## 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.

Like any other living system, the internal operations of a spacecraft can be analyzed with Living Systems Theory, to discover sources of interesting plot complications.

## Strategies

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 increase the exhaust velocity or increase the mass ratio. Or both. 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. And you ain't gonna be able to run a large thrust ion-drive with solar cells.

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. All of it will have to be trimmed.

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 mesh 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. NASA uses all of these techniques heavily.

If your technology is high enough, 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

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 general rule, 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.

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 needed for that original kilogram of payload will require a second slug of propellant so that it too can be delta-Ved to 5 km/s.

And the second slug of propellant has mass as well, so you'll need a third slug of propellant for the second slug of propellant — 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 easiest 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. Translation: spacecraft with a mass ratio of 20 or above are basically constructed out of gossamer and soap bubbles.

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

Orion drive spacecraft and other torchships are not subject to this constraint, because they are unreasonably powerful.

It also does not apply to "stationary" items such as space stations and planetary bases, since they do not move under rocket propulsion. In fact, the added mass might be useful to stablize a space station's orbit, or as additional radiation shielding. Rocket vehicles might use aluminium, titanium, magnesium, or other lightweight metal as their structural material; but a space station would be better off using heavy iron or Invar.

The only consideration is if the station or base components have to be transported to the desired site by a rocket-propelled transport. Then it makes sense to make the components low mass, because then the station bits are payload. It makes even more sense to construct the space station or base on site using in-situ resources, so you don't have to eat the transport costs at all.

## Everything Is Connected

Like aircraft and sea-going warship design, one soon discovers that everything is connected to everything else. When the designer changes one aspect of the design this causes a series of related changes to ripple through the rest of the design.

For instance, if the designer reduces the propellant tank capacity by 5% this has implications for the spacecraft's mass ratio. If it is important for the spacecraft's delta V to stay the same, the payload will have to be reduced by the same amount. This might cut into the amount of life support consumables carried, which will reduce the number of days a mission can last. If the same amount of scientific observations have to be done in the reduced time, another crew member might have to be added. This will decrease the mass available for consumables even more. And so on.

The technical term is "cascading changes." The only thing worse is cascading failures.

As an example, I have some notes of graphing various space warship optimizations with examples of how various warship classes map onto the graph.

## 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. Sometimes the keel is reduced to just a thrust-frame on top of the engine, with the other components stacked on top.

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.

### Rockets Are Not Hotels

If you look at most blueprints for the various iterations of the Starship Enterprise, you will notice that every single part of the spacecraft interior is pressurized, with doors, rooms, and toilets. The corridors are wide enough for five people to walk abreast on nice carpeted floors with indirect lighting.

This is ludicrously wrong. And it is not just Star Trek that does this, pretty much all of media science fiction has ships like this. TV Tropes calls this fallacy "Starship Luxurious".

This is an extension of the "Rockets are Boats" fallacy. Passenger aircraft and luxury liners have their entire interior pressurized because so is everything else at sea level on a planet with a breathable atmosphere. For free. So careless starship designers, without a thought, made the unconscious assumption that spacecraft would be totally pressurized as well.

Wrong. Tain't no air in space, and atmosphere is expensive when you have to cart it up out of Terra's gravity well. Not to mention the expensive pressurized hull that has to encase it.

And it is not just the cost of hauling it up the gravity well, the spacecraft's engine has to accelerate the mass of all that junk. Every Gram Counts, so every gram of carpeting, atmosphere, and pressure hull is one less gram of payload, i.e., the reason the spacecraft was created in the first place. See The Tyranny of the Rocket Equation.

In the real world, spacecraft will be mostly tanks of propellant, propulsion system, payload bays, and a lacy lattice-work of support struts holding everything together. The part the people live in will be a tiny pressurized habitat module tucked away somewhere.

Ignorant starship designers have the unconscious assumption that the important part of a spacecraft is the crew, so they designed ships with their priorities reversed. Their ships were mostly gigantic habitat modules with a tiny engine stuck to the rear. Their ships are also ludicrously wrong. If the designers thought about it at all, they might grudgingly include a tiny fuel tank. Which is like the cherry on top of their big icecream sundae of Fail.

So quit drawing ship blueprints with every square inch pressurized and human-accessible. On a real spacecraft if the ship's engineer has to repair the propulsion system, heat radiators, power plant, propellant tanks, or anything like that, they will have to put on their space suit. They will not have the luxury enjoyed by Scotty the engineer, waltzing down a carpeted floor in a shirt-sleeve atmosphere.

The ships above are tail-sitters, so properly avoid the "wrong way is down" problem. But the artist made the second problem much worse. Apparently they figured the entire interior of the spacecraft was for habitable volume. Notice what they got wrong? Well, where the heck is the space for the rocket engines? I lay the blame for this at the artist, I know from experience that writer Jack Williamson knew better.

### Modular Construction

An attractive notion is the practice of constructing one's spacecraft out of mix-and-match replaceable components. So if your spacecraft needs to do a planetary landing you can swap the low thrust ion drive for a high thrust chemical rocket. In Charles Sheffield's The MacAndrews Chronicles, the protagonist just calls her ship "the assembly", customized out of whatever modules it needs for the current mission contract.

For detailed examples, see the Boeing Space Tug, NASA Space Tug, JPL Modular Hab System, and the Minimal Volume Spacecraft Cabin.

This will also make ships basically immortal. It will also make it really easy for space pirates to fence their captured prize ships. All they have to do is get the prize ship to the spacecraft equivalent to an automobile chop-shop. There the ship vanishes as an entity, becoming an inventory of laundered easily sold anonymous ship modules with the serial numbers filed off.

One can also imagine junker spacecraft, lashed together out of salvaged and/or junk-heap spacecraft modules by stone-broke would-be ship captains down on their luck.

Or mechanically inclined teenagers who want a ship. This would be much like teens in the United States back in the 1960's used to assemble automobiles out of parts scavenged from the junkyard, since they could not afford to purchase a new or used car. Such teens would gain incredible practical skills as spacecraft mechanics. I wonder if this is how Kaylee from Firefly learned her trade.

Yet another scenario is Our Hero stranded in the interplanetary Sargasso Sea of lost spacecraft, trying to scavenge enough working modules from three broken spacecraft in order to make one working spacecraft.

Rick Robinson notes that attractive as the concept is, there are some practical drawbacks to extreme modularity:

I thought of a problem with modular designs, based on the ancient Ship of Theseus paradox.

This is my Grandfather's ax.
This is my Grandfather's ax.
My Father replaced the handle.
This is my Grandfather's ax.

Is it really still Grandfather's ax or not?

Plutarch first wrote about the paradox in 75 CE. But it was that 17th-century smart-ass Thomas Hobbes who slipped the exploding cigar into the box. He asked the question: what if somebody saves the original discarded handle and ax-head, then assembled them into a second ax. Which one of the two axes is Grandfather's ax? Both, neither, the new one, the old one?

This sounds academic, until you apply it to modular spacecraft.

For purposes of insurance, liability, national registration, contract penalties, mortgages, and a host of other expensive issues; it is crucially important to know the identity of the spacecraft in question. Which ship exactly is being referred to in all those legal documents?

But what if the SS SkyTrash's modules are replaced and the old modules used to make a new ship? Legally which one is the SkyTrash? For that matter, intentionally making a stolen ship vanish by passing it through a spaceship chop-shop can make another set of legal headaches.

The problem of spacecraft identity has got to be legally nailed down.

Don't look to the Theseus Paradox for a solution. The problem was stated almost two thousands years ago and they are still arguing about it

Off-hand I'm not sure what a fool-proof solution would be. My first thought was to attach the identity of the spacecraft to some sine qua non "must-have" ship module. Unfortunately there does not seem to be any. Not all ships are manned, so the habitat module won't work. The only must-have module I see is the propulsion bus (otherwise you have a space station, not a spacecraft). However Captain Affenpinscher might find it strange that the identity of her ship has changed just because she swapped out the propulsion module.

I had a discussion on Google Plus with some of my brain-trust:

### Specialized Ship Types

Broadly speaking, a spacecraft has multiple uses. Just change the payload. However, for certain jobs the spacecraft will require drastic optimization.

