Atomic Rockets

Cheat Sheet

For some good general notes on designing spacecraft in general, read Rick Robinson's Rocketpunk Manifesto essay on Spaceship Design 101. Also worth reading are Rick's essays on constructing things in space and the price of a spaceship.

For some good general notes on making a fusion powered spacecraft, you might want to read Application of Recommended Design Practices for Conceptual Nuclear Fusion Space Propulsion Systems. There are also some nice examples on the Realistic Designs page.

For less scientifically accurate spacecraft design the Constant Variantions blog has a nice article on historical trends in science fiction spacecraft design.

Strategies

RocketCat sez

This is the living breathing core of all rocket design. Delta Vee equals Vee Ee times Natural Log of Arr. This is the secret that makes rocket design possible. Now it is time to see the practical application of the key to rocketry.

Everything about fundamental spacecraft design revolves around the Tsiolkovsky rocket equation. Δv = Ve * ln[R]. The variables are the velocity change required by the mission (Δv or delta-V), the propulsion system's exhaust velocity (Ve ), and the spacecraft's mass ratio (R). Remember the mass ratio is the spacecraft's wet mass (mass fully loaded with propellant) divided by the dry mass (mass with empty propellant tanks).

The point is you want as high a delta-V as you can possibly get. The higher the delta-V, the more types of missions the spacecraft will be able to perform. If the delta-V is too low the spacecraft will not be able to perform any useful missions at all.

Looking at the equation, the two obvious ways of increasing the delta-V is to either increase the exhaust velocity or increase the mass ratio. Turns out there are two more sneaky ways of dealing with the problem which we will get to in a moment.


Historically, the first approach has been increasing the exhaust velocity by inventing more and more powerful rocket engines. Unfortunately for the anti-nuclear people, chemical propulsion exhaust velocity has pretty much hit the theoretical maximum. The only way to increase exhaust velocity is by using rockets powered by nuclear energy or by power sources even more frightful and ecologically unsound.


The second approach is increasing the mass ratio by reducing the spacecraft's dry mass. This is the source of the rule below Every Gram Counts. Remember that the dry mass includes a spacecraft's structure, propellant tankage, lifesystem, crewmembers, consumables (food, water, and air), hydroponics tanks, cargo, atomic missiles, toilet paper, clothing, space suits, dental floss, kitty litter for the ship's cat, the ship's cat itself, and other ship systems. Everything that is not propellant, in other words.

To reduce dry mass: use lightweight titanium instead of heavy steel, shave all structural members as thin as possible while also using lightening holes, make the propellant tanks little more than foil balloons, use inflatable structures, make the floors open gratings instead of solid sheets, hire short and skinny astronauts, use life support systems that recycle, impose draconian limits on the mass each crewperson is allowed for personal items, and so on. Other tricks include using Beamed Power so that the spacecraft does not carry the mass of an on-board power plant, and avoiding the mass of a habitat module by hitching a ride on an Aldrin Cycler. Finally the effective mass ratio can be increased by multi-staging but that should be reserved for when you are really desperate.


The third approach is trying to reduce the delta-V required by the mission. Use Hohmann minimum energy orbits. If the destination planet has an atmosphere, use aerobraking instead of delta-V. Get more delta-V for free by exploiting the Oberth Effect, that is, do your burns while very close to a planet. Instead of paying delta-V for shifting the spacecraft's trajectory or velocity, use gravitational slingshots. Use space tethers, launch catapults, and MagBeams.


The fourth and most extreme approach is to cheat the equation itself, to make the entire equation not relevant to the spacecraft. The equation assumes that the spacecraft is carrying all the propellant needed for the mission, this can be bent several ways. Use Sail Propulsion which does not use propellant at all. Use propellant depots and in-situ resource utilization to refuel in mid-mission. The extreme case of ISRU is the Bussard Ramjet which scoops up propellant from the thin interstellar medium, but that only works past the speed of 1% lightspeed or so.


In our Polaris example, given the mass ratio of 3, we know that the Polaris is 66% propellant and 33% everything else. Give the total mass of 1188.9 tons means 792.6 tons of propellant and 396.3 tons of everything else. Since each GC engine is 30 tons, that means 150 tons of engine and 246.3 of everything else.

Every Gram Counts

RocketCat sez

Listen up, rocket designers. Write these words in letters of fire on your cerebellum. Every Gram Counts! Add an extra gram and you will pay for it with extra propellant as if the Mafia loan shark wants you to pay up with liquid hydrogen.

The most fundamental constraint on designing a rocket-propelled vehicle is Every Gram Counts.

Why? Short answer: This is a consequence of the equation for delta-V.

Why? Slightly longer answer: As a rule of thumb, a rocket with the highest delta-V capacity is going to need three kilograms of propellant for every kilogram of rocket+payload. The lower the total kilograms of rocket+payload, the lower the propellant mass required. This relates to the second strategy of rocket design mentioned above.

Why? Long Answer:

Say the mission needs 5 km/s of delta-V. Each kilogram of payload requires propellant to give it 5 km/s.

But that propellant has mass as well. The propellant for that original kilogram of payload requires a second slug of propellant so it too can be delta-Ved to 5 km/s.

And the second slug of propellant has mass as well — you see how it gets expensive fast. So you want to minimize the payload mass as much as possible or you will be paying through the nose with propellant.

This is called The Tyranny of the Rocket Equation.

Even worse, for a given propulsion system, the only way to increase the delta-V you can get out of that system is by increasing the mass ratio. It probably is not economical to push the mass ratio above 4.0, which translates into 3 kg of propellant for every 1 kg of rocket+payload. And it is nearly impossible to push the mass ratio above 20.

This is why rocket designers are always looking for ways to conserve mass.

Fundamental Design

As mentioned in Rick Robinson's Spaceship Design 101, all spacecraft are composed of two sections: the Propulsion Bus and the Payload Section.


The Propulsion Bus has the propulsion system, propellant tankage, fuel container (if any), power plant, power plant heat radiator (if any), anti-radiation shadow shield (if any), and a keel structure to hold it all together.


The Payload Section is what the propulsion bus is pushing from planet to planet. It can include crew, flight control station, propulsion/power plant control station and maintenance center, astrogation station, detection and communication equipment, habitat module with life support equipment (including environmental heat radiators) and consumables (air, food, water), space taxis, space pods, and docking ports.

But most importantly, the payload section must contain the reason for the spacecraft's existence. This might be organized as a discrete mission module, or it might be several components mounted around the payload section.

Planetary Exploration Vessel
Scientific instruments, space ferries, airless landers
Cargo Vessel
Cargo holds
Tanker
Extra propellant tanks (and a remarkably large mass ratio)
Space Tug
Ship grappling equipment, push plates, and an over-sized high-thrust propulsion bus.
Coast Guard vessel
rescue equipment, ship grappling gear, ship repair supplies space taxis, space pods, and a propulsion bus with extra delta V.
Orbital Guard vessel
Asteroid redirecting equipment
Troop transports
Huge habitat modules
Blockade Runner
Stealth technology, small cargo hold, and a propulsion bus with high acceleration

You get the idea.

A warship's payload section can include anti-spacecraft weapons, orbital bombardment weapons (for revolt suppression spacecraft as well), weapon mounts, weapon control stations, combat information center, armor, point defense, weapon heat radiators and heat sinks, and anything else that can be used to mission-kill enemy spacecraft.

Pirate ships and privateers might forgo defenses if they only expect to be engaging unarmed cargo ships. But they will regret this if they have the misfortune to encounter armed enemy convoy escort ships or are surprised by a Q-ship.


Spaceship Design 101

I will argue that deep space craft have essentially two sections that can largely be treated separately from one another. One section is the propulsion bus — drive engine, reactor if any, solar wings or radiator fins, propellant tankage, and a keel structure to hold it all together. The other is the payload section that it pushes along from world to world.

There are both conceptual and economic reasons to treat them separately. Conceptually, because a propulsion bus might push many different payloads for different missions, such as light payloads on fast orbits versus heavy payloads on slow orbits. A little noticed but important feature of deep space craft is that you cannot overload them. They do not sink, or crash at the end of the runway, or even bottom out their suspension. They merely perform more sluggishly, with reduced acceleration and (for a given propellant supply) less delta v.


Conceptual logic is also economic logic. The outfits that build drive buses would like to sell them to lots of different customers for a broad range of assignments.

This is not necessarily an argument for true modular construction, with drive buses hitching up to payloads on an ad hoc basis like big-rig trucks and trailers. Building things to couple and uncouple adds complexity, mass, and cost — plug connectors, docking collars, and so forth. Moreover, drive buses intended for manned ships need to be human-rated, not just with higher safety factors but provision for supplying housekeeping power to the hab, etc. But these things, along with differing sizes or number of propellant tanks, and so forth, can all be minor variations in a drive bus design family.

The payload we are most interested in is, naturally, us. The main habitat section of a deep space ship closely resembles a space station. It is likely that habs intended for prolonged missions will be spun, for health, efficiency, and all round convenience. (Flush!) The design of a spin hab is dominated by the spin structure and — unless you spin the entire ship — the coupling between the spin and nonspin sections.

Because ships' spin habs have the features of stations they may be used as stations, and again we can imagine design families, with some variants intended for ships and others as orbital platforms having only stationkeeping propulsion. Habs are the one major part of a deep space ship that correspond fairly well to our concept of a hull. Spin habs are entirely different in shape, but the shape is constrained; once you build it you can't easily modify it, beyond adding another complete spin section.


For those with bank cards at the ready, buying a deep space ship might be not unlike buying a computer. If your mission needs are fairly standard, you check off options on a menu. Those with more specialized requirements can select major components — perhaps a drive bus from one manufacturer, a main crew hab from another, along with custom payload sections, service bays, and so forth, assembled to your specifications.

In fact, both technology and probable historical development suggest that fabrication and overall assembly will be two distinct phases, carried on in different places, quite unlike either shipyard or aircraft assembly practice. In the early days, large deep space craft will be built the way the ISS was, assembled on orbit out of modules built on Earth and launched as payloads. In time fabrication may move to the Moon, or wherever else, but final assembly (at least of larger craft) will continue to be done at orbital facilities. I call them cageworks, on the assumption that a cage or cradle structure provides handy anchoring points for equipment.

For game or sim purposes, my advice would be to treat drive buses and hab sections as the primary building blocks for ships, whether these components are permanently attached to each other or simply coupled together. Both approaches might be in use.

A couple of provisos. All of the above applies mainly to deep space craft, especially with high specific impulse drives. Ships for landing on airless planets have some similar features. Ships that use rapid aerobraking, however, are aerospace craft and broadly resemble airplanes, even if they never land or even go below orbital speed.

And I have said nothing of warcraft. Kinetics are essentially just another payload. Lasers, and other energy weapons such as coilguns, probably draw power from the drive reactor, calling for some modifications in the drive bus. These things don't much affect the overall configuration. Armor protection would, but discussions here have left me doubtful of its value against either lasers or kinetics. Laser stars and other major warcraft may not be dramatically different in appearance from civil craft of similar size.


Nyrath: I'm reminded of Sir Arthur C. Clarke's early space science books. He noted that a nuclear powered spacecraft would probably resemble a dumb bell, that is, two spheres connected by a stick. The hab module is the forward sphere, the nuclear drive is the rear sphere, the stick is long to provide some inverse square protection from radiation, and the propellant tanks would be on the stick, probably clustered near the nuclear drive.

One can also imagine modules designed by diverse corporations being incompatible with others on purpose. "Not invented here" syndrome.

One can also imagine a tramp freighter composed of incompatible modules, being held together with bailing wire and spit.


Qwert: The compatibility between modules will mostly depend on how the market develops. One extreme maybe Microsoft, a monopoly that basically sets the standard, as everything has to adhere to it. The other one extreme is the current hardware industry. Your memories and components have to fit on every motherboard if you want to sell them.

