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.
Why? Short answer: This is a consequence of the equation for delta-V.
Why? Slightly longer answer: As a general rule, a rocket with the highest delta-V capacity is going to need three kilograms of propellant for every kilogram of rocket+payload. The lower the total kilograms of rocket+payload, the lower the propellant mass required. This relates to the second strategy of rocket design mentioned above.
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, magnesium, or other lightweight metal as their structural material; but a space station would be better off using heavy iron or Invar.
The only consideration is if the station or base components have to be transported to the desired site by a rocket-propelled transport. Then it makes sense to make the components low mass, because then the station bits are payload. It makes even more sense to construct the space station or base on site using in-situ resources, so you don't have to eat the transport costs at all.
Like aircraft and sea-going warship design, one soon discovers that everything is connected to everything else. When the designer changes one aspect of the design this causes a series of related changes to ripple through the rest of the design.
For instance, if the designer reduces the propellant tank capacity by 5% this has implications for the spacecraft's mass ratio. If it is important for the spacecraft's delta V to stay the same, the payload will have to be reduced by the same amount. This might cut into the amount of life support consumables carried, which will reduce the number of days a mission can last. If the same amount of scientific observations have to be done in the reduced time, another crew member might have to be added. This will decrease the mass available for consumables even more. And so on.
The technical term is "cascading changes." The only thing worse is cascading failures.
As 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.
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 general rule 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.
If you look at most blueprints for the various iterations of the Starship Enterprise, you will notice that every single part of the spacecraft interior is pressurized, with doors, rooms, and toilets. The corridors are wide enough for five people to walk abreast on nice carpeted floors with indirect lighting.
This is ludicrously wrong. And it is not just Star Trek that does this, pretty much all of media science fiction has ships like this. TV Tropes calls this fallacy "Starship Luxurious".
This is an extension of the "Rockets are Boats" fallacy. Passenger aircraft and luxury liners have their entire interior pressurized because so is everything else at sea level on a planet with a breathable atmosphere. For free. So careless starship designers, without a thought, made the unconscious assumption that spacecraft would be totally pressurized as well.
Wrong. Tain't no air in space, and atmosphere is expensive when you have to cart it up out of Terra's gravity well. Not to mention the expensive pressurized hull that has to encase it.
And it is not just the cost of hauling it up the gravity well, the spacecraft's engine has to accelerate the mass of all that junk. Every Gram Counts, so every gram of carpeting, atmosphere, and pressure hull is one less gram of payload, i.e., the reason the spacecraft was created in the first place. Payload is what you are being paid to load, less payload means less pay. See The Tyranny of the Rocket Equation.
In the real world, spacecraft will be mostly tanks of propellant, propulsion system, payload bays, and a lacy lattice-work of support struts holding everything together. The part the people live in will be a tiny pressurized habitat module tucked away somewhere.
Ignorant starship designers have the unconscious assumption that the important part of a spacecraft is the crew, so they designed ships with their priorities reversed. Their ships were mostly gigantic habitat modules with a tiny engine stuck to the rear. Their ships are also ludicrously wrong. If the designers thought about it at all, they might grudgingly include a tiny fuel tank. Which is like the cherry on top of their big icecream sundae of Fail.
So quit drawing ship blueprints with every square inch pressurized and human-accessible. On a real spacecraft if the ship's engineer has to repair the propulsion system, heat radiators, power plant, propellant tanks, or anything like that, they will have to put on their space suit. They will not have the luxury enjoyed by Scotty the engineer, waltzing down a carpeted floor in a shirt-sleeve atmosphere.
The ships above are tail-sitters, so properly avoid the "wrong way is down" problem. But the artist made the second problem much worse. Apparently they figured the entire interior of the spacecraft was for habitable volume. Notice what they got wrong? Well, where the heck is the space for the rocket engines? I lay the blame for this at the artist, I know from experience that writer Jack Williamson knew better.
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:
Full load mass and physical size depends upon assumptions about fuel mass ration, fuel bulk, etc.
