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.
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.
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.
The most fundamental constraint on designing a rocket-propelled vehicle is Every Gram Counts.
Why? Short answer: This is a consequence of the equation for delta-V.
Why? Slightly longer answer: As a rule of thumb, a rocket with the highest delta-V capacity is going to need three kilograms of propellant for every kilogram of rocket+payload. The lower the total kilograms of rocket+payload, the lower the propellant mass required. This relates to the second strategy of rocket design mentioned above.
Why? Long Answer:
Say the mission needs 5 km/s of delta-V. Each kilogram of payload requires propellant to give it 5 km/s.
But that propellant has mass as well. The propellant 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.
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, or magnesium as their structural material; but a space station would be better off using 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. It makes even more sense to construct the space station or base on site using in-situ resources.
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.
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.
You get the idea.
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.
Pirate ships and privateers might forgo defenses if they only expect to be engaging unarmed cargo ships. But they will regret this if they have the misfortune to encounter armed enemy convoy escort ships or are surprised by a Q-ship.
This section is intended to address some gaps in available information about spacecraft design in the Plausible Mid-Future (PMF), with an eye towards space warfare. It is not a summary of such information, most of which can be found at Atomic Rockets. The largest gap in current practice comes in the preliminary design phase. A normal method used is to specify the fully-loaded mass of a vessel, and then work out the amounts required for remass, tanks, engine, and so on, and then figure out the payload (habitat, weapons, sensors, cargo, and so on) from there. While there are times this is appropriate engineering practice (notably if you’re launching the spacecraft from Earth and have a fixed launch mass), in the majority of cases the payload mass should be the starting point. The following equation can be used for such calculations:
Where P is the payload mass (any fixed masses, such as habitats, weapons, sensors, etc.), M is the loaded (wet) mass, R is the mass ratio of the rocket, T is the tank fraction (or any mass that scales with reaction mass) as a decimal ratio of such mass (e.g., 0.1 for 10% of remass), and E is any mass that scales with the overall mass of the ship, such as engines or structure, also as a decimal.
This equation adequately describes a basic spacecraft with a single propulsion system. It is possible to use the same equation to calculate the mass of a spacecraft with two separate propulsion systems.
The terms in this equation are identical to those in the equation above, with R1 and T1 representing the mass ratio and tank fraction for the (arbitrary) first engine, and R2 and T2 likewise for the second. Calculate both mass ratios based on the fully-loaded spacecraft. If both mass ratios approach 2, then the bottom of the equation will come out negative, and the spacecraft obviously cannot be built as specified. Note that when doing delta-V calculations to get the mass ratio, each engine is assumed to expend all of its delta-V while the tanks for the other engine are still full. In reality, the spacecraft will have more delta-V than those calculations would indicate, but solving properly for a more realistic and complicated mission profile requires numerical methods outside the scope of this paper.
One design problem that is commonly raised is the matter of artificial gravity. In the setting under discussion, this can only be achieved by spin. The details of this are available elsewhere, but these schemes essentially boil down to either spinning the entire spacecraft or just spinning the hab itself. Both create significant design problems. Spinning the spacecraft involves rating all systems for operations both in free fall and under spin, including tanks, thrusters, and plumbing. The loads imposed by spin are likely to be significantly larger than any thrust loads, which drives up structural mass significantly. This can be minimized by keeping things close to the spin axis, but that is likely to stretch the ship, which imposes its own structural penalties. A spinning hab has to be connected to the rest of the spacecraft, which is not a trivial engineering problem. The connection will have to be low-friction, transmit thrust loads, and pass power, fluids, and quite possibly people as well. And it must work 24/5 for months. All of this trouble with artificial gravity is required to avoid catastrophic health problems on arrival. However, there is a potential alternative. Medical science might someday be able to prevent the negative effects of Zero-G on the body, making the life of the spacecraft designer much easier.
When this conclusion was put before Rob Herrick, an epidemiologist, he did not think it was feasible.“The problem is that they [the degenerative effects of zero-G] are the result of mechanical unloading and natural physiological processes. The muscles don't work as hard, and so they atrophy. The bones don't carry the same dynamic loads, so they demineralize. Both are the result of normal physiological processes whereby the body adapts to the environment, only expending what energy is necessary. The only way to treat that pharmacologically is to block those natural processes, and that opens up a really bad can of worms. All kinds of transporters would have to be knocked out, you'd have to monkey with the natural muscle processes, and God knows what else. Essentially, you're talking about chemically overriding lots of homeostasis mechanisms, and we have no idea if said overrides are reversible, or what the consequences of that would be in other tissues. My bet is bad to worse. As the whole field of endocrine disruptors is discovering, messing with natural hormonal processes is very very dangerous.
Even if it worked with no off-target effects, you'd have major issues. Body development would be all kinds of screwed up, so it's not something you'd want to do for children or young adults. Since peak bone mass is not accrued until early twenties, a lot of your recruits would be in a window where they're supposed to still be growing, and you're chemically blocking that. Similarly, would you have issues with obesity? If your musculature is not functioning normally (to prevent atrophy), how will that effect the body's energy balance? What other bodily processes that are interconnected will be effected? Then you get into all the effects of going back into a gravity well. Would you come off the drugs (and thus require a washout period before you go downside, and a ramp-up period before you could go topside again)?
Spin and gravity is an engineering headache, but a solvable one. Pharmacologically altering the body to prevent the loss of muscle and bone mass that the body seems surplus to requirements has all kinds of unknowns, off target-effects and unintended consequences. You're going to put people at severe risk for medical complications, some of which could be lifelong or even lethal.”
This is a compelling case that it is not possible to treat the effects of zero-G medically. However, if for story reasons a workaround is needed, medical treatment is no less plausible than many devices used even in relatively hard Sci-Fi.
The task of designing spacecraft for a sci-fi setting is complicated by the need to find out all the things that need to be included, and get numbers for them. The author has created a spreadsheet to automate this task, including an editable sheet of constants to allow the user to customize it to his needs. The numbers there are the author’s best guess for Mid-PMF settings, but too complicated to duplicate here.
Rick Robinson’s rule of thumb is that spacecraft will (in the sort of setting examined here) become broadly comparable to jetliners in cost, at about $1 million/ton in current dollars. This is probably fairly accurate for civilian vessels, at least to a factor of 3 or so. Warships are likely to be more expensive, as most of the components that separate warships from civilian ships are very expensive for their mass. In aircraft terms, an F-16 is approximately $2 million/ton, as is the F-15, while the F/A-18E/F Super Hornet is closer to $4 million/ton. This is certainly a better approximation than the difference between warships and cargo ships, as spacecraft and aircraft both have relatively expensive structures and engines, unlike naval vessels, where by far the most expensive component of a warship is its electronics. For example, the ships of the Arleigh Burke-class of destroyers seem to be averaging between $150,000 and $250,000/ton, while various cargo ships seem to hover between $1000 and $5000/ton.
