Let's say we like the Space Shuttle design so much, we want to use it as a reference for our new rocket. But we want to build rocket which will be capable of launching larger payload into Earth's orbit. In order to save time, we will only scale up the already proven design and keep materials and fuel composition.
But one problem seems to appear. Although the rate of combustion depends on many factors, above all pressure, the combustion of solid rocket fuel is a surface/near surface phenomenon. If we scale up the dimensions of the SRBs uniformly in all directions, the combustion surface will grow with the square of the scale and the volume (hence the mass of rocket fuel) will grow with the cube, following square – cube law. Therefore the trust/weight ratio will decrease with scaling. Things get worst if we consider that rate of combustion depends on pressure, and volume of combustion chamber increases with the cube of scale also, therefore pressure inside chamber will gradually decrease. Hence booster becomes less efficient in converting chemical energy into trust.
What is the value of scaling factor at which we can with great confidence say SRB will not be able to lift its own weight and become ballast instead of lifting force? Is it possible that Space Shuttle SRBs already had optimal design for given composite fuel?