So you give someone an inch and they want a yard. Given them a rocket ship and suddenly they want a star ship. SF writers want to use exotic settings on alien planets, but the real estate in our solar system mostly looks like a bunch of rocks. "That's OK," the writer thinks, "There are a million-jillion other solar systems in the galaxy, surely they are not all a bunch of rocks (I know they are there, I've got a map). I know that those spoil-sports at NASA have ruined our solar system for SF writers since their nosy space probes failed to find dinosaur-infested jungles of Venus and scantily-clad Martian princesses. But they haven't sent probes to other stars yet! Why not turn my rocket ship into a star ship?"
Unfortunately it isn't that easy. The basic problem is that interstellar distances are freaking huge.
Let's make a mental model. Say the scale is such that one astronomical unit is equal to one millimeter (1/25th inch). There is a glowing dot for the Sun, and one millimeter away is a microscopic speck representing the Earth. The edge of the solar system is about at Pluto's orbit, which varies from 30 mm to 50 mm from the Sun (about 1 and 3/16 inch to almost 2 inches). Imagine this ten-centimeter model floating above your palm.
This would put Proxima Centauri, the closest star to the Sun, at about 272 meters away. That's 892 feet, the length of about two and a half football fields or four and a half New York city blocks! Glance at the ten-centimeter solar system in your hand, then contemplate the nearest solar system four and a half city blocks away.
And the center of the galaxy would be about 1600 kilometers away (about 990 miles), which is a bit more than the distance from Chicago, Illinois to Houston, Texas.
"All right, all right!" the SF author grumbles, "So the distance is outrageous. What of it?"
This of it. How long do you think it is going to take to travel such distances? As an example, the Voyager 1 space probe is currently the fastest human made object with a rest mass, zipping along at a blazing 17.46 km/s. This means that in the space of an eyeblink the little speed demon travels a whopping eleven miles! That's smokin'. What if it was aimed at Proxima Centauri (it isn't), how long would it take to reach it?
About 74,000 years! Which means that if Neanderthal men had launched something as fast as Voyager 1 to Proxima, it would just barely be arriving right now. And the joke's on them. Neanderthals are extinct so not even their descendants would reap the benefit of any scientific broadcasts from the Proxima probe. A similar argument could be used against any interstellar probes we could launch.
This leaves us with two alternatives: deal with the fact that average human lifespan is 74 years, not 74,000; or make the starship go faster.
Well, three, if you count "faster than light", but that will be covered later.
As Gordon Woodcock put it, the three methods of travelling to other stars are "go slow", "go fast", and "go tricky." This means "deal with short human lifespan", "use relativistic speeds", and "go faster than light".
The first of Gordon Woodcock's methods of interstellar travel is "go slow".
Distance between stars is huge, traveling said distance slower-than-light will take a huge amount of time, human beings have a very limited lifespan. And it is much easier to travel at 10% the speed of light than it is to travel at 99.99999% the speed of light
"Go Slow" means to focus on the limited human lifespan problem, and be content to travel slowly ato 10% c or so.
There are several ways of dealing with the lifespan issue. Go to the Tough Guide to SF and read the entry "Slowboat".
Since every atom of mass is a penalty, the logical starship would just carry a master computer and no human crew. This avoids the payload mass of the crew, the habitat module, the life support system, food, water, and everything. The starship might be under a meter long, which would make this concept the lowest mass of all the slowboat starships.
However, nobody wants wants to read about the adventures of a computer (yes, I know there have been a couple of SF stories on this theme, but it requires extraordinary skill on the part of the author, and the stories are not wildly popular).
Enter the "digital crew" concept. You postulate technology capable of "uploading" human brain patterns into a computer. In essence, the ship's computer is running incredibly advanced simulations of the crew, creating a virtual reality much like that found in the movie The Matrix. This also allows the author to pontificate upon the nature of reality, ask if we are actually unaware virtual people in a virtual reality, and stuff like that. Authors who have used this concept include Sean Williams, Shane Dix, and Greg Egan.
The point is the author is allowed to write stories about human beings, but the digital humans and their digital environment take up zero mass.
One could add equipmment capable of manufacturing artificial bodies for the crew from local materials upon arrival at the destination. However, the advantage of a digital crew ship over a seed ship is the lower ship mass due to the absence of frozen embryos, artificial wombs, and robot mommies. Adding artifical body manufacturing facilites would reduce or remove the advantage. The only remaining advantage is that the new bodies inhabited by adults instead of babies.