As mentioned in Section 5, some have suggested that the drive would be modular, with the front end of the ship (containing weapons, crew, cargo, and the like) built separately and attached for various missions. This is somewhat plausible in a commercial context, but has serious problems in a military one. However, the idea of buying a separate drive and payload and mating them together is quite likely, and could see military and civilian vessels sharing drive types. (This is not as strange as present experience would lead us to believe. It was only during WWII that military aircraft clearly separated from civilian ones in terms of performance and technology.) This simplifies design of spacecraft significantly, as one can first design the engine, and then build payloads around it.
One common problem during the discussion of spacecraft design is the rating of the spacecraft. With other vehicles, we have fairly simple specifications, such as maximum speed, range, and payload capacity. However, none of these strictly applies in space, and the fact that spacecraft are not limited by gravity and movement through a fluid medium makes specifying the equivalents rather difficult. Acceleration and delta-V obviously depend on the masses of the various components, which can be changed far more readily than on terrestrial vehicles, and cargo capacity is limited only by how long you’re willing to take to get where you’re going. A replacement might be a series of standard trajectories, and the payload a craft can carry on them. This works well if all of the spacecraft being rated are generally similar in terms of performance, and take similar trajectories in reality. However, it does not work as well in a scenario where different types of ships take wildly different trajectories with different amounts of cargo. In that scenario, ships might be rated by the minimum time for certain transfers (Earth-Mars at optimum, for instance) with a specified payload, either a fixed percentage of dry mass, or a series of specified masses for various sizes of ships. This allows a comparison between ships of different classes, but within a class (liner, bulk cargo, etc.) the first method would probably be preferred.
A related problem is the selection of an appropriate delta-V during preliminary design. In some cases, this is relatively easy, such as when a spacecraft is intended to use Hohmann or Hohmann-like trajectories, as numbers for such are easily available. But such numbers are inadequate for a warship, or for any ship that operates in a much higher delta-V band, and unless the vessel has so much delta-V and such high acceleration that Brachistochrone approximations become accurate (and even then, if the vessel is not using a reactionless drive, the loss of remass can throw such numbers off significantly, unless much more complicated methods are used, numerical or otherwise). The author has attempted to fill this gap by creating a series of tables of delta-Vs and transit times between various bodies, with the tables giving the percentage of the time that a vessel leaving one body can reach another within a specified amount of time with a given amount of delta-V. The tables can be found at the end of this section. Table 9 covers Earth-Mars transits, while Table 10 describes Earth-Jupiter transits.
The tables are generated in MATLAB by solving Lambert’s problem for a large number of departure days and transit times, and calculating the delta-V to go from stationary relative to the departure planet to stationary relative to the destination planet. This involved assuming that there was a single instant delta-V burn at each end, which is a good approximation if the burn time is short compared to the transit time, as it would be for chemical or most fission-thermal rockets. For systems which burn a significant amount of the time, this approximation is not as good, and the tables should only be used as a general guide to the required delta-V.
Each table is the composite of 16 different tables generated with different starting geometry, and with each table containing data from at least one synodic period. Note that this was all done in a sun-centric system, and that the delta-V necessary to deal with either planet’s gravity well was not included. This will add some extra delta-V, the necessary amount shrinking in absolute terms as the overall delta-V is increased due to the Oberth effect. The decision to not include escape and capture delta-V was made because to do otherwise would have involved specifying reference orbits to escape from and capture to, and would have added significant complexity to the program at a minimal gain in utility for most users.
One thing that is apparent from these tables is the degree to which Jupiter missions are more hit-or-miss than Mars missions. For Jupiter transfers, 84% of the options are either going to be viable all of the time, or not going to be viable at all. For Mars, the equivalent value is only 56%. Some of this is due to the much larger and more variable time increments used in the Jupiter calculations, but much of it is due to the fact that the geometry changes significantly less between Earth and Jupiter than it does between Earth and Mars.
It should also be noted that these tables are an attempt to find an average over all possible relative positions of the two bodies. For the design of an actual spacecraft, analysis would instead start with modeling of geometries over the projected life of the spacecraft. The approximations given here are reasonably close for theoretical use, but should not be used to plan actual space missions.
Heat management is a vital part of the design and operation of a space vessel, particularly a warcraft.
Section 3mentioned some of the issues with regards to stealth, but a more comprehensive analysis is necessary. There are two options for dealing with waste heat in battle: radiators and heat sinks. If the waste heat is not dealt with, it would rapidly fry the ship and crew.
All space vessels will need radiators to disperse the heat they produce as part of normal operations. If using an electric drive, power (and therefore waste heat) production will be no higher in battle then during cruise. This would allow the standard radiators to be used indefinitely during battle without requiring additional cooling systems. The problem with radiators is that they are relatively large and vulnerable to damage. The best solution is to keep them edge-on to the enemy, and probably armor the front edge. The problem with this solution is that the vessel is constrained in maneuver, and can only face one (or possibly two) enemy forces at once without exposing the radiator. If the techlevel is high enough to make maneuver in combat a viable proposition, then radiators are of dubious utility in combat. On the other hand, the traditional laserstar battle suits radiators quite well. The faceplate and the forward edge of the radiators are always pointed at the enemy, and almost all maneuvers are made side-to-side to dodge kinetics. The only problem is vulnerability to a direct kinetic hit. If a projectile were to arrive precisely edge-on, it could tear the entire radiator in two. Bending the radiator slightly would eliminate this vulnerability, but would also increase armor requirements. However, even a bent radiator would still have issues with grazing impacts. A projectile coming in very close to parallel with the radiator’s surface would tend to tear a long hole in it, as opposed to the small hole left by a projectile traveling perpendicular to the surface. However, the low-incidence projectile would have to penetrate much more material, so kinetics designed for such attacks would naturally have more mass or fewer pieces of shrapnel than one designed for normal attacks.
Heat sinks avoid the vulnerability to damage of radiators, but have a drawback of their own. By their very nature, they have a limited heat capacity, which places a limit on how much power a ship can produce during an engagement, and thus on the duration of an engagement. If the heat sinks fill up, the ship would begin to fry unless the radiators were extended immediately. In the game Attack Vector: Tactical, extending the radiators is used to signal surrender. Obviously, the heat clock is a major disadvantage, but it is necessary when the vessel expects to expose several aspects to the enemy.
