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Face-Hardened Armor on German Tanks


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U.S. penetration data in TM-9-1907 for face-hardened (FH) armor shows some unusual characteristics.

Face-hardened armor has very thin layer of brittle, hard steel backed by ductile, non-brittle armor than absorbs impact and supports hard layer. Hard layer is supposed to break projectile nose, even when rounds have armor piercing caps that help to defeat face-hardening.

German manufacturing used face-hardening on all front and side hull plates of 30mm to 50mm thickness till mid-1944, which might apply to 30+50 on StuG III, and a large number of panzers with 30mm-50mm on sides.

This is a critical issue for wargaming and research because some APCBC rounds can penetrate much more face-hardened armor than homogeneous. Sherman 75 penetrates 91mm homogeneous (same all the way thru and 240 Brinell hardness) at 0m, but 104mm face-hardened. And face-hardened penetration may fall off slower than homogeneous with velocity changes, according to Krupp equation and TM-9-1907.

If one uses 75L40 APCBC FH penetration as norm and estimates other rounds from it (using Krupp equation for FH penetration with 75L40 performance as standard):

76 APCBC about 14% low vs. FH

90 APCBC about 14% low vs. FH

57 APCBC about 7% low vs. FH

37 APCBC about 3% low vs. FH (after adjusting for solid shot)

When U.S. Navy fired 76mm APCBC against homogeneous armor hardnesses from 250 to 490 Brinell, shatter gap penetration occurred at from 5% to 15% over 50% penetration limit, which is consistent with some of above results.

Were armor piercing caps on 57, 76 and 90 APCBC inferior to 75, or was shatter gap playing a role?

When one examines the 76mm APCBC FH penetration curve vs. impact velocity, the curve follows 75 APCBC up to 2000 fps impact and then FH penetration falls off like crazy. This 2000 fps limit is where we estimate shatter gap starts to become a potential reality.

U.S. Navy tests of 76 APCBC do not show brittle behavior against hard armor above 2000 fps, but they do show shatter gap against hard armor, similar to FH results.

To help answer this question and judge its impact in CM, the following points are raised:

1. Can CM provide back-up for brittle American ammo theory that leads to shatters above 2000 fps, reducing penetration. This info would be most helpful.

2. Can CM identify German tanks with face-hardened armor in game.

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Somewhat related. I had asked a similar question many moons ago as a result of a discussion on small caliber APCBC vs. FH (37mm or 57mm rounds). Here is some email correspondence stuff.

From L. Sims, a Materials Engineer from Germany who also dabbles in TankTalk as a hobby.

Hi Jeff,

It is my opinion that the effectiveness of any particular shell from this period (circa 1944) is heavily dependant upon the quality of the manufacturing process of not only the target armour plate, but also of the shell itself and its inherent kinetic energy, which is dependent upon a consistent muzzle velocity being generated by consistent charges. Variations in the quality and tolerances in the manufacturing processes, especially in Germany, would have had a large impact on the reliability of a given weapon/shell/charge combination to generate consistent and repeatable results. Pictures of destroyed tanks which appear to have 'cracked' like chocolate are classic examples of failures in the metal occurring due to poor manufacturing/material quality.

your questions,

1) Face Hardened armour plate has been given a hardening process whereby one surface of an iron plate is heated and cooled faster than the opposite face. The rate of cooling determines the microstructure transformation in the face. If the cooling rate is controlled and cooling occurs 'quickly' a 'martensitic' grain structure will form. The type of martensite formed is dependent on the percentage of carbon and other alloying elements present. (This is why quality control is fundamental in determining whether the steel achieves the desired properties or not.) Martensitic structures vary but most are very granular and irregular and therefore very brittle. They are however also extremely hard.

Russian AP and APBC used a steel which in comparison to FH steel was more ductile. Upon impact with FH armour AP and APBC is more prone to deform, thereby losing kinetic energy, before shattering due to the heat build up in the shell tip as it is compressed. If the remaining kinetic energy is too low, because muzzle velocity is too low, or the cross section is too small, penetration will not occur. However, the extremely hard cap used to top Western munitions helped to concentrate the kinetic energy of the impacting shell.

These two concepts are exploited in modern AT munition types:

a) Dense, hardened, penetrating shell tip - APDS with its high kinetic energy containing sabot,

B) Extremely large, almost oversized, 'soft' shells - HESH which are designed to completely deform upon impact, transferring its energy as a shock wave through the armour plate.

