Life in the Lonely Void

A major consideration behind constructing a spacecraft that is often glossed over is the brain of the spacecraft. In most cases, this is a crew module, or a remote control module relaying orders from somewhere.

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A look inside the ISS.

The reason crew compartments don’t receive the same amount of consideration, as say, the engines or the weapons, is that crew compartments have no real surprises about their design, and on larger capital ships, they are rarely a bottleneck in terms of mass, volume, power usage, or heat dissipation.

But before we discuss crews, what about alternatives? Crew provide decision making, the brains of the spacecraft, as well as providing fine grained manipulation of equipment and tools for repairs, maintenance, and so on.

The fine grained manipulation could be accomplished by minidrones, automated repair bots and the like, though handling unexpected situations is rather tricky without a human or artificial intelligence.

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Though if DARPA’s work is any indicator, humanoid robots may be the ideal maintenance workers rather than minidrones.

Brains of the spacecraft can be replaced with remote control, or with an artificial intelligence.

Remote control can be spoofed or jammed, but there are countermeasures and counter-countermeasure. The main issue with remote control is the speed of light lag. Beyond high orbit of a moon, for example, the speed of light lag is too great for combat. Additionally, long term journeys have much greater potential for unexpected failure.

This means remote control is restricted to drones and missiles, remotely operated and ordered by the nearest capital ship or celestial body.

Artificial Intelligence (AI) is an interesting solution to the problem of having crews. Crews are expensive to train, take up precious mass and volume, and require power. On top of that, the heat they need to dump out can be a problem if you want to talk Stealth in Space.

However, AI is more than a series of algorithms running on a laptop. Currently, certain problems of space warfare are best solved with algorithms (see Misconceptions about Space Warfare), such as leading targets hundreds of kilometers away moving at multiple kilometers per second.

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AlphaGo is a one-problem AI, but it could be the first step towards a general intelligence.

On the other hand, other classes of problems are best solved with intelligence and creativity. In particular, how to see through enemy deceptions, laying deceptions, handling unexpected scenarios and failures, and so on are all problems that algorithms would fail badly at. Anything creative or anything an algorithm is not explicitly designed for would throw it for a loop.

That means full blown Artificial General Intelligence is needed for actually commanding a military spacecraft if you want to go without crew. Additionally, it needs to be able to very carefully and precisely control minidrones to repair and maintain a spacecraft.

The field of AI today is nowhere near that sort of capability. However, even if it does progress to being usable in military scenarios, it is unclear if it would be less massive, voluminous, or require less power than humans. The first AIs will likely be extremely massive and require huge amounts of power, and it’s not clear how far they could be miniaturized.

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If IBM’s Watson is any predictor of strong AI, AI may be rather massive and consume a lot of power compared to a crew.

Even when feasible AIs are developed, space militaries would be very hesitant to deploy AI-controlled spacecrafts without at least some human oversight or failsafe.

With that in mind, we are left with crews for our capital ships, and remote controls for our missiles and drones.

But just how few people can you cram into a spacecraft? Modern Supercarriers crew over 4000 people in 25 decks. In space, most of that space would be propellant tanks, and you can’t really dedicate much mass to the crew compartment. Capital ships in space would run only skeleton crews, with only small sections of the spacecraft pressurized.

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Of course, you might be able to skimp on sleeping quarter space given that you can attach sleeping crew to the floor, walls, and ceiling.

In space, crew modules are somewhat massive, yet systems like radiators, armor, and weapons usually take up far more mass.

Volume is the main problem with crew modules. Crew modules are mostly empty space filled with air. Even when you pack your humans in like sardines, the majority of the crew module remains empty space. Aside from the propellant tanks, crew modules take up the most volume of any module.

This makes Modern Nuclear Submarines the closest analog to spacecrafts in terms of crew: somewhat over 100 crew for a submarine over 100 meters long.

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Cutaway of a modern nuclear submarine.

However, nuclear submarines are fully pressurized, while spacecrafts would not. This means spacecrafts would have even less space for people, and so crew requirements were estimated at roughly half that of a modern nuclear submarine. Of course, some jobs you can’t simply halve, and larger ships with more systems require more crew.

It should be noted that crew in a spacecraft is certainly not a novel topic. Winchell Chung’s Atomic Rockets website has a great break down on all of the considerations of crew.

In Children of a Dead Earth, most capital ships run between 40 to 80 crew, and are based heavily on modern nuclear submarine crews.

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Crew complement of a very large capital ship massing about 10 kt.

screen-shot-2016-09-21-at-2-59-05-pmThese numbers are based on a tally of all the jobs needed, which scales based not by mass of the ship, but on the number of subsystems, type of subsystems, and several other factors. Thus, an enormous 10+ kiloton methane tanker can run on a tiny crew, while a small, 1 kiloton fast attack craft may require a much larger crew.

screen-shot-2016-09-21-at-2-59-10-pmWith such small crews, they would have to be highly trained to take over multiple jobs in case of injury or death of other crew members. Similar to modern nuclear submarines, crew members live 18 hour days, 6 hours on watch, and 12 hours off watch. Meals between each watch, with the enlisted men and women hot bunking to save on the precious space.

While a pure oxygen atmosphere (as seen on Skylab) is less massive and requires less pressurization than a 22% oxygen, 78% nitrogen atmosphere (as seen on the ISS), it is a fire hazard. And in combat, fire hazards are never fun.

screen-shot-2016-09-21-at-2-59-06-pmWater can be easily recycled as on the ISS. However, recycling food from human waste is a lot trickier, requiring a small ecosystem, likely using algae, to photosynthesize food from nuclear reactor grow lights. The technology to do this is much closer than AI is, and is very easily foreseeable as a staple in modern space travel.

A complete algae ecosystem able to supply nearly infinite food would be excellent for long voyages with lots of crew, such as for a colony ship or space liner. However, the dumb solution is far simpler, cheaper, and less error prone. Store the food, just like how modern nuclear submarines work, and restock at every spaceport. And in combat, getting your provisions shot up is far less of a concern than getting your algae beds destroyed.

In Children of a Dead Earth, ships by default carry provisions for 6 months, which is greater than most campaign mission in game. Only a few missions exceed 6 months, and most are one month or less.

screen-shot-2016-09-21-at-2-59-09-pmCrew modules produce a small amount of heat primarily from the lighting system, the galley cooking system (unless you’re forcing your crew to only eat Soylent), and the heat emitted by each crew member into the air. While the heat produced is minor (kilowatts) compared to the main reactor (megawatts), the low temperature (room temperature, 293 K) that the coolant runs at forces the radiators to be only somewhat smaller than the main reactor radiators.

As mentioned in prior posts, radiation is a concern for crew, which is one reason why the cylindrical shape is preferred. Getting your crew module far away from the reactors is a free way to reduce radiation below the 50 milli-Sieverts annual limit. Additionally, radiation shielding, while not negligible, is cheap and low mass enough to not be too much of a concern. It tends to only be a mass or cost problem if you absolutely want your crew module next door to your reactor.

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Radiation types and how easy they are to block.

