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I was just looking at a small but impressive compressed air/water rocket that launches off of a metal rod that runs through the nozzle and spans 3/4 of the length of the rocket. As the team increased pressure for subsequent launches, I wondered about a great or terrible idea to really make something like it move.

Suppose the rod was an anode, and the water tank was a cathode. Could an extremely high voltage be discharged through the water to quickly split it into hydrogen and oxygen, which would then ignite from compressive heating?

I would image that the simplest design, a full tank of water with a large durable anode rod would simply explode, but there are some things we could do to increase the odds of survival for the rocket:

  • Use a long, narrow body so that there is lots of surface area on the electrodes, compared to the volume of water
  • Ensure that the anode immediately flashes to a plasma, so that it does not obstruct the escaping fuel. For a very short time period, that column of plasma might still function as a conductive anode as the last of the water splits
  • Wrap the tank in the highest ultimate tensile strength material known to Wikipedia, monolayer graphene (130 GPa!), and expect it to deform during launch
  • Don't fill the tank completely full of water, include a compressible gas like helium to dampen the forces from explosion to a sort-of controlled burn
  • Try to prevent the oxygen and hydrogen from mixing too quickly, so that it burns instead of detonating

This all hinges on the ability to electrolyse many litres of water in milliseconds. Has this been investigated? Is there any fundamental reason why it couldn't work?

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  • $\begingroup$ The arcjet is a related concept, that uses electricity to directly energize propellant; it produces low thrust (with any practical amount of electrical power) but gets good specific impulse. en.wikipedia.org/wiki/Arcjet_rocket $\endgroup$ – Russell Borogove Oct 18 '15 at 23:07
  • $\begingroup$ Another more extreme and more plausible technique is using an intense electric current to initiate nuclear fusion, the technique in general is called Z-pinch, see: en.wikipedia.org/wiki/Z-pinch#Fusion-based_propulsion, this has the advantage of actually adding energy to the system. $\endgroup$ – Blake Walsh Oct 19 '15 at 9:14
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You'll need a nuclear reactor for that because the process of dissociation of water into constituent hydrogen and oxygen consumes vast amounts of energy and for an ascent stage you'll also need a very high energy density to provide sufficient thrust.

Direct anode/cathode system like you describe (i.e. electrolysis) is wasteful when you don't require separation of produced hydrogen and oxygen for later storage, and all you want is great expansion that steam provides, so it's much simpler to just superheat reaction mass to its dissociation temperature and then expel that at great pressure. Because electrolysis of water is so energy consumptive, most industrial use hydrogen is actually produced through natural gas reformation.

So, basically, a better solution to what you're asking about is called a Nuclear Thermal Rocket, and while working directly with hydrogen is preferable (simply because of $E_\text{k} =\tfrac{1}{2} mv^2 $ small molar mass exhaust products are preferred where there's linear relationship between their mass and their stored or absorbed energy density that can be later converted into kinetic energy of exhaust products), huge exhaust temperature that it produces often calls for mixing of reaction mass with water to reduce it.

Heat dissociated NTR exhaust products also provide roughly twice the specific impulse ($I_\text{sp} \approx 800-900 \text{ s}$, depending on exhaust temperature but it could go much higher, say, with metallic hydrogen, if you can somehow produce it) of recombining oxygen and hydrogen into water steam in LOX/LH2 cryogenic chemical rockets ($I_\text{sp} \approx 450 \text{ s}$).

In orbit, it would be possible to do away with a nuclear reactor and use solar thermal propulsion, but you'd probably want to make that a beam-powered propulsion system and separate your source of energy from your rocket to reduce its mass. 

