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Apr 8, 2013

Digging Deeper (1) - Shell Normalization [revisited]

By Thor_Hammerschlag

The article was first of all released in an unfinished form. I am sorry therefore, Silent Stalker released it because I send it to him, however I only wanted to let him see on what I am working on. I didn’t write it down in the email that it shouldn’t be posted in this from so it is my mistake as well.
From now on mistakes like that won’t happen again, I joined the blog as you might read already!

About the article itself: It contains a lot of technical content. I wouldn’t be able to write it without an study of mechanical engineering, especially the mechanical part probably is not easy to understand.
Therefore I recommend reading it twice before trying to understand it for anybody who isn’t familiar with the subject of armor penetration.
I prepared a FAQ based on the confusion of the first article, you can find it in the end of this version. Also I reworked the article to make it easier to understand.

Digging Deeper (1) – AP Shell Normalization [revisited]

„God damn, I can’t believe that he penetrated me with that penetration at that angle! – that can’t be realistic!” 

We all know this kind of situation and most probably know the reason for penetration on such occasions:

But how realistic is the way shell normalization was introduced into the game? Currently the value – ingame - is for both APCR and AP shells between -5° and -4°. What does that mean? The angle of armor is negated by these values, resulting in less effective armor against AP and APCR shells than armor/cos(angle) suggest. Angling your tank at up to 20° barely makes a difference because of this phenomenon.

First of all, we need to consider that ingame AP-shells (armor piercing) been in reality a lot of different kinds of shells. Mostly, these 3 shells were in use:

Common shells of World War 2 [2]

AP: Armor Piercing round

Most common during the first years of the war, they were used by all nations.

APC: Armor Piercing round – with armor piercing Cap

Cap was set on the top of the AP a round to reduce shatter tendency.

APCBC: Armor Piercing round – with armor piercing Cap – and Ballistic Cap

Like APC - with an additional cap to reduce wind resistance.

These shells had all compareable normalization values, with AP having slightly worse values than APC and APCBC rounds. In this article all will be treated the same way.

After discussing the 3 most common kinds of shells, we will shoot such a shell against an armor plate and make a mechanical analysis. I prepared it for a AP shell. The following graph might explain the key problem with the penetration of sloped armor. The contact forces are calculated with F=p*A (pressure, and contact-Area, a rounded area all around the shell). This kind of 3 dimensional pressure-contact can mechanically be simplified by summing up the pressure of the lower and the upper part of the shell to 2 resultant forces. This is reflected here [1]:

(For all who want to dig even deeper, I prepared the whole mechanical treatment of the shell in the contact zone, something like this is seemingly missing all-over the web. It’s basically the static treatment from above and the dynamic treatment (principle of D’Alembert [1]) – it explains why the shell penetrates armor at all.)

The result:

There is no Normalization for AP projectiles which negates armor (the term normalization is misleading mathematically, but to prevent confusion this article will still refer to it). On the basis of “WWII Ballistics - Armor and Gunnery” it is possible to calculate normalization values as we know them. Technically it is uncommon to work with them at all because of the complexity of the shell trajectory. However, these values are fairly good to understand the basics of AP shell penetration and the difference between World of Tanks and Reality.

Probably out of blue for the majority of WOT-players: The reality values are positive. Sloping leads to more effective armor than 1/cos(angle) suggests.  Also new - “normalization” gets higher values with a greater shell diameter (that means more mass per mm²). In other words: Small calibers are worse against sloped armor.  The normalization value increases significantly against higher angles. [2]

Also this kind of sloping explains most battle reports which were not understandable yet. Just to name a few: The IS-2 had problems penetrating the Panthers glacis on distance (with AP), or the 8,8cm L/71 of the Kingtiger was unable to penetrate the 100mm frontalarmor of the postwar T-54. [2]


- (1) Bigger shells were more effective against sloped armor than smaller ones

- (2) Armor angling was a lot more effective than reflected ingame

  (3) HEAT shells are more effective against sloped armor than AP/APC/APCBC shells [2]

- (4) The conversion of german penetration-data from 30° to 0° was done with Armor/cos(30°+normalization) as basis, however negative normalization values were put into the formula, which were actually positive values, creating less penetration for 0° data

[1] Prof. Dr. –Ing. von Bredow: Script Dynamics (University of Applied Sciences Würzburg-Schweinfurt)
[2] Lorrin Rexford Bird and Robert D. Livingston: WWII Ballistics: Armor and Gunnery

Now for those whos brain is not broken yet, here is a FAQ which might clear up some unclear things. 


1: Wargaming explained normalization in a different way..

