RocketCat sez

Ken Burnside said it best.

Friends Don't Let Friends Use Reactionless Drives In Their Universes.

Yeah, I know that the blasted Tyranny of the Rocket Equation ruins science fiction writer's fun by making every gram count. But a Reactionless Drive is a solution that makes even worse problems. Kind of like removing lice by setting your hair on fire.

Sure you'll be giving Tyranny of the Rocket Equation concrete overshoes and dumping it into the ocean. But you will also be giving every space fleet, astromilitary, corrupt corporation, James Bond Villain and little Jimmy in his garage lab access to civilization-destroying relativistic weapons. Are you sure you wanna do that?

And besides, there's the iron-clad Law of Conservation of Momentum which says You Can't Do That. Sure, a future scientific breakthrough might let you have your way, but that's not the way to bet.

Mass ratios are the bane of atomic rocket designers. No matter how potent the drive is, you are going to have several kilograms of propellant for each kilogram of rocket. This puts severe limits on the sorts of missions a rocket can perform before the ever-hungry engine has to be fed again. Every gram counts due to the The Tyranny of the Rocket Equation

This is because all rockets utilize Newton's Third Law of action and reaction. You throw something backwards (the propellant) and in reaction the rocket moves forward. This is why rockets are called "reaction drives."

Naturally, the thought occurs that if you can figure out how to make a spacecraft move without using propellant, all the problems with mass ratio vanish. You'd have a "reactionless drive."

Which would be great, were it not for the unfortunate fact that it would violate the law of conservation of momentum.

Now, it is true that Newton's third law has some rare occasions where it does not apply (certain situations with magnetically coupled particles and gravitational forces acting between objects moving very rapidly), but the law of conservation of momentum is a genuine iron-clad rock-solid no-exception law. In a closed system the total quantity of momentum cannot change. It has been verified to within one part in 1e15, and no exception has ever been found.

Which means in a closed system, a reactionless drive is impossible, since it would change the total quantity of momentum.

(Note that it is possible to avoid that law with an open system, with something like a solar sail, a spacecraft launched by a mass driver based on an asteroid, pellet-stream propulsion, or a Starwisp. In these cases, the propulsion system is external to the spacecraft, so the system is open and the law does not apply.)

However, a little thing like violating a law of physics isn't going to stop the crack-pots. Face it, the second law of thermodynamics hasn't stopped all the people attempting to create perpetual motion machines of the first kind.

And even if you, the science fiction author, hand-waved one into existence for your SF novel, you've still got problems.

A working reactionless drive could turn a cheap solar power array and a brick into civilization destroying weapon of ubermassive destruction.

Burnside's Advice is Friends Don't Let Friends Use Reactionless Drives In Their Universes.

The trick is making a reactionless drive that doesn't give you the ability to shatter planets with the Naval equivalent of a rowboat (which would throw a big monkey wrench into the author's carefully crafted arrangement of combat spacecraft). Reactionless drives, with no fuel/propellant constraints, will give you Dirt Cheap Planet Crackers. If you have a reactionless drive, and stellar economics where most of the common tropes exist (privately owned tramp freighters), you also have gravitic drive missiles. Unfortunately avoiding Planet Crackers Done Real Cheap is almost impossible to justify on logical grounds, so SF author is faced with quite a daunting task.

Dean Drive

Oh, the Dean Machine, the Dean Machine,
You put it right in a submarine,
And it flies so high that it can't be seen —
The wonderful, wonderful Dean Machine!

Damon Knight

The fun started back in 1960 when the John W. Campbell (the father of the Golden Age of Science Fiction) decided to make some excitement by giving free publicity to Norman Dean and his infamous "Dean Drive". It allegedly could convert rotary motion into linear motion, i.e., it was a reactionless drive. U.S. Patent 2,886,976. "Just think," Campbell said, "stick one of these in a submarine and you have instant spaceship!"

Another common name for the Dean Drive is the "inertial drive."

Campbell was miffed that mainstream scientists were not even interested in looking at the drive. But in this case, the scientists were acting properly. Faced with the fact that the Dean Drive obviously violated the law of conservation of momentum, well, extraordinary claims require extraordinary proof. A box vibrating on a pan balance that makes the beam scale look like it had lost an ounce or two is not anywhere near convincing enough.

Interest in the Dean Drive faded away as Dean refused to let anybody examine the gadget, with the notable exception of John W. Campbell and G. Harry Stine. At least without forking over some money first. Even (now) SF author Jerry Pournelle tried to get permission to examine the drive on behalf of the airplane company he was employed at the time, but was turned down.

After Dean died, Stine made a brief resurgence of interest in the 1980's, but it died too, and later so did Stine. A close examination of the patent reveals that the device is actually a complicated ratchet pulling itself along a metal tape, not a reactionless drive.

