[Kakurin]

Originally Posted by AC-Phoenix

Too long for today, tomorrow.
The same side also shows statistcs that Iowa's and Bismarcks guns could have both penetrated Yamato's deck armor. Bismarcks penetration being slightly below

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http://www.combinedfleet.com/f_guns.htm
Maybe I'm reading those numbers wrong(Considering that I'm bad at math very possible) - But her deck armor would have gotten penetrated at Bismacks maximum Range which was roughly 40'000 km

To be blunt, it's much more complicated than that. While Bismarck's guns could've penetrated up to 9.3" of armour at maximum range it only factors in a single sheet of that thickness. Ships' deck armour layout, however, is much more complex. Some ships have more than one armoured deck. Then there are also other objects and layers obstructing the path, so even if the initial deck is penetrated the damage will be limited. And Yamato's deck armour was pretty much impenetrable for Bismarck's 38cm guns. There was only a single 6.1x12.2m window where Bismarck's shell could've penetrated and then the damage would be limited to a single boiler room only (there are 12 total in the area). The complete analysis of Yamato's deck armour against Bismarck's 38cm guns is here:

Spoiler for Yamato's deck armour:

The Japanese IJN YAMATO had an armored third deck with a 7.87" (200 mm) flat central deck and a 9.06" (230 mm) sloped outer region that took up about 25% of the deck area from each of the side edges. The main armor deck was set at the top edge of the main armor belt and the slope connecting the 7.87" flat central region to the belt edge was only 8o from the horizontal and lifted the armor deck slightly to allow the boilers and engines more space. This deck was made of Japanese Molybdenum Non-Cemented (MNC) homogeneous armor (slightly inferior to U.S. STS, but not by much) and were totally proof against a deck hit from the German 38 cm gun. Even the funnel uptake armor grating plate, which was drilled through with many holes to allow the stack gases to pass through the armored deck and was thus only equal to about 40% of its actual thickness of solid MNC armor without holes, was 14.96" (380 mm) thick, giving a 6" (152 mm) effective thickness. This grating is surrounded by a cylindrical 1.97" (50 mm) homogeneous CNC armor plate wrapped around the raked funnel base and rising several decks into the superstructure, which is a unique armor arrangement used in these ships only. For the BISMARCK's gun projectile to reach the grating through the weather deck at an obliquity where penetration is worth calculating requires passing through a lot of superstructure bulkheads and decks that would probably reduce the striking velocity somewhat, but this is hard to determine (I am going to use the full 1.97" thickness of the grating shield instead of reducing it by 5%, which I would normally do with CNC, because of this).

The YAMATO's flat middle deck region (with the grating at its center over the boilers) could only be reached from above after passing through two lightly armored decks spaced 8.5' (2.6 m) apart and 8.5' above the main armor deck or from the side through a lightly armored upper hull side 17' (5.2 m) high. The upper two decks and upper side hull were made of single plates or two laminated plates of British-type D-steel, which I give a quality factor of 0.9, as given in the table above. The plates were arranged so that they were thickest at the hull side for the decks and thickest at the top of the upper side hull. This meant that the more steep the angle of fall and, thus, the slower the attacking projectile was going, the thinner the upper hull or deck plating that was hit near the centerline, allowing the plates near the side that would be hit at more shallow angles of fall by more rapidly moving projectiles to be reinforced considerably. Incidentally, this also was the best arrangement for strengthening the ship for bad weather, since heavy waves would bear down mostly near the ship's side. The weather deck had only 0.5" (13 mm) D-steel at the centerline, giving an effective STS thickness of 0.45" (11 mm), but this increased in regular steps to 1.42' (36 mm) at the hull side edge, made up of two laminated plates 0.79" (20mm) over 0.63' (16 mm), giving an effective D-steel thickness of 1.29" (33 mm) and an effective STS thickness of 1.16" (30 mm) at its thickest. The second deck only used single plates and it started out at the centerline at 0.39" (10 mm) - equaling 0.35" (9 mm) of STS - and gradually thickened to 1" (25 mm) - equaling 0.9" (23 mm) STS - for the 25% area directly above the outer sloped portion of the main armor deck. The lower half of the upper side hull between the second and third decks was made of a 0.31" (9 mm) D-steel plate laminated to a 1" D-steel plate, giving an effective D-steel thickness of 1.22" (31 mm) and an effective STS thickness of 1.1" (28 mm). The upper half of the upper side hull between the weather (first) and second decks was made of a 0.71-0.87" (18-22 mm) D-steel plate laminated to a 1" D-steel plate, giving an effective D-steel thickness of 1.56-1.7" (40-43 mm) and an effective STS thickness of 1.4-1.53" (36-39 mm).

This plate arrangement would always set off the 38 cm projectile's base fuze, usually on the first plate hit, but only the outer edge of the weather deck or upper half of the upper side hull would decap the projectile.

The 6"-effective-STS-thickness armored grating seems to be a design flaw in the YAMATO and the only vulnerable spot on the deck amidships. Could a "down the stack" hit from the BISMARCK damage the YAMATO? Let's see!

The lower half of the upper side hull is marginal for setting off the projectile's fuze and it would not decap the projectile but the surrounding 1.97" cylinder would slow down and decap any incoming projectiles which try to get hits on the armored gratings reducing their penetration ability somewhat. Also, the impact would be at most at an angle of fall of 8.9o assuming that the grating was 20' (6.1 m) wide and centered on the ship centerline, giving an obliquity of 81.1o which I consider impenetrable, anyway.

