Specific event: T-34(76mm) vs PIV H (late)

[Kauz]

Hello Vanir,

would like to get further information about the formula.....

The formula has obviously limitations......... you may only be allowed to use this formula under special conditions.

Why do i think that? you may ask....here comes the answer:

For example:

Try to use a 200 mm thick armor plate against this 76,2 mm round and tell me what the formula calculates as result.

Here the results:

at impact-angle of:

0°= 8,06mm :eek:

10°=16,97mm

20°= 36,6mm

30°= 82,34mm

40°=199,91mm

50°= 556,56mm

60°=1981,59mm

70°=10974,68mm

80°=134420,36mm

89,9°= 6520086,52

Sorry...but the Elefants should then have died like flys when they got shot by T-34/76 tanks and only had an equivalent armorprotection of 8-16mm steel instead of 200mm....

another funny example into the other direction...

a 67,4mm thick armor plate vs this 76,2 mm round:

0° : 105,74

1° : 105,02

10° : 99,46

20° : 95,78

30° : 96,24

40° : 104,35

50° : 129,75

60° : 206,32

70° : 510,31

80° : 2791,49

89,9°:60960,86

1. thing is that the armor is overmatched by the 76,2 mm round but always pretends to be bigger than its nominal thickness is.

2. thing the armor starts high.......then decreases.....and then increases again.

The more i test the formula....the more i think "something" (to be careful) is a little (to be careful again) wrong ....

Please give me more information about the forumla...and especially check if you get the formula itself and its condition for proper use in a right way.

[Kauz]

it gets even more funny:

you remember that the 20mm plate had an equivalent armor protection of about 16-17mm @ 70,5° ..., right?

Did you plot...what happens for all other angles?

Here the answer:

0°: 1874,99

1°: 1701,85

10°: 716,73

20°: 280,52

30°: 114,55

40°: 50,48

50°: 25,51

60°: 16,49

70°: 16,57

80°: 36,84

89,9°: 329,96

no comment..............................................

[c3k]

I do not have a copy of book with these formulas. However, I'm also curious if the formula in question has been correctly transcribed or if it has specific limits associated with its use.

Thanks for driving more solutions and showing the oddities.

[JasonC]

Kauz - of course you go back to the actual Cosine function, not a polynominal approximation to it, if you want to test angles far from the one used to create the approximation. I personally think the overmatch correction is far smaller than any of the formulas cited. It exists but it is minor.

[Amizaur]

Kauz:

I took a look into The Source

The values of F and G coefficients are valid only for given range of angles like 55 to 60deg.

So it's pointless to plot results from 0deg to 90deg for this function using fixed F and G.

You should combine your 0-90deg plot from parts using corrent F and G coefficients for each given range of angles.

Only then it can be determined if the formula gives credible results or is it bogus.

[Childress]

JasonC and Amizaur, separated at birth?

[Amizaur]

Exact result for 71.68deg (73deg minus 1.32deg for shell descent angle) is: 34.2mm for APBC formula.

Here you have a properly calculated range of 0 to 85deg using above formula and proper F and G values for each angle. Input values: D=76mm, T=25mm, Quality 100%.

For APBC

Angle Result

0 24,81

5 24,77

10 24,89

15 25,25

20 25,88

25 26,82

30 28,08

35 29,61

40 31,29

45 32,87

50 33,86

54 33,73

55 28,24

59 27,18

60 26,30

65 26,66

70 31,25

75 44,48

80 82,13

85 214,97

There is some range (50 to 60deg for APBC) where the T actually decreases, when angle increases. I do not believe that increasing the angle could give les protection everythibg else being equal so it is probably some error between 50 and 60deg...

For APCBC and APC

Angle Result

0,0 24,7

5,0 24,6

10,0 24,7

15,0 25,1

20,0 25,8

25,0 26,9

30,0 28,5

35,0 30,7

40,0 33,7

45,0 37,7

50,0 43,0

55,0 48,4

60,0 58,6

65,0 71,8

70,0 84,9

75,0 111,4

80,0 145,7

85,0 189,8

A graph for the AP & APCBC formula gives nice curve, with ends of the angle ranges almost connected (small inconsistence at 55deg).

APBC formula (red one) is not so nice, there is inconsistency visible and a region where increasing the angle reduces the effective protection.

[JonS]

I personally think the overmatch correction is far smaller than any of the formulas cited. It exists but it is minor.

You are free to believe whatever you want, as long as you are consistent.

So, with that in mind, please do regale us with all those tales of single sheets of household tinfoil resisting 7.62mm when the angle is 'just right.'

[JasonC]

Nobody is talking about foil, it is just silly. The issue is when a round is barely even striking a plate (very "glancing" angles), how poor the overmatch linear approximation to the fall-off in the slope benefit becomes.

