# Supercriticality

One of the most complex parts of a spacecraft is the power supply, which usually takes the form of a nuclear reactor.

Nuclear fission is about 600,000 times more energy dense than the most energetic chemical power reactions, which very easily makes it the best power supply for space. In space, mass is a premium, so energy density is critical. Most capital ships use fission reactors to get their power.

Similarly, Radioactive Decay runs about 15,000 times more energy dense than chemical reactions, which is why Radioisotope Thermoelectric Generators (RTGs) are the next best thing. Most drones and missiles with significant power needs use RTGs. Anything with lesser power needs simply use small batteries.

Chemical energy requires tremendous amounts of mass produce reasonable amounts of power, after which this mass is ejected. This makes it not very viable for space except as rocket propellant.

Solar power becomes more or less useless further away from the sun (at Jupiter, the irradiance is 30 times lower than that on Earth). They are also much harder to armor than radiators, making them a poor investment for space warships.

Beamed power suffers from the beam waist widening very quickly over distance, which limits its effectiveness to very low orbits around celestial bodies. This occurs even with a constellation of mirrors to extend the range. Beamed power similarly require receivers that can be damaged easily, and if they are to be used in close combat, they can’t be covered up, making beamed power fairly infeasible for warfare.

Fusion Power is a power source that could make all other sources obsolete if it can be developed. In its current state, it is too far future of a technology. An additional consideration about Fusion Power is that it, along with Fission Power, are not limited by energy density, unlike the other aforementioned power sources. While the other power sources are limited by not producing enough power, Fission and Fusion Power both generate more power than modern systems could ever dream of using. Fission Power is not limited by how much nuclear fuel you have, it is limited primarily by how large your radiators are. This means any limitations on Fission Power currently will still remain even if Fusion Power replaces it.

All of this means that the main power supply in Children of a Dead Earth is nuclear fission.

In Children of a Dead Earth, nuclear reactor cores are governed by the Six Factor Formula. This rather large and complex equation which determines the effective neutron multiplication factor. Given the masses of all the materials inside the core from the fuel to the moderator to the neutron poison to the coolant, the operational characteristics of the reactor can be determined. This means the rate at which a core achieves criticality or shuts down can be predicted, and it usually takes microseconds.

Given a working reactor core, the neutron flux of a reactor can be arbitrarily controlled. The neutron flux directly determines the amount of heat the reactor will produce, which means the reactor can arbitrarily control the heat produced, and by extension, the power produced.

These fission reactors are not limited by the Uranium-235 fuel (or Pu-238 or Am-242m, etc.) inside the core. In practice, the amount of nuclear fuel is minuscule compared to the rest of the reactor elements. This is why 3% enrichment of U-235 is actually quite reasonable for reactor fuel. Contrast this with nuclear weapons, where around 97% enrichment of U-235 is preferred.

The main power limit inside the core is how hot you can make it. And generally how much heat your reactor can withstand is dependent on how large you can make the reactor to reduce energy per unit area. Additionally, the design of your fuel makes somewhat of a difference, as fuels such as TRISO allow for a Pebble Bed Reactor design, which yields somewhat higher heat tolerances.

The reason temperature is the limiting factor of a nuclear reactor, rather than the actual fuel mass, is that the energy density is so high that a nuclear reactor will never come close to unlocking all of the power of even a small amount of fuel mass. Nuclear reactor design mostly boils down to how much energy can be extracted from a tiny amount of nuclear fuel without melting to slag.

Thus, how much nuclear fuel is needed has nothing to do with how much power you need, and everything to do with whether or not your reactor can achieve a critical mass.

For this reason, using more or less energy dense nuclear fuels is basically pointless, as they all produce “too much”. The main difference between fuels is how they affect the neutron multiplication factor. Certain fuels, like Am-242m, can achieve a critical mass more easily, and thus, less nuclear fuel is needed. This means the reactor design might be made smaller for the same amount of power.

In practice, however, the mass of the radiators ultimately end up being the limiting factor on nuclear reactors.

Of course, simply creating an atomic pile and letting it spew neutrons and radioactive waste is not enough to produce power. Power needs to be extracted from the heat of these fast moving nuclear byproducts. A number of methods have been devised to do so.