You could regain the advantage if the manufacturing equipment is really tiny. Say a couple of grams worth of nanotechnology self-replicating machines, intended to work on handy asteroids or other free materials lying around the destination solar system. The nanotechnology bootstraps itself by replicating using in-situ resources as feedstocks until it has mass of a few tons, then shifts gears to start manufacturing artificial bodies.
The next higher mass class of slowboat is the Seed ship aka Embryo Space Colonization via an embryo-carrying interstellar spaceship (EIS). It will tend to have more mass than a Digital Crew ship and less than a Sleeper Ship.
The starship is tiny, containing a payload of millions of frozen fertilized eggs, artificial wombs, robot factory, and a master computer. No mass is needed for life-support, habitat modules, or any human crew.
After traveling for thousands of years, the ship lands in a good spot for a colony. The robot factory starts cranking out robots. Robots build the settlement buildings and start growing food (if the planet is really nasty they might have to spend a few centuries terraforming the planet first). Then the master computer thaws out enough eggs for the available artificial wombs, brings the babies to term, then tries to convince the babies that the robots are mommy and daddy.
I don't know about you but I suspect that the first generation is going to grow up a little bit emotionally stunted.
The most straightforward method is to cryogenically preserve human embryos. The more difficult but more flexible method is to carry frozen sperm and egg cells, and do in vitro fertilization at the destination. The most unobtanium method is to carry genetic information in computer files, then synthesize the required genetic sequences at the destination.
As with all interstellar colonization proposals, there are quite a few technological challenges to solve:
The ship robots will have to be advanced enough to raise and nurture the children, as well as building the settlement and growing crops. They could be teleoperated drones controlled by the ship's computer.
The side problem is they will have to be manufactured at the destination using in situ resources. The whole idea behind the Seed Ship is to minimize the payload mass, carrying an army of robots negates this.
Examples of Seed Ships in science fiction include The Song of Distant Earth by Sir. Arthur C. Clarke, 2001 Nights chapter Night 4 by Yukinobu Hoshino, "Longshot" by Vernor Vinge and the movie Interstellar.
Sleeper ship tend to have more mass than a Seed Ship and less than a Generation Ship.
The crew is frozen into suspended animation, so they do not age nor require food and oxygen during the thousand year journey. Or spacious living accomodations. The Sleeper Ship does require the mass of the crew, enough mass for a spartan habitat module, and only enough consumables for the time the crew will be awake.
Poul Anderson warned that frozen crew have a limited shelf life. Naturally-occurring radioactive atoms in the human body will cause damage. Normally the body will repair such damage, but one in suspended animation cannot. After a few hundred years, enough damage will accumulate so that a corpse instead of a living person is thawed out at journey's end. This may force one to thaw each crew member every fifty years or so to allow them to heal the damage, then freezing them again.
The highest mass type of slowboat tends to be the Generation ship. This is because it has to carry the mass of an entire community as crew, a habitat module at the minimum the size of a small town, and enough life support for the people for however many hundreds of years the journey takes. As the ship crawls to its destination, generations of people are born, have children, and die of old age.
Problems include the later generations refusing to cooperate with their forefather's vision, civil wars that wreck the ship, failure of the closed ecological life support system, and the later generations forgetting where they came from, forgetting where they are going, and indeed forgetting the fact that they are in a starship.
An interesting incremental approach is the Cross-generation ship.
In Larry Niven and Jerry Pournelle's FOOTFALL, the aliens deal with the "forgetful generation" problem by including a group of original crew frozen in suspended animation. Members of the original crew are periodically woken so they can ensure that the generational crew keeps the faith.
If the generation ship is escaping from some Terra-destroying catastrophe; carrying Terra's scientific and cultural heritage, a representative sample of animal species, colony equipment and supplies, and a fertile representative sample of humanity, the craft is termed an Interstellar Ark.
A variation of the "Increase Lifespan" technique was in Charles Sheffield's Between The Strokes Of Night. A technique was discovered that would allow human metabolism to enter the "S-state." In this state, humans age at a rate 1/1000th normal, and perceive things at the same rate. So with ships traveling at a slow 10% light speed, the trip to Proxima Centauri seems to take only a few weeks to an S-state person. But normal humans move so fast that S-state humans cannot see them, and normal humans will still perceive the trip taking about forty years.
