# What are the deal-breakers with a preheated Hydrogen gas tank orbital rocket?

Consider this thought process:

1. In selecting the propellant for a reaction engine, lower atomic mass is better because equipment is largely temperature limited, and lighter gas will get higher specific impulse
2. Nuclear thermal rockets beat liquid-hydrogen specific impulse (over twice) by using only Hydrogen, which is the lightest you can ever hope for
3. Why not just use a big vat of Hydrogen?

In fact, I've even heard of proposals that would use ground-based lasers to heat Hydrogen, used as the rocket's reaction mass. Both laser-thermal and nuclear-thermal use a unique form of heat input. You can't just open the bottom of a $H_2$ gas pressure tank and fly it into orbit, because you're also limited by the thermal velocity of the molecules.

But that's not very convincing. Why can't we just heat $H_2$ gas to the temperature you would have gotten from the nuclear thermal rocket, then load that into a tank / rocket, and blast to orbit?

Sure, you lose a large amount of thrust as the depletion of the tank reduces P and T. And you have lots of structural mass from the (now) pressurized rocket boosters. But the advantage is going from $18 \text{amu}$ of the reaction mass to $2 \text{amu}$. I mean, there are valid cases for nuclear thermal where that would justify the weight of an entire nuclear reactor. After all, the main engineering reason we don't use those is because of the radiation nightmare.

Even in very fanciful compilations of would-be rocket technologies, I've never seen anyone touch on this concept. Putting hot Hydrogen gas in a pressure tank just doesn't seem that difficult (okay, there's H embitterment, but it won't stay there long). And after all, if the Hydrogen you put in the tank has similar conditions to what the exit from a nuclear thermal rocket would, it's not that much different. I can only think of one possible thing that could kill it - which is the structural mass for pressurization. You could do that calculation, and my bet would be on it maintaining viability.

What kept this line of design out of the discourse in classical rocketry? It's probably a laughable idea, but with my knowledge I have no way to rule it out.

• I'm not sure I quite understand the question. Are you suggesting that you, on the ground, heat Hydrogen to near-fusion temperatures. Then shove the resulting plasma into some form of tank, which you then fire out of the back-end of a rocket engine? – Nicol Bolas Sep 5 '13 at 9:01
• @NicolBolas Not fusion, because nuclear thermal rocket temperature is limited by materials. This is still well below the dissociation temperature of the H-H bond (I think). So, whatever that limit is, yes. – AlanSE Sep 5 '13 at 11:14

Actually, for gasses, higher atomic numbers are actually better than lower atomic numbers. This is the primary reason why Xenon is the gas of choice for ion drives, it is the most massive elemental non-radioactive gas around. The reason behind this logic falls under the Ideal Gas Law, $PV=nRT$. Essentially, as the temperature goes up, so does the pressure. However, as the atomic number goes up, the pressure goes down. As the most important part of spacecraft is the momentum, and momentum equals mass times speed, basically you want the most mass for your volume. Liquid hydrogen, however, can be stored much denser.

Okay, for your specific idea, what pressure would the hydrogen need to be stored at to make it work? Well, the proposed temperature for NTR rockets is around 3000k. Let's assume you want a density similar to liquid hydrogen as well. That density, according to google, is 70.85 kg/m³. Okay, so let's take those numbers and plug them into the ideal gas law, assuming a volume of 1 m³. That gives a total of 35425 mols of hydrogen. Using this calculator, that would provide a pressure of 9514 atmospheres, which would need to be maintained at 3000K. I don't know of any substance that can contain such pressure that wouldn't weight a ton.

Just for the fun of it, let's assume a super dense gas, say, Sulfur Hexafluoride. I'm going to ignore the fact that this would almost certainly be banned due to it's extremely high greenhouse gas potential. It's atomic mass number is 146, thus the number of mols per 1 m³, assuming the same mass as hydrogen, would be 485.3. Putting it in to the same calculator, the pressure would be 130 atmospheres, which is manageable, but probably not at such high temperatures.

The bottom line, storing high temperature, high pressure substances is pretty much impossible with today's technology. Perhaps sometime in the future someone will come up with a better way to make this happen, but for now, I wouldn't count on it.

• The tanks would have to have a very low net density. The liquid hydrogen density is clearly unworkable, as you've shown. The low density would increase air resistance, but that could be overcome with scaling. That could still rule out any practical use, although it would remain possible for mega rockets (I haven't calculated anything yet). But I don't see heavier gases as being better since the relevant equation is $1/2 m v^2 = 2/3 k T$, and v is the only thing that matters for the kinematics. – AlanSE Sep 5 '13 at 12:38
• The ideal gas law is not applicable at a pressure of 9514 atmospheres. – Uwe Mar 22 '19 at 17:02

I found it. The reason is because of the pressure vessel weight. My intuition was wrong on that point.

Assume a long cylindrical tank. The weight of the tank itself is the following.

$$M_t = 2 PV \frac{\rho}{\sigma}$$

The mass of gas in the tank is the following where $m$ is the formula mass.

$$PV = N R T = \frac{ M_g }{m} RT$$

Combine these two to get the ratio of the gas weight to the tank weight.

$$\frac{M_g}{M_p} = \frac{ m \frac{\sigma}{\rho} }{ 2 RT }$$

One of the best options for structural material is carbon fiber. The strength to weight value for that is:

$$\frac{ \sigma}{\rho} = 2457 \frac{kN-m}{kg}$$

If I assume that the gas is held at $1500 K$, then that limits the idea to a pathetic specific impulse of $440 s$. This is useful for a conservative calculation. If the tank to gas mass ratio isn't good for this value, it will never be a competitive idea.

$$\frac{M_g}{M_p} = \frac{ ( 1 \text{amu} ) \left(2457 \frac{kN-m}{kg} \right) }{ 2 R (1500 K) } = 0.2$$

The tank would weight 5 times as much as the propellant it stores. This is with the most optimistic assumptions. This rules out the idea. We conclude this idea is basically impossible because it is impossible to make a material light enough and strong enough to pull it off.

• I wouldn't call 440 a pathetic ISP, but... – PearsonArtPhoto Sep 5 '13 at 20:29
• You may find that your carbon fiber doesn't work at 1500 degrees K either. – user8269 May 25 '19 at 7:40