On the field of big aircraft manufacturing, standardisation dominates almost everything... excerpt the end product. If you manufacture engines, they have to fit on Airbus as well as on Boeing's aircraft. The components industry is dispersed and competition is intense.

On the other side, a pilot trained to flight with a Boeing can´t immediately switch to an Airbus without some training. Competition centers around two big players and nobody is interested in making life easier to the other.

In short: how spaceship components will be build, will mostly depend on how the industry evolves. A monopoly, strict government regulation, competition between many small producers or a highly dispersed specialised components industry may benefit a system of standards. On the other side competition between a small number of giants, may produce different incompatible systems.


Rick Robinson: True modularity is by no means a given. But some features of modularity, call it demi-modularity, are inherent to deep space technology.

You probably want to keep your propellant tanks separate from the corrosive, explosive stuff we breathe. Drive engines are essentially bolted onto the tail. Generally the major parts of a deep space ship don't have to fit together snugly. If you want to hang something out on a bracket you probably can.


Ferrell: I think that the engine package, mated to a suitable tank, mated to a hab module, mated to a mission module (a seperate entity from the hab module) would (as the last step in design) incorporate the heat management system suitable to the final design. Then construction/assymbly would occure.

If there aren't landers/shuttles at the final destination and you need them, then you can carry landers/shuttles in place of cargo. A mission module may be an extended docking module that a number of small modules 'plug' into, (or your transfer craft).

Manuvering thrusters should be at mutliple points/modules (distributed from the 'nose' to the 'tail').

Of course, you could stand it all on it's ear and have the mission module be on the inside of the ship, the hab ring be around the middle (with its radiators in arcs between its connecting pylons),with the engines, tanks, powerplants, radiators, and nav sensors clustered around both ends of the mission module; and any docking would be at the tips of the mission module, or on the inside walls of the mission module.


Nyrath: There might be a brisk trade in "interface modules", that would connect modules made by different manufacturers. I'm reminded of the Apollo ASTP Docking Module used in the Apollo-Soyuz mission. This was a tiny airlock module with a NASA style docking collar on one end, and a Soviet style docking collar on the other.


Rick Robinson: Sabersonic — Yes, I'm gliding over a host of devils in the details. The payload section will surely have attitude thrusters, for example, and these must coordinate with attitude thrusters on the drive bus end.

Nyrath — 'Standards,' indeed! Again this is a promo for full service cageworks that will provide things like docking adapters.


Jean Remy: On standards:

Currently the main type of freight vessel is the container-carrier. They are favored because the containers can be loaded/unloaded easily, then simply popped on a freight train or a truck. I can see the same things for a cargo spaceship. There won't be a cargo "module" but rather anchoring hard points for standard containers. Those containers will be loaded on a booster to orbit, transferred onto a ship, then at the other end the container is loaded into a simple remote-controlled lifting body (for planets with an atmosphere, say, Mars) or just a simple frame with thrusters (for the Moon) where they will be loaded into maglev trains if needed, etc.

The command post/bridge:

I'd still put in in the non-rotational part of the ship, certainly on warships (you want it as deep inside the ship as you can for protection) Not only that, but I would stop rotation in combat: precession might alter your maneuverability, and damage might weaken the structure or cause a wobble which would rip your ship apart. I would also put it in the middle for a civilian vessel, as then the command module can double as storm cellar, or if there's a separate storm cellar, you'll still have access to the command post during a solar flare. It's also a good defense against micrometeorites. The command center is just too important to risk placing it on the outer rim of a ship, no matter how convenient or comfortable it would be to the crew.


Sabersonic: Even so, it would probably be prudent to not have all command, or at least navigation control, be monopolized by the CIC. At minimum and barring mass budgeting, there should be two for overall spacecraft control: One that is the CIC/Navigation primary with the second being the engine room for mostly emergency purposes. If only because for something as complex and (for the first few decades if not centuries of interplanetary travel, let alone interstellar) inevitably as fragile as a spacecraft, one should avoid "putting ones eggs into one basket" and to always "have a plan B". Space and interplanetary/interstellar travel is not a place for the ill-prudent, and that's just the natural dangers.

As for standards, well, before standards could ever become "standard" for lack of a better word, there lies the inevitable "Format War" in one form or another that would occur when one believes that their system is more efficient and reliable than the other or worse: a new industry/business standard that has the potential to supplant the jobs of numerous Dock workers or in this case "Cage Workers" that could drive hostility and perhaps a little bit of political pressure before the whole matter is settled in one way or another. It would not be a full parallel to the Teamsters Strike that is basically Teamsters vs Trucks, but it would not be a completely quiet deal when paychecks are involved.


Rick Robinson: My division of ships into drive buses and payload sections is more because of operational factors than manufacturing considerations.

For example, ships inherently have (at least) two big 'hull' structures, the crew hab and the main propellant tank. These are probably at very different temperatures, which right away is a big reason to keep them physically separate.

Using the propellant tankage as shielding is appealing, but even with a vacuum separation it means that your 290 K hab shell is dumping 350 W/m2 of waste heat right into your 20 K liquid hydrogen tanks.

Jean — The containership principle seems highly likely for most space cargo, with the standard pod being defined originally to fit Earth orbital shuttle bays.

In this case, your typical space freighter is a drive bus pushing a rack structure with clamps for pods. The rack might be configurable so that you can also carry 'oversize' loads.

Jean and Sabersonic — In a parallel discussion at SFConsim-l, the question was raised whether civil ships need a 'control room' at all, or whether people could just stand watch from their regular work stations.

I think that any spacecraft with a fair number of passengers or crew will have a watch at the main life support panel, because life support is always running, has constantly changing loads, and things can go very bad very quickly. The life support panel will almost certainly be in the spin section, because that is where the life support is.

You may as well put the engineering panel here as well. There's no reason for an 'engine room' in the maritime sense, since the drive is mounted externally, and if it is nuclear you don't want to go anywhere near it.

No doubt you could maneuver and navigate the ship from here as well. But en route there is very little of this to do.

The only time you really conn a (civil) spacecraft is during rendezvous and docking, or similar evolutions. At these times you surely de-spin, but you might want a separate control station next to the main airlock, with viewports for maximum situational awareness.

Because of its location, this station would also naturally serve as the ceremonial 'quarterdeck' where VIPs are greeted, and ordinary mortals report aboard.

Warcraft are a whole 'nother matter, with protective considerations arguing for a control room at the center of the hab section.


Jean Remy: Multiple Command posts: Yes. That's why I used the term command post rather than CIC, Bridge, DCC, Main Engineering. It was meant to be generic and refer to all these. There ought to be at least CIC and DCC, if not a redundant third post, all of them capable of doing every job, but each ideally suited to one. The ship is more efficient with all of them, but can still work with the loss of one or two.

Decentralized Command posts: Possibly, but I don't think it likely. First of all we could do that now, but we don't. Psychologically, I think crews want to have the "Captain on Bridge" so to speak. It is generally recognized that good officers are the ones who stick by their men when the going gets tough. Caesar rode into battle at Alesia, rallying his troops to victory when it looked uncertain. Washington rode with his men. Patton led from a tank. Now granted the captain of a ship can't go anywhere, but seeing him on the Bridge will be a boost to morale.


Rick Robinson: The question of having a control room at all was in the context of civil spacecraft. If they have an sudden emergency it is most likely to be a life support crisis such as fire, for which the classic 'bridge' functions are fairly irrelevant.

Military craft are a special case, and I'd certainly expect them to have a control center.

And maybe all ships, because to extend a point Jean makes, existing space programs are quasi-military in origin. The military outlook toward emergency response is coded into their DNA, so to speak.

All human carrying deep space ships will need a storm shelter in any case, and it would be fairly natural to configure this as an emergency control center.


Luke Campbell: Re: Shielding. It now seems likely that a plasma magnet generated by a low mass antenna could deflect any charged solar radiation, so the crew would be safe from flares and CMEs. It does not seem like a plasma magnet could stop galactic cosmic rays, GCRs are a steady source of background radiation, not the sort of thing that a "storm cellar" would help with. A plasma magnet also would not protect against neutral particle radiation, but the only neutral particle radiation likely to be a threat is man-made: neutron radiation from nukes and possibly high energy photons from x-ray or gamma ray lasers.

For those not in the know, a plasma magnet uses low frequency radio waves to produce a rotating field that induces a current in the surrounding solar wind plasma. This current forms a dipole magnetic field that deflects and reflects charged particles. The field is not strong enough to deflect solar wind protons, but it does deflect the electrons, leading to charge separation that pulls the protons back to the electron cloud before they reach the section being protected.

Yes I was trying to stop GCRs (but calculations showed it would need an unreasonably huge magnet). The plasma magnets wouldn't stop the solar wind protons either, when considered as individual particles — you need the plasma effects of the electrons to stop the solar wind. This lets you get by with a much smaller magnet.

However, there is one possible additional method of mitigating the GCR dose - medication. As we learn more about cellular repair and cell "suicide", new treatments may become possible for both chronic and acute radiation poisoning (and oddly, you are likely to want the opposite reaction in these two cases - for chronic exposure, you want the damaged cells to destroy themselves to prevent cancer; for acute exposure you want the damaged cells to repair themselves to prevent anemia, hemophilia, a compromised immune system, and digestive difficulties). Incidentally, it has been shown that vitamin D helps with chronic radiation exposure, although the mechanism is not clear.


Rick Robinson: To keep cryogenic propellant from boiling off on long missions you will need active refrigeration, pumping heat out of the tank. Otherwise heat buildup will be inexorable.

The ship will be designed to keep the propellant tanks away from the main radiator fins and such, and generally minimize heat absorption from the rest of the ship, so the heat you mainly have to deal with is from sunlight.

The tanks will be painted white or silvery to reflect away most sunlight. I assume that you can reflect about 90 percent. For a spherical tank at 1 AU, that means about 35 W/m2 of absorbed solar radiation that you'll have to pump out of the tank.

A 20 meter diameter tank holds about 250 tons of hydrogen, or 1500 tons of methane. Surface area is 1250 m2, so at 1 AU you'd need 44 kW of refrigerating capacity, i.e. heat extraction, to keep propellant cold.

At Jupiter distance, 5 AU, solar flux is reduced by 96 percent, and you only need 2 kW of refrigeration for hydrogen - none for methane, which will stay liquid or even tend to freeze.

Suppose you put a 10 meter diameter hab inside the tank {to give the hab some radiation protection}. (This only reduces tank capacity by 1/8.) But even with a vacuum layer you will have IR heating from the hab surface, at room temperature: 400 W/m2 * 314 m2 = ~125 kW.

So in this case putting the hab inside the fuel tank multiplies your propellant refrigeration bill by 4x. Which is a lot, but not horrible; the shielding might be worth it. But wrapping propellant around a spin hab is tougher.

From Spaceship Design 101 by Rick Robinson (2009)

Structure

What is the structure of the ship going to be composed of? The strongest yet least massive of elements. This means Titanium, Magnesium, Aluminum, and those fancy composite materials. And all the interior girders are going to have a series of circular holes in them to reduce mass (the technical term is "lightening holes").

Fire

There are some hazards to worry about with these space-age materials . Titanium and magnesium are extremely flammable (in an atmosphere containing oxygen). And when I say "extremely" I am not kidding.

Do not try to put out a magnesium fire by throwing water on it. Blasted burning magnesium will suck the oxygen atoms right out of the water molecules, leaving hydrogen gas (aka what the Hindenburg was full of). A carbon-dioxide fire extinguisher won't work either, same result as water except you get a cloud of carbon instead of hydrogen. Instead use a Class D dry chemical fire extinguisher or a lot of sand to cut off the oxygen supply. Oh, did I mention that burning magnesium emits enough ultraviolet light to permanently damage the retinas of the eyes?

