So a Dreadnaught fires a 20kg slug at 4025km/s over 800m. This gives an acceleration of:
800 = 0.5at^2
4,025,000 = at
t = 4,025,000/a
800 = 0.5a(4,025,000/a)^2
800 = 0.5 * a * 16,200,625,000,000 / a^2
800 = 0.5 * 16,200,625,000,000 / a
800a = 0.5 * 16,200,625,000,000
a = 0.5 * 16,200,625,000,000 / 800
a = 10,125,390,625m/s/s
For a Force of:
F = 20 * 10,125,390,6253
F = 2,025,078,125,060N
If we assume that a 100m accelerator can generate the same force, reasonable given that the limit on speed is more to do with barrel length, and that a 100m accelerator also fires a 20kg projectile then:
100 = 0.5 * 10,125,390,625 * t^2
t^2 = 100/(0.5 * 10,125,390,625 )
t = sqrt(100/(0.5 * 10,125,390,625))
t = 1.4054296272030758248960881731277e-4
t = 0.00014054296272030758248960881731277
v = 10,125,390,625 * 0.00014054296272030758248960881731277
v = 1,423,052.397137926892856699278708m/s
v = 1,423,052m/s
v = 1,423km/s
Kinetic Energy = 0.5 * 12.5 * 1,423,052.397137926892856699278708^2
Kinetic Energy = 12,656,738,281,249.999999999999999502J
Kinetic Energy = 3kt
At a speed of 1,423km/s the projectile is traveling over 200 times the speed of sound in steel, and almost any other material. So Newton's approximation from
Impact Depth is applicable.
Depth = Projectile Length * Projectile Density / Target Density
Iron has a density of 7.874g/cm^3. Silaris Armor is made from Nanotubes (~2.2g/cm^3) and Synthetic Diamonds (~3.51 g/cm^3) which combined have an average density of ~2.9g/cm^2. Now the Codex does mention them being crushed into "super-dense" layers. How dense "super-dense" is is unclear however lets say it's 20x denser which at 29g/cm^2 makes it the highest known density stable at STP.
The length of the projectile is unknown. The volume however must be:
V = 20,000 / 7.874
V = 2,540.0050800101600203200406400813cm^3
So let's say it's a cylinder with a face of 45cm^2 and a length of 56.44cm:
Depth = 56.44 * 7.874 / 29
Depth = 15.32cm
So even the galaxy's most advanced and expensive armor would need to be 7 inches thick to stop a simple Frigate round. That is a
lot of mass. At that density and thickness each square cm of hull adds 444.28g, almost half a kilogram, to the ships total mass.
Even a rough hull area estimate of a cube 100x10x10 meters gives 42,000,000cm^2 which would mean a hull mass of 18,659.76 metric tons. A similar sized submarine
in total masses a
third of that.