Deadweight (inert mass) 1 17% Cargo (payload) 2 33% Fuel (propellant) 3 50% TOTAL 6 100%
Note that total mass is three times the cargo capacity. As you can see, deadweight is the ship proper, structure, engines, anything that is not cargo or propellant.
With this assumption, the big freighters will have a fully loaded mass of 60,000 tons. The largest ships might be twice as big: 120,000 tons.
Our building cost is $500,000 per ton of cargo capacity, the mass assumption makes a building cost equal to $1 million per ton of deadweight. Annual service cost is $100,000 per ton of cargo capacity, the mass assumption makes the annual service cost equal to $200,000 per ton of deadweight. The starship hulls are not cheaper, but they can carry more cargo in proportion to their structural mass.
Type of ship Cargo capacity Purchase price Large 20,000 tons $20 billion Medium 5000 tons $2.5 billion Small 1500 tons $750 million
At $500,000 per ton of cargo capacity, largest giant freighter cost $20 billion to build, but it it has a cargo capacity of 200 Boeing 747 jets, and accounts for over one percent of whole fleet's cargo capacity all by itself. Small freighter costs $750 million, and has seven time the capacity of 747.
With a 30 year service life, the combined shipbuilding yards of the 12 planet trade network will turn out about 25 ships per year.
Hulls will last longer than 30 years but the equipment wears out and has to be replaced. Ships go back to the yards for an overhaul every decade or so, but eventually the cost of stripping everything and replacing it will exceed the value of the ship. Depending upon overhaul costs the shipyards may make more money on rebuilding than on constructing brand new ships. Some ships will stay in service for many decades. Others will be retained as the futuristic equivalent of naval hulks or the old passenger equipment that railroads use as work trains. Every big commercial space station will have a bunch of these old ships in the outskirts.
If modular design is taken to its limit, "ships" will have no permanent existence. Instead they will be assembled out of modules and pods specifically for each run, much like a railroad train. In that case, a ship's identity is attached to a service, not a physical structure. Example: the Santa Fe "Chief" was identified by a timetable and reputation, not a particular set of locomotive and cars.
The analysis up until now focused on money and economics. Businessmen only care about how long it takes to deliver the cargo and how much transport costs, they could care less about the scientific details of the ship engines. But authors care.
As with everything else, it all depends upon the assumptions. Your assumptions will be different, so feel free to fiddle with these and see what the results are.
Assumption: the time spent in FTL transit is zero (jump drive). For the FTL segment of the transit you can use whatever you want, as long as the details do not affect the analysis. The main thing is that the required time spent in FTL transit will add to the total trip time, and thus the number of cargoes a starship can transport per year.
Assumption: starships use reaction drives for normal space travel.
We know that the mass ratio is 2.0. So the Tsiolkovsky rocket equation tells us that the starship's total delta V will be the propulsion system's exhaust velocity times 0.69 (i.e., ln(2.0) ). Since starships accelerate to half their delta V, coast, then decelerate to a halt, their maximum speed is half their delta V, or exhaust velocity times 0.35 (i.e., ln(2.0) / 2). In practice you would accelerate up to a bit less than half their delta V in order to allow a fuel reserve in case of emergency.
It will be even less if the FTL drive happens to use the same type of fuel that the reaction drive does. Basically part of the fuel mass will have to be considered as cargo, not propellant, which will alter the ship's mass ratio.
Reaction drive Exhaust velocity
Nuclear powered Ion ~100 km/s Fusion a few thousand km/s Beam core matter-antimatter about 100,000 km/s
( 1/3 c )
We have assumed that the ship spends 27 days in route (with an instantaneous FTL jump), so the outbound and inbound legs are 13.5 days each (1.17 million seconds).
Assumption: the acceleration on each leg is constant. In reality at the same thrust setting the acceleration will increase as the ship's mass goes down due to propellant being expended. The thrust will probably be constantly throttled to maintain a constant acceleration. Makes it easier on the crew and easier on our analysis. The implication is that obviously the average speed will be half the maximum speed (which is half the delta V)
Reaction drive Exhaust velocity
or Early Fusion
400 km/s 130 km/s 75 million km
0.01 g Advanced Fusion 10,000 km/s 5000 km/s 20 AU
0.44 g Beam-core
c 0.3 c 350 AU
(x5 Pluto's orbit)
8 g !!!