(link to WG video, at 4:30)  
Probably a really confusing video. The video is good, however the effect they describe was only reflected by a single type of shell in the 2nd World War. The Soviet APBC shell (Armor Piercing Ballistic Capped), I might explain that effect in an article in the future. [2]

You can see it besides the types of shells we know already, it is on the right side. You can recognize it on the blunt nose (behind the white Ballistic Bap) which is also in the video. [2]

2: Wikipedia says, that the length of the projectile is also very important when it comes to normalization..

That is correct. Follow the digging even deeper link, it shows where this effect comes from. This is a really complex feature but I will explain it. You will see the moment of inertia in the link, the blue circle around the center of gravity. This moment works against the moment created by the forces which turn the shell and make the shell ricochet. The moment of inertia increases with shell lengh, thus makes it harder for the contact forces to turn the shell, which results in less normalization.

3: You are saying there is a big mistake? Why you are not making suggestion on eu forums about it?
Yes there is quite a big mistake. I might do that one day, but realistic shells and slope effects would require massive rebalancing.

4: My IS-3 sure would appreciate that...
Absolutly, the frontarmor of a real IS-3 was incredible strong against most WW2 projectiles.
Also, WOT is somehow unabled to reflect 3D sloped plates armor ingame. (angleing it does take into account however)
IS-3 front works like 110mm @56° which is currently 175mm ingame.
Same for is-7, 150mm @65° which is 300mm frorm the front (tested)

source is for the IS-7.

Might write an article about actual performance of Pike-Nose armor one day.. 

5: there is nothing wrong in converting data, WG simply used Soviet criteria (Which was most strict then German, US and UK) for most guns.
Soviet criteria is less strict than the german one [2]. German criteria is 5 successfull penetration is a row and not 50% success.
According to [2] you have to multiply soviet test results by 1,06 and german by 1,14 in order to receive 50% success data. To estimate german combat ammo results you have to multiple the data by 0,943 [2] (for example for a 88mm shell) in order to estimate combat ammo penetration.

Article about how to estimate german 0° penetration at 50% success will follow.
(doubt the 1,14, but the book has great sources, will see what i will do regarding the article)

6:  F=p*A equation, it is quite useless, since you do not know the pressure involved..
Here lays another engineering aspect. Over the extent of the shell the pressure is pretty constant, with the one on the lower possibly being higher than the on the higher side because of more plastic deformation and solidification.

But even if the pressure on the lower side is as high as on the upper side, there is one significant difference. The area on the lower side - it is in any case larger than that of the upper side of the shell. Thus creating a larger resultant force.

7: Soviet guns penetrated more IRL as well..
I said nowhere that they didnt. But the subject is normalization and thus sloped armor and the error WG made specially at this point in armor conversion was my last point of the conclusion.

If you compare german to soviet penetration ingame the difference to RL data is not that huge (only talking about the differences) but compared to any other nations data (which used AP based projectiles) the german data is really damn wrong.

Germans get ~30° data, to compensate that they get APBC normalization. On the other hand
US data for example is 50% success data (at a softer plate), ingame they get APBC like normalisation for their full penetration at 0° (for many guns).

Some penetration data where nerfed and buffed others were just buffed. That would be okay regarding balance. But they say also that its technically correct what they do, and that is very very wrong.

Anyways, soviet data is also worth an article..

8:How can they have same normalization when the latter ones are developed FROM the former AP shell IN ORDER TO IMPROVE normalization?
APC and APCBC were NOT developed to improve normalization. 

APC - this cap was specially developed in order to reduce shatter tendency [2]

APCBC - like APC, with a cap which let penetration drop less on distance [2]

9:I have just put my hands on a library copy of "WWII Ballistics: Armor and Gunnery". Could you, please, post a short comment on how you calculated the "real" normalization angles. 

First of all we need to be aware of the fact, that normalization values are something to simplify the process of penetration and give an idea about how the angle of the armor changed the shell directory.


  1. Dafuq?
    But gave me a well read.

    1. haha.. but im glad you like it.
      Give it another try and you might understand it aswell :)

  2. Very short summary: WG uses AP penetration numbers but APBC penetration effects.

  3. You are saying there is a big mistake? Why you are not making suggestion on eu forums about it?

    1. Very simple reason: You want even more bouncing from heavily sloped armor?

    2. You don't want armor back to hightier? After all powercreep for penetration (hey let's give mediums that are supposed to use their speed as advantage same pen as slow heavyes) and lastly goldshells for credits, armor is more of hinderage (as form of more weight -> less speed/agility) than advantage, most prominently seen with Maus as that tank getting worse and worse at every patch.