The same goes for burning titanium. Except there is no ultraviolet light, but there is a chance of ignition if titanium is in contact with liquid oxygen and the titanium is struck by a hard object. It seems that the strike might create a fresh non-oxidized stretch of titanium surface, which ignites the fire even though the liquid oxygen is at something like minus 200° centigrade. This may mean that using titanium tanks for your rocket's liquid oxygen storage is a very bad idea.

An emergency crew at a spaceport, who has to deal with a crashed rocket, will need the equipment to deal with this.

And if the titanium, magnesium, or aluminum becomes powdered, you have to stop talking in terms of "fire" and start talking in terms of "explosion."

Corrosion

As an interesting side note, rockets constructed of aluminum are extremely vulnerable to splashes of metallic mercury or dustings of mercury salts. On aluminum, mercury is an "oxidizing catalyst", which means the blasted stuff can corrode through an aluminum beam in a matter of hours (in an atmosphere containing oxygen, of course). This is why mercury thermometers are forbidden on commercial aircraft.

Why? Ordinarily aluminum would corrode much faster than iron. However, iron oxide, i.e., "rust", flakes off, exposing more iron to be attacked. But aluminum oxide, i.e., "sapphire", sticks tight, protecting the remaining aluminum with a gem-hard barrier. Except mercury washes the protective layer away, allowing the aluminum to be consumed by galloping rust.

Alkalis will have a similar effect on aluminum, and acids have a similar effect on magnesium (you can dissolve magnesium with vinegar). As far as I know nothing really touches titanium, its corrosion-resistance is second only to platinum.

Protective Paint

If you want a World War II flavor for your rocket, any interior spaces that are exposed to rain and other corrosive planetary weather should be painted with a zinc chromate primer. Depending on what is mixed into the paint, this will give a paint color ranging from yellowish-green to greenish-yellow. In WWII aircraft it is found in wheel-wells and the interior of bomb bays. In your rocket it might be found on landing jacks and inside airlock doors.

Naturally this does not apply to strict orbit-to-orbit rockets, or rockets that only land on airless moons and planets.

Radial Symmetry

When laying out the floor plan, you want the spacecraft to balance. That is, if you draw a line straight through the exhaust bell (in the direction that thrust is applied), it had better pass through the spacecraft's center of gravity, and if the ship is intended for atmospheric flight, it should also go through the spacecraft's nose. Otherwise your ship is going to loop-the-loop or tumble like a cheap Fourth of July skyrocket (Heinlein calls this a rocket "falling off its tail").

This also means that each deck should be "radially symmetric". That's a fancy way of saying that if you have something massive in the north-west corner of "D" deck, you'd better have something equally massive in the south-east corner. This is another reason to strap down the crew during a burn. Walking around could upset the ship's balance, resulting in the dreaded rocket tumble. This will be more of a problem with tiny ships than with huge cruisers, of course. Small ships might have "trim tanks", small tanks into which water can be pumped in order to adjust the balance. The ship will also have heavy gyroscopes that will help prevent the ship from falling off its tail, but there is a limit to how much imbalance that they can compensate for.

Propellent Tankage

PropellentEngineTank %
ArgonIon rocket4
WaterNuclear salt water rocket4
HydrogenNTR / GCR10
LOX/Hydrogen6

A cursory look at the rocket's mass ratio will reveal that most of the rocket's mass is going to be propellant tanks.

Nuclear thermal rockets generally use hydrogen (if it is a Gas Core NTR, the fissionable fuel will probably be less than 1% of the total propellant load) since you want propellant with the lowest molecular mass. Liquid hydrogen has a density of 0.07 grams per cubic centimeter. 792.6 tons of propellant = 792,600,000 grams / 0.07 = 11,323,000,000 cubic centimeters = 11,323 cubic meters . The volume of a sphere is 4/3πr3 so you can fit 11,323 cubic meters in a sphere about 14 meters in radius . Almost 92 feet in diameter, egad! It is a pity hydrogen isn't a bit denser. If this offends your aesthetic sense, you'll have to go back and change a few parameters. Maybe a 2nd generation GC rocket, and a mission from Terra to Mars but not back. Maybe use methane instead of hydrogen. It only has an exhaust velocity of 6318 m/s instead of hydrogen's superior 8800 m/s, but it has a density of 0.42 g/cm3, which would only require a 1.7 meter radius tank. (Methane has a higher exhaust velocity than one would expect from its molecular weight, due to the fact that the GC engine is hot enough to turn methane into carbon and hydrogen. Note that in a NERVA style engine the reactor might become clogged with carbon deposits.)

Robert Zubrin says that as a rule of thumb, the mass of a fuel tank loaded with liquid hydrogen will be about 87% hydrogen and 13% tank. In other words, multiply the mass of the liquid hydrogen by 0.15 to get the mass of the empty tank (0.13 / 0.87 = 0.15). So our 792.6 tons of hydrogen will need a tank that masses 792.6 * 0.15 = 119 tons.

87% propellant and 13% tank is for a rocket designed to land on a planet. An orbit-to-orbit rocket could get by with more hydrogen and less tank. This is because the tanks can be more flimsy since they will not have to endure the stress of landing (A landing-capable rocket that uses a propellant denser than hydrogen can also get away with a smaller tank percentage). Zubrin gives the following ballpark estimates of the tank percentage:

Heat Shield

If you are going to use aerobraking to land your rocket, Zubrin says mass of the heat shield and thermal structure will be about 15% of the total mass being braked. As a wild guess, aerobraking will be limited to killing a velocity of no more than 15 to 30 kilometers per second. The rule of thumb is that aerobraking can kill a velocity approximately equal to the escape velocity of the planet where the aerobraking is performed (10 km/s for Venus, 11 km/s for Terra, 5 km/s for Mars, 60 km/s for Jupiter).

This will mostly be used for our purposes designing a emergency re-entry life pod, not a Solar Guard patrol ship. With a sufficiently advanced engine it is more effective just to carry more fuel, so our atomic cruiser will not need to waste mass on such a primitive device.

In the movie 2010, the good ship Leonov had a one-lung propulsion system, so they needed an aerobraking "ballute" to slow them into Jovian orbit. If you are thinking about aerobraking, keep in mind that many worlds in the Solar System do not have atmospheres.

Power Plant

If you cannot tap your propulsion system for electrical power, you will need a separate power plant (or it's going to be real dark inside your spacecraft). Since rocket designers are concerned with the mass of various components, they use a term called "alpha". This is the ratio of power plant mass (kilograms) to the electrical output (kilowatts). In other words, divide the plant mass by the kilowatts to get Alpha. So if a solar power array had an alpha of 90,and you needed 150 kilowatts of output, the array would mass 90 * 150 = 13,500 kg or 13.5 metric tons.

Occasionally you'll see a power plant with a rating in "Specific Power." This is kilowatts divided by plant mass. In other words it is 1/alpha (though sometimes specific power uses watts instead of kilowatts).

Radioisotope Thermoelectric Generators

Radioisotope thermoelectric generators (RTG) are slugs of radioisotopes (usually plutonium-238 in the form of plutonium oxide) that heat up due to nuclear decay, and surrounded by thermocouples to turn the heat gradient into electricity (it does NOT turn the heat into electricity, that's why the RTG has heat radiator fins on it.). There are engineering reasons that make it impractical to design an individual RTG that produces more than one kilowatt. However nothing is stopping you from using several RTGs in your power room.

Nuclear weapons-grade plutonium cannot be used in RTGs. Plutonium-238 has a half life of 85 years, i.e., the power output will drop to one half after 85 years. To calculate power decay:

P1 = P0 * 0.9919^Y

where:

  • P1 = current power output (watts)
  • P0 = power output when RTG was constructed (watts)
  • Y = years since RTG was constructed.
Example

If a new RTG outputs 470 watts, in 23 years it will output 470 x 0.9919^23 = 470 x 0.83 = 390 watts

Wolfgang Weisselberg points out that this equation just measures the drop in the power output of the slug of plutonium. In the real world, the thermocouples will deteriorate under the constant radioactive bombardment, which will reduce the actual electrical power output even further. Looking at the RTGs on NASA's Voyager space probe, it appears that the thermocouples deteriorate at roughly the same rate as the plutonium.

Plutonium-238 has a specific power of 0.56 watts/gm or 560 watts per kilogram, so in theory all you would need is 470 / 560 = 0.84 kilograms. Alas, the thermoelectric generator which converts the thermal energy to electric energy has an efficiency of only a few percent. If the thermoelectric efficiency is 5%, the plutonium RTG has an effective specific power of 560 x 0.05 = 28 watts per kilogram (0.036 kilogram per watt or 36 kg/kW). This means you will need an entire 17 kilos of plutonium to produce 470 watts.

Currently RTGs have an alpha of about 200 kg/kW (though there is a design on the drawing board that should get about 100 kg/kW). So an RTG with the theoretical maximum output of 1 kilowatt would obviously mass 200 kilograms.

Many RTG fuels would require less than 25 mm of lead shielding to control unwanted radiation. Americium-241 would need about 18 mm worth of lead shielding. And Plutonium-238 needs less than 2.5 mm, and in many cases no shielding is needed as the casing itself is adequate.

Solar Power Arrays

At Terra's distance to the sun, solar energy is about 1366 watts per square meter. This energy can be converted into electricity by photovoltaics.

Solar power arrays have an alpha ranging from 20 to 100 kg/kW. The current state of the art is about 45 kg/kW. Of course their power level goes down the farther from the Sun they travel.

The International Space Station uses 14.5% efficient large-area silicon cells. Each of the Solar Array Wings are 34 m (112 ft) long by 12 m (39 ft) wide, and are capable of generating nearly 32.8 kW of DC power. 19% efficiency is available with gallium arsenide (GaAs) cells, and efficiencies as high as 30% have been demonstrated in the laboratory.

Obviously the array works best when oriented face-on to the sun, and unshadowed. As the angle increases the available power decreases in proportion to the cosine of the angle (e.g., if the array was 75° away from face-on, its power output would be Cos(75°) = 0.2588 or 26% of maximum). Solar cells also gradually degrade due to radiation exposure (say, from 8% to 17% power loss over a five year period if the panel is inhabiting the deadly Van Allen radiation belt, much less if it is in free space).

Typically solar power arrays are used to charge batteries (so you have power when in the shadow of a planet). You should have an array output of 20% higher voltage than the battery voltage or the batteries will not reliably charge up. Sometimes the array is used instead to run a regenerative fuel cell.

Like all non-coherent light, solar energy is subject to the inverse square law. If you double the distance to the light source, the intensity drops by 1/4. As a rule of thumb:

Es = 1366 * (1 / Ds2)

where:

  • Es = available solar energy (watts per square meter)
  • Ds = distance from the Sun (astronomical units)

Remember that you divide distance in meters by 1.49e11 in order to obtain astronomical units.

Example

What is the available solar energy at the orbit of Mars?

Mars orbits the sun at a distance of 2.28e11 meters. That is 2.28e11 / 1.49e11 = 1.53 astronomical units. So the available solar energy is:

  • Es = 1366 * (1 / Ds2)
  • Es = 1366 * (1 / 1.532)
  • Es = 1366 * (1 / 2.34)
  • Es = 1366 * 0.427
  • Es = 583 watts per square meter

This means that the available solar energy around Saturn is a pitiful 15 W/m2, which is why the Cassini probe used RTGs.

A more exotic variant on solar cells is the beamed power concept. This is where the spacecraft has a solar cell array, but back at home in orbit around Terra is a a huge power plant and a huge laser. The laser is fired at the solar cell array, thus energizing it. It is essentially an astronomically long electrical extension cord constructed of laser light. It shares the low mass advantage of a solar powered array. It has an advantage over solar power that the energy per square meter of array can be much larger. It has the disadvantage that the spacecraft is utterly at the mercy of whoever is currently running the laser battery.