These figures will be lower if time is consumed in FTL flight, maybe be only Terra-Luna distance
Propulsion system's thrust power is thrust times exhaust velocity, then divide by 2. To get the thrust, we know that thrust is ship mass times acceleration. The ship mass goes down as fuel is burnt. As a general rule for ship mass, figure that it only has 2/3rds of a propellant load. That is, multiply the total ship mass by 0.83. So our 120,000 metric ton ship would have a general rule mass of 120,000 * 0.83 = 100,000 metric tons (100,000,000 kilograms).
Reaction drive Exhaust velocity
Thrust Thrust power Advanced Ion
or Early Fusion
1.08×107 N 2.16×1012 W
Advanced Fusion 10,000,000 m/s
4.3×108 N 2.15×1015 W
7.65×109 N 1.15×1018 W
(1 million terawatts)
Where does fuel come from and who does it get into the ship's fuel tanks? Easiest if it is obtained locally at the destination's solar system. The economics of interplanetary transport is same as interstellar (since we did a lot of work making interstellar a cheap as interplanetary).
if fuel from a gas giant at a distance comparable to Terra-Jupiter and round trip is to only take weeks, interplanetary tankers will need speeds of around 1000 km/s. So tankers will be almost as expensive as starships. If tankers use low speed (to make them cheaper), the round trip balloons to a year or more. To service the starship fleet's thirst for fuel, tankers will need to be huge or there will have to be a lot of them. Either way, fuel shipped from gas giants ain't gonna be cheap.
If we forgo interplanetary tankers and instead have starships make extra leg to the local gas giant to refuel, it will cost you more than you will save.
The alternative is shipping fuel up from destination planet. Yes, we know about how surface to orbit is "halfway to anywhere" in terms of delta V cost. But in order to colonize space at all, surface-to-orbit shipping cost will have to be cheap anyway. The industrialization of space will start with using space based resources, but eventually surface-to-orbit will have to be cheap or there is no rocketpunk future. Laser launch, Lofstrom loop, space elevator, something like that.
Assumption: surface-to-orbit shuttle economics are equivalent to current day airliner economics. Round trip to LEO and back is about two hours (not counting loading/unloading). With loading/unloading and maintenance, figure 4 flights a day. Implication is that a round trip passenger ticket is $250 and round trip freight service is $1000/ton (which is +10% added to interstellar transport costs)
Fuel is not round trip, it only goes from surface to orbit, but shuttles have to go orbit to surface in order to get the next load. You will have to streamline the process. High capacity pumps to minimize load/unload times, crew-less shuttle. You might be able to squeeze fuel lift cost to $500/ton. So if starships carry 1.5 tons of fuel per ton of cargo, surface-to-orbit fuel lift costs adds $750/ton to interstellar shipping cost.
So total surface-to-orbit overhead is $1000/ton + $750/ton = $1750/ton or 17.5%. This is an ouch but not a show-stopper.
Back to starships. How big are they?
Present-day maritime tonnage rule: 1 registered ton = ~3 cubic meters.
Assumption: 1 ton = 3 m3 applies to fuel and hull (e.g., crew quarters, engineering spaces, etc) as well as cargo. Therefore, if the absolutely hugest cargo starship in service has a cargo capacity of 40,000 tons (twice that of a large cargo starship), then:
Wet Mass Payload mass to total mass ratio is 3. So wet mass is 3 * 40,000 = 120,000 tons Starship Volume 1 ton of total ship mass = 3 m3 of volume. 120,000 * 3 = 360,000 cubic meters.
Volume of a sphere is 4/3πr3, so the radius of a sphere is 3√(v/(4/3π)) or
radius = CubeRoot( v / 4.189)
diameter = (CubeRoot( v / 4.189)) * 2
Assumption: a "cigar-shape" for a spacecraft is a six times as long as it is wide, with the proportions indicated in the diagram above. The center body is a cylinder 1 unit in diameter (0.5 units radius) and two units high. The two end caps are cones of 0.5 units radius and 2 units high.
