ID:0054325 Additional - APHE fragmentation and power - addendum

[Godman_82 9,389]

Hello,

 

I would like to publish additional information to already submitted bug reports.

 

The report 0054325 about APHE fragmentation zone was based on T3 HE round fragmentation tests. Although the fragmentation pattern is common for most shells with HE component, where explosive material is formed as cylinder inside the shell, there are differences in velocities of the shell and its fragments, which is affecting the fragmentation zone a lot. Further and more detailed investigation of this case led me to a conclusion, that what I proposed in original report is not correct for most APHE rounds, and could be used only for small percent of them.

 

The report 0054326 about lethality of APHE rounds was based on reports from allied (mostly British) reports about casualties in tank crews. Although I analyzed those reports very carefully, there is few things that missed my attention, and I discovered them later. My first report was submitted in February this year, and since then I’m constantly investigating the case to provide more detailed information, but also to remove any errors and incorrect data from my work.

 

This additional report is made with more emphasis on technical side of the case, and suggestions about ways to implement this complex case into War Thunder damage mechanism in simple form.

 

Fragmentation zone (0054325)

First source I am going to use is the 1943 book by Ronald Wilfred Gurney “The initial velocities of fragments from bombs, shells, grenades”. In his work Mr Gurney tried to find the simple formula to estimate the velocity of fragments of exploding shell, which is in form of cylinder or sphere. Despite it is given for “perfect” cylinder, in the book we find that Mr Gurney is comparing his results to actual ammunition. If we look at the M61 round fragmentation pattern, that I used in previous report, we can see that the top of the round is not fragmented, and the rest of the projectile is very similar to cylinder. The formula is very simple and the we can say that results are “estimations” rather than precise calculations, but that is all we need here. I can point out that even in books from 1970s Gurney equations are still considered as very good and reliable way to estimate the velocity of fragments.

ADA289704.pdf

 

The equation itself is very, very simple. We need few values:

M - the mass of the cylinder, in other words - metal around HE filler. The HE cavity in most cases is about half of the length of the projectile, so I am suggesting using half of the mass of the projectile. Although the M61 round, which weighs 6800 grams, was all fragmented except the tip (estimated weight 2000 grams), so the fragmented part was 70% of the round, and German and Soviet APHE was using explosives with higher brisance value (ability to fragmentate), so even higher percent of the round could be used as cylinder weight. But 50% should be minimum and safe value.

C - mass of the explosive filler. Note - real mass, not the TNT equivalent

√2E - value attributed to explosive type, we can find it in literature. This is roughly ⅓ of explosion velocity. It is also labelled as V₀ and I am going to use this designation.

 

The Gurney equation for cylinders:

 

V_I = V₀  * (M/C)^-½

 

For example:

 

88 mm PzGr 39.

M = 5000 grams (half of 10 kg mass of whole round)

C = 64 g

V₀ = 2930 m/s (PETN value used)

 

V_I = 2930 m/s * (5000/64)^-½ = 330 m/s

 

As You can see, it’s very simple way to estimate the velocity of the fragments.

 

In the table You can find fragments velocity for popular rounds:

https://docs.google.com/spreadsheets/d/1cz9dkehFKm5cQJBsXE9Enk0VRT-F6BzldgNs9g07Rfc/edit?usp=sharing

 

But this value alone is not giving us anything yet. We need to find the velocity of the round after penetration. Only knowing both velocities we can see how the fragmentation zone would look like.

 

For this, I’m going to use another source - British report "ADM 213/951 - German steel armour piercing projectiles and theory of penetration". In section 10.16 (page 85) we can find an explanation, that calculating remaining velocity is nothing more than finding the difference between striking kinetic energy and the minimum energy needed to penetrate the armor. To be precise V_H which is used in original equation is the “minimum velocity to penetrate the armor while round remains intact”, but not all round are suffering from shattering close to their maximum penetration, and even if they are, the difference between “minimum velocity”, and “minimum intact velocity” is negligible.