Beamed Power

This is where the spacecraft receives its power not from an on-board generator but instead from a laser or maser beam sent from a remote space station. This is a popular option for spacecraft using propulsion systems that require lots of electricity but have low thrusts. For instance, an ion drive has great specific impulse and exhaust velocity, but very low thrust. If the spacecraft has to power the ion drive with a heavy nuclear reactor with lead radiation shielding, the mass of the spacecraft will increase to the point where its acceleration could be beaten by a drugged snail. The drawback includes the distance decrease in power due to diffraction, and the fact that the spacecraft is at the mercy of whoever is running the remote power station. Also maneuvers must be carefully coordinated with the remote station, or they will have difficulty keeping the beam aimed at the ship.

Mercury Boilers

Back in the 1950's, on artist conceptions of space stations and space craft, one would sometimes see what looked like mirrored troughs. These were "mercury boilers", a crude method of harnessing solar energy in the days before photovoltaics. The troughs had a parabolic cross section and focused the sunlight on tubes that heated streams of mercury. The hot mercury was then used in turbines to generate electricity.

These gradually vanished from artist conceptions and were replaced by nuclear reactors. Generally on a long framework boom sticking out of the hub, with a radiation shadow shield big enough to shadown the wheel.

Such systems are generally useful for power needs between 20 kW and 100 kW. Below 20 kW a solar cell panel is better. Above 100 kW a nuclear fission reactor is better. They typically have an alpha of 250 to 170, a collector size of 130 to 150 watts per square meter, and a radiator size of 140 to 200 watts per square meter.

He wasn't surprised when he was assigned to the job of helping paint the solar mirror. This was a big trough that was to run all around the top of the station, set to face the Sun. It was curved to focus the rays of the Sun on a blackened pipe that ran down its center. In the pipe, mercury would be heated into a gas, at a temperature of thirteen hundred degrees Fahrenheit. This would drive a highly efficient "steam" turbine, which would drive a generator for the needed power. When all its energy was used, the mercury would be returned to the outside, to cool in the shadow of the mirror, condensing back to a liquid before re-use.

It was valuable work, and the station badly needed a good supply of power. But painting the mirror was done with liquid sodium. It was a silvery metal that melted easily at a low temperature. On Earth, it was so violently corrosive that it could snatch oxygen out of water. But in a vacuum, it made an excellent reflective paint. The only trouble was that it had to be handled with extreme caution.


It was nasty work. A drop on the plasticized fabric of the space suits would burn a hole through them almost at once. Or a few drops left carelessly on the special gloves they wore for the job could explode violently if carried into the hut, to spread damage and dangerous wounds everywhere nearby.

Jim worked on cautiously, blending his speed with safety in a hard-earned lesson. But the first hour after the new man came out was enough to drive his nerves to the ragged edge. At first, the man began by painting the blackened pipe inside the trough.

Jim explained patiently that the pipe was blackened to absorb heat, and that the silver coating ruined it. He had to go back and construct a seat over the trough on which he could sit without touching the sodium, and then had to remove the metal chemically.

Finally, he gave up. The man was one of those whose intelligence was fine, but who never used it except for purely theoretical problems. He was either so bemused by space or so wrapped up in some inner excitement over being there that he didn't think—he followed orders blindly.


"All right," he said finally. "Go back to Dan and tell him Terrence and I can do it alone. Put your paint in the shop, and mark it dangerous. I'll clean up when I come in."

He watched the man leave, and turned to the boy who had been working with him.


Then suddenly Terrence dropped his brush into the sodium and pointed, his mouth open and working silently.

Jim swung about to see what was causing it, and his own mouth jerked open soundlessly.

The roof of the hut ahead of them was glowing hotly, and as they watched, it suddenly began crumbling away, while a great gout of flame rushed out as the air escaped. Oxygen and heat were fatal to the magnesium alloy out of which the plates were made.


The fire had been coming from the second air lock, installed when the hut was extended. The old one still worked, and men were inside the hut, laboring in space suits. An automatic door had snapped shut between the two sections at the first break in the airtight outer sheathing. But there were still men inside where the flames were, and they were being dragged out of a small emergency lock between the two sections.

One of them yanked off his helmet to cough harshly. His face was burned, but he seemed unaware of it. "Kid came through the lock with a can of something. He tripped, spilled it all over—and then it exploded. We tried to stop it, but it got away. The kid—"

He shuddered, and Jim found that his own body was suddenly weak and shaky. The third man must have done it. He'd taken the orders too literally—he'd gone to report to Dan first, before putting away the sodium. A solid hour's lecture on the dangers of the stuff had meant nothing to him.

From Step to the Stars by Lester Del Rey (1954)

Fuel Cells

Fuel cells basically consume hydrogen and oxygen to produce low voltage electricity and water. They are quite popular in NASA manned spacecraft designs. Each PC17C fuel-cell stack in the Shuttle Orbiter has an alpha of about 13 kg/kW, have a total mass of 91 kg, have an output of 7 kW, and produces about 2.7 kilowatt-hours per kilogram of hydrogen+oxygen consumed (about 70% efficient). The water output can be used in the life support system.

A "regenerative" fuel cell saves the water output, and uses a secondary power source (such as a solar power array) to run an electrolysers to split the water back into oxygen and hydrogen. This is only worth while if the mass of the secondary power source is low compared to the mass of the water. But it is attractive since most life support systems are already going to include electrolysers anyway.

Nuclear Fission Reactors

Los Alamos reactor
ComponentMass
Fuel region157 kg
Reflector154 kg
Heat pipes117 kg
Reactor control33 kg
Other support32 kg
Total Reactor mass493 kg

For a great in-depth analysis of nuclear power for space applications, I refer you to Andrew Presby's engineer degree thesis: Thermophotovoltaic Energy Conversion in Space Nuclear Reactor Power Systems (PDF file). There is a much older document with some interesting designs here (PDF file).

As far as the nuclear fuel required, the amount is incredibly tiny. Which in this case means burning a microscopic 0.01 grams of nuclear fuel per second to produce a whopping 1000 megawatts! That's the theoretical maximum of course, you can find more details here.

Nuclear fission reactors are about 18 kg/kW. However, Los Alamos labs had an amazing one megawatt Heat Pipe reactor that was only 493 kg (alpha of 0.493 kg/kW):

Nuclear Thermal Rockets are basically nuclear reactors with a thrust nozzle on the bottom. A concept called Bimodal NTR allows one to tap the reactor for power. This has other advantages. Since the reactor is running warm at a low level all the time (instead of just while thrusting) it doesn't have to be pre-heated if you have a burn coming up. This reduces thermal stress, and reduces the number of thermal cyclings the reactor will have to endure over the mission. It also allows for a quick engine start in case of emergency.

In the real world, during times of disaster, US Navy submarines have plugged their nuclear reactors into the local utility grid. This supplies emergency electricity when the municipal power plant is out. In the science fiction world, a grounded spacecraft with a bimodal NTR could provide the same service.

Here is a commentary on figuring the mass of the reactor of a nuclear thermal rocket by somebody who goes by the handle Tremolo:

Now, onto a more practical means for generation 1 MW of power using a Plutonium fission reaction.

To calculate the mass required to obtain a certain power level, we have to know the neutron flux and the fission cross-section. Let's assume the flux is 1E14 neutron/cm2/sec, the cross section for fast fission of Pu-239 is about 2 barns (2E-24 cm2), the energy release per fission is 204 MeV, and the Pu-239 number density is 4.939E22 atoms/cm3. Then the power is

P = flux * number density * cross section * Mev per fission * 1.602E-13 Watt/MeV

P = 1E14 * 4.939E22 * 2E-24 * 204 * 1.602E-13 = 323 W/cm3

So, for 1 MW, we need 1E6/323 = 3100 cm3. Given a density of 19.6 gm/cm3, this is 19.6*3100 = 60,760 gm or 60.76 kg.

The next question to ask is: how long do you want to sustain this reaction? In other words, what is the total energy output?

For example, a Watt is one Joule per second. So, to sustain a 1 MW reaction for 1 year, the total energy is 1E6 J/s * 3.15E7 s/year = 3.15E13 J.

For Pu-239, we have 204 Mev per fission and we have 6.023E23./239 = 2.52E21 atoms/gm. So, the energy release per gram is 2.52E21 * 204 Mev/fission * 1.602E-13 J/Mev = 8.24E10 J/gm.

Therefore, to sustain 1 MW for 1 year, we will use 3.15E13 J / 8.24E10 J/gm = 382 gm of Pu-239 or 0.382 kg. This is only a small fraction of the total 60.76 kg needed for the fission reaction.

Finally, this is thermal energy. Our current light water reactors have about a 35% efficiency for conversion to electric power. So, you can take these numbers and essentially multiply by 3 to get a rough answer for the total Pu-239 needed: 3 x 60.76 = 182 kg. Rounding up, you would need roughly 200 kg for a long term sustained 1 MW fission reaction with a 35% conversion efficieny.

These calculations assume quite a bit and I wouldn't use these numbers to design a real reactor, but they should give you a ballpark idea of the masses involved.

Tremolo

New reactors that have never been activated are not particularly radioactive. Of course, once they are turned on, they are intensely radioactive while generating electricity. And after they are turned off, there is some residual radiation due to neutron activation of the reactor structure.

How much deadly radiation does an operating reactor spew out? That is complicated, but Anthony Jackson has a quick-and-dirty first order approximation:

r = (0.5*kW) / (d2)

where:

  • r = radiation dose (Sieverts)
  • kW = power production of the reactor core, which will be greater than the power output of the reactor due to reactor inefficiency (kilowatts)
  • d = distance from the reactor (meters)

This equation assumes that a 1 kW reactor puts out an additional 1.26 kW in penetrating radiation (mostly neutrons) with an average penetration (1/e) of 20 g/cm2.

As a side note, in 1950's era SF novels, nuclear fission reactors are commonly referred to as "atomic piles." This is because the very first reactor ever made was basically a precision assembled brick-by-brick pile of graphite blocks, uranium fuel elements, and cadmium control rods.

Fusion Reactors

A fusion reactor would produce energy from thermonuclear fusion instead of nuclear fission. Unfortunately scientist have yet to create a fusion reactor that can reach the "break-even" point (where is actually produces more energy than it consumes), so it is anybody's guess what the value for alpha will be.

The two main approaches are magnetic confinement and inertial confinement. The third method, gravitational confinement, is only found in the cores of stars and among civilizations that have mastered gravidic technology. The current wild card is the Polywell device which is a type of inertial electrostatic confinement fusion generator.

Fusion is even more efficient than fission. You need to burn 0.01 grams of fission fuel per second to generate 1000 megawatts. But among the most promising fusion fuels, they start at 0.01 grams per second, and can get as low as 0.001 grams per second. You can find more details here.

Exotic power sources

There are all sorts of exotic power sources. Some are reasonably theoretically possible, others are more fringe science. None of them currently exist, and some never will.

Antimatter Power

Any Star Trek fan knows that the Starship Enterprise runs on antimatter. The old term is "contra-terrene", "C-T", or "Seetee". At 100% of the matter-antimatter mass converted into energy, it would seem to be the ultimate power source. The operative word in this case is "seem".

What is not as well known is that unless the situation is non-standard, antimatter is not a fuel. It is an energy transport mechanism. Let me explain.

The same situation exists with respect to the so-called "hydrogen economy". Proponents point out how hydrogen is a "green" fuel, unlike nasty petroleum or gasoline. Burn gasoline and in addition to energy you also produce toxic air pollution. Burn hydrogen and the only additional product is pure water.