Physicist Milton Rothman notes that Dean Drive apologists wave their hands and talk about the strange relationship between force and changing acceleration as a justification for the drive, but all they are doing is revealing the depths of their ignorance about basic physics.


Yes, before you all email me, I have heard about Roger Shawyer's EmDrive. It too violates the law of conservation of momentum, and the inventor's experiments have not been replicated.

Since I wrote the above sentence back in 2010, there have been a couple of quote "replications" unquote. One was in China, the other at NASA.

My take is:

  1. Inventor Roger Shawyer's theoretical basis for his EmDrive appears to be total rubbish. It violates conservation of momentum, which would basically mean scrapping all of physics and starting over from scratch, yet still predicting the same results of every experiment in physics in the last few hundred years. This is because of the Correspondence Principle. Conservation of momentum is required and maintained in Maxwell's equations, Newtonian mechanics, special relativity, electrodynamics and quantum mechanics (and their combination, quantum electrodynamics).
  2. Shawyer's theoretical basis may have nothing to do with the equipment. That is, his basis may be rubbish but he accidentally stumbled onto an arrangement of equipment that actually does create anomalous thrust.
  3. It is a good rule of thumb to be skeptical of positive results when the measurements are at the limit of accuracy.
  4. The fact that three experiments by three different researchers have shown positive results is interesting. However, there are questions about the results.
  5. If the EmDrive actually works, it really and truly is a reactionless drive. Which means it is a weapon of mass destruction that would make the Dinosaur-killer asteroid look like a wet fire-cracker.

John Baez points out that the NASA experiment measured a force that was one thousandth as big as from the Chinese experiment (The incredible shrinking force! In 10 years the device will be using quantum gravity and producing even less force. ). And also that there were some serious problems with the experimental setup (which Mr. Baez goes into in detail).

Corey Powell has an interesting analysis of the history of this affair in an article entitled Did NASA Validate an “Impossible” Space Drive? In a Word, No..

Ethan Siegel does further analysis, along with the red-flag warnings that should tip off careful readers that something suspicious is underway, in his article How to fool the world with bad science

Power Requirements

I had thought that one could hand-wave a reactionless drive but control it with some kind of limit on the damage. Specifically I thought that one could figure the kilowatt equivalent of the momentum change created by such a drive, and use that as the required power.

The experts at quickly educated me as to how naive I was.

The underlying problem is that breaking the law of conservation of momentum shatters the entire mathematical framework. The specific problem is that you will get different values for the kinetic energy expended depending upon the reference frame of the observer.

Isaac Kuo said:

There are basically two approaches you can use:

1. There is a special frame of reference. In this case, the "reactionless" drive is really pushing against an infinitely massive special frame of reference.

(ed note: which means you've just destroyed Einstein's Relativity, with all the collateral science damage that implies)


2. There is no special frame of reference. In this case, the only way to sort of preserve conservation of energy is to limit drive efficiency to that of a photon drive. This is not a very useful drive, though, since it has the same (low) performance as a photon drive.

(ed note: the photon drive, where one lousy Newton of thrust takes three hundred freaking megawatts!!)

Isaac Kuo

Dr. John Schilling said:

There is the complication that "energy of the thrust" is as meaningless a phrase as, e.g., "mass of the time".

Thrust is a force, not an energy. Force, multiplied by distance, gives an energy. A force of one pound, applied as an object moves over a distance of one foot, equates to (unsurprisingly) one foot-pound of energy. The same force, over a greater or lesser distance, comes to proportionately more or less energy.

In MKS, by the way, that would be one Newton of force over one meter of distance equals one Joule of energy. If we assume constant force and motion, we can extend that to one Newton of force applied constantly at a velocity of one meter per second, equals a power of one watt.

The question is, velocity relative to what?

If it is a rocket, the relevant velocity is that of the rocket's own exhaust relative to the rocket itself. For an "intertialess thruster", the answer isn't clear and the power or energy associated with a given thrust will change widely depending on what reference frame you use to measure your velocity.

Which is one facet of the reason "inertialess thrusters" seem to be physically nonsensical. However, if you really need one for some SFnal purpose, you could try either

  1. the one universally invariant velocity in real physics. That being the velocity of light, giving you a figure of three hundred megawatts of power per Newton of thrust. A tad high for most purposes, I think, and functionally equivalent to saying your thruster is a photon drive or a (nearly-)massless-neutrino drive or a Dark Energy Rocket or whatever.
  2. the velocity of the spacecraft relative to some absolute reference frame. Either a cosmic absolute, or a local absolute tied e.g. to the nearest massive body or bodies in whatever manner is most convenient to the story. This is functionally equivalent to the old aetheric theories, and you can mine those for ideas.
Dr. John Schilling

Why doesn't this reference frame problem occur with an ordinary rocket? Isaac explains:

Because an ordinary rocket has a "reaction". The amount of kinetic energy added to the rocket by a rocket thrust depends upon what frame of reference you look at it. Indeed, there are plenty of frames of reference where the rocket thrust subtracts kinetic energy from the rocket! So you can't meaningfully talk about THE amount of kinetic energy added to the rocket. However, you CAN meaningfully talk about how much kinetic energy the rocket adds to the system because kinetic energy is also added to (or subtracted from) the rocket exhaust. No matter what frame of reference you use, the total amount of kinetic energy in the rocket plus the exhaust is increased by the same amount.