One topic that briefly needs to be addressed is electric propulsion. In discussions, VASIMR-type engines are usually considered the baseline. However, Dr. Joshua Rovey of Missouri S&T told the author that Hall Effect thrusters today are capable of the sort of performance that VASIMR is currently promising after development is finished. VASIMR is apparently getting attention due to good marketing people.
Another topic that deserves discussion is the effect of nuclear power on spacecraft design. For large warcraft, nuclear power, both for propulsion and for electricity is a must-have. Even if the design of solar panels advances to the point at which they become a viable alternative for providing electrical propulsion power in large civilian spacecraft, there are several major drawbacks for military service. The largest is that solar panels only work when facing the sun, unlike radiators, which work best when not facing the sun. The distinction between the two is important, as it is nearly always possible to find an orientation which keeps the radiator edge-on to the enemy and still operating efficiently, while a solar panel must be pointed in a single direction, potentially exposing it to hostile fire. A solar panel is particularly vulnerable to laser fire, as it is by nature an optical device. While hard numbers on this are surprisingly difficult to find, it appears that damage will probably occur to photovoltaics when exposed to intensities of around 300 KJ/m2, for short pulses (<10-4 seconds), with threshold requirements increasing from there as the pulse length increases. For a CW laser (>1 second), the power flux required for damage is approximately 10 MW/m2. Photovoltaics can also be attacked using small particles such as sand,
as described in Section 7for use against lasers. While a full analysis of the potential damage is beyond the scope of this section, it appears that sand would be a reasonably effective means of attacking photovoltaics, particularly given the large area involved. The size of a solar array also complicates maneuvering the panels edge-on to the incoming particles, and could potentially raise structural concerns.
Radiators, on the other hand, are more resistant to damage. Firing lasers at them will only decrease the thermal efficiency of the reactor slightly, as the radiator is designed to disperse heat. Particle clouds that are designed for surface effects would be ineffective against a properly-designed radiator, or at very best reduce the emissivity by a small amount. Small pieces of shrapnel designed to pierce the radiator entirely would be the best means of attack (described above), as fully armoring a radiator is likely to be impossible because of the mass requirements.
However, it could be argued that this ignores the vulnerability of the reactor itself to damage. While in Hollywood, “They’ve hit the reactor!” is usually followed by a massive explosion, that is not the case in reality. First, the reactor is a very small target, usually shielded by the bulk of the ship, so it’s unlikely to be hit in the first place. Second, nuclear reactors simply do not turn into bombs under any circumstances, and particularly not random damage to the core. The few cases in history in which a reactor has gone prompt critical (SL-1 and Chernobyl being the best-known) were caused by poor procedure, and are vanishingly unlikely to happen due to random damage.
That said, it still seems a potentially bad idea to put all of one’s eggs in a single basket. Solar panels are highly redundant, but the reactor could still be put out of action with a single hit. The response to this is fairly simple. First, there are reactor designs using heat pipes that have sufficient redundancy to continue operation even if the reactor core itself is hit. The specific heat pipe will be put off line, but if the design has 150, that’s not a great worry. Second, the reactor and associated gear (power converters and such) are buried deep in the ship, where they will be difficult to get at, and the power converters can be duplicated for redundancy.
One last concern is the ejection of reactor core material after a hit, and the potential for said material to irradiate the crew. This is also probably minor, as the crew is still being shot at, and the spacecraft will have some shielding against both background radiation and nuclear weapons. (Thanks to Dr. Jeffrey King of the Colorado School of Mines for providing much of the material on space nuclear power and propulsion.)
A couple of other issues with nuclear power are relevant and of interest. The first is the choice of remass in nuclear-thermal rockets. While hydrogen is obviously the best possible choice (the reasons for this are outside the scope of this paper, but the details are easy to find), it is also hard to find in many places. With other forms of remass, the NTR does not compete terribly well with chemical rockets, but it can theoretically use any form of remass available. The biggest problem with alternative remasses is material limits. With most proposed materials, oxidizing remasses will rapidly erode and destroy the engine. The alternatives to avoid this are rhenium and iridium, which are both very expensive, explaining why they are not in use today. However, both elements are common in asteroids, making them viable choices in a setting with large-scale space industry.
As discussed in Section 7, vibration is a serious issue for laser-armed spacecraft. Any rotating part will produce vibrations, and minimizing these vibrations is of interest to the designer. While there is undoubted a significant amount that could be done to reduce the vibrations produced by conventional machinery (the exact techniques are probably classified, as their primary application is in submarine silencing), it seems simpler to use systems with no moving parts, which should theoretically minimize both vibration and maintenance. Heat pipes, as mentioned above, are an entirely passive means of moving heat around, both from a reactor to an energy converter (which could mean a turbine, a thermocouple, or any of the other wonderful things engineers can think of) and from the energy converter to the radiator. There are also electromagnetic pumps for liquid metal which while not entirely passive, but will cut down on the vibration load.
There are even proposed systems of energy conversion which are reasonably efficient and involve no moving parts. The best-known of these proposed systems is probably the Alkali Metal Thermal-to-Electric Converter (AMTEC), which has been extensively studied. However, a recent effort by NASA to bring the technology into deployment failed, giving the technology a bad name. There are some, however, who believe it still holds promise.
If systems like AMTEC are not available, the spacecraft will have to use conventional hat engines. These are likely to use one of the two standard thermodynamic cycles, the Brayton cycle (gas turbine), and the Rankine cycle (steam turbine). The primary difference between the two is that in the Brayton cycle, the working fluid remains a gas throughout, while in the Rankine cycle, it moves from liquid to gas and back again. In theoretical design, radiators are normally sized assuming constant temperature throughout, which is true for most Rankine cycle systems (as the radiators are where the fluid condenses at a constant temperature) and produces the well-known result that radiator area is minimized when the radiator temperature is 75% of the generation temperature. However, this is not true for Brayton cycle radiators. There is no convenient mechanism to release the necessary heat at a constant temperature, so the radiator performs differently as the gas cools. There is not a simple formula here, but an iterative procedure can be used to minimize radiator area for an ideal system (which is close enough for our purposes). Use of this method does require some knowledge of the basics of gas turbine propulsion, but it is not terribly esoteric. (Thanks to Dr. David Riggins of Missouri S&T for presenting this material in class. Those who have had more experience in propulsion and fluid dynamics might recognize some simplifications of the explanatory material, and some nomenclature changes. This was intended to hold down the length of this section and clarify it without sacrificing accuracy of the results.)
An ideal gas turbine can be thought of as being made of 4 separate stages. First, isentropic compression, which means that there is no heat transfer and all energy put into the system by the compressor, is used to compress the gas instead of heating it. Second, isobaric (constant-pressure) heat addition, which occurs in the reactor. Third, isentropic expansion through a turbine, which outputs mechanical work (the goal of this whole process). Lastly, isobaric heat rejection, through the radiator, which returns the working fluid to the condition it was at before entering the compressor. The compressor and turbine are defined by their pressure ratios, written as πc and πt respectively. The pressure ratio is the pressure of the fluid after the component divided by the pressure ahead of the component.