Much like a covert smuggler ship. Except instead of trying to sneak past a few putt-putt custom boats, it is trying to sneak past a blockading enemy military battlefleet armed to the teeth who is currently investing the planet. So blockade runners might tend to have better acceleration, weapons, and defenses than you'd find in your average covert smuggler ship.
Cargo Vessel
A cargo ship or freighter ship is a merchant ship that carries cargo, goods, and materials from one port to another. Unlike tramp freighters these ships are cargo liners, operating as "common carriers" and calling a regularly published schedule of ports.
A tanker is a specialized cargo vessel. Cargo vessels Cargo holds and a remarkably large mass ratio. Common carriers use standardized cargo containers
Clan Ship
Huge ship used as a space-going home for tribes of space nomads. Kind of like a faster-than-light generational starship, but with no fixed destination. They often support themselves by interstellar trading.
Couriers
You only find these in science fiction universes that have faster-than-light starships but no faster-than-light radios. These are ultra-optimized ships that are designed for one single purpose: to deliver messages between stars as fast as possible. Some do not even have normal-space propulsion systems.
Customs Border Patrol Boat
Cutter-class ships used by the spacial branch of the planetary customs agency. They check out incoming spacecraft: collecting tariffs, halting or confiscating contraband, and apprehending smugglers. High acceleration because the bootlegger ships will often be running away. Extensive sensor suites because bootlegger ships will be doing their darnedest to be invisible. Armed because you never know when desperate bootleggers decide to open fire.
Dropships
Spacecraft designed to insert army units into a hot landing zone on a planet you are invading. "Hot" means "full of enemy troops shooting at you."
Tramp freighter spacecraft, generally owned by the free trader crew. Generally the ship is also the crew's only home.
Sometimes they try their hand at being amateur trade pioneers, which is a dangerous task for the professionals and insanely dangerous for the amateurs. If they try, they will have rudimentary planetary exploration gear.
Merchant Ship
A merchant vessel, trading vessel, or merchantman transport cargo and/or passengers for hire. They can be either cargo ships or tramp freighters
Orbit Guard Vessel
Vessels used by the space-going version of the Coast Guard. Their ships have rescue equipment, ship grappling gear, ship repair supplies space taxis, space pods, and a propulsion bus with extra delta V.
Pirate Corsair
A warship barely strong enough to defeat an unarmed merchant ship, with enough cargo space to carry off the cream of the looted booty from the merchant. Manned by the futuristic equivalent of one-eyed peg-legged brigands waving cutlasses and saying "AAArrrr.." a lot.
Planetary Exploration Vessel
Exploration scout ship used by the Survey Service to discover and evaluate potential colonizable planets, to boldy go where no one has gone before. First-In scout ships do the discovery of promising planets, while also being alert for dangerous anomalies. Exploration ships do in-depth studies of planets the first-in scouts think are worthy of a closer look. The ships are equipped with extensive remote sensing suites on the lookout for biosignatures, technosignatures, and necrosignatures. They carry space ferries, airless landers, or other landers to transport survey crews to the surface. They also carry mobile bases/labs and exploration flitters.
Privateers
See Pirate Corsair. Except ship is also equipped with a Letter of Marque and Reprisal.
Q-ship
A warship disguised as a helpless merchant ship, hoping to lure a pirate ship to its doom.
Revolt Ships
Enforcement warships an interstellar empire stations over member planets which are in danger of rebelling and trying to secede from the empire. Some revolt ships are optimised for orbital bombardment. May operate in association with space superiority platforms.
Safari Ship
This is a science fictional ship that turns up occasionally in some novels. This is a ship for wealthy but impotent individuals who try to get it up by exploring strange new worlds, seeking out new life, shooting them, and hanging the poor innocent animal's head on the wall as a trophy. For those impotent individuals who cannot afford their own ship, there are safari services for hire. For a reasonable price they will transport you and other customers to a wilderness planet to participate in a prefabricated big game hunt. For example: Star Hunter by Andre Norton.
Spaceguard ships
Ships used by the spaceguard services of all spacefaring nations. They keep a close watch to prevent unauthorized alterations in the orbits of potential civilization-wreaking asteroids. They will be equipped with large telescope arrays to monitor asteroid trajectories, and nuclear detonation detectors since nukes can be use for orbital alteration. They will have equipment to alter the orbits of dangerous asteroids, such as casaba howitzers and mass-driver propulsion. These can also be used as weapons, in case the asteroids still contain the evil villains who nudged the rock in the first place.
Space Patrol Ships
Semi-warships used by the Space Patrol. Depending upon the planetary government the patrol will have one or more of the following jobs: police, coast guard, border patrol, pirate fighters, spacecraft safety inspectors, and customs agents.
Smuggler Ships
These are for entrepreneurs trying to move contraband goods past the Customs agents.
Overt smuggler ships are designed to look exactly like a run-of-the-mill merchant ship, but equipped with secret compartments for contraband that is elaborately sensor-hardened to hide from custom agent hand-held scanners. Overt smuggler ships openly land at the planetary spaceport and try to act innocent.
Covert smuggler ships try to sneak past the orbiting custom ships and secretly land at a hidden rendezvous. They rely upon a drastically reduced sensor signature, and the stealth provided from the bulk of the planet.
Tanker
A tanker is a freigher designed to carry liquids or gas in bulk. In space the liquids are commonly liquified propellant. They have extra propellant tanks and a remarkably large mass ratios.
Tramp Freighter
A merchant cargo ship that does NOT have a fixed schedule or published published itinerary/ports-of-call, as opposed to cargo lines. Instead they trade on the spot market.
Troopships
These are military logistics ships use to transport space army soldiers to combat zones. They mostly are huge habitat modules
Tug
Tugboats are slow but powerful spacecraft used to slowly but accurately move larger spacecraft and bulk cargo to and from orbital spaceports. They have ship grappling equipment, push plates, and an over-sized high-thrust propulsion bus.
Warship
Military combat ships.
A warship's payload section can include anti-spacecraft weapons, orbital bombardment weapons (for revolt suppression type 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.
I have an entire page devoted to the theory and practice of warship design.
Zoo ship
This is a science fictional ship that turns up occasionally in some novels. It travels from planet to planet, capturing examples of exotic alien critters, storing them in cages that recreate their normal environment, and eventually transporting the lot of them to some large zoological research station. For example: Hiding Place by Poul Anderson and The Soul Eater by Mike Resnick.

## Spacecraft Parameters

For an given type of automobile, there are parameters that tell you what kind of performance you can expect. Things like miles per gallon, acceleration, weight, and so on.

Spacecraft have parameters too, it is just that they are odd measures that you have not encountered before. I am going to list the more important ones here, but they will be fully explained on other pages. Refer back to this list if you run across an unfamiliar term.

Habitat Module
The pressurized part of the spaceraft where people live. Included in Payload Section. Remember that Rockets Are Not Hotels. Unlike the Starship Enterprise a real spacecraft is a huge expanse of airless machinery with a tiny pressurized habitat module tucked away in a corner where people can walk around without spacesuits.
The part of the spacecraft that is its reason for existance. For a satellite booster, the payload is the satellite it is lifting into orbit. For a transport ship: habitat module, passengers, ship controls. For a warship: habitat module, crew, weapons, defenses, ship controls. For a robot freighter: robot controls and cargo. Some payload like cargo and crew are removable from the spacecraft. Some payload like weapons and habitat modules are fixed parts of the spacecraft. Included in Payload Section.
Engine or Thruster
The rocket engine that moves the spacecraft, and the empty propellant tanks. Included in Propulsion Bus.
Power Plant
Part that generates electricity. Included in Propulsion Bus.
Struture
Struture is the skeleton and skin of the spacecraft. Included in both Propulsion Bus and Payload Section.
Propellant and Fuel
Propellant or Reaction mass (remass) is what the thruster fires out the exhaust nozzle to create thrust. Fuel is the source of energy used to propel the propellant. Remember that Fuel Is Not Propellant. In chemical rockets, the chemicals are both propellant and fuel. In nuclear rockets the liquid hydrogen is the propellant and the uranium is the fuel. Included in Propulsion Bus.

Mass of all the payload. For NASA vessels this is typically 26.7% of Dry Mass.
Payload mass as percentage of wet mass. Mpl / M
Structural Mass (Mst)
Mass of all the struture. For NASA vessels this is typically 21.7% of Dry Mass.
Propellant Mass (Mpt)
The mass of all the propellant in the spacecraft's propellant tanks. Does not include fuel that is retained after it is burnt, e.g., uranium fissioned inside a solid core reactor. For some calculations, you will use instead the mass of propellant that will be expended in a given maneuver.
Power Plant Mass (Mpp)
The mass of the electrical generation system. Includes any heat radiators. For NASA vessels this is typically 28% + 3.4% of Dry Mass
Thruster System Mass (Mts)
The mass of the rocket engines, including the empty propellant/fuel tanks. For NASA vessels this is typically 3.7% of Dry Mass
Propulsion System Mass (Mps)
Thruster System Mass + Power Plant Mass.
Inert Mass (Mi)
Mass of spacecraft with no propellant and no payload. Propulsion System Mass + Structural Mass.
Inert Mass Fraction (δ)
Inert mass as percentage of wet mass. Mi / M
Dry (Empty, Burnout) Mass (Me)
Mass of spacecraft with no propellant but with payload. Propulsion System Mass + Structural Mass + Payload Mass.
Wet (Total, Ignition) Mass (M)
Total mass of spacecraft. Propellant Mass + Propulsion System Mass + Structural Mass + Payload Mass.
Mass Ratio (R)
Ratio of wet mass to dry mass. Wet Mass / Dry Mass.
Parametric Mass Ratio (r)
λ + δ.
Propellant Fraction (Pf, PMF, or ζ)
Percentage of wet mass that is propellant. 1 - ( 1 / MassRatio )

Propellant Mass Flow (mDot or )

How quickly does the Thruster System drain the propellant tanks? Rated in kilograms per second.

mDot constrains the amount of thrust the propulsion system can produce. Changing the propellant mass flow is a way to make a spacecraft engine shift gears.

