## Introduction

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

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

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

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

## Go Fast

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

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

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

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

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

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

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

### Relativity

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

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

First is of course the well-known fact that Special Relativity forbids any object possessing a rest mass from traveling at the speed of light in a vacuum (Which boils down to no FTL travel for you. Not yours. Science fiction authors have been cursing Einstein for decades over that one).

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

Thirdly it makes calculating transit times and mass ratios much more difficult.

V/cγ
0.00011.0000000
0.0011.0000005
0.011.000050
0.021.000200
0.051.001252
0.11.005038
0.141.010000
0.21.020621
0.31.048285
0.41.091089
0.51.154701
0.61.250000
0.71.400280
0.81.666667
0.8662.000000
0.92.294157
0.922.551552
0.953.202563
0.985.025189
0.997.088812
0.99922.366272
0.999970.712446

### GAMMA

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

γ = 1 / Sqrt[ 1 - (v2 / c2) ]

where

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

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

γ = 1 / Sqrt[ 1 - (vpercent2) ]

vpercent = Sqrt[ 1 - (1 / γ)2 ]

where

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

How do you use gamma?

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

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

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

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

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

### FUNCTIONAL LIGHTSPEED

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

What does this mean?

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

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

### NO FTL

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

Well, there is a problem there:

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

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

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

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

### RELATIVISTIC VELOCITIES DON'T ACTUALLY ADD

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

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

### WHO NEEDS ANTIMATTER?

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

### RELATIVISTIC BRACHISTOCHRONE

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]

where

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

Remember this equation assumes a constant 1 g acceleration.

#### Starship Bumpers

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

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

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

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

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

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

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

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

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

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

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

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

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

where:

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.

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

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

#### Mass Ratio

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

Mass Ratio

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

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

Substituting (2) into (1):

R = e(a * T / c)

where

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

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

#### Other Relativistic Effects

FAIRY TIME

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

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

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

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

RELATIVISTIC ABERRATION

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

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

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

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

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

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

This will make navigation a bit of a challenge.

THE STARBOW

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

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

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

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

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

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

Sänger called it a Starbow.

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

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

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

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

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

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

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

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

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

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

### Bussard Ramjet

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

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

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

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

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

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

#### Ramjet Problems

Of course not everything is rainbows and unicorns, there are a few problems.

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

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

A Bussard ramjet has to be boosted to a certain minimum speed before the scoop can operate. Estimates range from 1% to 6% of c, which is pretty awful. There is an equation here but it depends upon other assumptions about the minimum mass-collection rate.

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

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

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

#### Ramjet Show Stopper

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

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

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

#### Ramjet Show Starter

Things look bleak for the Bussard Ramjet, but it isn't quite dead yet. First off, Dr. Andrews and Dr. Zubrin's analysis depends upon certain assumptions. But even if the drag problem is as severe as calculated, there may be ways to avoid it.

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

##### Bussard Scramjet

The drag is caused by bremstrahlung and synchrotron radiation produced by the motion of the charged particles as they spiral through your collector fields and into your fusion chamber. It is theoretically possible to recover energy instead of it being wasted as drag. Then the energy could be added to the fusion energy and used to accelerate the exhaust stream, thus defeating the drag.

It would be a Bussard Scramjet, in other words.

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

##### Toroidal-Field Ramscoop

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Bussard Ramjet Combat

##### Orion Wargame

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

##### Rec.Arts.SF.Science

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

### RAIR

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

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

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

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

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

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

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

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

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

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

### Black Hole Starships

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

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

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

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

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

Primordial black holes
R
(am)
M
(Mt)
kT
(GeV)
P
(PW)
P/c2
(g/sec)
L
(yrs)
0.160.10898.1551961400≲0.04
0.30.20252.3152717000≲0.12
0.60.40426.236740901
0.90.60617.416017803.5
1.00.67315.712914305
1.51.0110.556.262616—17
2.01.357.8531.334839—41
2.51.686.2819.822175—80
2.61.756.0418.320485—91
2.71.825.8216.918995—102
2.81.895.6115.7175106—114
2.91.955.4114.6163118—127
3.02.025.2313.7152130—140
5.83.912.713.5038.9941—1060
5.93.972.663.3737.5991—1117
6.04.042.623.2636.21042—1177
6.94.652.282.4327.11585—1814
7.04.712.242.3626.21655—1897
10.06.731.571.1112.34824—5763

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

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

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

6 × 10-8 / M kelvins

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

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

In the table:

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

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

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

### Black Hole Generator

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

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

### Proper Black Hole Size?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Mass comparable to a starship?

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

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

### Quark Nuggets

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

Suffice to say that it is weird stuff.

