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Calculating angled armor to equivalent vertical armor protection is not that simple as pure cosine. In most cases the angled armor resist better than on FatPartizan's picture. Not only the projectile path trough the armor is longer because of the angle, as on the picture (the "pure cosine" result, or "normalized" thickness, this one is used for penetration of HEAT warheads) but also pointed projectile has tendency to ricochet and is less effective in digging trough the armor. So when at 60deg pure cosine predicts 2x armor increase (90mm), the actual protection increase can be up to 3 times better than armor thickness (135mm).

The most commonly used formula is protection = thickness * 1/cos(angle)^K where K is usually something bewteen 1.4 and 1.6.

Example of US table for angled penetration from WW2:

This table would predict multipler of 2.5 for 60deg and resulting T-34 armor of 112.5mm

But this is again more complicated and depends also on projectile diameter, projectile shape, armor quality and hardness. The table above assumes one projectile shape, and projectile caliber similar to armor thickness.

Sometimes when large caliber blunt projectile hits angled armor, armor may resist worse than pure cosine predicts (in case of T-34 hit by large caliber - armor less than 90mm).

In other cases when small diameter sharp projectile hits highly angled armor, the armor resist better than pure cosine predicts (more than 90mm) and sometimes even better than the formla I gave (better than 120-130mm) - this would be in case of small sub-caliber projectile hitting T-34 glacis. The resulting armor could be easily over 120mm or even much more.

So, for 50mm PzIII projectiles, T-34 45mm 60deg plate could resist like 100-120mm of vertical armor, which makes any penetration questionable if flat plate was hit, but penetrations are possible if joints, welds, base of tow hooks or base of driver hatch are hit - angle can be close to 0deg then and thicknes is just 45mm. For 50mm subcaliber projectiles (even smaller caliber and more pointy) the 45mm 60deg plate can act like something like 200mm vertical and be impossible to penetrate - just ricochet. PzIII kills on T-34 are unlikely to be made with penetrating front hull plate. Either they were turret penetrations, lucky "weak point" penetrations of front hull from very close, or side/rear kills. Germans didn't need superior tanks and penetration advantage to win with T-34s at this stage of war (Barbarossa), Even if they had problems penetrating frontally, they could win anyway with superior tactics. crew training and experience.

On the other hand for 88mm APC projectile, with diameter twice as large as armor thickness, the 45mm 60deg plate of poor quality can resist only like 70-80mm of vertical armor sometimes, and good quality plate as 80-90mm of vertical. If hit by huge 152mm AP projectile, thin 45mm plate would just break in pieces regardles of it's high angle and "theoretical" 113mm resistance

All values from the head, just examples.

So... highly sloped armor (like T-34 front hull) has NO single "armor value", in reality it depends on what strikes it. As in current version of AB I had to chose one value, I chosed for most commonly hitting it 75-88mm projectile so around 80mm of protection. And, "accidetally" this value gives also historically correct penetration ranges for all 75 and 88mm German guns in game , and not too bad for 50mm gun (with exeption of APCR which should ricochet and not penerate) so it's a good compromise IMO.

Not sure if I explained this before... I hope this makes T-34 front hull "45mm" armor issue a bit more clear, why such value was chosen and not 45mm, 57mm (how this one was calculated ?), 90mm or any other. I hope case is closed now. Now I return to the cave I'm hiding...

Calculating angled armor to equivalent vertical armor protection is not that simple as pure cosine. In most cases the angled armor resist better than on FatPartizan's picture. Not only the projectile path trough the armor is longer because of the angle, as on the picture (the "pure cosine" result, or "normalized" thickness, this one is used for penetration of HEAT warheads) but also pointed projectile has tendency to ricochet and is less effective in digging trough the armor. So when at 60deg pure cosine predicts 2x armor increase (90mm), the actual protection increase can be up to 3 times better than armor thickness (135mm).

The most commonly used formula is protection = thickness * 1/cos(angle)^K where K is usually something bewteen 1.4 and 1.6.

Example of US table for angled penetration from WW2:

This table would predict multipler of 2.5 for 60deg and resulting T-34 armor of 112.5mm

But this is again more complicated and depends also on projectile diameter, projectile shape, armor quality and hardness. The table above assumes one projectile shape, and projectile caliber similar to armor thickness.

Sometimes when large caliber blunt projectile hits angled armor, armor may resist worse than pure cosine predicts (in case of T-34 hit by large caliber - armor less than 90mm).

In other cases when small diameter sharp projectile hits highly angled armor, the armor resist better than pure cosine predicts (more than 90mm) and sometimes even better than the formla I gave (better than 120-130mm) - this would be in case of small sub-caliber projectile hitting T-34 glacis. The resulting armor could be easily over 120mm or even much more.

So, for 50mm PzIII projectiles, T-34 45mm 60deg plate could resist like 100-120mm of vertical armor, which makes any penetration questionable if flat plate was hit, but penetrations are possible if joints, welds, base of tow hooks or base of driver hatch are hit - angle can be close to 0deg then and thicknes is just 45mm. For 50mm subcaliber projectiles (even smaller caliber and more pointy) the 45mm 60deg plate can act like something like 200mm vertical and be impossible to penetrate - just ricochet. PzIII kills on T-34 are unlikely to be made with penetrating front hull plate. Either they were turret penetrations, lucky "weak point" penetrations of front hull from very close, or side/rear kills. Germans didn't need superior tanks and penetration advantage to win with T-34s at this stage of war (Barbarossa), Even if they had problems penetrating frontally, they could win anyway with superior tactics. crew training and experience.

On the other hand for 88mm APC projectile, with diameter twice as large as armor thickness, the 45mm 60deg plate of poor quality can resist only like 70-80mm of vertical armor sometimes, and good quality plate as 80-90mm of vertical. If hit by huge 152mm AP projectile, thin 45mm plate would just break in pieces regardles of it's high angle and "theoretical" 113mm resistance

All values from the head, just examples.

So... highly sloped armor (like T-34 front hull) has NO single "armor value", in reality it depends on what strikes it. As in current version of AB I had to chose one value, I chosed for most commonly hitting it 75-88mm projectile so around 80mm of protection. And, "accidetally" this value gives also historically correct penetration ranges for all 75 and 88mm German guns in game , and not too bad for 50mm gun (with exeption of APCR which should ricochet and not penerate) so it's a good compromise IMO.

Not sure if I explained this before... I hope this makes T-34 front hull "45mm" armor issue a bit more clear, why such value was chosen and not 45mm, 57mm (how this one was calculated ?), 90mm or any other. I hope case is closed now. Now I return to the cave I'm hiding...

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