Children of a Dead Earth simulates all types of radiation, from Alpha DecayBeta Decay, and Gamma Decay from Radioisotope Thermoelectric Generators, to Neutron Radiation (both fast and thermal) from Nuclear Fission Reactors. However, in practice, Alpha Decay and Beta Decay are more or less irrelevant to humans due to their low penetration, and Gamma Decay is rarely an issue.

Neutron radiation, on the other hand, is the bulk of the radiation problem, and it is often the main reason why your spacecraft will need radiation shielding. It generally is far worse of a problem than even the Cosmic Rays from space.

Another consideration mentioned a few times in previous posts is that crew modules are put close to the center of mass in case of fast rotations. Spinning a multi-kiloton spacecraft around fast enough to produce 9 g’s or more, enough to cause fatal damage to the crew, is rare, but it does happen in game. Keeping the crew near the center of mass reduces the centripetal acceleration on the crew in such cases.

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Although it seems you can withstand up to 46 g’s like John Stapp did, it’s not really recommended without extreme harnessing, especially in an uncontrolled or unpredictable manner.

It is very difficult to knock a multi-kiloton spacecraft into a fast spin, and if you have enough firepower to do so, you generally don’t need to slush the crew in this manner.

On the other hand, for smaller spacecraft, under a kiloton fast attack spacecraft, knocking them into a tailspin is actually rather common. To exacerbate this, small spacecraft with enormous projectile weapons can often knock themselves into unpleasant spins through recoil alone. As such, keeping the crew near the center of mass is most important on smaller spacecraft.

So that is what you need to keep your capital ships running smoothly over the months, and able to react to unexpected situations in combat! And with a crew, the brains of your ship, you have the final piece needed to assemble a spacecraft and go to war.

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Go Small or Go Home

Just how big can you feasibly make a spacecraft? The size of an aircraft carrier? The size of an asteroid? How about the size of a small moon? Today we will look at scalability of spacecrafts and the systems within.

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A large (190 m) capital ship compared against the Space Shuttle Orbiter (37 m).

When designing a spacecraft, certain questions inevitably arise concerning how it should be sized. Crewed spacecrafts very obviously have a lower size bound, since you can’t really miniaturize people like you can lasers or rocket engines. At the very least, your spacecraft needs to be able to fit people. However, there is no clear upper size bound. With missiles and drones, there is no obvious lower size bound either.

Let’s take a look at size limits of subsystems.

Power usage is more or less the primary way to increase effectiveness of systems, and size is generally the way to reduce thermal and mechanical stresses caused by this power use. But these laws are almost never linear, and often hit ultimate limits.

Take lasers, for instance. As outlined in The Photon Lance, scaling a laser up or down in size produces very little difference in power output. However, scaling it up in size reduces the power per volume and power per area so it won’t melt when activated.

This means you often want to keep your weapons and subsystems as small as possible, but it’s physical limits that force them to grow larger.

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A Nuclear Thermal Rocket (NTR) next to a Magnetoplasmadynamic (MPD) Thruster at the bottom of the image. The NTR is roughly 60 times as long, and masses 6000 times as much. Much of that difference is in the NTR’s enormous nozzle.

A trend with sizing of subsystems is that systems tend to work more efficiently when larger. A single 200 kN rocket thruster, for example, will perform more efficiently and be less massive than ten 20 kN thrusters. Larger singular systems distribute mass better and require fewer complex parts than many smaller systems.

On the other hand, those ten lower efficiency thrusters would probably be preferred in combat to the single high efficiency thruster because of redundancy. Compare a stray shot taking out all of your thrust versus taking out only one-tenth of your thrust. Clearly, there is a balance to be struck, between redundancy and efficiency.

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The Saturn V used five rockets for its first stage. If one rocket failed unexpectedly, they still had 80% of their thrust remaining. This actually happened on the Apollo 13 mission, and they were able to continue their mission (until later failures).

Similarly, crew modules come with significant overhead, such as the plumbing for the sewage and air recirculators. As a crew module expands in size, this overhead reduces proportionally to the number of people within. However, bunching all of your crew together in a single module is a major liability in combat.

Alternatively, rather than making a single large spacecraft with highly redundant systems, some playtesters went the route of smaller spacecraft with no redundant systems. In that case, the redundancy is with the spacecrafts themselves, rather than with the subsystems.

Another consideration is that smaller subsystems can be manufactured more cheaply on assembly lines compared to single large subsystems. In the era of widespread, highly advanced Additive Manufacturing, these benefits are less pronounced, however.

There are certain minimum size limits that show up with drones and missiles, too. For instance, nuclear warheads have a minimum size. The smallest nuclear device ever made was the W54 at about 20 kg and the size of a large suitcase. This lower limit is due to Critical Mass needed for fission. Thus, for missiles, their warhead tends to determine just how small you can make the missile. If your missile has no warhead, their lower size limit is based on the rocket motor generally.

For drones, it is similarly the mass and volume of the weapons on that drone which limit the size of them.

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A small drone compared to the size of a human. The majority of the drone is reaction mass to offset the mass of the weapon and radiators.

But these are all lower limits. What about upper limits?

Generally, lower limits are all the rage because you want to make everything small, compact, and low mass. The smaller (volumetrically) you can make everything, the less armor you’ll need. The less massive you make everything, the greater the delta-v and thrust you’ll have.

There is actually very little stopping you from making enormous lasers or railguns, but simply making them bigger doesn’t actually improve their effectiveness or power, it only makes them deal with thermal and mechanical stress better. Essentially, you make things big because you have to, not because you want to.

But suppose you don’t care about making the most effective spacecraft, you just want to go big.

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A large civilian craft compared to a human. The human is the small black dot in the lower right.

At this point the Square-Cube Law begins to rear its head, and that is that volume scales cubically, while surface area scales quadratically. This is why large animals are built very differently than small ones. Without gravity, these issues are not quite as severe, but they still appear.

For instance, on the positive side, larger spacecraft are more efficient about their armor-to-everything-else ratio, because armor scales by surface area, and everything else scales by volume. Large capital ships tend to be armored like tanks while smaller ships run much lighter.

But on the negative side, acceleration suffers badly. Attaching thrusters to a spacecraft scales by surface area, and the mass of spacecraft scales by volume. Thus, the larger a spacecraft becomes, the lower and lower its acceleration inevitably becomes. As found in Burn Rockets Burn, thrust is hugely important, which is why only Nuclear Thermal Rockets and Combustion Rockets see major use in combat.

A ship that can’t dodge is a sitting duck to all manner of weapons. Most capital ships in Children of a Dead Earth range from hundreds of milli-g’s to full g’s of acceleration, and even that affords only partial dodging usually. Dropping that acceleration further is often fatal in combat.

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The smallest and largest capital ships in game. Roughly a 8x difference in mass, but only a roughly 4x difference in length (219 m vs 60 m).

Another negative aspect of growing in size is that the the cross sectional area of the spacecraft grows accordingly. And having a fat targetable cross section vastly increases enemy projectile ranges against you.

For combat spacecrafts, then, miniaturizing your spacecrafts is often the most ideal choice. But what about civilian crafts? Civilian crafts make a lot more sense to balloon up in size, especially for the sanity of the passengers.

The acceleration is still a problem, as if it’s too low, the spacecraft will have difficulty getting anywhere taking enormous amounts of time. But the other issues are gone. If travel time is not an issue, such as with a multi-generational colony ship, then you could try scaling up to truly enormous sizes.