    3. Who are going to benefit the most from such mechanism? Think about it.

    4. My IS-3 sure would appreciate that... though not necessarily when running into its higher-tier cousins. :|
      [/subtle hint]

  4. So the effect of normalization, the way WG describes it, is the characteristic effect of APBC rounds (as I understood it). So could you please say how widely they were actually used, examples of guns in which they were used and how often.

    And about APCBC I assume the anti shattering cap was too soft to have any effect on changing the angle and at best reduced ricochet chances? (I'm a bit too lazy to research so this is just trying to think logically)

    1. You are right on the 2nd point, the effect was very little.

      I need to research the first one further, but it was only used by the soviets, besides the common AP shells they had this genius piece as well.
      I only know that for the 100mm and for the 122mm gun test were done in Kubinka in september 1944 [2].

      For the smaler calibers such rounds were more common and used during earlier years than the bigger ones. For example the 85mm APBC round was produced during 1939 already [2].

      We probably have some guys around here who know more about the indroduction of the rounds

      But Yea, You guys are getting it... im glad to see that

    2. From what I know, only the Soviets had true APBCs, with the APCBC being referred to APBC at times. But then, there is no real difference between APCBC and APBC in the function of the BC by deforming, spreading and “sticking” to the armor on impact and thereby reducing the tendency of the shell to deflect at an angle.

      I guess this is how WG tried to get around the system of there being AP, APC, APCBC/APBC shells: All rounds have the penetration of AP shots, all "normalization" is conducted as if they're APCBC/APBC shells.

  5. That's more like it, Thor! Keep it up.

    It is also interesting to note that armies made antidotes for their own poison. For example, Germans hardened armor on their tanks, which not only increased effective armor thickness but also increased the chance that projectile striking that armor would shatter from excessive internal stress (since armor hardness was greater than projectile hardness). They also made ammunition (APC) that had reduced tendency to shatter. Russians, on the other hand, made extensive use of sloped armor and thus made ammunition (APBC) that was more effective at combating such armor.


    1. 'Course, hardened steel also has the unpleasant tendency to be *brittle* - certainly the captured tanks the Soviets used for tests at times seem to have had their plates shattered like so much *glass*.

      Makes sense that whoever adopts a particular protection-improvement scheme would as a logical corollary also start looking into means of overcoming the trick in question - all the more so as the opposition is only too likely to copy it sooner or later. Plus the necessary specimen to run tests on oughta be readily enough available. :P

    2. Generally speaking, that's correct. However, Germans used face (sometimes also called case) hardening. In short, only the top, outer layer of armor receives hardening, while underlying layer is softer ("normal" hardness). Thus, harder top part of the armor increases chance to shatter incoming rounds, while lower part acts as a cushion (while also being part of armor shell overall, of course). Best of both worlds. Japanese smiths use similar technique while forging swords.

      Regarding "armor shattering like glass" - there are a lot of those myths. Low caliber guns causing spalling and killing crew without penetration, tanks being decapitated (turrets flying off), killing dozens of tanks with a single bomb etc. What nobody mentions is: what kind of guns were used, at what distance, where did shell hit, was the effect consistent etc.? Lots of these stories were used for propaganda purposes (by all sides) so important facts were largely omitted.


    3. Japanese, schmapanese. Every ironworking culture that figured out steel and tempering knew that; Western Eurasian smiths had figured it out already before the Japanese were off *bronze*. European weaponsmiths and armourers in particular would go on to take it to heights their Japanese colleagues, mostly stuck with some very poor raw iron indeed, could only dream of - by the Early Modern period the heavy cavalry was being kitted out in "proofed" duplex or even triplex cuirasses and helmets, made by welding together plates of different hardnesses and ductility for optimum protection. Thirty Years' War period Swedish military regulations required such to stop a pistol ball from some five paces and musket from fifteen or so...

      As for German armour plate, well, go check out Ensign Expendable's blog and see for yourself. That's some pretty dramatic shattering even from 85mm hits.

    4. By no means was knowledge limited to certain area or group of people. I simply used Japanese as an example since they had superior metalworking compared to, for example, European one, right up to about end of medieval period. But never mind...

      Yes, I saw his blog before, and have to say that it is one of the most single-sided ones out there. Heavy and super heavy anti-tank guns (122mm and 152mm) firing HE and concrete piercing shells into medium tanks? Shooting 76mm and 85mm shells into weaker side armor, from 500m or less? German welding good for aesthetics only? Comparing different caliber guns or even widely produced and used ones vs. experimental and never used ones? Yeah...I wonder why it took 2 whole years for Russians to defeat an enemy who had such terribly bad arms and armor, was heavily outnumbered (both on land and in the sky), fighting on two fronts simultaneously and still manged to achieve 3:1 tank kill ratio?