If the monstrous cargo starship is spherical, it would have a diameter of 88 meters. If it is cigar shaped then length = 300 meters and diameter of 50 meters.
A 1500 ton cargo capacity tramp freighter would have a wet mass of 4500 tons and a volume of 13,500 m3. Spherical shape would have a diameter of 30 meters, cigar shaped length = 100 meters long and diameter of 17 meters.
Modular ships dimension would be similar but a bit larger due to being assembled out of component parts.
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) : General rule practical minimum for ion drive, laser sail or other low thrust / long duration drive. Otherwise the poor spacecraft will take years to change orbits. Unfortunately pure solar sails are lucky to do 3 milligees.
0.6 gee (5.88 m/s2) : General rule average for high thrust / short duration drive. Useful for Hohmann transfer orbits, or crossing the Van Allen radiation belts before they fry the astronauts.
3.0 gee (29.43 m/s2) : General rule minimum to lift off from Terra's surface into LEO.
For a more in-depth look at minimum accelerations look here.
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.
This is the von Braun Round the Moon Ship
- At the bottom are the four rocket motors. During a burn, the rocket thrust they create pushes upward.
- The rocket thrust pushes upward on the thrust frame (dark blue), which is right above the motors.
- Built on top of the thrust frame is the spaceframe (light blue), the same way that the skeleton of a skyscraper is built atop the ground. The spaceframe is pushed upward by the thrust frame.
- All the other spacecraft components: personnel sphere, hydrazine tank, nitric acid tank, solar mirrors, radar antennae, and everything else is hung from the spaceframe. As the spaceframe is pushed upwards, it drags along all the spacecraft components.
Getting back to the spine/spaceframe. 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, allowing a handsome increase in valuable payload mass. It also dramatically increase the separation between a dangerously radioactive propulsion system and the crew, allowing a drastic decrease in the radiation shadow shield mass. This allows yet more handsome increases in valuable payload mass. As the cherry on top of the cake, it allows using the tumbling pigeon method of spin gravity without the direction of gravity inverting.
Please note this has never actually been used in a serious nuclear spacecraft design due to its unorthodox nature.
And warships with such a design would have their manoeuvring critically handicapped (or it's "crack-the-whip" time and the cable breaks).
The concept comes from the observation that for a given amount of structural strength, a compression member (such as a girder) generally has a higher mass that a corresponding tension member (such as a cable). And we know that every gram counts.
Charles Pellegrino and Dr. Jim Powell put it this way: current spacecraft designs using compression members are guilty of "putting the cart before the horse". At the bottom is the engines, on top of that is the thrust frame, and on top of that is rest of the spacecraft held together with girders (compression members) like a skyscraper. But what if you put the engine at the top and have it drag the rest of the spacecraft on a long cable (tension member). You'll instantly cut the structural mass by an order of magnitude or more!
And if the engines are radioactive, remember that crew radiation exposure can be cut by time, shielding, or distance. The advantage of distance is it takes far less mass than a shield composed of lead or something else massive. The break-even point is where the mass of the boom or cable is equal to the mass of the shadow shield. But the mass of a shadow shield is equal to the mass of a incredibly long cable. The HELIOS cable was about 300 to 1000 meters, the Valkyrie was ten kilometers.
But keep in mind that this design has no maneuverability at all. Agile it ain't. If you turn the ship too fast it will try to "crack the whip" and probably snap the cable. This probably makes the design unsuitable for warships, who have to jink a lot or be hit by enemy weapons fire.
Certain propulsion systems incorporate the waterskiing concept in spacecraft that use the propulsion. The main one is the Medusa, which sets off nuclear explosions inside a huge parachute-shaped sail. The sail accelerates, and drags along the payload on a long cable. Long because the payload does not want to be any closer to a series of nuclear explosions than it has to be.
The various types of sail propulsion drag the payload with a long cable as well. But for them, the long cable is not because the sail is radioactive, just that it is typically several kilometers in radius.
