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In a campaign I'm running, I have players who want to attack an enemy ship. Their current plan is to use Water Breathing and swim along the bottom of the body of water the ship is in to get under the ship, then start attacking to put some holes in it and try to sink it.

I'm trying to figure out how to run the encounter. From DMG (p.119), ships have a damage threshold that must be exceeded in order to deal damage, and they have an AC. From the PHB, underwater combat places the attacker at a disadvantage if they aren't using certain weapons (dagger, trident, etc).

Thing is, the HP of the ship in the DMG is probably representative of the whole thing.
Is there any published material for the mechanics behind putting a hole in the hull of a ship, or what that does to a ship?

There are no such published mechanics. That means it's time to improvise.

So what you have here is a unique encounter. That's great! Those can be a lot of fun, but they require a bit of improvisation.

First, figure out what rules do apply. You know that the underwater fighting rules apply. You know that the AC is 15, and no hit that deals less than 15 damage is going to matter at all. Okay. Cool. Now figure out how you want the encounter to play out for the characters. It sounds like you're aiming for a stealth encounter of sorts, so you're going to want to figure out what things can alert the crew, what things might draw other attention, and what the crew and/or other attention can do about it. Just as a rough example...

• Give the ship some number of "flood points". This indicates how much water it can take on before it sinks.


• Have some function by which damage done to the hull translates to flood points per round.


• Have something about how dealing damage to the ship in various ways can alert the crew (from the smashing noises). You can go into as much or as little detail as you want to here - either different parts of the crew get alerted at different times or they all get alerted at once or whatever. Similarly, various amounts of flooding would be likely to alert the crew (they'll notice that the ship is sinking) and possibly some other stuff.


• Figure out what the crew can do to try to thwart the PCs once alerted. (like, say pumping out water, trying to fix the holes, trying to attack, calling for help, moving the boat, or whatever). Put in some rules for those things.


• Figure out if there are any sea critters nearby that might be attracted to the noise and need to be fought off (which might make its own noise).

...something like that. You can make it more or less complicated and more or less challenging as you like depending on how much of a big deal you want this to be, and what kind of an encounter would work well with your players. When you're figuring out levels of challenging, remember that the first challenge is going to be dealing at least 15 damage while flailing about underwater in the first place. Also, as always, try to make sure that everyone who comes along on this underwater adventure has at least something useful they can do.

I recommend reading the Unearthed Arcana: Of Ships and the Sea

It has many good examples, giving Stat Blocks, combat, and other useful information you might seem important.

For example, the sailing ship entry says this:

Hull

Armor Class 15

Hit Points 300 (damage threshold 15)

You can have instead of reducing the HP of the ship to 0, you can have them focus on a part of the shell so they can make a small hole, making a timer so the ship sinks, or so they can infiltrate.

As this is a playtest material, you may with to work with this and adapt it once you see how it plays out at the table. Also remember that if people are damaging the ship, there is a chance that someone on the ship notices.

If you want to introduce a note of (unwelcome) realism:

Wooden ships don't sink (usually)

Up until the development of ironclads, it was rare for a ship to be sunk in combat. Partly this was because the opposition didn't want to sink them, they wanted to capture them, but mostly its because wood, unlike steel, floats in water. If you need to know why this matters have a look at how ships work. In essence, if the average density of the ship, the stuff on and in it (including air/water) is less than the density of water (about $1027text kg/m^3$ for sea water or $1000text kg/m^3$ for fresh water although they both vary with temperature and salinity - not all seas have the same salt content) it floats, otherwise it sinks.

Putting holes in a ship below the waterline allows the water (at the density above) to displace air (about $1.3text kg/m^3$ which will increase the density of the ship. This will cause it to reach neutral buoyancy with less ship above the water and more ship below the water. At some point, the waves on the sea start going over the ship rather than around the ship so the water starts getting in at the top rather than the bottom - at that point the transition from 'sinking' to 'sunk' happens rather quickly. When this happens depends on the design of the ship, the size of the waves and if its settling evenly or with one end down and the other end up.

Many, many wooden ships were 'wrecked' but that is different from being 'sunk'. A shipwreck happens when the ship strikes something - a reef, the shore etc. and becomes stuck. The waves then twist and buckle the ship until it suffers structural failure and breaks apart. This can happen to steel ships as easily as wooden ones although modern navigation aids and charts mean this is today a very rare occurrence - Costa Concordia springs to mind.

In combat, the biggest threat to a wooden ship was fire - either caused by enemy incendiary attack or by accidents with their own fires. An out of control fire could easily burn a ship to the waterline after which the hull would sink because see above.

Ram armed galleys could sink each other but this worked because of their relatively light construction and the low freeboard that the oars made necessary. Even so, sinking was a secondary objective - you rammed the enemy to allow your troops to board and capture the ship while their troops had to deal with the consequences of being rammed - like being dead, trapped under debris or trying to stop their ship from sinking.

A fire attack is going to be more realistic than knocking holes in the bottom - unless its a really big hole - like that from a Passwall spell. Or a really small ship.

Of course, your idea is way more fun - so do what @BenBarden says.

What the crew can do

All ships leak and therefore they have pumps designed to remove the water quicker than it can get in - usually a lot quicker because the pumps require manpower and you don't want to have to work the pumps 24/7. Of course, if someone has knocked holes in the bottom of your ship, you will do it 24/7 until you fix the holes.

You can also change the average density of your ship by throwing heavy stuff overboard - anything made of metal is really, really dense, for example, steel is 8 times denser than water. A cargo ship can offload its cargo and a warship can get rid of its weapons.

The other thing the crew will do is plug the holes - to this day navies employ ship's carpenters for exactly this purpose. Even though ships are built from steel by boilermakers they are patched at sea with timber by carpenters because timber is quicker and easier to work with than steel - a vital consideration when people are shooting at you.