Turboelectric Fission Reactors involves letting the neutrons heat up the coolant and using the hot vaporized coolant to turn a turbine. This technique is the most common, being used in just about every nuclear reactor in the world. It requires a large turbine to effectively extract the heat, as well as plenty of coolant and turbomachinery to run it properly. Due to the size, it can take a while to warm up. Due to the mass and complexity, it generally is not used for spacecrafts.

Turboelectric Fission Reactors are heat engines, meaning they can never exceed the efficiency of a Carnot Cycle:

$\eta = 1 - \frac{T_c}{T_h}$

Where $\eta$ is the efficiency, $T_c$ is the cold temperature of the coolant prior to passing through the reactor, and $T_h$ is the hot temperature of the coolant after passing through the reactor.

As noted in Why does it look like that? (Part 3), the cold temperature needs to stay high because this is the temperature the radiators will cool the reactor at. Cold radiators function abysmally and require huge amounts of mass. Similarly, the hot temperature needs to stay low to prevent the systems from cracking from the thermal stress.

The sample reactor has a radiator temperature of 1200 K and 1688 K as the hot temperature. Using the above equation, this means the efficiency of that reactor can never exceed 29%, if it were theoretically perfect. In practice, the actual reactor runs at 22% efficiency.

On Earth, turboelectric reactors often quoted at running at 60% efficiency. This is possible because the cold temperature can be brought much lower if you are using conduction or convection to cool off the reactor. In space, using only radiators forces the cold temperature to be rather hot (> 1000 K usually) in order to keep the radiators from getting too large.

Thermoelectric Fission Reactors are heat engines as well. However, instead of passing the hot coolant through a turbine, it instead passes against as a thermocouple heat exchanger. It involves much less turbomachinery, and thus can be produced in much smaller sizes with much lower masses. On the flip side, it is often much further from the theoretical Carnot Cycle efficiency than turboelectric reactors. In space, it is the primary go-to reactor design due to its low mass, simple design, and cheap cost.

Thermionic Fission Reactors uses the concept that the flow of charge carriers (such as electrons) across a potential barrier can produce power. This flow of electrons is triggered thermally, and thus is set up very similarly to the way Thermoelectric Fission Reactors work. It is also a heat engine, and sees similar use in space as the thermoelectric fission reactor.

Fission Fragment Reactors do not use coolant at all, and instead extract power by decelerating the neutrons and radioactive waste products using a magnetohydrodynamic generator. This bypasses the Carnot Cycle entirely, allowing efficiencies estimated up to 90%, far greater than any of the previously mentioned heat engines. However, it is also the least developed of all the technologies, and to date, no working Fission Fragment Reactor has been produced.

Since Children of a Dead Earth restricts itself to functioning technologies, this means nuclear reactors are restricted to Heat Engine designs. And due to the Carnot Cycle, the efficiency is forever limited by the cold temperature, or the radiator temperature.

Due to this restriction, the most massive part of a nuclear reactor is the radiators that accompany them. The power extraction machinery tends to be the next most massive piece, with the reactor core itself generally being negligible in terms of mass. On the flip side, the tiny amount of reactor fuel tends to be one of the most expensive parts of the entire system.

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# Sensors and Countermeasures

There are numerous ways to guide a missile or drone to the target. But for every potential way to guide an autonomous payload to the target, there is a countermeasure, and possible counter-countermeasures, and so on.

These techniques remain relatively unchanged from Earth, but there are a few significant differences in space. One is that there is no horizon.

Two, there is no significant intervening medium (air or water). This first makes sonar and acoustic homing irrelevant, but it also vastly reduces the effectiveness of any gaseous countermeasure like smoke. Another consequence is that exhaust plumes fade out very quickly. However, the biggest change this makes is that it reduces the noise floor heavily, making targets stand out much more against the background.

Three, there is no GPS or satellite network for additional guidance help, and if there is one, only the defender would have access to it.