Exhaust-Velocity (Ve)

How fast does the propellant shoot out the exhaust nozzle of the Thruster System? Rated in meters per second. Exhaust velocity (and delta V) is of primary importance for space travel. For liftoff, landing, and dodging hostile weapons fire, thrust is more important.

Broadly exhaust velocity is a measure of the spacecraft's "fuel" efficiency (actually propellant efficiency). The higher the Ve, the better the "fuel economy".

Generally if a propulsion system has a high Ve it has a low thrust and vice versa. The only systems where both are high are torch drives. Some spacecraft engines can shift gears by trading exhaust velocity for thrust.

For a more in-depth look at exhaust velocity look here

Specific Impulse (Isp)
Another way of stating exhaust velocity. Exhaust Velocity / 9.81 where 9.81 = acceleration due to gravity on Terra in meters per second. Specific Impulse is rated in seconds. It is also a broad measure of the spacecraft's "fuel" efficiency.
Delta V or Δv

Spacecraft's total change in velocity capability. This determines which missions the spacecraft can perform. Arguably this is the most important of all the spacecraft parameters. Rated in meters per second.

This can be thought of as how much "fuel" is in the tanks of the spacecraft (though it is actually a bit more complicated than that).

Velocity Ratio
Δv / Ve
Thrust (F)

Thrust produced by Thruster System. Rated in Newtons. Thrust is constrained by Propellant Mass Flow. Thrust (and acceleration) is of primary importance in liftoff, landing, and dodging hostile weapons fire. For space travel exhaust velocity (and delta V) is more important.

Generally if a propulsion system has a high Ve it has a low thrust and vice versa. The only systems where both are high are torch drives. Some spacecraft engines can shift gears by trading exhaust velocity for thrust.

Acceleration (A)

Spacecraft's current acceleration. Current total mass / Thrust. Rated in meters per second per second. Divide by 9.81 to get g's of acceleration.

In space, a spacecraft with higher acceleration will generally not travel to a destination any faster than a low acceleration ship. But a high acceleration ship will have wider launch windows for a given trajectory.

Note that as propellant is expended, current total mass goes down and acceleration goes up. If you want a constant level of acceleration you have to constantly throttle back the thrust.

5 milligee (0.05 m/s2) : General rule practical minimum for ion drive, laser sail or other low thrust / long duration drive. Otherwise the poor spacecraft will take years to change orbits. Unfortunately pure solar sails are lucky to do 3 milligees.

0.6 gee (5.88 m/s2) : General rule average for high thrust / short duration drive. Useful for Hohmann transfer orbits, or crossing the Van Allen radiation belts before they fry the astronauts.

3.0 gee (29.43 m/s2) : General rule minimum to lift off from Terra's surface into LEO.

For a more in-depth look at minimum accelerations look here.

Thrust Power (Fp)
Power produced by Thruster System. ( Thrust × Exhaust Velocity ) / 2. Rated in watts.
Specific Power (Fsp)
Power density of spacecraft. Thrust Power / Dry Mass. Rated in watts per kilograms.
Specific Mass
Alpha of Thruster System. Thruster System Mass / Thrust Power. Rated in kilograms per watt.

## Structure

Typically the percentage of spacecraft dry mass that is structure is 21.7% for NASA vessels.

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").

### Spacecraft Spine

Many (but not all) spacecraft designs have the propulsion system at the "bottom", exerting thrust into a strong structural member called the ship's spine. The other components of the spacecraft are attached to the spine. The spine is also called a keel or a thrust frame. In all spacecraft the thrust frame is the network of girders on top of the engines that the thrust is applied to. But only in some spacecraft is the thrust frame elongated into a spine, in others the ship components are attached to a shell, generally cylindrical.

If you leave out the spine or thrust frame, engine ignition will send the propulsion system careening through the core of the ship, gutting it. Spacecraft engineers treat tiny cracks in the thrust frame with deep concern.

OK, forget what I just said. On top of the engine will be the thrust frame or thrust structure. On top will be the primary structure or spaceframe. The thrust frame transmits the thrust into the spaceframe, and prevents the propulsion system careening through the core of the ship.

The spaceframe can be:

• A long spine/keel with the propellant tanks and payload section bits attached in various places.
• A large pressurized vessel, either propellant tank or habitat module. Other propellant tanks and payload section bits are attached to main tank or perched on top.
• Something else.

The engineers are using a pressurized tank in lieu of a spine in a desperate attempt to reduce the spacecraft's mass. But this can be risky if you use the propellant tank. The original 1957 Convair Atlas rocket used "balloon tanks" for the propellant instead of conventional isogrid tanks. This means that the structural rigidity comes from the pressurization of the propellant. This also means if the pressure is lost in the tank the entire rocket collapses under its own weight. Blasted thing needed 35 kPa of nitrogen even when the rocket was not fueled.

As Rob Davidoff points out, keel-less ship designs using a pressurized tank for a spine is more for marginal ships that cannot afford any excess mass whatsoever. Such as ships that have to lift off and land in delta-V gobbling planetary gravity wells while using one-lung propulsion systems (*cough* chemical rockets *cough*).

This classification means that parts of the propulsion bus and payload section are intertwined with each other, but nobody said rocket science was going to be easy.

In von Braun Round the Moon Ship the thrust frame (dark blue) is right on top of the rocket motors. The spaceframe (light blue) is a cage attached to the thrust frame. The rocket motors push upwards on the thrust frame, which pushes upwards on the spaceframe. The personnel sphere, hydrazine tank, and nitric acid tank are all basically inflated balloons hung on the spaceframe.

Getting back to the spine. Remember that every gram counts. Spacecraft designers want a spine that is the strongest yet lowest mass structural member possible. The genius R. Buckminster Fuller and his science of "Synergetics" had the answer in his "octet truss" (which he called an "isotrophic vector matrix", and which had been independently discovered about 50 years earlier by Alexander Graham Bell). You remember Fuller, right? The fellow who invented the geodesic dome?

Each of the struts composing the octet truss are the same length. Geometrically it is an array of tetrahedrons and octahedrons (in terms of Dungeons and Dragons polyhedral dice it uses d4's and d8's).

Sometimes instead of an octet truss designers will opt for a weaker but easier to construct space frame. The truss of the International Space Station apparently falls into this category.

A bit more simplistic is a simple stack of octahedrons (Dungeons and Dragons d8 polyhedral dice). This was used for the spine of the Valley Forge from the movie Silent Running (1972), later reused as the agro ship from original Battlestar Galactica.

Spacecraft spines are generally down the center of the spacecraft following the ship's thrust axis (the line the engine's thrust is applied along, usually from the center of the engine's exhaust through the ship's center of gravity).

This can be a pain to spacecraft designers if they have anything that needs to be jettisoned. Such items will have to be in pairs on opposite sides of the spine, and jettisoned in pairs as well. Otherwise the spacecraft's center of gravity will shift off the thrust axis, and the next time the engines are fired up it's pinwheel time.

In a NASA study TM-1998-208834-REV1 they invent a clever way to avoid this: the Saddle Truss.

The truss is a hollow framework cylinder with a big enough diameter to accommodate standard propellant tanks, consumables storage pods, and auxiliary spacecraft. One side of the cylinder frame is missing. The thrust axis is cocked a fraction of a degree off-center to allow for the uneven mass distribution of the framework.

The point is that tanks and other jettison-able items no longer have to be in pairs if you use a saddle truss. When it is empty you just kick it out through the missing side of the saddle truss. No muss, no fuss, and no having to have double the amount of propellant plumbing and related items.

Examples of the saddle truss can be found in the Bimodal NTR and the SNRE Spacecraft.

#### Waterskiing Spacecraft

This is a quite radical method to drastically reduce the structural mass of a spacecraft, allowing a handsome increase in valuable payload mass. It also dramatically increase the separation between a dangerously radioactive propulsion system and the crew, allowing a drastic decrease in the radiation shadow shield mass. This allows yet more handsome increases in valuable payload mass. As the cherry on top of the cake, it allows using the tumbling pigeon method of spin gravity without the direction of gravity inverting.

