugger" was inspired by the term "lightskimmer", invented by Ian Watson and Michael Bishop in their novel "Under Heaven's Bridge".


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

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

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

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

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

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


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

(ed note: obviously this is total technobabble)

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

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

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

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


(ed note: obviously this is total technobabble)

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

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

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

Project Star

Project Star is a very speculative interstellar mission to Proxima Centauri. On the one hand there are one or two items that are handwaving, the "and then a miracle occured" kind. On the other hand it was printed in Space Journal, a periodical that had on its board of consultants such worthies as Hermann Oberth, Eugen Sänger, and Frederick Ordway III.

The study was conducted by Helmut Hoeppner and B. Spencer Isbell, who were noted rocket scientists.

First they propose Proxima Centauri as the destination for the first interstellar exploration mission, obviously because it is the closest. At the time of writing the authors did not know that Proxima is much less likely to host habitable planets than the other members of the Alpha Centauri system. So traveling a mere 0.21 light-year farther would dramatically increase their chances.

They named the hypothecial planet around Proxima the mysterious planet "X" {cue spooky Theremin music}. Which sounded very dramatic back in 1959 but now sounds like something out of a hackneyed Buck Rogers film serial.

The large diagram above is meant to hammer into your head that while Proxima Centauri is incredibly distant from Sol, they are practically adjacent when compared to galactic distances.

Enter the big hand-wave. The study notes that spacecraft travelling at conventional rocket speed will take so long to travel to Planet X that the astronauts will die of old age before they get half-way. They invoke Dr. Eugen Sänger, who was of the optimistic opinion that man will be able to travel at a speed of 299,000 kilometers per second (0.999 c) within the next 50 years (i.e., by the far-flung future year of 2009).

They postulate the invention of some kind of photon drive. While it is true that such a drive has the maximum possible specific impulse and exhaust velocity allowed by the laws of physics, the researchers didn't know that photon drives were also the ultimate power hogs. You need three hundred freaking megawatts of power in order to generate one measly Newton of thrust. The specs are that the ship will accelerate at two gees, which means you'll need 5.9 gigawatts for the photon drive. Per kilogram of spacecraft. For half a year of acceleration and half a year of deceleration.

Thats a lotta gigawatts. The hand-wave is they leave unmentioned what sort of power supply could possibly manage this much gigawattage. Without running out of fuel in three nano-seconds. Even antimatter ain't good enough.

The trip to Proxima starts with a brutal two gees of acceleration that lasts for six months. I'm sure this will not be healthy for the crew. At the end of the acceleration period, the spacecraft will be moving quite close to the speed of light. It will then coast for four years and five weeks of Terra time. The "proper time" experienced on board the ship will be much less due to the savage gamma factor. During this time the crew will be in free-fall, which will also be quite unhealthy. At the end of the coast phase (assuming the ship has not collided with anything more massive than a hydrogen atom) it will start deceleration. Again a brutal two gees of deceleration for six months of Terra time. It will then be inside the Proxima Centauri system and can start looking for planets.

In reality they would do well to use huge telescope back on Terra to ensure that Proxima has planets to start with, before they go to all the time and expense of sending astronauts.

The ship is designed in two parts: the photon drive and everything else. The "everything else" includes the habitat module and the spaceplane lander section. It would actually be safer to have the habitat module separate from a small lander with a surface habitat, the way most Mars missions do. But the study did not include such refinements.

The ship separates from the photon drive, leaving it parked in orbit. The rest of the ship attempt to land.

The ship is a four-stage chemical rocket, using a combination of rocket engines and turbo-ram jet engines mounted on outriggers. This make the spacecraft an upside-down ship, which has many advantages.

Notice the assumption: they are assuming that the planet's atmosphere contains oxygen! That way they can avoid the need to carry heavy liquid oxygen for the jet engines. If there is no oxygen, the jet engines will be worthless and the spacecraft will augur into the planet at high velocity, leaving a sad smoking crater.

The fuel in the deceleration stage slows the ship down from orbital velocity and allows a soft landing.

The crew will now do as much exploring as they can cram in, while trying to avoid being eaten by hungry dinosaurs.

When it comes time to depart, the deceleration stage acts like a launching platform for the three upper stages. The ship will climb back into orbit, shedding the first and second stages in the process like any other multstage vehicle. Because chemical fuel just ain't up to the challenge of single-state-to-orbit.

