Children of a Dead Earth will release on Steam on Sept 23rd!

Mark your calendars! Children of a Dead Earth launches on Steam on September 23rd, 2016 at 9am PDT!

Also, in case you missed the latest gameplay trailer, here it is:

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.

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.

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.

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.

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.

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.

I see a lot of misconceptions about space in general, and space warfare in specific, so today I’ll go ahead and debunk some. In the process, we’ll go through the moment to moment of space warfare itself.

Zeroth misconception, no, there won’t be stealth in space, let alone in combat. It is possible through a series of hypothetical technologies or techniques, but it won’t be possible for any reasonable spacecraft under reasonable mass and cost restraints.

Now then, on to the first real misconception. Wouldn’t missiles dominate the battle space, being fired from hundreds of thousands of kilometers away? Wouldn’t actual exchange of projectile weapons never happen in reality?

The answer is no, actually. There is a prevailing hypothesis that missiles will soon be the only relevant weapon on the battle space, and it is likely borne out of current trends in modern warfare. ATGWs are already starting to upend tank warfare, and Anti-ship missiles are doing something similar to naval warfare. Indefinitely extrapolating this trend would lead one to conclude warfare will soon be nothing but people sitting in their spacecrafts launching missiles at one another.

But this is not true. CIWS point defense systems are already starting to shift the balance away from missile strikes. As suggested in an earlier blog post, military strategists are even beginning to suggest the development of CIWS systems may bring naval warfare full circle, all the way back to World War I battleship warfare. This isn’t to suggest that missiles are useless. Indeed, enormous salvos of missiles are effective at overwhelming CIWS systems, and they are in game as well.

Yet we begin to see the limitations of each system. Point defense systems, railguns, coilguns, conventional guns, or even lasers, are power limited in this exchange. There is a finite amount of power to use when firing, except for conventional guns. Conventional guns suffer from low muzzle velocities, and high muzzle velocities are crucial to intercepting missiles coming at you at greater than 1 km/s. This power limitation is what prevents these point defense systems from being impervious to missile salvos. Power consumption is limited by radiator mass actually, as simply slapping down more nuclear reactors is easy, but trying to deal with the added mass of all the radiators needed to cool those reactors is much more difficult.

Missiles, on the other hand, are also limited by mass. A hundred-missile salvo is sure to overwhelm any point defense system, but the amount of mass this requires the launching ship to take on is enormous, and will kill its mass ratio. In the end, it turns out the Rocket Equation governs just how effective missiles and point defense systems are. In game, the systems ended up surprisingly balanced, with neither being a dominant strategy, with either being more effective in certain situations, and weaker in others.

Next misconception, wouldn’t lasers dominate the battle space? Lasers do not suffer from many of the inaccuracy problems that projectile weapons do, and move at the speed of light, so they are literally impossible to dodge. So lasers are the king of the battle space, right?

Wrong. Lasers suffer from diffraction. Badly. The power of lasers in space drops painfully fast with distance, and frequency doubling only ameliorates the issue slightly. Lasers are notoriously low efficiency compared to projectile weapons. But that’s not the main issue. When comparing hypervelocity projectile impact research with laser ablation research, one discovers a stark contrast in their efficacy. Laser ablation is simply less effective at causing damage than projectile impacts. Whereas hypervelocity projectiles cause spallations and cave in armor effectively, laser ablation is poor, with energy wasted to vaporization, radiation, and heat conduction to surrounding armor. On the other hand, at very close ranges, where diffraction is not an issue, lasers outperform projectiles easily. Unfortunately, nothing aside from missiles will likely ever get that close, and even then, they will likely be within close focus ranges for milliseconds at most.

Lasers still useful at long ranges, though. Lasers fill a very specific niche in space warfare, and that is of precision destruction of weakly armored systems at long distances. Lasers are very good at melting down exposed enemy weapons, knocking out their rocket exhaust nozzles, and most importantly, killing drones. While missiles have very few weak points, and can shrug off laser damage with thick plating, drones have exposed weapons and radiators, which makes them very vulnerable to lasers.

In terms of actually destroying enemy capital ships, however, lasers can cut into the enemy bulkhead all day with basically zero effect (I measured the ablation of a monolithic armor plate at one point, and found that the ablation was happening at micrometers per second).

Final, misconception, wouldn’t computers just control everything in combat?

Yes and no, but mostly no. CIWS systems are already computer controlled, and all weapon aiming is similarly already controlled by the computer in game. Anything that has easily computable maxima are solved by computers in game. But there are numerous choices in combat which have no obvious local maxima, and these require human decisions. In other words, you the player and commander need to make these choices. As it turns out, the right or wrong decision can mean the difference between victory and failure.

In game, you won’t be aiming any weapons and firing them, nor will you be flying drones around. The computer can do both better than you, and so the computer will be in control of these things (besides, do you really think you could effectively aim at a speck of light 50 km away moving at 1 km/s at you?).

What you will have control of are the higher level strategic decisions. The orders you give your missiles, drones, and capital ships are crucial decisions you must make in combat. Will you send your missiles in a beeline at your enemy, or perhaps order them to spend valuable delta-v dodging enemy point defense fire? Should you retract your radiators to reduce your heat signature to avoid enemy missiles, and risk the loss of your firepower for the precious few seconds? Should you hold your drones in reserve, close to your carrier, or send them guns blazing as the enemy capital ships approach?

Also as well, one of the critical choices you can make is what to target of the enemy. Each subsystem of every enemy spacecraft is simulated in real time. The reactors draw power, the radiators expel heat, the turrets and guns drain power, all in real time. If you want to disable the enemy’s ability to harm you, the obvious choice is to go for the weapons. But weapons are small, hard to hit unless you have a laser. Going for the enemy’s radiators might be an alternative strategy, with radiators being large, easy targets, although radiators, once armored, are surprisingly sturdy. Not remotely as strong as monolithic armor, but still able to take a reasonable beating of projectile and laser hits. Of course, maybe taking out of the enemy’s engines is more your style, the rocket nozzles being flimsy and poorly armored to allow them to gimbal easier. Plus, a ship that can’t move or dodge is a much easier target.

But most importantly, orbital mechanics are king in Children of a Dead Earth. Indeed, orbital mechanics are the core mechanic of the game, even, counterintuitively, in combat. Once you reach weapon range, orbital mechanics lose most of their relevance, but everything up to that point hinges on orbital mechanics.

Your incoming speed and angle of attack entering combat, two critical attributes which govern how the combat unfolds, are determined entirely by your ability to use orbital mechanics to your advantage. How near or far you are from the nearest gravity well (planet, moon, or asteroid) has a huge effect on combat speeds. Additionally, evading the enemy before even entering combat is a big part of the game. If you can drain the enemy’s delta-v through effective orbital mechanics, they may fight at reduced effectiveness in combat. If you’re good enough, you might be able to run them out of delta-v entirely, and never even have to enter combat at all!

That’s all for now. Next time, we’ll dig into the science of the rockets themselves!