Please note this has never actually been used in a serious nuclear spacecraft design due to its unorthodox nature.

And warships with such a design would have their manoeuvring critically handicapped (or it's "crack-the-whip" time and the cable breaks).

The concept comes from the observation that for a given amount of structural strength, a compression member (such as a girder) generally has a higher mass that a corresponding tension member (such as a cable). And we know that every gram counts.

Charles Pellegrino and Dr. Jim Powell put it this way: current spacecraft designs using compression members are guilty of "putting the cart before the horse". At the bottom is the engines, on top of that is the thrust frame, and on top of that is rest of the spacecraft held together with girders (compression members) like a skyscraper. But what if you put the engine at the top and have it drag the rest of the spacecraft on a long cable (tension member). You'll instantly cut the structural mass by an order of magnitude or more!

And if the engines are radioactive, remember that crew radiation exposure can be cut by time, shielding, or distance. The advantage of distance is it takes far less mass than a shield composed of lead or something else massive. The break-even point is where the mass of the boom or cable is equal to the mass of the shadow shield. But the mass of a shadow shield is equal to the mass of a incredibly long cable. The HELIOS cable was about 300 to 1000 meters, the Valkyrie was ten kilometers.

But keep in mind that this design has no maneuverability at all. Agile it ain't. If you turn the ship too fast it will try to "crack the whip" and probably snap the cable. This probably makes the design unsuitable for warships, who have to jink a lot or be hit by enemy weapons fire.

Examples include HELIOS, the Valkyrie Antimatter Starship, the ramrobots from Larry Niven's A Gift From Earth and the ISV Venture Star from the movie Avatar.

Certain propulsion systems incorporate the waterskiing concept in spacecraft that use the propulsion. The main one is the Medusa, which sets off nuclear explosions inside a huge parachute-shaped sail. The sail accelerates, and drags along the payload on a long cable. Long because the payload does not want to be any closer to a series of nuclear explosions than it has to be.

The various types of sail propulsion drag the payload with a long cable as well. But for them, the long cable is not because the sail is radioactive, just that it is typically several kilometers in radius.

Cosine Thrust Loss

If the exhaust is radioactive or otherwise dangerous to hose the rest of the spacecraft with, you can have two or more engines angled so the plumes miss the ship.

Angled engines do reduce the effective thrust by an amount proportional to the cosine of the angle but for small angles it is acceptable. The delta V of the spacecraft is also reduced by the same proportion.

Note in the HELIOS design Krafft Ehricke figured that the 300 meter separation was enough to render the exhaust harmless so it does not angle the engine at all. Krafft has a single engine blasting straight at the habitat module. The only concession to the exhaust is mounting the cables on outriggers, so the cables do not pass through the zillion degree nuclear fireball exhaust plume. It would be most embarassing if the cables melted.

#### Space Trains and Truckers

This section has been moved here

### 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. Well, now that I think about it, some of the lunar dust is like clouds of microscopic razor blades so they are dangerously abrasive.

### Rocket Tumble

The basic idea is that the Axis of Thrust from the engines had better pass through the the spacecraft's center of gravity (CG) or everybody is going to die. In addition, if the spacecraft is currently passing through a planet's atmosphere the axis of thrust had better be parallel to the aerodynamic axis or the same thing will happen.

Specifically, "everybody is going to die" means the spacecraft is going to loop-the-loop or tumble like a cheap Fourth-of-July skyrocket (Heinlein calls this a rocket "falling off its tail"). If this happens during lift-off the ship will auger into the ground like a nuclear-powered Dinosaur-Killer asteroid and make a titanic crater. If it happens in deep space, the rocket will spin like a pinwheel firework spraying atomic flame everywhere. This will waste precious propellant, give the spacecraft a random vector, and severely injure the crew with unexpected spin gravity. If they are lucky the crew's broken bones will heal about the same time that they run out of oxygen.

The axis of thrust is a line starting at the center of the exhaust nozzle's throat, and traveling in the exact opposite direction of the hot propellant. It is the direction that the thrust is pushing the rocket. As long as the axis of thrust passes through the CG, the spacecraft will be accelerated in that direction. If the axis of thrust is not passing through the CG, the spacecraft will start to spin around the CG. When done on purpose this is called a yaw or pitch maneuver. When this is done by accident, it is called OMG WE'RE ALL GOING TO DIE!

Some engines can be gimbaled, rotating their axis of thrust off-center by a few degrees. This is intended for yaw and pitch, but it can be used in emergencies to cope with accidental changes in the center of gravity (e.g., the cargo shifts).

When laying out the floor plan, you want the spacecraft to balance. This boils down to ensuring that the ship's center of gravity is on the central axis, which generally is the same as the axis of thrust. There are exceptions. The Grumman Space Tug has its center of gravity shift wildly when it jettisons a drop tank. To compensate, the engine can gimbal by a whopping ±20°.

Balancing 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. Otherwise the center of gravity won't be centered.

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. The same goes for the cargo. The load-master better be blasted sure all the tons of cargo are nailed down so they don't shift. And be sure the cargo is evenly balanced around the ship's axis to keep the center of gravity in the center.

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

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

For anything but a torchship, the spacecraft's mass ratio is going to be greater than 2 (i.e., 50% or more of the total mass is going to be propellant). Presumably the propellant is inside a propellant tank (unless you are pulling a Martian Way gag and freezing the fuel into a solid block). Remember, RockCat said all rockets are giant propellant tanks with an engine on the bottom and the pilot's chair at the top.

If you have huge structure budget, you have a classic looking rocket-style rocket with propellant tanks inside. If you have a medium structure budget, you have a spine with propellant tanks attached. If you have a small structure budget, you'll have an isogrid propellant tank for a spine, with the rest of the rocket parts attached.

And if you are stuck with a microscopic structure budget, you'll have a foil-thin propellant tank stiffened by the pressure of the propellant, with the rest of the rocket parts attached. But the latter tends to collapse when the propellant is expended and the pressure is gone. This was used in the old 1957 Convair Atlas rocket, but not so much nowadays. You cannot really reuse them.

Our running example Polaris spacecraft has a gas core nuclear thermal rocket engine.

The fuel is uranium 235. It will probably be less than 1% of the total propellant load so we will focus on just the propellant for now.

Nuclear thermal rockets generally use hydrogen since you want propellant with the lowest molecular mass. Liquid hydrogen has a density of 0.07 grams per cubic centimeter.

The Polaris has 792.6 metric tons of hydrogen propellant. 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.)

Propellant Tank Mass

Robert Zubrin says that as a general rule, 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 the Polaris' 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 or that is capable of high acceleration. 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:

PropellentEngineTank %
ArgonIon rocket4
WaterNuclear salt water rocket4
HydrogenNTR / GCR10
LOX/HydrogenChemical6

But if you want to do this the hard way, you'd better warm up your slide rule.

The total tank volume (Vtot) of a tank is the sum of four components:

1. Usable Propellant Volume (Vpu): the volume holding the propellant that can actually be used.
2. Ullage Volume (Vull): the volume left unfilled to accomodate expansion of the propellant or contraction of the tank structure. Typically 1% to 3% of total tank volume.
3. Boil-off Volume (Vbo): For cryogenic propellants only. The volume left unfilled to allow for the propellant that boils from liquid to gas due to external heat.
4. Trapped Volume (Vtrap): the volume of unusable propellant left in all the feed lines, valves, and other components after the tank is drained. Typically the volume of the feed system.

Vtot = Vpu + Vull + Vbo + Vtrap

No, I do not know how to estimate the Boil-off Volume. A recent study estimated that in space cryogenic tanks suffered an absolutely unacceptable 0.1% boiloff/day, and suggested this had to be reduced by an order of magnitude or more. When the boil-off volume is full, a pressure relief valve lets the gaseous propellant vent into space, instead of exploding the tank.

Tanks come in two shapes: spherical and cylindrical. Spherical are better, they have the most volume for the least surface area, so are the lightest. But many spacecraft have a limit to their maximum diameter, especially launch vehicles. In this case cylindrical has a lower mass than a series of spherical tanks.

The internal pressure of the propellant has the greatest effect on the tank's structural requirements. Not as important but still significant are acceleration, vibration, and handling loads. Unfortunately I can only find equations for the effects of internal pressure. Acceleration means that tanks which are in high-acceleration spacecraft or in spacecraft that take-off and land from planets will have a higher mass than tanks for low-acceleration orbit-to-orbit ships. My source did say that figuring in acceleration, vibration, and handling would make the tank mass 2.0 to 2.5 times as large as what is calculated with the simplified equations below.

In the Space Shuttle external tank, the LOX tank was pressurized to 150,000 Pa and the LH2 tank was pressurized to 230,000 Pa.

