Exact formula for AP penetration?

[Guest Martin Cracauer]

I didn't find that in the FAQ:

Is the exact for AP penetration formula for range and angle available?

I ran a few tests over the values, looks too complex to figure out in reasonable time. I.e. the caliber seems to have influence on the tendency to decrease with raising angle, all other things being equal.

Don't tell me CMBO does complete aerodynamics to compute the shell's speed on impact. Or rather, please do, but only it it's true

I have a concrete reason to ask, I need penetration values for arbitrarily armor angles.

Thanks

Martin

[tss]

Martin Cracauer wrote:

Is the exact for AP penetration formula for range and angle available?

Do a search on the board for threads initiated by 'rexford'. You'll find lots and lots of data and formulas for armor penetration.

- Tommi

[Jeff Duquette]

Milne -de- Marre, not exact, but nothing really seems to be. You can might start here for the basics.

http://www.warships1.com/W-Nathan/Hstfrmla.htm

[aka_tom_w]

Originally posted by Martin Cracauer:

I didn't find that in the FAQ:

Is the exact for AP penetration formula for range and angle available?

I ran a few tests over the values, looks too complex to figure out in reasonable time. I.e. the caliber seems to have influence on the tendency to decrease with raising angle, all other things being equal.

Don't tell me CMBO does complete aerodynamics to compute the shell's speed on impact. Or rather, please do, but only it it's true

I have a concrete reason to ask, I need penetration values for arbitrarily armor angles.

Thanks

Martin

They algorythms to determine hits and penetration. They seem to be very closely guarded trade secrets.

BUT they are VERY accurate and based on REAL physics with a certian amount of random chance thrown in to make things interesting and unpredictable.

you won't find any published reports or statements as to EXACTLY how they work, but some here have conducted gunnery range "experiments" in an attempt to retro engineer those equations and figure out how they work.

YES and defeintely read what Rexord has to say he has been VERY active posting about this.

If you know how armour pentration was modeled in the OLD AH game Tobruk then that is a good place to start to understand the inner workings of this game, only now you don't have to roll the dice to:

a) see IF you hit anything?

IF you if did hit WHERE did it hit?

c) Depending on WHERE it hit DID it PENETRATE

d) IF it DID Pentrate What DAMAGE did it cause?

Trying playing Tobruk and rolling the dice 3 or 4 times for EVERY damn round your AFV's fire then you will KNOW what HUGE Break through this game REALLY is!

-tom w

[This message has been edited by aka_tom_w (edited 02-21-2001).]

[Dan Robertson]

I don't know precisely how BTS are doing it but I can tell you how I would if I were them.

First of all the probiblity of the round hitting is worked out, if it does the angle between the surface and the incoming round is calculated.

then you could use the De Marre formula.

which is

(velocity ^2 * Mass * (cosine angle) ^(2/n))/ diameter ^3

= C(thickness of plate/diameter of shell)^n

where n and C are constants.

However for sub caliber rounds at high angles +30 degrees the n in the (2/n) part of the equation is reduced to 1.11, the represent s the tendancies of these round to break up at steep angles. This was a change that was added in the most recent patch as certain people had noticed the penetration of sub claiber rounds was too high at extream angles.

Now to use the equation you will need a scientific calculator and the values for constants.

CM uses the German 75 L48 as a base on which all rounds are standardised (I think).

In which case the value for C is 4.25 approximatly.

The value for in is around 1.4-1.5 the higher value the flatter the nose is.

For APDS the values is 5.6 for C and 1.37 for N reducing to 1.11 for angles greater than 30 degrees.

BTW this is only how I would do it and it can get alot more complicated as any one who has read Rexfords posts will know.

There are some other factors smaller shells can be destroyed by larger plates that simply will not move out of the way even though the penetration should be greater than the plates thickness, this is the so called shatter gap.

Also the t/d ratio can have an effect on this process.

Rexford will be producing a book on the subject soon I think that will answer any possible quesions on the subject.

[Ben Galanti]

This is a quote from Charles on the source of the penetration equations:

How do I reach this conclusion? The simple physics behind it. Combat Mission does not use "penetration tables" or charts to determine armor penetration. Instead it uses the mathematical equations described in "Penetration of Armour Plate" originally by (British) Ordnance Board Subcommittee of the Armour Piercing Projectile Committee (reproduced by U.S. Dept. of Commerce National Technical Information Service #PB91127506).

You can order a copy of the study for $45 (US) from the following website: neptune.fedworld.gov/cgi-bin/waisgate?waisdocid=896857949+0+0+0&waisaction=retrieve

Ben

[Guest Martin Cracauer]

Originally posted by Ben Galanti:

This is a quote from Charles on the source of the penetration equations:

You can order a copy of the study for $45 (US) from the following website: http://neptune.fedworld.gov/...

