Hi Suntracker,
>I think it would be easier to land 20 to 30 hits of 50 cal.
Well, a numerical comparison is only meaningful if you define a basis for the comparison.
For example, you could say you'd allocate 1000 lbs to the armament of a fighter and see what kind of firepower that would give you. (That's about the weight of the P-47's battery.)
Here's what would result from formulating such a requirement to an aircraft designer if you'd also specify using an equally destructive ammunition load for each battery:
6x MK 108 - 14 rpg - 411 kg - 30,2 MW firepower - firepower per weight: 73,5 kW/kg - 60 shells/second
2x MK 103 - 37 rpg - 351 kg - 8,2 MW firepower - firepower per weight: 23,3 kW/kg - 14 shells/second
8x MG 151/20 (MX) - 47 rpg - 416 kg - 11,2 MW firepower - firepower per weight: 27 kW/kg - 96 shells/second
8x MG 151/20 - 52 rpg - 424 kg - 10,1 MW firepower - firepower per weight: 23,9 kW/kg - 96 shells/second
8x Hispano V - 53 rpg - 440 kg - 9,9 MW firepower - firepower per weight: 22,4 kW/kg - 96 shells/second
7x Hispano II - 59 rpg - 451 kg - 7,4 MW firepower - firepower per weight: 16,5 kW/kg - 70 shells/second
10x MG-FF - 45 rpg - 432 kg - 7,8 MW firepower - firepower per weight: 18,1 kW/kg - 80 shells/second
5x MG 151 - 239 rpg - 427 kg - 2,2 MW firepower - firepower per weight: 5,1 kW/kg - 60 shells/second
12x MG 131 - 259 rpg - 447 kg - 2,5 MW firepower - firepower per weight: 5,7 kW/kg - 180 shells/second
8x ,50 Browning M2 - 250 rpg - 452 kg - 2,3 MW firepower - firepower per weight: 5 kW/kg - 104 shells/second
15x Browning ,303 - 665 rpg - 449 kg - 1,3 MW firepower - firepower per weight: 2,9 kW/kg - 300 shells/second
(Edited to fix rpg figure)
For evaluating the results, just compare each battery suggestion to any other.
For example, you could compare the Browning M2 battery to the MG151/20 battery: Both use 8 barrels and put out about the same number of projectiles, but the MG151/20 is about 4.4 times more destructive.
Though in that example, each cannon is a bit heavier than each MG, the higher destructiveness of cannon shells means that the ammo load is a bit lighter, making up for the difference in weapon weight.
For an equal battery weight, the machine guns don't even have an advantage over the cannon in bare projectile count, so there's not much reason to assume you'd have any hit ratio advantage with MGs (at least not with the Browning M2).
If you think the Browning M2's trajectory gives it a hit rate advantage (usually, the literature tends to overestimate the effect since fighter combat was decided at rather short range in WW2), you can swap the MG151/20 for the Hispano II, which still has about 3 times the firepower of the Browning M2 with a similarly flat trajectory.
Projectile count for the Hispano II goes down slightly, but since each projectile is vastly more destructive with cannon, the Hispano in the end wins in this comparison just as easily as the MG151/20.
If you decide to use real-life batteries for comparison, you'll find that the machine-gun armed aircraft usually carry a lot more weight in terms of armament and ammunition to achieve similar firepower as cannon-armed aircraft, so the superiority of cannon is somewhat hidden. Still, every MG-equipped WW2 fighter would have benefitted from a firepower increase if it would have been switching to cannon.
Regards,
Henning (HoHun)