The design burst pressure of a tank is:

Pb = fs * MEOP

where:

Pb = design burst pressure (Pa)
fs = safety factor (typically 2.0)
MEOP = Maximum Expected Operating Pressure of the tank (Pa)

Tank Materials
Material

Density
ρ
kg/m3
Allowable Strength
Ftu
GPa
Efficency
Ftu/(ρg0)
km
Mass Factor
φtank
m
2219 - Aluminum2,8000.413
0.214 welded
15.042,500
Titanium4,4601.2328.812,500
4130 - Steel7,8300.86211.232,500
Graphite Fiber
Composite
1,5500.89558.8810,000

Spherical Tanks

You have to make Vs so it is equal to Vtot, or at least equal to Vtot - Vtrap.

Vs = 4/3 * π * rs3

As = 4 * π * rs2

ts = (Pb * rs) / (2 * Ftu)

Ms = As * ts * ρ

where:

rs = radius of sphere (m)
As = surface area of sphere (m2)
Vs = volume of sphere (m3)
ts = wall thickness of sphere (m)
Pb = design burst pressure (Pa)
Ftu = allowable material strength (Pa) from tank materials table
Ms = mass of spherical tank (kg)
ρ = density of tank structure material (kg/m3 from tank materials table

Cylindrical Tanks

Cylindrical tanks are cylinders where each end is capped with either hemispheres (where radius and height are equal) or hemiellipses (where radius and height are not equal). As it turns out cylindrical tanks with hemiellipses on the ends are always more massive than hemispherical cylindrical tanks. So we won't bother with the equations for hemielliptical tanks. In the real world rocket designers sometimes use hemielliptical tanks in order to reduce tank length.

What you do is calculate the mass of the cylindrical section of the tank Mc using the equations below. Then you calculate the mass of the two hemispherical endcaps (that is, the mass of a single sphere) Ms using the value of the cylindrical section's radius for the radius of the sphere in the spherical tank equations above. The mass of the cylindrical tank is Mc + Ms.

Vc = π * rc2 * lc

Ac = 2 * π * rc2 * lc

tc = (Pb * rc) / Ftu

Mc = Ac * tc * ρ

where:

rc = radius of cylindrical section (m)
lc = length of cylindrical section (m)
Ac = surface area of cylindrical section (m2)
Vc = volume of cylindrical section (m3)
Pb = design burst pressure (Pa)
Ftu = allowable material strength (Pa) from tank materials table
ρ = density of tank structure material (kg/m3 from tank materials table
tc = wall thickness of cylindrical section (m)
Mc = mass of cylindrical tank section (kg)

Ullage

When the rocket is sitting on the launch pad, the planet's gravity pulls the propellant down so that the pumps at the aft end of the tank can move it to the engine. When the rocket is under acceleration, the thrust pulls the propellant down to the pumps. Once the engines cut off and the rocket is in free fall, well, the remaining pooled at the bottom turns into zillions of blobs and starts floating everywhere. See the video:

This isn't a problem, up until the point where you want to start the engine up again. Trouble is, the propellant isn't at the aft pump, it is flying all over the place. What's worse, some of the liquid propellant might have turned into bubbles of gas, which could wreck the engine if they are sucked into the pump. Vapor lock in a rocket engine is an ugly thing.

In 1960 Soviet engineers invented the solution: Ullage Motors. These are tiny rocket engines that only have to accelerate the rocket by about 0.001g (0.01 m/s). That's enough to pull the propellant down to the pump, and to form a boundary between the liquid and gas portions. In some cases, the spacecraft's reaction control system (attitude jets) can operate as ullage motors.

In the Apollo service module, they use a "retention reservoir" instead of an ullage burn (but they have to burn anyway if the amount of fuel and oxidizer drops below 56.4%).

Liquid oxygen in the oxidizer storage tank flows into the oxidizer sump tank. During an engine burn, oxygen flows to the bottom of the sump tank, through an umbrella shaped screen, into the retention reservoir, then into a pipe at the bottom leading to the engine. The same system is used in the fuel tanks.

When the burn is terminated and the oxygen breaks up into a zillion blobs and starts floating everywhere, the oxygen under the screen umbrella cannot escape. Surface tension prevents it from escaping through the screen holes. The oxygen is trapped under the umbrella, inside the retention reservoir.

When the engines are restarted there is oxygen right at the pipe to feed into the engine, instead of a void with random floating blobs. The engine thrust then settles the oxygen in the sump tank for normal operation.

As near as I can figure, the 56.4% ullage limit happens when the storage tank is empty, so the sump tank is only partially full. But I'm not sure.

### Heat Shield

Aerobraking is used to get rid of a portion of a spacecraft's velocity without using a rocket engine and reaction mass. Or as NASA thinks of it: "For Free!" This can be used for landing, for planetary capture, for circulating spacecraft's orbit, or other purposes.

Robert Zubrin says mass of the heat shield and thermal structure will be about 15% of the total mass being braked.

The general rule 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.

NASA on the other hand uses aerobraking every chance it gets, since they do not have the luxury of using atomic engines. Many of the Mars probes use aerobraking for Mars capture and to circularize their orbit. Some use their solar panels as aerobraking drage chutes in order to make a given piece of payload mass do double duty. Some of the Space Tug designs listed in the Realistic Design section economize on reaction mass by using a ballute when returning to Terra orbit.

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 Generation

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).

Typically the percentage of spacecraft dry mass that is power systems is 28% for NASA vessels.

Spacecraft power systems have three subsystems:

• Power Generation/ Conversion: generating power
• Energy Storage: storing power for future use
• Power Management and Distribution (PMAD): routing the power to equipment that needs it

There are a couple of parameters used to rate power plant performance:

• Alpha : (kg/kW) power plant mass in kilograms divided by kilowatts of power. 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
• Specific Power : (W/kg) watts of power divided by power plant mass in kilograms (i.e., (1 / alpha) * 1000)
• Specific Energy : (Wh/kg) watt-hours of energy divided by power plant mass in kilograms
• Energy Density : (Wh/m3) watt-hours of energy divided by power plant volume in cubic meters

NASA has a rather comprehensive report on various spacecraft power systems here . The executive summary states that currently available spacecraft power systems are "heavy, bulky, not efficient enough, and cannot function properly in some extreme environments."

Scroll to see rest of infographic

### Energy Harvesting

Energy Harvesting or energy scavenging is a pathetic "waste-not-want-not" strategy when you are desperate to squeeze every milliwatt of power out of your system. This includes waste engine heat (gradients), warm liquids, kinetic motion, vibration, and ambient radiation. This is generally used for such things as enabling power for remote sensors in places where no electricity is readily available.

### Fuel Cells

The general term is "chemical power generation", which means power generated by chemical reactions. This is most commonly seen in the form of fuel cells, though occasionally there are applications like the hydrazine-fired gas turbines that the Space Shuttle uses to hydraulically actuate thrust vector vanes.

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 10 kg/kW, specific power 98 W/kg, have a total mass of 122 kg, have an output of 12 kW, and produces about 2.7 kilowatt-hours per kilogram of hydrogen+oxygen consumed (about 70% efficient). They also have a service life of under 5000 hours. The water output can be used in the life support system.

Different applications will require fuel cells with different optimizations. Some will need high specific power (200 to 400 W/kg), some will need long service life (greater than 10,000 hours), and others will require high efficiency (greater than 80% efficient).

### Solar Thermal Power

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 in the form of a long framework boom sticking out of the hub, with a radiation shadow shield big enough to shadown the wheel.

The technical name is "solar dynamic power", where mirrors concentrate sunlight on a boiler. "Solar static power" is Photovoltaic solar cells.

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 at Terra orbit (i.e., about 11% efficient), and a radiator size of 140 to 200 watts per square meter.

### Solar Photovoltaic Power

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. Of course the power density goes down the farther from the Sun the power array is located.

The technical name is "solar static power", where photovoltaic solar cells convert sunlight into electricity. "Solar dynamic power" is where mirrors concentrate sunlight on a boiler.

Solar power arrays have an alpha ranging from 100 to 1.4 kg/kW. Body-mounted rigid panels an alpha of 16 kg/kW while flexible deployable arrays have an alpha of 10 kg/kW. Most NASA ships use multi-junction solar cells which have an efficiency of 29%, but a few used silicon cells with an efficiency of 15%. Most NASA arrays output from 0.5 to 30 kW.

Some researchers (Dhere, Ghongadi, Pandit, Jahagirdar, Scheiman) have claimed to have achieved 1.4 kg/kW in the lab by using Culn1-×Ga×S2 thin films on titanium foil. Rob Davidoff is of the opinion that a practical design with rigging and everything will be closer to 4 kg/kW, but that is still almost three times better than conventional solar arrays.