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Maybe you could hollow out a small moon to make a colony ship.

When you start hitting small moon or asteroid sizes, though, then you begin to have to worry about gravitational stresses collapsing your ship into itself! But that’s far beyond the scope of what you’ll find in Children of a Dead Earth.

The Wheels on the Spacecraft Go Round and Round

Spinning a ten kiloton spacecraft around is no easy feat. Even more impressive if you want to be able to turn on a dime. This article covers the issues of Attitude Control of spacecrafts.

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A capital ship with four main engines gimbaled off to the side to provide torque.

On land, sea, or in air, rotation is easily done by pushing off the nearest medium, with anything from a tractor tread to an impeller to a rudder. In space, no such thing is possible, which means rotation can only be accomplished in one of two ways: by expelling mass via a rocket engine, or by storing rotational momentum internally. Incidentally, the second technique is only really viable in space due to the lack of any major medium, as friction would quickly degrade stored internal momentum.

The goal of these systems is to rotate enormous spacecrafts at reasonable or high speeds in combat, while being both cheap and non-massive.

The first technique is simple. Firing a thruster off center of your spacecraft will cause it to torque. Since rotation is the goal, and rotational acceleration is not, a second thruster must be fired to decelerate it at the end. And because such a thrust would send the center of mass off center, often two thrusters on opposite sides are used to start rotating, and two different opposing thrusters are fired to stop rotating.

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A capital ship fires two vernier thrusters at opposite ends and directions to rotate. The rockets are water resistojets (hence the transparent plumes) and they tap into the main NTR propellant tanks.

These are called Vernier Thrusters, and see heavy use in space travel.

There are significant disadvantages to this method, however, chiefly that additional reaction mass is needed. Not only that, such thrusters usually can’t be Nuclear Thermal Rockets (NTRs), due to radiation concerns (recall that most crew modules are placed as far away from the main engine NTRs as possible). Cold gas thrusters don’t provide near enough thrust to be useful in combat, which means combustion rockets and resistojets are in.

Combustion rockets suffer from the issue that they require propellant(s) that are almost guaranteed to be different than NTR propellants, so additional propellant tanks must be added in, which takes up space and mass. This leaves resistojets as the prime method of providing torque to your spacecraft, since they can use the same propellant as your NTR.

Alternatively, instead of a system of multiple Vernier Thrusters spread out across your hull, simply putting a gimbal on your main thruster will do the trick instead. This allows your main engine to turn, producing off center thrust on your ship, rotating it. In this way, your main engines can serve the dual purpose of getting you places as well as orienting you in combat. This is one of the cheapest forms of thrust vectoring.

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A few more complex thrust vectoring designs for achieving reverse thrust.

The primary disadvantage of it is that propellant is still expended when turning, however, no additional propellant tanks are needed as your main thrusters are doing the turning. For capital ships, the amount of delta-v spent turning is negligible, though for smaller crafts like missiles, the delta-v spent can raise a few eyebrows.

A more subtle disadvantage of gimbaled thrusters is that the size of the opening that the engines need to have can balloon significantly. This can yield much larger aft sections of the ship, and increase the targetable cross section of the spacecraft heavily.

Gimbaled thrust tends to be the cheapest and simplest solution to turning in space, and many capital ships and all drones and missiles in Children of a Dead Earth use them. Some capital ships opt for resistojet Vernier Thrusters, primarily for getting a smaller targetable cross section.

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A missile’s rocket nozzle is slightly gimbaled to the side, only a few degrees off center, generating tremendous torque. Screen distortion is from the camera being inside the rocket plume.

But suppose you don’t want to spend precious propellant turning? Then you need to invest in the second technique towards turning in space: exploiting Conservation of Angular Momentum.

Given a system without little or no external medium (such as space) and assuming you don’t want to expend propellant, the only way to rotate is by using conservation of angular momentum.

A quick example. Consider a pair of identical masses loosely attached to one another, floating in space. If one of the masses begins to spin in one direction, the other mass must spin in the opposite direction at an equal speed, otherwise it would violate Newton’s Laws of Motion.

This is the basic principle of operation for a Reaction Wheel, which is a flywheel with a motor attached. A flywheel is a mass with a high Moment of Inertia, or ability to resist rotational changes, along a single axis. When you spin a reaction wheel inside your ship using the motor, your spacecraft must spin in the opposite direction. Three reaction wheels must be used to get a full range of motion (one for each axis: pitch, yaw and roll). The Kepler Spacecraft uses reaction wheels.

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A simple reaction wheel.

A Momentum Wheel is a reaction wheel which is constantly spinning at a very high speed. If a momentum wheel is spinning inside a spacecraft, simply braking it can cause a huge change in rotational momentum, causing a significant torque on your ship. Six momentum wheels are needed instead of three, two for each axis in opposite directions.

Momentum Wheels are often used for spin stabilization, as the huge amount of stored rotational energy will resist external torques. The Hubble Space Telescope uses Momentum Wheels.

Control Moment Gyroscope (CMG) is a single momentum wheel on a dual-axis gyroscope. By rotating the momentum wheel about the two gimbal axis, the angular momentum balance of the spacecraft can be altered at a whim. A single CMG can rotate a spacecraft along any axis by simply rotating the gyroscope to be in line with that axis. They are the most expensive and complex of the above systems, and are used on the ISS.

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A Control Moment Gyroscope. The two axis of the gimbal allow the wheel to be oriented in any direction.

These systems promise the ability to rotate your spacecraft without expending propellant. Not only that, they require no exposed external systems, so they can’t be damaged unless the main bulkhead armor is penetrated. Sounds like a win-win, right?

Unfortunately, their effectiveness is very poor for combat operations. Modern CMGs are often used to very slowly change orientations over the course of minutes and hours. I originally had never intended to implement Vernier Thrusters or Gimbaled Thrusters in game, and was only going to use Momentum Wheels and CMGs. That rapidly fell apart when I did the math on them.

Consider the above example with the two masses on a string. Because they are identical, the spins will be equal and opposite. But if one mass has twice the moment of inertia, it will spin at half the (reverse) speed as the other. The greater the moment of inertia, the slower the spin.

If one of these masses is the spacecraft and the other is the reaction wheel, you want the spacecraft to have a lower moment of inertia. Thus, if your spacecraft has a moment of inertia 100 times that of your reaction wheel, it will spin 100 times slower than that reaction wheel.

Moment of Inertia is proportional to mass and the square of distance from the rotation axis. Roughly speaking then, very voluminous and very massive objects will have the greatest moment of inertia.

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When headspinning, rotational speed can be increased by pulling ones’ legs in. This reduces the distance from the rotation axis and thus reduces the moment of inertia.

Spacecrafts by nature will have a greater volume than your reaction wheels, since they envelope these wheels. And they are guaranteed to have a greater mass than your reaction wheels, unless you are okay with an abysmal mass ratio (less than 2). Thus, you are guaranteed a moment of inertia far tinier than your spacecraft’s moment of inertia. And as I discovered, even spinning your wheels at enormous speeds yields rotations that take minutes or even hours.

In short, these techniques were not viable for combat rotations, barring some sort of future technology.

This leaves thrusters as the only viable method of spinning about in combat. How fast can they spin?