Spoiler

 

All 3 KE values (before penetration, required for penetration, after penetration) are using the same value for mass, so the equation can be simplified only to squares of velocities.

 

V_R = (V_S² - V_M² )^0,5

 

V_R - remaining velocity

V_S - striking velocity

V_M - minimum velocity (ballistic limit)

 

The required velocity needed to penetrate the armor is something that we are already familiar with - ballistic limit. We don’t have this value in War Thunder, but we know at which distance the round will penetrate exact thickness of armor. To find the velocity we will use the well known De Marre equation. At first, it looks very complicated, but soon it will be very simple formula.

 

First, the original De Marre equation:

 

P= rP * (V / rV)^1.4283 * (D / rD)^1.0714 * (W / D³)^0.7143 / (rW /  rD³)^0.7143

 

Lot of numbers and symbols. Let’s divide it into sections:

 

P - penetration value we are looking for

rP - reference penetration, so penetration value that we already know

(V / rV)^1.4283 - V is the velocity for which we want to calculate penetration, and rV is reference velocity - for this one we know the penetration value

(D / rD)^1.0714 - this part includes change in round diameter. We are talking about the same round, so D = rD, and the whole part = 1, so we can ignore it.

(W / D³)^0.7143 / (rW /  rD³)^0.7143 - weight (W) is the same as reference weight (rW), so W/D³ = rW/rD³, so again, this whole part =1, and we can also ignore it.

 

For this case De Marre equation is just:

 

P= rP * (V / rV)^1.4283

 

In War Thunder we know penetration values, but we don’t have velocities, except muzzle velocity. We need to convert this formula, so we can calculate velocity from penetration values.

 

Converting:

 

P= rP * (V / rV)^1.4283 | /rP

P/rP = (V / rV)^1.4283 | ^0,7

(P/rP)^0,7 = V/rV | *rV

 

V = rV*(P/rP)^0,7

 

In War Thunder we only have muzzle velocity, so only this value can be our reference (with maximum penetration as reference). But that is enough.

 

We can use that formula for calculating both striking velocity, and minimum velocity. For striking velocity we will use calculated penetration power for particular shot, while for minimum velocity - armor thickness value that was attacked.

 

V_S = V_Muzzle*(P_S/P_Max)^0,7

 

V_M = V_Muzzle*(P_M/P_Max)^0,7

 

Now we can easily calculate the remaining velocity after penetration.

 

The original equation

 

V_R = (V_S² - V_M²)^0,5

 

V_R = ( (V_Muzzle*(P_S/P_Max)^0,7)² - (V_Muzzle*(P_M/P_Max)^0,7)² )^0,5

 

V_R = ( V_Muzzle² * P_S^1,4 / P_Max^1,4 - V_Muzzle² * P_M^1,4 / P_Max^1,4)^0,5

 

V_R  = (V_Muzzle2 / P_Max^1,4 (P_S^1,4 - P_M^1,4))^0,5

 

 

V_R  = V_Muzzle / P_Max^0,7 * (P_S^1,4 - P_M^1,4)^0,5

 

 

Where:

V_R - remaining velocity

V_Muzzle - muzzle velocity

P_Max - point blank penetration at 90 degrees

P_S - penetration value at given range at 90 degrees

P_M - armor value (this must also include slope modifier)

We established quite simple formula, that is only using values we already have in game.

 

Example

We are shooting with Tiger 1 to our favorite KV-2 with his perfectly flat side turret armor of 75 mm (this is minimum penetration value). Point blank penetration of Tiger 1 PzGr 39 is 165 mm (our maximum penetration), with muzzle velocity of 773 m/s

We are shooting from 1000 meters, so the penetration value drops to 138 mm (this is our striking penetration)

Remaining velocity:

 

V_R = 773 / 165^{0,7 *} (138^1,4 - 75^1,4)

 

V_R=517 m/s

This value could be also used in the future to determine the exact distance after which the HE filler will explode, if Devs would ever decide to change current simplified model.