In 2015 researchers at Georgia Institute of Technology demonstrated a photovoltaic cell using an optical rectenna. They estimate that such rectennas could have a power conversion efficiency of up to 40% and a lower cost than silicon cells. No word on the alpha, though.

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.

To power a ion drive or other electric propulsion system with solar cells is going to require an array capable of high voltage (300 to 1000 volts), high power (greater than 100 kW), and a low alpha (2 to 1 kg/kW).

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.

Solar Power
PlanetSol Dist
(AU)
Power
Factor
Power
(W/m2)
☿ Mercury0.3876.6779,121
Venus0.7231.9132,613
⊕ Terra1.0001.0001,366
Mars1.5200.433591
⚶ Vesta2.3620.179245
⚵ Juno2.6700.140192
⚳ Ceres2.7680.131178
⚴ Pallas2.7720.130178
♃ Jupiter5.2000.03751
♄ Saturn9.5800.01115
♅ Uranus19.2000.0034
♆ Neptune30.0500.0012

POWER DROP-OFF

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.

Translation: if you travel farther from the sun than Terra orbit, the solar array will produce less electricity. Contrawise if you travel closer to the sun the array will produce more electricity. This is why some science fiction novels have huge solar energy farms on Mercury; to produce commercial quantities of antimatter, beamed power propulsion networks, and other power-hungry operations.

As a general rule:

Es = 1366 * (1 / Ds2)

where:

• Es = available solar energy (watts per square meter)
• Ds = distance from the Sun (astronomical units)
• 1366 = Solar Constant (watts per square meter)

Remember that you divide distance in meters by 1.496e11 in order to obtain astronomical units. Divide distance in kilometers by 1.496e8 to obtain astronomical units

This means that the available solar energy around Saturn is a pitiful 15 W/m2. That's available energy, if you tried harvesting it with the 29% efficient ISS solar cell arrays you will be lucky to get 4.4 W/m2. Which is why the Cassini probe used RTGs.

Special high efficiency cells are needed in order to harvest worthwhile amounts of solar energy in low intensity/low temperature conditions (LILT). Which is defined as the solar array located at 3 AU from Sol or farther (i.e., about 150 watts per square meter or less, one-ninth the energy available at Terra's orbit).

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 (or Mercury) 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. It has the further disadvantage of being frowned upon by the military, since they take a dim view of weapons-grade lasers in civilian hands. Unless the military owned the power lasers in the first place.

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 currently 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. Engineers are trying to figure out how to construct a ten kilowatt RTG.

Current NASA RTGs have a useful lifespan of over 30 years.

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). Efficiency is about 6%. The near term goal is to develop an RTG with an alpha of 100 to 60 kg/kW and an efficiency of 15 to 20%.

An RTG based on a Stirling cycle instead of thermionics might be able to reach an efficiency of 35%. Since they would need less Pu-238 for the same electrical output, a Sterling RTG would have only 0.66 the mass of an equivalent thermocouples RTG. However NASA is skittish about Sterling RTGs since unlike conventional ones, Sterlings have moving parts. Which are yet another possible point of failure on prolonged space missions.

Nuclear weapons-grade plutonium-239 cannot be used in RTGs. Non-fissionable 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.

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 6%. If the thermoelectric efficiency is 6%, the plutonium RTG has an effective specific power of 560 x 0.06 = 30 watts per kilogram 238Pu (0.033 kilogram 238Pu per watt or 33 kgP/kW). This means you will need an entire 15.5 kilos of plutonium to produce 470 watts.

This is why a Sterling-based RTG with an efficience of 35% is so attractive.

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. Plutonium is the radioisotope of choice but it is hard to come by (due to nuclear proliferation fears). Americium is more readily available but lower performance.

At the time of this writing (2014) NASA has a severe Pu-238 problem. NASA only has about 16 kilograms left, you need about 4 kg per RTG, and nobody is making any more. They were purchasing it from the Russian Mayak nuclear industrial complex for \$45,000 per ounce, but in 2009 the Russians refused to sell any more.

NASA is "rattled" because they need the Pu-238 for many upcoming missions, they do not have enough on had, and Congressional funding for creating Pu-238 manufacturing have been predictably sporadic and unreliable.

The European Space Agency (ESA) has no access to Pu-238 or RTGs at all. This is why their Philae space probe failed when it could not get solar power. The ESA is accepting the lesser of two evils and is investing in the design and construction of Americium-241 RTGs. Am-241 is expensive, but at least it is available.

### 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 . There is a much older document with some interesting designs here .

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 an alpha of 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):

Fission reactors are attractive since they have an incredibly high fuel density, they don't care how far you are from the Sun nor if it is obscured, and they have power output that makes an RTG look like a stale flashlight battery. They are not commonly used by NASA due to the hysterical reaction of US citizens when they hear the "N" word. Off the top of my head the only nuclear powered NASA probe currently in operation is the Curiosity Mars Rover; and that is an RTG, not an actual nuclear reactor.

For a space probe a reactor in the 0.5 to 5 kW power range would be a useful size, 10 to 100 kW is good for surface and robotic missions, and megawatt size is needed for nuclear electric propulsion.

Here is a commentary on figuring the mass of the reactor of a nuclear thermal rocket by somebody who goes by the handle 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 per second)
• 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.

#### Bimodal NTR

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.

#### Dusty Plasma Fission Reactors

Rodney Clarke and Robert Sheldon were working on a fission-fragment rocket engine when they noticed a useful side-benefit.

There is a remarkably efficient (84%) electrical power plant called a Magnetohydrodynamic Generator (MHD generator). They also have the virtue of being able to operate at high temperatures, and have no moving parts (which reduces the maintenance required and raises reliability). A conventional electrical power generator spins a conducting copper wire coil inside a magnetic field to create electricity. An MHD generator replaces the solid copper coil with a fast moving jet of conducting plasma.

Because many designs for fusion rocket engines and fusion power plants produce fast moving jets of plasma, MHD generators were the perfect match. Ground based power plants just sprayed the jet of fusion plasma into the MHD.

Fusion spacecraft could be bimodal. An MHD generator could be installed in the exhaust nozzle to constantly bleed off some of the thrust power in order to make electricity, this was popular with inertial confinement fusion which need to recharge huge capacitors before each fusion pulse. Alternatively the MHD generator could be installed at the opposite end of the fusion reaction chamber. The fusion plasma goes down out the exhaust nozzle for thrust, but it can be diverted upwards into an MHD generator for electrical power.

Finally getting to the point, Clarke and Sheldon realized that a fission-fragment rocket engine also produces a jet of plasma. Therefore, it too can be bimodal with the addition of an MHD generator.

Cutting to the chase, they would have a jaw-dropping specific power of 11 kWe/kg! The rough design they made had a power output of 448 megawatts and a total mass of 38,430 kg (38 metric tons).

Dusty Plasma Power Reactor
Specs
Power Output448 MW
Specific Power11 kWe/kg
Mass Schedule
U235 Fuel4.27 kg
Am242m Fuel1.25 kg
Moderator9,424 kg
TOTAL38,430 kg

### 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.

#### 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 using 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. But with beamed power the power generator adds zero mass to the spacecraft, since the heavy generator is on the remote station instead of onboard and laser photons weigh nothing.

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.

The other drawback is the laser beam is also a strategic weapons-grade laser. The astromilitary (if any) take a very dim view of weapons-grade laser cannon in the hands of civilians. The beamed power equipment may be under the close (armed) supervision of the Laser Guard.

#### 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. Unless there exist "antimatter mines", antimatter is an energy transport mechanism, not a fuel. In Star Trek, I believe they found drifts of antimatter in deep space. An antimatter source was also featured in the Sten series. 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.

How much energy are we talking about? Nobody knows. Estimates based on the upper limit of the cosmological constant put it at a pathetic 10-9 joules per cubic meter (about 1/10th the energy of a single cosmic-ray photon). On the other tentacle estimates based on Lorentz covariance and with the magnitude of the Planck constant put it at a jaw-dropping 10113 joules per cubic meter (about 3 quintillion-septillion times more energy than the Big Bang). A range between 10-9 and 10113 is another way of saying "nobody knows, especially if they tell you they know".

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

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

Ladderdown transmutation reactors are fringe science invented by Wil McCarthy for his science fiction novel Bloom. It is certainly nothing we will be capable of making anytime soon, but it will take somebody more knowledgeable than me to prove it impossible. Offhand I do not see anything that straight out violates the laws of physics. Ladderdown is unobtainium, not handwavium

Basically ladderdown reactors obtain their energy the same way nuclear fission does: by splitting atomic nuclei and releasing the binding energy. It is just that the ladderdown reactor can work with any element heavier than Iron-56, and the splitting does not release any neutrons or gamma radiation. Nuclear fission only works with fission fuel, and any anti-nuclear activist can tell you horror stories about the dire radiation produced.