The problem is that while there exist petroleum wells, there ain't no such thing as a hydrogen well. You can't find hydrogen just lying around somewhere, the stuff is far too reactive. Hydrogen has to be generated by some other process, which consumes energy (such as electrolysing water using electricity generated by a coal-fired power plant). This is why hydrogen is not a fuel, it is an energy transport mechanism. It is basically being used to transport the energy from the coal-fired power plant into the hydrogen burning automobile.

This means that unless there exist "antimatter mines", antimatter is also an energy transport mechanism, not a fuel. In Star Trek, I believe they found drifts of antimatter in deep space. In real life, astronomers haven't seen many matter-antimatter explosions. Well, they've seen a few 511 keV gamma rays (the signature of electron-positron antimatter annihilation), but they've all been from thousands of light years away and most seem to be associated with large black holes. If they are antimatter mines, they are most inconveniently located. In Jack Williamson's novels Seetee Ship and Seetee Shock there exist commercially useful chunks of antimatter in the asteroid belt. However, if this was actually true, I think astronomers would have noticed all the antimatter explosions detonating in the belt by now.

And antimatter is a very inefficient energy transport mechanism. Current particle accelerators have an abysmal 0.000002% efficiency in converting electricity into antimatter (I don't care what you saw in the movie Angels and Demons). The late Dr. Robert Forward says this is because nuclear physicist are not engineers, an engineer might manage to increase the efficiency to something approaching 0.01% (one one-hundredth of one percent). Which is still pretty lousy, it means for every megawatt of electricity you pump in to the antimatter-maker you would only obtain enough antimatter to create a mere 100 pathetic watts. The theoretical maximum is 50% due to the pesky Law of Baryon Number Conservation (which demands that when turning energy into matter, equal amounts of matter and antimatter must be created).

In Charles Pellegrino and George Zebrowski novel The Killing Star they deal with this by having the Earth government plate the entire equatorial surface of the planet Mercury with solar power arrays, generating enough energy to produce a few kilograms of antimatter a year. They do this with von Neumann machines, of course.

Of course the other major draw-back is the difficulty of carrying the blasted stuff. If it comes into contact with the matter walls of the fuel tank the resulting explosion will make a nuclear detonation seem like a wet fire-cracker. Researchers are still working on a practical method of containment. In Michael McCollum's novel Thunder Strike! antimatter is transported in torus-shaped magnetic traps, it is used to alter the orbits of asteroids ("torus" is a fancy word for "donut").

Converting the energy from antimatter annihilation into electricity is also not very easy.

The electrons and positrons mutually annihilate into gamma rays. However, since an electron has 1/1836 the mass of a proton, and since matter usually contains about 2.5 protons or other nucleons for each electron, the energy contribution from electron-positron annihilation is negligible.

For every five proton-antiproton annihilations, two neutral pions are produced and three charged pions are produced (that is, 40% neutral pions and 60% charged pions). The neutral pions almost immediately decay into gamma rays. The charged pions (with about 94% the speed of light) will travel 21 meters before decaying into muons. The muons will then travel an additional two kilometers before decaying into electrons and positrons.

This means your power converter needs a component that will transform gamma rays into electricity, and a second component that has to attempt to extract the kinetic energy out of the charged pions and convert that into electricity. The bottom line is that there is no way you are going to get 100% of the annihilation energy converted into electricity. Exactly what percentage is likely achievable is a question above my pay grade.

The main virtue of antimatter power is that it is incredibly concentrated, which drastically reduces the mass of antimatter fuel required for a given application. And mass is always a problem in spacecraft design, so any way of reducing it is welcome.

The man known as magic9mushroom drew my attention to the fact that Dr. James Bickford has identified a sort of antimatter mine where antimatter can be collected by magnetic scoops (be sure to read the comment section), but the amounts are exceedingly small. He foresees using tiny amounts of antimatter for applications such as catalyzing sub-critical nuclear reactions, instead of just using raw antimatter for fuel. His report is here.

Dr. Bickford noted that high-energy galactic cosmic rays (GCR) create antimatter via "pair production" when they impact the upper atmospheres of planets or the interstellar medium. Planets with strong magnetic fields enhance antimatter production. One would think that Jupiter would be the best at producing antimatter, but alas its field is so strong that it prevents GCR from impacting the Jovian atmosphere at all. As it turns out, the planet with the most intense antimatter belt is Earth, while the planet with the most total antimatter in their belt is Saturn (mostly due to the rings). Saturn receives almost 250 micrograms of antimatter a year from the ring system. Please note that this is a renewable resource.

Dr. Bickford calculates that the plasma magnet scoop can collect antimatter about five orders of magnitude more cost effective than generating the stuff with particle accelerators.

Keep in mind that the quantities are very small. Around Earth the described system will collect about 25 nanograms per day, and can store up to 110 nanograms. That has about the same energy content as half a fluid ounce of gasoline, which ain't much. However, such tiny amounts of antimatter can catalyze tremendous amounts of energy from sub-critical fissionable fuel, which would give you the power of nuclear fission without requiring an entire wastefully massive nuclear reactor. Alternatively, one can harness the power of nuclear fusion with Antimatter-Catalyzed Micro-Fission/Fusion or Antimatter-Initiated Microfusion. Dr. Bickford describes a mission where an unmanned probe orbits Earth long enough to gather enough antimatter to travel to Saturn. There it can gather a larger amount of antimatter, and embark on a probe mission to the outer planets.

Vacuum energy

Vacuum energy or zero-point energy is one of those pie-in-the-sky concepts that sounds too good to be true, and is based on the weirdness of quantum mechanics. The zero-point energy is the lowest energy state of any quantum mechanical system, but because quantum systems are fond of being deliberately annoying their actual energy level fluctuates above the zero-point. Vacuum energy is the zero-point energy of all the fields of space.

Naturally quite a few people wondered if there was a way to harvest all this free energy.

Currently the only suggested method was proposed by the late Dr. Robert Forward, the science fiction writer's friend (hard-SF writers would do well to pick up a copy of Forward's Indistinguishable From Magic). His paper is Extracting Electrical Energy From the Vacuum by Cohesion of Charged Foliated Conductors, and can be read here.

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

Kerr-Newman black hole

The popular conception of a black hole is that it sucks everything in, and nothing gets out. However, it is theoretically possible to extract energy from a black hole, for certain values of "from."

And by the way, there appears to be no truth to the rumor that Russian astrophysicists use a different term, since "black hole" in the Russian language has a scatological meaning. It's an urban legend, I don't care what you read in Dragon's Egg.

For an incredibly dense object with an escape velocity higher than the speed of light which warps the very fabric of space around them, black holes are simple objects. Due to their very nature they only have three characteristics: mass, spin (angular momentum), and electric charge. All the other characteristics got crushed away (well, technically they also have magnetic moment, but that is uniquely determined by the other three). All black holes have mass, but some have zero spin and others have zero charge.

There are four types of black holes. If it only has mass, it is a Schwarzschild black hole. If it has mass and charge but no spin, it is a Reissner-Nordström black hole. If it has mass and spin but no charge it is a Kerr black hole. And if it has mass, charge and spin it is a Kerr-Newman black hole. Since practically all natural astronomical objects have spin but no charge, all naturally occurring black holes are Kerr black holes, the others do not exist naturally. In theory one can turn a Kerr black hole into a Kerr-Newman black hole by shooting charged particles into it for a few months, say from an ion drive or a particle accelerator.

From the standpoint of extracting energy, the Kerr-Newman black hole is the best kind, since it has both spin and charge. In his The MacAndrews Chronicles, Charles Sheffield calls them "Kernels" actually "Ker-N-el", which is shorthand for Kerr-Newman black hole.

The spin acts as a super-duper power storage device. You can add or subtract spin energy to the Kerr-Newman black hole by using the Penrose process. Just don't extract all the spin, or the blasted thing turns into Reissner-Nordström black hole and becomes worthless. The attractive feature is that this process is far more efficient than nuclear fission or thermonuclear fusion. And the stored energy doesn't leak away either.

The electric charge is so you can hold the thing in place using electromagnetic fields. Otherwise there is no way to prevent it from wandering thorough your ship and gobbling it up.

The assumption is that Kerr-Newman black holes of manageable size can be found naturally in space, already spun up and full of energy. If not, they can serve as a fantastically efficient energy transport mechanism.

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

Alert readers will have noticed the term "manageable size" above. It is impractical to use a black hole with a mass comparable to the Sun. Your ship would need an engine capable of moving something as massive as the Sun, and the gravitational attraction of the black hole would wreck the solar system. So you just use a smaller mass black hole, right? Naturally occurring small black holes are called "Primordial black holes."

Well, there is a problem with that. 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 deadly radiation it emits. 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.

In The McAndrew Chronicles Charles Sheffield hand-waved an imaginary force field that somehow contained all the deadly radiation. One also wonders if there is some way to utilze the radiation to generate power.

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.

Table is from Are Black Hole Starships Possible? (PDF file), thanks to magic9mushroom for this link.

"I think Earth's worst problems are caused by the power shortage," he said. "That affects everything else. Why doesn't Earth use the kernels for power, the way that the USF does?"

"Too afraid of an accident," replied McAndrew. His irritation evaporated immediately at the mention of his specialty. "If the shields ever failed, you would have a Kerr-Newman black hole sitting there, pumping out a thousand megawatts—mostly as high-energy radiation and fast particles. Worse than that, it would pull in free charge and become electrically neutral. As soon as that happened, there'd be no way to hold it electromagnetically. It would sink down and orbit inside the Earth. We couldn't afford to have that happen."

"But couldn't we use smaller kernels on Earth?" asked Yifter. "They would be less dangerous."

McAndrew shook his head. "It doesn't work that way. The smaller the black hole, the higher the effective temperature and the faster it radiates. You'd be better off with a much more massive black hole. But then you've got the problem of supporting it against Earth's gravity. Even with the best electromagnetic control, anything that massive would sink down into the Earth."

"I suppose it wouldn't help to use a nonrotating, uncharged hole, either," said Yifter. "That might be easier to work with."

"A Schwarzschild hole?" McAndrew looked at him in disgust. "Now, Mr. Yifter, you know better than that." He grew eloquent. "A Schwarzschild hole gives you no control at all. You can't get a hold of it electromagnetically. It just sits there, spewing out energy all over the spectrum, and there's nothing you can do to change it—unless you want to charge it and spin it up, and make it into a kernel. With the kernels, now, you have control."

I tried to interrupt, but McAndrew was just getting warmed up. "A Schwarzschild hole is like a naked flame," he went on. "A caveman's device. A kernel is refined, it's controllable. You can spin it up and store energy, or you can use the ergosphere to pull energy out and spin it down. You can use the charge on it to move it about as you want. It's a real working instrument—not a bit of crudity from the Dark Ages."

from The McAndrew Chronicles by Charles Sheffield (1983)

In this model of the interaction of a miniature black hole with the vacuum, the black hole emits radiation and particles, as though it had a temperature. The temperature would be inversely proportional to the mass of the black hole. A Sun-sized black hole is very cold, with a temperature of about a millionth of a degree above absolute zero. When the mass of the black hole is about a hundred billion tons (the mass of a large asteroid), the temperature is about a billion degrees.

(ed note: one hundred billion tons is 100,000 million tons or 5 × 10-17 solar masses. 6 × 10-8 / 5 × 10-17 = 1,200,000,000 Kelvin)

According to Donald Page, who carried out lengthy calculations on the subject, such a hole should emit radiation that consists of approximately 81% neutrinos, 17% photons, and 2% gravitons. When the mass becomes significantly less than a hundred billion tons, the temperature increases until the black hole is hot enough to emit electrons and positrons as well as radiation. When the mass becomes less than a billion tons (a one kilometer diameter asteroid), the temperature now approaches a trillion degrees and heavier particle pairs, like protons and neutrons are emitted. The size of a black hole with a mass of a billion tons is a little smaller than the nucleus of an atom. The black hole is now emitting 6000 megawatts of energy, the output of a large power plant. It is losing mass at such a prodigious rate that its lifetime is very short and it essentially "explodes" in a final burst of radiation and particles.