Isaac Kuo

In an ordinary rocket, both the kinetic energy of the rocket and the kinetic energy of the exhaust will change. Different observers will disagree about the absolute change of each, but will agree about the net change in kinetic energy, and so energy conservation can be enforced.

Example: A hundred-kilogram satellite ejects one gram of nitrogen through a cold-gas thruster at a velocity, relative to the spacecraft, of one hundred meters per second.

An observer at rest relative to the initial position of the spacecraft will see it accelerate to 0.001 meters per second, increasing its kinetic energy by 0.05 millijoules. The exhaust will be observed to accelerate to 99.9995 meters per second, with resulting kinetic energy of 4.99995 Joules. The total kinetic energy increase, provided by the expanding gas, comes to 5 Joules.

An observer zipping along in the opposite direction at 1,000,000 meters per second, will see both the spacecraft and the propellant as having had an initial velocity of 1,000,000 meters per second, and an initial kinetic energy of 50,000,000,000,000 Joules and 500,000,000 Joules, respectively. The spacecraft accelerates to 1,000,000.001 meters per second, giving it a new kinetic energy of 50,000,000,100,000 Joules - a gain of 100,000 Joules. Far cry from the .05 millijoules the stationary observer had thought the spacecraft acquired.

But the moving observer will have seen the slug of exhaust gas decelerate from 1,000,000 m/s to 999,900.0005 meters per second, with a new kinetic energy of 499,900,005 Joules. That's a loss of 99,995 Joules. So the net change in energy is, spacecraft +100,000.0, exhaust -99,995.0, or plus 5.0 Joules. Both observers agree on conservation of energy. And, for that matter, momentum.

If there were only the spacecraft involved, they'd be arguing about the missing hundred kilojoules.

Dr. John Schilling

If you're talking about a "true" reactionless drive, where energy is converted directly into momentum (or angular momentum), then there are lots of complications. Consider for instance that kinetic energy goes as the square of the speed:

K = (1/2) m v^2

So the power P you need to accelerate is dK/dt:

dK/dt = (1/2) m [2 v dv/dt] = m v a

As you can see, the power is a function of not only the acceleration that you want (which seems obvious), but also the speed at which you're currently traveling. The snag there is that your current speed is frame dependent. Consider that you're already doing your job and accelerating along nicely. At that point you pass someone who is already coasting at nearly the same speed you are. He sees you using much less power! Who's right?

The solution is that you either need to play by the rules of the game and use reaction drives (even if it's just reaction momentum, like a photon drive), or posit a special frame in violation of special relativity. With the special frame, now there's a "correct" frame where all the kinetic energy calculations are "official" and everyone agrees on them.

Erik Max Francis

Reactionless Drives That Ain't

Science Fiction author (and holder of two degrees in Physics) Thomas Mays came up with a marvelous unobtanium idea that sure acts like a reactionless drive, but it isn't. He used it in his short story "Bumped".

Ordinary matter in general and rocket reaction mass in particular transfers momentum by atoms colliding with each other. In Thomas Mays' gadget, there is still momentum transfer by collision but it is non-local. Essentially they are transferring their momentum through microscopic wormholes. So you could, say, transfer some momentum from part of Luna to your spaceship. Some of orbital momentum of Lunar crust orbiting Terra and orbiting Sol is stolen and transferred to the spacecraft, as if they had collided. Only they could be millions of kilometers apart, because wormholes.

The point being that the spacecraft does not have to carry its reaction mass. Which instantly frees the spacecraft from the Tyranny of the Rocket Equation, and gives you the benefits and problems of a reactionless drive (even though it technically is not reactionless). It still violates Burnside's Advice, though.

It is similar but not quite the same as the Challenger from Tom Swift in the Race to the Moon. It uses "repellatrons" (read "tractor beams" or "repulsors") which repel Terra thus propelling the spacecraft upwards. Basically it is using Terra as reaction mass. Another related concept is doing an end run around spacecraft mass ratio by somehow "teleporting" (read "Star Trek Transporter") the reaction mass from home base to the spacecraft's propellant tanks.