Back in orbit, what's left of the spacecraft does a rendezvous with the photon drive unit. They re-attach the photon unit and remove the aerodynamic nose cone (presumably because it is not needed any more and has become penalty mass). The ship departs Proxima for another year of two-gee acceleration/deceleration, with a four years and five weeks coasting period in the middle.

Once back in Terra orbit, the ship separates from the photon drive unit and lands back on Terra. Actually it would make more sense if the ship stayed in orbit to be refurbished while the crew was returned home in a space shuttle or something. That would save tons of fuel.

Semyonov Antimatter Starship

This is from Pros and Cons of relativistic interstellar flight and Relativistic rocket: Dream and reality by Dr. Oleg G. Semyonov.

The paper started when Dr. Semyonov read about the Frisbee Antimatter Starship and noticed how certain technical difficulties were being ignored or glossed over. Such as the miniscule cross-sections of electron–positron and proton–antiproton annihilation. Meaning if you crossed a stream of anti-protons with a stream of protons, a dissapointingly low number of particles would actually hit each other and react. This creates the requirement for lengthy “annihilation zones” to make sure every last particle of expensive antimatter reacts and contributes thrust. While it is relatively easy to get two hydrogen atoms to collide, a proton or an anti-proton is 60,000 times smaller.

And, as a consequence, creates poor alignment of the propulsion jet. Meaning that since the annihilation zone is a long cylinder instead of a small sphere, the propulsion jet is going to be an unfocused cone instead of a laser-like focused line. Thrust will be wasted.

So Dr. Semyonov did an analysis to design an antimatter drive starship with a more efficient engine.

The paper agrees that if a multi-ton starship carries its energy source and propellant onboard, you are going to have to use antimatter if you want to get a relativistic speed above 0.1c. Chemical, fission, or fusion are nowhere near powerful enough. The alternative is to make the energy source and propellant external, like a laser sail or something like that.

FuelEnergy Density MJ/kg
Hydrogen fusion650,000,000
DT fusion340,000,000
Natural U81,000,000
H chemical burning140
Rocket chemical fuels50

The two traditional antimatter rocket engines are lepton antimatter and baryon antimatter.

Lepton antimatter is when you annihilate positrons with electrons, and somehow direct the all-destroying gamma-ray flux into a beam to make a photon drive. Usually directing the beam means putting the annihilation point at the focal spot of a gamma-ray parabolic mirror.

The first problem is there ain't no such thing as a gamma-ray mirror, not with anywhere near 100% efficiency at any rate. This means the bulk of the reaction energy is not going to provide thrust, it will instead heat up the mirror with the hideous fury of burning antimatter. The fraction of a second the mirror will last before vaporizing into ionized plasma will have to be written in scientific notation with a huge negative exponent.

Second problem is the abysmally tiny cross section of the annihilation reaction. Only a fraction of the positrons are going to react, the rest will travel past the focal point. Then they will either:

  • Impact the mirror, destroying it in an antimatter explosion
  • Fly into the depths of intergalactic space, wasting all that expensive and vitally needed antimatter
  • Be forced to react by making the reaction zone hundreds of meters long, with the problem of re-directing the gamma rays not at the focal point left as an exercise for the reader
  • Somehow be caught with magnetic scoops and sent back into the focal point, increasing the chance of an antimatter accident with each catch and recycle.

Baryon antimatter is when you annihilate protons with anti-protons. Unlike lepton antimatter the reaction does not produce just gamma rays. Instead it creates an assortment of pions plus gamma rays. Beam-core antimatter rockets like the Frisbee Starship use the reaction products as propellant. Plasma-core antimatter rockets use the annihilation energy to heat up propellant, which increases thrust at the expense of specific impulse. Still others use baryon antimatter annihilation to catalyze fission or fusion reactions, but the resulting specific impulse is so low that it ain't worth it. Not for a starship, it is good enough for an interplanetary ship.

Problems include:

  • The "prompt" gamma-rays contribute nothing to the thrust, they just damage the engine and any other part of the starship that is too close
  • The neutral pions decay almost instantly (90 attoseconds) into "delayed" gamma-rays which do the same thing as the prompt gamma rays.
  • The abysmally tiny cross section of the annihilation reaction

Naturally with both lepton and baryon antimatter, the elephant in the room is how do you carry antimatter fuel when the stuff blows up like a supernova if it touches the matter walls of the fuel tanks? The answer is very carefully, using electromagnetic or electrostatic fields.

The report figures that neither Lepton or Baryon antimatter drive starships are efficient enough. It will be far more efficient to use antimatter in some sort of annihilation electrical power generator, and using that to run some sort of super-duper ion drive. Such a generator will be using the ultimate in concentrated fuel, and the generator will have a much lower mass than a fission or fusion reactor. Ion drives are notorious power hogs, but with antimatter power who cares?

