Which are the benefits and the challenges for a new Space Launch System (SLS) version with four Solid Rocket Boosters (SRB)? Benefits i mean what would gain in payload capabilities, how much more payload would put in low Earth orbit and beyond Earth's orbit, or what kind of payload could handle and support (for example an entire space station or "spaceship" for missions beyond Earth's orbit). Of course calculations or simulations would be needed to have very accurate values, but I would like to have an idea and interested for some approximate possible values not neccesarily very accurate. With this configuration and new payload mass capability in orbit or Earth escape, one mission that requires two SLS rocket launches would require only one. With challenges I mean technical and engineering difficulties not opinions about the cost or if the government would support and fund this SLS version or not. I am speaking for that case where everything has a "go" and supported. Which are the profits and challenges in theory for this design?
closed as too broad by Tristan, Puffin, uhoh, Jan Doggen, ForgeMonkey Dec 22 '16 at 10:46
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Let me be clear: Rockets are not LEGO elements. Real life is nothing like KSP.
The capability to selectively include multiple SRBs would have to be designed into a vehicle from the very beginning of its design. The presence or absence of boosters, especially ones as large as SLS's, means changes at just about every level of the program: structural design, launch trajectory, control systems, sizing of stages, payload environment, abort capability, ground segment design (up to and including building a whole new launch pad to support the massive weight).
A four-booster SLS would not be SLS -- it would be a wholly different rocket. As such, this question isn't really that meaningful.
That said, adding boosters would mean you have more liftoff thrust, which means that in general, you can launch heavier payloads to orbit. It's not really that simple though, and you play a game of diminishing returns, wherein more is simply more, not better.
Some preliminary numbers.
Going from this site, each SRB has around 16000 kN of thrust and a gross liftoff mass of 731885 kg.
Leaving everything else equal (which as Tristan points out isn't realistic, but I'm not qualified to do realistic), adding 2 boosters gives you about a 57% increase in gross liftoff mass, 80% increase in total liftoff thrust, and about a 16% increase in liftoff T/W. You also gain an additional 27% or so of cross-sectional area, so you get a proportional increase in aerodynamic drag.
So using liftoff T/W as a very rough proxy, you're looking at 16% or less increase in payload for a given mission (for SLS Block 1, that means going from 70 t to a little over 81 t).
Edit Note that Block 2 offers an 85% increase in payload (130 t) by still using 2 boosters (lighter and more powerful than the current set) and a more powerful upper stage. Improving the upper stage gets you the most bang for your buck.