Finally there is the "Methuselah" concept. Advances in medical technology might increase human lifespan to thousands of years. So prolonged interstellar trips are more a problem of boredom instead of life-span.
In Dr. Robert L. Forward laid it all out in his classic paper "Roundtrip Interstellar Travel Using Laser-Pushed Lightsails," Journal of Spacecraft and Rockets 21 (1984), pp. 187–195.
The advantage is the starship does not have to carry the mass of the engine and the propellant, you leave it at home. This makes the task of designing the starship merely incredibly difficult, instead of utterly impossible.
The home system can also add to the laser batteries gradually after the starship's journey starts, as needed (the inverse-square law will weaken the beam as the range increases). You cannot do this with a self-contained starship, all of its engines have to be built before the journey starts.
And if a home system's laser battery or two break down, no problem! The resources of the home system are available to fix it. If a self-contained starship engine breaks down on the other hand, they are in trouble. They do not have the resources of the home system to help, all alone in interstellar space. They have to fix it themselves with whatever spare parts they managed to bring along. Or die all alone in the night.
The disadvantage is the starship is at the mercy of whoever is in charge of the laser station back in the Solar System. If there is a revolution back home and the Luddites seize power, the starship and crew are up doo-doo pulsar with no gravity generator. Dr. Forward came up with two clever ways of using the home system's lasers to decelerate the starship into the target solar system. In Larry Niven and Jerry Pournelle's classic The Mote In God's Eye the Motie aliens laser sail starship rather pointedly do NOT use Dr. Forwards deceleration methods, because they absolutely do not trust the laser station controllers back at their homeworld. In Dr. Forward's The Flight of the Dragonfly aka "Rocheworld" political foot-dragging and short-sighted policies almost lead to disaster for the laser station and starship. In Buzz Aldrin and John Barnes's Encounter With Tiber politics does kill the laser station and starship.
Starwisp is an ultra-low mass interstellar probe, a tiny sail driven by a beam of microwaves. The concept was invented by Dr. Robert L. Forward, and expanded upon by Dr. Geoffrey A. Landis.
Dr. Forward assumed that the microwave beam would be efficiently reflected by starwisp, so he calculated it would be a superconducting metal mesh with a sail mass of 16 grams and a payload mass of 4 grams; total mass of probe is 20 grams. Dr. Landis found this turned out not to be the case, it would absorb quite a bit of microwaves and heat up (i.e., the design is thermally limited). In Dr. Landis' design the starwisp is woven out of carbon wires with a sail mass of 1,000 grams, a payload mass of 80 grams, and a diameter of 100 meters.
Acceleration is 24 m/s2, microwave lens 560 km in diameter transmitting 56 GW of power, accelerating the probe to 10% of the speed of light.
Yes, it probably could be weaponized. See Accelerando by Charles Stross.
So your gigantic laser battery at home pushes the laser sail starship to its destination, accelerating it to about half the speed of light. Presumably you want to stop at your destination instead of streaking through it at 0.5c. But how?
If you were going about an order of magnitude slower, you might be able to use the sunlight from the destination star to put on the brakes. However that ain't gonna be enough at 0.5c. You'll just pancake into the star at a substantial fraction of the speed of light and be vaporized.
Dr. Philip Norem had a clever idea. Interstellar space has large magnetic fields. So one can use large electrical charges on the starship to make huge light-year wide sweeping turns by the Lorentz force.
Say you were going to Alpha Centauri. You aim the starship not at the destination, but instead off to one side. How far off depends upon the starship's turning radius. The laser battery back at the solar system pushed the starship up to relativistic velocities over the next 27 years or so. Then the lasers turn off.
The starship deploys one hundred metal cables, each about 50,000 kilometers long. It then charges them up to 800,000 volts and 3.7×104 coulombs. This is timed to interact with the interstellar magnetic field (as mapped) so that the starship makes a huge gradual turn, until it is approaching Alpha Centauri from the back door. That is, so that a line drawn from the starship to Alpha Centauri will pass directly through the solar system and the laser battery.
Meanwhile, the solar system laser battery starts up its barrage long enough in advance so that the leading edge of the laser wavefront will reach the starship just as it is aligned properly. It then continues the barrage for the years required to bring the starship to a halt exactly at Alpha Centauri.