Because thrusters affect acceleration rather than velocity, the answer is that it varies. For instance, the time to spin 90 degrees is not going to be twice the time it takes to spin 45 degrees. And it varies based on which axis of rotation is used.

A simple metric is the Full Turnabout Time, which is the time it takes to spin 180 degrees about the slowest axis. This is essentially the “slowest” possible turning time for the ship, and most turns will be much faster, a fraction of this time.

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When the enemy targets parts of your ship away from your center of mass, you can dodge simply by spinning along one axis. This particular ship is spinning with a single gimbaled NTR.

For medium sized capital ships with gimbaled thrusters in game, 20-30 seconds is a common value. Capital ships with vernier thrusters tend in the 10-20 second range, as do small sized capital ships. Very large capital ships can take up to a minute to do a full turnabout. Gimbaled drones and missiles tend to take 5 seconds or less for a full turnabout, with some being able to do a 180 in under a second.

Much faster turnabouts are possible by simply adding more and more vernier thrusters or gimbaled thrusters. However, this is often fast enough to deal with the rapidly changing nature of space combat. It is rare for a capital ships to ever need to flip a 180. Most of their turns are much smaller angle shifts, small dodges and broadsides.

The Photon Lance

We’ve looked into mass weapons, now let’s take a peek at lasers.

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A laser firing. This one is visible when fired within the atmosphere.

Comparatively, lasers are far more complex than any of the weapon designs we’ve looked into, with far more components and considerations.

For example, in module design, railguns and the like can be optimized by simple tweaking and trial and error. On the other hand, it is very difficult to do so when designing lasers. The relations between the inputs and outputs are not only nonlinear, they are absolutely not monotonic, so simply using trial and error to find ideal cases is not always possible.

While there was an explosion of different design options and choices for railguns as we saw in Origin Stories, with lasers, it was far worse. First you’ll choose your laser type from amongst a staggering array of types. Then you’ll need a pumping source, which includes a nearly infinite number of pumping and lasing geometries, each with different advantages. And you’ll probably want to add a nonlinear crystal to harness Frequency Switching in order to double, triple, or quadruple your photon frequency.

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All the laser inputs you can tweak on the right, and the outputs on the left.

Then you need to worry about the optics between each and every subsystem, ensuring the photons don’t seriously damage each lens, mirror, or nonlinear crystal at each point. Plus, you need to arbitrarily focus your beam at different distances, either with a Zoom Lens or with a Deformable Mirror (though in practice, zoom lens tend to be impractical for extremely long ranges, meaning you’re usually stuck with using a deformable mirror).

Also, and if you want to pulse your laser, you’ll need to use Mode LockingQ Switching, or Gain Switching to do so. Finally, while mechanical stress are basically irrelevant for lasers (recoil of lasers is minuscule), thermal stresses are huge. Cooling your laser effectively is one of the most important parts of building a working laser.

Laser construction is not for the faint of heart, but the outputs of lasers are actually fairly simple compared to mass weapons. While mass weapons produce a projectile of varying dimensions and materials at a certain speed, possibly with excess temperature, and possibly carrying a complex payload, lasers just shoot a packet of photons. Even if the laser is continuous, the beam fired can be considered series of discrete packets.

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Simplified diagram of laser ablation effects.

Since laser beams move at the speed of light, it is actually impossible to dodge a laser unless you are always dodging. This is because the speed of light is the speed at which information travels in the universe. Thus, you can never determine where a laser will be until it actually hits you. This would be impossibly overpowered in warfare were it not for diffraction.

A packet of photons is focused on a single point of a certain size, and carries a discrete amount of energy of a single wavelength/frequency. Technically, due to quantum mechanics, particularly the Uncertainty Principle, there will be many different wavelengths, an uncertain size, and an uncertain amount of energy. These quantum effects are glossed over because approximating the entire packet as a discrete bundle is both simpler and still remains very close to reality.

The only quantum effect that significantly affects the output of a laser in terms of warfare is Diffraction.

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Diffraction pattern of a red laser passing through an aperture.

Diffraction causes a laser beam to diffuse the further it gets from its exit aperture, spreading out the energy of the laser. This is a problem because the energy a beam carries is not what inflicts damage. The energy per unit area, or Fluence, is what causes damage. For continuous beams, it would be the power per unit area, or Irradiance.

A hypothetically perfect laser will suffer from diffraction and is referred to as being Diffraction Limited. But this is not what is actually limits most actual high powered lasers in warfare.

Most high powered lasers will never even come close to being diffraction limited.

Truth is, the Beam Waist, or the minimum diameter the beam will achieve, is a more effective measurement of how damaging a laser is. A perfect laser will have a beam waist limited only by diffraction, but lasers like that don’t exist. And the greater the power of a laser, the further and further away that laser strays from being diffraction limited.

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The Beam Waist is twice of w_0

A good way to measure this is with the Beam Quality of the laser, or with the M Squared. M^2 is the beam quality factor, which can be considered a multiplier of the beam waist. So, an M^2 of 5 means the beam waist is 5 times that of a diffraction limited beam. In terms of area, this means the beam is 25 (5^2) times the area of a diffraction limited beam, or 25 times as weak. As you can see, having a M^2 even in the high single digits will yield beams a far cry from “perfect” diffraction limited beams.

In practice, it is not the pumping efficiency, nor the power supply, nor diffraction, which ultimately limits lasers. It is the beam quality factor. In the end, M^2 ends up being the number one limit on laser damage in combat.

In small lasers, M^2 close to 1 is easily achieved without issue, but in high power lasers, M^2 can easily reach into the millions if not accounted for. This is because generally, M^2 scales linearly with laser power.

Each optical component of a laser affects the M^2. In particular, using a deformable mirror to focus a laser at arbitrarily long ranges (such as from 1 km to 100 km) is measured at reducing M^2 to between 1.5 to 3. Problematic, but not exactly debilitating.

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A high energy laser developed jointly by the US and Israel. Note the deformable mirror it uses for focusing the beam at arbitrarily long ranges.

But the main issue is Thermal Lensing (Note that this is different from Thermal Blooming, which only occurs outside the laser in the presence of an atmosphere). The heating of a laser gain medium generates a thermal lens which defocuses the beam, ultimately widening the beam waist, preventing the beam from focusing properly. Also note that thermal lensing actually occurs in every single optical component of the laser, though it is strongest in the lasing medium.

Thermal lensing increases M^2 roughly linearly with input power. This means if you have 1 kW laser with a M^2 of 1.5 (which is reasonable), this means dumping 1 MW into that same laser will yield a M^2 of about 1500 (going the other way does not work, since M^2 can’t be less than 1).

One might try to predict the thermal conditions and add in an actual lens reversing the thermal lens. Unfortunately, the thermal lens is not a perfect lens either, and the imperfections of this lens remain the primary cause of beam quality reduction.

Fiber lasers are often touted as a solution to thermal lensing. They are considered immune to thermal lensing except in extreme cases. Unfortunately, dumping hundreds of megawatts through a fiber laser constitutes an extreme case, and fiber lasers suffer thermal lensing nearly as badly as standard solid state lasers.

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Free Electron Lasers (FELs) are a design which do not have a gain medium to suffer thermal lensing in, however they still suffer thermal lensing is all other optical components.