A practical example - the T/D linear approximation predicts that German 88L71 should penetrate 45mm plate despite slope effect up to an impact angle of 85 degrees, when the cosine formula expects starting at more like at 80 degrees. These are impacts so close to parallel to the armor that they are barely impacts - the most likely outcome is deflection, unless the shell cap "grips" the armor face particularly well and the shell nose deforms onto a lower angle into the surface. If the shell remains rigid, it is more likely to skip off.

Is either formula going to perfectly predict the max angle at which that round breaks such a 45mm armored plate vs where it skips off? No. Neither was designed to predict that sort of event. There is no particular reason to believe the 85 degree figure. The true answer may be higher than the 80 degree figure from the cosine effect alone, but how much greater we just don't know.

When your armor slope effects from slope are within 1x and 2x and your T/D ratios are between 1x and 2x, sure it is a helpful correction term. Extrapolating that to overmatch ratios of 3.75 times as in the example, and to extreme angles, will make nonsense. Just not what the formula can be expected to do, because not the parameter region in which is was fitted to data.

[c3k]

Is the change in relative thickness due to the hardened "flat" of the round digging into the armor and reducing obliquity?

[JasonC]

C3k - the modeling isn't that specific, it is just empirically observed. The reduction by t/d in the benefit of slope is a first order approximation, and most sensible when both the overmatch factor and the slope benefit factor are modest, like under 1.5. Already when both are in the range of factors of two it can overrate the reduction if effective thickness. When the slope effect is a factor of 3 and the overmatch is 3.75 times (which is where we are with a 20mm plate hit by a 76mm shell at 73 degrees), expecting it to be accurate is heroic extrapolation, and there is no particular reason to expect the linear relationship to still hold.

[Vanir Ausf B]

Here you have a properly calculated range of 0 to 85deg using above formula and proper F and G values for each angle. Input values: D=76mm, T=25mm, Quality 100%.

For APBC

Angle Result

0 24,81

5 24,77

10 24,89

15 25,25

20 25,88

25 26,82

30 28,08

35 29,61

40 31,29

45 32,87

50 33,86

54 33,73

55 28,24

59 27,18

60 26,30

65 26,66

70 31,25

75 44,48

80 82,13

85 214,97

There is some range (50 to 60deg for APBC) where the T actually decreases, when angle increases. I do not believe that increasing the angle could give les protection everythibg else being equal so it is probably some error between 50 and 60deg...

I get slightly different values than you for a x (T/D)^b (pg 118)

76mm APBC vs 25mm

10°   25.5mm

15°   25.7mm

20°   25.9mm

25°   26.2mm

30°   26.5mm

35°   26.8mm

40°   27.2mm

45°   27.4mm

50°   27.6mm

55°   28.2mm

60°   26.5mm

65°   26.2mm

70°   31.5mm

75°   44.2mm

80°   81.3mm

I agree that the 60-65 degree results look suspicious. There is a cautionary note on page 21 that may explain the problem:

The APBC program equation is valid within the range of test penetration data, and may produce unrealistic results when used for T/D ratios below those included in base data.

Also:

Results below the base armor thickness should be treated as the base thickness.

So the 16.7mm value I calculated earlier (vs. 20mm thick plate) would actually have been 20mm, or 19.5mm at 95% armor quality. Although given that we are dealing with APBC at a very low T/D ratio we may need to take that with a grain of salt.

[Kauz]

Kauz:

I took a look into The Source

The values of F and G coefficients are valid only for given range of angles like 55 to 60deg.

So it's pointless to plot results from 0deg to 90deg for this function using fixed F and G.

You should combine your 0-90deg plot from parts using corrent F and G coefficients for each given range of angles.

Only then it can be determined if the formula gives credible results or is it bogus.

Good to know....

Vanir established this formula without telling about restricions to calculate the special case of 70,5° and the 20mm plate.

But then even the result for 70,5° is not correct because it is only meant for angle between 55-60°.

Another point i discussed with a physicist-friend is the problem that it makes no sense that an armor plate has less protection then it nominally thickness.

What i mean is, that 20mm @ 0° is simply 20mm.....increasing the angle will always increase the armor-protection, too. The only discussion is how far this increase will go.

For example:

A 20mm plate at 0° is just 20mm. This is for the physical fact that you always have to spend kinetic energy of the round to break up the potential energy between the atomic bounds. This fact you will never be able to evade.

Further:

Cosinus like it would have minimum 59,9mm minimum (@70,5°), because of the geometrical armor protection.

Because of the Overmatch problem i can argue and imagine a lot under the 59,9 mm.....BUT NEVER under 20mm.

I mentioned this because the formula (ignoring it was may be wrong one for this angle) gave us: 16,8mm ...........