For this method, values for Cp, γ, ηc, ηt, and T3 must be selected. Cp is the constant-pressure specific heat capacity of the fluid, while γ is the ratio of specific heats. Definitions and values for various fluids can be found online. ηc and ηt are the efficiencies for the compressor and turbine respectively. Values between 0.8 and 0.9 are probably reasonable. T3 is the temperature at the outlet of the heat addition stage, and is normally set by the design of the reactor itself. Representative values might be 1600-1700 K for a conventional nuclear reactor, although higher values are possible. (All temperature values throughout should be in Kelvin, not Celsius.)
The first step is to select a value for πc, with anything from 2 to 10 being plausible. Because it is a closed system, πt will be equal to 1/ πc. Once this is known, it is possible to calculate T4 (temperature downstream of the turbine) using .
At this point, a value for T1 must also be selected. This is the temperature at the entrance to the compressor. Using this, the value for T2, the temperature at the compressor exit, can be calculated using . This allows the overall efficiency of the power-generation system, &eta (work output/heat input), to be calculated using . All of this information can then be used to find the radiator area per unit work output (A’, m2/W) with where σ is the Stefan-Boltzmann constant (5.670373×10-8) and ε is the emissivity of the radiator (0.9-1.0). Once you have this value, select a different value of T1, and repeat the rest of the paragraph. When a minimum has been found, select a different value for πc and repeat the entire procedure until a global minimum has been found. It would probably be a good idea to use a spreadsheet to automate this.
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.
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.
I replaced the ax-head.
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:
This is an interesting design example from the always worth reading Bootstrapping Space blog by Chris Wolfe. It is mostly centered around estimating a mission delta V and sizing a propulsion system to fit, but his thought processes are interesting.
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.
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.
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
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).
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.
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) : Rule of thumb 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) : Rule of thumb 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) : Rule of thumb minimum to lift off from Terra's surface into LEO.
For a more in-depth look at minimum accelerations look here.
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").
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.
This is a quite radical method to drastically reduce the structural mass of a spacecraft (and also dramatically increase the separation between a dangerously radioactive propulsion system and the crew). Please note this has never been tried, and warships with such a design would have their manoeuvring critically handicapped (or it's "crack-the-whip" time).
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.
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. This does reduce the effective thrust by an amount proportional to the cosine of the angle but for small angles it is acceptable.
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.
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."
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.
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.
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.
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 rule of thumb, the mass of a fuel tank loaded with liquid hydrogen will be about 87% hydrogen and 13% tank. In other words, multiply the mass of the liquid hydrogen by 0.15 to get the mass of the empty tank (0.13 / 0.87 = 0.15).
So 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:
|Water||Nuclear salt water rocket||4|
|Hydrogen||NTR / GCR||10|
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:
- Usable Propellant Volume (Vpu): the volume holding the propellant that can actually be used.
- 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.
- 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.
- 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
Pb = design burst pressure (Pa)
fs = safety factor (typically 2.0)
MEOP = Maximum Expected Operating Pressure of the tank (Pa)
|2219 - Aluminum||2,800||0.413|
|4130 - Steel||7,830||0.862||11.23||2,500|
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
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 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
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)
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.
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 rule of thumb is that aerobraking can kill a velocity approximately equal to the escape velocity of the planet where the aerobraking is performed (10 km/s for Venus, 11 km/s for Terra, 5 km/s for Mars, 60 km/s for Jupiter).
This will mostly be used for our purposes designing a emergency re-entry life pod, not a Solar Guard patrol ship. With a sufficiently advanced engine it is more effective just to carry more fuel, so our atomic cruiser will not need to waste mass on such a primitive device.
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.
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 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.
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).
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.
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.
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 rule of thumb:
Es = 1366 * (1 / Ds2)
- Es = available solar energy (watts per square meter)
- Ds = distance from the Sun (astronomical units)
Remember that you divide distance in meters by 1.49e11 in order to obtain astronomical units.
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
- 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.
|Fuel region||157 kg|
|Heat pipes||117 kg|
|Reactor control||33 kg|
|Other support||32 kg|
|Total Reactor mass||493 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 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.
Nuclear Thermal Rockets are basically nuclear reactors with a thrust nozzle on the bottom. A concept called Bimodal NTR allows one to tap the reactor for power. This has other advantages. Since the reactor is running warm at a low level all the time (instead of just while thrusting) it doesn't have to be pre-heated if you have a burn coming up. This reduces thermal stress, and reduces the number of thermal cyclings the reactor will have to endure over the mission. It also allows for a quick engine start in case of emergency.
In the real world, during times of disaster, US Navy submarines have plugged their nuclear reactors into the local utility grid. This supplies emergency electricity when the municipal power plant is out. In the science fiction world, a grounded spacecraft with a bimodal NTR could provide the same service.
Here is a commentary on figuring the mass of the reactor of a nuclear thermal rocket by somebody who goes by the handle Tremolo:
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)
- 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.
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.
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.
This is where the spacecraft receives its power not from an on-board generator but instead from a laser or maser beam sent from a remote space station. This is a popular option for spacecraft using propulsion systems that require lots of electricity but have low thrusts. For instance, an ion drive has great specific impulse and exhaust velocity, but very low thrust. If the spacecraft has to power the ion drive with a heavy nuclear reactor with lead radiation shielding, the mass of the spacecraft will increase to the point where its acceleration could be beaten by a drugged snail. The drawback includes the distance decrease in power due to diffraction, and the fact that the spacecraft is at the mercy of whoever is running the remote power station. Also maneuvers must be carefully coordinated with the remote station, or they will have difficulty keeping the beam aimed at the ship.
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 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 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.
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.
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.
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.
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).
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.
Specific energy 4–40 kJ/kg
Energy density less than 40 kJ / L Specific power 10–100,000 kW/kg Charge/discharge
95% Self-discharge rate >0% at 4 K
100% at 140 K
Cycle durability Unlimited cycles
Superconducting Magnetic Energy Storage (SMES) systems store energy in the magnetic field created by the flow of direct current in a superconducting coil which has been cryogenically cooled to a temperature below its superconducting critical temperature.
A typical SMES system includes three parts: superconducting coil, power conditioning system and cryogenically cooled refrigerator. Once the superconducting coil is charged, the current will not decay and the magnetic energy can be stored indefinitely.
