Aircraft gun accuracy

I’m looking for data on aircraft gun accuracy.

So far I’m aware of .50cal AN/M2 accuracy being 4 mils for 75% of shots and 20mm AN/M2s with 3 mils.

100% accuracy:
MG FF 2.0 mil
MG 151/20 3.8 mil
MK 108 3.0 mil
MK 103 4.0 mil

I also remember seeing some data for the Soviet Berezin before, so I might be able to dig that up.

If you have more data to share, feel free to share.

Edit: I made a mistake. The German values where hit radius and to convert them to mil values they needed to be doubled.

Hey mate now I just spent some time trying to research this for just the 151/20 because you sparked an odd curiosity, and from a purely theoretical vacuum, the MG 151/20 should have a 1.4 mil dispersion, however as I said, this is in a vacuum, with purely theoretical numbers. I got most of the technical details as correct as I could but I did have to guesstimate two of them (cannon barrel external diameter which I used 50mm, and velocity variation, which I put at about 0.5%), all other information I was able to find online (albeit one was from just a facebook post, cant remember what one). Does that help at all? I’m not entirely sure if it does but I was curious enough. Since its 0203 here right now I cant be bothered calculating and researching the others as this took me a solid half an hour at least.

Maybe. If you tell me how you come up with that number.
I mean it’s already better than what I’ve found in a German document.
Which was based on firing only 11 rounds but didn’t specify the exact circumstances.

The main point was to compare accuracy between the different cannons and that longer barrels lead to decreased accuracy.

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Disclaimer I did have to use ai to help me with this formula it may not be entirely accurate, and as I said is part of a vacuum not real life calculated. Another thing to note is that I used figures for Minengeschoss I forgot to mention that in my original post, using AP or standard HE would yield different results, those shells are heavier than Minengeschoss, have slightly different propellant and have a much slower muzzle velocity

Formula

I have to hope the screenshot worked properly otherwise I’ll type it out but

σ = Dispersion (appears as radians but easy to convert)

J = recoil impulse per shot (appears as Newtons/Second)
Mg = cannon mass (not to be confused to be Mass*gravity)
v = muzzle velocity

F = force generated by shell leaving the barrel
L = barrel length NOT cannon length
E = Young’s modulus (stiffness of barrel steel ~2.1x10¹¹)
I = inertia, resistance to barrel cross section bending
Square root of 2 = RMS conversion factor (converts vibration into statistical spread generated by barrel vibrations)

σexit = angular error generated by ammunition consistency (usually autocannons of this time have 0.4 - 0.7% variation, I went with 0.5%)

And then lastly 1 Mil = 0.001 Radian, easy to convert

Does that make sense? My tired brain tried explaining that the best I could on 3 hours of sleep

Could be due to vibrations and the likes, the longer it stays in the barrel the more vibration cycles that it goes through leaving its angular velocity to be partially randomised upon exit. That would make sense to me?

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Yes

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I found this:

This would give the ShVAK 2.6-2.68 mils accuracy for 100% of hits. But it’s for single shots.

The MG 151/20 got 1.9 but only for 11 rounds, which is a very low sample size.
Accuracy also decreases as the barrel gets hot, so the numbers can’t really be used as comparison.

Edit: MG 151/20 accuracy is actually 3.8 mil not 1.9.
This makes the ShVAK more accurate, as can be expected, since it’s gas operated while the MG 151 is recoil operated.

But I also found a accuracy table where the MG 151/20 scored 2.6 mil as well. Probably also from single shots.

This is apparently from some Australian WW2 document for Beaufighter armament.

Here the 75% accuracy for a 20 shot burst is 2.9 mil. Comparable to the US figure of 3 mil for the AN/M2 cannon.

100% accuracy is roughly 4.78 mil.

10 single shots from a cold gun are somehow less accurate than from a hot gun but maybe the tables got switched.
Cold 100% → 2.75 mil
Hot 100% → 1.52 mil

Anyone got info on the 13mm Mg 131?

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