  6. Thor, one note, as I wrote in deleted post there is nothing wrong in converting data, WG simply used Soviet criteria (Which was most strict then German, US and UK) for most guns.
    If you want 226mm* pen 88/71 then you will also get 210mm* pen 100mm D-10 and 203mm* pen 122mm D-25, which would require a lot of rebalancing.

    *All from US testings.

    1. That isn't the problem. The "problem" is that the Soviets tested with Pzg. (AP), not Pzgr. 39 (APCBC).

    2. This comment has been removed by the author.

    3. 88/71 did not use plain PzGr.

      US tests show relation of 226mm:210mm:203mm or 1:0.92:0.89 for 88/71:100mm:122mm.
      Soviet tests show ~same relation in performances between those guns as does US ones.
      British tests show same (they are withing few mm with US tests, so probably similar criteria).
      Soviet tests will always show ~10-15% less then US/UK/German tests said, but that is due stricter criteria.
      You can not use data for Soviet guns from Soviet sources and data for German guns from German sources, since methodologies are incompatible and you will get only bullshit as did most games before WoT (Steel Panthers series being worst offender).

      Devs used data by Soviet criteria, deal with it and put a end to that "German guns should pen more" BS story - if you go that route ALL guns should penetrate more, which would open HUGE can of worms.

      Look at this for example:
      Going by US relations from tests, if in game 88mm pens 203mm, 175mm for D-10 and D-25 is actually less then they should penetrate.
      ~Penetration should be 187mm for D-10 and 180mm for D-25.
      Going by US data (which is ironically close to German data), let's say 88/71 pens 226mm. Then D-10 will penetrate 210mm and D-25 203mm.
      Do you really want that?

    4. I'm just curious - I used to play Steel Panthers (mostly World at War, but even the first one) a lot and would like to ask how much screwed the pen data was?

      Because I don't remember any pen data from this game anymore...just one thing regarding armor comes to my mind and that is the 200 mm of frontal hull armor on Tiger I to keep it alive longer :)

    5. You seem to be seriously misunderstanding me, bojan.

      1. I support the current peneration numbers except for the 5 cm KwK 39 L/60.

      2. I proved that the Soviets did use AP rounds instead of APCBC rounds in their comparison tests:

      3. German tests were at least as strict, if not even more strict, than the Soviets. German tests called for complete penetration without any fragmentation behind the plate:

      4. WoT uses AP penetration numbers for the game anyway, so if we're discussing game mechanics the Soviet comparison tests for the German guns is the standard to go by.

    6. OK
      1. 5cm was incapable of penetrating KV-1 sde hull (75mm vertical) with anything but APCR.
      In Yugo tests 5cm PzGr.39 could not penetrate T-34-85 side turret (75mm@20deg, ~80mm equivalent). So penetration was less then what German tables say, I would up it to ~72-73mm, but nothing more.
      2. Ah, you are talking about 5cm, not 88/71, then OK, it should get a boost, as should some other guns (not just German).
      3. If German tests were so strict then how you explain how US tests got results pretty similar to German results, but got much higher results for Soviet guns then Soviets did.
      No, if you don't belive me, ask on Tank-Net (If you doubt that forum ask The_Chieftain what he thinks of it :) ).
      Soviets used tests with very high quality test plate, higher quality then anyone's armor in WW2. Also 100% of rounds had to penetrate, with penetration being defined as at least 80% of round material behind armor, with rounds stuck in armor half-way not counting. None else used that strict criteria for standard penetration tests, period.

      FFS, just look above for 88/71, 100mm and 122mm results - US data for 88/71 is pretty much same as German, while data for 100/122mm is ~ 12% higher.
      Unless you have data for German tests of Soviet 100mm and 122mm to compare you can not use German data in vacuum, you have to use data by someone who tested all guns, and neither British, US, Soviet or Yugo tests show that mythical "superiority" for German guns.
      So, stop whining, other then few isolated cases most data in WoT is OK in with each other.
      4. I have no clue WTF are you talking about. WoT uses data for AP, APBC, APCBC or whatever guns fired.

    7. Gappa, things like Tiger's 200mm armor, or "FCS" values that were totally fucked up, or penetration of some guns (128mm having less pen then 88/71), etc, etc.

    8. @bojan
      whats your source regarding these value?
      "Penetration should be 187mm for D-10 and 180mm for D-25"
      and also your L/71 source would interest me, mine gives slighty different values!

    9. US Aberdeen tests give us data for 88/71, D-10 and D-25 as 226mm/210mm/203mm @ 100yards @ 0deg.
      Btitish tests are quite close,
      If we take WoT value for 88/71 (203mm) as constant and using same scale as US tests then D-10 and D-25 should penetrate slightly more then they do ATM (about as one of Chinese 100mm penetrate)
      British tests have almost same data as US ones.
      Yugo tests have slight difference, but scale to US and UK ones.