Before we discuss guidance techniques, a quick primer on sensors. Sensors are built as Photodetectors for a specific wavelength likely with a telescope lens. While they can be expensive, especially if you want them diffraction limited, they require so little power that power use is assumed negligible, especially in comparison to all the high power systems of a spacecraft, missile, or drone. Sensors actually give you power, but this will be less than any rotators or computing system utilizing the sensor.

Unlike lasers, sensors can be made very close to being diffraction limited because they are so low power (if kept very cold).

What can they see? As mentioned in Stealth in Space, you can detect the radiators and the exhaust plume from far away, so there’s no doubt you will see them up close. At combat ranges, the ship itself will be visible from light reflecting off the hull. Less sensitive sensors will be needed at that close of ranges, lest you burn out your sky-scanning sensors.

But what is the visual resolution of these sensors? Although you can see the exhaust plume billions of kilometers away, it will show up as a single pixel, which is not helpful. Note that you can not achieve stealth in this way. You can’t hide multiple identical ships in a single fleet via pixel resolution. Careful study of the spectrum of this single pixel over time will reveal multiple overlapped exhaust plumes.

Visual resolution of a diffraction limited optic can be easily calculated using the angular diameter (follow the links for the relevant equations). Here are a few example calculations to give sense of range:

Given a detector 10 cm in diameter (reasonable for a drone, missile, or capital ship) looking for visible (550 nm, green) wavelengths, what’s the visual resolution?

At 1000 km away (orbital distance, close missile launching distance), each pixel is about 7 m in size.

At 100 km away (very long range projectile combat), each pixel is about 70 cm in size.

At 10 km away (close range projectile, drone, and laser combat), each pixel is about 7 cm in size.

At 1 km away (only missiles about to hit and maybe close ranged drones would ever get this close), each pixel is about 7 mm in size.

In Children of a Dead Earth, capital ships tend to be at least 50 m in length, often around 100 m long, or twice that for the flagships. Drones and missiles tend to be 10 m long at most, and usually much shorter.

This means that at missile launching distance, enemy ships are a tiny blob of a pixels while missiles are single pixels on screen. At very long range projectile combat, the enemy ship might be distinguishable as a shape with radiators, while missiles will be a few blurry pixels. At close projectile range, you’ll get a nice view of the enemy and their missiles as your shots tear them apart.

Larger sensors will give you better feedback though larger sizes tends to be a problem for missiles and drones. Additionally, infrared sensors will have half the resolution stated above at best (since pixel resolution decreases as wavelength increases).

Visual resolution is rather important for missiles and drones, however, as their guidance systems need to be able to distinguish what they need to hit versus decoys. The better the visual resolution, the further away decoys need to be launched to fool the missiles.

Let’s go into the guidance techniques available in space.

Infrared (IR) Homing is a passive technique where the missile or drone chases infrared wavelengths. Often it would chase the greatest heat source, though this is easily fooled with decoys. Infrared Homing is the most important of all guidance techniques in space, principally because all ships give off tremendous amounts of heat from their engine and their radiators.

Ultraviolet Homing chases after the ultraviolet part of the spectrum instead of the IR portion of the spectrum. This is beneficial because UV decoys are much more difficult to produce and field. On the other hand, low heat radiators like life support radiators emit very little UV light, which means turning engines off and retracting powerplant radiators is an effective countermeasure.

Spectral Seeking is a little more sophisticated, where a specific spectra is targeted. For instance, the spectra of methane at 3000 K is unique among spectra, and only exhaust plumes of methane at 3000 K would be targeted. This means in order for decoys to throw this type of guidance off, the decoy needs to match the spectra exactly (which is difficult). On the other hand, the target needs only change the spectra of the engine or the radiators to throw off the guidance system.

Passive Radar is another passive technique where the missile chases after radio signals bouncing off of the target from third party sources (likely civilian). In space, due to distance, the signals are significantly weaker than on Earth.

Active Radar Homing is the same technique, but with an active radar system specifically illuminating the target. This is much more effective, and doesn’t rely on weak third party civilian signals. However, all radar systems can be fooled very easily by chaff. Additionally, Radar Absorbent Material is another effective countermeasure.

