Shortround6
Major General
To try to summarize it -
Heavy machine guns like the M2 have the advantage of a little bit higher velocity (890 m/s vs 700-800) and therefore longer range, flatter trajectory and better armor penetration*. Shells are also a bit lighter and smaller I think so you can pack more rounds in the plane (and in train cars, cargo ships etc.)
Light cannon like the MG 151/20, the ShVAK and the Hispano have the advantage of shooting exploding shells which are better at destroying aircraft structures, tearing off wings and so on.
Both did have their advantages but the general consensus is that cannons were better. Some weapons were also particularly well suited to certain airplanes.
Even more simplistic than my comparison and it may be in error. Look again at the pictures. The Italian 12.7mm machine gun use 35.4 Gram AP projectiles vs the American 46 gram projectiles so armor penetration is already at about 77% even if the velocities were the same, which they are not. The Italian round had MV of 760 mps vs the American 870mps and since penetration is proportional to the square of the speed the Italian round is in big trouble. Throw in the fact that the Italian, Japanese and German 13mm projectiles had a rather poor shape compared to the American (or Russian) projectiles and so impact velocities are even poorer than the Muzzle velocity suggests.
Muzzle energy per round is 9,800 to 10,600 Joules for the Italian/Japanese round vs 16,600-17,400 joules for the American round depending on ammo. Russian ammo can peak at 19,200 joules for their 52 gram AP projectile.
German 13mm is just under the Italian/Japanese round.
yes the light cannon are better at blowing stuff up but the Hispano also had a MV of about 850-880 meters per second out of the long barreled guns and had a similar time of flight to any reasonable air to air distance. A 20mm Hispano ball round (HE shell with no filling and sold nose replacing fuse) could penetrate most aircraft armor and structure and was quite good abraking things. Muzzle energy was 46,900 to 50,300 joules. But the Hispano was sort of in a class of it's own.
The MG 151/20 had muzzle energies of just about 29,000 joules and rather depended on it's special mine shell to blow things up, which with it's 18-20 grams of HE it did rather well.
However the thin walled shell didn't penetrate very well and didn't carry any tracer which called for mixed belts of ammo with more conventional projectiles for AP and tracer. These were heavier and slower but match pretty well to 300 meters or so.
The ShVak cannon had high velocity but it's light (96-99 gram) projectiles were poorly shaped and lost velocity quicker than the 20mm Hispano or indeed their own 12.7mm machine gun. The HE capacity was 4-7 to 6.1 grams of HE depending on exact shell (AP wouldn't have any)
Part of the problem with the american .50 and the Russian 12.7 was the weight of the ammo. While the projectiles were much lighter than the 20mm cannon the weight of the cartridge case and powder charge was disproportionately heavy. An American .50 cal round could weigh about 112 grams while 20mm Hispano round weighed 257 grams, the 20mm Shvak round weighed about 183 grams compared to the 125 grams of the 12.7x108 machine gun round (note that the russian round is about 12-13 grams heavier than the American but only 6 or less of that is the projectile.)
The Italian and Japanese Machine gun ammo was much lighter, about 82 grams, as befits it's lower power. again note the difference in weights of the complete round vs the difference is projectile weight. The case and powder of the American round was 20 grams heavier, mostly the brass case.
But then the Italian and Japanese heavy machine gun round don't have an advantage in range or trajectory over the light cannon.
I would note that in most cases any advantage in range or trajectory is mostly in the minds of post war commentators/writers. The difference of 6-9 inches in trajectory when you are shooting at a fuselage 4-5 feet high is minor at best. Only a small fraction of 1% of the pilots in WW II had any business shooting at planes more than 400 meters away so the whole range/trajectory argument is bogus. Doesn't mean that tons of ink and paper and the internet equivalent hasn't been wasted on it though.
What was important was time of flight as that dictated the amount of lead needed for deflection shooting. A short time of flight could mean only aiming several plane lengths ahead of the target instead of 5 or 6 plane lengths.
It is this time of flight thing that makes something of joke of the planes that used the mixed batteries of guns and claims of long range shooting by fuselage mounted guns.
The time of flight for a German 7.9mm round to 600 meters was 1.159 seconds, while the time of flight for the 15mm HE round was 0.816 seconds for .343 second difference. a 300mph airplane is going to cover 150ft in that amount of time making total nonsense of trajectory problems, you are either hitting with one type of gun or the other, not both and much more likely hitting with neither. since the target plane is moving over 350 ft from when the bullet left the muzzle of the 15mm gun and it arrived in the target "area"
Granted that is an extreme example and worst case at sea level but illustrates the problem.
The extra guns (and the extra bullets per second) increased the hit chances for less than expert pilots. Some pilots started shooting behind the target plane and swung through the target plane ending up shooting in front of it. They may have only been "on target" for a fraction of second. The guns were not synchronized with each other to fire in salvos. At 90 degrees (worst case) a 300mph airplane is traveling 44 ft for every round fired by a 600rpm gun and 22 ft for 1200rpm gun. You might have to be very close to get a high percertage of hits.More guns is an advantage, but only if you can bring them to bear. HItting the target is what matters. There wasn't a single fighter in the war that could wishtand sustained 20mm cannon fire OR 12.7mm heavy machine gun fire. The extra guns were mainly needed to counter heavier or better armored bombers (B-29, B-17, B-24, B-25, B-26, Il2 Sturmovik, Hs 123) or for strafing. The FW 190 was excellent, as was the P-47, and the Tempest but that was only one variation out of many to solve the problem of fighter design.