As I knew nothing about this topic, I have been using Google to try to find something to say. I still know very little but I have begun to suspect that the effective range of light AA was as much determined by the gun sights as by the gun's ballistics and rate of fire. There is of course a trade off in that a predictive gun sight has less work to do if the time of flight is reduced.
One of the source found was a discussion here a few years ago viewtopic.php?f=36&t=897&start=45
from which I can quote dunmunro giving the RN view:
The "Maximum Effective Ranges" of close range weapons are as follows:-
2-pdr. multiple Pom-Pom and Bofors in local control 1,700 yards.
Oerlikon 20 mm. single gun 1,000 yards.
0.5 in. Machine gun. 800 yards.
0.303 in. and 0.30 in. weapons 400 yards.
(paragraph 470 for above data)
An interesting unofficial USN view from Robert Wallace, who trained many USN gunners, can be found at http://ibiblio.org/hyperwar/USN/rep/DamnNeck/index.html
including some interesting points.
For example, his view of the 1.1 inch was not wholly positive:
“...while the 1.1-inch proved to be a disappointment in many ways. A number of critics have mentioned the frequent premature explosions of the excessively sensitive shells within the gun barrel itself. Commander Gallery commented that they would "go off when fired into heavy rain." Our "prematures," like those at Dam Neck, tended to explode just abaft the flash shield, to the great discomfiture of both crew and bystanders. Unlike at Dam Neck, however, we were lucky that nobody ever got hurt in the process. Even if satisfactory ammunition had been developed, our 1.1-inch required the nearly full-time service of a gunner's mate first-class to keep it firing with a minimum of jams.”
He mentions that the Oerlikon and the 40 mm Bofors were much more reliable and explains the advantage of self-destructing shells:
“To anyone who has ever had the terrifying and helpless experience of being in an anchorage during a night or twilight air attack (real or imagined), in company with a lot of auxiliaries whose nervous 20mm gunners needed only a shot or two to cause panic, the 40mm Bofors had another advantage. The old saying "What goes up must come down," while unfortunately true of the Oerlikon, did not apply to the Bofors. Once the tracer element burned out at 4,000 to 5,000 yards, the ammunition self-destructed.”
His estimate of effective range was on the low side, i.e. “In practice, range setting was less important than it might seem, particularly within the ranges at which the 20s and 40s could be expected to have their main effectiveness, say inside 600-800 yards for the 20mm and 1000-1500 yards for the 40mm. The reason was that out to these ranges the trajectories were relatively flat.”
However, the best part may be his discussion of gun sights. Wallace was an advocate of using the gyro sight rather than using tracers to aim (tracers were still useful to distract enemy pilots).
“As a lifelong wing-shot, I became enamored of the Mark 14 sight and was soon an advocate. The sight needed an advocate at that point in the war because it tended to have a bad reputation among many old hands. Older gunner's mates would sometimes tell trainees to look around the sight and direct the tracers like a stream of water. This method was known as tracer control. What its advocates did not realize was that the human eye, with limited inter-pupillary space, could judge distance only to about 400 yards, beyond which all is optical illusion. As soon as I began firing it myself, the reason for the problem became clear. Firing-line instructors were gunner's mates. They felt their job was to teach the guns and to put the students through the firing line. The guns were not the problem. The students simply were firing before they were ready. I soon had students dry-tracking and learning to handle the reticle before actually firing. And just to show that the Mark 14 was not as bad as they might have heard, I often fired demonstration runs myself in those early months, sometimes on the 20mm and sometimes on the 40mm. I well recall an experience that indicated something of the nature of the problem. With Larry Springer setting range, I announced that we would fire three runs with a 40mm twin. However, when we shot the sleeves down on the first two runs and the flyer was stringing another sleeve, our chief came to me and said, "Mr. Wallace, I wish you and Mr. Springer wouldn't shoot anymore. We have to get these men to lunch."
This matches Yoshida Mitsuru comments from “Requiem for the Battleship Yamato”, pages 75-6:
“The muzzle velocity of a 25 mm machine-gun bullet is less than 1,000 meters per second, barely five or six times the average speed of the American planes.
Using tracers to correct the aim of weapons at such a speed disadvantage is like chasing after butterflies with our bare hands.”
Thus the 25 mm Type 96 was a reliable gun with high velocity but with its rof limited by a small magazine. Changing barrels was also much slower than for the Oerlikon, which may have made a large magazine less attractive. However, the Type 96's real problem was that the single mount had only iron sights whilst the Type 95 short range H.A. director, which normally controlled three triple mounts, received the comment “It is curious that the Japanese Navy took no steps at all to design any other form of sight based on more advanced principles or which were tachymetric” in the USN Technical Mission to Japan Report O-30, page 54, http://www.fischer-tropsch.org/primary_ ... 200-30.pdf
. By “more advanced”, they may have meant something containing gyroscopes, which was an area where Japan was behind the USA.
Finally, note that the IJN may have been asking their 25 mm guns to do a job that even the Bofors could not have managed. When the IJN chose the 25 mm in preference to the Oerlikon, the main aerial threat to battleships were torpedoes dropped by biplanes less advanced than the Swordfish at about 90 knots. During the dispute in the 1930s between Yamamoto Isoroku and Takahashi Sankichi advocating air power and battleship admirals such as Nakamura Ryozo, Koga Mineichi, the leader of the General Staff section in charge of equipment, stated that battleships could defend themselves. He may have meant that such a slow biplane forced to fly a constant course for up to 20 seconds to set the torpedo's gyro could be hit.
Unfortunately for Yamato in April 1945, torpedoes had improved. By 1944, the recommended dropping speeds and heights for USN torpedoes were 260 knots and 800 ft. This gives a flight distance of about 1000 yards and thus the torpedo is dropped at a range of 1,400 yards to allow it to arm https://www.youtube.com/watch?v=R552QfbD8AU
. The time to set the gyro was reduced to 10-12 seconds, so that the aircraft was flying a predictable course from just beyond 3,000 yards to 1,400 yards.
Of course, IJN torpedoes had also improved. Even in 1941, IJN torpedoes had been able to be dropped at higher speeds than other nations torpedoes (note Adm. Phillips insistence as the first attack on Prince of Wales developed that the IJN aircraft were flying too fast to drop torpedoes) and the 45 cm Type 91 Mod 3 from 1943-4 http://www.navweaps.com/Weapons/WTJAP_WWII.htm
could more or less match the torpedoes described in the USN video. However, the USN had the 5”/38 with the proximity fuze.
Interestingly, the last battleship to be completed, Jean Bart, had 57 mm “light” AA and Germany had a prototype 55 mm working by 1945 http://www.navweaps.com/Weapons/WNGER_55_Gerat58.htm
, which could get shells to 3,000 metres in about 4.34 seconds.