The stored energy can be released back to the network by discharging the coil. The power conditioning system uses an inverter/rectifier to transform alternating current (AC) power to direct current or convert DC back to AC power. The inverter/rectifier accounts for about 2–3% energy loss in each direction. SMES loses the least amount of electricity in the energy storage process compared to other methods of storing energy. SMES systems are highly efficient; the round-trip efficiency is greater than 95%.
Due to the energy requirements of refrigeration and the high cost of superconducting wire, SMES is currently used for short duration energy storage. Therefore, SMES is most commonly devoted to improving power quality.
Low-temperature versus high-temperature superconductors
Under steady state conditions and in the superconducting state, the coil resistance is negligible. However, the refrigerator necessary to keep the superconductor cool requires electric power and this refrigeration energy must be considered when evaluating the efficiency of SMES as an energy storage device.
Although the high-temperature superconductor (HTSC) has higher critical temperature, flux lattice melting takes place in moderate magnetic fields around a temperature lower than this critical temperature. The heat loads that must be removed by the cooling system include conduction through the support system, radiation from warmer to colder surfaces, AC losses in the conductor (during charge and discharge), and losses from the cold–to-warm power leads that connect the cold coil to the power conditioning system. Conduction and radiation losses are minimized by proper design of thermal surfaces. Lead losses can be minimized by good design of the leads. AC losses depend on the design of the conductor, the duty cycle of the device and the power rating.
The refrigeration requirements for HTSC and low-temperature superconductor (LTSC) toroidal coils for the baseline temperatures of 77 K, 20 K, and 4.2 K, increases in that order. The refrigeration requirements here is defined as electrical power to operate the refrigeration system. As the stored energy increases by a factor of 100, refrigeration cost only goes up by a factor of 20. Also, the savings in refrigeration for an HTSC system is larger (by 60% to 70%) than for an LTSC systems.
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.
Alert readers will have noticed the term "manageable size" above. It is impractical to use a black hole with a mass comparable to the Sun. Your ship would need an engine capable of moving something as massive as the Sun, and the gravitational attraction of the black hole would wreck the solar system. So you just use a smaller mass black hole, right? Naturally occurring small black holes are called "Primordial black holes."
Well, there is a problem with that. In 1975 legendary physicist Stephen Hawking discovered the shocking truth that black holes are not black (well, actually the initial suggestion was from Dr. Jacob Bekenstein). They emit Hawking radiation, for complicated reasons that are so complicated I'm not going to even try and explain them to you (go ask Google). The bottom line is that the smaller the mass of the black hole, the more deadly radiation it emits. The radiation will be the same as a "black body" with a temperature of:
6 × 10-8 / M kelvins
where "M" is the mass of the black hole where the mass of the Sun equals one. The Sun has a mass of about 1.9891 × 1030 kilograms.
In The McAndrew Chronicles Charles Sheffield hand-waved an imaginary force field that somehow contained all the deadly radiation. One also wonders if there is some way to utilze the radiation to generate power.
In the table:
- R is the black hole's radius in attometers (units of one-quintillionth or 10-18 of a meter). A proton has a diameter of 1000 attometers.
- M is the mass in millions of metric tons. One million metric tons is about the mass of three Empire State buildings.
- kT is the Hawking temperature in GeV (units of one-billion Electron Volts).
- P is the estimated total radiation output power in petawatts (units of one-quadrillion watts). 1—100 petawatts is the estimated total power output of a Kardashev type 1 civilization.
- P/c2 is the estimated mass-leakage rate in grams per second.
- L is the estimated life expectancy of the black hole in years. 0.04 years is about 15 days. 0.12 years is about 44 days.
Table is from Are Black Hole Starships Possible?, 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. See Thermophotovoltaic Energy Conversion in Space Nuclear Reactor Power Systems and HIGH TRADER for details.
Ken Burnside also noted that radiators are large, flimsy, and impossible to armor (except perhaps for the droplet radiator). A liability on a warship. 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."
If you want to calculate this for yourself use the Stefan-Boltzmann law:
P = A * ε * σ * T4
A = P / (ε * σ * T4)
- 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
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.
I had initially thought that the heat from the life-system could be simply dumped by the same radiator system dealing with the multi-gigawatt waste heat from the propulsion system. Richard Bell pointed out that I had not thought the problem through. Due to the difference in the temperatures of the waste heat from life-system and propulsion, unreasonably large amounts of energy will be required to get the low-level life-system heat into a radiator designed to handle high-level propulsion heat. The bottom line is that there will be two separate radiator systems.
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?
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.
But do realize that if the spacecraft does indeed have a nuclear propulsion system and/or a nuclear reactor, and it also has heat radiators, they must be tapered to keep inside the radiation shadow shield. Or bad things happen.
Electrical powered drives like ion drives will require radiators on their power plants. Fusion drives may or may not require radiators, depending upon whether the design can dump the waste heat into the exhaust or not.
My source (Matthew DeBell) says that if 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.
You noted that having too many radiators distributed about an axis causes them to radiate into each other. It all boils down to what's known as a face factor, essentially how much of the radiation released by a surface is intercepted by another one. For two plates of equal length separated by an angle alpha (α), the face factor is:
F = 1 - sin(α/2)
So you can see right off the bat that for 2 radiators opposite each other, α = 180°, α/2 = 90° and the face factor is 0, no interception. But go up:
Multiple Radiator Panels # Face
Emit Efficiency 1 0.000000000 1.00000000 1.000000000 2 0.000000000 2.00000000 1.000000000 3 0.133974596 2.598076211 0.866025404 4 0.292893219 2.828427125 0.707106781 5 0.412214748 2.938926261 0.587785252 6 0.500000000 3.000000000 0.500000000 7 0.566116261 3.037186174 0.433883739 8 0.617316568 3.061467459 0.382683432 9 0.657979857 3.078181290 0.342020143 10 0.690983006 3.090169944 0.309016994 11 0.718267443 3.099058125 0.281732557 12 0.741180955 3.105828541 0.258819045
- # number of radiators spaced around the ship's long axis
- Face Factor how much heat radiation from a radiator is wastefully intercepted by another radiator
- Emit how much heat is effectively radiated by the total radiator array, in units of single radiator panels
- Efficiency how efficient is this array at getting rid of heat, single panel = 100%
The second column is face factor, the third column is how much is emitted relative to a single surface, and the last is "efficiency", how much every individual panel is emitting relative to a single unlimited surface (efficiency is just 1 - F = sin(α/2), which is itself the face factor for the surface relative to its unobstructed surroundings). As you can see, it falls off very very quickly; the third radiator is only 60% as effective (goes up from 2.00 to 2.60), and the fourth adds to this only marginally (goes up from 2.60 to 2.80). Unless there really isn't room to simply stretch out the panels, it just doesn't seem worth it to pack more than 3 about an axis, and even 3 might be a stretch.