The top half of the upper side hull would absolutely set off the 38 cm projectile's base fuze and decap the projectile and the angle of fall at the grating would be at most 17.8o, which for the German 38 cm gun occurs at a striking velocity of 1624 feet/second (495 m/sec) at 23,000 yards (21,000 m), giving an impact obliquity of 72.2o. The analysis of the SOUTH DAKOTA showed that this was too oblique for penetrating a 6" plate, making the grating invulnerable even if the projectile could reach the 56.7' (17.3 m) slant distance to the near edge of the grating prior to its fuze setting it off. The top half of the upper side hull and the second deck plating together cost the 38 cm projectile about 15 feet/second (3.7 m/sec), which gives a nominal 56.3' (17.2 m) travel for the designed 0.035-second German base fuze delay at 1609 feet/second (490 m/sec). This means that only about half of the striking 38 cm projectiles would even reach the grating after an upper side hit, even if penetration were possible which it isn't.

The German 38 cm projectile hitting the upper side hull could only damage a boiler if it hit the armored grating and exploded before ricocheting off, where the downward blast might rupture an uptake pipe and cause the nearby area to be abandoned due to poison fumes. Pretty small chance!

The path through the weather and second decks to the grating is now the only one left. The angle of fall for the 38 cm gun at 37,580 yards (34,300 m) is 39o with a striking velocity of 1506 feet/second (459 m/sec), which gives a 51o obliquity against the deck armor and a minimum 39o vertical obliquity against the circular 1.97" funnel shield. The slant distance is 27' (8.2 m) from the weather deck to the grating. If the average 30o horizontal obliquity for a vertical cylinder is added in, the average total obliquity far the 1.97" funnel shield at maximum range is 47.7o, which requires a minimum striking velocity of 394 feet/second (120 m/sec) for complete penetration. At this angle of fall we would be going through the weather deck where it is about 0.63" (16 mm) thick - a 0.57" (14 mm) STS equivalent - and where the second deck is only 0.5" (13 mm) thick - a 0.45" (11 mm) STS equivalent. These would not decap or deflect the projectile, but it probably would set off the base fuze. The weather deck requires about 138 feet/second (42 m/sec) to penetrate and the second deck about 108 feet/second (33 m/sec) to penetrate at 51o obliquity. These decks reduce the striking velocity on the 1.97" funnel shield to 1496 feet/second (456 m/sec). The remaining velocity after penetrating the funnel shield is 1443 feet/second (440 m/sec) and the projectile is decapped, though not deflected. Without an AP cap we switch to my U.S. penetration formula and this gives at 51o obliquity a necessary striking velocity to completely penetrate the 6"-effective-STS thickness armored grating of 1447 feet/second (441 m/second), which is essentially right on the money. Therefore, the German 38 cm projectile can destroy a centerline boiler room (one of the 12 in that area!) of the YAMATO (but nothing else) if it hits the armored grating region, which is about 20' wide by 40' long (6.l x l2.2 m) just behind the forward conning tower, at a range over 37,500 yards. (Calling Luke Skywalker!)

And I pointed to the documentary because it was generally interesting, due to having interior shots as well as the precise damage done by all weapons inspected from really close range.
in the end a total of over 2000 (2800 I think?) Shots were fired with, according to Wikipedia ~400 hitting, with a penetration of mere 4 shells at the armor belt.

In other worlds less than 1 percent of all fired shots during that battle actually penetrated her hull.
Up until here its still fine, but the english battleships also fired from afar. Even if you take flat 2000 shells fired in total thats a hit rate of less than 1 % on a ship that could only go in circles.
So unless the Bismarck was still pretty good at escaping those shotsm a lot of the hits that were close enough(Edit: as in impacted close enough) to damage her still didn't manage to do so.

Bismarck's side armour was pretty weak. Her strength stemmed from an internal armour behind the main belt. Factoring in the loss of the AP cap and speed from the belt armour Bismarck's internals were pretty much impenetrable. So yeah, just looking from a single penetration angle the armour looks fantastic.

However, that design also had shortcomings that make it doubtful whether it really provided a benefit. First, the weak side armour meant that the upper hull area (where some critical equipment and cables were stored) could be taken out at far greater ranges than for other battleships. Meaning it's easier to cripple the ship's ability to actually carry out the fight. Second, this design cost considerable weight - weight that could've been spent to beef up the weak deck armour that was quite vulnerable. Third, the belt armour's shallow extension allowed for dangerous penetration below the waterline, as shown during the engagement with Prince of Wales. There are also additional drawbacks, for that I refer back to the link I posted.

The British ships closing the distance therefore just reduced their chances to actually deal mortal damage. All they did was bang their head against a brick wall. Had they maintained a bigger distance they could've dealt significant damage either via the deck, or through underwater hits.

German Ships probably had stern instabilities, which is why they got refits in that regard after Prinz Eugen was damaged.

Do you have a source for that? I suspect you may confuse that for the problems with the stem the Germans had. Due to the rough Atlantic the German ships (especially the Gneisenaus) tended to take on much water which caused floodings in some areas and damage to the equipment. So they refitted practically all capital ships with a so-called "Atlantic bow". Bismarck already had that when she went out to sea.

Precision aside, that still doesn't warrant 'no chance' the first thing being that both ships had recon planes, so its not like they wouldn't have known the other one was there.
And that is a reason a pointed to Cameron's documentation - Bismarcks planes were unable to launch.

A couple of recon planes make little difference. First of all, they can cover only a small part of the area. Then, launching them is a very delicate affair that quite often didn't go as planned. Last but not least, spotting by recon plane proved to be prone to human mistakes. Like mistaking ships, reporting the wrong position etc. Radar is far more accurate in this regard.