Armor penetration formula
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#1: Armor penetration formula Author: blair PostPosted: Sat Apr 14, 2007 10:05 pm
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A long time ago I had cme across an article that described a formula regarding the increased resistance of armor depending on the degree of angle. I'm sure I have my numbers mixed up but basically the formula stated that If you took a a plate of armor 2 inches thick and then angled it by 25 degrees the armor would then have the same penetration resistance depth of 4 inches of vertical armor.

The higher the angle then the higher the resistence depth.

Does anyone know any more about this principle/theory?

#2: Re: Armor penetration formula Author: JimWebLocation: The back of beyond PostPosted: Sun Apr 15, 2007 3:29 am
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Blimey this is really basic geometry!!!

Pick up a book which will represent our armour plate - measure its width then angle it at 45 degrees and measure it from corner to corner - That how thick the armour becomes along the horizontal....

Rolling Eyes

#3: Re: Armor penetration formula Author: bsmartLocation: Central Maryland PostPosted: Sun Apr 15, 2007 5:55 am
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Where is Lorrin (from the old board) when you need him Rolling Eyes

If I understand your question Jim has the basics laid out pretty well. When I explain this on tours at Aberdeen I use my hand spaced about3" apart first vertically then at an angle. A 45 degree angle gives you about 1.707 times the thickness that vertical plate will, a 60 degree angle doubles the thickness. This is all geometry , Sines & Cosines (depending on if you are measuring the angle from the horizontal or vertical)

There would be a higher chance of the round 'glancing off' as the angle increases but I'm not sure this would be easy to calculate especially since the shape of the nose and the relative hardness probably play into the factoring.

And if you hit an angled plate (say the 47 degree nose of a Sherman) at an angle off of dead ahead (say 45 degrees off to the side) the angle effect is compunded. ( you get thickness * 1.7 (approx factor for 47 degree armor * 1.7 factor for the angle shot) or a total increase in thickness of 2.89.

#4: Re: Armor penetration formula Author: JWB2 PostPosted: Sun Apr 15, 2007 1:29 pm
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IIRC ricochet or "skip" starts when the slope is 45* or greater. Firing tests have shown that resistance can actually degrade when the slope exceeds about 56*. I imagine these facts heavily influenced the slope of both the Sherman and the Panther glacis plates.

#5: Re: Armor penetration formula Author: JimWebLocation: The back of beyond PostPosted: Mon Apr 16, 2007 3:30 am
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- JWB2
IIRC ricochet or "skip" starts when the slope is 45* or greater. Firing tests have shown that resistance can actually degrade when the slope exceeds about 56*. I imagine these facts heavily influenced the slope of both the Sherman and the Panther glacis plates.


Yes but rounds have been designed to overcome this by having flat angled fronts under ballistic caps to enable them to dig in.

Cool

#6: Re: Armor penetration formula Author: clausb PostPosted: Mon Apr 16, 2007 4:08 am
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- blair
A long time ago I had cme across an article that described a formula regarding the increased resistance of armor depending on the degree of angle. I'm sure I have my numbers mixed up but basically the formula stated that If you took a a plate of armor 2 inches thick and then angled it by 25 degrees the armor would then have the same penetration resistance depth of 4 inches of vertical armor.

The higher the angle then the higher the resistence depth.

Does anyone know any more about this principle/theory?


Goes like this:

Y/cos(Z)=X

where Y is the thickness of the armour plate
where Z is the angle of the armour, with vertical=0
and X is the effective thickness of the armour.

As an example using the frontal hull armour of the Soviet T34 , you get

Y=45mm
Z=60 degrees

and thus:

45/cos(60)=90

meaning that the distance the projectile has to travel through the armour plate is doubled when the plate is sloped at 60 degrees.

However......

That is not by any means equal to the actual resistance of the armour plate in any condition. Far from it. To even begin to approach that issue, you need to take into account a large number of factors including armour quality and hardness, projectile type (AP, APC, sub-caliber, HEAT etc.), projectile design, projectile caliber, projectile hardness and a lot of other elements.
The problem is mainly that while a perpendicular hit on the armour plate will spend most of its energy on going through the armour plate, once the projectile hits a sloped surface, it will have a tendency to move away from the plate and under the right conditions simply bounce off. Whether it bounces or not depends among other things on the shape of the projectiles nose: a pointed nose will tend to bounce, a flat nose will tend to dig in. It also depends on the relationship between the diameter of the projectile (d) and the thickness of the armour (t): if the so-called t/d ratio is more than 1 (say, 45mm of armour hit by a 37mm round) hitting, the projectile will be more likely to bounce off. If the t/d ratio is less than 1 (say, 45mm of armour hit by 75mm projectile) then the projectile will be less likely to bounce off.

It soon gets very complicated....... Smile

I'm deeply suspicious of the idea that an angle of more than 56 degrees will degrade performance, at least not in general. If that was the case, then tanks would have 55 degree slopes on their front hull and no more, which is clearly not the case. The T34 had 60 degree slope on the front hull and post-war tanks tend to get as much slope as possible, just look at Soviet designs. Also, US tanks like the M48 (60 degree front hull) and the M60 (65 degree front hull) shows an increase in slope over the WWII designs (M4 Sherman 56 and 47 degrees, M26 Pershing 56 degrees).

Claus B

#7: Re: Armor penetration formula Author: LeeW PostPosted: Mon Apr 16, 2007 5:09 am
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In addition once a projectile starts to penetrate it will tend to turn toward the orthoganal.

Face hardened vs homogenious can effect this as well.

