The disadvantage of a solid fuel rocket is the whole block of
solid fuel must be located inside a though rocket motor. This
implies an excess of weight and of volume. Perhaps there is a
way to avoid this drawback.
The basic way a modern rocket motor works is the following.
Hot gasses with a high pressure are produced inside a chamber
by a block of solid rocket fuel (or by liquid fuels injected
inside the chamber). The gasses move at subsonic speed towards
the outlet were they are accelerated by a converging nozzle up
to the speed of sound. At that speed they arrive inside a
diverging nozzle where they accelerate above the speed of sound
up to the maximum supersonic speed their heat and the outside
pressure allow.
One could smear a little bit of solid fuel inside the
supersonic diverging nozzle (or inject some liquid fuel). The
gasses produced by that additional fuel will be driven to
supersonic speed by the gasses coming from the inside of the
motor and they will be allowed to expand and accelerate inside
the diverging nozzle just like the other gasses. (I believe so,
which is not a proof.)
This makes the whole diverging nozzle could be made of solid
rocket fuel. That fuel will burn and add the propulsive power
of its gasses to that of the gasses coming from the inside of
the motor.
This implies the whole rocket motor can be made of solid
rocket fuel. Provided the burning speed of the different zones
of the powder block are tuned the right way. What matters is
that while the rod of solid rocket fuel burns up its burning
end keeps the shape of a rocket motor. In the following drawing
the light green fuel is supposed to burn very fast, the yellow
medium fast and the dark green slowly. The whole block burns
from left to right and just leaves the end mantel.
I made some little rocket motors "that way" that lift of even
though the gasses were subsonic and I used a only one burning
speed. So this system works for sure. But I don't know if it
would have a better yield than a normal modern rocket motor. If
it has a good yield, then it has some advantages upon normal
rocket motors, since it needs no outer container and it burns
up gradually leaving no useless weight. It could allow a single
stage solid fuel rocket to go into orbit.
Another question is whether the carving out by burning of the
rocket motor shape will keep symmetrical enough. This can
perhaps be attained by using circles of very high speed rocket
fuel to force the symmetry.
I don't know what a possible outer mantel should be made of.
Perhaps a lightweight porous and rigid material.
I don't know either if such a rocket would be easier to
manufacture than a normal solid fuel rocket motor. Anyway, it
would be an interesting alternative to consumable rocket.
To guide the rocket maybe the outer mantel can be pulled by
ropes to bend a little bit. Another solution would be to use
little hydrazine motors at the top of the rocket.
Perhaps an aerospike version of this motor can be build.
A layer of fast fuel would be placed just beneath the outer
mantel. It would then really have a pencil shape while burning.