2/3) So, following on from what I have already introduced, Rolled Homogenous armour is heat treated after rolling to introduce a very fine lammelar microstructure of alpha phase Ferrite and Cementite Fe3C, know as Pearlite. This is achieved from eutectoid alloys and is extremely strong and tough, with a high tensile strength but without being brittle. Due to the increase in toughness but decrease in brittleness, an equivalent plate of RHA is indeed better than FHA at resisting APCBC and APC munition. The inability of 37mm or 57mm APCBC rounds to penetrate FH is simply a function of inherent kinetic energy. i.e. whether or not a 37mm APCBC round penetrates FH is dependent upon the ratio between the diameter of the round and the (relative) thickness of the target FH plate and also upon the initial muzzle velocity. The apparent inability of these small calibre rounds is due mainly to the fact that most FH armour was 50mm i.e. thicker than the shell diameter. It does not necessarily follow therefore that there is anything inherently special in the characteristics of FH that would make it more effective at defeating smaller calibre APCBC rounds than larger rounds. Capped rounds are in general simply better than non - capped, whether fired at RHA or FHA. The hardness and density of the core, coupled to the impact velocity is all important in determining whether penetration will occur. FH armour plate was simply more effective versus the 'softer' Russian munition.

From: David Michael Honner's (author\editor of the "Guns vs Armour" web page)

Dear Jeff,

A quick and short answer is better than none at all - I hope! Your questions

are quite pertinent and are, indeed, at the core of why I have the web site

up in the first place. Unfortunately it has taken me a long time to develop,

because of time constraints. Ideally I'd like to get all data up first

before trying to analyse it. However, I tend to really pick at a subject and

cross refer as much as possible so that I have the "right" answer. As an

example barrel lengths are notoriously difficult to get a consistent answer

to, let alone penetration data or accuracy data.

> 1) Can you elaborate on why APCBC or APC was more effective against FH

> armour than AP and APBC?

No, not really. A quick answer is that the harder you make steel (or any

material, really) the more brittle it becomes. Glass is very, very hard but

I wouldn't make a tank out of it. FH armour tried to make the armour so hard

that it would shatter the incoming AP round. To prevent shatter caps were

put on AP projectiles. If the FH fails to shatter the incoming round, it is

worse than RHA armour because it is more brittle. There is also a best BHN

for a particular T/D ratio (and a whole lot of other parameters) which is

around 250 to 350 BHN. So you can see a FH armour plate with >555 BHN is not

going to be as effective (more on this later). The Soviets had no caps on

their AP ammunition in WW2.

> 2) Was FH armour actually less effective than an equivalent

> thickness of RHA

> armour against penetration by APCBC and APC?

Yes.

> 3) Was FH armour more effective at defeating smaller caliber APCBC rounds

> than larger caliber APCBC rounds (please elaborate any answers as

> to weather

> this is a function solely of diameter to thickness ratio effects...or

> weather there is something else going on here). Is there some reason to

> think that APCBC rounds below say 57mm or 37mm diameter fired at FH armour

> were less effective than these same calibers being fired at RHA

> armour...or

> am I mixing apples with oranges here?

Below about 57mm we get a scaling effect, sort of similar to Reynolds number

effects in fluid dynamics. I have scant information for projectiles below

about 50mm, but it still seems to be that RHA is better than FH provided the

T/D ratio is about 1 (say from 0.5 to 1.5). I'd hesitate to go further than

this without looking at more material. I have recently received an excellent

report from the Armour Board (1946) which should shed some light on this

topic. Stay tuned.

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Krupp equation for face-hardened penetration:

pen=constant x (velocity) raised to 1.25 power x (diameter) raised to 1.25 power x (weight/(diameter)cubed)raised to 0.625 power.

Above equation fits U.S. and British face-hardened penetration very well, constant a function of caps and other factors.

Note that if 75mm and 57mm APCBC hit face-hardened armor at same velocity and with same (weight/diameter cubed) ratio, penetration for 75mm will be 1.41 times greater than 57mm.

Against 240 Brinell Hardness homogeneous armor, 75mm would penetrate 34% more at same velocity and (w/d cubed), so face-hardened penetration is more sensitive to projectile size.