In Mallove and Matloff's The Starflight Handbook, they note that if the interstellar magnetic fields have not been well mapped, this scheme could potentially doom the starship to a lonely death. If the starship misses the beam, it just goes sailing off into the Big Dark. The Starflight Handbook has the equations for a starship using the Lorentz force, if you are interested.
A related issue is mechanical reliability. Currently the best space probe NASA can build cannot be guaranteed to properly function past about forty years. The starship will need an extensive self-repair capability or have some way of having humans periodically available to fix things.
A common science fiction gag is the "jumping the gun" plot. A slower than light ship departs on a 500 year journey to Alpha Centauri. About 100 years after launch, some joker on Terra invents a faster-than-light starship. Fleets of FTL ships fly to Alpha Centauri and colonize the place. The slower than light ship arrives to find not the virgin planets they were expecting, but instead 400 year old colonies. Har, har, silly slowboat.
The earliest example of this trope that I could find was A. E. van Vogt's "Far Centaurus" (1944)
In 2006, scientist Andrew Kennedy actually studied the problem. He published his analysis in a paper called Interstellar Travel: The Wait Calculation and the Incentive Trap of Progress. In it, he introduced his solution: the Wait Calculation.
The Wait Calculation allows future space explorers to avoid the "jumping the gun" problem (and also avoid being paralyzed with indecision by terror of jumping the gun). The equation shows that, assuming technology develops in such a way that there is exponential growth in the velocity of travel, there is an optimal departure time for arriving earliest. Kennedy states that the equation applies even if somebody invents faster-than-light travel.
You see, there comes a time when although technological advances continues to produce higher speeds, the waiting time for that advance is too long to make up the velocity difference. If you wait too long for a higher speed, a slower ship launched sooner will have enough of a head start to beat you.
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.
And thirdly is the fact that space is not 100% empty. Remember Rick Robinson's First Law of Space Combat. At near light speeds hitting a dust speck will be like a contact explosion from a thermonuclear bomb. Indeed, individual protons will be transformed into deadly cosmic rays.
Einstein's theory of Special Relativity is an incredibly complicated topic, and I don't pretend to understand it all. Certainly I don't understand it enough to try and teach it. I'd advise you to go study the Wikipedia Special relativity for beginners or Jason Hinson's tutorial. If you want an intuitive feel for this: run, don't walk and get a copy of Poul Anderson's classic novel TAU ZERO.
But there are only a few implications of relativity that we have to worry about. First is of course the well-known fact that Special Relativity forbids any object possessing a rest mass from traveling at the speed of light in a vacuum (Which boils down to no FTL travel for you. Science fiction authors have been cursing Einstein for decades over that one). The second concern is "time dilation", crew members on a starship moving relativistically (i.e., faster than about 14% c) will age and experience time at a slower rate than people who stayed at home on Terra. Thirdly it makes calculating transit times and mass ratios much more difficult.
In relativistic equations, a common factor called gamma (γ) appears often. Its value depends on the velocity of the starship.
γ = 1 / Sqrt[ 1 - (v2 / c2) ]
- γ = gamma, the time dilation factor (dimensionless number)
- Sqrt[x] = square root of x
- v = current ship's velocity as measured in Terra's frame of reference (m/s)
- c = speed of light in a vacuum = 3e8 m/s
Or more conveniently, you can make c = 1.0 and v the percentage of c, e.g., a starship moving at three-quarters light-speed would have v = 0.75. The ship's γ would be about 1.51.
If a starship is moving at 0.99c relative to Terra, it's γ = 7.09. When the crew mark off one day passing inside the ship (the so-called "proper time"), 1 day * 7.09 = 7.09 days will pass on Terra. From the view point of people on Terra, the starship crew will be living and moving in slow motion, experiencing time at about 1/7th the rate on Terra (Due to the weird non-intuitive implications of relativity, from the viewpoint of the crew it will be the inhabitants of Terra who are moving in slow motion, but if you are not going to take the time to learn more about relativity you'd best ignore this).
With respects to a viewer on Terra, the starship's mass will increase by a factor of γ (which makes relativistic kinetic weapons quite deadly). The ship's length in the direction of travel will decreased by a factor of 1/γ, but nobody cares since this has little practical effect.
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:
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."
