>>10525471I'm not sure of exact figures, but I can hazard a guess.
One of the biggest limiting factors in making big rockets are the first stage engines. A big rocket requires a huge amount of thrust at launch to lift it off the pad. More thrust requires either larger engines or more engines. There is an upper limit to how big kerolox engines can be before combustion instabilities become a huge problem, the F-1 engines from the Saturn V. There is also an upper limit to how many engines can be used on one stage before the plumbing required would be an issue, thirty engines on the N-1.
m0 = F*N/(R*g0)
m0 = Mass of rocket at launch
F = thrust of one engine
N = number of engines
R = thrust to weight ratio at launch
g0 = acceleration due to Earth's gravity
Assuming a thrust-to-weight ratio of 1.35 (which is pretty low, but usable), it can be found that thirty F-1 engines (each with a thrust of 6770 kN at sea level) can lift a 15,340.5t rocket off the pad (note, that this is the total mass of the rocket, not the payload). The F-1 is 3.7m in diameter at it's widest. If they were ideally packed so that they took up the least amount of space, then the rocket would be approximately 20.35m in diameter (the actual diameter would be larger because you don't want engines to be so close to each other).
So the largest possible rocket would have a total mass of 15,340.5 metric tons with a diameter of over 20 meters.
Obviously this takes some very general assumptions. Such as thirty engines being the hard limit of number of engines as the BFR and later ITS will challenge that. Once much higher numbers of engines can be used, then it may not be necessary to use F-1s.
