# Gasping for Fumes

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

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

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

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

After all, remember the rocket power equation:

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

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

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

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

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

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

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

$T=\dot{m} v_e$

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

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

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

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

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

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

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

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

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

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

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

So where does this leave us?

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

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

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

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

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

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

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

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

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

## 21 thoughts on “Gasping for Fumes”

1. xassix says:

So, no nuclear pulse propulsion?
You mentioned in an earlier post, that “Torchships” would be too far future for this setting but project Orion was researched in the 1950s. That is decidedly not far future.
Or did you decide against it, because some of the technical details are still classified?
I heard this game will have modding support, so eventually it might get more advanced engines.
Still, i think that a lot of hard sci-fi fans might be a bit dissapointed if nuclear pulse engines are not in the base game. It just seems like the go-to propulsion system for an interplanetary setting.

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1. It would depend on the exact economics of the future Solar system, but I can imagine Orion drives costing much more than NTR drives due to needing to use enriched plutonium as fuel. Whether this makes them economically impractical for mass deployment will depend on said cost and how badly the outperform NTR drives.

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2. Right, there are enough technical details classified about the Orion drive that I wasn’t confident I could produce the same technical fidelity that I used when implementing the NTR or any other technology used. A lot of Orion heat and stress analysis was never released.

This is one reason why there is in-engine modding support, for developing any sort of future technology not covered by the base game.

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2. Eth says:

Any chance there will be – or at least can be modded in – Orion-style nuclear pulse propulsion? I guess there isn’t enough info to model it in detail, but it did seem like a workable design. Also, it could open modding for more hypothetical drives.
Then there is the use of pulse units as weapon, which may do interesting things…

The title and the focus on near-present technologies (even if this choice is based on info availability) make me wonder what the setting looks like. How detailed is the CoaDH world?

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1. The base game is entirely near-future technology that can be modeled with high accuracy. Many of the Orion details are still classified, which put a damper on trying to model it with such accuracy.

However, I expected many fans would be interested in that sort of thing, which is why I added in-engine modding support for any sort of hypothetical engine you’d like.

The setting was made by extrapolating current human growth trends, and spans the entire solar system (but nothing beyond). It features a number of political factions dominating the major planets and moons of Sol, all grappling for more territory, more rocks, more places to establish orbits around.

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1. I would speculate that any workable “torchship” class engine, such as the Project Orion concept, that delivers both high thrust and exceptional specific impulse would be a total game changer. With one you can massively increase the amount of armour on warships, leave chemical and NTR ships for dust, and pretty much ignore orbital mechanics. It would be at least as big a shake-up to space warfare as the invention of the cannon, steam engine, or aeroplane were to Earth warfare. CoaDE presents space warfare before the invention of such “torchships”, which will render the spaceships it has as obsolete as the USS Constitution.

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1. Elukka says:

I could see the mobility advantage alone being sort of a jet fighter vs WW2 prop situation. With significantly more thrust and many times the isp you can pull so many more maneuvers and you can dictate the terms of the engagement with utter impunity. (the fighter analogy breaks when it comes to systems other than propulsion; the conventional ship here would have weapons on par with the Orion, if not in terms of mass then at least in technological sophistication)

There’s a big disadvantage when it comes to operational cost. Those conventional rockets are venting whatever bulk volatile out of their tailpipe. The Orion’s exhaust is instead made up of precision manufactured industrial products incorporating various expensive materials. Still, if it has as big of an advantage as it seems to, it would still completely upend space warfare.

I could see Orion feasibly being initially ignored. You might have fleets made up of small, sane, economical craft, keeping the peace, fighting low intensity conflicts and whatnot. Then some confrontation between larger polities starts looming on the horizon, and as soon as one of them starts drawing up Orion blueprints, everything changes.

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3. “And if you want middling thrust and an even higher delta-v,”

I don’t understand. If you want a high mass-flow rate, high temperature nuclear engine, can you not add more channels through the core for more flow? The energy needed to do this can come from a slightly larger and much more reactive core.

For nuclear thermal the most immediate and obvious answer is to select your most efficient readily available fuel (H2) and to scale the engine(s) until you have adequate thrust. I don’t quite follow your explanations as to why you cannot do this, other than the one on having more H2 tanks to armor.