Alistair Young was inspired by Mass Effect to create something similar to Thomas May's device for his Eldraeverse: Vector Control. He got the name from A Miracle of Science.

Reactionless Drive: The important thing to remember about a reactionless drive is that it’s not reactionless.

A vector control drive is a member of the entire family of vector-control technologies, and like all the other members of said family, it obeys Newton’s Third Law. Vector control used for artificial gravity transfers the reaction to the action it’s applying to the stuff between the gravity rotors to the structural framework it’s bolted to. Vector control used in tractor/pressor beams pushes the party of the first part every bit as much as it pulls the party of the second part, and on the precisely opposite vector. And a vector control drive, while it utilizes extremely fancy ontotechnological trickery to spread the reaction to the action out across all the ambient mass in appropriately vast volumes (if not the entirety of, but that’s real hard to measure) of the local universe, is absolutely no different in this respect.

What you get from a vector control drive is not needing to haul all those vast quantities of reaction mass around with you. Note: only the remass. Vector control drives still need fuel, and since there are certain inevitable inefficiencies in coupling the action to the reaction quite so indirectly, they need significantly more fuel than an equivalent reaction drive. You aren’t getting away from having those huge spherical tanks of D and He3 strapped to the back of your starship that easily.

Another thing you might get is a degree of, um, stealth, inasmuch as you don’t have the huge bright drive flare that most reaction drives tend to produce. Of course, as we all know, there ain’t no Stealth In Space, because apart from your life support’s comfortable temperature alone making you stand out like a lighthouse against the 3K sky background, you’re also running a bloody great reactor (and radiating its heat) to power your vector control drive.

In short: the existence of vector control permits you to build something damned close to a classic SFnal reactionless drive. It provides you with rather fewer reasons as to why you might want to, outside a few highly specialized edge cases.

(Side note: the mad scientists out at Resplendent Exponential Vector have also been experimenting along the lines of the Alcubierre drive to get reactionlessness and a working fittler in one package. After their prototype vaporized a fortunately-spare dwarf planet and exploded first time out, their tort insurers have been reluctant to cover further development at a price they can afford.)

Infinite Energy Drives

Photon drives have the ultimate exhaust velocity. You can't get faster than the speed of light, if you make a rocket with an FTL exhaust the shade of Albert Einstein will rise from the grave and give you an atomic wedgie. Such high exhaust velocites make for truely awesome delta V.

Even better: since you are not expending propellant, you will never run out. So if you never run out of propellant and never run out of "fuel" it means you have something like a Bussard Ramjet on steroids. Without all the pesky fuel scooping problems.

The fly in the ointment is that you will be expending energy like crazy. You will pay in energy as if you borrowed a few gigawatts from Sparky the Loan Shark. We are talking Three! Hundred! Megawatts! for one solitary pathetic newton of thrust.

Science fiction authors, hungry for the ultimate torchship, quickly started looking for some bottomless source of torrents of energy so they can feed their thirsty photon drives. It didn't take them long to find Zero-Point energy.

The fly in that ointment is that physicists cannot figure out if the energy is at worthwhile levels and have no idea how to extract vacuum energy. Except for Dr. Robert Forward's Charged Foliated batteries, and they are more an energy storage device than an energy source. But that didn't stop the science fiction authors.

Vacuum energy was used in All the Colors of the Vacuum by Charles Sheffield, Encounter with Tiber by Buzz Aldrin John Barnes, and The Songs of Distant Earth by Sir Arthur C. Clarke.

Arguably the Grand Unified Theory (GUT) drives and GUTships in Stephen Baxter's Xeelee novels are also a species of vacuum energy power sources.

But don't forget the Jon's Law. A gamma-ray laser hooked up to a vacuum energy power source will make the Death Star's main weapon look like a damp firecracker. You'll be able to punch holes in Jupiter.

The Song of Distant Earth

Of all the psychological hammer blows that the scientists of the twentieth century had to endure, perhaps the most devastating — and unexpected — was the discovery that nothing was more crowded than ‘empty’ space.

The old Aristotelian doctrine that Nature abhorred a vacuum was perfectly true. Even when every atom of seemingly solid matter was removed from a given volume, what remained was a seething inferno of energies of an intensity and scale unimaginable to the human mind. By comparison, even the most condensed form of matter — the hundred-million-tons-to-the-cubic-centimetre of a neutron star — was an impalpable ghost, a barely perceptible perturbation in the inconceivably dense, yet foamlike structure of ‘superspace.’

That there was much more to space than naive intuition suggested was first revealed by the classic work of Lamb and Rutherford in 1947. Studying the simplest of elements — the hydrogen atom — they discovered that something very odd happened when the solitary electron orbited the nucleus. Far from travelling in a smooth curve, it behaved as if being continually buffeted by incessant waves on a sub-submicroscopic scale. Hard though it was to grasp the concept, there were fluctuations in the vacuum itself.