Semi-active Radar Homing is also the same technique, but with the radar illuminator being separate from the radar homing device. In this case, the capital ships would have the illuminator, while the missiles would chase the illuminated targets. This yields a somewhat cheaper option, but it still has the same limitations as previously mentioned.

Laser Guidance swaps out radar for lidar, radio waves for Visible, IR, or UV light. The target is illuminated by a laser either with a separate device (Semi-Active Laser Homing) or with the homing device itself (Active Laser Homing). It can be fooled by paint absorbent to the particular wavelength, and such paint is much cheaper to produce than Radar Absorbent Materials. On Earth, this sort of countermeasure can be fooled by simply aiming near the target instead of directly at the target, but in space, no such solution is possible, since there is no nearby “terrain” to aim at.

Beam Riding is a technique which uses either a laser beam or a radar beam to illuminate the target. Then, the missile “rides” the beam down, using the beam as a guide. On Earth, this restricts the missile to line-of-sight attacks, which is problematic, but in space, this is not a problem at all. Unlike laser guidance, it is immune to absorbent materials. The main issue, however, is diffraction. Any laser or radio beam will diffract, meaning the beam gets increasingly inaccurate as range increases. This restricts missile usage to very close combat, similar to lasers themselves.

Neutron Homing is a guidance technique that does not currently exist on Earth, but is likely to gain prominence in space. The nuclear reactors on a capital ship dump out an extraordinary amount of neutron radiation (both fast and thermal) in every direction, and these neutrons more or less pass through any material short of radiation shielding. Trying to shield this radiation in every direction requires a huge amount of mass, so weak unidirectional shielding in a single direction (towards the crew compartment) is used instead in addition to long distance.

This means that the neutron radiator of the reactor will be dumped out in a sphere shape, attenuated with the inverse square law. The background neutron of space is essentially zero in the absence of an atmosphere. This means very even trace quantities of neutrons can be picked up and used by homing missiles. The main countermeasure besides tons of expensive shielding would be launching neutron decoys: cheap, highly radioactive waste materials spewing off plenty of neutron radiation. Alternatively, a highly directional beam of neutrons can be generated as a way to throw off such missiles.

Command Guidance dispenses with all those sophisticated tracking methods, and relies solely on the launching ship to guide the missile with manual controls. It is immune to all countermeasures except for communications jamming and spoofing. This is a common technique for drones, since they do not need to collide with the target, they only need to aim at the target. In Children of a Dead Earth, this is the go-to method for aiming missiles if the enemy has countermeasures for every other technique tried.

Inertial Guidance is the ultimate “dumb” missile method, which rejects all attempts at actual guidance and homing, and simply follows a preset trajectory based on the target’s initial velocity and position. It is the least accurate of all homing techniques, but it is completely immune to all countermeasures. It can be defeated by simple acceleration or dodging, however.

Whew! That’s a lot of different guidance techniques and countermeasures and counter-countermeasures. So what is employed? All are employed to a small degree, but the primary homing technique used is one of the simplest: Infrared Homing.

This is because of the heat radiators on ships, and the extremely bright exhaust plumes. Countermeasures can be developed for every other homing technique, but for IR Homing, countermeasures are much more expensive.

First off, smoke (including thermal smoke) dissipates rapidly in space. Without an atmosphere, smoke expands at a constant velocity, required a huge amount of mass to provide a smokescreen for any extended period of time.

Second, deploying thermal decoys is expensive in terms of mass. Concealing hundreds of megawatts of radiator heat against a black background requires a similar amount of power emitted by the decoys. And these decoys have to be burning for a decent amount of time (10 seconds seems to be the minimum). This means the decoys will be rather massive pyrotechnic payloads.

Extremely massive payloads are difficult to launch at high velocities away from ones own spacecraft. If they aren’t far enough away by the time the missiles hit, significant damage can still result even if the missiles hit the decoys. Launching very massive decoys at high speeds requires significant amounts of power, which requires even larger decoys, which requires even larger launchers, and so on.

Third, using a high powered IR laser to blind the incoming missiles works great, except these missiles are insensitive to all but the brightest signals. This means the laser needs to produce comparable power to the radiators they decoy, which is costly.