If the exhaust is radioactive or otherwise dangerous to hose the rest of the spacecraft with, you can have two or more engines angled so the plumes miss the ship.
Angled engines do reduce the effective thrust by an amount proportional to the cosine of the angle but for small angles it is acceptable. The delta V of the spacecraft is also reduced by the same proportion.
Note in the HELIOS design Krafft Ehricke figured that the 300 meter separation was enough to render the exhaust harmless so it does not angle the engine at all. Krafft has a single engine blasting straight at the habitat module. The only concession to the exhaust is mounting the cables on outriggers, so the cables do not pass through the zillion degree nuclear fireball exhaust plume. It would be most embarassing if the cables melted.
The waterskiing spacecraft designs are trying to subsitute almost mass-less engine standoff distance for ultra-penalty-mass radiation shield. Because on the one hand: Every Gram Counts, but on the other: nuclear radiation kills crewmembers dead.
Goddard's rocket was designed for totally different reasons (which you should have been tipped off by the fact it had no nuclear engine).
Goddard reasoned that if you put the rocket engine at the bottom and build the rest of the rocket on top of that, it would be as unstable as a waiter carrying a tall tippy bottle of wine on a tray held overhead by one hand. One minor shake of the hand and the wine goes crashing to the ground.
But if you put the rocket engine at the top and had it dragging the rest of the rocket, it would be as inherently stable as holding a pendulum by its string. If the engine tips over from its upward flight, the weight of the rest of the rocket will un-tip the engine. Right?
Nowadays rocket designers call this the Pendulum Rocket Fallacy. Meaning it looks good on paper, but it just doesn't work. Having the engines at the top is no more stable than at the bottom. A top-engine design superficially resembles a pendulum, but the system of forces acting on it are totally different.
Goddard discovered this the hard way with Nell's test flight. It rose barely 41 feet, tipped over, flew 184 feet horizontally, then augered into a cabbage field. All of his subsequent designs had the now-standard engine on the bottom arrangement.
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. Well, now that I think about it, some of the lunar dust is like clouds of microscopic razor blades so they are dangerously abrasive.
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.
For a cargo ship, the Loadmaster has to ensure that the cargo is stored in a radially symmetric balance.
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 general rule, the mass of a fuel tank loaded with liquid hydrogen will be about 87% hydrogen and 13% tank. In other words, multiply the mass of the liquid hydrogen by 0.15 to get the mass of the empty tank (0.13 / 0.87 = 0.15).
So the Polaris' 792.6 tons of hydrogen will need a tank that masses 792.6 * 0.15 = 119 tons.
87% propellant and 13% tank is for a rocket designed to land on a planet or that is capable of high acceleration. An orbit-to-orbit rocket could get by with more hydrogen and less tank. This is because the tanks can be more flimsy since they will not have to endure the stress of landing (A landing-capable rocket that uses a propellant denser than hydrogen can also get away with a smaller tank percentage). Zubrin gives the following ballpark estimates of the tank percentage:
|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 general rule is that aerobraking can kill a velocity approximately equal to the escape velocity of the planet where the aerobraking is performed (10 km/s for Venus, 11 km/s for Terra, 5 km/s for Mars, 60 km/s for Jupiter).
This will mostly be used for our purposes designing a emergency re-entry life pod, not a Solar Guard patrol ship. With a sufficiently advanced engine it is more effective just to carry more fuel, so our atomic cruiser will not need to waste mass on such a primitive device.
NASA on the other hand uses aerobraking every chance it gets, since they do not have the luxury of using atomic engines. Many of the Mars probes use aerobraking for Mars capture and to circularize their orbit. Some use their solar panels as aerobraking drage chutes in order to make a given piece of payload mass do double duty. Some of the Space Tug designs listed in the Realistic Design section economize on reaction mass by using a ballute when returning to Terra orbit.
In the movie 2010, the good ship Leonov had a one-lung propulsion system, so they needed an aerobraking ballute to slow them into Jovian orbit. If you are thinking about aerobraking, keep in mind that many worlds in the Solar System do not have atmospheres.
You can find a more in-depth look at heat shields here.
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.