Some scientist have become fascinated by the concept because:

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

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

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

Why do we care?

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

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

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

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

### Nearlight Starships

#### Alabama

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

#### Avatar ISV Venture Star

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

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

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

##### Departing from Earth

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

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

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

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

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

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

##### Braking at Alpha Centauri

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

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

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

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

##### Cargo Modules

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

##### Interface Craft

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

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

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

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

##### Crew Modules

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

##### Shield

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

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

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

#### Colonized Interstellar Vessel

This section has been moved here

#### Encounter With Tiber

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

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

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

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

##### Wahkopem Zomos

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

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

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

##### Egalitarian Republic

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

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

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

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

##### Tenacity

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

#### Frisbee Antimatter Starship

Antimatter Starship
(one stage)
PropulsionAntimatter
Beam Core
ΔV7.5×107 m/s
(0.25c)
Exhaust Velocity9.99×107 m/s
(0.3333c)
Thrust1.174×107 N
Thrust Power587.4 TW
Average Accel0.098 m/s
(0.01 g)
Mass Ratio5.45
Dry Mass
Dust Shield6,530 MT
Power Systems1,064.6 MT
Misc.100 MT
Propellant tanks,
insulation,
feed system
26,698.8 MT
Propellant tank
refrigeration
104.7 MT
361.6 MT
R. R. +
Magnet Shield
15,533.7 MT
Magnet, structure,
insulation
282.3 MT
Magnet
refrigeration
3,707.4 MT
30% Contingency
Mass
16,347.8 MT
Total Dry Mass70,940.6 MT
Propellant Mass
Propellant Total
matter LH2
159,450 MT
Propellant
boiloff loss
matter LH2
1,579 MT
Propellant Usable
matter LH2
157,872 MT
Propellant Total
antimatter LH2
165,765 MT
Propellant
boiloff loss
antimatter LH2
7,894 MT
Propellant Usable
antimatter LH2
157,872 MT
mass103 MT
volume5.337 m3
thickness0.173 m
cross-section area0.088 m2
minimum distance
to ignition point
10.639 m
center distance
to ignition point
11.038 m
attenuation8.496×10-15
fraction of gamma
flux intercepted
0.460%
gamma power
intercepted
1.455×104 GW
mass6.434 MT
volume0.332 m3
diameter19.9 m
height0.125 m
cross-section area2.488 m2
minimum distance
to ignition point
along hypotenuse
11.455 m
minimum distance
to ignition point
along x-axis
5.123 m
attenuation1.272×10-11
fraction of gamma
flux intercepted
0.151%
gamma power
intercepted
1.503×103 GW
mass361.09 MT
volume18.661 m3
diameter19.9 m
height0.064 m
cross-section area311.026 m2
minimum distance
to ignition point
along hypotenuse
5.152×105 m
attenuation1.286×10-5
fraction of gamma
flux intercepted
9.325×10-11%
gamma power
intercepted
9.29×10-5 GW
gamma power
16,052 GW
2-sided area1.025×107 m2
width19.9 m
height515,189 m
(515 kilometers)
mass15,533.7 MT

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

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

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

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

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

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

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

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

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

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

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

#### Lighthugger

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

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

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

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

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

#### Project Star

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### Semyonov Antimatter Starship

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

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

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

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

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

FuelEnergy Density MJ/kg
Antimatter89,900,000,000
Hydrogen fusion650,000,000
DT fusion340,000,000
U-23588,000,000
Natural U81,000,000
Pu-23815,000,000
H chemical burning140
Rocket chemical fuels50
Gasoline44
Coal24
Wood16

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

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

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

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

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

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

Problems include:

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

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

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

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

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

• 3: Refrigerators for antihydrogen tank and magnetic shield

• 4: Heat insulators

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

• 6: Annihilation reactor

• 7: Control bridge

• 8: Crew quarters or AI module

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

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

• 12: Antihydrogen tank

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

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

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

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

You may have noticed a new problem.

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

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

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

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

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

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

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

#### Valkyrie Antimatter Starship

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

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

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:

### AsteronX Valkyrie Gallery

#### Rocheworld

This section has been moved here

#### Enzmann Starship

This section has been moved here

#### Project Daedalus

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#### Project Icarus

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##### Firefly Starship

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##### Ghost Ship

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##### Resolution

This section has been moved here

##### Ultra-Dense Deuterium

This section has been moved here

#### Shepherd Generation Starship

This section has been moved here

## Atomic Rockets notices

This week's featured addition is SPIN POLARIZATION FOR FUSION PROPULSION

This week's featured addition is INsTAR

This week's featured addition is NTR ALTERNATIVES TO LIQUID HYDROGEN