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Since you tried to evade the question of destruciveness with a hand-waving argument, let me remind you of the math... As P_hit_round, the probability of a hit for a single round, is not likely to be any worse for the Hispano cannon than for the 12.7 mm Browning...
You are comparing a four guns against two cannons, and trying to back it up with statistics that make a one-for-one comparison. The Browning M2 aircraft gun weighed roughly half what the Hispano cannon did, which makes your one-for-one comparison entirely fallacious,
especially since you're trying to argue efficiency per pound.
Thus- any comparison made must compare an equivalent weight of armaments, which means roughly two Browning M2's versus one Hispano cannon. This answers your "rate of fire" complaint nicely: If the browning fired 13 rounds/second, then two Brownings were firing 26 rounds a second compared to the Hispano's 10.
That is an over-simplification, of course- "rate of fire" isn't the same as "pattern density," but they have somewhat similar consequences on accuracy. Either way, to claim that the probability of impact between an equivalent weight of cannon and machine gun favors the cannon is erroneous. More on this later.
HoHun said:
You're way removed from reality ... the vast majority of kills were scored at short ranges where the trajectory curvature did not matter at all. And at long ranges, the out-of-centre mounting introduced aiming problems for wing-mounted armament that was more serious than trajectory curvature anyway. Rate-of-fire fallacy, see above.
You don't need to quote combat data at me to establish one of the most obvious truths of the war- most pilots were lousy shots, and most of them were trained to close to point-blank range before firing. That is obviously the optimal firing position, no matter if you have a feather duster or a laser beam to attack with. This also goes a long way towards forgiving the poor ballistics of many cannon, like the Japanese Ho-99 (which has remarkable raw efficiency, weighing slightly less then a Browning .50.)
Regardless, to say that cannon velocity is a moot point at standard combat ranges is foolish. Are you familiar with the problems of deflection shooting? Even at two hundred yards, the difference between the anemic ballistics of the Ho-99 cannon and the Hispano have a notable effect in how much lead one needs to pull. Even the difference of a few degrees of lead (when the deflection already demands X degrees) can be enough to put the target below an aircraft's nose, and out of sight, making the shot difficult, if not outright untenable.
There are other advantages, such as being able to hammer bombers from safely outside effective defensive gun range, but the lead issue in deflection shooting is the most poignant.
HoHun said:
Of the 272 "destroyed" claims resulting from these 482 combats, 86 % were from combat distances of 400 yards or less.
400 yards
is long-range, for air-to-air gunnery against fighters. Extremely long range, at that. Against a manuvering target, 300 is pretty much the max range any decent shot could expect to score at. 200 yards can still be a tricky shot, especially against a manuvering target in a deflection shooting scenario.
My experience is not scientific, but having played an excessive amount of reasonably accurate simulation games (and having been able to sample a broad array of different modeling approaches,) generally I have found that the differences in gun ballistics are still felt very, very much in deflection shooing even at two-hundred yards. And that's just in a game. In real life the difficulty is greater by a few orders of magnitude.
HoHun said:
Note that from switching to Hispano cannon, you get a 20% firepower increase coupled with a 27 kg weight reduction and an ammunition supply increase, both expressed in duration of fire and in total energy, by more than a factor of two.
Where are you getting your weight data? I got mine from here:
linky. That data only shows a 16kg advantage for the Hispanos (assuming the earlier model Hispano, which is what we seem to be discussing.)
EDIT: Disregard that, I looked at the wrong column when I wrote that.
Now, as for "pattern density." This is fancy talk for the fact that for roughly equivalent weight, you have two machine guns firing for every one cannon. I hesitate to equate this with "rate of fire," because ROF describes the density of the bullet "stream," not the pattern of hits it effects upon the target, but nonetheless the machine guns put more then twice the number of projectiles in the air. Due to gun vibration and other factors, this pattern is spread out a bit, though not enough to be terribly problematic at standard combat ranges.
Assuming a decent pilot firing in deflection at two-hundred yards, this means a random clustering of hits around the fuselage. Even two-hundred yards in a deflection shot is a bit long to allow for precise aiming (such as targeting the wing root,) and since the planar view allowed by deflection allows access to the pilot and engine anyway, we'll assume a random clustering of hits on the fuselage. Clearly, with twice the amount of projectiles in the air, the M2 Brownings have twice the chance of scoring on a vital area, such as the engine, or the cockpit. (Also recall that even at shorter ranges, most shots will still result in a pattern bigger then the target. Even zero-deflection shots from the cold six in gun camera film shows half the burst missing, due to the lower target profile.)
Conversely, of course, cannon shells make for dynamic and exciting explosions no matter where they hit. A 20mm cannon strike in the center of the wing will do damage that effects aerodynamics, whereas a .50 will not. This goes some way towards forgiving the lower pattern density of cannons, obviously. On the other hand, I question just how effective cannon strikes on non-vital areas are. A hole punched in a wing will affect aerodynamics and performance, certainly, but it still will not take a plane out of the fight like one or two .50 rounds in the engine block will. (This is a bullet the size of your thumb, after all.)
Additionally, there is the question of the statistical probability of delivering a
sufficient amount of damage to a vital area. What constitutes a sufficient amount of destructive power, to a vital area? Clearly raw megajoules might not be the proper measure here (I'd rather have three .50 API rounds punch into the bowels of a liquid-cooled engine rather then a single 20mm hit which would expend half of it's explosive force on the cowling in the wrong direction- assuming a non-shaped charge, which I think they were.) Even if the cannon could deliver more destructive force to the vital area, it
is a vital area- it might be more important to simply land a hit there in the first place, rather then deliver superior energy haphazardly.
Now we have a lot of factors to consider. How wide or tight is the pattern, (assuming two guns to equate one cannon?) How many .50 BMG strikes does it take in a vital area to score lethal damage? One? Two? Five, Ten? If it's too high, the .50 still loses. What exactly is the effectiveness of cannon strikes on non-vital areas? How does this vary with caliber? (A 20mm hole in the wing is annoying, but a 30mm may just amputate it.) Does the raw megajoule rating of the chemical explosive in cannon shells accurately reflect actual energy delivered to target, given the nature of unshaped explosives? Given that explosive cannon shells had roughly the same amount of armor penetration as AP .50 cal, does that mean .50 cal was more effective because it was twice as likely to score a hit on a vital area, and yet just as likely as the cannon shell to penetrate and wreak mayhem? Does a .50 cal round retain more energy after breaching amour then raw chemical explosives, or does the superior amount of energy in the cannon shell more then compensate for it? Even if the .50 caliber guns prove more effective at landing sufficient damage in vital areas, does the greater ammunition efficiency of the cannon make up the difference in hit probability by virtue of extended firing duration? How does the characteristics of various aircraft effect this, given that some were much better gun platforms then others?
Try writing me a function that can calculate
that. Do it in Lisp for extra points.
The myriad factors at play here are why I am still undecided on the question of cannons. I will note here that the Hispano is not representative of most WWII fighter cannon- it had both a good rate of fire, low weight, AND excellent ballistics, while most cannons of the war could claim at most one, perhaps two, of those traits. The chart from Mission4Today is a nice reference for weight and ROF, but most of what I know of their ballistic traits has been learned from extensive reading, some of it being pilots accounts (and therefore not easily referenced.) The .50M2's good rate of fire and reliable ballistic performance made it competitive against most WWII cannons. The Hispano, of course, is another story.