We compared homogeneous and face-hardened penetration data for alot of projectiles, with uncapped AP small rounds like 2 pounder penetrate alot less face-hardened than homogeneous, while 152mm AP penetrates more face-hardened than homogeneous.

Since face-hardened is more sensitive to impact due to brittle nature of high hardness layer, larger shells do things than 20mm can only dream of.

75mm on Sherman does 91mm of homogeneous at 0m and 0°, does 104mm of face-hardened.

Research for our armor penetration booklet looked at all the face-hardened penetration equations and curves, compared equations to published data and identified the equations that made sense. We then estimated face-hardened penetration for ammo and guns that didn't have published data.

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Another interesting aspect of face-hardened penetration is that penetration falls off as (velocity)raised to 1.25 power, while homogeneous penetration falls off as (velocity) raised to 1.4283 power.

Homogeneous penetration more sensitive to velocity, face-hardened more sensitive to projectile diameter.

There are some cases where above isn't true, and we believe it may be related to shatter gap failure where T is greater than D, and velocity is over 2000 fps.

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One of the on going problems on tring to predicte armor penetration is to asses the impact of hard plates as armor. Its clear that harder armor produces less penetration but its also clear that there are other issues at work. For one fracture toughness is important as is steel yield strenght. In fact from the 70s on the reference to the relation of the projectile hardness and the target hardness has been replace by the relation of the Yield strenghts of the projectiles and plates.

Does any one know what the yield strength of Face hardened armor was?

In addition modern armor calcutations assume layers of armor with differing qualities [ IE hardness etc], can be assess from a linar approach. So if Face hardened thickness is universally 5mm in depth and offers 1.8 times the resistance of RHA then a plate 20mm thick should offer..... 1 x 1.8 + 3 x 1.0÷ 4 = 1.2 times the resistance compared to RHA.

If the plate were 80mm thick, the approximation should be; 1.8 + 15 ÷16= 1.05 times the RHA resistance.

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I must have missed this one. Heaven forbid that I should let it slip. What? No backslapping 'good on you rexford' posts?

What does this mean? Well one could suggest that it means that German FHA armour isn't so good against western allied tank rounds as against russian.

What are the implications of this for the so-called 'undermodelling' of the Panther glacis?

Should the slope modifier for APCBC be different for FHA than for RH armour?

More anon.

------------------

"As has been said, we only listen to bootlickers, and Simon is one of the best out there!"

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Great post once again Rexford. It's always nice to learn new things. Keep on posting please.

But why you are so bitter Simon?

It is true that most of Rexford's posts seem to suggest some kind of tweaks for axis's good in the game, but is that wrong? Not by my thinking as long as it helps CM to get more realistic. If there are similar things to be enhanced in the allied arsenal then that should be done too. If face hardened armor was the 'weak link' in the German tanks on the western front, let it be that in CM1 too. No offense, but let's not get too emotional on these things wink.gif

Btw. is there any considerable difference between face hardened and homogenous armor's reaction against hits from steep angles? Is the projectile more likely to ricochet from homogenous armor and penetrate fh armor for instance? Or vice versa?

Ari

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Well, since people have posted figures of knocked-out tanks on this thread and I have one already online, I could put a link here:

tank3.gif

I'm not certain whether this KV-II had face-hardened armor or not, but it can be said that its armor definitely was penetrated by the 60 kg explosive charge that was sneaked under it in the cover of night.

- Tommi

[This message has been edited by tss (edited 01-30-2001).]

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But why you are so bitter Simon?
An interesting interpretation of my mood. Wryly amused would be more accurate or cackling with glee even. Is that "emotional"? In a sense perhaps. I was just amused that this thread didn't get quite the response some others do hehe. Surely Ari you've been around here long enough to know that the only bitter I get is the "Vic" variety.

I would definitely like to see some more comment from "rexford" on this issue of FHA vs RH and the relative performance of APCBC against them. Also do slope effects vary. It is interesting to note that many of the armour penetration results bandied in discussions about are against RH plate and I wonder how that might vary?

------------------

"As has been said, we only listen to bootlickers, and Simon is one of the best out there!"

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Originally posted by Simon Fox:

Wryly amused would be more accurate or cackling with glee even.

Ok. Sorry for wrong diagnonsis. Seems that I'm not qualified as an psychologist. Not a surprise really smile.gif

Anyway I have noted that usually you seem to be quite wary about Rexford's posts. Particularly if he proposes impairments for allied tanks. Of course nothing should be accepted on face value only and good critics has always it's place.