  7. They calculate at 30' from normal for german Tanks and 0 for others , its not fair but bias propaganda exist urss dosn t exist

  8. Same crap yet again.

    I'm sorry, but this article is complete nonsense.
    Beginning with the wrong thesis that:
    "AP, APC, APCBC: These shells had all compareable normalization values."
    How can they have same normalization when the latter ones are developed FROM the former AP shell IN ORDER TO IMPROVE normalization??
    Also soviet APBC works pretty much the same as the APCBC, with the difference that with APBC the armor is penetrated by the flat nose instead of a sharp nose hidden within APC or APCBC. Thus APBC should actually perform slightly WORSE than APCBC (on both sloped an unsloped armour), while the advantage of APBC is merely its simplicity in production and lower cost.

    Also the scheme with a "shell's actual way" is nonsense.
    Read proper articles on that, for instance:

    Schemes from there:

    Or simply look at cuts through penetrated armor like here
    or especially here:

    P.S: I'm sorry for CAPS, but the possibilities here are poor - no bold text. no inbed images in replies...

    1. Ok, you guys need straight facts backing you up, that is if you wish to prove anything.

      I am no expert in this stuff, so I'll just point out what I see from what both of you have written.
      Thor_Hammerschlag bases mostly on theory and mechanics section of physics. And he has two literature sources to back him up, first (Prof. Dr. –Ing. von Bredow: Script Dynamics (University of Applied Sciences Würzburg-Schweinfurt)) to back up his part of theories in physics, second (Lorrin Rexford Bird and Robert D. Livingston: WWII Ballistics: Armor and Gunnery) I assume is backing the ballistics part of his article ( and different shell type characteristics and guns).
      LoserDestiny. You don't have solid facts to back you up. "Read proper articles on that, for instance", ok, did read it, and apart from that scheme there was nothing about it (could we get a serious literature source with something written about normalization that isn't just an animated picture). "How can they have same normalization when the latter ones are developed FROM the former AP shell IN ORDER TO IMPROVE normalization??" Well if you did read it yourself at all (the article you posted), then you would have read that the APC was made to help prevent shattering AND it was FOUND that the softer caps also improved “grip” against sloped armor which was an added bonus. APCBC was made to give APC proper ballistic shape. There is difference between the soviet APBC (with blunt end) and APCBC, as the blunt cap of APCBC was relatively soft while the soviet shell had the main part of the shell blunt (main part was a lot harder). About the pictures of cuts through penetrated armor, it is not told what kind of shell penetrated these armors, and even more so, in first picture we can see an APDSFS shell (right lower corner), so was that the type of shell that penetrated? Please next time link the pictures to valid source.

      As I said I am no expert here, but I am trying to have a constructive, neutral look at all this, and right now Thor_Hammerschlag has more facts backing him up.

    2. @LoserDestiny

      How about a little civility?

    3. Dear Daedalus,
      can You probably tell me, which part of Hammerschlag's article is actually based on those 2 souces?
      What I can take from it is that first source (by a Prof.Dr.Ing.) was taken for the physics formula, but I really doubt this original source was about shell penetrating armour.
      As for the second source - obviously the schemes of the different type shells were taken from it.
      But what about the text?
      I have access to neither article, do you?

      As for my sources. You say it yourself - the article I linked to proves better normalization for APC. What else is actually expected?
      The pictures - in fact both most probably show a penetration by a APDS. But the head of APDS is nothing different than AP, being an aerodynamically sharp cone. No caps, just solid projectile but with a bonus speed.
      Still same physics work for it, as for the simple AP shell. So why wouldn't AP normalize when a real photograph (compared to Hammerschlag's pseudoscientific research) SHOWS that APDS normalize?

      So what I see is: theoretical cripcrap on Hammerschlag's side; hard photographic evidence and common sense on my side.
      Prove me wrong and I'll stand corrected.

    4. Hi LoserDestiny,
      Sadly I too don't have access to any of these 2 books. Tried to search about second and found out it is hard to acquire but there is a scanned copy on the internet, didn't search really hard but didn't find it.
      About which part is taken from which source. As usually it is done in this kind of studies, the source is numbered (like this [1] or [*]) after the written paragraph according to which the info was taken from (He even does this when replaying to comments with info from books, as you may notice). It doesn't have to be strictly copied text, it can be text rephrased in your words, as long as it stays true to original source. Sometimes also conclusions may be referenced this way.