Ben

Thank you all for your help, I'll be probably

able to figure out formulas to get value for arbitrary range and angle from it, given the basic penetration value I have from CMBO.

I receive an empty reply from the url above, anyone knows whether that is a temporal error and/or another source is available?

Thanks again

Martin

[This message has been edited by Martin Cracauer (edited 02-22-2001).]

[Guest Martin Cracauer]

Another question:

How precise is cover computation for a tank? Hull down is clear but can the lower hull be in cover when the upper hull is not?

Or in other words, is there any point in not just taking the lower of the hull values for "can kill or not from that position"?

And can turretless armored vehicles get hull down position? I assume superstructure is treated the same as a turrent, but what about vehicles with neither (i.e. Nashorn)?

Thanks

Martin

[This message has been edited by Martin Cracauer (edited 02-22-2001).]

[Mattias]

Martin,

CM models only one state of hull down.

Basically once the tank achieves hull down status CM reduces the hit chance due to the smaller silouet and uses a secondary "where to hit" chart. The lower hull is, as far as I have seen, not possible to hit on that chart, but the upper hull can be.

A turretless tank achieves hull down just as the tank, the superstructure and upper hull is visible, the latter perhaps only partly.

The same goes for the Nashorn, though one could possibly argue that it should be able to go "full" hull down seeing as the gun is mounted so high.

M.

[Guest Martin Cracauer]

Thanks.

I just checked, the Nashorn can reach hull down status and hits are reported as "upper hull penetration".

I had a situation where a target command from the M18 to the Nashorn reported both a "hull down", but the other way round only the Nashorn was. I assumed this status is symmetric, what's the logic behind it? Savegame available.

Martin

[Guest Martin Cracauer]

Originally posted by Dan Robertson:

De Marre formula:

(velocity ^2 * Mass * (cosine angle) ^(2/n))/ diameter ^3

= C(thickness of plate/diameter of shell)^n

where n and C are constants.

Dan, I have two difficulties:

First, do you really mean velocity or speed? I assume it's neither kinetic enery nor impulse since the mass is the next factor anway.

And I have trouble figuring out the units. If velocity == speed, then the unit is m/sec and the whole left-hand is:

(m^2 * kg) / (sec^2 * m^3)

==>

kg / (m * sec^2)

which must the the unit for C.

If I assume that velocity == speed and use this unit for C, I get shell weigths around nanograms.

Example mass for 75mm L48 at 0 grad:

4.25 * ((0.141 / 0.075)^1.4) * 0.075^3 / 790^2

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

4.25 * 2.42 * 0.00042 / 624100

==> 6.92 * 10^-9 kg

Also, I asumme the left-hand term is

C * ((thickness of plate/diameter of shell)^n)

not

(C * (thickness of plate/diameter of shell))^n

, right?

[Vanir]

Originally posted by Ben Galanti:

How do I reach this conclusion? The simple physics behind it. Combat Mission does not use "penetration tables" or charts to determine armor penetration. Instead it uses the mathematical equations described in "Penetration of Armour Plate" originally by (British) Ordnance Board Subcommittee of the Armour Piercing Projectile Committee (reproduced by U.S. Dept. of Commerce National Technical Information Service #PB91127506).

An important addition to this:

Charles:

Guys - two things I want to point out:

1. The 1950 Brit report on armor penetration indeed does not deal with slope. That data came from Robert Livingston. It could very well be imperfect, but is the best algorithm available that I know of, because the interaction between impact and slope is a very tricky one and test data is (unfortunately) woefully incomplete. There is probably room for improvement here, but I think it will have to wait for Robert to finish his book.

2. The penetration figures in CM are not measured against 'test plate' of friendly manufacture (like they are in real-life test firing data). They're measured against 'typical' enemy armor plate. This makes the CM numbers harder to compare directly to test-firing data, but gives a better sense of capability on the battlefield, so that's why we did it that way.

Charles

And:

Charles:

What I received from Mr. Livingston, and used, were his armor basis multipliers for given shell-diameter-to-plate-thickness ("T/D") ratios and armor slopes.

Mr. Livingston's armor basis multipliers for T/D and slope are, in my opinion the best of their kind, that I was able to locate. There could be errors or limitations in them, but until someone shows me something better I will stand by these numbers and continue to use them. If you feel there is a problem with these values, you'll have to take it up with Mr. Livingston.

Hope this helps.

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

What a bunch of horsecrap. -Steve

[This message has been edited by Vanir (edited 02-22-2001).]

[Ben Galanti]

Thanks for the clarifications, Vanir.

The above link worked yesterday, but not today... Dunno.

You can get there by searching for document number PB91127506 at the following link.

www.ntis.gov/support/orderingpage.htm

Ben

[Matthew_Ridgeway]

Interesting quotes Vanir. And yet there is no mention of Robert Livingston in CM screen credits or CM manual.

