A further note on AAA defenses. I'll be referencing the USN's post-war study of AAA effectiveness.
http://www.ibiblio.org/hyperwar/USN/rep ... mary-1045/
Per the report, the USN spent 654 5in (non-VT) rounds per aircraft killed. For 40mm, it was 1,1713 rounds.
To translate this into my Mega-BB's performance:
I'll project that the lethal volume of explosion - and thus likelihood of kill - for a time-fuzed AAA round is proportional to the cube of the round's diameter. This is basic physics; the charge of a round expands cubically with diameter. In fact it may underestimate the value of larger rounds in AAA, as larger shell fragments have carrying power that is more-than-linear with their size. The USN for example, found that Japan's 15cm AAA round was more effective than its 12cm round by a greater degree than cubic escalation would predict.
https://en.wikipedia.org/wiki/Type_5_15_cm_AA_gun [accurately reproduces chart from the very-long USN study cited therein].
To translate this into 5in shell equivalents, an 18in shell is worth 46.7; a 9.5in worth 6.9.
By these estimates and ww2 average performance, you'd kill one aircraft for every 14 18in shells, and one per 95 9.5in shells.
That seems about right to me intuitively... It would imply that if Yamato fired 2 full broadsides at attacking aircraft it should kill basically one aircraft. OTL the Yamato was using weird shells effective only at 1,000 yards for some reason - despite that fact we can't have expected its 18in guns to fight off hundreds of planes even with good shells.
For MegaBB, however, it's literally different orders of magnitude.
First, the MegaBB has 480 18in guns instead of 9.
Second, these guns can elevate up to 75 degrees as shown in my sketch of a turret mostly "buried" in the hull.
Third, this arrangement enables firing up to 5 shells/minute and loading at 45 degrees due to separation of compartments for powder/shell staging from the gunhouse (again, see sketch - probably needs more explanation though...).
Basically the MegaBB has ~150x the RoF of Yamato.
Returning to our 5in equivalents and implied AAA capability...
The 18 and 9.5in guns would begin engaging targets out to at least 15,000 yards [The 5in/38 DP would engage at ~12,000 yards].
A plane closing at 200kn on a 30kn ship covers ~6,000 yards/minute depending on angle of ship/plane. So ~2.5 minutes engagement time.
In that period, the MegaBB can fire 18/9.5in shells equivalent in lethality to 501,000 5in DP shells, implying 766 aircraft kills. (!)
For light AAA, let's say we have 1,000 40mm barrels. If each fires 100 rounds/min and has 1.5min engagement time, then we have 87 additional aircraft kills - probably those stragglers that survive the heavy-shell aerial holocaust.
And all these projections assume that the planes come in a single wave timed all to arrive on target at once. Reality would be different. At Pearl Harbor, for example, Nagumo's carriers had 414 planes but launched 183 (44%) in the first wave. It takes time to get a lot of planes aloft and they don't have the endurance to fly around and wait for everyone to form up.
Furthermore, this calc ignores plane losses when flying away from the ship.
So realistically the MegaBB could meet a 1,000-plane single-wave attack and splash 80+% of the attackers. To launch such an attack would require ~30 fleet carriers carrying ~80 planes apiece. The MegaBB would survive the attack; the carrier's air arm would be devastated. The conventional fleet could then destroy the enemy carriers.
One further note: As the study notes, most AAA kills were by the ships targeted by the planes rather than nearby supporting ships. The study doesn't break down shells/kill for targeted vs. non-targeted ships, however. The takeaway is that targeted ships would have lower shells/kill rates than reflected in these statistics.
A further further note: Many of the shells in the OTL WW2 sample were fired from lighter ships that were pitching/rolling violently (Atlanta-class, DD's). Many were fired by ships lacking the most-sophisticated fire-control systems. Neither would be true of MegaBB.
For these reasons, the sample is somewhat biased against the MegaBB and it isn't a stretch to suggest it could shoot down >1,000 planes before they even reached her.
If that seems implausible, consider the fact that MegaBB's 501,000 5in-equivalents is over twice the number of normal-fused 5in AA shells fired by the USN during the entire war (223,000).
No aerial attack force in either naval or land-based warfare has ever encountered an AA artillery barrage on even the same order of magnitude as that which MegaBB could throw up.