+1 for reminding me about incendiary rounds. Can a single 37mm round set fire to an entire ship of the line?

@Inthenameofthestory, a question of chance. There must be a hit, which is not a given. The hit must be near something flammable. A few little fires might be started, which can be extinguished by the crew (or just die down through pure luck). If the fire is not extinguished in time, it will spread.

It should be pretty easy to hit their black powder reserves especially since ships of the line could only move at a max speed of 12 knots.

I think a hit is pretty much guaranteed. I'll be generous and say the ship-of-the-line can fire from 500 yards. The sights on the battleship's anti-aircraft guns can accurately aim at fast moving, small planes much further away. They will have absolutely no trouble repeatedly hitting a huge, slow-moving ship-of-the-line.

@PatriciaShanahan, I would guesstimate that it will be impossible to arrange all the sailing ships in a circle like that. They are not very maneuverable and dependent on the wind. There could be lines of sailing ships passing on both sides of the battleship, maybe.

@Inthenameofthestory, the magazines will be low in the hull and smallish AA shells will not penetrate that far, anyway. I think starting fires in the rigging and sails is the best option. Once they burn, the hull will burn. Also, 12 knots under battle conditions are completely improbable. A sailing ship might go that fast in a good wind which happens to come from the right direction, but in a battle it will not be at the best point of sailing.

@o.m. The 20mm Flak 38 AA guns could penetrate 20mm of steel at 500 meters. The 37mm Flak 37 could penetrate 38mm of steel at 500 meters. I don't think a ship-of-the-line's wooden hull would be anywhere near as effective as steel. I think some of these rounds could actually go in one side and out the other. Source: panzerworld.com/armor-penetration-table

@Ryan_L, don't forget the size of the ship. A round aimed at the magazines would have to penetrate either decks at a very shallow angle or even quite a bit of water. It is one thing to have effects in a few cubic metres of tank or aircraft, and quite another to have effects in thousands of cubic metres of ship.

Although the magazines will be low in the hull, the ship is firing broadsides. There will be supplies of black powder on every gun deck.

@PatriciaShanahan It's even worse. Many of these 20mm and 37mm rounds will be tracers, which are great at starting fires. Ships-of-the-line are extremely flammable, look at how much tar and black powder they have on board.

Also even without possible marines the ship would have weapons for boarding and landing parties. And at that time they would still probably be bolt-action rifles with uselessly powerful cartridge with effective range similar to those broadside cannons but with better accuracy. A marine detachment might have a sniper and maybe even a machine gun. So you can just order captains of all ships that fire at you shot.

@o.m. The question specifies surrounding. A more likely tactic would be the one the ships were designed for, sailing in a line past the enemy firing a broadside whenever guns bear on it.

If the ships are using magic to control the winds, there might be a huge conflict between the controlled winds. This might prevent anybody from being able to benefit from this.

@o.m. wrong. The magazine of the ships is usually just below the waterline - and battleship shells are designed to blow at times into the whip about 2 meters below the waterline.Which would result in the whip getting ripped open whole side and flooding.

@Trish, the proposal was to conserve main gun ammo by using the more plentiful light AA. If the fuse of a 38cm or 15cm shell triggers anywhere in the ship, the sailing ship is toast.

@VilleNiemi : Good point. A Bismarck-sized battleship had a crew of about 2000. That's an army by itself, and with WW2 era small arms it could wipe out any blackpowder-era army.

@Trish, from some googling it seems that HMS Victory had two smaller magazines below the gun deck and a larger one in the lowest hold.

What this answer is forgetting is that the Bismark will most likely have star shells for its 15cm (if not its 38cm) guns, and those will eat enemy rigging for lunch. In the Battle off Samar, US destroyers used them to startling effect against contemporary IJN warships, starting damage-control-sapping fires throughout the superstructures of Japanese heavy vessels.

@Shalvenay, the battleship is supposed to preserve ammunition, especially the scarce ammo for the big guns. I was arguing that main gun ammo is not needed, and that AA ammo will do.

+1 for acknowledging that the superstructure/bridge is typically much less armored than the hull. It's smaller thus harder to hit, but a cannonball or two through a bridge window (assuming you could get within range) could seriously damage the ship's ability to function. Aside from all the important equipment located in the superstructure, that area also tends to house the most important people (who are squishy and completely unarmored). It's unlikely you'd sink it, but you could conceivably disable it.

@bta, at battlestations there would be armored shutters and protected conning stations. I'd be more worried about the radars and searchlights.

@o.m. Not everywhere. I happened to tour a large WWII-era ship last week, and was amazed to learn that not only was the main bridge not armored, it didn't even originally have glass in the front to protect it from the elements (great for visibility, but torture in bad weather). My first thought was that a single shell (or in this case, cannonball) could come flying through the opening, take out the captain and a dozen key crew members, and destroy the throttle/steering controls.