v90 Penetration datamine and analysis

[Evil4Zerggin]

Base penetration values

Base penetration values are defined using a precomputed table and linearly interpolated with respect to range. Here are plots (re-rendered using higher resolution and different linestyles than the first time):

These do not include modifiers from gun Mark (between 0.935x to 1.33x; there's also a slight additional dependence on diameter but this is negligible), nor penetration modifiers from techs/components. But these affect all shells close to proportionally so it doesn't matter much.

Vertical shell trajectory is computed separately using a different formula and has no causal effect on penetration. The actual angle of fall only affects belt/deck hit chance, not penetration.

Horizontal trajectory (i.e. azimuthal impact angle) does affect penetration for AP but not HE, using a line-of-sight thickness model (i.e. multiply penetration by cosine of the impact angle, with normal = 0 degrees).

Edited October 8, 2021 by Evil4Zerggin

[Evil4Zerggin]

Line-of-sight/momentum/linear model

I'll leave the comparison to empirical real-world data to others. However, I will use the game's table to produce implied normal penetration and angle of fall using a couple of theoretical formulas.

The first is the line-of-sight model, where the effective penetration is multiplied by the cosine of the impact angle (or equivalently, the effective armor thickness is divided by the same). The shell is imagined to penetrate a fixed distance in a straight line regardless of impact angle.

In terms of the historical formulas compiled by Okun, assuming that we simply take the velocity component normal to the armor, this corresponds to models where the penetration is linearly proportional to the velocity normal to the armor, i.e. "Fairbairn" and "Krupp KC vs. Uncapped AP Projectiles". (This doesn't necessarily imply that these models had the same imagined physical mechanism in mind, just that they produce the same result in this case.)

Under this model, the implied penetration against a plate normal to the shell's trajectory would be computed from the side and deck penetrations as sqrt(side*side + deck*deck), and the implied angle of fall as arctan2(deck, side).

What's with the "sag" in the implied normal penetration curves? There's two possible causes (not mutually exclusive).

One is that the game's tables could be off, but I don't have an opinion on that at time of writing.

The other is that the formula could be off. The "sag" in the middle coincides with the implied angle of fall being close to 45 degrees, i.e. not near normal to either the belt or the deck. Thus, this would imply that oblique angles do a better job of deflecting shells than the line-of-sight model predicts. Notably, this is contrary to the "shell normalization" mechanic used in World of Tanks and World of Warships---effectively, the shell is being anti-normalized.

Edited October 8, 2021 by Evil4Zerggin

[Evil4Zerggin]

Thompson "F-Formula"/kinetic energy/square model

At the other extreme of models cited by Okun is the Thompson "F-Formula" All-Purpose Armor Penetration model, which is also the latest of the cited models. In this model, the penetration is proportional to the square of the velocity normal to the armor surface. This thus assigns a stronger effect to the angle.

Under this model, the implied penetration against a plate normal to the shell's trajectory would be computed from the side and deck penetrations as side + deck, and the implied angle of fall as arctan2(sqrt(deck), sqrt(side)).

Here the "sag" in the implied normal penetration plot is reduced, since this model expects oblique angles to be penalized more than the linear model.

[neph]

Why is there such a difference between shells <15" & shells >=15" at range?

[Evil4Zerggin]

Not sure why the table has such a dropoff at that range. Though you can't actually reach those ranges with 14" guns in-game (since maximum range is a separate calculation from both penetration and trajectory).

Edited October 8, 2021 by Evil4Zerggin

[Draco]

Zerg's graph program doesn't appear to allow him to leave something as a non-value, so when the guns no longer have range they will just rapidly trend toward zero, rather than stop mid-graph. Same with the angle of fall graphs, a 2" gun can't shoot 20 kilometers, so it just trends towards the extreme when it runs out of data, in this case the 90 degree/40 km extreme.

Once again nicely done zerg I could compare it to another compilation of numbers from navweaps, but I think everyone would be better served with the conclusions right off the bat.

Implied angle of fall is problematic, since no gun I've ever read of was capable of over 55 degree angles of fall, and both your graphs would Imply that all 15"+ guns could do that, although the linear more than the F-formula.

I've stated my position on the raw data before, but to summarize. penetration should trend further down before values re-ascend overall, and no gun should start re-ascending before they have reached the last 1/10th of their max range capability. The bigger the gun, the later the re-ascension. Rule of thumb of no less than 30km before the switch happens, and another rule of thumb should also be no deck pen should ever exceed 1/2 of max belt pen equivalent at their respective extremities of pen.

Would free up tons of displacement for players, improve gameplay and realism simultaneously, and require no tweaks to AI armour algorythms since they already armour their ships as though a 7" deck actually did something.