γ = Cosh[a*T/c] (given acceleration and proper time)
γ = Cosh[(Ve / c) * ln(R)] (given exhaust velocity and mass ratio)
γ = Sqrt[1 + (a*t/c)2] (given acceleration and Terra time)
γ = a*d/(c2) + 1 (given acceleration and distance)
- a = acceleration (m/s2) remember that 1 g = 9.81 m/s2
- T = Proper Time, the slowed down time experienced by the crew of the rocket (s)
- t = time experienced non-accelerating frame of reference in which they started (e.g., Terra) (s)
- d = distance covered as measured in Terra's frame of reference (m)
- v = final speed as measured in Terra's frame of reference (m/s)
- c = speed of light in a vacuum = 3e8 m/s
- Δv = rocket's total deltaV (m/s)
- Ve = propulsion system's exhaust velocity (m/s)
- R = rocket's mass ratio (dimensionless number)
- γ = gamma, the time dilation factor (dimensionless number)
- Sqrt[x] = square root of x
- ln[x] = natural logarithm of x
- Sinh[x] = hyperbolic Sine of x
- Cosh[x] = hyperbolic Cosine of x
- Tanh[x] = hyperbolic Tangent of x
The hyperbolic trigonometric functions should be present on a scientific calculator and available as functions in a spreadsheet.
In many cases it will be more convenient to have T and t in years, distance in light-years, c = 1 lyr/yr, and 1 g = 1.03 lyr/yr2.
Here are some typical results with a starship accelerating at one gravity.
T Proper time elapsed t Terra time elapsed d Distance v Final velocity γ Gamma 1 year 1.19 years 0.56 lyrs 0.77c 1.58 2 3.75 2.90 0.97 3.99 5 83.7 82.7 0.99993 86.2 8 1,840 1,839 0.9999998 1,895 12 113,243 113,242 0.99999999996 116,641
Of course, as a general rule starships want to slow down and stop at their destinations, not zip past them at 0.9999 of the speed of light. You need a standard torchship brachistochrone flight plan: accelerate to halfway, skew flip, then decelerate to the destination (which makes sense, since such starships will have to be torchships). To use the above equations, instead of using the full distance for d, divide the distance in half and use that instead. Run that through the equations, then take the resulting T or t and double it.
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.
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.
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)
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.
The crew of a ship moving at relativistic velocities will notice some weird effects. The view of the sky will be distorted both fore and aft by relativistic aberration. Doppler shift will make the stars ahead look more blue, and the stars behind will appear more red. Back in the 1970's it was thought that the two effects would combine to make a sort of a rainbow of stars around the ship's destination. Alas, in 1980 a study published in the Journal of the British Interplanetary Society did the math and proved that it just wasn't going to happen.
So, there is the obscenely-huge-mass-ratio problem, and the deadly-space-junk problem. SF authors were depressed. Then in 1960, a brilliant physicist named Robert W. Bussard proposed to use these two problems to solve each other.
If your starship is moving fast enough, the widely scattered hydrogen atoms will hit your hull like cosmic rays, and damage both the ship and the crew. One can theoretically use magnetic or electrostatic fields to sweep the hydrogen atoms out of the way so the ship doesn't hit them.
But wait a minute. Hydrogen is propellant, and could also be fusion fuel. Instead of sweeping it away, how about gathering it?
And if you are gathering your propellant instead of carrying it along with you, your mass ratio becomes infinity. This means you could theoretically accelerate forever.
This is the legendary "Bussard Interstellar Ramjet." No mass ratio problems, and no space junk problems. Pretty slick, eh? Accelerating at 1 g a Bussard ramjet could reach the center of the galaxy in a mere twenty years of proper time, and could theoretically circumnavigate the entire visible universe in less than a hundred years.
(Keep in mind that twenty years to the galactic core is in terms of "proper time", that is, the time as experienced by the crew. The people who stay at home on Earth will still see the Bussard ramjet taking the better part of 25,000 years to make the trip.)
Of course there are some other problems.
The density of the vacuum of space is about 10e-21 kg/m3. This means you have to scoop a gargantuan 10e18 cubic meters in order to harvest a single gram of hydrogen. Bussard, working with an estimate of one hydrogen atom per cubic centimeter, and desiring a 1,000-ton spacecraft with an acceleration of 1 g, figured that the scoop mouth will need a frontal collecting area of nearly 10,000 km2. Assuming the scoop mouth is circular, I figure the mouth will have to be about 56 kilometers radius or 112 kilometers diameter. Other estimates have the scoop orders of magnitude larger. It is probably out of the question to build a physical scoop of such size, so it will have to be an immaterial scoop composed of magnetic or electrostatic fields.