Neat thing is, using the face factor you can figure out the efficiency of radiators in weird geometries. My textbook has face factors for cylinders, enclosed spaces and plates of unequal size, if you so desire, which is to say I could tell you how much is going into your spaceship, or out an open dock.
Another neat side effect of face factors is that you can make a radiator more efficient per given mass by poking holes right through it, since the inner surface of the hole radiates at least partly out into its surroundings (the rest radiates back into itself, but that isn't really a problem). This reduces efficiency per unit area (though interestingly not by much for giant holes), and the panel is significantly weaker as a result (even more than you'd think, since the hole provides an area of stress concentration — it can reach multiples what it would normally there), but for very small holes that are very close together, you can get efficiencies per mass that are many times higher than they would be for a straight panel.
Take this arrangement: a square grid of side L, with a hole in the center of each square and one on each vertex, each hole being of radius 0.35L so that the holes at the vertices are nearly touching that in the middle. Say, for L varying from 0.1 to 1, 10 and 100 times thickness, relative mass efficiency goes up 4.342, 4.010, 1.828 and 1.094 times(by the way, because the relative size of the hole is the same, you need 4.660 times the area of panelling to get the same mass as a continuous radiator).
(ed note: the above was orginally erroneously writen as 1.199, 2.204, 4.184 and 4.609 times)
You can force even more holes into there if they're arranged hexagonally; take a hexagon of side L, with a hole at the center and one each vertex, you can reach a radius of up to 0.5L. Now, for L varying again from 0.1 to 1, 10 and 100 times the thickness, relative mass efficiency goes up 10.741, 9.610, 2.763 and 1.193 times over (in this case, you need 10.74 times the area of panelling to get the same mass as a continuous radiator)!
(ed note: the above was orginally erroneously writen as 1.486, 5.035, 9.816 and 10.644 times)
Given that "every gram counts", it's almost certainly worth the fragility. You could probably thicken the panels somewhat to make up for it and hit a sweetspot
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.
- Decide how many kilowatts of waste heat the radiator will have to handle (from the engine, the power reactor, the laser cannon, etc.)
- Select which radiator type to use, and examine its Specific Area table.
- Divide the total waste head in kilowatts by the Heat Cap. entry of the table to get the square meters of radiator area required.
- 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
- radiatorMass = mass of radiator array (kg)
- wasteHeat = amount of waste heat to dispose of (kWth)
- specificAreaHeat = Heat Cap. from radiator table (kWth/m2)
- specificAreaMass = Mass from radiator table (kg/m2)
Note that Step 3 calculates the radiation surface of the radiator. If the radiator is layered flat on the ship's hull, the radiation surface is the same as the physical radiator size. However, if the radiator is attached edge on so it extends out as a fin or a wing, the physical radiator size will be one-half the radiation surface. This is because you can use both sides of the physical fin as radiator surface. Yes, even a liquid droplet radiator. This might not apply for some of the stranger radiator designs, but details are scarce.
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|
|Marangoni Flow||293.04 kWth/m2||24.4 kg/m2||853 m2||20,816 kg|
|Electrostatic Membrane||51.3 kWth/m2||4.275 kg/m2||4,873 m2||20,833 kg|
|Hula-Hoop||300 kWth/m2||33 kg/m2||833 m2||27,500 kg|
|Buckytube Filament||293.03 kWth/m2||48.839 kg/m2||853 m2||41,667 kg|
|Curie Point||212.75 kWth/m2||35.459 kg/m2||1,175 m2||41,667 kg|
|Tin Droplet||38.49 kWth/m2||6.4154 kg/m2||6,495 m2||41,669 kg|
|Flux-Pinned Superthermal||76 kWth/m2||17 kg/m2||3,289 m2||55,921 kg|
|Attack Vector: Tactical||357 kWth/m2||100 kg/m2||700 m2||70,028 kg|
|Bubble Membrane||21.01 kWth/m2||7.00 kg/m2||11,899 m2||83,294 kg|
|Mo/Li Heat Pipe||453.54 kWth/m2||151.18 kg/m2||551 m2||83,333 kg|
|Microtube Array||102.6 kWth/m2||34.2 kg/m2||2,437 m2||83,333 kg|
|ETHER||212.75 kWth/m2||70.92 kg/m2||1,175 m2||83,337 kg|
|Ti/K Heat Pipe||150.22 kWth/m2||100.14 kg/m2||1,664 m2||166,656 kg|
|SS/NaK Pumped||90.83 kWth/m2||60.554 kg/m2||2,752 m2||166,669 kg|
|Salt-Cooled Reflux tube||75 kWth/m2||75 kg/m2||3,333 m2||250,000 kg|
|Life Support||0.19 kWth/m2||3.1 kg/m2||1,315,789 m2||4,078,947 kg|
|Heat Cap.||~0.19 kWth/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 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 range||coolant type||example|
|250 K – 350 K||silicone oils|
|370 K – 650 K||liquid metal eutectics|
|500 K – 1000 K||liquid tin|
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.
Triangular LDRs have a tiny collector a fraction of the width of the droplet generator. The droplet density increases across the flight path. It is 40% less massive compared to a comparable Rectangular LDR due to the smaller collector. 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.
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.
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
- 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
Specific Area Heat Cap. ~38 kWth/m2 Mass 6.4 kg/m2 Op. Temp. 1030 K Emissivity 0.96
Tin droplet radiator
Atomization increases the surface area with which a fluid can lose heat. A hot working fluid sprayed into space as fine streams of sub-millimeter drops readily loses heat by radiation. The cooled droplets are recaptured and recycled back into the heat exchanger. If tin (Sn) is used as a working fluid, the kilos per power radiated is minimized, using a heat rejection temperature of 1030 K and a total power in the megawatt range (comparable to the game value of heat rejection of 120 MWth per therm). The low emissivity of liquid tin (0.043) is increased by mixing in carbon black, which distributes itself on the surface of the droplet. Evaporation losses are avoided by enclosing the radiator in a 1 μm plastic film, which transmits radiation in the 2 to 20 μm (IR) range. Such a film would continue to perform its function even if repeatedly punctured by micrometeoroids. The illustration shows a triangular liquid droplet geometry. The collector, located at the convergence point of the droplet sheet, employs centrifugal force to capture the droplets. The total specific area is 6.4 kg/m2.