This is exacerbated by the fact that missiles are launched in salvos, not one by one. As a result, the laser needs to widen its beam in encompass an entire formation of missiles, vastly reducing the power. And missile salvo formations can easily reach hundreds of meters wide, which means your beam needs to be hundreds of meters wide too, which is pathetically weak. Either that, or you need hundreds of high power lasers, each focused on tracking and blinding each individual missile, which is prohibitively expensive.

Generally speaking, IR homing is the most effective guidance system, and IR decoys are the most commonly used counter-measure. In particular, dropping radiators and shutting off the engine while launching decoy flares is a common survival technique against missiles, though it is not foolproof. Things are especially difficult for large laser crafts with enormous amounts of waste heat.

In the end, no exact technique trumps all other techniques, and most electronic warfare focuses around IR homing and counter-measures. And when counter-measures are effective, Command Guidance is the usual response.

# Stealth in Space

Few concepts of space warfare have inspired as much controversy (and hate mail) as discussing stealth in space, so I figured it’s time to have an article about that.

For starters, though, I’d recommend checking out Winchell Chung’s website, Atomic Rockets, which has an excellent discussion on this topic, aptly titled There Ain’t No Stealth in Space. I will summarize the main points about stealth here, but for an in-depth discussion of them, see the above link.

• Carefully scanning the entire celestial sphere takes 4 hours or less.
• Thruster burns of any drive with reasonable power can be detected all the way across the solar system (billions of km away).
• Even with engines cold, the heat from radiators attached to life support will be detectable at tens of millions of km away, which is still far too large to get any sort of surprise.
• Radiating heat in a single direction (away from the enemy) is easily defeated by fielding a number of tiny detector probes which idly coast about the system. Additionally, the narrower of a cone in which you radiate heat, the larger and larger of radiators you need to field. A 60 degree cone of radiation is roughly 10% as efficient, and it only gets worse the tighter of a cone you have.
• Making a huge burn and then trying to stealthily coast for months to the target is do-able, but as long as your enemy can track your first burn, they can very accurately predict where you’ll be as you coast across the solar system. And you still have to worry about radiating your heat for months.
• Decoys are only really viable on really short time scales, such as in combat. Over the long term, study of a decoy’s signature over time will reveal it’s true nature. It would need a power source and engine identical to the ship it’s trying to conceal, as well identical mass, otherwise the exhaust plume will behave differently. This means your decoy needs to be the same mass, same power, same engine as your real ship, so at that point, why not just build a real ship instead?

There are a few more points that are not mentioned but I get messaged about them a lot, so I’ll put them here.

• Hiding behind a planet to make a burn is not really feasible. All it takes is two detectors at opposite sides of this planet to catch this. In reality, a web of tiny, cheap detectors spread across the solar system will catch almost all such cases.
• A combat-ready ship will require very hot radiators for its nuclear powerplant for use in combat. If these radiators are going to be completely cold for the journey, they will suffer enormous thermal expansion stress when activated. In order to avoid this, very exotic and expensive materials for your radiators will be needed to get from 10 K to 1000 K without shattering. Not only that, your radiator armor will need to be similarly exotic, which means it will likely not be very good at armoring your radiators anyways.

Now there are plenty of dissenting views (as Atomic Rockets is good to point out, as well as rebuttals to the rebuttals). Certain partial solutions, such as using internal heatsinks, and so on, are pointed out, but they all are very limited.

Ultimately, stealth in space is somewhat possible, but current proposed solutions are either ridiculously expensive, impractical, or require you to accept limitations that defeat the purpose of stealth in the first place. Indeed, rather than consider it a ‘yes-or-no’ question, it’s simply a matter of how close you can get to the enemy before they detect you.

In practice, ‘how close’ generally means halfway across the solar system, with expensive stealth solutions reducing that distance only partially. Given this, Children of a Dead Earth runs with the assumption that stealth is not a reasonable military tactic for near future space warfare.

But let’s look at an example of possible stealth: replacing your main engine (nuclear rocket or combustion rocket) with a solar sail. Your exhaust plume is now nonexistent, but now you have to take decades to centuries deliver a military payload anywhere (troops or weaponry). Your best bet is to keep your payload very small if you want to get anywhere in reasonable time. And you still have to worry about your radiators.

