# Is there a theoretical limit to the size of launch vehicles?

Is there a limit to the size (mass, structural issues) of boosters that can be launched either to orbital or escape velocity? I am asking about such constraints as the required thrust to weight ratio with existing technology, square-cube scaling, and the ability of the vehicle to physically support itself. I am not asking about the size of the infrastructure needed to operate the vehicle such as pad size, etc.

• This is an interesting question! You might find the answers to How much bigger could Earth be, before rockets would't work? a bit interesting, but this is definitely a different question than that.
– uhoh
Commented Oct 15, 2017 at 3:46
• The rocket equation requires a good ratio between structural mass and fuel mass. But the square cube law requires more structural mass for a gigantic rocket of 10 times the size of a Saturn V. Would anybody try to build a first stage with 50 % structural mass?
– Uwe
Commented Oct 15, 2017 at 9:40
• is there a theoretical limit to a power source we have not found yet? Commented Oct 15, 2017 at 11:41
• There might be some insight in reading about the largest rocket ever designed. en.wikipedia.org/wiki/Sea_Dragon_(rocket) Commented Oct 19, 2017 at 2:38
• I'd think the square-cube law works in favor of large rockets, not against them (more propellant volume per tank mass, so a more efficient design). Commented Oct 20, 2017 at 16:42

I believe the answer is yes--there should be a theoretical maximum rocket size for a given set of rocket technology (available structural materials, propellants, and engine design), but I don't currently have the resources at hand to give a specific answer. Here are the places I would start looking:

• Engine size. Unless the Technology Readiness Level (TRL) of aerospikes gets improved by more testing, bell nozzles will probably get size-constrained by their cooling needs, which generally require plumbing the nozzle with a jacket of propellant. More pipe requires more turbopump pressure, which certainly has some practical limit, though whether it gets dictated by pump size or the plumbing itself I don't know. Once engines hit their size limit they have to multiply, requiring supporting structure to distribute their thrust into the rocket, driving down the propellant mass fraction, decreasing available delta-V and thus the capability to reach orbit.
• Propellant tank sizes would probably ultimately be limited by hoop stress, which increases in proportion to the radius of the tank. For a given material and propellant choice there should be an ultimate tank size, after which there need to be multiple tanks with connecting structures, which begins driving the propellant mass fraction down, which directly affects the delta-V and thus the capability to reach orbit.
• As you get into REALLY big rockets, you may start to have structural torsion problems (essentially, the tail steers one way, but the rest of the rocket...doesn't) if you try to do steering without spreading the controlling forces along the structure. This multiplication of steering motors, associated structure, plumbing, and controlling electronics should also eat into the propellant mass fraction.

Obviously. There are limits to how tall a building can be because of the weight of the materials used. A rocket is in a sense a building, you'll reach the structural limits a lot sooner with a rocket because such a low fraction of it's mass is capable of bearing a load at all.

As your rocket gets taller and taller more and more of it's mass will have to go into it's own strength, eventually you will reach a point that making it bigger reduces performance instead of increases it.

There is no such limit on getting wider, however. In practice, though, the wider it gets the more torsion will matter and the more precisely things will have to be balanced. Somewhere down that road will lie a limit to what you can actually build without the rocket tearing itself apart but there is no theoretical limit in this aspect.

• A sphere is the theoretical optimal shape of a fuel tank, minimal surface combined with maximal volume. Building a tank much wider and less taller than a sphere is increasing the structural mass. A flat upper and lower bulkhead of the tank needs more structural mass than a bulkhead in the optimal shape of a hemisphere. There is a limit on getting wider when the ratio of structural mass and fuel mass gets too worse.
– Uwe
Commented Oct 23, 2017 at 14:09
• @Uwe You could make an abomination like I've used in KSP at low tech levels: Build a rocket that's basically copies of itself stacked in parallel. Commented Oct 23, 2017 at 17:27
• Stacking of rockets in parallel is also limited, you need additional structural mass for stacking. Imagine a first stage build from a lot of parallel stacked rockets and the mounting of a second stage above it.
– Uwe
Commented Oct 24, 2017 at 10:46
• @Uwe That's vertical, not horizontal. The KSP abomination I'm picturing was basically 5 rockets side by side. That meant one reaction wheel instead of 5, it meant 19 seats with tourists to 1 pilot vs 4 seats with tourists to 1 pilot. Commented Oct 24, 2017 at 22:31