I find this discussion very interesting even if I don’t have a sufficient knowledge about different types of armor, AP projectiles and virtues of different patterns of armor arranging.
I understand that this discussion has to be theoretical one as both ships never met. However I think that there is a possibility of moving this discussion a bit further as considerable number of posts relates to capabilities of horizontal armor schemes of South Dakota and Bismarck/Tirpitz.
My point is that both ships suffered bomb hits in deck which can reveal some additional information (especially in case of Tirpitz).
1. Tirpitz before its destruction with Tallboys, was an object of several attacks of British carrier planes, which scored some hits with more conventional bombs.
According to http://www.bismarck-class.dk
during attack of 24 August 1944:
“A 726 kg (1,600 lb) AP bomb hit just forward of the bridge on the port side and penetrated not only the upper deck but the armoured deck below, finally coming to rest in No. 4 Switch Room on the lower platform deck, having gone through 14,6 cm (5¾ inches) of decking, mostly armoured steel”
2. South Dakota was hit during Battle of Philippine Sea.
Of course I have awareness that there are fundamental differences (weight, velocity at impact, inner construction and angle of impact) between bombs and projectiles. However I believe that examination of results of damages suffered by Tirpitz can give additional knowledge about quality of its horizontal armor.
Additionally I would like bring one argument in favor of South Dakota which as I think haven’t been used yet. South Dakota had 9 gun while Tirpitz had only 8. Assuming the same level of precision of both ships fire that South Dakota’s advantage would mean that:
• each of South Dakota’s salvos would have 12,5% more chances of hitting its opponent than vice versa;
• it would at least partially reduce any Tirpitz’s advantage resulting from faster rate of fire.
Finally, having in mind such things like luck, level of crew training and my mediocre knowledge of technical issues, I assume that South Dakota should win 7 of 10 duels.