      "You say it yourself - the article I linked to proves better normalization for APC." No, I didn't say that. What I said is that there is only the animated picture showing this effect, while I did not see any written text describing this effect. I quote your source "An added bonus was that it was found that the softer caps improved “grip” against sloped armor, squashing on impact to allow the main shot to penetrate rather than glancing off." And that only means it reduced chances of ricochets as the soft cap acted as I would describe it as Plasticine in simple words. Please quote where it is written exactly that shells angle changed to be more directed at armor.
      About the pictures, next time please put the source from where they come from so that there would be more information (right now it looks like you randomly picked pictures from google image search).

      I am not saying you are wrong and he is right. To be honest I am a bit confused myself. But what I see is (while I don't know if he hasn't mashed something up) Thor_Hammerschlag is using literature source that has been recognized as reliable in shell ballistics. About the physics part I agree the Knobbys comment that this is actually a rather sophisticated stuff and possibly it has been too simplified.
      There must be some other reliable source that we could hopefully get information from, as something like this should definitely be written about by some experts in russian, english or german...

      Well, but we can be sure, that when he gets the chance to read all this, he will definitely make a reply and make his own argumentation about this all.

    5. LoserDensity, i updated the FAQ in the first of your matters.

      For your source. The shell digging in the armor should refect an APBC shell according to your source, however what is shown is a APC shell. Sorry but i cant take this as a serious source, the effects and shell structure was mixed up.

      My source [2] is based on tests - graphs which are based on these test and these graphs are validated by combat reports. Its probably the most complete source regarding armor penetration (of the 2nd ww) out there.

    6. Simple do the math with a test example from Kubinka from September 1944 [2]:
      Panthers glacis which is 85mm @55° ricochets the 88mm L/71 (which has more than 220mm penetration [2] against a vertical plate) at 625m.

      Just do it .. try around with some armor/cos(55+normalization) .. and you will quickly see how wrong you were above and your source as well.

      Normalization values are positive especially for AP/APC/APCBC shells thats an fact proven by tests and combat results.

    7. @Daedalus: regarding the source of the photos - I believe I found them in a discussion on some Russian military forum.
      But does a photo really needs a provenance? It's obvious the damage was not carved in the armour with a screw driver...

      @Hammerschlag: Yes in fact the animation really depicts a APBC shell.
      Still there are these two other pictures of modern armour penatrated by APDS shells, revealing negative normalization. What do you say about it?

      As to Your physics - the formula doesn't at all take into account the materiality of the shell which necessarily deforms by impact and usually nearly vaporises while travelling through armour.
      The second drawback is that it's not directly clear, what shells are actually being used! Yes, we have "WWII APCBC & APC" but shells exactly? (I believe to have read the Germans used APHE instead of SP, which also needs to be researched and taken into account)

      As for the book - since no one of us has access to it, you can quote information from it, to support Your very position but actually isn't the position of the the whole book.
      The results You posted in the table speak about "slope" but have You actually taken in consideration that "armour slope" CAN and actually is BEING given from both vertical and horizontal? So is it noted anywhere, which type of slope is actually used throughout the book?

      But actually it is enough to look at those photos to notice that something gone wrong in Your calculation!

    8. (1) this article is not about APDS.

      (2) This is not my physics, its WGs way to make it simple

      (3) You can download the book somewhere in the internet another user just mentioned.
      Its more than clear in the book.

      (4) Those photos are worth nothing, they doesnt even refer to AP shells.

      Did you do the calculation based on the test?

    9. 1. Could you please tell me the difference between an AP shell and the penetrator of an APDS?

      2. This is your physics that are supposed to prove a positive normalization.
      You don't even deny my arguments?
      I consider it an acknowledgement of my right.

      3. I don't seem to see a link. You could simply post it here, but instead you prefer to hint me to "other user who posted it somewhere".
      I see you don't really want anybody to be able to prove your interpretation of the book, limiting our knowledge of it to what you tell us.

      4. See point 1. The APDS penetrator is the same as a non-capped AP shell. Thus same penetration physics work for it.
      Thus those photos are much worth since they are a hard proof of a negative normalization.

      You have yet not shown ANY hard proof, except of some hand-drawn schemes.

      I don't know any conditions of the test, not even the shell type used, why bother myself with calculations that are anyway same as in the table shown before?

    10. insert the name of the book in google and you will find it ..

      Positive normalisation is not based on "my" physics, it is based on the graphs of the book which are based on test data. The physics are there to explain it.

      Than search for the conditions or the test itself and do the math.

      And again, this article is not about APDS and i will not research that for you, and show me a proof that the "physics" for AP and APDS - and not just a theory.

      Anyways.. its pretty much senseless to discuss with you. I wont reply to another "all you say is wrong because in my opinion it works in another way" post.

      Give me proofs or let it be.