Since the time of the Greeks, philosophers had been divided into two schools — those who believed that the operations of Nature flowed smoothly and those who argued that this was an illusion; everything really happened in discrete jumps or jerks too small to be perceptible in everyday life. The establishment of the atomic theory was a triumph for the second school of thought; and when Planck’s Quantum Theory demonstrated that even light and energy came in little packets, not continuous streams, the argument finally ended.

In the ultimate analysis, the world of Nature was granular - discontinuous. Even if, to the naked human eye, a waterfall and a shower of bricks appeared very different, they were really much the same. The tiny ‘bricks’ of H2O were too small to be visible to the unaided senses, but they could be easily discerned by the instruments of the physicists.

And now the analysis was taken one step further. What made the granularity of space so hard to envisage was not only its sub-submicroscopic scale — but its sheer violence.

No one could really imagine a millionth of a centimetre, but at least the number itself — a thousand thousands — was familiar in such human affairs as budgets and population statistics. To say that it would require a million viruses to span the distance of a centimetre did convey something to the mind.

But a million-millionth of a centimetre? That was comparable to the size of the electron, and already it was far beyond visualization. It could perhaps be grasped intellectually, but not emotionally.

And yet the scale of events in the structure of space was unbelievably smaller than this — so much so that, in comparison, an ant and an elephant were of virtually the same size. If one imagined it as a bubbling, foamlike mass (almost hopelessly misleading, yet a first approximation to the truth) then those bubbles were …

a thousandth of a millionth of a millionth of a millionth of a millionth of a millionth …

… of a centimetre across.

And now imagine them continually exploding with energies comparable to those of nuclear bombs — and then reabsorbing that energy, and spitting it out again, and so on forever and forever.

This, in a grossly simplified form, was the picture that some late twentieth-century physicists had developed of the fundamental structure of space. That its intrinsic energies might ever be tapped must, at the time, have seemed completely ridiculous.

So, a lifetime earlier, had been the idea of releasing the new-found forces of the atomic nucleus; yet that had happened in less than half a century. To harness the ‘quantum fluctuations’ that embodied the energies of space itself was a task orders of magnitude more difficult — and the prize correspondingly greater.

Among other things, it would give mankind the freedom of the universe. A spaceship could accelerate literally forever, since it would no longer need any fuel. The only practical limit to speed would, paradoxically, be that which the early aircraft had to contend with — the friction of the surrounding medium. The space between the stars contained appreciable quantities of hydrogen and other atoms, which could cause trouble long before one reached the ultimate limit set by the velocity of light.

The quantum drive might have been developed at any time after the year 2500, and the history of the human race would then have been very different. Unfortunately — as had happened many times before in the zig-zag progress of science — faulty observations and erroneous theories delayed the final breakthrough for almost a thousand years.

The feverish centuries of the Last Days produced much brilliant — though often decadent — art but little new fundamental knowledge. Moreover, by that time the long record of failure had convinced almost everyone that tapping the energies of space was like perpetual motion, impossible even in theory, let alone in practice. However — unlike perpetual motion — it had not yet been proved to be impossible, and until this was demonstrated beyond all doubt, some hope still remained.

Only a hundred and fifty years before the end, a group of physicists in the Lagrange 1 zero-gravity research satellite announced that they had at last found such a proof; there were fundamental reasons why the immense energies of superspace, though they were real enough, could never be tapped. No one was in the least interested in this tidying-up of an obscure corner of science.

A year later, there was an embarrassed cough from Lagrange 1. A slight mistake had been found in the proof. It was the sort of thing that had happened often enough in the past though never with such momentous consequences.

A minus sign had been accidentally converted into a plus.

Instantly, the whole world was changed. The road to the stars had been opened up — five minutes before midnight.


The first suggestion that vacuum energies might be used for propulsion appears to have been made by Shinichi Seike in 1969. (‘Quantum electric space vehicle’; 8th Symposium on Space Technology and Science, Tokyo.)

Ten years later, H. D. Froning of McDonnell Douglas Astronautics introduced the idea at the British Interplanetary Society’s Interstellar Studies Conference, London (September 1979) and followed it up with two papers: ‘Propulsion Requirements for a Quantum Interstellar Ramjet’ (JBIS, Vol. 33,1980) and ‘Investigation of a Quantum Ramjet for Interstellar Flight’ (AIAA Preprint 81-1534, 1981).

Ignoring the countless inventors of unspecified ‘space drives,’ the first person to use the idea in fiction appears to have been Dr Charles Sheffield, Chief Scientist of Earth Satellite Corporation; he discusses the theoretical basis of the ‘quantum drive’ (or, as he has named it, ‘vacuum energy drive’) in his novel The McAndrew Chronicles (Analog magazine 1981; Tor, 1983).