Still I haven't found Rexford to be biased and majority of his posts are very convincing. Rexford clearly and openly tells the reasons for his interpretations and beliefs. And when somebody comes up with a reasonable counter-argument he seems to be able to change or at least revise his opinion if needed.

And yep, this FHA-issue is interesting. It's quite obvious that face hardening had many effects. Positives and negatives depending on circumstances. Any further knowledge would be welcome.

Ari

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Anyway I have noted that usually you seem to be quite wary about Rexford's posts. Particularly if he proposes impairments for allied tanks.
Purely coincidental as early rexford threads were slanted that way, also coincidentally I presume smile.gif . My only concern was the brevity of the early posts which required some prompting to produce dialogue.

------------------

"As has been said, we only listen to bootlickers, and Simon is one of the best out there!"

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Responding to previous posts:

Face-hardened slope effects are similar to RHA and vary with T/D ratio

German armor has advantages that CM should model, and disadvantages. We prepared the original flaw equations that found their way into CM through armor quality multipliers, and Panther glacis is major weak area. About half the Panthers carried alot of face-hardened armor, we wonder if this is in CM. A list of CM panzers with face-hardened armor would be interesting.

Face-hardened armor will be a big plus on Eastern Front where Russians did not use armor piercing capped rounds. Allies using APCaps on most or all rounds by 1944, face-hardened not so good.

Since face-hardened armor is more sensitive to projectile size than RHA, and face-hardened penetration falls off slower with velocity changes than RHA penetration, big rounds on Eastern Front (85,100,122,152) not good for face-hardened panzers. Face-hardened penetration falls off with velocity raised to 1.25 power, RHA variation is velocity raised to 1.428 power.

Face-hardened penetration dependent on projectile diameter to 1.25 power, while RHA is diameter to 1.0714 power. If projectile diameter increases from 75mm to 122mm, RHA penetration increases by 68.4% while face-hardened pen. increases by 83%.

U.S. face-hardened penetration curves in TM-9-1907 show reduced penetration at high velocities by 76, and lower pen. at all velocities by 57 and 90. These effects do not show up with RHA.

Americans fired captured German 75mm against RHA and face-hardened armor, German 75 outdid U.S. 75mm against RHA but was the same against face-hardened. You just can't predict some things.

To be realistic a game should catch all of the little things that make tanks good and/or bad. Germans had alot of advantages that CM may not use in all cases, and panzers had weaknesses. We try to be fair and unbiased, and have promoted some allied tank advantages.

Churchill tanks with 88mm frontal armor are being promoted on "my" thick British armor thread. Front armor was 89+13 around driver hatch on front (it isn't 88mm armor, it's 89mm), and an incredible 89+89+13 around hull MG. And nose was at 20° slope. And 38mm at 70° glacis, which significantly exceeds 88mm at 0° resistance. CM has none of this from what we can see. We have design drawings and specs for Churchill tanks and CM understates armor resistance. Churchills were harder to defeat than CM portrays, although they could still be knocked-out fairly easily, but a more difficult target than a Sherman.

British tankers complained bitterly about how easily Churchills were being penetrated in France. We're saying Churchills are better than CM portrays while still having major weak areas.

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KV tanks fought during 1941 do not appear to have face-hardened armor, since 50mm rounds that hit them were reported to dig into armor and then rebound without leaving a dent. Face-hardened armor defeats hits by shattering the projectile nose, softer cast and rolled homogeneous armor (RHA) by deflecting and absorbing energy.

British tested KV-1 tank and it was either homogeneous armor in 240-290 Brinell Hardness range (machineable quality), or homogeneous hard on add-on pieces (like extra plates added to driver plate, nose and side turret protection).

Soviets generally used high hardness for armor used on faster tanks and homogeneous machineable quality for tanks designed to take hits and trade blows. High hardness good against rounds smaller than armor thickness, like 37mm gun against T34 side.

U-boats reported to have used face-hardened armor on conning tower to help defeat hits by aircraft cannon.

All those PzKpfw III's, and alot of IV's, in North Africa were loaded with face-hardened armor. British thought Tiger had face-hardened armor when 6 pounder hits shattered. It was shatter gap failure when rounds that should have penetrated failed against Tiger 80mm plates.