Hydrogen ignores magnetic and electrostatic fields unless it is ionized. This means you will need a powerful ultraviolet beam or strong laser to ionize the hydrogen heading for the scoop.
A Bussard ramjet has to be boosted to a certain minimum speed before the scoop can operate. Estimates range from 1% to 6% of c, which is pretty awful.
The Sun has the misfortune to be located near the center of a huge region about 330 to 490 light-years in diameter called "The Local Bubble". The interstellar medium within the Local Bubble has a density of about 0.07 atoms/cm3, which is about ten times lower than in the rest of the galaxy. This makes a thin fuel source for a Bussard ramjet. The Local Bubble is thought to have been caused when the star Geminga went supernova about 300,000 years ago.
And to top it off, trying to use hydrogen in a fusion reactor would require mastery of proton-proton fusion, which is so much more difficult than deuterium fusion that some scientist doubt that we will ever learn how to do it.
But none of these were show-stoppers. There was a Renaissance of science fiction novels written using Bussard ramjets. Arguably the best is the classic Tau Zero by Poul Anderson, which you absolutely must read if you haven't already. Other include Larry Niven's Protector and short stories set in his "Known Space" series, Footfall by Larry Niven and Jerry Pournelle, A Deepness in the Sky by Vernor Vinge, and The Outcasts of Heaven's Belt by Joan Vinge.
Things started to unravel in 1978. T. A. Heppenheimer wrote an article in Journal of the British Interplanetary Society entitled "On the Infeasibility of Interstellar Ramjets." Heppenheimer applies radiative gas dynamics to ramjet design and proves that radiative losses (via bremsstrahlung and other similar synchrotron radiation-type mechanisms) from attempting to compress the ram flow for a fusion burn would exceed the fusion energy generated by nine orders of magnitude, that is, one billion times. The energy losses will probably show up as drag. This was confirmed by Dana Andrews and Robert Zubrin in 1989.
The effect of drag? What it boiled down to was that the ramjet had a maximum speed, where the relative velocity of the incoming hydrogen equaled the drive's exhaust velocity. It has a "terminal velocity", in other words.
A proton-proton fusion drive has an exhaust velocity of 12% c, so a proton-proton fusion Bussard Ramjet would have a maximum speed of 12% c. You may remember that a spacecraft with a mass ratio that equals e (that is, 2.71828...) will have a total deltaV is exactly equal to the exhaust velocity. So if a conventional fusion rocket with a mass ratio of 3 or more has a better deltaV than a Bussard Ramjet, what's the point of using a ramjet?
Things look bleak for the Bussard Ramjet, but it isn't quite dead yet. First off, Dr. Andrews and Dr. Zubrin's analysis depends upon certain assumptions. But even if the drag problem is as severe as calculated, there may be ways to avoid it. The drag is caused by bremstrahlung and synchrotron radiation produced by the motion of the charged particles as they spiral through your collector fields and into your fusion chamber. It is theoretically possible to recover energy instead of it being wasted as drag. Then the energy could be added to the fusion energy and used to accelerate the exhaust stream, thus defeating the drag.
It would be a Bussard Scramjet, in other words.
But only theoretically. It is incredibly difficult, as in "we might not manage to do it with five hundred years of research" level of difficult.
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.
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.
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.
Also note that as far as your headache severity goes, it does not matter if you are quote "standing still" unquote and the brick is traveling at 1 m/s or if you are moving at 1 m/s and the brick is "standing still." In both cases you will be damaged by the exact same amount of energy. Actually according to Einstein's relativity, both cases are just two ways of saying the same thing, but we won't get into that.
What does this have to do with starships? Well, 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.
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.
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.
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.
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.
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.
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.
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:
- the contents of two cargo pods and 100 passengers OR
- the contents of six cargo pods and no passengers
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.
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.
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.
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 m (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.
The Enzmann starship is a concept for a manned interstellar spacecraft proposed in 1964 (date is disputed) by Dr. Robert Enzmann. Over the years the basic design has evolved, and there were several types in the initial design. It was quite popular in the science fiction community. An analysis of the Enzmann starship can be found here.