[Dan Robertson]

Ok working from the 75 L48

What I need to know.

Velocity =790ms

Mass =6.8kg

diameter =75mm

Constants/scale factors. c=4.25 n=1.45

(790^2*6.8)/ 75^3= 10.05

(10.05/4.25)^(1/1.45)= 1.81 = t/d

t = 1.81 * 75 = 135mm at the muzzle.

From Guns Verse armour.

75 L48 at 100m angle 30 degrees = 106mm

correcting angle 106/ ((cos 30) ^ (2/1.45))

=129mm verse 135mm.

Thats 6mm difference this can be explained away by either the fact the shell has traveled 100m or that penetrating armour is not that precise.

Note that there is much more to take into account like scale factors due to the respective sizes of the shell and plate and also the quality of both plate and shell.

[Jeff Duquette]

There has been a series of threads on weather 75mmL48 muzzle velocity was 750m/s or 790m/s (pzgr 39).

In either case velocity will decrease with range. Some German wartime documentation that Rexford was kind enough to send me indicates: v@0m = 750m/s and v@100m = 738m/s.

Assuming mv = 750m/s I back calculated to get LOG C = 8.10456. I also employed m = 1.43. I think m typically varies between 1.25 and 1.43. m=1.43 assumes a combined plug + ductile failure of plate.

Anyway plug and chug and @30 degrees I arrive at 106.079mm at 100meters….or rounded to 106mm @30 degree @ 100 meters range. David Honner on Guns vs Armour also indicates 106mm @30 degree @ 100 meters range which is odd since Honner indicates a muzzle velocity of 790m/s for pzgr39.

[Guest Martin Cracauer]

Dan, Jeff,

thank you for your examples. In fact I got

the formula right but was confused since it

had m and mm mixed and missed the units.

If I treat it like...

<pre>

C = 4.25 * 1000^3 sec^2 * m

---------

kg

</pre>

...it fits my mind and my cal. specified in

meters

Finding individual shell speed for the

penetration data given in the game is no

problem anymore, since

speed_ratio = penetration_ratio^(n/2)

If we simplify that the 780 m/sec are at 100m

we arrive at the following speeds:

<pre>

100m 780 m/sec

500m 736 m/sec

1000m 663 m/sec

2000m 572 m/sec

</pre>

However, the formula used here is probably

nontrivial as the first derivation of speed

over way is not monotonous (spelling in

English?). This may be a result of misusing

the 0m value for 100m, but if we leave it out

we only have two deltas left, not enough to

guess a curve.

So, including your data that the shell loses

12 m/sec on the first 100m we have

<pre>

speed loss/100m

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

0m 780 m/sec

12.0

100m 768 m/sec

10.75

500m 725 m/sec

14.4

1000m 653 m/sec

9.0

2000m 563 m/sec

</pre>

Even less monotonous :-(

[This message has been edited by Martin Cracauer (edited 02-22-2001).]

[Jeff Duquette]

Part of my point is that 790m/s does not appear to be the correct muzzle velocity for 75mmL48 firing pzgr 39. This is why the use of mv = 750m/s seems to work out so nicely with well documented penetration values for the L48 (i.e. 106mm @ 100m @ 30 degrees). I suspect 790m/s is infact a typo that may have originated with Chamberlain's WWII Encyclopedia of German Armour, and has been copied by other authors over and over

As far as the velocity degradation vs range numbers you thrown up, I would have to examine them more closely to see how you are arriving at the degradation values. How is it you are determining the various velocities losses vs. range? Is this simple extrapolation based upon only two numbers? The velocity loss vs range is not typically linear. Its close...but not quite.

[Paul Lakowski]

Originally posted by Matthew_Ridgeway:

Interesting quotes Vanir. And yet there is no mention of Robert Livingston in CM screen credits or CM manual.

Yes Well I can tell you from talking to Robert that he was NOT AMUSED!

As to the formula it ignores the 'L/d effect' and the increasing impact of erosion as striking velocity increases,and theres no reference to the impact that differing nose shape makes .

[Guest Martin Cracauer]

Originally posted by Jeff Duquette:

As far as the velocity degradation vs range numbers you thrown up, I would have to examine them more closely to see how you are arriving at the degradation values. How is it you are determining the various velocities losses vs. range? Is this simple extrapolation based upon only two numbers? The velocity loss vs range is not typically linear. Its close...but not quite.

I didn't have a formula to get the speed value at arbitrary range, but you can simplify your formula to get a speed ratio if you have a penetration ratio. For constant angles, diameter and mass.

(velocity ^2 * Mass * (cosine angle) ^(2/n))/ diameter ^3

= C(thickness of plate/diameter of shell)^n

Throwing out the constants just listed you can say:

speed_ratio^(2/n) = penetration_ratio

That is how I arrived at the four-value speed table I wrote, I derived it from the penetration ratios given by CMBO.