(ed note: one billon tons is 1000 million tons. An atomic nucleus is about 1750 to 15,000 attometers in diameter.)


If it turns out that small black holes really do exist, then I propose that we go out to the asteroid belt and mine the asteroids for the black holes that may be trapped in them. If a small black hole was in orbit around the Sun in the asteroid belt region, and it had the mass of an asteroid, it would be about the diameter of an atom. Despite its small size, the gravity field of the miniature black hole would be just as strong as the gravity field of an asteroid and if the miniature black hole came near another asteroid, the two would attract each other. Instead of colliding and fragmenting as asteroids do, however, the miniature black hole would just penetrate the surface of the regular asteroid and pass through to the other side. In the process of passing through, the miniature black hole would absorb a number of rock atoms, increasing its weight and slowing down slightly. An even more drastic slowing mechanism would be the tides from the miniature black hole. They would cause stresses in the rock around the line of penetration and fragment the rock out to a few micrometers away from its path through the asteroid. This would cause further slowing.

After bouncing back and forth through the normal matter asteroid many times, the miniature black hole would finally come to rest at the center of the asteroid. Now that it is not moving so rapidly past them, the miniature black hole could take time to absorb one atom after another into its atom-sized body until it had dug itself a tiny cavity at the center of the asteroid. With no more food available, it would stop eating, and sit there and glow warmly for a few million years. After years of glowing its substance away, it would get smaller. As it got smaller it would get hotter since the temperature rises as the mass decreases. Finally, the miniature black hole would get hot enough to melt the rock around it. Drops of melted rock would be pulled into the miniature black hole, adding to its mass. As the mass of the black hole increased, the temperature would decrease. The black hole would stop radiating, the melted rock inside the cavity would solidify, and the process would repeat itself many centuries later. Thus, although a miniature black hole left to itself has a lifetime that is less than the time since the Big Bang, there could be miniature black holes with the mass of an asteroid, being kept alive in the asteroid belt by a symbiotic interaction with an asteroid made of normal matter.

To find those asteroids that contain miniature black holes, you want to look for asteroids that have anomalously high temperatures, lots of recent fracture zones, and anomalously high density. Those with a suspiciously high average density have something very dense inside. To obtain a measure of the density, you need to measure the volume and the mass. It is easy enough to get an estimate of the volume of the host asteroid with three pictures taken from three different directions. It is difficult to measure the mass of an object in free fall. One way is to go up to it with a calibrated rocket engine and push it. Another is to land on it with a sensitive gravity meter. There is, however, a way to measure the mass of an object at a distance without going through the hazard of a rendezvous. To do this, you need to use a mass detector or gravity gradiometer.


Once you have found a suspiciously warm asteroid that seems awfully massive for its size, then to extract the miniature black hole, you give the surface of the asteroid a strong shove and push the asteroid out of the way. The asteroid will shift to a different orbit, and where the center of the asteroid used to be, you will find the miniature black hole. The black hole will be too small to see, but if you put an acoustic detector on the asteroid you will hear the asteroid complaining as the black hole comes to the surface. Once the black hole has left the surface you can monitor its position and determine its mass with a mass detector.


The next step in corralling the invisible black maverick is to put some electric charge on it. This means bombarding the position of the miniature black hole with a focused beam of ionized particles until the black hole has captured enough of them to have a significant charge to mass ratio. The upper limit will depend upon the energy of the ions. After the first ion is absorbed, the black hole will have a charge and will have a tendency to repel the next ion. Another upper limit to the amount of charge you can place on a black hole is the rate at which the charged black hole pulls opposite charges out of the surrounding space. You can keep these losses low, however, by surrounding the black hole with a metal shield.

Once a black hole is charged, you can apply forces to it with electric fields. If the charged black hole happens to be rotating, you are in luck, for then it will also have a magnetic field and you can also use magnetic fields to apply forces and torques. The coupling of the electric charge to the black hole is very strong—the black hole will not let go. You can now use strong electric or magnetic fields to pull on the black hole and take it anywhere you want to go.

from Indistinguishable From Magic by Robert L. Forward (1995)

Mass Converters

Mass Converters are fringe science. You see them in novels like Heinlein's Farmer in the Sky, James P. Hogan's Voyage from Yesteryear, and Vonda McIntyre's Star Trek II: The Wrath of Khan. You load the hopper with anything made of matter (rocks, raw sewage, dead bodies, toxic waste, old AOL CD-ROMS, belly-button lint, etc.) and electricity comes out the other end. In the appendix to the current edition of Farmer in the Sky Dr. Jim Woosley is of the opinion that the closest scientific theory that would allow such a thing is Preon theory.

Preon theory was all the rage back in the 1980's, but it seems to have fallen into disfavor nowadays (due to the unfortunate fact that the Standard Model gives better predictions, and absolutely no evidence of preons has ever been observed). Current nuclear physics holds that all subatomic particles are either leptons or composed of groups of quarks. The developers of Preon theory thought that two classes of elementary particles does not sound very elementary at all. So they theorized that both leptons and quarks are themselves composed of smaller particles, pre-quarks or "preons". This would have many advantages.

One of the most complete Preon theory was Dr. Haim Harari's Rishon model (1979). The point of interest for our purposes is that the sub-components of electrons, neutrons, protons, and electron anti-neutrinos contain precisely enough rishon-antirishon pairs to completely annihilate. All matter is composed of electrons, neutrons, and protons. Thus it is theoretically possible in some yet as undiscovered way to cause these rishons and antirishons to mutually annihilate and thus convert matter into energy.

Both James P. Hogan and Vonda McIntyre new a good thing when they saw it, and quickly incorporated it into their novels.


Back about the same time, when I was a young man, I thought I had come up with a theoretical way to make a mass converter. Unsurprisingly it wouldn't work. My idea was to use a portion of antimatter as a catalyst. You load in the matter, and from the antimatter reserve you inject enough antimatter to convert all the matter into energy. Then feed half (or a bit more than half depending upon efficiency) into your patented Antimatter-Makertm and replenish the antimatter reserve. The end result was you fed in matter, the energy of said matter comes out, and the antimatter enables the reaction but comes out unchanged (i.e., the definition of a "catalyst").

Problem #1 was that pesky Law of Baryon Number Conservation, which would force the Antimatter-Maker to produce equal amounts of matter and antimatter. Which would mean that either your antimatter reserve would gradually be consumed or there would be no remaining energy to be output, thus ruining the entire idea. Drat! Problem #2 is that while electron-positron annihilation produces 100% of the energy in the form of gamma-rays, proton-antiproton annihilation produces 70% as energy and 30% as worthless muons and neutrinos.

Pity, it was such a nice idea too. If you were hard up for input matter, you could divert energy away from the Antimatter-maker and towards the output. Your antimatter reserve would diminish, but if you found more matter later you could run the mass converter and divert more energy into the Antimatter-maker. This would replenish your reserve. And if you somehow totally ran out of antimatter, if another friendly ship came by it could "jump-start" you by connecting its mass converter energy output directly to your Antimatter-maker and run it until you had a good reserve.

Heat Radiators

Power plants and some propulsion systems are going to require heat radiators to avoid system meltdown. There are only three ways of getting rid of heat: convection, conduction, and radiation; and the first two do not work at all in the vacuum of space. So the ship designer is stuck with heat radiators. See Thermophotovoltaic Energy Conversion in Space Nuclear Reactor Power Systems and HIGH TRADER for details. Ken Burnside also noted that radiators are large, flimsy, and impossible to armor (except perhaps for the droplet radiator). A liability on a warship. If you want to calculate this for yourself:

∂Q/∂t = Re * (5.67x10e-8) * Ra * Rt4

where

  • ∂Q/∂t = amount of waste heat to get rid of (watts)
  • 5.67x10e-8 = Stefan's Constant
  • Re = emissivity of radiator (theoretical maximum is 1.0)
  • Ra = area of radiator (m2)
  • Rt = temperature of radiator (degrees K)

Ken Burnside says that if one examine the equation carefully one will notice that the radiator effectiveness goes up at the fourth power of the heat of the radiator. The higher the temperature, the lower the surface area can be, which lowers the required mass of radiator fins. This is why most radiator designs use liquid sodium or lithium (or things more exotic, still). 1600K radiators mean that you need a lot less mass than 273 K radiators.

Propulsion systems like nuclear thermal rockets do not need heat radiators because the waste heat is carried away by the exhaust plume. In effect, the exhaust is their radiator (the technical term is "Open-Cycle Cooling"). Electrical powered drives like ion drives will require radiators on their power plants. Fusion drives may or may not require radiators, depending upon whether the design can dump the waste heat into the exhaust or not.

My source (Matthew DeBell) says that if ∂Q/∂t = 150 gigawatts and Rt = 3000 K, Ra would be 34,941m2. Actually it could be half that if you have a two-sided radiator, which would make the radiator a square 90-odd meters on a side. I have no idea how to estimate how much mass a radiator of a given size will be. At a rough guess, you are looking at 0.01 to 0.05 kilograms per kilowatt dissipated. (The table I was looking at said that a flimsy radiator operating at 1100 K would be 0.01 kg/kW and an armored meteor proof radiator operating at 2000 K would be 0.05 kg/kW)

Liquid Droplet

An advanced design is the liquid droplet radiator. Dr. John Schilling had a few comments:

Liquid-droplet radiators are also a possibility. There do exist liquids which have extremely low vapor pressure at high temperatures - certain organics up to ~600K, liquid metals (esp. lithium) to ~1500K. Using a carefully-designed nozzle to create a fan-shaped spray of fine droplets towards a linear collector results in a very efficient radiator, with minimal weight per unit radiating surface, high temperature, and high throughput.

The radiator would be essentially triangular when "deployed", with the spray nozzle at one vertex and the collector along the opposite side. If the nozzle-vertes is adjacent to the ship body, the collector "arm" will have to extend outwards. Alternately, the collector can be run along the side of the ship, and the spray nozzle extended on a boom and aimed inwards. A series of closely-spaced, narrow-angle nozzles would approximate a rectangular array.

There is always some loss of coolant due to evaporation in vacuum, hence use of liquids with extremely low vapor pressure. You also lose coolant if such a radiator is run under acceleration, unless the collector is over-long and aligned parallel to the thrust axis, which imposes a constraint on system geometry. You also lose coolant if the radiator "panel" is hit by enemy weapons fire; on the other hand there is no mechanical damage unless the much smaller nozzle or collector arms are hit. Bottom line - you'll need a small surplus of coolant, unless you are running a warship, in which case you'll need a large surplus.

If liquid metal is used as the coolant, MHD pumping can be used at the collector arms, resulting in a simplified design with no moving parts. Indeed, in such a case the coolant could also be used as the working fluid in an MHD generator, resulting in a single-fluid, single-cycle power system from primary energy generation to waste heat radiation. Again, a simple, efficient design with no moving parts.

Eric Rozier has an online calculator for droplet radiators here, and for coolant systems in general here. He had this analysis:

Given that the main thing we want to determine is the surface area of the lithium droplets to calculate the heat it can radiate, I decided to build a model of the surface area.

Since no such radiator has been built we have to work with some plausible model data. To model the lithium drops themselves I dug into some meteorological data and found that raindrops typically range in size from 1mm to 3mm, sounds pretty reasonable. Assuming droplets are spherical (a reasonable assumption in zero gravity) then the surface area of any given droplet is of course 4*π*r2.