In 1972 space artists Don Davis and Rick Sternbach worked with Dr. Enzmann to develop the idea. This refined the "lollypop" look of the ship. For some odd reason most paintings of the Enzmann starship show two of them in formation. The original design had a naked sphere of frozen deuterium as fuel. Calculations with Sternbach and Davis revealed that the deuterium could not be kept frozen and was too structurally weak to be accelerated. So the redesign encased the deuterium in a huge tank.
The Enzmann exploded into the science fiction community with the October 1973 issue of Analog magazine. G. Harry Stine wrote an extensive article about the concept, accompanied by a stunning piece of cover art by Rick Sternbach. Stine said the ships were 12 million tonnes, could reach 0.30 c (highly unlikely), had 8 engines, and used spinning habitats for artificial gravity.
- Command center 30 meters in diameter
- Central core load bearing struture 15 meters diameter
- Frozen deuterium 300 meters diameter
- Living modules 90 meters diameter × 90 meters long
- Engineering compartments 70 meters diameter
In Science Digest, Rick Sternbach's 1972 piece depicts a pair of Enzmanns departing from an asteroid factory. The number of engines was increased from 8 in the original design to 24. Modular sections were created that can separate from the starship. Height of starship was 690 meters. 3 million tonnes of deuterium, with metal shell (doubling as a radiation shield). Magnetic confined fusion propulsion. 20 decks per habitat, 100 rooms per deck. Cruising speed 0.09c.
Thomas Schroeder wrote an article entitled "Slow Boat to Centauri" in Astronomy Magazine. Claimed a cruising speed of 0.1c, and an advanced design might reach 0.3c. 12 million tonnes deuterium. The outer layers of the habitats were composed of bulk material as radiation shielding for the inner layers. Bulk means nuclear reactor, store rooms, heat exchangers, airlocks, landing craft, observation areas, communication equipment. Eight Project Orion nuclear pulse units.
- Frozen deuterium 305 meters diameter
- Height 609.6 meters
- Living modules 91.5 meters diameter × 91.5 meters long
- From bottom of fuel sphere to top of Orion engines 305 meters
In the 1980's Dr. Enzmann started designing variants.
In 2011, K. F. Long, A. Crowl, and R. Obousy did a study on the Enzmann starship, and tried to rationalize it with recent developments in astronautics. First they took the historical concepts:
|Sphere Diameter||305 m||same||same|
|Total Habitat Length||273 m||same||same|
|Individual Habitat length||91 m||same||same|
|Habitat Diameter||91 m||same||same|
|Core Diameter||15 m||same||same|
|Propellant Mass||3×106 metric tons||12×106 metric tons||3×106 metric tons|
|Cruise Speed||27,000 km/s|
Long et al created three variants. The primary difference is the size of the population carried. The rest of the design was re-sized to handled the population. As near as I can calculate, the cruise and mission times for all three are for a mission to Alpha Centauri.
|Specific Power||11.5 MW/kg|
|Thrust Power||344 terawatts|
|Length||620 m||979 m||1752 m|
|Dry Mass||30,000 MT||300,000 MT||3,000,000 MT|
|Propellant Mass||3 × 106 MT||3 × 106 MT||3 × 106 MT|
|Exhaust Velocity||11,700 km/s||11,260 km/s||12,119 km/s|
|Cruise Velocity||27,000 km/s|
|18.95 yrs||98.67 yrs||84.9 yrs|
|41.05 yrs||51.33 yrs||265.1 yrs|
|60 yrs||150 yrs||350 yrs|
|Mass Flow Rate||5.02 kg/s||0.96 kg/s||1.12 kg/s|
|Thrust||58,730 kN||10,810 kN||13,573 kN|
|Wet Mass||17,800 metric tons|
|Dry Mass||2,365 metric tons|
|Payload||150 metric tons|
|Propulsion||Z-Pinch DD Fusion|
|Exhaust Velocity||1.289×107 m/s|
|Accel time||4 years|
|Coast time||93 years|
|Decel time||1 years|
|Wet Mass||45,000 metric tons|
|Dry Mass||3,000 metric tons|
|Payload||150 metric tons|
|Propulsion||Z-Pinch DD Fusion|
|Specific Impulse||one million seconds|
|Accel time||25 years|
|Coast time||70 years|
|Decel time||5 years|
Most of the other Icarus fusion designs use inertial confinement fusion. That's because IC fusion is easier to get halfway worthwhile power levels. Magnetic confinement fusion would be nicer but once you get enough nuclear fusion going to to be worthwhile, the magnetic bubble pops like a cheap balloon.
