Armor Penetration Formula Errors

Machinery of War Discussion Ground Vehicle
1

I took a deep dive into why some shells in game have incorrect penetration values and, while I did make some headway into what is incorrect, there is an anomaly I don’t quite understand:

Using the newer Jeanquartier and Odermatt formula for perforation, it matches up with specific cases quite nicely and appears to be more accurate than Gaijins formula and is far better than the longrods website calculator (their formula doesn’t have the units matching up in the equation). But an issue starts to appear when we are trying to solve the max penetration. As we change the angle of the target towards the extremes we get some insane values for perforation like using the 125-I as an example and 80 degree target 2km away, perforation is 103mm and translated to flat is 594mm, surely that is not true, is it? Using the 61.5 degree 2km test data China has conducted, aka 61.5 degrees 2km, we get the very close to the correct values of 226mm and 473mm flat that are listed by secondary sources (220mm, 440mm). Yet if we run the equation at 0 degrees 2km we get only 400mm of pen, which is below what we should expect. As the shell gets more advanced and I try running the 125-II, the 0 degree performance has an even larger gap of 471mm instead of the expected 600mm listed by secondary and primary sources.

Inside the article by Odermatt, they have additional conditionals that modify the equations, such as when L/D gets to above 20 than the equation simplifies. The accuracy here is about the same, perforation depths are a bit lower from what I can tell. Then again, for perpendicular impacts (obliquity = 0 degrees) and L/D > 20 the equation further simplifies to d = L * SQRT (ρp / ρt).

This is quite interesting as the perforation amount is actually very high using this and does not drop off based off velocities. For the 125-II (580mm penetrator) we get 843mm and the 125-I (460mm penetrator) we get 666mm of flat penetration. That is some insane amounts of flat penetration.

Yet I can’t just say I don’t believe the equation. The equation has matched up very reliably with real world performance data I’ve plugged into it. And I mean, we would expect a tungsten penetrator to erode more RHA than the length of the penetrator it has. The changes of flat pen with target angle would make sense then as they all remain below the upper limit of the shell.

HOWEVER what doesn’t make sense is why does the penetration actually decrease with angle? For instance, lets take the 125-I and a 45 degree 2km case. The equation tells us the limit is a 281mm plate, which translates to a flat pen of 397mm, which is BELOW the 666mm upper limit. Why does this occur? This is actually a LOWER limit based off the flat pen translation than the 80 degree case, where we would expect to see part of the rods tip break off from the angle.

Here is a link to the article: [PDF] POST-PERFORATION LENGTH AND VELOCITY OF KE PROJECTILES WITH SINGLE OBLIQUE TARGETS | Semantic Scholar

Screenshots of parts of calculations:

125-I 45 degree @ 2km:
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125-I 0 degrees @ 2km:
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125-I 61.5 degrees @ 2km (secondary source verified):
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125-I 80 degrees @ 2km:
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125-I 0 degrees @ 2km simplified formula:
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Wouldn’t we expect to see on each case the flat penetration translation to equal the max penetration, or close to the max, in the simplified formula?

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Fun post to read through, but I got rather sceptical once I got to the simplified formula part. Always double check when people simplify. You missed a crucial point however when simplifying, it specifically mentions VERY high velocities, which you omitted. I plotted a simple scenario below to showcase how high the velocities really need to be for the ‘TS’ term to tend to 0.

Spoiler

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As you can see, not very applicable for long rods. This gives as a result way too high values.

Also I think you’re a bit confused about how angled performance differs from flat pen. It’s indeed all very nice and cool to translate angled performance back to flat pen, but it gives a skewed result. It’s very important to mention the impact angle, because of the face effect of the back of the armor plate. The path of perfortion tends to direct itself to the normal of the plate once sufficiently deep into the armor plate (or rather because of how much armor there is left). This gives in essense the long rod an easier time perforating angled plates over flat plates, as with flat plates, taking the path perpendicular to the normal of the plate is no shortcut.

The longrods website goes into some detail between the difference of penetration (which is against an infinite thickness plate, thus impact angles are neglected) and perforartion (where angles matters).