The largest innovation for combating thermal lensing are negative thermal lenses. Most gain mediums have a positive thermo-optic coefficient, and this is what generates the thermal lens. Certain optical materials have a negative thermo-optic coefficient, which produces a thermal lens inverse of what the gain medium produces. Ideally, this negative thermal lens would perfectly reverse the positive thermal lens, but in practice, the M^2 still suffers.

In the end, the primary way to combat thermal lensing is with cooling. And the primary way to cool your laser is to make it bigger.

If the proportions of a laser are kept identical, lasers can be scaled up or down with minimal change to the laser’s efficiency or output power. Indeed, you can pump 100 MW or power into a tiny palm-sized laser just as well as you can into a building-sized laser, and they will produce roughly equal beams in terms of efficiency and M^2. The only difference is that the palm-sized laser will melt into slag when you try to fire it.

Laser size is mostly a matter of how much do you need to distribute the heat of the laser pumping. And if you want to combat thermal lensing, you’ll want a really big laser. This means laser size is essentially about cooling, and by extension, having a low M^2.

And because size is closely related to mass, and mass is so critical to spacecraft design, the limiting factor of using lasers in space is how poor of an M^2 you want to have, given a certain power level. Though the radiator mass needed for the enormous power supplies is the other major consideration.

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For crafts built around high powered lasers, most of the size and mass ends up being the radiators.

A final way to combat thermal lensing is to use Beam Combining of many smaller lasers. Combining beams side by side increases the beam waist linearly, which defeats the point, but Filled Aperture Techniques can combine beams without increasing the beam waist. However, this technique produces greater inefficiency to the final beam. The ideal way to combine beams is to simply use multiple separate lasers which all focus on a single point.

In Children of a Dead Earth, either single large lasers or multiple small, separately focused lasers can be used, and both have varying pros and cons.

Of course, designing lasers in Children of a Dead Earth is often far more difficult than designing any other system, so there are plenty of factory-made options for players to use. But the option is always there for those who really want to explore the depths of laser construction!

Space Guns

In the prior post, Misconceptions about Space Warfare, combat was roughly explored.

The general idea was that missiles and drones dominate long range combat since given enough delta-v, they can go anywhere a capital ship can go. Projectile weapons tend to dominate mid range combat, when capital ships or drones are tens or hundreds of kilometers away. And finally, lasers dominate short range, but also see use for mid range precision damage.

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What it’s like on the receiving end of a drone projectile barrage. The occasional ricochet is also physically based.

Today, we’ll explore projectile weapons. The big three projectile launchers used most are Conventional GunsRailguns, and Coilguns. There are also Linear Induction Motors used (railguns are technically a specialization of Linear Motors), which do not see major use aside from electromagnetic catapulting.

At their core, projectile weapons are concerned with two things: how big of a projectile it can launch, and how fast it can launched.

However, there are a multitude of other considerations as well. Mass. Cost. Size. Power Consumption. Cooling speed and temperature. Turning speed and angle. Armor against enemy attacks. Ammunition mass, cost, volume, and volatility. These are all accounted for in Children of a Dead Earth.

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Firing a railgun. Ganymede in the background.

Before we contrast our three weapons, let’s start with commonalities.

All three weapon designs end up being tubular shaped, and accelerate their projectiles down that tube. This means these weapons are Cantilever Beams, or beams supported at one end, and as such, they will vibrate upon firing, causing inaccuracy and possibly shattering the weapon if the stress is too great. This is one limitation alluded to in a previous post (Origin Stories).

Another consideration is recoil, which all weapons must have, lest they violate conservation of momentum. Recoil stresses can also damage the weapon, and must be accounted for. Unless you use a Recoilless Rifle. Recoilless rifles have the issue that they need an exit pathway for the exhaust gases, which is tricky to make work in a large spacecraft, especially if the weapon is turreted.

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Diagram of a recoilless rifle.

Note: Recoilless railguns or recoilless coilguns have never been attempted, but they are hypothetically possible, if you wish to eject the rails or the coils. That would likely be more expensive than what it’s worth, however.

A final concern is cooling. All of these weapon designs can use simple radiative cooling effectively in space to cool down, letting their long, exposed barrels radiate away all their excess heat. This is actually quite effective, and it is uncommon for projectile weapons to require additional radiators beyond their own gun barrel (unless you count the reactors powering them, which is a different story).

Now the differences.

Conventional guns detonate an explosive, and use the expansion of gases from that combustion reaction to accelerate a projectile down the tube. It’s more or less a combustion rocket engine with a bullet stopping it up. The tube is nothing more than a container to keep the gases in. As a result, the tube is cheap, the explosive ammunition is cheap, and no external power is needed. The downsides are lower muzzle velocities (less than 2 km/s usually) and the ammunition is very volatile.

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An ammo bay explodes, tearing the capital ship in half. Note the explosion is faint and spherical. Explosions in space lose all brightness and color microseconds after combusting.

Volatile ammunition is a problem not just for when your ammo bays get hit, but for lasers as well. Precision lasers love conventional guns, as they can heat up the tube, prematurely detonating the round, and also potentially shattering the weakened gun barrel in the process.

Railguns run current through a pair of rails with a sliding armature between them, and the Lorentz Force that results from the current loop accelerates the projectile armature. They tend to have much higher muzzle velocities (<10 km/s) and nonvolatile ammunition. On the other hand, they require huge power draws, and the rails/barrel tend to be much more expensive and massive. Due to the way the rails ablate from heat and friction, railguns excel with smaller projectiles, and suffer with larger ones. All things considered, smaller projectiles are easier to make more accurate.

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Designing a powerful 13 MW coilgun.

Coilguns run current through a series of loops, and use the magnetic field that results from these current loops to accelerate a magnetic armature down the barrel. They tend to have comparably high muzzle velocities as railguns, and also have nonvolatile ammunition. Their downsides are huge power draws again, but the coils/barrel tends to be somewhat cheaper and less massive than railguns. On the flip side, the ammunition is usually very expensive (unless you want to use cheap magnetic material like Iron, which yields much lower exit velocities compared to exotic stuff like Magnetic Metal Glass). In stark contrast to railguns, coilgun projectiles excel with larger projectiles, and suffer with smaller ones. This is due to Magnetic Saturation, where projectiles become saturated, and begin accelerating much slower, and it can only really be fought by using more and more massive projectiles (longer barrels do not help).

In a way, the three weapons tend to have their own niche in space warfare.

Conventional guns are cheap, and perfect for putting on disposable drones and small crafts without huge power supplies. Also, small crafts will be fast enough to get into range, as conventional guns have lower exit velocities and thus shorter ranges.

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Conventional guns are cheap, low power, and small, which makes them the ideal weapon for small drones. Ceres in the background.

Railguns and Coilguns both have comparable exit velocities and power consumptions, much higher than conventional guns, and they dominate the capital ship battle space.

Railgun projectiles, though, tend to be smaller, less damaging, yet more accurate. This makes railguns the main point defense projectile system against drones and missiles (though lasers tend to beat them out against drones). Railguns also enjoy prominent use against enemy capital ships, great for perforating Whipple Shields and wearing down main bulkheads. The main autocannons in any capital ship engagement.

