This depends greatly on the type of missile she is hit by. Neither Harpoon nor Exocet is going to do more damage than a 5" HE round would. The much larger Russian and Chinese ASMs would do much more damage, but like the smaller Harpoon or Exocet the warheads are "blast" type, not shaped to my knowledge. At around 750kg to 1200kg warhead weight in a missile as large as a lot of fighter planes this is more than sufficient against modern warship designs.Henry Brown wrote:But the converse of this is, the battleship has even less defense against guided missiles. While they might withstand one or two hits, I am less sure if they could keep taking multiple hits from guided missiles. Keep in mind modern missiles often use shaped charges in the warheads, so in some ways they are more dangerous than WWII era heavy naval guns.
Oddly, the smaller anti-TANK missiles are better able to handle the heavy deck, side and turret armor of a BB. But while the larger missile would do a large amount of damage to superstructure and such, a jet of molten metal coming in through the side of a turret would likely trigger a turret explosion and possibly magazine explosion. Remember the Iowa turret explosion? Had that explosion traveled down the ammo hoists to the handling flats below the turret gunhouse, we might today be laying wreaths on the ocean surface where Iowa blew up in a blast similar to the one that claimed Arizona.
But even if they can withstand the hits and keep coming, I don't think the treaty battleships are fast enough to ever get in range of a guided missile cruiser. If memory serves me, the top speed of the North Carolina and South Dakota class ships was somewhere between 26 and 28 knots. Pretty sure all modern missile cruisers can do in excess of 30 knots, so I don't see how the battleships could ever catch up.
The Iowa class battleships could do 33 knots, so there is a chance that they might be able to catch a guided missile cruiser. However, the original post specified treaty battleships. And the Iowas are not treaty battleships.
Fast note, neither the North Carolina class nor the South Dakota class can be considered "treaty" battleships. Both classes were put into service with 16" rifles as main armament, the treaty limit was 14". The NC originally was designed with 12 - 14" but the design was modified during construction to 9 - 16"/45 cal weapons. The SD class was designed from the start with 16"/45 cal main armament.