Which doesn’t entirely make sense, either – one would think that you only really need propellant to reach the battlefield and then for a small amount of propellant to survive during the fight. Realistically, a duel between peer space warships is probably going to leave the “winner” full of holes and without enough remaining propellant to get home…

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1. A. Sutton says:

I think that last bit is an assumption the author does not share – the idea behind this project was that one went in without preconceptions, built simulations, and tested what worked. Most of the designs rules here are stated to be the result of that testing for practicality.

As a counterargument for the “propellant to reach the battlefield” bit, what if the place you are trying to get is not a place, but a target? If your fleet is trying to reach and destroy the martian separatist fleet or whatever, you need to catch them. If they’ve got much better d/v reserves than you, you’re going to be hard pressed to be able to keep with them, because they can see you coming and burn to make your life more difficult. If they can keep that up until you’re out of propellant, then they don’t even need to fight you, because at that point there is no battlefield – just a formation of warships on the slow road to Enceladus doing the math on food consumption and then wondering if they have enough sidearm rounds for everyone.

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1. Sure. And a more efficient rocket that has more dV is better. Play KSP for an evening and you’ll want all the dV you can possibly fit in a rocket. Hence, where the author – who is inserting assumptions in how he restricts the parameters of his simulation – ends up with ships that are just barely better than existing rockets, I just wonder why. NERVA is supposed to have worked with 1960s tech and given usable ISPs of 800+. One would expect to not use propellant/engine combinations that give you anything less.

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1. A. Sutton says:

Sure, but as discussed, thrust:delta-v is a tradeoff, and practical mass ratios re: density and such are also a limiter – in reference to KSP, if you mess about with Real Fuels (as I suspect you have), you’ll note that some fuels are just maddening (like H2) to try and get any decent amount of because so little mass fits in a tank. Better to have 20:1 mass ratio than 3:1 with a somewhat more efficient engine, after all.

As far as the engine tech itself, the design philosophy as expressed was to only touch technologies with the ‘rough bits’ and confounding factors known, not just the potential upsides. Limiting scope in the name of preserving authenticity of each thing included – particularly given how madcap complex the engine design appears to be, given that it literally seemed to let you choose the materials and size ratios of the internal components of your reactor, fuel enrichment percentages, the whole nine yards. A speculative gas-core torch or the like is never going to be able to be made with that level of fidelity.

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4. I’m a bit confused about the thrust equation. T = m’ Ve implies that Ve is directly proportional to T, not inversely. So I don’t see how the high Ve of a NTR explains the low T. I was under the impression that the disadvantage of NTR was the excessive weight needed for a reactor.

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1. NTR reactors can be made very light if you’re clever about it (like the MITEE engine, which miniaturized the NTR design very heavily.

$v_e$ would be proportional to $T$ in that equation, if you can keep $\dot{m}$ constant. However, this is not something you can easily do, as cranking up your mass flow in the equation will cause the NTR temperature to drop, causing $v_e$ to fall.

In the power equation, $P=\frac{1}{2} T v_e$, you will find that $T$ is inversely proportional to $v_e$ (just divide each side by $v_e$ to see). This inverse relationship does hold for a constant amount of power, which is the most common case for an NTR. Under constant power, thrust and exhaust velocity must be directly opposed.

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5. What about using mass drivers as engines? The game already has a wide variety of guns, it’s just missing the option to use their recoil as propulsion. Whether it would be any good compared to the other options, I can’t know until it’s added to the game!

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6. Berkut says:

And what about liquid or gaseous nuclear cores ? The famous “nuclear light bulb” a.k.a. Cavradyne in Kubrick’s rendition of2001 ? Not enough litterature to make a good model? Not enough time I guess ?

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1. Literature is very scant for nuclear light bulbs, they’re rather far future.

Liquid core engines are a much closer technology, though there are a few hurdles that remain. In particular, keeping the reactor from exhausting with the propellant is still an issue. Some solutions have been proposed, such as spinning the core, or applying a heavy magnetic field, but in both cases, an in-depth model of either has yet to be developed. And because of that, there’s no real knowledge on if either solution will work, or how effective they will be, etc.

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8. Samrat says:

I was thinking about can we use some metal as propellant, like they are much heavier than liquids or gases. We may use powered iron and use a screw to put them in the reactor. Also if the tanks are made to stick to the sides then they can act as sand bags (iron bags). Btw thanks for the post

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9. Samrat says:

I mean powdered iron

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