An admittedly naive calculation by Richard Feynman suggests that every cubic centimetre of vacuum contains enough energy to boil all the oceans of Earth. Another estimate by John Wheeler gives a value a mere seventy-nine orders of magnitude larger. When two of the world’s greatest physicists disagree by a little matter of seventy-nine zeros, the rest of us may be excused a certain scepticism; but it’s at least an interesting thought that the vacuum inside an ordinary light bulb contains enough energy to destroy the galaxy … and perhaps, with a little extra effort, the cosmos.

In what may hopefully be an historic paper (‘Extracting electrical energy from the vacuum by cohesion of charged foliated conductors,’ Physical Review, Vol. 30B, pp. 1700-1702, 15 August 1984) Dr Robert L. Forward of the Hughes Research Labs has shown that at least a minute fraction of this energy can be tapped. If it can be harnessed for propulsion by anyone besides science-fiction writers, the purely engineering problems of interstellar — or even intergalactic — flight would be solved.

From The Song of Distant Earth by Sir Arthur C. Clarke (1985)
Extreme Relativistic Rocketry

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

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

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

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

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

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

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

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

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

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

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


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

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

this can be solved for time quite simply as:

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

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

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

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

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

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

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

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

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

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

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

This modifies the Rocket Equation to:

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

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

which becomes:

As and , then we have

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

Of course the trick is creating energy via GUT physics…

From Extreme Relativistic Rocketry by Adam Crowl (2015)

Submarines In Space

Several times in science fiction, a reactionless drive is invented. And then the scientist gets the bright idea that if they mount the drive inside a submarine they will have Instant Spaceship.

In reality this would not work very well. A submarine is build to resist stronger pressure outside pressing in, not stronger pressure inside pressing out. And if the submarine is nuclear powered, you had better attach some kind of heat radiator. Nuclear submarines get rid of heat by sucking in cold ocean water and spewing out hot heat sink water. This won't work in space, there isn't any ocean. Not to mention the fact that a sub nuclear reactor's coolant system requires gravity to work.

This trope seems to have been invented by John W. Campbell jr., in an article he wrote about the Dean Drive in 1960. Other novels that use this theme include The Daleth Effect by Harry Harrison (1969), Gilpin's Space by Reginald Bretnor (1983), Salvage and Destroy by Edward Llewellyn (1984), and Vorpal Blade by John Ringo (2007). There is a mention of an "inertial drive" (another name for a Dean Drive) in Randall Garrett's Anything You Can Do but there it is used as a way to make recon drones float in the air.

This also seems to have influenced a certain Matt Jeffries, designer of the original Starship Enterprise, Klingon Battle Cruiser, and related works. A couple of his designs feature a "sail" or "conning tower" which are common to submarines. Perhaps he read Campbell's Dean Drive article and was inspired. If the first few starships were actually refitted submarines, maybe purpose-built starships would retain the conning tower for tradition.

The first Matt Jeffries design with a conning tower was the Botany Bay aka DY-100 from the Star Trek episode "Space Seed." It was later re-used as Automated Ore Freighter Woden in "The Ultimate Computer".

Around 1967, the AMT plastic model company wanted to cash in on Star Trek mania. They wanted to make a line of plastic model starship kits, but of their own design. So they hired Matt Jeffries to make a starship, the Galactic Cruiser Leif Ericson. Again it had the signature submarine conning tower. Unfortunately the kit was a financial disappointment, and further starships in the line were cancelled. The kit was re-issued in 2011 due to demand from those who had the original kit when they were young.

In the early 1970's, when Larry Niven and Jerry Pournelle were writing the classic The Mote in God's Eye, they used the Leif model as the inspiration for the INSS MacArthur.

Around 1975 Matt Jefferies was hired by George Pal to work on a TV series based on THE WAR OF THE WORLDS. As you can see the Hyperspace Carrier Pegasus is an outgrowth of the Leif Ericson. Note that instead of two side engines, the Pegasus has four, two on each side. For the TV series, Jefferies actually had the Pegasus upside down in relation to the Leif Ericson, in order to make the connection less obvious. The TV series was never picked up, alas. But this is a facinating glimpse of what might have been.

Occasionally in later science fiction illustrations one again finds the submarine conning tower.

Analog Dean Drive Article

A modern nuclear-powered submarine needs only relatively minor adaptations to make an ideal spaceship; it has everything it needs, save for the space drive.

The Dean drive requires a rotary shaft drive; our nuclear submarines turn nuclear energy into heat, produce steam, drive a turbine, and generate electric power. Electric power is perfect for running the Dean drive.

