Slope Multiplier Equations

[eliw00d]

Hello,

I recently came across a copy of WORLD WAR II BALLISTICS: Armor and Gunnery, and had a few questions.

In the book, there is a section for HVAP and APDS slope multiplier equations as a function of angle. However, when I try to use the equation for 76mm HVAP, I end up with incorrect results (when compared to some of the data found here in the forums and elsewhere in the book).

For example, trying to convert 100m penetration @30° (192mm) to 100m penetration @0° results in ~149mm, which is far less than the figure posted in the book (239mm).

I found a post here in the forums where rexford was talking about 76mm HVAP versus Panther lower front hull, and how it had a slope multiplier of 3.3 at 55°. Using the equation given in the book, I end up with a slope multiplier of 0.85, though.

So, are the HVAP/APDS equations in the book wrong? I've had no problems adapting the other formula for AP, APBC, and APC/APCBC.

Also, how would one determine the slope multipliers for German, Soviet, and other APCR rounds? I couldn't find any equations for those in the book, but I may have missed it.

I am trying to create a more realistic armour and penetration system for a game, and if there are any other resources besides this book that could help, please let me know! Thanks!

[Thomm]

If a shell penetrates a 192 mm thick plate at 30 degrees between shell velocity vector and surface normal, then it actually travels through 192 mm / cos(30) = 221.7 mm of material.

This is pretty close to the number you found in the book (239 mm).

Best regards,

Thomm

[Redwolf]

If a shell penetrates a 192 mm thick plate at 30 degrees between shell velocity vector and surface normal, then it actually travels through 192 mm / cos(30) = 221.7 mm of material.

This is pretty close to the number you found in the book (239 mm).

Best regards,

Thomm

That's not how WW2 ballistics work, they react to slope worse than cosinus. Things only improved and got closer to "line of sight thickness" with the very slim (almost point shaped) DU rods in later 20th century tank gunnery.

You of all people should know that.

[Thomm]

Redwolf,

This is what the guy posted:

For example, trying to convert 100m penetration @30° (192mm) to 100m penetration @0° results in ~149mm, which is far less than the figure posted in the book (239mm).

He gets 149 mm, but wants 239 mm. With just the "LOS thickness", I get a number of 222 mm, which is much closer to the desired result. So we moved from an error of -38 % to an error of -8 %.

Since the 222 mm (LOS) are smaller than 239 mm (actual value?), they are consistent with what you wrote (penetration being worse than pure LOS thickness for angled plates).

Not sure what your problem here is.

Best regards,

Thomm

[eliw00d]

@Thomm

I appreciate your response, but unfortunately it is not what I am looking for. I am trying to find the formula/equation used to get the figure in the book. Using the formula for shell types dependent on the T/D ratio, I am able to get figures nearly identical to those in the book (no more than 2% error in most cases). Here are the ones presented in the book:

Slope Effect at Angle = a * (T/D)^b

Where a and b are given in a table, depending on angle and shell type.

76mm HVAP

Compound angle equals 0° through 25°

1.0000 * e^(A * 0.0001727), where A = (compound angle)^2.20

Compound angle greater than 25°

0.7277 * e^(A * 0.003787), where A = (compound angle)^1.50

Edit: Just realized after typing this that I must have fat-fingered 0.003787 as 0.0003787. I am now getting ~260mm, which is a bit higher than 239mm, but closer than ~149mm. Any thoughts as to the reason for this margin of error?

[Thomm]

I appreciate your response, but unfortunately it is not what I am looking for.

Ah, okay, after re-reading your post this is painfully clear.

Unfortunately, I do not have the answer to your actual question.

Best regards,

Thomm

[eliw00d]

@Thomm

No worries, I appreciate you taking the time to answer, anyways. At one point we were using a similar approach, with cosine, but after looking through this forum and the book we realized that it is not that simple for higher angles.

I edited my post above with a few additional remarks, though.

Edit: Also, any thoughts on where to find equivalent formulas/equations for German and Russian APCR? It's strange that the section on slope effect has no mention of either.

Edit: I should point out that I took the table of a and b factors from the book and created best-fit trendlines in Excel and am using the equations from those to extrapolate data at the different angles. If there is a better way, let me know!

[Redwolf]

Redwolf,

This is what the guy posted:

He gets 149 mm, but wants 239 mm. With just the "LOS thickness", I get a number of 222 mm, which is much closer to the desired result. So we moved from an error of -38 % to an error of -8 %.

Since the 222 mm (LOS) are smaller than 239 mm (actual value?), they are consistent with what you wrote (penetration being worse than pure LOS thickness for angled plates).

Not sure what your problem here is.

Best regards,

Thomm

WW2 rounds do not perform as line of sight indicates (which you get from doing cosinus). So you arrived at a wrong value which somehow also made it into the book.

To make round perform closer to what line of sight thickness indicates you must have a thin rod projectile that disgards the sabot (HVAP with aluminium mantle that stays on doesn't count), but you also need a hard, scatter resistance core such as DU, not a soft one such as tungsten.

Any WW2 values that confirm to LOS/consinus to angles like 30 degrees are guaranteed to be erroneous. It's basic physics.

[Thomm]

eliw00d,

I think you are converging on the correct solution. Your new slope multiplier ...

Edit: Just realized after typing this that I must have fat-fingered 0.003787 as 0.0003787. I am now getting ~260mm, which is a bit higher than 239mm, but closer than ~149mm. Any thoughts as to the reason for this margin of error?

