Perhaps the BEST B1G Forum anywhere, here at College Football Fan Site, CFB51!!!

The number of battles in WW 2 between battleships is suprisingly small.

Way more often, and as antiaircraft platforms.  They were studded with dual purpose 5 inch batteries, and other 40 and 20 mm.

Radar proximity shells greatly enhanced their capabilities.

Somewhere I saw a tactical sheet for the specs and armament of the USS Texas for WW1, and WW2.  In WW1 it had a lot of smaller secondary armament, but for WW2 they'd removed a lot of that and replaced it with AA weaponry.  It was interesting to see how the times changed, and the battleship's armament had to change with them.

The American DP 5" was a great weapon. Some navies had separate guns for AA and for floating/land based targets. The 5" gun was "Dual Purpose" which effectively meant that American ships had a lot more of either AA or secondary armament than ships equipped with both an AA gun and a separate secondary armament. 

Back in the day, a British officer named "Shrapnel" invented a shell designed to explode in the air and rain "shrapnell" down on the enemy.  But you had to cut the fuze to the correct length for it to work properly.  This was used a lot in the UC Uncivil War.

The 5" 38 caliber DP gun was also effectively against lesser armored ships, and was used with some effect at the "Battle of the Tin Can Sailors".  At one point they got under the ability of the Japanese main guns to depress and fired at the battleship/cruiser bridge areas.

Caliber has a different meaning for naval and tank guns.

In theory, there could be some ROI from such things in terms of promoting tourism.

It will depend on where it ends up of course.  

Way more often, and as antiaircraft platforms.  They were studded with dual purpose 5 inch batteries, and other 40 and 20 mm.

While I love the big BB's and I'm one of the few who appreciate the oddity that is the Alaska Class, their main disadvantage was that their cost didn't justify their construction relative to simply building more cruisers as AA platforms.  I just made this chart from WIKI:


Weight is a pretty good rough proxy for cost.  The ships are the Iowa Class Battleships, the Alaska Class Large Cruisers (arguably Battlecruisers but not according to the USN), Baltimore Class Heavy Cruisers, and Cleveland Class Light Cruisers.  The main armament is a different issue entirely but that wasn't used against aerial targets anyway*.  Simply for AA purposes, the above is what each ship carried during WWII.  

Note also that the range is longest/highest for the larger guns and shortest for the smaller guns so the most effective guns are the 5" while the 40MM and especially the 20MM are less effective particularly at defending another ship.  These, especially the 20MM are mostly close-in weapons for use against targets that got past the 5" and have probably already dropped their ordinance so the damage is already done.  

So for roughly the same cost you could build two Iowa's, three Alaska's, seven Baltimore's, or eight Cleveland's and here is the number of each weapon you'd get by doing that:

Strictly as AA platforms, the Iowa's and Alaska's are insanely inefficient choices.  The more numerous ships also have the advantage of being able to spread out their fire since there are more of them so they can be sent in different directions and while a hit on one of them will be more damaging it will only be damaging to THAT ship, the other seven Cleveland's or six Baltimore's will remain undamaged from a single hit.