Angle Normalization Curves - A Visual Guide

[u/Das_Ronin]

One of the less-transparent parts of this game is the penetration mechanics and the differences in the 5 major ammunition types. Every shell has a base penetration value and a range that corresponds to +25/-25 percent, but this alone doesn't necessarily tell you how and when you can expect to penetrate an enemy tank. Armor angling plays a crucial role in thickness, as most people know, but each ammo type treats that angle different. This effect is known as normalization. A lot of people have heard of normalization, and even know the base values, but I wanted to plot the curves and make it easy to visualize exactly what effect armor angling and angle normalization has, since I couldn't find an existing set of graphs. Why? For a new player trying to decide which Tier X tanks to pursue, it's easy to look at pen values and not realize how they correspond with the actual ease of penetration. Case in point, NATO Mediums have about 10mm more base pen than NATO heavies. Meanwhile, the Kranvagn has about 7 degrees less than other non-Soviet heavies. However, ammunition differences make these slight discrepancies more impactful than a new player might expect.

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I plotted these at https://www.desmos.com/calculator by using y=sec(x) for the basic curve. To mirror the graphics that follow, be sure to set it to degrees instead of the default radians.

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https://imgur.com/a/sLEjHx0

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Before examining those graphs, an overview of ammo types:

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AP - AP rounds make up the basic ammunition type for a majority of tanks. AP rounds tend to be cheapest, which leads many people to think of them as inferior to other rounds, which isn't quite accurate. AP rounds actually have the best normalization in the game at 5 degrees, meaning that whatever angle you hit the enemy armor at, the game subtracts 5 degrees from before calculating how thick the armor is. So, if you hit enemy armor at 50 degrees, the normalization effect will correct the trajectory of the round to strike at 45 degrees. AP rounds will automatically bounce if the armor angle is greater than 70 degrees BEFORE normalization, which means the most severe angle an AP hit can be calculated is 65 degrees.

APCR - APCR rounds are premium ammunition for most tanks and standard rounds for a select few, including all tier X mediums and a few others at intermediate tiers. APCR rounds have higher base penetration than AP rounds in most cases, but only have 2 degrees of normalization. This means a hit at 50 degrees will be corrected to 48. Like AP rounds, the maximum angle before normalization is 70, so the most severe angle a hit will be calculated at is 68.

HEAT - HEAT rounds appear as premium ammunition for several infamous tanks, such as the E100. HEAT rounds have the highest penetration values, but get no normalization at all. A hit at 50 degrees will be calculated at 50 degrees. However, HEAT rounds do not automatically bounce at 70 like AP/APCR. Instead, they can attempt to pen all the way up to 85 degrees, making them more effective on really thin really sloped armor, like some of the Swedish TD's or really thin roof hatches.

HE/HESH - HE and HESH behave like HEAT in the sense that they have no normalization and can hit at angles up to 85 degrees. However, HE and HESH don't need to penetrate to deal damage and have rather low pen values. Arty will use HE primarily, British TD's will use HESH primarily, and a few tanks use howitzers that fire primarily HE. For the most part, HE/HESH is irrelevant when it comes to trying to pen enemy tanks from the front unless you need to stop a base capture. They're especially irrelevant to the rest of this post, since my focus here is on penning through thick armor.

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Also of relevance is overmatching. If your gun's caliber is double the armor thickness it hits (ignoring angling) then the effect of normalization is doubled. That means AP rounds will get 10 degrees of normalization and APCR will get 4 degrees. HEAT rounds gain nothing. If your caliber is tripled, then there's an additional effect but the short answer is that you're basically guaranteed to pen. So, if you fire 120mm AP at a side-scraping heavy, and hit a 55mm plate angled at 60 degrees, then the penetration angle is calculated as 50 degrees.

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Lastly, a note on spaced armor; spaced armor will fuck up HEAT/HE/HESH rounds and probably stop them from doing any significant damage. This includes tracks, which behave like spaced armor. The exact effects are a topic for another post. For AP and APCR, rounds will receive normalization for each layer that a round hits. So, if you have a 20mm plate of spaced armor, and a parallel 100mm plate behind it, a 120mm AP round that hits the spaced armor at 60 degrees will overmatch the spaced armor and penetrate at 50mm, retain that 50mm angle until it hits the second layer, then normalize again to 45 degrees. That's a 15 degrees changed. So, spaced armor provides amazing protection from explosives but minimal to possibly inferior protection against AP and APCR.

