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.

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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!

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.

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Point defense railguns firing tiny 10 gram bullets against a missile salvo.

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?

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A fin stabilized Kinetic Energy Penetrator.

 

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.

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A single-stage and a multi-stage Whipple Shield after impact.

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.

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Cut in half but still threatening. Probably not for much longer though.

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.

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Of course, if you don’t have enough power behind your bullets, you won’t penetrate the main bulkheads at all.

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.

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A flak barrage slices through a Laser Frigate.

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.

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Railgun point defense against a salvo of armored missiles. The missiles and their exhaust plumes are too small and dark to see, so they are each highlighted by the green circle.

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.

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Whipple Shields perform the worst between the Ballistic Range and the Shatter Range, which is approximately 3 km/s.

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.

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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.

 

Origin Stories

Today I thought I’d break from the usual, and go into detail about how this project of mine came to be. As you know, it started with the question: “What would space warfare actually be like?” A lot of sources, mostly hard science fiction literature, have tried to answer that question at one point or another. Other sources, like the Atomic Rockets website, does a great job of detailing the ideas at a high level.

For me, though, I wanted a simulation, one that was actually based on real equations. This is because in my experience, whenever you develop system this complex, it tends to surprise you, and will often overturn your assumptions. And trust me, it has surprised me continuously throughout the project.

The project originally was going to be not nearly as detailed as it is today. The original project would use black boxes for technologies: a railgun would be a system with X mass, Y volume, Z exit velocity of a W mass armature. The details would be glossed over. That worked fine for existing chemical rocket designs, because I simply had to copy and paste the numbers cited for SpaceX’s or NASA’s rocket engines.

It all started with railguns, though. When I went to do the same for railguns, there was a problem. The field of modern military railguns is limited to a handful of actual railguns that have undergone testing and deemed viable. I could implement these particular railguns as black boxes as well by collecting all the data I could find on them.

ONR 32MJ electromagnetic railgun (EMRG)
Railgun developed by the US Navy. The flame behind the projectile is not propellant, but rather the oxygen being ignited by the projectile’s launching. In space, no such flame would occur.

But what I wanted was scaling relations. If I took this railgun design, and doubled the power consumption, could I double the exit velocity? If I doubled the rail length, would that double the exit velocity? Is it possible to assume a simple efficiency percent, and derive my exit velocity based on the input energy and armature mass?

This answer to these questions, as I later discovered, are No, No, and No.

What I was looking for was simple equations which would relate the mass, power consumption, exit velocity, and dimensions. If I had these, I could scale these weapons up or down in various ways depending on the situation. A small drone would need a low power, low mass railgun, while a capital ship might have a ship-sized railgun of incredible power. I was looking for simple (ideally linear) relations between these attributes of a railgun.

As it turns out, that is not possible. The equations are complex, highly nonlinear, and many were unsolvable unless using numerical integration.

But I still wanted scaling laws for railguns, so I pressed on.

I started with the lumped parameter model for railgun force:

F=\dfrac{L'I^2}{2}

Okay, simple enough. At this point, I thought I could still have a simple equation describe my railguns. All I need is the inductance L' and the current I and I can integrate the force across the length of the rails to get the exit velocity.

First the inductance. Wikipedia gives a gross estimate for this, as well as a simple equation which estimates the inductance by treating the railgun as a pair of wires. I wasn’t too keen on the estimate nor the equation because I was interested in a railgun that was cylindrical bore, and this thesis conveniently had what I was looking for. It developed an inductance equation for a cylindrical bore railgun based on the railgun’s bore radius, rail length, and rail thickness. Perfect for developing scaling laws relating the railgun’s dimensions and mass to the exit velocity. The equation itself was derived in the next chapter of the thesis and is duplicated below (for a given rail opening angle of 40 degrees).

L' = a + b \ln(T/S) + c (1/S) + d (\ln(T/S))^2 + e (1/S)^2 + f (\dfrac{\ln(T/S)}{S}) + g (\ln(T/S))^3 + h (1/S)^3 + i (\dfrac{\ln (T/S)}{S})^2 + j (\dfrac{(\ln(T/S))^2}{S})

Where S the rail separation, T is the rail thickness, and the coefficients a through j are derived constants which can be found in the thesis itself.