80mm face-hardened German armor would have less resistance than rolled homogeneous against Sherman 75mm APCBC, but would perform better than homogeneous against uncapped 75mm AP. Our penetration data for U.S. ammo will show this when the booklet is released.

The armor penetration booklet is about 85% complete and will primarily present results with enough explanation to use the curves and data. Tank armor data will indicate thickness, slope, flaw tendency and what type it was (cast, face-hardened, high-hardness, etc.). Data will also identify spaced and plates-in-contact armor areas and text will present equations that explain how to convert spaced or contact plate armor to an equivalent single plate thickness.

Two 40mm plates that are spaced resist like a single plate with 72mm thickness, as a starting point. However, capped rounds and uncapped rounds adjust the equivalent thickness and rounds with HE bursters may detonate in the space as they leave the first plate. We're trying to simplify how these things are handled.

Not a simple thing, spaced plates or plates in contact.

The intent of the armor booklet is to present basic data to analyze and predict penetration ranges and probability. There is alot of data out there that does not address all guns, all ammo types or all armor types. We have compiled information and estimated figures to fill in missing data. Available equations were used to estimate after alot of cross-checking data for other guns to be sure the equations worked reasonably well for other cases.

The booklet won't be 100% accurate or totally consistent with published sources, but should be the best single document available. CM armor penetration analysis is based on many of the curves that will be presented in the booklet.

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Just a note about spaced plated armor[ from memory]. Research in the 70s showed that if the spacing between plate and main armor is large [ IE > 15 times the spaced plate thickness] The resistance Vs APFSDS and APDS AP is 10-20% more than the solid thickness figure, provided the striking velocity is > 1300m/s for APFSDS, > 1100m APDS & AP type shot . This research also suggest that the resistance of these two targets is identical at the following striking velocities

APFSDS 700-1100m/s

APDS 800-1000m/s

AP 900-1000m/s

When I get home I'll review the paper in question and update the above figures.

Also what about Decapping plates. The spaced armor on the front of the Pz-III was designed to Decap APCBC ammo. I gather from test it was very good at this and even 'predetonated' the bursting charge in APHE ammo.

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WW II steel projectiles are different than modern ammo. It can be shown using penetration curves in TM-9-1907 that two spaced 40mm plates don't equal 80mm single plate resistance if round doesn't detonate.

Merkava has spaced hull armor?

Long thin penetrators or tungsten behave differently from steel AP or APCBC. In fact, if two parallel plates are hit at 45° to outer plate, the initial plate will turn the round towards the second plate so that the impact angle on the inner plate is alot less than 45°. Alot less resistance than a single plate, especially since slope effects are function of T/D (armor thickness/projectile diameter) and two single plates offer alot less sloped resistance than one plate.

Nathan Okun has done alot on this subject regarding WW II naval penetrations.

When PzKpfw IIIN spaced armor didn't detonate round, it wasn't that good. However it would blunt sharp nose AP rounds so penetration against inner plate dropped.

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Originally posted by rexford:

WW II steel projectiles are different than modern ammo. It can be shown using penetration curves in TM-9-1907 that two spaced 40mm plates don't equal 80mm single plate resistance if round doesn't detonate.

I have TM-9-1907 and I can't find this , what pages ?

Long thin penetrators or tungsten behave differently from steel AP or APCBC. In fact, if two parallel plates are hit at 45° to outer plate, the initial plate will turn the round towards the second plate so that the impact angle on the inner plate is alot less than 45°. Alot less resistance than a single plate, especially since slope effects are function of T/D (armor thickness/projectile diameter) and two single plates offer alot less sloped resistance than one plate.

Yes but the projectile will undergo Yaw in the process and the longer the projectile the more its vunerable to Yaw.In addition studies of spaced plates show that the YAW is not predictable for short AP type projecties some times its large other times its quite low. So spaced plates normal have a ± 30% variation in resistance.

Tests on tumble rate on APFSDS resulting from spaced plate impact @ angle suggest the following .A 1.0° YAW vs a spaced plate arrangement @ 75° results in 15 fold increase in YAW or COS² .The same impact on a 45° sloped array results in a 1.5° YAW becoming 4.5° or 3 fold increase ,closer to 1.41^3.2 . However this amount of YAW occurs only after the projectile has traveled more than one times its length from the outer to the inner plate ….in modern tanks that would require at least 30cm airgap between plates @ 75° far too impractical . Immediate Post impact tumble rates are much lower and in the above case the 1 ° YAW @ 75° becomes 2° or COS ^ 0.5 ° and 1.5° YAW @ 45° becomes 1-5- 2° or again about COS ^ 0.5 ….