K. Alan White, "Liquid Dropbt Radiator Devebpment Status," Lewis Research Center, 1987
Specific Area Heat Cap. ~300 kWth/m2 Mass 35 kg/m2 Op. Temp. 1200 K
Curie point radiator
A ferromagnetic material heated above its Curie point loses its magnetism. If molten droplets of such a substance are slung into space, they radiate heat and solidify. Once below their Curie temperature, they regain their magnetic properties and can be shepherded by a magnetic field into a collector and returned to the heat exchanger. A 120 MW system operating at 1200 K includes a 13 tonne magnetic heat exchanger and a rotating dust recovery electromagnet on a 25-meter boom, plus 7 tonnes of dust spread in a spiraling disk 27-meters in diameter (35 kg/m2). The usual medium is iron dust, which has a Curie point of 1043 K and is easily scavenged by magnetic beneficiation from regolith.
M.D. Carelli, 1989
Specific Area Heat Cap. 51 kWth/m2 Mass 4.3 kg/m2 Op. Temp. 1000 K Emissivity 0.85
Electrostatic membrane radiator
This heat-rejection concept, also called a liquid-sheet radiator, encloses radiating liquid within a transparent envelope. It consists of a spinning membrane disk inflated by low gas pressure, with electrostatically-driven coolant circulating on its interior surfaces. The liquid coolant is only 300 μm thick and has an optical emissivity of 0.85 at a temperature of 1000 K. An electric field is used to lower the pressure under the film of coolant, so that leakage through a puncture in the membrane wall is avoided. The membrane has a specific area of 4.3 kg/m2 and 51 kWth/m2.
Shlomo Pfeiffer of Grumman, 1989
Specific Area Heat Cap. 213 kWth/m2 Mass 71 kg/m2 Op. Temp. 1200 K
ETHER charged dust radiator
To avoid the evaporation losses suffered by radiators that use liquid droplets in space, dust radiators use solid dust particles instead. If the particles are electrostatically charged, as in an electrostatic thermal radiator (ETHER), they are confined by the field lines between a charged generator and its collector. If the spacecraft is charged opposite to the charge on the particles, they execute an elliptical orbit, radiating at 1200 K with a specific area of 71 kg/m2 and 213 kWth/m2. The dust particles are charged to 10-14 coulombs to inhibit neutralization from the solar wind.
Specific Area Heat Cap. ~469 kWth/m2 Mass 150 kg/m2 Op. Temp. 1450 K
Mo/Li heat pipe radiator
A heat pipe quickly transfers heat from one point to another. Inside the sealed pipe, at the hot interface a two-phase working fluid turns to vapor and the gas naturally flows and condenses on the cold interface. The liquid is moved by capillary action through a wick back to the hot interface to evaporate again and repeat the cycle. For high temperature applications, the working fluid is often lithium, the soft silver-white element that is the lightest known metal. Molybdenum heat pipes containing lithium can operate at the white-hot temperatures of 1450 K, and transfer heat energy at 240,000 kWth/m2, almost four times that of the surface of the sun. The specific area is 150 kg/m2.
David Poston, Institute for Space and Nuclear Power Studies at the University of New Mexico, 2000
Specific Area Heat Cap. ~153 kWth/m2 Mass 100 kg/m2 Op. Temp. 1100 K
Ti/K heat pipe radiator
A Rankine evaporation-condensation cycle heat pipe uses metal vapor as the coolant, which is liquefied as it passes through a heat exchanger connected to the radiator. A liquid metal near the liquid/vapor transition is able to radiate heat at a nearly constant temperature. The pipe is made from SiC-reinforced titanium (Ti) or superalloy operating at up to 1100 K, and the working fluid is potassium (K). The pipe is covered with a lightweight thermally-conductive carbon foam, which protects the pipe from space debris and transfers heat to the radiating fins. The total specific area is 100 kg/m2.
Specific Area Heat Cap. ~21 kWth/m2 Mass 7 kg/m2 Op. Temp. 800 K
Bubble membrane radiator
This high-temperature concept uses a spinning bubble-shaped membrane to reject waste heat. A two-phase working fluid (hot liquid or gas) is centrifugally pumped and sprayed on the interior surface of the bubble. The fluid wets the inner surface of the sphere and is driven in the form of a liquid film by centrifugal force to the equatorial periphery of the sphere. As the liquid flows along the inner surface of the envelope it loses heat by thermal radiation from the outer surface of the balloon. The use of membranes woven from space-produced carbon nanotubes and cermet fabrics offers a specific area of 7 kg/m2, radiating from one side at 800 K. Liquid metal pumps return the liquid out of the sphere through rotated shaft seals to its source.
Specific Area Heat Cap. ~300 kWth/m2 Mass ~100 kg/m2 Op. Temp. 1300 K
Buckytube filament radiator
Waste heat may be rejected by moving thousands of loops of thin (1 mm) flexible "Buckytubes" (carbon nanotubes), which radiate their thermal load prior to return to the heat exchanger. Cables constructed of Arm-chair type nanotubes are the strongest cables known, with design tensile strengths about 70% of the theoretical 100 GPa value. The moving filaments are heated by direct contact around a molybdenum drum filled with the heated working fluid, and then extended into space a distance of 70m by rotational inertia. Their speed is varied according to the temperature radiated (from 273 K to 1300 K). The loops are redundantly braided to prevent single point failures from micrometeoroids. Each element is heat treated at 3300 K to increase the thermal conductivity through graphitization to about 2500 W/mK.
Richard J, Flaherty, "Heat-transfer and Weight Aialysis Of a Moving-Belt Radiator System for Waste Rejection in Space", Lewis Research Center, Cleveland, Ohio, 1964.
Specific Area Heat Cap. 76 kWth/m2 Mass 17 kg/m2 Op. Temp. 928 K Emissivity 0.9
Flux-pinned superthermal radiator
Variable configuration radiators take advantage of the surprising physics of high-temperature flux-pinning superconductors. These materials resist being moved within magnetic fields, allowing stable formations of elements. No power or active feedback control is necessary. The radiating elements fly in a flux-pinned formation, not physically touching, but connected by superthermal ribbon. Superthermal compounds hypothetically conduct heat as effortlessly as superconducting materials conduct electricity. The radiating surfaces are graphite foams, which have both a high emissivity (0.9) and a high thermal conductivity (1950 W/m°K) if the heat conducts in a direction parallel to the crystal layers. Operating at 928K, the superthermal radiator has a specific area of 17 kg/m2 and 76 kWth/m2.
Dr. Mason Peck, 2005
Specific Area Heat Cap. 300 kWth/m2 Mass 33 kg/m2 Op. Temp. 1300 K
By imparting heat to twin washer-shaped disks by direct conduction, the Hula-Hoop radiator avoids the diseconomies of scale that plague fluid radiators. Furthermore, they are robust against micrometeoroid strikes and hostile attack. The two hoop are 100-meters in diameter. They are made of braided cermets coated with graphite, and lubricated in a heat exchanger with tungsten disulfide (WS2). Radiating at 1300 K, each has a specific area of 33 kg/m2 and 300 kWth/m2.