 

Now we have velocity of the fragments after HE explosion, and also the velocity of the round after penetration. Take again a look at HE explosion pattern. Tested T3 HE round was traveling with 1085 ft/s, so 331 m/s. Thanks to Gurney equations we can easily calculate that fragments - 771 m/s. The side spray of this particular round is directed a little bit to the rear, what is visible on the fragmentation pattern of stationary round. This is negligible detail, but just this once I will include it into calculating the example, to prove the equations.

 

Stationary explosion:

Spoiler

Vectors of forces - red is force of explosion, green - round's inertia

Spoiler

 

 

I will set 96 degrees as angle of side spray.

Side spray is accumulation of two forces - fragmentation and round inertial.  If we divide the original spraying vector (fragmentation force) we have two vectors - one pushing fragments to the rear (771 * sin(6) = 81 m/s) and one pushing to side (771 * sin(84) = 767 m/s), and rounds inertia is pushing the fragments to the front with 331 m/s. Rear and front vectors are reducing into one, going forward with 250 m/s, and the side vector remains. Joining those two vectors we have one vector, with 807 m/s power, and 72 degrees angle.

 

Looking at the pattern of round with velocity we can see it’s 74-75, while averaging from document we have 73,5. I think it is close enough to call it a reliable method of calculations.

Spoiler

 

 

 

Calculating fragmentation zones

In my original report I divided the zones into 3 - frontal, side and rear. For HE rounds it is correct, as the fragments velocity is much greater than the round velocity, so fragmentation pattern is only little affected by the rounds velocity (as seen in pictures above). But when it comes to APHE rounds, most of the times the fragments velocity is smaller than remaining velocity of the round, especially when penetrated armor is 70% of the round penetration value, or less. That means that forward vector is bigger than side vector, and the angle of side fragmentation will be even less than 45 degrees. In this case there is no point in detailing the fragmentation into very narrow frontal zone, and just a bit bigger side one. We can join those two zones, into one zone, which would be in a form of simple cone, just like the cone after penetrating the armor. The cone of the angle would depend on both calculated velocities - fragments and round. The cone of the angle is very easy to calculate

 

α= arctan(V_I / V_R)

 

We have already calculated velocity of the fragments for 88 PzGr 39 (330 m/s), and its remaining velocity after penetrating flat armor of KV-2 (517 m/s). Using ArcTan function we have 33 degrees angle, which gives us a cone of shrapnels with 66 degree angle.

 

In the table we have remaining velocities for popular rounds, striking against armor equal to 50%, 70% and 90% of the round penetration value at 500 m distance, and calculated the cone of fragments for given scenarios.

https://docs.google.com/spreadsheets/d/19VefXCNMWBOdhObwbzdCmbeJnhkebaviLRPZp6nlXmw/edit?usp=sharing

 

 

We have one zone left - rear zone. For HE round this is quite important one, for APHE - not very much. Mostly because fragments velocity is smaller than round velocity, so it’s not possible for any fragment to fly backward. Fragments velocity must be significantly faster for back fragmentation to be possible. We know the velocity of fragments for a few rounds we have already calculated.

 

Basing on remaining velocity of example penetrations, we can see that for most rounds rear fragmentation is not possible, or very questionable. Rounds like PzGr 128 mm from Jagdtiger have quite big fragments velocity (575 m/s), but also the remaining velocity is bigger than assumed 400 m/s (after penetrating 150 mm or armor from 500 m the remaining velocity is 590 m/s). There is just a few rounds with velocity of the fragments that is big enough to send fragments everywhere, no matter what is the remaining velocity. Some of them have fragments traveling faster than the round muzzle velocity.

