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Would this rocket propulsion concept work?

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Would it be possible to make solid fuel structurally stable?

For instance, i know that rubbery ammonium perchlorate composite propellant is usually held in place by hydroxyl-terminated polybutadiene. Would it be possible to replace the polybutadiene with stronger and more stable (but still combustible) medium?

My theory is, if you could do this, you could create a solid fuel stage that would require much less housing and structural support, perhaps even none at all. you could even remove the nozzle, instead opting to design the fuel block with a bell-shaped cavity at the bottom, and the fuel would have to be ignited and burned from the bottom up. And as has been proven with rockets like the SS-520, a controllable engine nozzle is not necessarily needed for a functioning rocket.

Of course the fuel block would have to be very well designed and catalysed so that it would burn completely and maintain its shape. However, with no structural support needed, a rocket like this could achieve incredible mass ratios, to the point where even with the low ISPs of solid fuels, significant payload fractions could be achieved. In addition, the cost of launch could be significantly reduced, as complicated casings and staging mechanisms wouldn't be needed. I see it as a great way to partially negate the tyranny of the rocket equation.

However, i'm not an aerospace engineer. Could any of you clarify if this propulsion method would be possible? :)

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Main problem would be to contain the nozzle at the end. 
You use solid rockets for TWR, hydrogen for ISP, optimized liquid fuel has very low dry mass ratios. You want the SRB to be cheap and simple. 
Note that some interstellar designs think of using structure as reaction mass or even fuel. 

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 Solid fuel needs to be under pressure to burn quickly and completely enough to be useful propellant; that's part of why their dry mass is so high, the casing needs to contain that pressure. If you end up with any holes, and it would be very difficult to avoid them in a situation like this, you're not going to have a useful engine anymore. If you do manage to avoid holes, you've just reinvented the casing.

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Well, SRBs are the jackhammer that gives you a huge boost in Dv during launch phase. Given they are usually discarded upon decoupling, they are designed to be very powerful in TWR but very bad in ISP. The thing that makes SRB very powerful is that the entire booster is basically a giant casing that enclose a controlled explosion with huge pressure inside and force it to be expelled from small nozzle beneath the structure. In your design, one of the problem that I see is that the lack of nozzle means the pressure inside the booster would be lower than normal SRB. This might reduce the overall TWR of that SRB, which coupled with low ISP of SRB, would make it very inefficient to use as an assist in first stage. It might makes the design simpler, but it comes with a cost of it's main function: huge TWR during launch

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Something like this has been proposed here before, if I recall correctly. **does a quick search**

Ah, no, it wasn't here; it was over on the xkcd forum.

One big problem. If all you have at the base is a bell-shaped cavity, then you have no choke, where flow moves from subsonic to supersonic. If you have no choke, you have no proper rocket engine at all.

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