Suppose replace your crew module with basic electronics, and do away entirely with the crew and their hot radiators. This is reasonable for any short term space travel, but over the course of months where things can and will go wrong with the ship or the strategic situation, having a human element is necessary. Alternatively, if Strong AI can be developed, this is another possible solution, but this assumes that such an AI won’t require lots of power and heat to radiate as well.

Given a solar sail and crewless ‘dumb’ ships with miniature payloads, you can build ships that can sneak across the solar system and do very little. Such ships would be unable to respond to complex and unexpected tactical decisions, and would be very easy to outsmart, as well as easy to spoof with electronic warfare. They could perhaps be used as mines, given a tiny amount of a delta-v and a small nuclear payload.

Ironically, this specification of tiny, ‘dumb’ stealth crafts is exactly what you need to build a web of detectors scattered about the solar system. This means the field of cheap detectors you want spanning the solar system can be created stealthily.

Defensive stealth in space exists in full force. When you enter orbit of an the enemy’s planet, they might have an inordinate amount military hardware and spacecrafts hidden beneath the surface. But as soon as they launch, the secret is out.

This idea plays a major role in Children of a Dead Earth, as when the enemy drops into orbit around your planet, one must always be wary that the enemy fleet is simply trying to draw out your forces to get a tally on what you actually have. This constantly requires balancing of launching just enough firepower to deal with the enemy without revealing too much about one’s own reserves.

The easiest way to conceal a large amount of military hardware for a long distance invasion is to hide it amongst commercial traffic. Of course, this requires complicity with the civilian traders, either bought with money or intimidation, but it is possible. And such perfidy also plays a key role in Children of a Dead Earth.

With that all in mind, I will admit that at the beginning of my project, I was dead set on getting stealth to work in space warfare. Ultimately, I came to the conclusion that while stealth in space is certainly possible, it is not feasible given mass, cost, and time constraints. If you want stealth, you need to pay the price of decades-long travel times, enormously massive ships, vastly reduced military effectiveness, or all of the above all at once.

At the beginning of the project, I did explore some more exotic solutions to stealth, but I ultimately wasn’t keen on implementing technologies that were not heavily reviewed and published in scientific articles. At some point though in future posts, I will go over all of the more ‘out there’ technologies I considered for all aspects of space warfare (like a hypothetical nuclear rocket which generates an exhaust plume at 30 K, for instance). Stay tuned!

# The Photon Lance

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

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.

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.

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.

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.

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.

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.

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.

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!

# What to shoot?

We’ve explored how we launch projectiles at the target (Space Guns), now we will explore what we launch at the target.

The simplest projectile is a solid block of mass with a burning pyrotechnic tracer on it. But even a block of mass has several complexities.

The material of a bullet can also be varied to cause for differing effects upon hitting. However, for railguns and coilguns, launching the armature itself is more cost effective than using the armature as a sabot for another projectile. This means railgun and coilgun rounds are restricted to highly conductive and highly magnetic materials respectively.

The bullets need to be cylindrical because they are launched from a tube, but they need not be aerodynamic in space. This means any sort of shape is viable in space, not just a bullet or thin penetrator. Fat blocky bullets are a viable shape, as are launching thin plates, flat side to target.

Given that aerodynamics is not a concern, what is the ideal shape of a bullet in space?

The answer is rather complicated. Certain relations are obvious though. For instance, a thinner shape applies a greater amount of pressure, as the energy is concentrated into a smaller area, so it seems like thin penetrators would be ideal.

However, there are two issues with that.

One is that Whipple Shields shatter thinner projectiles easier. Whipple Shields are often judged primarily by their critical diameter. This is the maximum diameter of projectile that they can be hit with and still successfully shatter or vaporize the projectile so that it causes no major damage. Obviously, material properties and impact velocity are both important, but projectile diameter is the main factor. Thus, thin penetrators are often not really worth the extra damage since Whipple Shields are ubiquitous.