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Analysis uses the curves in TM-9-1907, and we'll asume HE burster is not working and APCap remains undamaged on round. This will simplify analysis and make it easier to follow.

Find the velocity needed by 75mm M61 to penetrate a single 40mm plate at 0° on half the hits, assume 1142 fps (don't have my TM nearby). Then assume that a second 40mm plate is spaced behind the first, requiring 1142 fps.

Impact on first plate must have sufficient kinetic energy to pierce first plate 100% of time and then defeat second plate 50% of time.

100% penetration requires about 20% more penetration than 50% defeat, and 14% higher velocity.

Velocity needed to defeat both plates is then (based on kinetic energy analysis):

((1.14 x 1142)^2 + (1142)^2)^.5, or 1732 fps. 75 M61 penetration at 1732 fps is about 73mm.

The problem can be solved in other ways, and yields the same answer. We have factors that modify results for AP nose blunting on first plate and loss of APCap, which actually may increase penetration against second plate (haven't finished calculations yet).

Going backwards, what single plate thickness is the same as a 40mm and 53mm plate spaced apart.

(1297^2 + 1390^2)^.5 = 1901 fps

75 M61 penetrates about 83mm at 1901.

Spaced plates are easier to penetrate than a single plate of same total thickness because DeMarre equation has kinetic energy changing as plate thickness to 1.4 power. Make the plates half as thick as 80mm and it requires 38% as much energy to penetrate 40mm as 80mm.

Two times energy for one 40mm plate is 76% of energy needed to defeat 80mm.

The reason is due to plugging failure versus push aside, where plugging takes less energy than a round that must fight through the entire thickness.

When 75mm hits a 40mm plate, the round overmatches the armor thickness and failure tends to be by a plug of armor failing around the perimeter and then driving out in one piece. This is low energy failure.

When 75mm round hits 80mm plate, there is enough material to prevent plugging and the round must push through against continuous resistance, which takes alot of energy. One 80mm plate takes more energy to defeat than two 40mm.

Looked at another way, if one has a 1' thick wall and a 2' thick wall, the work needed to knock a hole in the thicker wall will be more than twice what is needed against 1'. The thinner wall may fail by having an entire piece give way around the edges while the thicker wall may only fail by pushing out a small hole.

Thin plates fail by punching out whole pieces, thick plates by drilling a hole. Simplistic explanation but that is why spaced plates generally aren't as good against WW II steel ammo (unless first plate detonates round or blunts the sharp nose, or removes APCap so face-hardened can break up nose).

If tungsten shatters or cracks against an outer plate, which is possible since the projectile is very brittle, the second spaced plate may be sufficient to stop the pieces. High hardness and brittle behavior often go together, like ceramic armor that can defeat hits but is then in pretty bad shape. Alternating layers of hard and soft material may serve to break-up a projectile against hard armor, and then soft armor absorbs fragment energy by deflecting.

Modern armor is not my best subject so excuse me if I exaggerate or make an error. Merkava uses alot of armor tricks to defeat rounds, and it is not clear if alternating hard/soft layers or open spaces would help against WW II steel projectiles. At Shoeburyness the U.S. HE detonators may have fizzled alot, but spaces would help detonate some rounds inbetween armor plates.

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Originally posted by Jeff Duquette:

Pg 129 - 155.

[This message has been edited by Jeff Duquette (edited 02-01-2001).]

Thanks for the explaination 'Rexford', I have problems with T/d figures though that Robert sent me years ago.

It shows no difference at 30o and I've found evidence from research test that show t/d effects at all angles even @ 0o impact. But such figures don't include the effects of Yawed impact.

For example I have tests of APFSDS Vs semi infinti RHA targets [ 260 BHN] and another target with stacked harder plates [ 340-380 BHN].In all cases the RHA armor target offers ~ 10% more resistance [per unit thickness], however only if there is no YAW at all in the projectile impact. All it takes is 1-2o Yaw [ happens all the time] and the stacked target offers 10-20% more resistance

In addition its clear that all projecitle ,including shaped charge , are effected by t/d.

THanks Jeff, I was asking more about the t/d question.

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