... now fits to an old post made by Rexford:

From http://www.battlefront.com/community/showthread.php?t=991:

U.S. and British data give differing views on the slope effects of APDS and HVAP, and the main projectile difference causing the differences would probably be nose shape.

Were the nose shapes on the British 17 pdr APDS and U.S. 76mm HVAP rounds similar or different? Both rounds had 3.9 pound cores with 38.1mm diameter.

The following is a comparison of slope multipliers that convert angled hits to an equivalent thickness of vertical armor:

76mm HVAP

1.35 at 30 degrees from vertical

2.26 at 45 degrees

4.24 at 60 degrees

17 pdr APDS

1.23 at 30 degrees from vertical

1.82 at 45 degrees

3.51 at 60 degrees

For British 37mm APDS (an experimental round), the penetration vs angle curve results in the following slope multipliers:

37mm APDS

1.39 at 30 degrees from vertical

2.01 at 45 degrees

4.01 at 60 degrees

For both sizes of British APDS, the slope effects at 45 and 60 degrees are lower than U.S. 76mm HVAP. This suggests that the 45 and 60 degree slope effects may have been a function of nose shape, but a comparison needs to be done.

At Isigny, 17 pdr APDS made it through the Panther glacis with an impact angle of 57 degrees from vertical due to ground tilt. Applying the British slope multiplier for 17 pdr APDS to 82mm at 57 degrees results in about 2.9 x 82mm or 238mm vertical, while the 76mm HVAP slope effect would result in 82mm x 3.6 or 295mm vertical.

Based on British data, 17 pdr APDS could penetrate 238mm vertical at about 900 meters and could not penetrate 295mm vertical at any range.

With regard to 17 pdr APDS against Panther, it might be useful to halve or third the APDS that is given to British tanks and TD's with 17 pdr guns due to the following factors:

1. rounds were erratic in behavior and often failed to hit known targets at known ranges during firing trials

2. rounds were erratic in behavior and might fail against a given plate one time in a test and then succeed at a much lower velocity

3. Panther glacis quality is not 0.85 for all tanks but really was quite random.

Best regards,

Thomm

[eliw00d]

@Thomm

You are right! A slope multiplier of 1.35 @30° results in an effective penetration of 259.2mm @0°, just shy of the 260mm I am getting. But, that raises the following question: why does the book give a figure of 239mm @0° at a range of 100m?

The book is a wealth of information, but unfortunately it is kind of a mess.

[eliw00d]

Hello again!

Are there any other equations/formulas that one can use to figure out the effect of slope for different World War II ammunition (including tungsten)? Last year, I tried to adapt as much as possible from the book, but there are a lot of holes and the data I end up with does not always match the book. Any help would be much appreciated!

If there are any other books or sources you guys recommend, that would help, too.

Edit: I use tarrif.net as a source for penetration data, by the way.

[Vanir Ausf B]

If you don't find what you're looking for here you might want to try TankNet or GameSquad forums. Specifically, you want to talk to Mobius. He also hangs out on the Matrix Panzer Command Ostfront forums (he worked on the game).

[eliw00d]

I will try those forums as well, thanks for the suggestion!

I should point out that these equations are being used for a game mod, where we are trying to make a realistic armor and penetration system.

[eliw00d]

In the book, there is the following:

HEAT is the only WW II ammunition where slope effects appear to follow the T/Cosine equation, effective resistance at 0 equals the plate or cast thickness divided by the cosine of the angle from vertical.

Would lateral angle be factored in to effective resistance against HEAT, such as when angling armor? Such as impact angle = acos(cos(lateral) * cos(vertical))?

[Michael Emrys]

Would lateral angle be factored in to effective resistance against HEAT, such as when angling armor? Such as impact angle = acos(cos(lateral) * cos(vertical))?

You betcha! Fire was almost never received exactly straight on.

Michael

[Vanir Ausf B]

Would lateral angle be factored in to effective resistance against HEAT, such as when angling armor? Such as impact angle = acos(cos(lateral) * cos(vertical))?

I think it would have to be if angle is considered at all. But I have not looked into the effects of HEAT much.

[eliw00d]

Thanks, guys! I figured it might, but the book didn't mention it so I wanted to make sure.

The book also doesn't seem to give any formulae for German or Soviet APCR, just American 76mm and 90mm APCR (and I think British APDS). Do you guys know of any sources for those, possibly with formulae?

Also, is there more information out there on how to apply BHN, high hardness, flaws, etc?

[John Kettler]

eliw00d,

Maybe this'll help.

Specification and Penetration of Soviet Tank Guns. Extensive!

http://english.battlefield.ru/specification-and-armor-penetration.html

Here are the actual penetration curves (1944) for Russian tanks (Lend-Lease included) vs various German armor through the Ferdinand. Data taken from live fire tests.

http://english.battlefield.ru/armor-penetration-curves.html

And this provides the basic armor penetration equation used by the Russians.

http://english.battlefield.ru/projectile-armor.html

The site, before a ruinous server crash years ago, used to have, in English, a very detailed breakdown of antitank projectiles and how they worked. If it still exists, it hasn't been translated yet and is in Russian.

Regards,

John Kettler

[eliw00d]

Thanks! I will definitely look these over. I feel like I've looked at this site before, but never bookmarked it. The ROF information is a nice bonus.