Most accurate divebomber

Uups, actually a polish book. AJ-Press Monografie Lotnice "Ju 87 Stuja" ISBN 83-86208-22-8

Going into more detail on the subject of battleship vulnerability I'll continue to use the South Dakota as an example.

Using caisson tests after the South Dakota was built, it was discovered that her torpedo protection was flawed. This is attributed to the side armor that extended all the way to ships triple bottom not allowing for the flex that was found in previous vessels. The previous North Carolina class was designed to be able to absorb three hits on one side without sinking. Of course, the designers knew nothing of the more powerful torpedoes the Japanese would employ. I assume the South Dakota was built to the same specification.

Like its predecessors, the South Dakota was a Washington Treaty capital ship limited to 35,000 tons (ready for sea in wartime). Ready for sea in wartime needed a little redefining CNO Admiral Leahy determined. It really meant no boats on board, no water in the machinery, not all of the libricating oils being counted, a standard amount of ammunition (about 60% of capacity), less potable water and less food. Actual full load was estimated to be close to 45,000 tons.

Then came the war with much increased upper hamper. This consisted mostly of light antiaircraft guns and the introduction of radar. In 1945 the BuShips set the maximum allowable displacement for the class at 47,000 tons
for "a draft of 36' 9" and an armored freeboard of 5'" - Friedman. Since the side armor came up to the main deck this meant the distance from waterline to weather deck was 5' plus one deck. The 40mm gun tub on the bow was not usually manned for fear the crew would drown.

Part of the problem was where the South Dakota served for much of the war – in the Western Pacific. And, so, because of the long distances traveled she was usually loaded to the gills.

The result is a vessel designed as a 35,000 ton Washington Treaty vessel (achieved with some admitted number fudging) going to the war loaded to 47,000 tons or possibly more.

In action against Kirishima in November 1942 the South Dakota took a number of hits to her starboard side but only one was a main gun hit, a HE shell at her bow. The other hits were smaller caliber shells and while they did little damage seams opened up all along underwater parts of South Dakota's hull.

So, the people here keep saying that these ships were very difficult to damage. However, as I have pointed out before, if damage did cause flooding, the amount of reserve buoyancy was small.

If we assume that South Dakota is a rectangular block and use your figures, we find that displacement increases by one foot for every 1279 tons of water, which is pessimistic as the bottom is curved. Thus assuming that the ship had just filled its tanks to the brim before damage, it would need to take in 6394 tons of water to bring the waterline to the top of the armour belt and 17904 tons to cover the weather deck. Interestingly, I have seen an estimate that HMS Prince of Wales had taken on 18,000 tons of water before being abandoned.

Most of that generation of battleships were about the same size. Wikipedia gives displacements of 42,237 (1940) to 44,460 tons (1944) at full load for the King George V class, 46,700 long tons for North Carolina, 45,029 long tons for Vittorio Veneto and 47,548 metric tons for Richelieu (after 1943 refit). Bismarck at 49,500 long tons and Vanguard at 51,420 long tons are slightly bigger, while the Iowas at 57,000 tons and the Yamatos at around 70,000 tons are significantly heavier.

We have estimates of the flooding due to torpedo hits on Vittorio Veneto at Matapan with 4,000 tons from a hit aft in the unprotected region (see picture at Italian battleship Vittorio Veneto - Wikipedia, the free encyclopedia) and around 2000 tons after being torpedoed by HMS Urge on 14th December 1941 in the protected area. North Carolina was reported to have taken on an excess weight of 970 tons on 15th September 1942 as "The total weight of liquid in the damaged area prior to damage was 597 tons".

Thus we can expect battleships of that generation to survive up to three torpedoes but perhaps not too many more. Prince of Wales was hit by four but suffered poor damage control. Littorio at Taranto suffered severe damage because the magnetically fused torpedoes exploded beneath the ship after passing under the anti-torpedo netting.

Hello cherry blossom

I have some numbers for the Massachusetts which are in close agreement with your calculations.

Draft of 34.625 feet at 43884 tons
Draft of 36.083 feet at 46041 tons
or 1479 tons per foot of freeboard

At the max loaded condition of 47000 tons the vessel would have about 13' of freeboard amidship. Therefore, to sink the vessel on the level to the weather deck would require 19227 tons.