I'm armchair admiral who will go against the Yamato; I have 15"/42 guns in the Mk I/N turrets -- maximal elevation 30 degrees -- and Garzke and Dulin just told me
I'm protected vertically against 15" from 14 thousand yards (but Yamato has more than 16", I suspect) and I have less than 6" of deck armor; what should I do??
1. Yamato had 16" belt inclined at 20 degrees, which makes its belt more or less equivalent to an vertical 18" plate. This means Yamato's side belt is totally immune to 15"/42 1920lbs AP shell, or immune at all but point blank range (~5km) for any other shells fired by that gun.
2. Yamato had 8" deck, protected by a 1.5" fuse trigger weather deck. It can not be penetrated by any 15"/42 shell fired up to maximum elevation of 30 degrees. So if vanguard's 15" turrets were limited to 30 degrees, Yamato's citadel is totally immune from vertical penetration.
3. Vanguard had 14" vertical belt. Yamato can penetrated it in optimal condition any any range out to slightly beyond 30km.
4. Vanguard had 5.25" deck, Yamato can penetrate it at somewhere between 20km and 30km, likely much closer to 20km than 30km. But let's be conservative and say 25kms.
Yamato's citadel has a colossal immunity zone from around 5km out to maximum range of vanguard's guns. Vanguard has no immunity zone whatsoever against Yamato. In fact there is a substantial zone of double jeopardy from <25km - >30km where Yamato's shells will penetrate both the deck and the belt on the vanguard. Yamato can absorb a large number of hits from vanguard at any range without serious threat of critical damage, where as the vanguard is vulnerable to serious mobility impairment or being blown up by even just a single hit at when fighting the Yamato at any range.
Other factors in play includes the design of Yamato's and Vanguard's armor arrangement, and the unique quality of Japanese APC shells.
The performances of Japanese APC shells in actual armor penetration are poor by WWII British standards. The Japanese had adopted few of the improvements the British made in light of experience of Jutland. As a result, Japanese shells are more likely to break up rather than penetrate if it hits the armor at an oblique angle. This reduces the actual potency of Yamato's guns to a point below nominal penetration data might suggest. Also, Japanese APC fuses are more likely to be destroyed during actual armor penetration than improved British fuses, so Japanese shells are more likely to be duds even when they successfully penetrates Vanguard's citadel. This increases the likelihood that Vanguard will escape serious damage from a citadel penetration. Finally, Japanese APC fuses are complicated by water entry feature that makes it more likely that they won't be activated when hitting light armor, or confusing light armor impact with water impact and initiate a unusually long fuse delay. This means Japanese APC shells are more likely to show excessive fuse delay, or no fuse activation at all, when they hit light armor and simple structural steel. So Japanese shells are likely to fail to detonate, or detonate only long after it has passed out the other side of the target, when it hits portions of Vanguard outside the main citadel.
Conversely, Japanese paid exceptional attention to the performance of their shells when the shells fell short of the target rather than actually hit the target. As a result, Japanese shells have long, stable, predictable trajectories underwater if it lands just short of the target, unlike other country's shells. Also, Japanese fuses have unique design features that allow them to detect a water impact, and would not explode prematurely upon hitting water. So Japanese shells landing short of the Vanguard are much more likely than British shells to continue underwater, dive under Vanguard's armor belt, and penetrate into Vanguard's citadel from below, and then explode inside. British shells in the same situation would likely be kicked into a wild unpreditcable underwater trejectory by water impact, and explode prematurely before going very far.
Yamato's armor design anticipates other countries might try to achieve the same underwater performances with their heavy shells (which none actually did). So Yamato's heavy armor belt goes all the way to the ship's bottom, the then continue as a thin 3" screen along the ship's bottom. So even if one of Vanguard's shells land short, somehow follow a good underwater trajectory and hit Yamato deep underwater, It would still encounter heavy armor up to 8" thick and would be unlikely to penetrate.
Vanguard's armor did not anticipate this degree of attention to making shells behave underwater. So while Vanguard's armor belt is deep compared to earlier British battleships, it only reach half way to the ship's bottom. If one of Yamato's shells land short by 30-40 meters, it would likely follow a good underwater trajectory and hit the Vanguard deep beneath the armor belt, and penetrate into Vanguard's citadel without encountering any heavy armor other than a thin torpedo bulkhead.
All in all, I think it is fair to say vanguard is massively outmatched in any combat environment where Yamato can see the vanguard with her optical fire control instruments. If visibility is perfect, Yamato's gun fire ought to be almost as good as vanguard's. In this case vanguard might as well run away to save her crew. If the visibility is zero, then vanguard can stand off and pummel the Yamato with radar directed gun fire until it wrecks all of Yamato's superstructure and then declare a win, but it would be nearly impossible vanguard to sink or immobilize the Yamato with gun fire alone.
But in between, other factors can change the picture somewhat. Vanguard can use her speed to always position the yamato 45 degrees off her bow or stern. This would maximize obliquity of impact of Yamato's shells against vertical armor, and effectively improve the protection offered by Vanguard's belt and transverse armor bulkhead. I don't know if this would reduce the Yamato's maximum range of penetration against vertical armor on the Vanguard to a point where Vanguard will now have something of an real immunity zone. But it would at least reduce the zone in which
any hit by Yamato on the Vanguard's citadel will likely penetrate. This approach will, of course, limit other tactical options for the Vanguard. If the gunnery officer of Yamato guesses the fact that Vanguard will always try to position the Yamato 45 degrees off bow or stern, then he would also have a easier time refining his range to the Vanguard, and improve the quality of optical fire control.
Vanguard was designed at a time when the British had no inkling that the Japanese were building monster battleships 50% heavier than anything the British were contemplating. Vanguard was intended to act as core of numberically inferior squadron that can use superior quality and speed to engage those older Japanese battleships that Japan might spare to send south from her confrontation with the US. Vanguard was actually described internally as "well armored battlecruiser" rather than a battleship. The reason is Vanguard was intended to fulfill the role Fisher had envisioned for fast battlecruisers before WWI, although with a very different ratio of armament than protection than Fisher had favored. Vanguard was not designed to handle an opponent like Yamato, and would have no business engaging the Yamato in any situation where the Yamato can effectively shoot back.