 

My suggestion is to divide all APHE rounds into two groups:

 

 

 

Big APHE. Those are the rounds with heavy HE filler and high C/M ratio. Those rounds are most probably completely destroyed by explosion, making it possible to “fill the tank” with fragments. For those rounds current damage model is correct, and should not be changed. Most obvious examples would be 152 mm PB-35 round, or 130 mm PB-46A.

 

Big APHE type is not requiring any changes to game code (except “marking” the type of the round), so let’s focus on programming suggestions for standard APHE rounds.

 

 

 

Standard APHE. Those rounds are not capable of spraying the fragments to the rear, and because of low fragments velocity, the round inertia is the major force, pushing all fragments to the front. In those cases HE filler only spread the fragments into cone, with angle dependent on remaining velocity, but in most cases the angle will be less than 90 degrees (2x45).

 

Spoiler

 

All equations and formulas I have posted are quite simple and easy to implement, but I can understand that Devs might want to save the computing power of the servers by using some average/standard values. Therefore I am suggesting 3 ways in which the fragmentation for Standard APHE be handled. In my opinion the second one is optimal, because it’s not including dynamic calculations, while making every round unique and historical, when it comes to damage.

 

1. Simple static version - set one angle for all rounds, without calculating fragments velocity or remaining velocity. In my opinion it would be good idea to use the average value of angle, where armor value is 70% of penetration value - for rounds I have calculated it is 33 degrees.

 

Required work:

• dividing all APHE rounds to Big APHE or Standard APHE
• changing the fragmentation zone for Standard APHE from sphere to cone with about 65-70 degrees angle, static value, common for every round

 

2. Detailed static version - calculate fragments velocity and average remaining velocity for every round, and therefore individual angle of cone for every round, still as a static value.

 

Required work:

• dividing all APHE rounds to Big APHE or Standard APHE
• assigning static value of cone angle to every Standard APHE round
• changing the fragmentation zone for Standard APHE from sphere to cone with angle assigned to particular round

 

3. Dynamic version - calculate remaining round velocity for every shot, and then calculate angle of cone from static fragment’s velocity value, and dynamic remaining velocity. This variant would also enable changing fuse delay value from static to dynamic.

 

Required work:

• dividing all APHE rounds to Big APHE or Standard APHE
• assigning static value of fragment’s velocity to every Standard APHE round
• for every successful penetration of Standard APHE round, calculate the remaining velocity using the formula:
  V_R  = V_Muzzle / P_Max^0,7 * (P_S^1,4 - P_M^1,4)^0,5
• changing the fragmentation zone for Standard APHE from sphere to cone with angle calculated using formula:
  α= arctan(V_I / V_R)
• optionally: assign historical fuse delay to every APHE round given in milliseconds, and calculate the exact distance after which HE filler should explode

INCREASING LETHALITY

From my observations there are two groups of WT players. One group care more about the gameplay and just want to have fun by playing the game, and does not care too much about realism and historical facts. The second group is very much interested in historical accuracy of the game. Those groups have often different opinions about features and mechanics of the game. But there is one thing in which almost all WT players are agreeing - they all are very appreciating the ability to knock out the opponent with single shot. The first group (“gamers”) likes the powerful damage output of their guns, while the second (“historicals”) sees it as simulation of real events from WW2, where tank was abandoned by the crew after first penetrating hit. By changing APHE fragmentation into cone, this highly valued feature of War Thunder will be limited. 

 

Therefore I am recommending two additional, simultaneous changes to neutralize the smaller volume of fragmentation zone.

Those changes will largely balance all other rounds, increasing their post penetration effects.

 

1. Remove the “wounded” state for tank crew.

Tanker affected by any amount of fragmentation (from penetrating round, or HE explosion) should be considered to be “out of action” immediately. Change should be universal for all round types in the game. Simple rule - wounded tanker is out of action, no matter how small or big the wound is.
 

