You’re actually over estimating it there, and you missed out Pi… Per gun at least.
Formula is pi r squared multiplied by the length. You’ve used the diameter squared.
So 0.0635 x 0.0635 x 3.14 x 0.52 x 680 = 4.47 cubic metres per barrel for the projectiles.
Though glad to see we are at least starting to agree that the hitbox volume should be at least equal to the volume of the ammunition. Magazines themselves would be a little bit larger to accomodate the people funnelling either shell cases or projectiles into the lower shell handling room, but not that much. They also carried about 10% extra shell cases to account for misfires.
So shell cases in the magazine would be stacked 13 high. You can see the actual magazines and lower handling room of the USS Massachusetts here, which was the same era and system only with DP rather than surface action only turrets.
Shell cases per barrel would be 5.85 cubic metres.
Hence the Porter, Atlanta and possibly others need their magazines resizing. American 5" was effectively 3 parts. The shell case with propellant, the projectile and the extra powder bags as 3 charge settings were used.
So the Torpedo damage diagram shows where the powder bags were kept clearly. It also shows the forward mount’s shell handling room with 2 storage areas flanking it labelled A3082CA and A308M. These must have been the case and projectile magazines. So the current model has it on the wrong deck, and it’s the wrong size. On the current model it should be roughly from the pumps to the rear of the hoists.
We can also see from the torpedo diagram that the area to the rear of the shell handling room is taken up with fuel. Hence the magazine for the B 5" turret must have been on the deck above as there just isn’t room according to the torpedo diagram to fit all that ammo into that space.
So to store 1360 shell casings which are stacked 13 high ( about 2 metres) in 2 rows you’d need a compartment 2m x 1.4m x 7m. Which looks about right for A-308-M.
1360 projectiles would be 2m x 1.1m x 7m. So A-308-2CA.
The hitbox currently on the model is probably about right for the extra propellant bags storage. Case and projectile storage on the other hand appears to be completely absent.
It appears on British destroyers that the shell handling room is considered to be part of the magazine. I don’t personally disagree with this as there would be a lot of ammo flowing through it given the dakka dakka ability of the guns. It should however be consistent across lines, hence the shell handling rooms of the American destroyers should also be part of the magazine for hit box purposes too.
Hence the upper handling rooms should have 40 shells cases and 40 projectiles, which were arranged on the port and starboard walls I believe. 3 rows would give 2m x 2m x 0.12m for the cases and 2m x 1m x 0.12m for the projectiles.
If we can get this fixed it will be a massive bonus for naval gameplay on all sides. Destroyers were squishy, generally unarmoured and quite cheaply built on the whole out of mild steel. They were expendable and relied upon speed, smoke, firepower and manoeuvrability.
I more than suspect that the current playstyle of sit there and spam is a result of the incorrect models. Rectifying this would also alleviate the bot problem I think.