Coilguns, with their expensive and massive projectiles, tend to be limited to select ships which can afford the mass of their weapons. They form the inaccurate but devastating heavy hitters of capital ship combat.

These are the main constituents of mid to close range combat. There are a few projectile weapon technologies that were passed over for various reasons, but should be mentioned here.

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A two stage light gas gun. Much bulkier than its electromagnetic brethren.

Light Gas Guns are a weapon which is capable of reaching similar exit velocities as railguns and coilguns. They are based on the principle that the speed of sound in a light gas (like hydrogen) is much higher than the speed of sound in air. With that in mind, a projectile can be accelerated at the speed of sound in the light gas using an explosive piston compressing that gas. In a sense, a light gas gun is like a spring airgun, only it uses a light gas instead of air. They also have none of the high power requirements of railguns or coilguns.

The downsides of light gas guns are their large size, and large and volatile ammunition. Each round launched requires not just explosives to hit the piston, but also a significant amount of light gas to accelerate it. As earlier posts pointed out (Gasping for Fumes), light gases like hydrogen have terrible densities, requiring huge volumes. Your ammo bay, in addition to exploding if hit, is going to be prohibitively large, making light gas guns not particularly viable for space warfare.

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A Ram Accelerator

Ram Accelerators are weapons which launch a projectile supersonically into a tube of combustable gases. Using scramjet technology, the weapon will accelerate even faster through the tube of gases. It has the advantages of a conventional gun (cheap, low power) with muzzle velocities comparable to railguns and coilguns. However, it requires additional combusting gases with each firing, giving it similar problems to light gas guns.

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An Explosively Formed Penetrator.

Explosively Formed Penetators are modern day weapons (they currently see heavy use in Iraq as IEDs) which uses a huge amount of explosives shaped in a lens to form a jet of molten metal and launch it at a target. Although it is primarily used as a warhead (and referred to as a Shaped Charge in that case), it can be used as a long range weapon. It is competitive with coilgun and railgun muzzle velocities, at the expense of only being able to shoot an explosively shaped projectile, meaning no payloads can be used with this. One major issue is the vulnerable ammo bay, which is like conventional gun’s ammo bay, but much worse. One hit, and the bay will have enough explosives to instantly shred the entire ship apart.

The other major flaw is that this weapon is that it’s absolute laser bait. The weapon is large, and the explosives are only covered by a thin coating of material, which makes for an easy precision laser hit. Because the explosives must be detonated in the correct manner, a laser-induced detonation is likely to severely damage the weapon as soon as any protective armor is pulled back.

Helical Railguns are a cross between a coilgun and a railgun. These systems have very little literature written on them, and the technology does not exist in a practical form, nor have their limitations and promises been studied heavily.

Nuclear Launched Projectiles are a technology where nuclear detonations are used to fling projectiles at a target (one test yielded a whopping 66 km/s). The main problem is that this requires the gun to be very far away from your capital ships, a single-shot drone essentially. Very little research has been done into this sort of weapon, so its actual viability for warfare is unclear. It is likely to be extremely cost ineffective.

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A Voitenko Compressor, the only known practical method for generating enormous velocities.

Finally, Voitenko Compressors are guns which uses explosives to shape a gas into a shockwave to launches projectiles at enormous velocities, 60 km/s or higher. It was developed in the 1960s but little progress has been made with it, as a firing of it destroys the entire weapon, as well anything surrounding it. This relegates its use to a single-shot drone, once again, if these problems can’t be resolved. In the future, it could end up being the most powerful projectile ever developed, but currently, it is not a viable technology.

That was a small survey of possible future technologies, and most were not implemented because Children of a Dead Earth is near future. Far future technologies do not have the same rigorous application of engineering analysis, and so there no data on these technologies’ limitations, scaling laws, or true performance.

But what do we actually shoot? There’s more to what you shoot than simply mass, even for small weapons. Even if you’re not launching a payload, or a small gyrojet, or even a full blown missile, the shape and material of your projectile still make a big difference on how it will damage the enemy. We’ll explore these in a future post.

 

Gasping for Fumes

Finally we take a look at which propellant we should use for our rocket motor here. As mentioned in earlier posts, the two prime candidates for near future warship propulsion are the combustion rocket, and solid core Nuclear Thermal Rocket (NTR).

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NERVA, the first Nuclear Thermal Rocket ever made, was developed in the 1970s. Later NTR designs have since improved on the concept.

Some reminders. Combustion rockets tend to achieve up to 5 km/s of exhaust velocity, and NTRs achieve almost twice that at their best. At the same time, NTRs suffer from lower thrust generally. NTRs in Children of a Dead Earth generally achieve around 3000 K temperatures in their reactor, limited by the materials that make up the core. Combustion rockets can achieve greater temperatures, but it’s wholly dependent upon the reaction used and the stoichiometric mixture ratio of the propellants (if using a multi-propellant reaction).

A popular combustion rocket is the LOX/LH2 engine, which uses liquid oxygen and liquid hydrogen to achieve almost 3000 K as well (assuming a 1:1 mixture ratio). This is the main engine of the space shuttle orbiter, and I’ll refer it to primarily when discussing combustion rockets, though later we’ll explore its limitations, and switch to different reactions.

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The Space Shuttle main engines, LOX/LH2 combustion rockets.

Looking at the energy densities of nuclear energy versus chemical energy, one comes to the realization that nuclear power is roughly 600,000 more energy dense than hydrogen. So how on earth is a hydrogen combustion rocket even remotely comparable to a nuclear rocket?

After all, remember the rocket power equation:

P=\frac{1}{2} T v_e

Where T is the Thrust, v_e is the exhaust velocity, and P is the power. If you increase the power by 600,000, either the thrust or the exhaust velocity must also increase by 600,000.

The trouble comes with releasing that power all at once. We have the ability to do so: it’s called a nuclear bomb. However, releasing it in a way that we can control is difficult, and must be done with a nuclear reactor. (This is one reason why the theoretical Nuclear Salt Water Rocket is so powerful: it tries to unlock that 600,000x power factor and still control it.)

A nuclear reactor’s rate of energy release can be seen through how high the temperature of the core can get. This means that between a NTR with a chamber temperature of 3000 K and a combustion rocket with a chamber temperature of 3000K, if they have identical mass flow rates, they must have identical rocket power.

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Three different ships with three different exhaust plumes. From the top, methane NTR, water NTR, combustion rocket. The exhaust plume shape and size is physically based, deriving from refractive index spectra data and gas expansion calculations. Note that the water NTR’s exhaust plume is invisible.

Mass flow rate is how fast you can feed propellant into the rocket, which is governed by the turbopump injector you use to feed the rocket. The flow rate increases with pump size and with pump speed, and in general, is the same between an NTR and a combustion rocket.

This means, given an NTR and a combustion rocket of similar sizes and similar temperatures, the total power is roughly the same. And if we assume the exhaust velocity of the NTR is roughly twice that of the combustion rocket, the thrust of the NTR must be roughly half that of the combustion rocket. By extension, if the NTR has the same exhaust velocity as the combustion rocket, then the thrust must be the same.

