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re: What is missing from this equation?

My off-the-cuff calculations (simple equation for cylinders: t = pd/2s) shows a minimum thickness of about .08. And that's with no safety factor!

There are a LOT of issues in pressure vessel design (something I do a lot of in the launch business) besides pure tensile strength numbers. Here's some of them:

Obviously, there's safety factor, which can range as low as 1.5 for some materials and unmanned space applications, up to 4 plus for things breathing bottles and the like. In many cases, there are regulations for these.

While steel doesn't melt until very high temperatures, its strength turns to crap when it gets hot, long before it melts. Something to seriously consider in a rocket design. This was also the bane of the World Trade Center. There are charts for specific materials. Different alloys behave very differently.

There is elasticity. Steels with very high tensile strength tend to have a very short distance between their yield point (where they start to "stretch") and their rupture point. Other alloys, not as strong, have a wider range. Some of my expendable rocket designs have specified 5000-series aluminum, which is not nearly as strong as something like the 2000-series alloys normally seen in rockets and aerospace, and makes for a heavier rocket, but it has no heat-treatment or welding issues, and is very forgiving as far as yield goes.

There is fatigue, or the tendency of a material to crack and weaken when stressed and unstressed many times. This is not much of an issue for disposable solid rockets, but is a prime issue for things like scuba tanks, and a critical issue in airframes.

Welded joints sometimes have the strength of the parent material. A lot of times they don't.

If you are going to build your own solid rocket motor, get some help with the numbers. If you insist on going it alone, I'd start with off-the-shelf pipe stock rated and stamped at the pressure and temperature I was using. Safety factors are built into this. Temperature is a BIG issue. Think about some serious insulation between your grain and your wall.

A solid rocket motor that is not designed right has another name: grenade.

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