Screen Shot 2016-05-06 at 2.36.33 PM.png

It’s a hefty equation, but it remains constant for a given set of railgun dimensions. What’s more is that it provides a very direct scaling relation between the dimensions and the ultimate railgun performance. A highly nonlinear relation, but a relation nonetheless. Just what I was looking for.

For the current, I found there are a number of ways to get pulsed power through your railgun: batteries, capacitors, inductors, compulsators, flywheels, hydrodynamic generators. Or, you can ignore these entirely and use continuous power. Where you attach the power supply also very significantly affects the final force. You can attach your power supply at the start of the rails, and the current will fall off as the projectile accelerates down them, or you can attach it at the end, or anywhere in between. Not only that, various designs implement multiple power supplies which attach at separate points along the rails to keep the current high.

At this point, the number of design choices was starting to undergo a combinatorial explosion, so I ended up setting some of the choices in stone. Only capacitors were implemented for pulsed power, and I implemented continuous power as well. Also, I set the power supply to only attach at the start of the rails.

In any case, the current was derived in two different ways for both pulsed and continuous power, and we’ll go into pulsed power. Resistance of the railgun is found easily by using the resistivity and dimensions of the rail and armature material. The capacitor itself requires knowledge of the capacitor’s capacitance (obviously), and the railgun was treated as an RC circuit, with the rails and armature being the resistor.

Discharging_capacitor.svg

The voltage of the circuit is found simply with:

V(t) = V_0 e^{-t/RC}

Where V(t) is the voltage at a certain time, V_0 is the initial voltage, t is the time, R is the circuit’s resistance, and C is the capacitance. From the voltage, the current can easily be calculated, and this current can be plugged back into the force equation.

There is one final wrinkle, though. The voltage relies on t, the time of the system, and the resistance relies on x, the distance along the rails. After some wrangling, I set the equation in terms of either dx or dt, but in either case, the integral ended up being non integrable.

Thus, I had to use numerical analysis to calculate the final exit velocity (specifically, I’m using a Fourth Order Runge Kutta method), and I finally had my exit velocity.

My inputs were the following values: Rail Bore Radius, Rail Thickness, Rail Length, Rail Material (for resistivity), Armature Material (for resistivity), Armature Mass, Capacitance, Power Consumption. Not bad. Capacitance is derived further, but that’s a whole other blog post. So what I finally end up with is a series of values that I can tweak in order to see just how the exit velocity turns out. Not only that, but because the dimensions of the railgun are enumerated, I now know the railgun size and using the material density, I have the mass of the railgun as well.

railgun.png
Design of a railgun. The inputs you can manipulate are on the right, the stats that result are on the left.

But we’re not done yet! These equations allow you to invent hypothetically ideal systems which can’t exist in real life. The missing link is thermal and mechanical stresses on the system. The following limitations are implemented and must be checked for in a railgun:

The railgun rails can melt if the temperature becomes too high. If you read through the thesis posted earlier, the temperature concentrates are certain points, and these points need to remain under the melting point of the material for the entire firing. Additionally, the armature itself suffers similar temperature excesses and must be accounted for. The rails ablate from thermal stresses occurring far below the melting points of the rail and armature materials, and close attention must be paid here as well.

The recoil stress of the railgun will push the rails apart, and the rails must be able to withstand this stress without deforming. The barrel itself can be treated as a cantilever beam and needs to be able to handle the cantilever beam deflection stress when it fires. The armature suffers significant stresses as it is accelerated down the rails as well, and needs to be able to withstand them, lest it shatter.

Also, the bulk temperature of the railgun increases with each firing, and the railgun needs to be able to dissipate this excess heat in a timely fashion either through a coolant loop using convective cooling, or radiatively, through the barrel into space itself. Finally, thermal expansion stress can cause both the rails or the armature to crack and needs to be dealt with.

railgun issues.png
This particular design has three issues with mechanical stress. These issues tend to crop up for crazy high exit velocities.

These limitations are all implemented, and will be covered in a later blog post, since I’ve rambled on long enough here.

But once the limitations are all enumerated, I finally had what I was looking for: scaling relations for railguns. Given simple inputs like rail length, armature mass, power consumption, and so on, I was able to get reasonably accurate metrics for the exit velocity of a railgun, in addition to much, much more.

So this is just one particular origin story of how Children of a Dead Earth came about, in particular, why the granularity of the simulation is the way it is. There will be more origin stories to follow, such as on how very disparate parts of the simulation came together.