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Recoil is an interesting issue. For a regular gun, it depends on the mass of both the power charge and the projectile (and sabot, etc, if present).

As a rough estimate, you can assume all that mass, including the gases resulting from the powder charge, acquires a velocity equal to the muzzle velocity of the projectile proper.

Thus, the total momentum can be approximated by the total of the above masses times the projectile velocity. This is the impulse, the ‘kick,’ that is transferred to the gun, the ship, and the ocean (according to the law of conservation of momentum).

I don’t know what the comparison of powder mass to projectile mass is for big guns, but for small ones you often find the same order of magnitude, meaning that somewhere around half the kick of a small weapon is due to the propellant gas.

If this holds true for large naval guns, then the railgun

1. Has no recoil contribution powder gases;
2. Has less recoil due to the smaller projectile (how much smaller I know not)
3. Has more recoil due the the higher ‘muzzle’ velocity.

(By the way, there are large peak forces internal to the power supply, regardless of the technology it is based on.)

I don’t know the numbers for traditional big naval guns, but let’s say the railgun projectile is, say, 100KG, which is much smaller than that of a big gun.

Taking the railgun postulated in my previous post, the peak reaction force on the railgun and the ship would be 28.8 million newtons, or around 3600 tons.

The firing will impart 2.88 million KG-M of recoil impulse, and the projectile will possess a kinetic energy of 288 megajoules.

They’d better have a good energy-absorbing mount, or the recoil from the gun will eventually tear the ship and its contents to pieces! Of course, this issue has been dealt with continually since the days of the rope-restrained cannon on wooden warships.

(Anybody have a clean napkin, check my math.)

Because of the length of the weapon I guess it would be a spinal-mounted rail-gun (it wouldn’t be turreted, you would turn the whole ship to aim it).

The whole ship would basically be engineered as a single piece of ocean-going artillery to absorb the humongous recoil.

Sucks for the crew with quarters near the muzzle. Every six seconds you get woken up by a sound like Mt Pinatubo erupting.