For naval vessels there some info at:
www.navweaps.com/index...x_tech.htm
and of course:
www.navweaps.com/index...nathan.htm
which has some formulas and programs as well as info.

Unfortuantly I don't know of a simlar site for AFVs some of this will relate but exactly how is not my area of expertise.

#8: Re: Armor penetration formula Author: JWB2 PostPosted: Mon Apr 16, 2007 6:43 pm
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Yes but rounds have been designed to overcome this by having flat angled fronts under ballistic caps to enable them to dig in.

That only happens if the projectile is harder than the armor.

I'm deeply suspicious of the idea that an angle of more than 56 degrees will degrade performance, at least not in general.

That is the result of a firing test conducted by the US Army. IIRC it was 90mm vs Panther type armor so it probably has a lot to do with undermatch. Post war tank armor was desiged to deal with HVAP and early APDS.

#9: Re: Armor penetration formula Author: clausb PostPosted: Mon Apr 16, 2007 11:22 pm
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That is the result of a firing test conducted by the US Army. IIRC it was 90mm vs Panther type armor so it probably has a lot to do with undermatch. Post war tank armor was desiged to deal with HVAP and early APDS.


But the T-34s armour wasn't.....

90mm projectile vs 80mm of Panther frontal armour gives a T/D of 0.88 which is not exactly a massive "undermatch", in fact it is in the same ballpark as, say, a German 75mm vs a late-war Sherman hull at 63mm (T/D 0.84). In the latter case, your logic would dictate that hitting the Shermans armour at an angle of 40 degrees from the side would have a better chance of penetring than a hit at 30 degrees from the side. That sounds rather counterintuitive to me.....
I've yet to see an actual test result, official penetration data or an emperically based penetration formula that would result in what you describe - resistance of armour degrading at angles over 56 degrees. So unless you can point to the exact tests, I'd have to say that it is either a fairy tale or at least a misunderstanding.

Claus B

#10: Re: Armor penetration formula Author: Doug_KibbeyLocation: The Great Satan PostPosted: Tue Apr 17, 2007 2:33 am
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- bsmart
Where is Lorrin (from the old board) when you need him Rolling Eyes


We'll remember you said that, Bob...especially if he actually shows up and registers to post. Wink (Be sure to notify Bushy, he'll need to lay on an extra terabyte or two of bandwidth). Alas, we don't have Russ on hand (owing to other "distractions" at the moment, lucky him) to keep him in check if he does.

...and I'm on my way out of the country for a couple of weeks, so if his apparition appears....handle it! Mr. Green

#11: Re: Armor penetration formula Author: bsmartLocation: Central Maryland PostPosted: Tue Apr 17, 2007 3:18 am
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Hey, I never had a problem with Lorrin. I didn't agree with all his theories (Heck I'm not sure I even understood all his theories Rolling Eyes ) but he did bring a passion and dedication to the discussions.

Have a good trip (you gotta arrange for a layover in the Philly/ Baltimore/DC) region on one of them so we can visit Aberdeen) and we'll try to keep everyone under control (or at least keep them from parking the tanks on the zoomies runway)

#12: Re: Armor penetration formula Author: Joe_DLocation: Razorback Country PostPosted: Tue Apr 17, 2007 3:59 am
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Doug,

Alas, we don't have Russ on hand (owing to other "distractions" at the moment, lucky him)


I was wondering how Russ was doing, good to here he's OK, I miss his posts.

Joe D

#13: Re: Armor penetration formula Author: pineyLocation: Republic of Southern New Jersey PostPosted: Tue Apr 17, 2007 8:08 am
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I miss Russ too. no fun not having to warn against spit takes

Jeff Lewis

#14: Re: Armor penetration formula Author: Doug_KibbeyLocation: The Great Satan PostPosted: Tue Apr 17, 2007 10:03 am
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- Joe_D
Doug,

Alas, we don't have Russ on hand (owing to other "distractions" at the moment, lucky him)


I was wondering how Russ was doing, good to here he's OK, I miss his posts.

Joe D


I spoke with Russ recently, and am happy to report that his absence is due to his having discovered romance that is occupying a lot of his time, which inexplicably, he is finding preferable to the company of a bunch of fellow curmudgeons. "Bully for him", I say! We mean to do a tour of the El Monte collection soon (when I get in off the road for more than two weeks at a time Rolling Eyes ) but he sounded great!

I miss his humor as well.....

This update brought you courtesy of the Flagship Lounge at Chicago O'Hare Airport....

#15: Re: Armor penetration formula Author: JWB2 PostPosted: Tue Apr 17, 2007 6:50 pm
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- clausb
That is the result of a firing test conducted by the US Army. IIRC it was 90mm vs Panther type armor so it probably has a lot to do with undermatch. Post war tank armor was desiged to deal with HVAP and early APDS.


But the T-34s armour wasn't.....

90mm projectile vs 80mm of Panther frontal armour gives a T/D of 0.88 which is not exactly a massive "undermatch", in fact it is in the same ballpark as, say, a German 75mm vs a late-war Sherman hull at 63mm (T/D 0.84). In the latter case, your logic would dictate that hitting the Shermans armour at an angle of 40 degrees from the side would have a better chance of penetring than a hit at 30 degrees from the side. That sounds rather counterintuitive to me.....
I've yet to see an actual test result, official penetration data or an emperically based penetration formula that would result in what you describe - resistance of armour degrading at angles over 56 degrees. So unless you can point to the exact tests, I'd have to say that it is either a fairy tale or at least a misunderstanding.

Claus B

I got the info from C.G. Erickson a few years ago at one of the visits to Littlefields.



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