Sweet spot sizes for AA guns

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wouldnt a faster firing gun with a time fuze or a proxy fuse be best? You would create something like a shot gun effect right?
 
wouldnt a faster firing gun with a time fuze or a proxy fuse be best? You would create something like a shot gun effect right?
That would be the post-war 3"/50 that was intended to replace the 40mm Bofors in USN service. The 3" was chosen as that was about the smallest size shell that could fit a VT fuze.

Nowadays similar capability can be done in smaller sizes. And we have things like programmable time fuzes, with a programming coil at the end of the barrel programming the fuze of each shell as it exits the barrel (taking into account the muzzle velocity differences between each shell), and of course combined with radar gun laying.
 
wouldnt a faster firing gun with a time fuze or a proxy fuse be best? You would create something like a shot gun effect right?
You are correct except for...................................
I'm looking for opinions on what you guys think were the sweet spot, or optimal, sizes for AA guns in the WWII period.

The Proximity fuse doesn't show up in service until late 1942 and that is in the 5in shell. It took a while to shrink it enough to fit in smaller shells, like 4in.
fuses for 3in guns didn't show up until mid 1944 (?) and 3in guns weren't that much faster firing than 5in guns. The prototype for the fast firing US 3in gun wasn't fired until Sept 1945 and with the post war slow down they didn't reach the fleet until 1948.
This was for a gun that fired 45-50rpm.
57MM proximity fuses didn't show up until sometime in the 1950s and 40mm proximity fuses didn't show up until sometime in the 1970s (correction welcome). The postwar Bofors 40mm/L70 may have gotten proximity fuses before the older 40mm/60 guns did.

The problem with time fuses is that the time fuses need to be set (during WW II) before the round is chambered in the gun and in WW II that pretty much meant that some sort of mechanical device had to twist the nose of the fuse or at least stick something into a slot in the fuse which is going to slow down the rate of fire on something like a 40mm or smaller gun. What you can do with electronics in the 1970s and later compared to what you could do in WW II are very different things.
 

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