  • 1: Ion accelerators: arrays of linear accelerators of high-energy ions

  • 2: Propellant tanks, and store of matter to annihilate with antihydrogen

  • 3: Refrigerators for antihydrogen tank and magnetic shield

  • 4: Heat insulators

  • 5: Turbines and electrical power generators to energize ion accelerators, life support et al

  • 6: Annihilation reactor

  • 7: Control bridge

  • 8: Crew quarters or AI module

  • 9: Magnetic shield to protect ship from interstellar medium relativistically transformed into particle radiation. A starship bumper in other words.

  • 10: Electron stripper: antidust shielding system. Second part of the starship bumper.

  • 11: Heat radiator

  • 12: Antihydrogen tank

Two heat radiators (11) are shown but four could be used without them thermally interfering with each other (much).

The report has the pious hope that the annihilation reactor will have a much lower mass than a fission reactor with the same power output. They figure that the lion's share of the mass goes to the radiation shielding, but since the antimatter reaction produces zero neutrons it can get by with just gamma-ray shielding. Offhand I'd say the mass reduction is not quite as much as they would hope. Looking at a sample shield it appears that for every kilogram of neutron shielding you need 33 kilograms of gamma-ray shielding. So removing the neutron shield will reduce the shield mass by only 3%.

On the other hand the annihilation reactor will not need things like uranium-235 fuel slugs, which also have lots of penalty mass. Stuff is more dense than lead, which is why the military replaced the lead in their artillery shells with depleted uranium.

Thin radial wings protruding from magnetic shield (9) and electron stripper (10) is to shield the leading edges of heat radiators (11).

You may have noticed a new problem.

[1]From the point of view of the starship, the relativistic "radiation" is coming from the opposite direction (blue arrows) that the ship is traveling in (red arrows).

[2] Rocket Engine 101: you point your rocket exhaust (red flames) in the exact opposite direction your ship is traveling (red arrows) in order to speed up (accelerate). You point the exhaust in the exact same direction as the ship's vector in order to slow down (decelerate). This means in the first half of the trip the ship's nose is pointing at the destination. Then the ship rotates to point the ship's tail at the destination. Heinlein calls this a "skew flip", The Expanse calls it a "flip-and-burn". The tail stays pointed at the destination for the second half of the trip.

[3] Rockets Are Not Arrows: starships do not necessarily travel in the direction their nose is pointing. During deceleration the ship's vector is pointed at the destination, but the nose is pointed away from the destination.

You see the problem? If your starship is traveling to Tau Ceti, you accelerate by pointing your rocket exhaust in the opposite direction (red flames) and burn until you are up to relativistic velocity. Relativistic radiation will appear to be coming from the direction of Tau Ceti (blue arrows), and will be warded off by the starship bumper on the ship's nose.

But when you want to decelerate so as to come to a stop at Tau Ceti, you have to skew flip. This means turning the ship so that the exhaust is pointed at Tau Ceti and burning until you come to a stop. Oh calamity and woe! Because rockets are not arrows, the relativistic radiation is still coming from the direction of Tau Ceti, but the starship bumper is no longer in position to ward off the deadly radiation! The radiation quickly kills the crew.

And no, the report did the math and apparently the rocket exhaust is not powerful enough to disperse the radiation.

According to the report, the recommended solution is to design the ion accellerators so they can rotate and point ahead while the rest of the starship does not change its orientation. This way the ion accellerators can decelerate the starship while allowing the starship bumper to keep facing the radiation. Now, understand that the ion accelerators cannot face directly ahead or they will torch the ship with the exhaust. They will have to be angled slightly off-center so that the exhaust misses the ship. This will mean the thrust is subject to cosine losses, but that can be managed.

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. Or maybe not.)

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

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

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

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

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

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

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

From TAU ZERO by Poul Anderson (1970)

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

— Paul Glister

by A. A. Jackson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Table 1. Cut-Offs and Range for Ramjet accelerating at 1g. Interstellar medium 1/cm-3 using the p-p fusion reaction.
dyn cm-2/gcm-3
Stainless Steel0.26136.27.5

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

From PRIDE by Poul Anderson (1985)

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)

AsteronX Valkyrie Gallery


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Enzmann Starship

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Project Daedalus

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Project Icarus

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Firefly Starship

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Ghost Ship

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Ultra-Dense Deuterium

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Shepherd Generation Starship

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