Conversely, high velocity projectiles can sometimes be too effective. Indeed, given a large coilgun, shooting extremely high mass, high velocity rounds, the bullets can often blast straight through the initial Whipple Shields, straight through the main bulkhead, through several filled propellant tanks, out the external bulkhead and Whipple Shield, and finally off into space again.

Because only the crew compartments are pressurized, a spacecraft can suffer complete penetration and still keep trucking at 100% effectiveness. Spacecrafts can even get blasted in half and both halves can still remain reasonably effective (assuming each half still has a functioning crew and powerplant). Or into thirds, or fourths, and so on.

This is one reason why heavy redundancy in spacecrafts is necessary. A single lucky shot can immediately disable a ship if there is only one crew compartment.

On the other hand, one of my alpha testers went a different route. Rather than a single large capital ship with multiple redundancies, he preferred tons of tiny capital ships with zero redundancy. Either solution works, and has different pros and cons. More on this in a later post.

But back to projectiles being too effective. A projectile works best if it can penetrate the outer Whipple Shield and bulkhead, but is stopped there. That way, it can ricochet around, or if it shatters into plasma, it can inflict the most damage on the internals. In a sense, a larger area of effect is more important than simply raw damage.

Not only that, a projectile which passes straight through a ship fails to transfer much of its momentum to that ship, while a projectile that hits inelastically transfers all of its momentum. With very massive and very fast projectiles, inelastically hitting can cause tremendous torques on the impacted ship. Ships that spin out lose their carefully aligned targeting, and require precious seconds to reorient, which can mean life or death in a battle.

Or if the ship is particularly small, fast spins will splatter the crew against the inside of their crew compartments. This is actually one reason why I try to keep the crew modules near the center of ship mass, to reduce the torque on the crew in such a scenario.

If your projectile is too powerful, then the obvious solution is to fire large, flat, plate shaped projectiles rather than thin penetrators. This reduces the pressure, and the damage area is increased. However, this can be tricky since large bores will mess with the performance characteristics of all projectile weapons.

Another solution is to split the projectile into smaller, less massive pieces right before hitting the target. Flak bursts were developed as anti-aircraft warfare, and they remain an effective way to distribute damage over a larger area of effect. A small explosive detonates the payload into a cylinder of fragments, and the detonation speed can be determined accurately (using the Gurney Equations). This allows you to have very fine grained control as to the size of this “sparse projectile”, and you can detonate it at different proximities to yield differently sized clouds of fragments.

Other payloads possible in Children of a Dead Earth include explosive payloads and nuclear payloads. Nuclear tends to be a very powerful but expensive option, though due to the lack of atmosphere, their damage is incredible within a few meters, and then it falls of painfully fast. Explosives are similarly restricted to very small areas of effect but are much weaker, though they are fantastically cheap.

Should your projectile have thrusters? You can put thrusters on the projectiles you launch, and this can greatly increase their accuracy, however, the mass of the rocket engine and propellant is very costly. From what I found, barrages of thousands of small “dumb” projectiles tend to win out against tens of large “smart” projectiles, though I’d be interested if someone managed to optimize them to be competitive.

Often, a laser battery can effectively point defense tens of smart rounds, but against thousands of incoming bullets, no laser battery can keep up. Generally, against point defense, either you saturate them with a storm of tiny bullets, or you launch full blown missiles with heavy armor and large delta-v stores to get through.

There is another interesting aspect of projectiles that is often overlooked. Muzzle velocity is often optimized to be as high as possible. It increases the range and the impact damage. And even if it is too damaging, increasing the area reduces the damage without sacrificing range. It seems velocity should always be maximized.

Yet the equations for damage on Whipple Shields and Bulkheads are very nonlinear, and they have very different damage responses between hypervelocity and hypovelocity impacts. Indeed, Whipple Shields lose effectiveness for low velocity impacts, as the projectiles suffer little to no break up at low velocities.

This is one particular case where conventional guns and their low muzzle velocity are actually desired. When the enemy is packing multiple and/or stuffed Whipple Shields optimized against high velocity railguns and coilguns, low velocity conventional guns tend to be the trump card. This is one case of many where drones, which usually carry conventional guns, tend to make short work of the enemy.

# 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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!

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.

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.

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.

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.

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.