FWIW, the Project Rho page I linked to also gives the derivation of the relativistic rocket equation. When I plugged in numbers, assuming an exhaust velocity of the speed of light (ie. impossibly high), I get a mass fraction of about 2,000,000 to reach top speed. Then another 2,000,000 to slow down.
Assuming the fully loaded RV weighs 5 tons, this means at max velocity the rest of the ship weighs 10 megatons, which is 10M cubic meters of water, or a cube 200m on each side.
That sounds like plenty of material, right?
The same Project Rho page links to https://arxiv.org/ftp/physics/papers/0610/0610030.pdf which calculates that at the relatively slow 0.995c "the penetration depth of protons of this energy will be ~40 m in water and ~10 m in titanium".
For 99.99999999993978% c, even 10M cubic meters isn't going to be enough.
Assuming the fully loaded RV weighs 5 tons, this means at max velocity the rest of the ship weighs 10 megatons, which is 10M cubic meters of water, or a cube 200m on each side.
That sounds like plenty of material, right?
The same Project Rho page links to https://arxiv.org/ftp/physics/papers/0610/0610030.pdf which calculates that at the relatively slow 0.995c "the penetration depth of protons of this energy will be ~40 m in water and ~10 m in titanium".
For 99.99999999993978% c, even 10M cubic meters isn't going to be enough.