Working off the wedge based idea you cited here. We then model the full radiating body of the droplets as a triangle, reducing the emitter to a point source for simplification. I'm not sure how space out the droplets should be, but I figure if the distance between any two droplets is roughly twice the radius, the model is probably pretty conservative. Thus for an emitter with distance h from the emitter to the collector, and a collector plate of length h, we get the number of droplets suspended between them to be:

(0.5 * b * h)/(16r2)

We can then model the surface area of the lithium droplets as:

(0.5 * b * h)/(16r2) * 4*π*r2

If you want to modify the spacing of the drops, you can change the inter-droplet gap to q instead of r, rendering the following equation:

(0.5 * b * h)/(4r2 + 4r*q + q2) * 4*π*r2

Eric Rozier

So the equations are:

a = (0.5*b*h) / (16*r2) * 4*π*r2

a = (0.5*b*h) / (4*r2 + 4*r*q + q2) * 4*π*r2

where:

  • a = surface area of lithium droplets in radiator surface
  • b = length of base of radiator triangle
  • h = length of height of radiator triangle
  • r = radius of indiviual droplet
  • q = inter-droplet gap

The Glow

What color will the radiators glow? A practical one will only glow dull red. You can use the Blackbody Spectrum Viewer to see what temperature corresponds to what color. If it was glowing white hot, the temperature would be around 6000 Kelvin. This would be difficult for a solid radiator, since even diamond melts at 4300 degrees K.

Life Support

Technically you also need radiators to keep the life-system habitable. Human bodies produce an amazing amount of heat. Even so, the life-system radiator should be small enough to be placed over part of the hull.

I had initially thought that the heat from the life-system could be simply dumped by the same radiator system dealing with the multi-gigawatt waste heat from the propulsion system. Richard Bell pointed out that I had not thought the problem through. Due to the difference in the temperatures of the waste heat from life-system and propulsion, unreasonably large amounts of energy will be required to get the low-level life-system heat into a radiator designed to handle high-level propulsion heat. The bottom line is that there will be two separate radiator systems.

The life-system radiators on the Space Shuttle are inside the cargo bay doors, which is why the doors are always open while the shuttle is in space.

Troy Campbell pointed me at a fascinating NASA report about spacecraft design (warning, 2 MB PDF file). In the sample design given in the report, the spacecraft habitat module carried six crew members, and needed life-system heat radiators capable of collecting and rejecting 15 kilowatts of heat (15 kW is the power consumption for all the systems included in the example habitat module). The radiator was one-sided (basically layered over the hull). It required a radiating surface area of 78 m2, had a mass of 243.8 kg, and a volume of 1.742 m3. It used 34.4 kg of propylene glycol/water coolant as a working fluid. In addition to the radiator proper, there was the internal and external plumbing. The Internal Temperature Control System (coldplates, heat exchangers, and plumbing located inside the habitat module) had a mass of 111 kg and a volume of 0.158 m3. The External Temperature Control System had a mass of 131 kg, a volume of 0.129 m3, and consumes 1.109 kilowatts.

Simple math tells me the radiator has a density of about 140 kg/m3, and needs a radiating surface area of about 5.2 m2 per per kilowatt of heat handled. The entire system requires about 35 kg per kilowatt of heat handled, and 0.13 m3 per kilowatt of heat. But treat these numbers with suspicion, I am making the assumption that these things scale linearly.

Number Crunching

Here is some scary math about radiators from Dr. Tony Valle and Ray Robinson, along with some interesting conclusion:

RocketCat sez

Their "interesting conclusion" is that ya don't wanna design your heat radiator to run at 100% efficiency or the blasted thing will be huge, unwieldy, and bloated with penalty mass. Remember every gram counts!

For the sweet spot between maximum efficiency and minimum mass, design the radiator to run between 3/5 and 3/4 of the power plant's hot end. But if you don't wanna take my word for it, feel free to dive into the following scary math.

It is surprising but there is an optimum temperature ratio at which to run a starship heat exchanger (or similar power source) to achieve maximum free power with a minimum of radiator area. The only assumptions necesary are that the power source obeys the laws of thermodynamics and that the starship may only get rid of waste heat by radiating.

Let us assume that we have a heat engine as a power source with a relative efficiency of η, and an absolute efficiency is η times the Carnot efficiency ε. We can write the available free power, F, as:

F = Qηε = Qη(1 - T1/T2)

where Q is the rate of heat flow into the exchanger and T1 and T2 are the temperatures of the cold and hot sides of the engine, respectively. The waste heat, H, released into the starship is Q - F, or:

H = Q(1 - η + ηT1/T2)
H = F (1 - η + ηT1/T2)/η(1 - T1/T2)

To simplify, we will measure temperature in units of T2 and let T1 be called just T. After dividing through by η the amount of waste heat associated with a given free power F is then:

H = F (η-1 - 1 + T) / (1 -T)

Now this waste heat must be radiated away from the ship. The power radiated by a black body at temperature T and with area A is given by the Stephan-Boltzmann Law:

P = σAT4

with σ a constant depending on the choice of units. Setting these equal to each other gives:

A = F (η-1 - 1 + T) / σ(T4 - T5)

Now we can ask what value of T will give the minimum radiator area. Taking the derivative of A with respect to T and setting it equal to zero gives:

(T4 - T5) - (4T3 - 5T4)(η-1 - 1 + T) = 0

Or, dividing by T3 and expanding:

T - T2 - 4η-1 - 4 + 4T + 5Tη-1 - 5T + 5T2 = 0

After collecting terms, we have:

4T2 + (5η-1 - 8)T + 4(η-1 - 1) = 0

or, dividing through by 4:

T2 + (5/4η-1 - 2)T + (η-1 - 1) = 0

We write η-1 as γ then the solution to the above quadratic can be written:

T = 1 - 5/8γ + 1/8 sqrt(25γ2 - 16γ)

In the special case where the exchanger runs at maximum theoretical efficiency, η = γ = 1 and the equation above gives T = 3/4. This means that the cold side of the heat engine is at 75% of the temperature of the hot side.

This is horribly inefficient as a Carnot heat engine goes, but if the radiator temperature drops, the surface area (and thus mass) must increase, because of the T4 behavior of the radiation law — colder radiators dump heat much less efficiently. This function is fairly flat — as η drops from 1 to a more plausible 0.1, T changes from 3/4 to 4/5

Dr. Tony Valle and Ray Robinson's commentary in Attack Vector: Tactical, "Science Behind The Rules: Power and Heat Generation" (2004)
Science Behind The Rules: Radiators and Heat Sinks

(ed note: This is from the tabletop wargame Attack Vector: Tactical, which is why it talks about weird units like "power points" and "heat points."

One game turn segment is 16 seconds.

One power point is 1000 megajoules delivered in 1 segment.

So a starship reactor that outputs 1 power point produces at a rate of 1000 MJ / 16 seconds = 62.5 megawatts.

1 heat point is 250 megawatts.

1 hull space holds 20 metric tons.)

Knowing that our reactors produce 62.5 MW as a base power unit, and using the proof at right, we get an efficiency of 4 J of waste heat per J of power generated. This tells us that wee need to radiate ~250 MW per point of power. The Sefan-Boltzman law states that the surface emits power at a rate of (1-A) 5.67 × 108 Wm2 K4 * T4 where A is the albedo, and T the absolute temperature in Kelvins. With an albedo of 0.1, a temperature of 1600K, and 250 MW of output, we need 700 square meters of radiating surface. Extending as a fin, radiating from both sides, this is roughly 18 meters square. At roughly 0.3m thick, and flexible enough to be retracted and extended, we get something that's reasonably 70 tons, or a bit shy of 3 hull spaces. For the sake of game play, one hull space of radiators dissipates 100 MW, or 0.4 heat points.

A civilian (starship) reactor has a built in 16 meter by 16 meter radiator that dissipates its waste heat; this radiator is built into the hull of the ship. This is why civilian reactors require part of the hull of the ship to be unarmored.

Storing the heat before radiation requires a heat sink. A sodium heat sink is ~21.5 cubic meters of sodium, with a density of 0.968 tons per cubic meter. Sodium has a thermal capacity of 28.2 J/mole/K. A mole of sodium weighs 22.98 grams. One gram of sodium absorbs 2.82/22.98 = 1.22 J per K of heat increase. A heat sink of sodium weighs 20.82 tons, raising that mass by 1 K absorbs 25.4 MJ. Sodium melts at 372 K and vaporizes at 1252 K. Pressurized, it remains liquid to 1600 K, our radiator temperature. Assuming a working range of 1300K (room temperature to 1600 K), each heat sink stores 1300 * 25.4 MJ = 33.02 GJ, which is one heat point, assuming other inefficiencies.

Lithium's thermal capacity of 24.8 J/mole/K and molar weight of 6.94 allows 1 gram to absorb 3.57 J per K of heat increase, or 2.92× the heat capacity of sodium. By using 22 tons of lithium, we get triple the capacity of the sodium heat sink.

Water's thermal capacity is 4.186 J/gram/K, 3.426 times that of sodium. Room temperature to boiling is ~85 K, which limits its usefulness. Raising 1 ton of water by 85 K takes 355.88 MJ. One heat point is 33 GJ, and the amount of water needed to store one heat point is 33 GJ/350.88 MJ = 93 tons. Including the extra mass for plumbing, that's 5 hull spaces all told.

Vaporizing water takes 2256 J/g, 6.3× the energy needed to raise it by 85 K. Because the vaporization is not quite perfect, we treat it as 6 heat points removed when the heat sink is vented. The liquid metal heat sinks aren't vented, as vaporized metal would deposit on the sensors of the ship.

From Attack Vector: Tactical Core Rulebook by Burnside, Finley, and Valle (2004)

From John Gwinner:

Take a classic space opera warship. Onboard power is generated by one or more fusion reactors. If the overall power is 2 gigawatts, and the efficiency is 90% (a pretty generous estimate, since projections I've seen for MHD power generation are around 60%) then at full power, the reactors create 200MW of waste heat. At these sorts of power levels the waste heat of the crew, computers, coffee makers, etc. can be ignored. If there are energy weapons, assume they too are 90% efficient and use 500MW of power when fired, generating another 50MW waste heat. Lump in a lot of other minor systems and you get something like 300MW total waste heat that has to be gotten rid of at peak.

Where it gets complex, AFAIK, is the question of how hot you can allow the ship's interior to get. Let's assume that the environmental areas have heat pumps that allow them to stay a fair amount cooler than the engineering areas (since they're not generating the majority of the heat to begin with) and there are no low-temperature superconductors and so forth to worry about. If the engines and weapons can operate happily at 150 degrees Celsius, that's 423 degrees Kelvin. So that's our starting point -- the coolant (probably liquid sodium or lithium at that temp) gets that hot before it's pumped through the radiators to cool off again, at which point:

Heat lost [watts] = 5.67e-8[Stefan's Constant] * area [m^2] * emissivity * T^4 [degrees Kelvin].

(ed note: same equation as above)

If the radiators are perfectly black (emissivity of 1), and the coolant temperature is 423 degrees K, then in order to radiate away 275MW of heat, the radiator needs be about 150,000 square meters in area (of course it's double-sided, so the actual fin(s) only need to be 75,000 m^2). That's a square 275 meters on a side, or roughly a large city block, simply to deal with the ship's own waste heat at full power. If the ship needs to radiate away additional heat due to taking in, say, 400MW of energy from an enemy ship's lasers, you'd probably have to double or triple that figure (and make darn sure to keep your fins edge-on to the enemy ship firing at you! :). Of course all this is very crude and assumes perfect efficiency of a number of things (some of which I'm probably unaware of :). In reality you might get 80% of that theoretical performance. Or perhaps less. And the first thing damaged in a battle would probably be the radiators (big, hard to protect).