Example:

100m penetration = 141, 500m penetration = 130, penetration_ratio = 1.085. speed_ratio => 1.06. Speed0/100 = 780 m/sec, speed500 = 735 m/sec.

But I still don't have a solution to get the values in between. I can't guess a formula since the values are distorted because I have speed at range=0, but not penetration at range=0. The first penetration is at range=100, where no speed is given.

The penetration goes way up for range much smaller than 100m, BTW, as I can tell from just shooting up King Tigers and Jagdtigers with (lots of) Stuarts.

Martin

[Jeff Duquette]

But I still don't have a solution to get the values in between. I can't guess a formula since the values are distorted because I have speed at range=0, but not penetration at range=0. The first penetration is at range=100, where no speed is given.

Try plotting an entire penetration data set for the 75mmL48 vs. range for 30 degree angle of attack. Go to David Honner’s most excellent web page at:

http://www.wargamer.org/GvA/weapons/german_guns5.html

for actual data if you don’t have a reference with this info available. After plotting the relationship between penetration and range you will see that it looks fairly linear. Now extrapolate back from the 100m data point to 0m. You now have a velocity (muzzle velocity), penetration (from the linear extrapolation) and range (zero meters) for one data point. Back calculate LOG “C” from this. Use this “C” value to back out velocity vs. range from Milne-de-Marre. This is a fairly good approximation of projectile velocity (+/- 1 to 2 percent of actual out to ranges of 2000 meters for high velocity rounds).

Remember that “C” will vary with angle of attack…so if you back “C” out from a 30 degree penetration data set, it wont necessarily work for the same round with a 50 degree angle of attack.

[Paul Lakowski]

Didn't Lorin have a formula for predicting velocity down range based on the MV ?

[Jeff Duquette]

Paul:

I heard from a Bird that R. Livingston was a bit perturbed about the whole thing.

[Jeff Duquette]

PL said:

Didn't Lorin have a formula for predicting velocity down range based on the MV?

Dunno…if he did he didn’t pass it along to me. I emailed him awhile back about back-calculating velocity down range using the method I just described. I think I sent you the same email (but you of course never replied ). Lorrin indicated that his group often backed velocity down range via Milne-de-Marre. From my own calcs, and from actual test fire data that Lorrin snail-mailed me, using Milne-de-Marre for velocity calcs is fairly reliable. As I indicated above the Milne-de_Marre predicted is +/- 1 to 2 percent of actual. Correlation does appear to decrease with increasing range. The point of my email was to determine if this method of backing out velocity was kind-of an exercise in “chasing your own tail”.

[rexford]

Our soon to be finished book will have sections on DeMarre equation use and how to predict velocity at range, with the needed equations and coefficients.

And data on how to compute flight time to target, and trajectory height (so the error involved in guessing the wrong target range can be computed), and dispersion, etc.

Penetration data in our book will NOT be based on the British PENETRATION OF ARMOUR PLATE NPL equation for penetration of armor, since that equation only applies to British armor and varies from the DeMarre equation in terms of penetration-vs-velocity: U.S. data shows that DeMarre is valid.

Besides which, NPL equation is for projectiles with British quality and German ammo was better, NPL is also for solid shot without caps and requires alot of modifiers to get to German APCBC with HE bursters.

Our book will have a section on NPL (National Physical Laboratory) equation, and show how it doesn't match with German and U.S. results when armor hardness is over 375 Brinell Hardness. ALOT of major tanks had hardnesses over 400 Brinell, so NPL equation may not be too good for high hardness without major adjustments.

Right now, CM appears to give German and U.S. ammo the same quality, although German projectiles averaged 61 Rockwell C hardness and American were around 54 to 55 average hardness. Estimate some German penetration figures using DeMarre equation from U.S. 75mm APCBC and results are close to CM figures.

We figure German ammo outpenetrates American and British by about 16%, for same projectile type, impact angle, weight, diameter and impact velocity.

Since 75mmL40 APCBC penetrates 90mm at point blank and 0 yards in U.S. tests, it would be interesting to see an explanation for higher values in CM. Past posts by others brought up issue that U.S. penetration would probably be less than test results, due to alot of factories that were converted to ammo production and may have put out inconsistent stuff.

Our book will present alot of the information that has been discussed or has been sought. And will bring up some previously unpublished, unshared and important factoids on Russian ammo and armor.

The book also presents a case, based on analysis of many test firing results, that German armor was usually equal in resistance to American and British penetration test plate, eeven late war stuff, so penetration tests for American and British ammo can be directly compared to German armor except where "flaws" are likely to occur.

Panther glacis is flawed, rest of tank tends to be equal to U.S. penetration test plate.

The fact is that our book will convert all armor and penetration data to American homogeneous or face-hardened test plate, as appropriate, so direct comparison will be possible.