2. Increase the chance to ignite ammunition rack to 100% for direct hit (by any round).

Historically speaking all means used to prevent ammunition from burning - armored bins, wet stowage, were practically useless against great power of the round body. After penetrating, round (as we could see in post penetration velocity calculations) still have a huge amount of kinetic energy (plus huge temperature from friction), and is able to penetrate the other side of the tank, so penetrating through ammunition was more than sure, and the penetration force, along with huge temperature inevitably ignites propellant cases, and produces overwhelming fire in the fighting compartment. The “hitpoints” system for ammo rack should be used only for fragments. Different amount of hit points could very well simulate tanks using armored bins or wet stowage.

 

 

 

As You can see, all my proposed changes are really simple, and require relatively small work. No new features are needed. The level of detail in calculating fragmentation cone for Standard APHE is only upto Devs decision, but any option will make a huge change in favor of balance between different round types. Increasing lethality of all rounds by disabling all affected tankers, and igniting the ammunition with every direct hit. Those are vital changes, as they will neutralize the negative effect for APHE rounds, while making all other rounds more powerful and more capable of destroying the enemy with a single shot.

 

CONCLUSIONS

 

The positive effects of the proposed changes:

• correct and realistic damage output of the APHE rounds
• much more balance between AP and APHE rounds - second cone of fragments will still make APHE rounds more effective, but in far more balanced and historical way
• rounds without HE component will have bigger chance in defeating the enemy with single shot by disabling more tankers and detonating ammunition with direct hits - a changes that will also benefit APHE rounds
• remove the problem with destroying a tank by shooting its cupola by Standard APHE round
• decrease the problem when low penetration APHE round is “thrown into” greatly armored tank through MG port - the penetration still will be possible, but the effects of such penetration can be smaller
• arrange projectiles types in more accurate and historical order - AP and APHE working against medium armored tanks from WW2, APCR against heavily armored tanks, but not efficient against sloped post war vehicles, APDS as upgrade of APCR in terms of high obliquity armor, and HEAT-FS and APFSDS as most modern, very powerful and most deadly rounds

 

 

 

 

Thank You

 

I want to thank @BPNZ for providing information about ADM 213/951, it made my work a lot better and easier  

 

[KnightoftheAbyss 3,387]

Hi Godman_82

                      If this is relating to two different reports that you want the additional information attached to, then please separate them into two reports.

As per the guidelines.

Quote

Please, follow "One Issue = One Thread" rule (do not post DIFFERENT / ISSUES THAT LOOK SIMILAR in existing threads, or start a topic about multiple issues).

 

Also, the first one. - Fragmentation Zone (0054325) reads more like this is your idea of how the Developers 'should calculate' a penetration value.   This would appear to be more a 'suggestion' than additional information on an existing report.  I will read the other report (ID:0054325|) and see if it interlinks better.

 

[Godman_82 9,389]

The fragmentation zone have nothing to do with penetration mechanism. I made estimations about post penetration velocity of the round, to calculate the angle of cone of fragmentation (along with fragments velocity from explosion). Main point was that for majority of APHE rounds it's not possible to send fragments backwards or straight to side, which is happening right now.

 

The formulas and equations are indeed just a suggestions how the issue can be handled, I also suggested the solution without dynamic calculations, but still the main idea is that the round can not send fragments all around itself (except few rounds with massive HE filler, which I also pointed out).

 

Let this thread be for 0054325, I will edit (delete the 0054325 part) this one, and create another topic.

 

 

[KnightoftheAbyss 3,387]

I can separate them.. I just needed to be sure that what I 'thought' was the situation was indeed the case before splitting the document.

 

That was more for future use.  The storage system that Gaijin uses is very much issue based thus multiple issues attached to one report, can cause problems or be mistranslated etc.

 

[Godman_82 9,389]

OK, thank You. May I ask to put "Conclusions" section to 0054325? Or both, if that's OK.

[KnightoftheAbyss 3,387]

Yep, that's fine.