The structural mass of a large radiator fin could be a substantial fraction of the entire ship's mass, and that slows down the acceleration of the ship, which needs more power for thrust, which gives off more waste heat, and so on... So the idea of using spray wands and droplet coolants is attractive.

OTOH, if you need to keep the whole ship at a comfy temperature like 20C, then it's almost hopeless. The radiating area required is so enormous that high acceleration isn't practical at all (something like half a million m^2).

Another alternative is to design the ship to only radiate away normal, routine power levels, and to boil off propellant to deal with peak loads. But that goes through a lot of propellant pretty fast at high power levels. Dreadnaughts become like modern jet fighters -- only good for a few minutes of intense combat before the fuel runs out. Once it's gone, you can't crash, but you have to surrender or be boiled...

(ed note: He is assuming that the radiator temperature is 423K. Some of the other estimates were for radiator temperatures of 1600K to 3000K, which would drastically lower the radiator surface area.)

John Gwinner

Discovery XD-1

The spherical pressure hull formed the head of a flimsy, arrow-shaped structure more than a hundred yards long. Discovery, like all vehicles intended for deep space penetration, was too fragile and unstreamlined ever to enter an atmosphere, or to defy the full gravitational field of any planet. She had been assembled in orbit around the Earth, tested on a translunar maiden flight, and finally checked out in orbit above the Moon.

She was a creature of pure space - and she looked it. Immediately behind the pressure hull was grouped a cluster of four large liquid hydrogen tanks - and beyond them, forming a long, slender V, were the radiating fins that dissipated the waste heat of the nuclear reactor. Veined with a delicate tracery of pipes for the cooling fluid, they looked like the wings of some vast dragonfly, and from certain angles gave Discovery a fleeting resemblance to an old-time sailing ship,

At the very end of the V, three hundred feet from the crew-compartment, was the shielded inferno of the reactor, and the complex of focusing electrodes through which emerged the incandescent star-stuff of the plasma drive. This had done its work weeks ago, forcing Discovery out of her parking orbit round the Moon. Now the reactor was merely ticking over as it generated electrical power for the ship's services, and the great radiating fins, that would glow cherry red when Discovery was accelerating under maximum thrust, were dark and cool.

From 2001 A Space Odyssey by Sir Arthur C. Clarke (1969)

The final decision was made on the basis of aesthetics rather than technology; we wanted Discovery to look strange yet plausible, futuristic but not fantastic. Eventually we settled on the plasma drive, though I must confess that there was a little cheating. Any nuclear-powered vehicle must have large radiating surfaces to get rid of the excess heat generated by the reactors — but this would make Discovery look somewhat odd. Our audiences already had enough to puzzle about; we didn’t want them to spend half the picture wondering why spaceships should have wings. So the radiators came off.

From Lost Worlds of 2001 by Sir Arthur C. Clarke (1972)

Other

Radar

Radiators are not the only thing spoiling the Polaris' sleek external lines. Roger Manning's radio needs large dish antennas. They might not be as large as the monsters on 2001's Discovery, but they won't be much smaller than the ones on the Apollo service module. It might also be a good idea to have landing radar on an outrigger or boom, so it won't be blinded by the exhaust. Both of these will be retracted during atmospheric re-entry, with the landing radar deployed when the air speed drops low enough so it won't be ripped off.

Cargo

Speaking of cargo, present-day cargo ships are rated in "Net register tonnage", where each "ton" actually indicates 100 cubic feet of volume (2.83 cubic meters). The average cargo they carry has a density of 350 kg/m3. If the cargo has a wildly different density, some math will be needed, but for most cargo the net tonnage gives a good idea of the ship's cargo capacity. In practice, while filling the cargo hold it will either "mass-out" or "bulk-out", depending on which it runs out of first: lifting capacity or cargo space. In MANNA by Lee Correy (AKA G. Harry Stine) a surface-to-orbit shuttle bulked-out because it was carrying a cargo of fluffy non-dense cotton underwear. While the shuttle could have theoretically lifted more cargo mass, there wasn't any more room in the cargo hold.

In international shipping, a standard cargo container is 33 cubic meters and can have a maximum mass of 24 metric tons (2.2 tons of container and up to 21.8 tons of cargo). An extra large cargo container is 67.5 cubic meters with a max mass of 30.5 metric tons (3.8 ton container with up to 26.7 tons cargo). Thanks to Karl Hauber for pointing out an error in the the old figures posted here.

Conserving Payload Mass

Penalty Weight

As you are beginning to discover, mass is limited on a spacecraft. Many Heinlein novels have passengers given strict limits on their combined body+luggage mass. Officials would look disapprovingly at the passenger's waistlines and wonder out loud how they can stand to carry around all that "penalty weight". There are quite a few scenes in various Heinlein novels of the agony of packing for a rocket flight, throwing away stuff left and right in a desperate attempt to get the mass of your luggage below your mass allowance.

Tex hauled out his luggage and hefted it. "It's a problem. I've got about fifty pounds here. Do you suppose if I rolled it up real small I could get it down to twenty pounds?"

"An interesting theory," Matt said. "Let's have a look at it -- you've got to eliminate thirty pounds of penalty-weight."

Jarman spread his stuff out on the floor. "Well," Matt said at once, "you don't need all those photographs." He pointed to a dozen large stereos, each weighing a pound or more.

Tex looked horrified. "Leave my harem behind?" He picked up one. "There is the sweetest redhead in the entire Rio Grande Valley." He picked up another. "And Smitty -- I couldn't get along without Smitty. She thinks I'm wonderful."...

...Matt studied the pile. "You know what I'd suggest? Keep that harmonica -- I like harmonica music. Have those photos copied in micro. Feed the rest to the cat."

"That's easy for you to say."

"I've got the same problem." He went to his room. The class had the day free, for the purpose of getting ready to leave Earth. Matt spread his possessions out to look them over. His civilian clothes he would ship home, of course, and his telephone as well, since it was limited by its short range to the neighborhood of an earth-side relay office...

..He called home, spoke with his parents and kid brother, and then put the telephone with things to be shipped. He was scratching his head over what remained when Burke came in. He grinned. "Trying to swallow your penalty-weight?"

"I'll figure it out."

"You don't have to leave that junk behind, you know."

"Huh?"

"Ship it up to Terra Station, rent a locker, and store it. Then, when you go on liberty to the Station, you can bring back what you want. Sneak it aboard, if it's that sort of thing." Matt made no comment; Burke went on, "What's the matter, Galahad? Shocked at the notion of running contraband?"

"No. But I don't have a locker at Terra Station."

"Well, if you're too cheap to rent one, you can ship the stuff to mine. You scratch me and I'll scratch you."

"No, thanks." He thought about expressing some things to the Terra Station post office, then discarded the idea -- the rates were too high. He went on sorting. He would keep his camera, but his micro kit would have to go, and his chessmen. Presently he had cut the list to what he hoped was twenty pounds; he took the stuff away to weigh it.

From SPACE CADET by Robert Heinlein (1948)

Long as he had been earthbound he approached packing with a true spaceman's spirit. He knew that his passage would entitle him to only fifty pounds of free lift; he started discarding right and left. Shortly he had two piles, a very small one on his own bed -- indispensable clothing, a few capsules of microfilm, his slide rule, a stylus, and a vreetha, a flutelike Martian instrument which he had not played in a long time as his schoolmates had objected. On his roommate's bed was a much larger pile of discards.

He picked up the vreetha, tried a couple of runs, and put it on the larger pile. Taking a Martian product to Mars was coal to Newcastle.

From BETWEEN PLANETS by Robert Heinlein (1951)

Keep in mind that every gram of equipment or supplies takes several grams of propellant. Try to make every gram do double duty.

Miniaturization

In Frank Herbert's DUNE, spacemen had books the size of a thumb-tip, with a tiny magnifying glass.

"If it's economically feasible," Yueh said. "Arrakis has many costly perils." He smoothed his drooping mustache. "Your father will be here soon. Before I go, I've a gift for you, something I came across in packing." He put an object on the table between them-black, oblong, no larger than the end of Paul's thumb.

Paul looked at it. Yueh noted how the boy did not reach for it, and thought: How cautious he is.

"It's a very old Orange Catholic Bible made for space travelers. Not a filmbook, but actually printed on filament paper. It has its own magnifier and electrostatic charge system." He picked it up, demonstrated. "The book is held closed by the charge, which forces against spring-locked covers. You press the edge-thus, and the pages you've selected repel each other and the book opens."

"It's so small."

"But it has eighteen hundred pages. You press the edge-thus, and so . . . and the charge moves ahead one page at a time as you read. Never touch the actual pages with your fingers. The filament tissue is too delicate." He closed the book, handed it to Paul. "Try it."

From DUNE by Frank Herbert

Rocketeers would tend to be short and wiry. In Sir Arthur C. Clarke's classic THE OTHER SIDE OF THE SKY, space station construction crews got a pay bonus if they kept their weight below 150 pounds. Note that this would also be a good argument for rocketeers being:

  1. Oriental
  2. Female OR
  3. Both

Ruthless Optimization

Other innovations are possible. Perhaps boxes of food where the boxes are edible as well. The corridor floors will probably be metal gratings to save mass (This is the second reason why female cadet shipboard uniforms will not have skirts. The first reason is the impossibility of keeping a skirt in a modest position while in free-fall.) In Lester Del Rey's Step to the Stars all documents, blueprints, and mail are printed on stuff about as thick as tissue paper (have you ever tried to lift a box full of books?).

With regards to low mass floors, the lady known as Akima had an interesting idea:

Unless the deck is also a pressure bulkhead, how about omitting deck plates and beams entirely, and making the floor a metal-mesh version of the trampoline decks used on sailing catamarans? That way, "weights" bearing on the decks would be transmitted into the tubular structure of the hull as an inward tension.

Akima

David Chiasson expands upon Akima's idea. There is an outfit called Metal Textiles which produces knitted wire mesh.

The meshes are knitted, as opposed to woven like a screen door. They are manufactured in densities (% metal by volume) from 10% to 70%. There are a wide variety of materials that the mesh can be made from, including aluminum, steels, Teflon, Nylon, even tungsten. Unfortunately, titanium is not on that list, I can only suspect that it must be difficult to get into a wire form suitable for making a knitted mesh.

Direct quote from site's main page: "In compressed form, knitted metal can handle shock loadings up to the yield strength of the material itself. The load may be applied from any direction-up, down or in from all sides."

I can speculate that with some kind of structural forming breakthrough, the mesh could be heated over a (ceramic?) mold to a near-melting point and simply pressed into place, compressing the mesh into a solid.

David Chiasson

Michael Garrels begs to differ:

I need to point out some issues with the idea of mesh floors.

First off there's the idea that bulkheads have to be bulky. In nautical settings, bulkheads have to be bulky to withstand the large pressure of water, to mount things like hatches on, and to provide overall rigidity to the ship during turning and impact. Most partitions in a spaceship would be a thin pressure membrane sandwiched between a mesh to avoid punctures. The skin on the Apollo lander module was thinner than common aluminum foil. If all you're trying to do is partition, pull up pictures of Skylab - you'll see curtains and isogrid all over the place.

Next is your distinction between floors and walls. Unless there is spin or thrust, there will be no such distinction.

Which brings us to the most important point - the floor that you're currently standing on isn't made out of mesh for a reason. Remember that classic description of a gravity well with a weight on a rubber sheet? Many building codes don't limit the weight allowed on floors but instead the amount of deflection allowed. Floors have to be bulky with occasional beams - otherwise you'll never be able to wheel a torpedo or a gurney, and debris will roll toward where you're standing. It might work in a hallway, or as on your boat for stowage of light items, but not for spans more than a couple meters at 1 g using real materials - especially if you want to mount something like a chair and a console in the center of the cabin.

Michael Garrels