    11. Oh well, neither I see a sense in further argument, since you are bull-headed and not willing to actually discuss and even consider a possibility you're not right here.

      1. You still advise me to search on google or do whatever instead of actually POSTING a link to the book.
      You don't want us have it. I understand that. But I don't understand WHY, if your arguments are ok, the book would prove it. But if you won't let us have it - maybe you use the book merely as a dead source that cannot be doublechecked?

      2. Why should I search somewhere for the data that you HAVE in that book. Why don't you simply post entire passages here, instead of keeping mentioning a book UNAVAILABLE for any of us??

      3. Yet again - APDS penetrator is same as AP shell - solid aerodynamically shaped cone-like projectile.
      How am I supposed to prove something such obvious? Next I'll have to prove the heaven is blue?

      4. You still have no explanation to a negative normalization shown on those 2 photos I posted previously.
      You are arguing about everything (I'm glad my grammar is OK, otherwise I would become a topic too) but NOT about the hard proof I shown.
      Obviously you simply cannot disprove it and instead try to skip to other topics. Very poor!

    12. 1. enter "ww2 ballistics armor and gunnery download" in google, check for a general files link just testet it the download works there

      2. you can download the book at mutiple sources, i just dont want to post a grey source here

      3. one of the ideas of APDS is a better length to diameter radio, check FAQ.. and wikipedia

      4. this article is about ww2 ap/apc/apcbc shells. i didnt say there is no negative normalization at all.

    13. You just repeat same odd "arguments" again and again.

      I don't need to check Wikipedia to see an APDS being a lengthened AP made of harder alloy. I just can't see at which point there are some ambiguous "new different physics" that start working with such a modified AP shell.
      From which l/d relation do these new physics work? Or from which grade of hardness?
      What you pose here as a supposedly hard argument is nothing but nonsense on a closer look.

    14. Obviously you dont understand my arguments. So yea, lets just call them odd and dont care about them!
      What I dont understand doesnt exist! YEAH!

      Did you read the book?
      its really good, i hope you enjoy it!

    15. @LoserDestiny:

      1. Maybe Hammerschlag is trying to empower you to do your own damn research in credible sources instead of whining about not having a link. Its not Hammerschlag's responsibility to cure you of laziness, and he even went out of his way to give you a step-by-step on how to find his source. 1)Open Google. 2)Search. 3)Stop being a lazy ass.
      You're on the internet, the greatest realm of knowledge in existence. Learn to use it.

      2. He doesn't have to deny your argument. They are inherently wrong. 2 versions of penetration mechanics are described here: one IRL, and one in WoT. The physics used here for real life are a simplified version of the physics described in the source (which once again you could just find yourself instead of crying about not having a link.) The physics used in WoT were created by WG for game balance. I don't even know what you're arguing here.

      3. Why are you even talking about sabot rounds? This has nothing to do with them. What kind of scientifically rigorous study tries to apply data from one type of round to theories about another? Ridiculous. A sabot penetrator is many times longer than it is wide, a much larger ratio than present in standard AP rounds. Don't take such huge differences lightly or your arguments will look like unscientific slag.

      4. Wtf, you're doing it again. We are talking about the mechanics of AP, APC, and APCBC rounds. You don't even know what rounds made the holes in those pictures, and if we're assuming it was APDS rounds, then why on God's Earth are you using them IN AN ARGUMENT ABOUT APC ROUNDS? What kind of hard proof is this? Its irrelevant bullshit, that's what it is. Don't even try to claim that Hammerschlag's argument is weak and nonsense when you're a prime offender.

      Seriously, stop acting like a helpless, mewling kitten, and go download that book. After you've done that, read some books about rigorous study. Then if you still think that proper sources and data that actually pertains to the discussion are weak, at least have the common decency to stop spreading your uneducated filth.

  9. Thor, could you be more specific on how you calculated the normalization angles shown in the table? It has been a while since I looked at the book you cited, but I seem to remember that the armor thickness was a very significant parameter in its calculations.

    As for F=p*A equation, it is quite useless, since you do not know the pressure involved.

    1. "Over the extent of the shell the pressure is pretty constant"
      There is no reason why it should be.

      "The area on the lower side - it is in any case larger than that of the upper side of the shell. Thus creating a larger resultant force."
      Sure. But even if the proposed moment is there, it still needs to be large enough to have a significant effect on the shell's trajectory. And this calculation is missing from the article.

    2. 1) The steel is stretched to its yield point, instead of higher resistance the steel deformation will go on under yield point tension.
      So far the theory, but because everything goes very fast here some more factors like material inertia (for example) may have an effect as well.

