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Why use SRBs instead of a simpler rocket design that dispenses with SRB's and instead has a bigger main engine?

The Saturn V escaped earth's gravity just fine without boosters. Since then though SRBs have been widely used.

Is it cost efficiency that lead to the use of SRB's rather than hydrogen/oxygen main engines for example, or are there other considerations?

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    $\begingroup$ $ / lb to where? Total lifecycle cost? Which parts of the system are reusable? Right now this is a "how high is up" question. It was cheaper in the short run to build shuttle with srbs instead of a fully reusable first stage. Maybe not in the long run. Details matter. $\endgroup$ – Organic Marble Sep 7 at 23:11
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    $\begingroup$ Relevant Wayne Hale (Former Space Shuttle Flight Director) blog post on measuring cost. waynehale.wordpress.com/2019/11/09/… Turns out it's very hard to measure such things. I think this question is in principle answerable, but will need a lot of hand waving. $\endgroup$ – Ingolifs Sep 7 at 23:22
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    $\begingroup$ Your question makes several unsupported assumptions and ignores many other things that impact cost. You treat hydrolox engines as the only alternative, but the Saturn V didn't use hydrolox on the first stage, and neither do SpaceX's Falcon 9 or Starship, Rocket Lab's Electron, Northrop Grumman's Antares, the Russian Soyuz and Proton, or many other rockets. Most of these don't use solid boosters, either. And concluding that "the lifting bang-for-buck is greater for SRB's" based on the Saturn V not using them is quite a logical leap. $\endgroup$ – Christopher James Huff Sep 8 at 0:45
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    $\begingroup$ The Saturn rockets were not cheap, and therefore not a good stick to measure by. $\endgroup$ – GdD Sep 8 at 8:42
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    $\begingroup$ @SteveLinton Delta IV Medium (now retired) and Delta IV Heavy use a hydrolox core with no SRBs. They were/are notably expensive, but so were the variants that did use SRBs. $\endgroup$ – Christopher James Huff Sep 8 at 15:02
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Liquid hydrogen makes a poor first stage fuel. First stages operate with the vehicle full of propellant and lifting itself directly against gravity, and need thrust more than specific impulse. That means a high mass flow rate, and liquid hydrogen's lower density makes it more difficult to pump enough of it through the engine. Solid rockets are from the high thrust/low specific impulse end of the spectrum, and serve to get the rocket moving when it's too heavy for hydrogen engines to do the job. A couple rockets additionally use variable numbers of SRBs to allow a "dial-a-rocket" functionality, adding more of them to support heavier payloads or higher orbits.

There's been many liquid fueled rockets that do not use either hydrolox first stages or solid boosters, instead using kerosene (Soyuz, Falcon 9/Heavy, Electron) or hypergolic propellants (Proton, various Long March rockets). Instead of adding boosters, they just build the rocket big enough to handle the largest payloads in the target market, and sometimes add additional upper stages. This has generally been more commercially successful: the Russian rockets have done a couple thousand launches over the years with relatively low launch costs, and SpaceX's Falcon 9 has recently been able to undercut them. In the case of the Falcon rockets, the booster returns for reuse and its cost gets spread over multiple launches, so it doesn't matter so much that it's oversized for many payloads. SpaceX's Starship is to carry this further, reusing both booster and upper stage, using methane as a fuel.

For some numbers: each SRB added to an Atlas V adds about $7M to its price. The GEM-63XL to be used on Vulcan makes changes to improve its economics, but it's also larger, so that's probably a decent estimate of its cost and matches up fairly well with the expected price range. For comparison, the Falcon 9 first stage is estimated to cost around \$20-30M to build, but is expected to do at least 10 flights, and SpaceX recently contracted a flight (the IXPE) for just \$42M.

One major reason for the continued use of SRBs is politics. SRB technologies are shared with ICBMs, and the manufacturers of such have substantial political influence. For examples, look at the events surrounding how Shuttle SRBs ended up being made in Utah (ultimately resulting in the Challenger disaster), or the fights around the Ariane 6 design, which originally was going to have first and second stages consisting entirely of solids.

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SRBs tend to be used for one of two types of purposes:

  1. The rocket core is the same, but sometimes needs a bit of extra performance (Atlas, Vulcan)
  2. The rocket core is hydrogen, and doesn't have enough thrust to get off the ground.

For the first one, a solid rocket is preferable as the rockets need to be cheap and small, and solid rockets are much easier, not requiring an expensive rocket engine. Solid rockets can be made any size, while liquid engines are much more difficult to make small. The small size makes them more configurable.

The Space Shuttle was not capable of lifting itself off the ground without the solid rockets. The hydrogen allowed for an extremely efficient vehicle, but not as high thrust as is really required to go. Solid rockets provide a good assistance with that, having higher thrust but lower efficiency.

Why did the main engine of the Space Shuttle use hydrogen? Well, the engines were reused frequently on the program. Using hydrogen avoids soot getting in to difficult places, making it easier to keep the engines going. The soot is a major concern today for reused RP1 engines, SpaceX has to keep an eye on the soot levels and periodically replace components when the levels are too high. SLS is using hydrogen because of the desire to mimic the Space Shuttle.

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