This design is a Philip Eklund original, published here for the frst time.
Specific Area Heat Cap. ~300 kWth/m2 Mass 24 kg/m2 Op. Temp. 1300 K
Marangoni flow radiator
In zero-g, a surface tension gradient can create a heat pump with no moving parts, or drive micro-refining processes. This phenomena, called Marangoni flow, moves fluid from an area of high surface tension to one of low surface tension. Bubbles operating at 1300 K have a specific area of 24 kg/m2.
G. Harry Stine, "The Third Industrial Revolution," 1979
Specific Area Heat Cap. ~104 kWth/m2 Mass 34 kg/m2 Op. Temp. 1000 K
Microtube array radiator
Nanofacturing techniques can fabricate large, parallel arrays of microtubes for high performance radiators. The radiating surface comprises a heavily-oxidized, metal alloy with a 100 nm film of corrosion resistant, refractory platinum alloy deposited on it. The working fluid is hydrogen, which has low pumping losses and the highest specific heat of all materials. This fluid is circulated at 0.1 to 1 MPa through the microtubes, and the heat radiates through the thin (0.2 mm) walls. This allows a specific area of 34 kg/m2, including the hydrogen. The rejection temperature for titanium alloy tubes is from 200 K up to 1000 K, if a high temperature barrier against hydrogen diffusion is used. High speed leak detection capability and isolating valves under independent microprocessor control provide puncture survivability.
F. David Doty, Gregory Hosford and Jonathan B. Spitzmesser, "The Microtube-Strip Heat Exchanger," 1990
Specific Area Heat Cap. ~75 kWth/m2 Mass 75 kg/m2 Op. Temp. 1100 K
Salt-cooled reflux tube radiator
In contrast to a heat pipe, that uses capillary action to return the working fluid, a reflux tube uses centrifugal acceleration. This design is more survivable than heat pipes, especially when overwrapped with a high-temperature carbon-carbon composite fabric. Unlike metals, the strength of these composites increases up to temperatures of ~2300K. However, they degrade when subjected to high radiation levels. The working fluid is molten fluoride salts, the only coolant (other than noble gases) compatible with carbon-based materials. Radiating at 1100 K, this radiator has a specific area of 75 kg/m2.
Charles W, Forsberg, Oak Ridge National Laboratory, Proceedings of the Space Nuclear Conference 2005, San Diego, California, June 5-9, 2005.
Specific Area Heat Cap. ~93 kWth/m2 Mass 61 kg/m2 Op. Temp. 970 K Emissivity 0.9
SS/NaK pumped loop radiator
A Rankine evaporation-condensation cycle exchanges heat using a liquid metal as a coolant, which is vaporized as it passes through a heat exchanger connected to the radiator. A liquid metal near the liquid/vapor transition is able to radiate heat at a nearly constant temperature. The usual medium is sodium (Na) or sodium-potassium (NaK), which has a saturation temperature of nearly 1200 K at 1.05 atm. The plumbing is stainless steel (SS) tubes operating at up to 970 K with an emissivity of 0.9. The tube wall is half a millimeter thick to guard against meteoroid-puncture, and each pipe is an independent element so that a single puncture does not cause overall system failure. Molecular beam cameras on long struts scan for meteoroid leaks, which are plugged with pop rivets installed by a tube crawler. Radiating at 970 K from both sides, this radiator has a specific area of 61 kg/m2, including fluid and heat exchanger.
J. Ca/ogeras, NASA/LaRC, 1990.
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."
Specific Area Heat Cap. 357 kWth/m2 Mass 100 kg/m2 Op. Temp. 1600 K Emissivity 0.9
(1 - 0.1)
Knowing that our reactors produce 62.5 MW as a base power unit, and using the proof at right, we get an efficiency of 4 J of waste heat per J of power generated. This tells us that wee need to radiate ~250 MW per point of power. The Stefan-Boltzman law states that the surface emits power at a rate of (1-A) * 5.67×108 Wm2 K4 * T4 where A is the albedo, and T the absolute temperature in Kelvins. With an albedo of 0.1, a temperature of 1600K, and 250 MW of output, we need 700 square meters of radiating surface. Extending as a fin, radiating from both sides, this is roughly 18 meters square. At roughly 0.3m thick, and flexible enough to be retracted and extended, we get something that's reasonably 70 tons, or a bit shy of 3 hull spaces. For the sake of game play, one hull space of radiators dissipates 100 MW, or 0.4 heat points.
A civilian (starship) reactor has a built in 16 meter by 16 meter radiator that dissipates its waste heat; this radiator is built into the hull of the ship. This is why civilian reactors require part of the hull of the ship to be unarmored.
Storing the heat before radiation requires a heat sink. A sodium heat sink is ~21.5 cubic meters of sodium, with a density of 0.968 tons per cubic meter. Sodium has a thermal capacity of 28.2 J/mole/K. A mole of sodium weighs 22.98 grams. One gram of sodium absorbs 2.82/22.98 = 1.22 J per K of heat increase. A heat sink of sodium weighs 20.82 tons, raising that mass by 1 K absorbs 25.4 MJ. Sodium melts at 372 K and vaporizes at 1252 K. Pressurized, it remains liquid to 1600 K, our radiator temperature. Assuming a working range of 1300K (room temperature to 1600 K), each heat sink stores 1300 * 25.4 MJ = 33.02 GJ, which is one heat point, assuming other inefficiencies.
Lithium's thermal capacity of 24.8 J/mole/K and molar weight of 6.94 allows 1 gram to absorb 3.57 J per K of heat increase, or 2.92× the heat capacity of sodium. By using 22 tons of lithium, we get triple the capacity of the sodium heat sink.
Water's thermal capacity is 4.186 J/gram/K, 3.426 times that of sodium. Room temperature to boiling is ~85 K, which limits its usefulness. Raising 1 ton of water by 85 K takes 355.88 MJ. One heat point is 33 GJ, and the amount of water needed to store one heat point is 33 GJ/350.88 MJ = 93 tons. Including the extra mass for plumbing, that's 5 hull spaces all told.
Vaporizing water takes 2256 J/g, 6.3× the energy needed to raise it by 85 K. Because the vaporization is not quite perfect, we treat it as 6 heat points removed when the heat sink is vented. The liquid metal heat sinks aren't vented, as vaporized metal would deposit on the sensors of the ship.
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.
In Frank Herbert's DUNE, spacemen had books the size of a thumb-tip, with a tiny magnifying glass.
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:
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.
For survival's sake, the crew will have little choice but to immediately throw the stowaway out the nearest airlock.
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.