[Draco]

On that note, succesful deck pens should also be far more likely to cripple a ship than as of present.
There aren't many examples of actual deck penetrations from real life, but the few ones we have almost universally crippled the ship in question then and there.
Examples would be Rodney disabling all of Bismarck's engines and rear turrets with a single hit during her last stand, or Warspite dropping Julio Cesare's speed by 1/3rd, resulting from both a secondary ammo det. and severe engine damage, again, from a single hit.
Of course, assuming that the Hood was actually sunk by a deck hit (which is still disputed) we all know how that went.
Compare this with in game where some classes of BBs can survive literal hundreds of deck pens with little effect other than HP loss.

Edited October 9, 2021 by Draco

[DougToss]

From Brown, Nelson to Vanguard

Edited October 9, 2021 by DougToss

[SpardaSon21]

On 10/7/2021 at 9:18 PM, Evil4Zerggin said:

The other is that the formula could be off. The "sag" in the middle coincides with the implied angle of fall being close to 45 degrees, i.e. not near normal to either the belt or the deck. Thus, this would imply that oblique angles do a better job of deflecting shells than the line-of-sight model predicts. Notably, this is contrary to the "shell normalization" mechanic used in World of Tanks and World of Warships---effectively, the shell is being anti-normalized.

That frequently happened IRL, actually.  The steeper the relative angle, the much greater the chances the AP cap would failingly fail (as opposed to successfully failing as intended).

On 10/9/2021 at 3:21 AM, Draco said:

Implied angle of fall is problematic, since no gun I've ever read of was capable of over 55 degree angles of fall, and both your graphs would Imply that all 15"+ guns could do that, although the linear more than the F-formula.

The 16"/50 got very, very close with 53.3, and the US 6"/47 was over that at 58, the 8"/55 at 54.3 when using SHAP.  Regardless, both ranges and velocities in-game are well below what they should be.  A 16" Mark 3 gun with Triple Base, TNT IV, and Super-Heavy has a range of 32.2km (34,995 yards) and a muzzle velocity of 719 m/sec (2,358 FPS), or far lower than the 16"/50 or even the 16"/45. And the USA was historically still using a single-base propellant until the end of WW2!  No, I don't know how they managed to accomplish that.

That said, the shell is far, far heavier than it should be at thanks to propellants magically adding mass to shells.  They really need to fix that and remove the reload speed effects.  I don't know why tube powders would reload faster than grain powders.  Are the crews manually bagging their powders or something just before firing?  

[Draco]

22 minutes ago, SpardaSon21 said:

The 16"/50 got very, very close with 53.3, and the US 6"/47 was over that at 58, the 8"/55 at 54.3 when using SHAP.  Regardless, both ranges and velocities in-game are well below what they should be.  A 16" Mark 3 gun with Triple Base, TNT IV, and Super-Heavy has a range of 32.2km (34,995 yards) and a muzzle velocity of 719 m/sec (2,358 FPS), or far lower than the 16"/50 or even the 16"/45. And the USA was historically still using a single-base propellant until the end of WW2!  No, I don't know how they managed to accomplish that.

That said, the shell is far, far heavier than it should be at thanks to propellants magically adding mass to shells.  They really need to fix that and remove the reload speed effects.  I don't know why tube powders would reload faster than grain powders.  Are the crews manually bagging their powders or something just before firing?  

I don't think the Mk.III is perfectly analogous to either the IRL 16"/50cal or the 16"/45cal. If you play the academy missions you'll find 16" weapons up to and including Mk.V that better resemble the real world weapons (not perfectly, but a lot closer).
Nick has stated that these more advanced versions will be researchable at a faster rate than the custom battles unlocking years seem to indicate, so judging everything only by what is available in custom might be a misstep.
Still, even these later marks of gun that we find in academy missions outperform their IRL equivalents in their deck/belt pen ratios by a considerable margin.

Seems I'll just have to stick to my 16" deck armour designs for now... man I miss the days when you could have reasonable immunity zones with just 10" of deck 😢

Edited October 11, 2021 by Draco

[SpardaSon21]

1 hour ago, Draco said:

I don't think the Mk.III is perfectly analogous to either the IRL 16"/50cal or the 16"/45cal. If you play the academy missions you'll find 16" weapons up to and including Mk.V that better resemble the real world weapons (not perfectly, but a lot closer).
Nick has stated that these more advanced versions will be researchable at a faster rate than the custom battles unlocking years seem to indicate, so judging everything only by what is available in custom might be a misstep.
Still, even these later marks of gun that we find in academy missions outperform their IRL equivalents in their deck/belt pen ratios by a considerable margin.

Seems I'll just have to stick to my 16" deck armour designs for now... man I miss the days when you could have reasonable immunity zones with just 10" of deck 😢

That's fair.  I still want them to do something about the deck pen, as well as resistance.  Those seem to be the two major complaints right now.

[Steeltrap]

Great stuff.

We'll just have to hope this is another case of placeholder that's good enough and will be revised to 'realistic' before full release.

No reason for it NOT to be when the known 'facts' are not hard to find.