This leads me to the next question:

Is there a limitation for the armor thickness respectively the T/D-ratio ?

Because ....if you calculate for a 20mm armor like you said only between 55-60° then you will find following results:

55°: 19,7

56°: 18,87

57°: 18,14

58°: 17,5

59°:16,95

60°:16,49

These results does not make any sense for two simple causes:

1. like i said....in a physical way it does not make any sense to assume, that an armor-plate no matter which angle it is orientated,will ever have less armor protection than its nominally thickness (in this case 20mm).

2. It is also suspicious that the armor-protection decreases with increasing angle like you can see.

[Vanir Ausf B]

But then even the result for 70,5° is not correct because it is only meant for angle between 55-60°.

Amizaur was using 55-60 as an example. The actual formula I used was for angles over 60°

Another point i discussed with a physicist-friend is the problem that it makes no sense that an armor plate has less protection then it nominally thickness.

See my corrective note in my last post.

[JonS]

A practical example - the T/D linear approximation predicts that German 88L71 should penetrate 45mm plate ...

that's all very nice, except the T/D ratio for that is quite high - more than .5. The example we're looking at (20/76.2) is much much lower. Since you already know the T/D effects are non-linear, are we to assume it mere coincidence that you selected an irrelevant example that supports whatever tangential point you're trying to make?

[Kauz]

Amizaur was using 55-60 as an example. The actual formula I used was for angles over 60°

See my corrective note in my last post.

....so this wise we see it the same way

According to your citate:

The APBC program equation is valid within the range of test penetration data, and may produce unrealistic results when used for T/D ratios below those included in base data.

I would like to ask...: What was the lowest T/D ratio they tested?

Because if the book itself mentions that the formula may will produce unrealistic results with T/D below the tested ones ...than you can be sure that these unrealistic results will far more increase with more extreme low T/D ratio.

What i try to say is, that in case the lowest armorer thickness they tested was for instance 50mm ....than it may not make any sense to transfer this formula for a 20mm plate.....

Some indications that you never should use this formula may be the following:

-The further afar (lower) the calculated result is from the nominally thickness (and 16 is far under 20) the less reliable the formula is ....and the less it is convinient to even assume 20mm instead of 16mm.

-The less consistent the behaviour gets the less reliable the formula is for your case.

In our case it is very suspicous that the armor thickness decreases which increasing angle.

To assume that at all angles then would be 20mm is not a good way to go. It makes the formula not more useful.

Additionally:

I would guess that the most important effect of overmatching is caused by the point that one part of the round (the lower part which has its impact before the upper areas) is causing a deformation of the armor and this wise will not only increase the grip...it will also reduce the effective angle of the armor.

So where i have before 60-70° i may only have effective 30-50° left because of the deformation.

So i would expect that the 20mm armor may then for instance have about 23-31mm effective armor protection....but only 20mm?

If it would only have 20mm.....i had no need to angle it anyway.....20mm i have at 0° too

[Vanir Ausf B]

I would like to ask...: What was the lowest T/D ratio they tested?

Unfortunately they don't specifically say. However, in a table of 122mm APBC slope multipliers at various angles and ranges the lowest T/D ratio listed is .44.

Some indications that you never should use this formula may be the following:

The game has to use something. Speculating that something may be off is the easiest part. Proposing alternatives is harder.

[Vanir Ausf B]

Unfortunately they don't specifically say. However, in a table of 122mm APBC slope multipliers at various angles and ranges the lowest T/D ratio listed is .44.

On the other hand, the formula does not begin producing results below the armor's base thickness until the T/D drops below .29 (at 70°).

[Kauz]

Unfortunately they don't specifically say. However, in a table of 122mm APBC slope multipliers at various angles and ranges the lowest T/D ratio listed is .44.

The game has to use something. Speculating that something may be off is the easiest part. Proposing alternatives is harder.

That is generally correct...i understand your point.

On the other side...:

Sometimes some numbres like 85% armor quality and 95% armor quality dancing around here.

And sometimes you can see in penetration tables that rounds loose penetration power more than expected if they have to penetrate an angled or very angled armor plate.

These effects are more or less about 5-15%.

So i am not sure if it gives point to assume that a for instance a 20mm plate has only 20mm (or even 16 ;-) ) @ 70,5 ° while it should have about 60mm.

There is not only a loss of 5-15% like at other effects....it is 75%.

So i do not think it is convinient to assume for (very) low T/D ratios this formula.....i would recommend to stay at the cosinus like behaviour then.

To illustrate the problem a little more the following comparison:

http://www.directupload.net/file/d/3649/nrb4waiv_jpg.htm

Like you can see ...the B results becoming completly utter the more the armor thickness decreases and we " have" to assume always the nominally thickness till we reached a nominally thickness of 22mm.