The drawback to IC fusion is that the confinement time is pathetic. The longer you confine the fusion reaction, the more of the fusion fuel actually burns and generates energy. But in IC fusion the first bit of fusion acts to blast the pellet apart, scattering the un-burnt fuel to the four winds.
Back in the olden days of fusion research, the darling was Z-Pinch fusion. You send a bolt of electricity (about 5 mega-amps) down the center of a long tube full of ionized plasma, creating magnetic field which compresses the plasma enough to ignite nuclear fusion. One of the big advantages with Z-Pinch was that the confinement time (and net energy output from the burn) can be increased by simply making the reaction chamber longer.
Unfortunatley, the disadvantage is that Z-Pinch fusion suffers from several hydrodynamic instabilities which disrupt the plasma. So researchers stopped working on it in.
But in 1998 Dr. Uri Shumlak discovered you could eliminate the instabilities if you made the plasma move at high velocities. Based on this work, Z-Pinch was selected for the Icarus design.
The Firefly's long thin tail is the Z-Pinch tube, frantically fusing and radiating x-rays like a supernova. So the starship was given its name for similar reasons as the one on the TV show: it is a flying thing whose tail lights up.
The spacecraft profile is long and skinny, for two reasons:
- Its cruise velocity is a substantial fraction of the speed of light (4.5c for the 2013 version). This make interstellar dust grains impact with about 9.1×10-4 joules worth of damage, the equivalent of 46,000 cosmic ray photons. You want to reduce the ship's cross section as much as possible to minimize the number of grain impact events.
- The longer the ship is, the farther the payload can be placed from the deadly radioactive Z-Pinch drive, taking advantage of distance shielding.
Many other starship designs use 3He-D fusion, because all the reaction products are charged particles that can be easily shieldied. The drawback is that 3He is rare, you'd have to harvest the atmosphere of Jupiter for twenty years in order to get enough.
Instead, Firefly uses D-D fusion, since deuterium can be easily found in common seawater. Of course then you have to deal with all the nasty neutrons and x-rays produced by that reaction. Firefly's approach is to forgo the use of massive radiation shields, and instead try to let as much of the radiation escape into space. The Z-Pinch core is almost totally open to space with only a triad of support rails connecting the aft electrode and magnetic nozzle to the rest of the vessel.
Even with that, the waste heat is going to be titanic. That's where the heat radiators come in. Notice how they are the bulk of the ship. Makes the thing look like a garantuan lawn-dart. The radiators use beryllium phase-change technology, and are positioned as close as possible to the heat loads on the tail.
A long conical shield forwards of the reactor core deflects x-rays away from the payload using shallow-angle effects. The electrodes, rails, and other structure near the core are constructed of zirconium carbide (which is capable of surviving the intensely radioactive environment.
The 2014 design had a total length of just under one kilometer, half of which is the fuel tanks. The forward part of the ship uses the old fuel tank in lieu of spine trick in an effort to save on ship mass.
A fission reactor provides secondary power.
|Exhaust Velocity||9.99×107 m/s|
|Thrust Power||587.4 TW|
|Average Accel||0.098 m/s|
|Gamma radiation||996.3 TW|
|Dust Shield||6,530 MT|
|Power Systems||1,064.6 MT|
|Payload Rad Shield|
|Radiator Rad Shield||6.4 MT|
|Magnet Rad Shield||103.3 MT|
|R. R. + |
|Total Dry Mass||70,940.6 MT|
|Engine Magnet Radiation Shield|
|cross-section area||0.088 m2|
to ignition point
to ignition point
|fraction of gamma|
|Radiator Radiation Shield|
|cross-section area||2.488 m2|
to ignition point
to ignition point
|fraction of gamma|
|System & Payload|
|cross-section area||311.026 m2|
to ignition point
|fraction of gamma|
|2-sided area||1.025×107 m2|
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.
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.
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:
Anyway, back to the main description:
The third of Gordon Woodcock's methods of interstellar travel is "go tricky".
This means to cheat and find a way to travel to the stars faster than light.
This is such can of worms that it has an entire page to itself.