How big could a rocket get?

Question

What are the practical limitations on the size of Earth based, orbital rockets? How tall/heavy might we make a rocket?

For the purposes of this question, I'm mostly interested in rockets using existing chemical fuels and building materials, no exotic technologies.

How much bigger could Earth be, before rockets wouldn't work? asks about hypothetical rockets on other super-Earth planets, but here please address larger rockets for larger payloads right here on this Earth.

Is there a theoretical limit to the size of launch vehicles? asks if there are limits to the size of rockets, but here please address what those limits are.

Answer 1

If we enlarge a big rocket by a scale factor of two for all diameters and heights what will happen? All area will increase by a factor of four and all volumes and weights increase by a factor of eight. For eight times the mass we need eight times the thrust. But if we take the same reliable rocket engines as before and don't build, test and debug larger engines, we need 8 times of engines as before. For a super size Saturn V we will need not 5 but forty engines. But we got only the double diameter of the rocket and 4 times the area and may mount only 20 engines instead of the needed 40 engines.

So we build new engines with double diameter and height and mount 5 such engines. Mass flow through the pipes, valves and nozzles will increase by a factor of 4, the same as the areas. The combustion chamber pressure will be the same. But using 5 engines with four times the thrust we can not take off, we need 10 engines with 4 times the thrust. Therefore we need new engines with double diameter and eight times the thrust. We need more powerful turbo pumps to get eight times the mass flow through pipes of double diameter.

If we want 8 times the thrust for an engine with the same combustion chamber pressure, we need to increase the engine diameter by a factor of 2.828 ( the square root of 8), the same scale factor for all pipes and valves diameters.

What about parallel staging as used by the Soyuz mentioned by uhoh? A Soyuz booster was about 2.7 m diameter and 19.6 m high, it used four rocket engines. If we bundle 64 of those boosters in a square of 8 by 8, the edges of this square are 21.6 m, that is more than the height of 19.6 m. The total number of engines is 256. I don't believe that a bundle of 64 boosters could be mounted, transported to the launch pad, fueled and launched with success.

The next step would be a bundle of 16 by 16 boosters, that is 256 boosters and 1024 engines, 43.2 m wide(horizontal). Of course these bundle has excessive atmospheric drag and does not make sense.

So we can't win by using a huge number of engines with the same size, doubling all dimensions of an existing engine does not help. Using engines with 2.828 diameter requires a rocket of double height and diameter but 2.828 the diameter of the lower end to mount the engines.

The Saturn V was 110 m high and 10 m diameter. If we scale up the Saturn V by a factor of 2, we need 28.2 m diameter at the lower end. The ratio between height and maximal diameter was 11 at the original size and is now 7.77. What happens to this ratio if we double the size several times? After two steps the ratio is 5.5, after 4 steps 2.75 and after 8 steps the ratio is only 0.6875. The rocket's diameter at the engines is now larger than the height of the rocket. This huge rocket would not only be ugly, the drag would be much too high. Acceleration to high speed would be impossible in the atmosphere.

Answer 2

Noting how practical limitations is the question, not physical limitations, the most serious one appears to be lack of large payloads.

While many super heavy launchers have been conceptualised, designed, or even built, what ultimately sets a limit is that nobody needs payloads that large.

The ambition and budget to land humans on the Moon caused a temporary demand for large rockets, but pretty much any other use of space can be served well by strapping a few cameras, computers and solar panels into a package massing at most a couple of tons. Even human space flight does not require more than capsules and modular habitats.

So there's no demand for larger rockets than those already built. That's a decisive practical limitation.

Answer 3

Well there is no theoretical limit it just gets progressively harder. I doubt we can go much bigger than starship without risking the destruction of the launch pad. There are sea based designs like the sea dragon that can get around that and they are insanely massive. There comes a point where we just dont have the infrastructure and manufacturing capabilities to build bigger but that can get expanded given enough desire. Also when you get big enough the square cube law doesnt get as good since you would need to brace the rocket a lot to make sure it doesnt collapse in on it self. There is also the issue that there would be nothing conceivable that you would use it for. I mean what do you do with for example 10 000 tons of payload? If I had to guess something in the range of x10 the sea dragon in capability would be the upper limit of anything conceivably useful under current technology.