A more direct way to see this is to look at the rocket thrust equation:

T=\dot{m} v_e

Where T is the thrust, \dot{m} is the mass flow rate, and v_e is the exhaust velocity. It’s obvious from this that given a constant mass flow rate, exhaust velocity and thrust are inversely proportional. On the other hand, in order to increase your rocket’s thrust, you simply need to increase the mass flow rate by using a bigger turbopump.

Essentially, this means the biggest advantage of NTRs, their high exhaust velocity, is the root cause of their lower thrust. Additionally, NTRs which do not have this advantage, the high exhaust velocities, have comparable thrust as combustion rockets!

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List of NTRs, showing their propellants and their exhaust velocities. You can also go for more exotic propellants not listed here if you so desire.

In Children of a Dead Earth, Methane is the primary propellant used, because it achieves slightly better exhaust velocities than the best combustion rockets, which means in terms of thrust, it’s only slightly worse than combustion rockets. Decane and Water are also other NTR propellants that see heavy use.

But at that point, is there a purpose to using NTRs at all? If we only use NTRs that yield roughly similar stats to combustion rockets, why not just go with combustion rockets altogether? After all, combustion rockets are cheaper, don’t spew neutron radiation, and are somewhat less massive.

The trouble with combustion rockets, particularly the LOX/LH2 rocket, is the propellants. As mentioned in the previous post (Slosh Baffles), each propellant tank has an ultimate mass ratio ceiling. Roughly speaking, higher density propellants have higher allowed mass ratios. Given standard tank materials, water has an excellent mass ratio ceiling (in the hundreds), while hydrogen has an awful mass ratio limit (< 10 generally).

When using a bipropellant (like LOX/LH2), this mass ratio limit is primarily governed by the worst propellant. So in the case of LOX/LH2, the mass ratio limit is extremely low, because hydrogen’s mass ratio limit is low. Compare that to a Water NTR. A Water NTR will achieve comparable exhaust velocities and thrusts, but water is very high density compared to hydrogen, allowing much higher mass ratios.

On top of this, high density propellants allow your ships to be much smaller, making them much harder to hit in combat, and as indicted in earlier posts, minimizing your targetable surface area is critical.

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A drone’s internals consists basically of propellant tanks and a rocket, emphasizing just how critical propellant density is towards reducing the targetable surface area.

Much more dense chemical propellants are needed to compete with the mass ratio limits. At this point, we have to discard the assumption that we are using the LOX/LH2 reaction. However, when looking into different chemical reactions, one finds that more dense chemical propellants tend to yield much higher exhaust molar mass.

In thermal rockets, the exhaust velocity is based primarily upon the temperature and the molar mass. Chemical reactions that have competitive or better mass ratio limits tend to yield somewhat lower exhaust velocities.

On the flip side, combustion rockets with certain reactions (particularly those involving fluorine) can achieve greater chamber temperatures than NTRs using clever cooling techniques not viable for NTRs. This means the total power of these rockets exceeds that of solid core NTRs. However, they tend to have low exhaust velocities once again, which means the power manifests as much higher thrusts.

Finally, what about the costs of propellants? Unlike just about every other equation in Children of a Dead Earth, determining the cost of something has no hard and fast rules. As a result, propellant costs are estimated primarily based on solar abundance, and on ease of extraction from common celestial bodies. In this way, common NTR propellants tend to be quite cheap. Combustion rockets with high density propellants end up being much more expensive comparatively.

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Solar abundance chart. Recall that Children of a Dead Earth is set entirely in space, which means that Solar abundance is used, not Terran abundance, which has a different chart.

So where does this leave us?

If you want thrust, thrust, thrust, you should go with combustion rockets with high density propellants. Find a reaction with a high chamber temperature and a low exhaust velocity. The high density propellants might comparatively pricey against NTR propellants, though. This sort of drive is generally what most drones and smaller capital ships in Children of a Dead Earth use.

If you want high thrust but still want a reasonable amount of delta-v, NTRs tend to win out with certain propellants like Methane or Decane. This is what ended up going on most large capital ships. These drives tend to be the good-at-everything, excel-at-nothing choice.

And if you want middling thrust and an even higher delta-v, go all the way and grab a Hydrogen Deuteride NTR. Very few ships ended up falling into this use case, though.

Finally, if you want cheap, go for a monopropellant combustion rocket. Good thrust, awful exhaust velocity, but cheaper than dirt. This is what most small, disposable missiles use in game.

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Nitromethane rockets. Cheap, light, tiny, and decent thrust. The nozzle is completely removed to save on mass, at the price of poorer thrust and exhaust velocity.

And of course, if thrust is totally irrelevant to you, maybe go for an ion thruster. Only a real option if you’re making a non-combat ship and don’t ever plan to dodge. And if you are okay with taking years to get anywhere.

One final note: It may surprise some readers to find that Hydrogen Deuteride (HD) NTRs performs better (9.1 km/s) than pure Hydrogen NTRs (9.0 km/s), especially considering that Hydrogen (H_2) has a lower molar mass than Hydrogen Deuteride. This surprised me when I saw it as well.

As it turns out, the Gibbs free energy of formation of monatomic Deuterium is lower than that of monatomic Hydrogen, which yields a much lower dissociation temperature. At 3000 K, H_2 dissociation is less than 1%, while HD dissociation is nearly 100%, yielding higher exhaust velocities. As a result, HD is both denser (has a higher mass ratio limit) than H_2 and has a higher exhaust velocity, making it better in nearly every way. The only real advantage is that H_2 is slightly cheaper than HD.

And there you have an analysis of the major near future rocket engines that would see use in space warfare.

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The choices allowed when designing your own rocket cover an enormous breadth of possibilities.

In the end, however, I am eager to see what sort of rockets that the players of Children of a Dead Earth can come up. Everything from the propellants to the stoichiometric mixture ratio, to the dimensions and shape of the rocket nozzle, to the turbopump injector attributes are editable in game. There are likely plenty of unexplored designs here that may beat out the designs I’ve made.

Slosh Baffles

So much time is spent discussing rocket engines that one of the most important parts of a rocket is glossed over: the propellant tanks. A significant amount of engineering goes into them, despite their simple appearance.

A rocket’s liquid propellant tank involves a number of considerations, such as propellant boil off, corrosion of the tank material, cryogenic insulation, slosh compensation, and pressurization. In space, without one g of gravity constantly pushing down, simply getting the propellant to the engine is a problem, since there is no force pushing the propellant into the rocket’s thrust chamber.

All of those issues must be dealt with using the least amount of mass, because of the rocket equation.

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NASA stopped painting the space shuttle’s external tank white after two launches and saved on roughly 272 kg of dry mass.

Indeed, propellant tanks tend to be one of the largest contributors of mass to a spacecraft. An oft made comparison is that rocket propellant tank walls tend to be proportionally thinner than aluminum cans in order to skimp on mass. In Children of a Dead Earth, armor tends to beat out propellant tanks in terms of mass, which immediately begs the question: why don’t we use a Monocoque design?

A Monocoque design builds the propellant tank into the outer skin of the spacecraft, rather than having separate propellant tanks at all, and it is used by a number of rockets in modern times, such as SpaceX’s Falcon 1. Thus, armor doubles as propellant tank as well.

 

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The Saturn V used a semi-monocoque design.