Apparently ladderdown reactors remove protons and neutrons from the fuel material one at a time, by quantum tunneling, quietly. Unlike fission, which shoots neutrons like bullets at nuclei, shattering the nucleus into sprays of radiation and exploding fission products.

As with fission the laddered-down nuclei releases the difference in binding energy and moves down the periodic table. The process comes to a screeching halt when the fuel transmutes into Iron-56, since it is at the basin of the binding energy curve. In the novel iron is the most worthless element for this reason, and so is used for cheap building material.

Ladderdown reactors can also take fuel elements that are lighter than Iron-56, and add protons and neutrons one at a time, to make heavier elements (called "ladderup"). This is the ladderdown version of fusion, except it will work with any element lighter than Iron-56 and there is no nasty radiation produced. This is handy because laddering down heavy elements produces lots of protons as a by product, which can be laddered up into Iron-56.

#### 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.

## Power Storage

Often the power plant generates more power than is currently needed. Spacecraft cannot afford to throw the excess power away, it has to be stored for later use. This is analogous to Terran solar power plants, they don't work at night so you have to store some power by day.

### Energy Transport Mechanism

There are a couple of instances where people make the mistake of labeling something a "power source" when actually it is an "energy transport mechanism." The most common example is hydrogen. Let me explain.

In 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 they are calling the hydrogen a fuel, which it isn't.

While there do 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). Not to mention the energy cost of compressing the hydrogen into liquid, transporting the liquid hydrogen in a power-hungry cryogenically cooled tank, and the power required to burn it and harvest electricity.

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. Or part of the energy, since these things are never 100% efficient.

In essence, the hydrogen is fulling much the same role as the copper power lines leading from a power plant to a residential home. It is transporting the energy from the plant to the home. Or you can look at the hydrogen as sort of a rechargable battery, for example as used in a regenerative fuel cell. But one with rather poor efficiency.

The main example from science fiction is antimatter "fuel." Unless the science fiction universe contains antimatter mines, it is an energy transport mechanism with a truly ugly efficency.

### Batteries

What is needed are so-called "secondary" batteries, commonly known as "rechargable" batteries. If the batteries are not rechargable then they are worthless for power storage. As you probably already figured out, "primary" batteries are the non-rechargable kind; like the ones you use in your flashlight until they go dead, then throw into the garbage.

Current rechargable batteries are heavy, bulky, vulnerable to the space environment, and have a risk of bursting into flame. Just ask anybody who had their laptop computer unexpectedly do an impression of an incindiary grenade.

Nickle-Cadmium and Nickle-Hydrogen rechargables have a specific energy of 24 to 35 Wh/kg (0.086 to 0.13 MJ/kg), an energy density of 0.01 to 0.08 Wh/m3, and an operating temperature range of -5 to 30°C. They have a service life of more than 50,000 recharge cylces, and a mission life of more than 10 years. Their drawbacks are being heavy, bulky, and a limited operationg temperature range.

Lithium-Ion rechargables have a specfic energy of 100 Wh/kg (0.36 MJ/kg), an energy density of 0.25 Wh/m3, and an operating temperature range of -20 to 30°C. They have a service life of about 400 recharge cylces, and a mission life of about 2 years. Their drawbacks are the pathetic service and mission life.

### Flywheels

A flywheel is a rotating mechanical device that is used to store rotational energy. In a clever "two-functions for the mass-price of one" bargain a flyweel can also be used a a momentum wheel for attitude control. NASA adores these bargains because every gram counts.

Flywheels have a theoretical maximum specific energy of 2,700 Wh/kg (9.7 MJ/kg). They can quickly deliver their energy, can be fully discharged repetedly without harm, and have the lowest self-discharge rate of any known electrical storage system. NASA is not currently using flywheels, though they did have a prototype for the ISS that had a specific energy of 30 Wh/kg (0.11 MJ/kg).

### Regenerative Fuel Cells

A "regenerative" or "reverse" fuel cell is one that 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.

In essence the secondary power source is creating fuel-cell fuel as a kind of battery to store power. It is just that a fuel cell is required to extract the power from the "battery."

Currently there exist no regenerative fuel cells that are space-rated. The current goal is for such a cell with a specific energy of up to 1,500 Wh/kg (5.4 MJ/kg), a charge/discharge efficiency up to 70%, and a service life of up to 10,000 hours.

### 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 flywheel. 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.

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

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?, thanks to magic9mushroom for this link.

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, or what NASA calls Active Thermal Control Systems

Functionally they are not too different from the radiator on your automobile. Pipes full of radiator fluid are coiled around the cylinder heads and engine block, sucking up the heat so the engine doesn't turn into molten lava. The hot radiator fluid is moved by the coolant pump, carrying the heat into the engine coolant radiator (that flat box on the automobile's nose with all the scalloped holes). In the radiator, the heat is removed from the radiator fluid by conduction with the wind. The cool radiator fluid travels into the engine and the cycle begins anew.

Actually, in spaceships the heat radiators get rid of heat by … well … radiating, instead of conduction. Different design because there is no wind in space. But you get the idea.

If you want to calculate this for yourself use the Stefan-Boltzmann law:

P = A * ε * σ * T4

A = P / (ε * σ * T4)

where

• P = the power of waste heat the radiator can get rid of (watts)
• σ = 5.670373×10-8 = Stefan-Boltzmann constant (W m-2K-4)
• ε = emissivity of radiator (theoretical maximum is 1.0 for a perfect black body, real world radiator will be less. Should be at least 0.8 or above to be worth-while)
• A = area of radiator (m2)
• T = temperature of radiator, this assumes temperature of space is zero degrees (degrees K)
• x4 = raise x to the fourth power, i.e, x * x * x * x

My source (Matthew DeBell) says that if P = 150 gigawatts, ε = 0.94, and T = 3000 K, A would be 34,941 m2. Actually it could be half that if you have a two-sided radiator, which would make the radiator 17,470 m2 (a square 132 meters on a side). Which is still freaking huge.

For estimating the mass of the radiator array, go here.

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.

Ken Burnside also noted that radiators are large, flimsy, and impossible to armor (except perhaps for the droplet radiator). A liability on a warship. However, Zane Mankowski (author of Children of a Dead Earth) makes a good case that heat radiators can indeed be armored. Mr. Mankowski says the thickness of the radiator material can be increased to provide armor-like protection for the working fluid tubes, with the price of reducing radiator efficiency.

Mr. Burnside has an entire essay about the problem of heat on combat spacecraft, entitled The Hot Equations: Thermodynamics and Military SF. Since thermodynamics is one of the most important (and most neglected in science fiction) factors in combat, the essay will repay careful study.

In the military the old bromide is that amateurs talk about battle tactics while professionals talk about logistics. In the real of spacecraft design, @AsteroidEnergy said "Amateurs discuss rockets, professionals discuss heat management."

But do realize that if the spacecraft does indeed have a nuclear propulsion system or something else dangerously radioactive, the radiators must be tapered to keep inside the radiation shadow shield. Or bad things happen.

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 or power 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.

Not only are you going to require two separate radiator systems, the one for the modest cooling required by the life-system is liable to have larger radiator surfaces than the one cooling the multi-gigawatt propulsion system. Radiator effectiveness goes up as the fourth power of the heat of the radiator, remember?

### OPEN CYCLE COOLING

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"). Note this only works if the propulsion system has a high propellant mass flow (called "mdot"). Note that the lower the thrust the lower the mdot. Once the thrust gets too low there is not enough propellant in the exhaust plume for you to use the open-cycle cooling trick.

Electrical powered drives like ion drives will require radiators on their power plants. Fusion drives may or may not require radiators, depending upon whether you can make them open-cycle or not.

### 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.

Here is some scary math about radiators from Dr. Tony Valle and Ray Robinson, along with some interesting conclusion. Remember that according to the radiator equation the hotter temperature the radiator is run at, the more waste heat it can dispose of.

Use the "Life Support" radiator data for life support and other low-waste-heat management. Use all the others for high-waste-heat management, such as fission/fusion reactors and weapons-grade lasers.

In each radiators Specific Area data table will be listed Heat Cap., Mass, and Op. Temp.

Heat Cap.: heat capacity in kWth/m2. This is how many kilowatts of waste heat each square meter of radiator can get rid of. Multiply the surface area of the entire radiator by the heat capacity to find the total amount of heat the radiator array can handle. kWth means "kilowatts of thermal energy" (i.e., waste heat) as opposed to kWe which means "kilowatts of electricity".

Mass: specific area mass of the radiator in kg/m2. This is the mass of each square meter of radiator in kilograms. Multiply the surface area of the entire radiator by the specific area mass to find the total mass of the radiator array.

