Single-use nuke-propelled mass driver spaceship
So this is in the context where space battles are fought by ships that are little more than giant railguns (or other electromagnetic mass drivers), and therefore are fought at extreme ranges with very fast projectiles.
I have this rather fanciful idea of a single-use spaceship that is essentially a giant tube housing a projectile and a nuke, plus some aiming and targeting systems. While the nuke would cause irreparable damage to the rest of the ship, the idea is that there would be enough time for the detonation to accelerate the projectile (or what remained of it) out of the barrel. The back end of the projectile would presumably have to be made from some ablative material.
Ignoring things like expense, practicality, targeting etc, I would like to know two things:
1. Is this even a feasible design?
2. 898
How would one estimate the velocity of such a projectile, given the projectile mass $M_p$, the ship mass $M_s$ and the yield of the nuke used (which let's say for simplicity is of the range of current nuclear weapons, from 10 kt 100 t to 25 Mt)?
I am aware of Operation Plumbbob, where they detonated a 300 t nuke underground with a steel lid on the shaft weighing 900 kg. The lid was estimated at moving above 66,000 m/s, which is six times earth escape velocity.
EDIT: comments have pointed out that some sort of transference of thermal energy to gaseous kinetic energy is needed. Below is my revised picture. Where A stands for ablator (not quite the right word I know, but I can't think of the right one off the top of my head), a mass of material that readily converts to a gas with high kinetic energy (I'm thinking of a slug of ice or solid ammonia, due to the hydrogen content) which then pushes on the projectile. I acknowledge that a megaton nuke is likely to disintegrate the entirety of the ship before any meaningful acceleration can be imparted on the projectile, but suspect that smaller ordnance will be better suited for creating appreciable acceleration on the projectile. 912