In industrial chemistry it's well known (Armagnac vs. Cognac) that continuous processes are more efficient than batch processes.

In-game microtransactions have competed so favorably with just handing cash to a vendor and getting a videogame in return that they're now regulated.

Similarly, has anyone considered rocket staging that is somewhat continuous rather than discrete ($n$ > 3), beyond the discarded research into literally continuous autophage rockets?

Or must we wait for nanobots to be able to build turbopumps thirty seconds before MECO?

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    $\begingroup$ Damn the t̶o̶r̶p̶e̶d̶o̶s down votes full speed ahead! The reference to the column still for continuous vs batch processing is probably lost on most readers. I remember the disruptive company Ball Semiconductor 1 2 3 was going to revolutionize the industry with a continuous process little 1mm balls flowing through tubes, each one a complete circuit instead of batches of wafers $\endgroup$ – uhoh Feb 16 '20 at 7:45
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    $\begingroup$ The question is nonsensical. Microtransactions have nothing to do with chemical processes, and what in the world do nanobots have to do with rocketry? It's not even clear from the question in what way rocketry should be considered a batch process. $\endgroup$ – Wayne Conrad Feb 16 '20 at 9:30
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    $\begingroup$ @WayneConrad While the presentation leaves a lot to be desired, the question is clear: Why do rockets use few, large stages, instead of a lot of small stages? $\endgroup$ – Polygnome Feb 16 '20 at 11:26
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    $\begingroup$ @Polygnome the first two links border on spam, without some serious additional explanation. $\endgroup$ – Moo Feb 16 '20 at 13:14
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    $\begingroup$ @StarfishPrime how about burning the fuel tank too as it's being used? I imagine a grinder-like "engine" which continuously eats a large fuel-sausage "skin" included. $\endgroup$ – Dragongeek Feb 16 '20 at 14:20

Conceptually, staging is getting rid of hardware we no longer need. Keeping useless hardware attached to the rocket is expensive, since added mass reduces acceleration.

Ideally, we would want to get rid of hardware as soon as it gets useless, instead of piling it up to a "batch", which is essentially what the question boils down to.

Rockets are very simple*, so a stage is essentially just:

  • Propellant
  • A propellant tank
  • Engines

Around 90% of the mass is propellant. Spent propellant is naturally discarded immediately in a rocket, so this is a continuous process. Most of the mass in a rocket is subject to continuous staging already.

Propellant tanks are a different matter. They have a natural batch size, the size of the tank. Discarding a tank before it's completely empty also discards the remaining propellant. The only way to get around this is by using multiple small tanks instead of one big tank, but since tanks are subject to the square–cube law, that would mean more mass in the tankage. There may be some trade-off there, but ultimately the increased complexity leaves it undesirable for launchers.

Finally, the engines. Rocket engines typically run at full throttle, and even throttleable engines aren't usually very adjustable. That's because a higher acceleration is an advantage for not wasting fuel fighting gravity. There's therefore no continuous discarding of them (and even if we throttle engines, they don't get lighter when the thrust goes down).

So we want to keep the engines running at max, until their mass is no longer worth it. That's a cutoff point, where we should get rid of them entirely. Design follows that. If these engines are discarded, they will no longer need propellant, so the tanks should only contain enough propellant up to this point. With no more propellant and useful engines, the package of empty tank + engines can be discarded simultaneously, as what's familiar as a "stage".

(n > 3 definitely happens. See for example Juno I, or N1)

  • $\begingroup$ This elegantly breaks down the "why not n much greater than 3" problem into individual engineering constraints. $\endgroup$ – Camille Goudeseune Feb 16 '20 at 18:59
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    $\begingroup$ Also worth noting that interstage assemblies add mass without providing any performance; the more interstages, the more dead weight. $\endgroup$ – Russell Borogove Feb 16 '20 at 22:33

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