The modern submarines are — we have learned from past sad experience — equipped with lifting eyes so that, in event of accidental collision, quick salvage is possible. Pontoons can be towed in place, sunk beside the ship, and hitched to the built-in lifting eyes, and the ship refloated. The eyes are, of course, designed into the ship so that the structure can be lifted by those eyes without structural damage to the hull.

Dean drive units could be attached directly to the existent eyes. (ed note: you can see this in the image. The two bands around the submarine's waist hold the Dean Drive units. This also means the ship's direction of motion is in the direction the conning tower is pointed, which would make sense.)

The pressure hull of modern submarines is designed to resist at least 600 feet of water pressure; its actual thickness is a piece of classified data, of course, but we can guesstimate it must be at least 4 inches thick. After the second Bikini bomb test, the old submarine Skate was still in pretty fair condition; the light-metal streamlining hull looked like the remains of an airliner crash, but the pressure hull was perfectly intact. Stout stuff, a sub’s pressure hull.

And very fine stuff indeed as protection against the average meteor; the light streamlining hull would stop the micrometeors, of course.

Not even 4 feet of steel would stop primary cosmic rays, of course… but those inches of armor steel would have considerable damping effect on the Van Allen radiation belt effects.

The nuclear subs have already been tested with full crews for 30 continuous days out of contact with Earth’s atmosphere; their air-recycling equipment is already in place, and functions perfectly. What difference if the ‘out of contact’ situation involves submersion in water, instead of out in space?

The modern nuclear submarine is, in fact, a fully competent space-vehicle, lacking only the Dean drive.

With the Dean drive, the ship, if it can lift off the Earth at all, can generate a one-G vertical acceleration. Since that acceleration is being generated by engines capable of continuous operation for months — if not years — at a time, the acceleration can simply be maintained for the entire run; there would be no period of free-fall for the ship or crew. Therefore the present ship structure, equipment, and auxiliary designs would be entirely satisfactory. Also, a sub has various plumbing devices with built-in locks so the equipment can be used under conditions where the external pressure is widely different from the internal.

In flight, the ship would simply lift out of the sea, rise vertically, maintaining a constant 1000 cm/sec drive. Halfway to Mars, it would loop its course, and decelerate the rest of the way at the same rate. To the passengers, and to the equipment on board, there would be no free-flight problems.

There is one factor that has to be taken in to account, however; the exhaust steam from the turbine has to be recondensed and returned to the boiler. In the sea, seawater is used to cool the condenser; in space, the cold vacuum would do the job.

The tough part would be the first 100 miles up from the Earth; ice could be used.

As a crash program, this could have been done — if work started when Dean first applied for his patent — in 15 months. The application went in in July 1956; 15 months later would have been October 1957.

Under the acceleration conditions described above, a ship can make the trip from Earth to mars, when Mars is closest, in less than three days. And even when Mars is at its farthest possible point, on the far side of the Sun, the trip would only take 5 days.

It would have been nice if, in response to Sputnik I, the US had been able to release full photographic evidence of Mars Base I.

from "The Space Drive Problem" by John W. Campbell, Jr in Analog Magazine June 1960

The Daleth Effect

Analog December 1969. Illustration for Harry Harrison's "In Our Hands, The Stars", which was later expanded into the novel The Daleth Effect.

Harry Harrison wrote an amusing but cautionary tale called The Daleth Effect. In the novel, an Israeli scientist discover the principle for a reactionless drive. Naturally the first real test is the Submarine Spacecraft trick.

He returns to his native Denmark to develop it. He wishes to develop the idea without it falling into the hands of the military, since it also has potential as a weapon. Good luck with that.

Denmark keeps it a secret until they feel obligated to use the technology in public to rescue some cosmonauts stranded on Luna. Any fool could have told the Danes that no good deed goes unpunished.

Naturally the US, Soviet Union, and other powerful nations will stop at nothing to lay their hands on this technology. The race is on! They try all sorts of tactics to pressure the Danes but to no avail. They look on with helpless rage as the Danes establish a Lunar base and make a large ship for a visit to Mars.

Like absolute idiots the Danes invite foreign dignitaries to ride on the Mars trip. Naturally pretty much 100% of the dignitaries turn out to be secret agents. Hilarity ensues. And then the novel has a most ironic and satisfying ending.

Gilpin's Space

Eccentric but brilliant scientist Saul Gilpin invents a magic hyperspace faster-than-light propulsion system / antigravity surface-to-orbit gadget which can be cobbled together from parts available from your local hardware store. He mounts it on a submarine and has instant starship. Then he and the submarine depart for parts unknown.

This makes the totalitarian government very unhappy. They want to use this technology, they do not want citizens getting their hands on it. Makes it far to easy to escape the totalitarian state. Then they find out that Gilpin has mailed blueprints of the gadget to quite a few people. Hilarity ensues.

