The Wheels on the Spacecraft Go Round and Round

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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A simple reaction wheel.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Raw Steel

Armor is one of the simplest things to manufacture, yet it holds some of the most complex results.

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Capital ship with armor visualizer enabled, demonstrating which main armor tiles are damaged or destroyed.

A 5 cm plate of steel is rather easy to produce, but analyzing how well it will perform under a wide variety of types of damage in different orders is rather difficult.

There are three main methods of damage: projectile, photonic, and plasma. Generally speaking, given equal amounts of energy, plasma damage is the least effective in many cases, and projectile damage tends to be the most effective. These differences vary significantly and may even reverse depending on the type of armor, however.

When a projectile hits armor, there are numerous ways that it may affect the armor. If the projectile does not penetrate, it can fracture the armor anyways, either where the bullet hit or on the other side of the armor. It could spall fragments off the inside of the armor, which can cause damage to internal compartments. And all of these scenarios are possible too if the projectile does fully penetrate.

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Different ways in which a projectile can affect armor.

Of course, with hypervelocity projectiles, in many cases, the projectile will shatter into plasma upon hitting. Not only that, the armor may shatter into plasma too. An interesting effect of this (which is modeled in Children of a Dead Earth) is that in certain cases, more armor can detrimental. Too much armor can get shocked into plasma or spallations and inflict even more damage than a thinner armor plate.

Laser damage is somewhat simpler. The primary method by which photons inflict damage is by ablating away the armor, causing material to melt, evaporate, or sublimate away.

Alternatively, a pulsed laser could be used to trigger shockwaves from the rapid expansion of the affected armor material. In this way, lasers can be used to inflict mechanical damage on the armor. A very thorough discussion on laser effects on armor can be found here.

Determining a model for how well a piece of armor reacts to every different scenario (or combination of scenarios) is rather difficult. On top of the different types of damage, there are many different kinds of armor materials and design choices.

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The armor visualizer clearly demonstrates the effectiveness of a drone projectile barrage.

Material properties that are important to armor materials follow.

The Ultimate Tensile Strength of a material is the capacity of that material to withstand tension, or being pulled apart. The Yield Strength, or the stress point at which plastic deformation of the material begins, is another metric which very important to determining the effect of mechanical damage.

The Density of a material plays a key role in resisting damage, particularly projectile impacts. One interesting point of note is that high density Whipple Shields perform worse due to a greater amount of Whipple Shield material being shocked into plasma, and hitting the main armor.

Against melt ablation by lasers, very different properties are used. Often, material strength is more or less irrelevant against laser damage. Instead, high Melting PointsBoiling Points, and Specific Heat Capacities are of crucial importance for armor to resist heating. All of these quantities allow the material to absorb more energy without failing.

Alternatively, some materials can get away with very poor heat resistance by instead having a very high Thermal Conductivity. If the material conducts heat away fast enough, a laser can dump energy into the material all day and never heat it up, as the material will conduct the heat away to surrounding armor tiles.

And of course, a number of other properties play a minor role in determining damage, like the Elastic Modulus and Shear Modulus. But generally when choosing armor, your main concern should be a high Ultimate Tensile Strength and a high Melting Point.

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Aluminum Whipple Shields are easily cut through by a laser beam.

So with those properties in mind, what material is best to use for armor?

Consider the material used for a single monolithic plate. Common choices are metals like lightweight Aluminum and Titanium, or the very dense Depleted Uranium.

Alternatively, metal alloys like Steel, particularly high strength steels like Maraging Steel make for great armor. However, on Earth, high density is valuable for lower volume, but in space, low density armor is more important, as armor can and will drastically affect your spacecrafts mass ratio.

This means ceramics like Reinforced Carbon-Carbon or Boron Nitride see use everywhere in space. They tend to be somewhat weaker than many high strength alloys, but their low density and resistance against laser damage more than makes up for it. On top of that, they are extremely cheap. In practice, ceramic armor tends to be the most common spacecraft armor.

Synthetic fibers like Aramid, which includes Kevlar, Technora, and Twaron have exceptional strength against projectile damage while having very low density as well. On the other hand, they suffer badly against laser damage, having rather low melting points.

Then there are the more exotic materials. UHMWPE, or Ultra-High Molecular Weight Polyethylene, is a plastic which has enormous strength and incredible low density. Similar to Aramids, though, its melting point is rather low. Nanocomposites tend to very strong as well, but are difficult and expensive to manufacture. And of course, you can use Aerogel in game, though its usefulness as armor is questionable. Same with Metallic Microlattice.