Op. Temp.: the operating temperature of the radiator. You probably won't need this unless you want to fool around with the Stefan-Boltzmann equation. The higher the operating temperature, the higher the heat capacity. Which means the value listed for the heat capacity is only valid if the radiator operates at this temperature.

Use the "Specific Area" values in the tables to calculate the radiator mass.

1. Decide how many kilowatts of waste heat the radiator will have to handle (from the engine, the power reactor, the laser cannon, etc.)
2. Select which radiator type to use, and examine its Specific Area table.
3. Divide the total waste head in kilowatts by the Heat Cap. entry of the table to get the square meters of radiator area required.
4. Multiply the radiator area by the Mass entry to get the total mass of the radiator required.

or in other words:

radiatorMass = (wasteHeat / specificAreaHeat) * specificAreaMass

where:

• wasteHeat = amount of waste heat to dispose of (kWth)
• specificAreaHeat = Heat Cap. from radiator table (kWth/m2)
• specificAreaMass = Mass from radiator table (kg/m2)

Having said that, things are complicated for liquid drop radiators. The radiation surface is the surface area of the droplets. Figuring out the physical radiator size is compilcated, you can find the equations here. There is also Eric Rozier's online calculator.

Note, in the illustrations from the High Frontier game, it uses very strange game-specific terms. Each "mass unit" is equal to 40 tonnes, each thermometer is one "therm" and represents the radiator dealing with 120 megawatts of thermal waste heat (120,000 kWth). When a specific area value was missing I uesd the therm, mass points, and radiator area on the cards to calculate.

Here is a table of the various radiator types. Their area and mass has been calculated as if they were sized to handle 250 megawatts of waste heat.

The table is sorted by array mass, so the better ones are at the top. At least if you want the lowest mass radiator. If the radiation area was an issue you'd probably prefer a Mo/Li Heat Pipe instead.

The life support radiator was included even though it was not intended to handle waste heat over 100 kilowatts or so.

Radiator for 250,000 kilowatts waste heat
heat
(Heat Cap.)
Specific area
mass
(Mass)
area
Array
mass
Marangoni Flow293.04 kWth/m224.4 kg/m2853 m220,816 kg
Electrostatic Membrane51.3 kWth/m24.275 kg/m24,873 m220,833 kg
Hula-Hoop300 kWth/m233 kg/m2833 m227,500 kg
Buckytube Filament293.03 kWth/m248.839 kg/m2853 m241,667 kg
Curie Point212.75 kWth/m235.459 kg/m21,175 m241,667 kg
Tin Droplet38.49 kWth/m26.4154 kg/m26,495 m241,669 kg
Flux-Pinned Superthermal76 kWth/m217 kg/m23,289 m255,921 kg
Attack Vector: Tactical357 kWth/m2100 kg/m2700 m270,028 kg
Bubble Membrane21.01 kWth/m27.00 kg/m211,899 m283,294 kg
Mo/Li Heat Pipe453.54 kWth/m2151.18 kg/m2551 m283,333 kg
Microtube Array102.6 kWth/m234.2 kg/m22,437 m283,333 kg
ETHER212.75 kWth/m270.92 kg/m21,175 m283,337 kg
Ti/K Heat Pipe150.22 kWth/m2100.14 kg/m21,664 m2166,656 kg
SS/NaK Pumped90.83 kWth/m260.554 kg/m22,752 m2166,669 kg
Salt-Cooled Reflux tube75 kWth/m275 kg/m23,333 m2250,000 kg
Life Support0.19 kWth/m23.1 kg/m21,315,789 m24,078,947 kg

#### Life Support

Specific Area
Heat Cap.~0.19 kWth/m2
Mass~3.1 kg/m2
Op. Temp.? K

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, since life-support waste heat is quite tiny compared to nuclear reactor or gigawatt laser waste heat.

Use this radiator type for life-support and other modest waste heat management. Use the other radiators for gigantic waste-heat producers.

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. 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.

What this boils down to is that the described system needs about 96 kilograms and 0.405 cubic meters of temperature regulating equipment per crew person. That's the total of the external radiator on the hull and the internal temperature control system.

Simple math tells me the radiator has a density of about 140 kg/m3, a specific area of 3.1 kg/m2 and needs a radiating surface area of about 5.2 m2 per per kilowatt of heat handled (1/5.2 = 0.19 kWth/m2). 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.

#### Liquid Droplet

Liquid Droplet Radiators use sprays of hot droplets instead of tubes filled with hot liquid in the radiator. This drastically reduces the mass of the radiator, which is always a good thing. A NASA report suggested that for 200 kW worth of waste heat you'd need a 3,500 kg heat pipe radiator, but you could manage the same thermal load with a smaller 500 kg liquid droplet radiator.

The droplet generator typically has 100,000 to 1,000,000 orifices with diameters of 50 to 20 μm. They are a bit more susceptible to damage than the components of more conventional radiators.

A drawback is that the spray is in free fall. This means if the radiator is operating and the ship starts accelerating, the spray will start missing the collector and precious radiator working fluid will be lost into space. Brookhaven National Laboratory has patented a way to magnetically focus the droplet stream. Using a large radiator it will allow the spacecraft to maneuver at acceleration of up to 0.001 g (0.00981 m/s2) which is barely an improvement. The acceleration can be increased but only if the single radiator is replaced by numerous smaller radiators. Which of course makes the sum of the radiators have a larger mass than the single large radiator. Oh, and Brookhaven's patent expired in 1994.

Many liquid droplet designs are well suited for warships, since they do not utilze large fragile panels vulnerable to hostile weapons fire. If a rail gun round or laser bolt passes through a spray of working fluid, it will just make a bit of fluid miss the collector. If weapons fire passes through a conventional panel it will wreck it.

temperature rangecoolant typeexample
250 K – 350 Ksilicone oils
siloxane
Trimethyl-Pentaphenyl-Trisiloxane
370 K – 650 Kliquid metal eutectics
500 K – 1000 Kliquid tin
##### Rectangular LDR

Rectangular LDRs have collectors the same width at the droplet generator. The droplet density remains constant across the flight path. It is a simpler more robust design than a Triangular LDR, and has a larger radiating surface (twice the surface area).

However the triangular LDR is lighter (40% less massive) due to its smaller collector. As previously mentioned, the rectangular LDR's collector is a long bar the exact same width as the droplet generator bar. By way of contrast the triangular LDR's collector is a small bucket, which has about 40% less mass than a corresponding rectangular LDR collector. But it has drawbacks.

##### Triangular LDR

Triangular LDRs have a tiny collector a fraction of the width of the droplet generator, unlike rectangular LDRs. The droplet density increases across the flight path. It is 40% less massive compared to a comparable Rectangular LDR due to the smaller collector, reduced mass is always a plus.

However it is a more complicated design with more failure points, and it has only half the surface area of a same sized Rectangular LDR. Because the radiating surface is a triangle instead of a rectangle.

For reasons that have not been made clear to me, Triangular LDR is currently the focus of much of the research and development. NASA likes them better than Rectangular LDRs. I guess in NASA's eyes lower mass trumps all other considerations.

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

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

#### Attack Vector: Tactical

This fictional radiaor is from the tabletop wargame Attack Vector: Tactical, which is why the description 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.)

## Propulsion

Typically the percentage of spacecraft dry mass that is propulsion is 3.7% for NASA vessels.

For a list of various spacecraft propulsion systems, go to the engine list.

## Habitat Module

This section has been moved here

### TransHab

This section has been moved here

### 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.

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.

### 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 cadet shipboard uniforms will not have skirts or kilts. Looking up at the ceiling grating will give you a peekaboo up-skirt glimpse of whoever is in the next deck up. No panchira allowed. The first reason is the impossibility of keeping a skirt or kilt 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:

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

Michael Garrels begs to differ:

### Stowaways

If you are dealing with a conventional spacecraft ruled by the iron law of Every Gram Counts, a stowaway is a disaster. If they had not jettisoned a payload mass equal to their mass, there will not be enough propellant to perform the vital maneuvers. The ship will run out, and go sailing off into the Big Dark and a lonely death for everybody on board.

Even if the stowaway jettisions enough mass, there probably won't be enough breathing mix and food aboard for the additional person. Everybody will suffocate and/or starve.

As Dr. Feynman observed about the Challenger disaster, "Nature cannot be fooled." If the equations say that your spacecraft does not have enough fuel, they don't mean "maybe."

For survival's sake, the crew will have little choice but to immediately throw the stowaway out the nearest airlock.

This was highlighted in a famous story called The Cold Equations by Tom Godwin. The story is chilling abet scientifically accurate, but it still caused an uproar when it first came out.

But if the ship is a torchship or uber-powerful faster-than-light starship, things are a little less tense. Since they are not actually threatening the lives of the crew, stowaways will be treated more like their terrestrial counterparts if discovered on a sea-going vessel.