However, when a propellant tank suffers an external force such as that from a projectile, a water hammer, or a fluid shockwave forms within the tank, which can and usually will destroy the propellant tank. Thus, a monocoque propellant tank need not even be penetrated to be disabled. Enemies can simply hit the armor of the spacecraft hard enough to trigger a water hammer, and never even have to get close to penetrating the armor to render the spacecraft unable to move.

As a result, propellant tanks are kept separate from the armor skin. It costs more mass, but not significantly more, because it means the propellant tanks can be made much thinner.

Since Children of a Dead Earth takes place entirely in space without gravity, getting the propellant from the tanks into the rocket engine doesn’t happen automatically. There are a number of solutions to this issue, from ullage rockets (small solid fuel rockets designed to push the spacecraft forward, forcing the liquid propellant to the rear of the craft) to pressure diaphragms to piston expulsion devices.

 

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Designs for both various pressurized diaphragms and a pressurized piston.

 

In Children of a Dead Earth, surface tension devices, or systems which use the surface tension of the propellant to pull it towards the engine, in tandem with a turbopump injector are used. They do not need the additional pressurized gas that pressure diaphragms require, and the turbopump feed needs only slight pressurization of the tanks, yielding thinner walls.

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Several designs of turbopump fed bipropellant rockets. Nuclear Thermal Rocket designs are much simpler, requiring a simple propellant pump, and using an external power source rather than a turbine.

The lower pressure of the propellant tank also is valuable for avoiding water hammers for when the spacecraft undergoes rapid acceleration. Low pressure tanks also makes it easier to compensate for slosh effects with anti-slosh baffles within the tank.

On top of those considerations, cryogenic propellants may need to be insulated, although this is much less of a problem in space, as spacecrafts are not built in atmosphere, and so there is no convection of room temperature air always around the craft. Some propellants are corrosive to a lot of materials, and can only be stored in propellant tanks of certain materials. Finally, cryogenic propellants boil away at a slow but steady rate, and this too needs to be taken into account.

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Assembly of the first stage of the Saturn V.

A last note on tank mass. Spherical tanks once again save the most mass, however, cylinders fit much better in cylindrical spacecrafts (discussed in blog post Why Does it Look Like That? (Part 2)), so capsule shaped propellant tanks are used.

All in all, there are a lot of details to worry about, and they all add mass, which is very troublesome for any spacecraft designer. After all, recall the rocket equation:

\Delta v = v_e \ln \frac{m_0}{m_f}

Where \Delta v is the final delta-v of your spacecraft, v_e is the rocket engine’s exhaust velocity, and \frac{m_0}{m_f} is the mass ratio, or the wet mass divided by the dry mass. Recall that the wet mass is the total mass of the spacecraft including propellant, and the dry mass is the total mass except for the propellant.

In a previous blog post, Burn Rockets Burn, I went over the fact that the only drives with reasonable thrust for space combat are chemical propulsion and nuclear propulsion. In our case, combustion rockets or solid core nuclear thermal rockets. This limits your exhaust velocity to single digits of km/s. Also recall that while thrust scales up with the number of engines, exhaust velocity remains constant.

This means that the only way to squeeze out any more delta-v for your craft is by increasing your mass ratio. In particular, reducing your dry mass, or adding more and more propellant mass. Assuming you’ve reduced your dry mass as much as possible, getting more and more delta-v is simply a matter of adding enormous amounts of propellant tanks.

Since the delta-v scales with the logarithm of the mass ratio, consider this example. Suppose you have a spacecraft with an exhaust velocity of 5 km/s, either an excellent chemical rocket, or a middling nuclear thermal rocket. A mass ratio of e (Euler’s number, ~2.7) will give you 5 km/s of delta-v. To get twice that, 10 km/s, you need a mass ratio of e^2 (~7.4), and to get three times that, 15 km/s, you need a mass ratio of e^3 (~20).

To make things less abstract, remember that a mass ratio of 20 means your spacecraft is 19 parts propellant, 1 part actual spacecraft. At that point, your actual spacecraft will be ballooning in size, because even the densest propellants tend to be lower density than the actual alloys and ceramics of spacecraft components.

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A methane tanker with a mass ratio of 29. Note that it is mostly just methane at this point (28 parts methane, 1 part spacecraft).

And how much delta-v do you need? Maneuvering in combat around a planet or high gravity moon, from what I’ve seen, requires around 5-10 km/s to remain effective in combat (for evading missiles, drones, and even the enemy fleet). Somewhat more is needed when planning interlunar transfers, and tens of km/s are needed for interplanetary traveling.

For anyone who has studied the rocket equation, this is all pretty elementary. However, there is one complication that appeared from the rocket equation which was not immediately apparent to me. Once you have a drive chosen, the exhaust velocity is absolute. Thus, to get more delta-v, you get a higher mass ratio, by adding more propellant.

But there is an ultimate limit to your mass ratio, and by extension, an ultimate limit to the delta-v of your spacecraft. Not only that, you can bump into that limit very quickly.

Most of my capital ships run Nuclear Thermal Rockets using Methane as a propellant (for reasons I’ll outline in later posts), which yields an exhaust velocity of about 6 km/s. I started making a tanker with the same engine to refuel my capital ship fleets, and I wanted them to have an enormously high delta-v in order to get just about anywhere. Yet, almost immediately, I started hitting a low delta-v ceiling, no matter how many propellant tanks I added.

This is because every propellant tank added has dry mass in addition to its propellant. Thus, each tank has it’s own separate mass ratio, and a spacecraft can never have a mass ratio that exceeds the mass ratio of its propellant tanks. This propellant tank mass ratio approaches very quickly, and it depends heavily on a number of different factors, primarily the propellant type, the tank material, and the aspect ratio of the tank.

Some numbers here. In game, I optimized Methane propellant tanks to yield a mass ratio of about 30, around 50 for Decane tanks, and several hundred for Water. Most propellants cap out at around 50. Given very exotic and expensive materials, this can be doubled or tripled, though this often runs into corrosion or insulation issues.

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A hydrogen tank with a very high aspect ratio. High aspect ratios tend to yield better mass ratios. Despite this, hydrogen tanks tends to have abysmal mass ratio because of how low density hydrogen is. This particular tank has a mass ratio of 4.2.

So, given a Methane rocket with an exhaust velocity of 5 km/s, and an ultimate mass ratio of 25 from the propellant tanks, the most delta-v your spacecraft can ever conceivably have is about 16 km/s. Yikes! That spacecraft will never make any significant interplanetary journey unless there are copious fuel depots along the way.

This emphasizes just how critical propellant depots are in space travel, and especially in space warfare.

One final way to push these limits are through rocket staging, which involves discarding your propellant tanks after use. However, if your spacecraft is armored, this involves likely dumping off a lot of expensive armor as well. A better way to do this is to take a number of propellant tankers with you, and then scuttling them after you’ve drained them out.

In Children of a Dead Earth, this is the primary way to stage an interplanetary invasion. When there are no allied propellant depots along the way, one has to take a huge number of tankers along for the ride, and then simply scuttle them at various points along the way as they are depleted.

Whew! That’s all for propellant tanks! We didn’t even get to a comparison of propellants in this post. I’ll have to get to them in a later post, but for now, you have all the challenges involved with managing your propellant tanks in space warfare.