A few materials are omitted, most prominently, Carbon Nanotubes (CNTs) and Carbyne. CNTs promise incredible strength, but with today’s technology, they are limited to bulk use. This entails essentially crushing a pile of CNTs together and hoping for the best, which performs very poorly compared to the strength of a single CNT. It is unclear if achieving CNT strength on a macro scale is possible or just a pipe dream. In all likelihood, they will likely be used as a way to bolster existing material strengths.

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This particular capital ship uses Reinforced Carbon-Carbon and Silicon Carbide as its main armor layers.

But armor is more than just a single plate of the strongest stuff you can find.

Whipple Shields are simple, cheap, and very effective. They are a specialized case of Spaced Armor. A thin plate of low density material spaced out far off from the main armor can shock incoming hypervelocity projectiles into plasma. The purpose of the spacing is to allow time for the plasma to expand into a greater area, and thus spread its damage thin.

In practice, Whipple Shields delay the inevitable. When the enemy is dumping a thousand bullets per minute at you, your Whipple Shield is going to get demolished very quickly. However, they buy you a small amount of time (less than a minute), and those tens of seconds might be exactly what you need to get in close with more powerful, closer range weapons.

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Using a laser at long ranges to etch away an enemy’s Whipple Shield is not the fastest method of dealing with it, but it works.

Composite Armor is a fancy term for multiple layers of very different materials. As shown above, different materials perform better under different situations, so having composite armor is a way to have the best armor for each situations. In Children of a Dead Earth, each layer can be spaced out as well, combining Composite Armor with Spaced Armor/Whipple Shields.

Sloped Armor is simple, cheap, and absolutely crucial. Simply angling the armor plates can have a tremendous effect on survivability. This is not just because the effective armor thickness increases with the angle, but also because it causes projectiles to ricochet, deform, or deflect. Sloped armor is arguably the most effective defensive measure.

In practice, missiles with extremely pointy faces survived far longer against enemy point defenses than missiles with flat faces. I discovered this when one of my alpha testers pointed out that between two of the smallest missiles, one with a tiny flak payload and one with a tiny nuclear payload, the flak missiles were surviving at 10x the rate of the nuclear missiles. As it turned out, the flak payload with long and thin, and convex armor hull wrapped it into a point, while the nuclear payload with short and fat, leading to a flat face.

All missile designs were given a sharp nose after that.

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Ever since that incident, missile noses were deliberately elongated into points, regardless of payload.

There are a few more design choices not in Children of a Dead Earth but should be mentioned for completeness.

Slat Armor uses a cheap grid around the armor to deform explosive projectiles. In space, however, most payloads are detonated before colliding, and explosive projectiles are already weak in space. Slat armor is easily defeated by Tandem Charges.

Reactive Armor layers the armor with explosives which detonate outwards when hit. While effective against incoming explosive payloads, again, explosive payloads are not used nearly as much as nuclear payloads and simple projectiles. Additionally, this armor needs to be outside of any Whipple Shield, lest the Whipple Shield blasts out numerous tiles with each expanding burst of plasma. Not a very effective armor if the enemy is carpeting you with bullets. Also defeated by Tandem Charges.

Electric Armor is two plates of armor separated by an electrical insulator, and one side charged. When a bullet hits and closes the circuit between the two plates, the electrical discharge will vaporize the bullet or even turn it into plasma. This would require an additional armor layer beyond the Electric Armor to shrug off the plasma, likely spaced out to let the plasma spread thin. While promising, this technology does not exist in any current form, and its limitations are unclear.

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Radiators dark, crew dead. A swath of holes have been cut longitudinally through the majority of the craft’s hull.

That’s all for armor! Armoring your spacecraft designs is very simple, but the ramifications end up being very complex. And as with many designs, optimal solutions are never as obvious as you may think.

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.

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Close up of photodetectors of a telescope.

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.

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Photodetectors being installed on the HESS telescope.

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.

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Data produced from a single pixel can be studied and differing emitters can be determined.

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.

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Of course, taking into account enemy countermeasures, your view screen will likely look as clear as this.

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.

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The eye of an IR homing missile.

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.

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A radar display affected by chaff. The left side is jammed by chaff, and produces no usable data.

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.

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Schematic of a laser guidance system. The laser is “painted” on the moving target, and the missile chases the dot like a cat.

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.

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Diagram of a missile riding a beam to the target.

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.

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Shielding against neutron radiation is rather costly in terms of mass.

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.

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Schematic of a Neutron Generator.

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.

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A salvo of missiles and a fleet of three ships in the background dropping numerous decoy flares.

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.

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These three ships really don’t want to get hit.

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.