      2) An exact mathematical description is well worth a doctorate. Pretty much nothing is constant here.
      However the BIOS report gives a really good idea about it and also a lot of estimations.
      But I think it’s far too deep in detail to post articles about that..

  10. A...... (3) HEAT shells are more effective against sloped armor than AP/APC/APBC shells [2]

    What? I thought HEAT is good only for non-sloped surfaces...

    1. Well, you thought it wrong then. He links a reference to that ([2] Lorrin Rexford Bird and Robert D. Livingston: WWII Ballistics: Armor and Gunnery) though i doubt many can doublecheck that.
      Also if tou think it, if solid ap-rounds tend to "normalize" themselves to bounce more, they need to penetrate more steel than HEAT, which practically goes just straight through. (See the picture in the article)

  11. Thank you for the article.
    I am not a physicist or any sort of expert, but the whole model as stated seems over-simplified. You have described how inertia effects impact, but how about the plasticity/brittleness of materials. You have assumed that the condition of the materials at impact remains solid rather than deforming plastically, with the material ahead of the penetrator being less plastic than the material left behind.
    There are other forces also at work ; surface energy, friction, gravity, angle of approach/trajectory, speed of rotation (all guns in game rifled?), direction of rotation in relation to angle of impact, area of penetrator in contact with the armour. A very small deviation in angle of momentum caused by these forces can lead to a modified direction of energy surely ?
    I think that one of the reasons there isn't a detailed penetration model is because it is so complex. That and national security.
    Also, the statement regarding length of the penetrator and normalisation fails to factor in the increased inertia of the shell due to implicitly increased mass. It's essential to account for every bit of kinetic energy in order to model impact accurately.

    1. increased inertia force (but that is done with larger projectiles as well) - because mass grows with ³ and diameter with ².
      What is so special about it is the increase of the moment of inertia, which cannot be seen greatly simple by enlarging the shells at all.
      Moment of inertia grows with areas/volume at a grater lengh especially [1].
      Thats so innovative about making a shell longer .. but yea i dont think that is any understandable anymore.

      And yea you are right with all you said in the first 2 paragraphs. I will update the detailed few with friction and gravity.

    2. Fairly sure that should be diameter (or whatever linear measure really) increasing in the first power, surface area in the second and *volume* (ergo mass) in the third unless I've completely forgotten my geometrics...

      Assuming the shape stays the same obviously, but I'm under the impression this was the case due to ballistical considerations and whatnot. And then the "long rods" toss that out of the window and go for insane sectional density instead, but they're not really relevant here anyway.

    3. Nitpickers, nitpickers everywhere! ;P

    4. I meant the cross sectional area wich grows with the diameter ², not the diameter itself.
      My mistake!

      *thus more inertia force per mm².
      (inertia force Fi= m*a)


      Yes please!

  12. Thor, please elaborate on this regarding shooting the lower hull of a tank.

  13. normal is defined to be normal direction from a plane.

    So in this case it means that the projectile turns towards normal of the plane which it hits. The effect that occurs in real life cannot be called normalization since the projectile turns away from the normal direction of the plane.

    1. Yep, exactly :) Thats what i was reffering to in my article.

  14. Thor, I have just put my hands on a library copy of "WWII Ballistics: Armor and Gunnery". Could you, please, post a short comment on how you calculated the "real" normalization angles. Thanks a lot.

    1. Alright, check the FAQ soon!
      I guess its not doable in a short comment :/

    2. Thanks, I figured it out. I got confused by the diagram, which has nothing to do with the book? The normalization angles come from "slope multiplier" values derived empirically form a large number of US test firings, right?

    3. Yea, it seems to be the commen way to deal with sloped armor because of the complexity of the material.

      Im glad you figured it out, took me a while to find it out as well..
      But its important that these values are only for cretian circumstances, i guess you know what i mean..

      calculated values for APBC already?

  15. I think that differences in USSR/DE/USA normalization tests are also due to the specs of the alloys used in different shells. I really doubt there were 2 shell alloys used in Germany and USSR. If that is correct, it would mean that shell normalization should be calculated for every shell and for every gun specificly -> this means WG's normalization systems is not completely senseless, hence creating a real life - realistic pen and norm system would be extremely hard

    1. Geometry of the shell's point should also play a large role, at least for some angles of impact.

  16. Nice post. I'll be talking about it in my next WoT youtube video probably...tomorrow. TBH I wish war gaming would use the real AP normalization model, even if it would make a certain nation stronger. It would bring back some tactical diversity to the game at high tier since the emergence of all the super guns and gold rounds for credits.

    My channel is if you care to check it out.


    1. would be glad to watch it, thanks for the link.

    2. Couldn't fit it in due to the 2 year anniversary, but it will be in shortly.


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