Hmmm. A 5" 38 cal would have one Helluva bottlenecked case.
A bit of the usual topic drift.
I served on the WWII fleet boats back in the '50s. One of the ones I was on had a 5" x 25 and used fixed ammo with a lesser charge. Even so, the muzzle blast can only be described as "vicious". Humping these "lighter" cases up through the after battery hatch was a treat also. No hydraulic ammo hoist here.
What blew my 17-year-old mind was when they had us go through an ammo-handling drill for the 5"x38. They used semi-fixed ammo (seperate shell and case). The projectile weighed 52 pounds and you had to pick these up and guide it into the shell hoist, one hand near the nose, the other gripping it near the base only by its circumferance. The BIG No-No was to lap your fingers over the base as sometimes the shell was immediately sent to the gun mount and the hoist would snip your fingers off neat as a whistle.
The mind-boggler was that the nose fit into a fuze-setter which was controlled from the gun director. That meant that the range as detected by the radar was immediately sent to the fuse. Super cool for WWII.
The surface ship guys said the 40MMs were aimed with these directors also and that the only people working during a raid was the loaders. That is until the directors got knocked out and you had to go to local control. It was REAL fun when the power got knocked out and you manually had to train, elevate and fire -- accuracy really went to hell.
They also told us that the 5" could be set on automatic fire. Hello? It just mean that when on automatic, the gun fired as soon as the shell was seated. I understand that even the 6" on the light cruisers could be fired this way. I guess it was the naval version of Fire-For-Effect.
Just as I was getting out, they were replacing the quad 40MMs with long-barrelled twin 3" that had a loading rack that looked like a revolver cylinder with the tops off. The guys said that when on full automatic, the loaders could barely keep up.
I think the caliber multiplier came about because as smokeless powder was developed for naval use, it was found that the longer barrel increased the range as the powder had longer to burn. Seems to me that was a reason for the long barrels on blackpowder guns even though BP was more of an explosive than a propellant. ???