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  • $\begingroup$ I figured that something like a nuclear reactor might be needed to crack enough water to get a large rocket to orbit, but the idea is to leave the reactor on the ground, and process the fuel just a few milliseconds before launch :D Beamed energy might work great for simply heating a reaction mass, I didn't realize that oxygen's oxidising energy isn't as useful as external heat directly applied to hydrogen. Not sure how you would prevent the beam from melting the rocket during ascent, but that's probably not harder than containing a lightning bolt in a bottle of rocket fuel. $\endgroup$ – Dan Ross Oct 18 '15 at 20:49
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    $\begingroup$ There's no need to process fuel a few milliseconds before launch, you're not solving anything that fueling cryogenic stages prior to launch doesn't solve (plus, you're making the process really inefficient in terms of invested energy to produce O/H, it won't have the density of LOX/LH2 and your launch system will likely be a whole lot more complex because of high voltage next to extremely reactive chemicals). Beam-powered propulsion could work tho, I added a link to Wiki article on it, and here's one paper on Solar Thermal Propulsion I liked. $\endgroup$ – TildalWave Oct 18 '15 at 20:54
  • $\begingroup$ "it won't have the density of LOX/LH2" -- LOX is only slightly denser than water, and LH2 much less dense, so surely equivalent mass of water is denser than separated LOX and LH2? $\endgroup$ – Russell Borogove Oct 18 '15 at 23:04
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    $\begingroup$ @RussellBorogove I meant that the hydrogen and oxygen produced with electrolysis won't have the density of LOX/LH2 (unless you invest even more energy to compress and cool it) ;) $\endgroup$ – TildalWave Oct 18 '15 at 23:08
  • $\begingroup$ Ah, I was envisioning the electrolytic dissociation being downstream of the pump. $\endgroup$ – Russell Borogove Oct 18 '15 at 23:14
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First we'll see how much energy you would need for the electrolysis:
Water has a molecular weight of 18.01528 g/mol, so 1 kg of water is 55.55 mol. You need 286 kJ/mol of energy to split water. 55x286=15.8 MJ for 1 kg of water.
15.8 MJ = 15.8 MW.s = 4.4 kWh of energy. If you wanted to split the water in 1 second, you need 15.8 MW of electrical power.
Assuming a 200 $\Omega$ resistance between cathode and anode, that translates to 56 kV at 280 A. Normal electrolysis cells operate at a little over 1.5 V. At those voltages, you are likely to get arcing between the anode and cathode.
Because you haven't separated the oxygen and hydrogen, any gas bubbles in contact with the arc will explode.
Also, the anode and cathode will heat up (in fact, you'd need big, heavy electrodes to keep them from evaporating at this much current), and part of your water will evaporate. This inhibits the electrolysis: water has to be in contact with the electrodes for electrolysis to happen.
So it's a race between the electrolysis process on one hand and the explosions plus steam formation on the other.
Finally, something strange happens when you put a large current through water:

However, once the maximum voltage standoff for water is exceeded and the dielectric effect breaks down, something strange happens: The discharge stops being electrolytic (as molecules can no longer move to the electrodes at the rate dictated by the current) and the resistance plummets all at once, allowing massive currents to pass through it. When that occurs a bright flash of light is observed and some of the water in the sample is atomized (atomization here is used to describe a change from the liquid to the gaseous state that does not involve heating, such as in ultrasonic water atomisers) following a very loud report and a powerful shock wave traveling through the liquid.

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  • $\begingroup$ I wish there a prize for "most quantitative answer"! While the accepted answer goes something like "...nuclear reactor… consumes vast amounts of energy … need a very high energy density." you go straight to kWh and MW. Then you describe what would limit the process if someone tried it. $\endgroup$ – uhoh May 20 '16 at 0:58
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A key physics limit is the conservation of energy. If you split water into hydrogen and oxygen, then let them "burn" to combine back into water, you cannot possibly gain energy from the process. The only energy you add to the system is that which actually turns into waste heat. Accordingly, there is nothing you could do with electrolysis here that you could not do with a simple heating element to boil the water nearby.

Alternatively, if you had a free multi-megawatt electrical power supply on board that cost you no weight and all of its fuel is weight-free also, you might be able to get quite a lot of power by high pressure steam with a giant heating element.

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  • $\begingroup$ The energy for splitting the water come from outside of the rocket, from a power plant or a huge bank of capacitors. It would electrolyse the water in the tank to high pressure hydrogen and oxygen, at the moment the rocket takes off. Now we have something similar to a conventional rocket, except that the fuel is under so much pressure that it does not need to be pumped; preventing the whole thing from just detonating would probably be the hardest problem. $\endgroup$ – Dan Ross Oct 19 '15 at 12:58
  • $\begingroup$ Rockets that use reaction mass are not about net energy gain but about conversion of stored potential (chemical, thermal,...) into kinetic energy. Actually, that part about "the only energy you add to the system is that which actually turns into waste heat" would be a perfect thermal rocket, if all of the generated heat could be converted to exhaust velocity. Problem with direct electrolysis for chemical rockets is that of required energy density and poor performance per energy invested into it. But it could work. $\endgroup$ – TildalWave Oct 19 '15 at 13:39
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    $\begingroup$ Yeah, that does make quite the bomb, doesn't it. Of course, if the energy is coming from a ground station, it has to actually be delivered, and that's a lot of juice. The kinetic energy of the space shuttle in orbit (most ideal case possible) is 4*10^12J. For perspective, that's almost identical to the energy contents of one CANDU nuclear fuel bundle. Unleashing it in a millisecond would be the power on par with the most powerful research lasers in the world (and would have to sustain that power for a millisecond). Just think of the wires involved in that kind of power/energy transfer! $\endgroup$ – Cort Ammon Oct 19 '15 at 19:52

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