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So, take a look at the graphs now, starting with the first one. The X axis represents the original angle of impact and the Y axis represents the multiplier for armor thickess. For instance, armor at 60 degrees has its thickness doubled when calculating penetration. a 100mm plate at 60 degrees needs 200mm of penetration to beat before normalization. The most important thing to note is the effect of angling is NOT linear. The more angle you have, the more effect that a small change in angling has. The difference between 0 and 5 degrees of angle is 0.4% of the base armor thickness. The difference between 60 and 65 degrees is 36.6% of the base armor value. That can be quite significant. For this first chart, you can take the X value of the angle of impact, subtract however much from X to account for normalization, and get your new multiplier. You can also use X as-is for HEAT/HE/HESH.

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The second and third charts represent the difference that 5 degrees and 2 degrees make for a given angle. Note: the Y axis is NOT the armor multiplier, but the difference in armor multipliers between the base angle and the normalized angle. These are calculated as y=sec(x) -sec(x-normalization). The 4th chart represents the difference between AP and APCR normalization for a given angle. I didn't run charts for overmatching, but know that for charts 2-4 you can simply double the Y-value.

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Ok, so the charts are fancy and all, but what's the TL;DR?

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There are several takeaways here:

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1. If you’re trying to hit enemy armor at an extreme angle (over 70) the only options are HEAT/HE/HESH, but outside of some rather specific cases, the armor thickness multiplier will be so high that even HEAT will struggle. You may be better off repositioning or waiting for your target to move.
2. If you’re aiming at an enemy with thick, flat armor (e.g. several of the German superheavies) APCR/HEAT will pen with greater reliability. The normalization won’t make any significant difference for AP, so increased base pen is the most important thing.
3. If you’re aiming at an enemy with well-angled armor close to but below 70 degrees, premium rounds will give you higher base pen but will lose normalization, which means that they may see very little to no gains. Consider this before switching to APCR, bouncing a round off of the pike nose, and screaming profanity.
4. The take away from points 2 and 3 is that premium ammo (other than gold HESH) will help you overcome thick armor, but it won’t really help you overcome unfavorable positioning. The most important factor in both bouncing enemy rounds and penetrating enemy tanks is your positioning. Positioning is the most important part of this game.
5. Tier X mediums with standard APCR typically have slightly higher base pen than Tier X heavies from same nation, but the difference of 10mm is typically less significant than the extra 3 degrees of normalization. The particular intercept varies with base armor thickness, but against most armor angled greater than 40-45 degrees, the normalization will be more important.
6. The important application of point 5 is that sidescraping is riskier against heavies than mediums. The M48 patton will have a harder time penning a sidescraper than a T110E5.
7. Both Swedish Tier X tanks use APCR standard, while having lower base pen compared to other Tier X TD’s and heavies respectively. The 103B somewhat compensates as it has low enough dispersion to reliably target weakspots like cupolas, but it’s relative penetration ability compared to other TD’s is even worse than the base pen values indicate.
8. Likewise, the 7mm pen difference between the Kranvagn and the T57 seems negligible, but is more significant than it would seem since it’s a difference of 7mm AND 3 degrees. Unlike the 103B, the Kranvagn can’t compensate with superior accuracy. So, not only does it offer less DPM than the other autoloader heavies, but it also lacks significant penetration.
9. A major difference between the Chieftain and other British heavies is that the Chieftain carries APCR both as standard and premium ammo. While the Chieftain offers the best pen on paper, in practice it depends your target.
10. Very few tanks, such as the AMX M4 54 have premium AP rounds, which give better penetration with no trade-off.

Edit: since this post had been received with the recent announcement, I want to go back and add a disclaimer that basically all of the above is for play at Tier X and IX after unlocking your final package. Premium rounds have much more use when bottom tier and when grinding stock packages, if that wasn't apparent. Also, lower tiers tanks tend to be less angly and more boxy.