Salvage and Destroy

An ancient alien interstellar empire is worried about the large US and Soviet submarine fleets. Once Earth discovered anti-grav and FTL drives, the warlike unstable Earthlings would have a ready-made fleet of combat starships. This could turn into a nasty problem.

(ed note: aliens on Earth are covertly observing a US submarine)

“She’s an attack sub.” Joshua altered course as the black hull came sliding toward us out of the dawn mists. He gave one blast on the horn. “Mark, can you read the number on her sail?”

“SSN-767.” Mark put down his binoculars and took Jane’s Fighting Ships from the book rack in the wheelhouse. “USS Muskelunge. Four thousand six hundred tons dived. One hundred and ten meters overall. Six torpedo tubes plus subsurface attack missiles. Pressurized water-cooled reactors feeding two steam turbines. Speed dived-fifty knots plus. Complement—one hundred and ten.” He closed the book. “She’s among the most powerful warships in the Cluster—now the Ult fleets are laid up.”

“Fit that sub with inertial drive and she’d be ready for space!” said Joshua. “And there’s over four hundred like her at sea.”

An instant space fleet!” remarked someone on the foredeck.

“They couldn’t make a vortex passage. They couldn’t get out of this starfield. They wouldn’t have anybody to fight.”

“They’d find somebody. Or settle for fighting each other!”

Add inertial drive and Earth would have a space fleet! However unlikely, the idea was chilling. The men and women with me would gladly crew a human fleet, apparently blind to the outcome of such madness, as the Terrans were blind to the imminent effects of their own folly.

From nuclear submarine to inertial spaceship—an immense leap. Yet that hunter-killer exemplified a leap of the like magnitude. From sail to atomics in a hundred years! If the Terrans survived the next hundred would they leap into the dark? Into the Cluster?

I shook myself. Not even their present exponential advance would take them to vortex transits within a century. But within centuries? Up to the stars or down to hell?

from Salvage and Destroy by by Edward Llewellyn (1984)

Vorpal Blade

Shortly after they'd stopped the invasion, the Adar had given him another strange device. On first tests, it had appeared to be the world's most powerful nuclear hand grenade. Any electrical power sent to it, so much as a spark of static, and, well, there was a boom. A really big boom. "There should have been an earth shattering Ka-Boom!" boom. Putting three-phase on it had, in fact, erased a solar system.

The Adar didn't know what it was supposed to do but Weaver had basically guessed that it was, in fact, some sort of Faster-Than-Light drive. It took nearly a year of tinkering, and two more planets, to figure out that it was, in fact, such a drive. It had taken another year to create the first prototype starship.

By then, Weaver had switched sides in the ongoing sales war, leaving the Beltway and taking a direct commission in the Navy, which was the lead service in developing the world's first spaceship. He'd pointed out even before switching sides that the Navy just made more sense. The President wanted a presence off-world as fast as possible. They'd picked up enough intel in the brief war to know that the Dreen had some sort of FTL as well. Finding out where the Dreen were, whether they were headed to Earth through normal space, was a high priority. The only way to make a spaceship, fast, was to convert something. The obvious choice had been one of the many ballistic missile submarines that were being decommissioned.

So Weaver, while continuing to consult on engineering issues, was now the astrogation officer of the Naval Construction Contract 4144. Despite a couple of shakedown cruises around the solar system, the Top Secret boat had yet to be named. The 4144 had all the beauty and problems of any prototype. Most of the equipment was human, much of it original to the former SSBN Nebraska. Other bits were Adar or Human-Adar manufacture. The fact that it worked at all was amazing.

"How fast are the missiles? I mean, space is big, right, so they have to be fast?" Miller continued peering out the window, on a submarine, in front of him. The window seemed to be harder to get used to than the fact that he was standing inside humanity's first starship. A freakin' window on a submarine, he thought.

"The propulsion system is a mix of Adar tech and human. The thing is basically designed around the old nuclear thermal rocket concept but uses a small quarkium reactor instead of a fission reactor. No radiators needed and we use a dense Adar coolant for propellant instead of LOX or hydrogen or water. The Adar stuff gives us waaaay better m-dot. Using an Adar material for the nozzle we were able to get over eight thousand seconds of specific impulse out of it."

(ed note: 8,000 Isp is an exhaust velocity of about 78,000 m/s. Which would make that propulsion system a torch drive. Freaking missile has performance better than a blasted Zubrin nuclear salt water rocket.)

from Vorpal Blade by John Ringo (2007)

Atomic Rockets notices

This week's featured addition is Antigravity

This week's featured addition is McDonnell Douglas Phase B Space Station

This week's featured addition is Megacorporations

Atomic Rockets

Support Atomic Rockets

Support Atomic Rockets on Patreon