Much more interessting is to observe what happens at thickness about 40mm.

Despite the armor is still heavily overmatched.....(*40mm/76,2mm ~Factor 0,5)

.....the calculated armor is thicker than the cosinus-function.

First time the calculation shows a overmatch behaviour is under 39mm....nominally thickness.

My conclusion is:

that even at this big overmatch Factor of 0,5 (40mm/76,2mm) the angle of 70,5 ° still provides the same or better protection like a cosinus-function is doing so.

In the opposite the formula becomes very utter alright under 30mm.

As long as i do not have more data/information about this formula....

My approach would be more like assuming a cosinus-function instead of loosing 75% of my armor protection.

[wadepm]

I wonder what the Germans were thinking when the designed the PzKw IV front this way. Did they do any testing on this particular combination of angles and armor thicknesses? At the time of the design the largest AT gun was a 50mm (?) so maybe the T/D ratio wasn't such a big deal to them at the time.

[Vanir Ausf B]

My conclusion is:

that even at this big overmatch Factor of 0,5 (40mm/76,2mm) the angle of 70,5 ° still provides the same or better protection like a cosinus-function is doing so.

In the opposite the formula becomes very utter alright under 30mm.

While I think there is a case to be made for adjusting the APBC slope modifier curve upwards earlier, you can't just throw out T/D at some arbitrarily chosen point (or one chosen to most greatly benefit the Pz IV, as the case may be). Whatever adjustment you propose, the APBC slope modifiers need to remain significantly lower than for APCBC against sloped, highly overmatched RHA because...

Versus rolled homogeneous armor at an angle, flat nosed APBC will be better than APCBC if the thickness is not too great. APBC digs in and counters ricochet forces that try to overturn rounds.

Slope modifiers @ 70° angle

@T/D .21 (76.2mm projectile vs 20mm)

APBC: .84

APCBC: 3.19

@T/D .5 (76.2mm vs 38.1mm)

APBC: 2.69

APCBC: 3.99

@T/D .75 (76.2mm vs 57.2mm)

APBC: 5.62

APCBC: 4.6

@T/D 1.0

APBC: 9.48

APCBC: 5.8

As you can see, the APBC advantage disappears between T/D .5 and .75. In order to maintain that circumstantial advantage T/D must be factored in to some degree.

[Vanir Ausf B]

I wonder what the Germans were thinking when the designed the PzKw IV front this way. Did they do any testing on this particular combination of angles and armor thicknesses? At the time of the design the largest AT gun was a 50mm (?) so maybe the T/D ratio wasn't such a big deal to them at the time.

That, plus the Soviets didn't start using APBC ammo in large quantities until mid-1944..

When CMx2 moves into the Kursk time period people who never played CMBB are going to be dismayed at how much worse Soviet armor performs compared to CMRT (except for Kaus, who will be in seventh heaven )

[Oddball_E8]

Wait... so did we come to a conclusion about the first post at all?

[c3k]

Wait... so did we come to a conclusion about the first post at all?

There is no first post. There is only the last post...

[JasonC]

JonS - it isn't an irrelevant example, it is an overmatch factor of 2, and my whole point is that the linear T/D approximation is already wrong with overmatch factors that high when the slope benefit effect is also high. Cutting in half the slope benefit when the slope benefit is 10 or 20% may be accurate. Cutting it in half when it is 5.5 *times* is not going to be accurate. It is already not terribly accurate when the slope benefit is itself a factor of 2.

If the overmatch is 1.5 times and so is the slope benefit, the simple T/D term is just fine - it is saying a 50% advantage from slope should be trimmed slightly to a 33% advantage from slope. If the overmatch is 2 times and the slope benefit is 5.5 times, the simple T/D term is taking that down to 3.25 times. That is just how products work, and believable adjusts for small factors become unbelievable ones when you multiply two terms well over 2 together.

Take the case that prompted the thread, 3.81 overmatch at 72 degrees. The thickness gain from geometry alone is 3.24 times at that extreme an angle. The T/D formula leaves the first 1 times of that alone and reduces the 2.24 slope benefit by a factor of 3.81, leaving only a 1+ 0.588 slope benefit, or 32mm resistance, as though the plate were at only 51 degrees, and just less than half its geometric thickness along the flight vector (65mm).

I flat do not believe that will plate at that angle will resist like only 32mm. It will resist less than 65mm certainly, but not by that much less. If the relation goes more like the square root of the overmatch we'd get 43mm resistance. That might still be low, but it is much more plausible than the original - it effectively predicts the plate resists like it was at a 62 degree angle rather than a 51 degree angle. There just is no reason to expect that the linear first order approximation of the T/D term will remain linear to parameter values that high. You would have to test those specific values - nothing just extrapolated out of the region of much lower angles and overmatches would be relevant.