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A salvo of 100 missiles on its way to the enemy defense force around Ceres. Enemy force is roughly 40 km away.

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.

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.

 

Fun with Orbital Mechanics

Children of a Dead Earth uses an N-Body Simulation to simulate its orbital mechanics. Most other games which simulate orbits use the much less accurate Patched Conic Approximation, and I’ll go into the details of why in this post.

What is the Patched Conic Approximation, first of all? The Patched Conic Approximation treats all orbits as ellipses around a celestial body. Then, when actually making thruster burns, the current ellipse is swapped out for a new elliptical trajectory. When making an exit from one orbit into the parent body’s orbit, a new ellipse around the parent body is swapped in for the child body.

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A perfectly elliptical orbit, although it rotates slightly with each period.

As you might expect, this is rather inaccurate. Indeed, when plotting actual spacecraft trajectories, NASA starts with the Patched Conic Approximation to get a “napkin estimate” of the trajectory, and then they switch to using an N-Body Simulation when they actually need to calculate it precisely.

Originally, Children of a Dead Earth was supposed to use Patched Conics. However, I discarded them when I wrote a simple N-Body Simulator to compare them against, and found the Patched Conics diverge very heavily from the N-Body Simulator. It was also the right choice: Switching to an N-Body Simulator allows a wealth of new orbital features, such as Orbital Perturbation and Lagrange Points.

So what is an N-Body Simulation? It’s simply a simulation which takes into account all gravitational forces in the entire system (in my case, the entire solar system) and applies them at each time step with a numerical integrator. Children of a Dead Earth uses a Fourth Order Symplectic Integrator by Forest and Ruth.

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An orbit around Mercury perturbed significantly by the Sun.

Orbital Perturbation is a phenomenon that only shows up in an N-Body Simulator, and it makes a world of difference. Perturbation is simply the effects of gravity from more bodies than just the primary orbited body. Patched Conics do not simulate perturbation because they are only concerned with the gravity of one body at a time.

When orbits can be perturbed, they lose their perfectly elliptical shape and become at best distorted, and at worse, completely unpredictable, losing all periodicity.

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Some orbits become perturbed so much that they become utterly unpredictable, and don’t seem to behave like orbits at all.

Why is this important? Consider the following story, which happened to one of my Alpha playtesters. He had spent a lot of delta-v injecting into orbit around Oberon in the Uranian system, and didn’t have enough delta-v to rendezvous with the destination space station around Oberon. His injection orbit was highly out-of-plane and succeeding seemed hopeless. But instead of giving up, he simply disabled stationkeeping, letting his spacecraft enter a free falling trajectory. Using the orbital perturbation of Uranus, he allowed the planet to perturb his out-of-plane orbit, gradually flattening it out into an orbit coplanar with the target space station. Eventually, by simply letting gravity do the work over several orbital periods, he had an orbit which could rendezvous with the target with minimal delta-v usage.

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Using orbital perturbation in combat around Ganymede.

In combat, using orbital perturbation to your advantage is another effective but difficult technique to use. Dropping into a low orbit is often a useful tactical choice, as it forces your opponent to expend copious amounts of delta-v. However, it reduces orbital perturbation of nearby bodies.

On the other hand, entering very high orbits causes combat speeds to slow heavily, yet it costs much less delta-v, and it greatly enhances orbital perturbation. A perturbed orbit is much harder for the enemy to intercept because of its unpredictability, and the enemy will have to expend much more delta-v to reach you while you let gravity pull you along.

Furthermore, techniques like Orbit Phasing, which is a very effective way to intercept enemies, get thrown out the window when your target stops stationkeeping and enters free fall. Intercepting the enemy requires much more care than using simple maneuvers. After all, Orbit Phasing and Hohmann Transfers were developed for the Patched Conics Approximation, and are much harder to pull off in an N-Body Simulation.

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A propellant depot in a tight orbit around the Jupiter-Europa L4 Lagrange Point.

Lagrange Points are also simulated only through N-Body Simulations; Patched Conics fail to correctly simulate these. Lagrange Points are five or fewer points around each celestial body and its parent where an orbit that remains stable relative to both bodies. Children of a Dead Earth simulates all manner of Lagrange Point orbits, from simple circular ones to more exotic Tadpole Orbits.

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A figure 8 orbit around Mercury’s fourth Lagrange Point, Sun-Mercury L4. This orbit is a tadpole orbit that is twisted on itself.

That’s all for the N-Body Simulator! There is one additional aspect of Children of a Dead Earth’s orbital mechanics that is unique, and that is the way it handles multiple frames of reference, however, that will be another full post in and of itself.