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.
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.