Gun over penetration needed to kill a tank.

[Last Hussar]

Good afternoon.

If a gun has penetration P, and armour effective thickness of A,

What would be a reasonable relationship between those two figures where the tank would be a "platform kill" 50% of thee time (ie k/o, crew dead, crew abandon battle etc)

For example; P + x% >=A

I realise that there a myriad of factors, but I need to pin down figures I can generate game stats from .

Thank you.

[fred.]

Most rules seem to separate out the hit, the penetration and the effect.

I'm not sure guaranteed penetration always means a kill. If you take the extremes of AT rifle vs 88. With light armour the AT rifle may happily penetrate, but it's not going to blow the tank up. The 88 is going to do both.

But against heavy armour, the 88 may just penetrate but it's going to cause a lot of problems for the tank (and crew)

For straight penetration, I'd be quite happy to have the 50% chance at P=A

[steve_holmes_11]

I've no data for tanks, but wonder whether the sort of over-penetration that goes in one side and out the other (Causing little damage) was a thing.

There are several accounts of WW2 destroyers taking hits form 6" or larger guns that left two holes but did little damage.
Understand that such accounts are extremely prone to survivor-bias, but it certainly happened.

[Orcs]

There were certain instances of overpenetration.  It isn definitely a factor.

i know from experience that if you can shoot a coke can with a high power air rifle and  the pelet can go through the can without knocking it over.  A low power air rifle will always knock it over. Its about the kinetic energy imparted onto the target.

So i think you are over thinking things. Just as thier are overpenetrative shots that may pass through with little or know damage, a shot that does not penetrate can take a tank out just as surely as blowing it up. - Jam the in turret ring so the turret does not traverse, Taking out the optics, or a common problem with the Jagdpanzer lV was dislodging the gun off the mount.

Even a burst of MG fire hitting the commander could take a tank out for the time frame in a game, just while the est of the crew deal with the wounded comander , or even the grisly remains all over them and the inside of the tank.

Just give all A/T guns a chance of taking tank out of the battle , the better guns get a better chance.

[Last Hussar]

I've got all the data, I've got all the mechanics. What I don't know is if the armour is effectively 'A' mm thick, what mm of penetration is needed to give a 'combat' kill.  It doesn't have to be BOOM, just enough damage to stop it fighting - be it Main gun out, so it leaves combat, or crew dead, or whatever.

For Info - because it is part of my delayed resolution game you don't find out immediately. If you hit, you mark the hit with PEN value.  It is only when that tank next activates you roll for any hits on it- each hit seperately (there is an obvious immediate kill mechanism in addition).

In game terms a 69mm penetration in real world is a PEN of 7. Statistically in my mechanism that will kill ARMOUR 4 50% of the time. So is ARM4 approx 60mm?

Just give all A/T guns a chance of taking tank out of the battle , the better guns get a better chance.

The problem with that is it is a matrix - Along the top I have PEN, down the side ARM.  6pdr > 2pdr
BUT
6pdr v 30mm armour > 9pdr v 50mm armour

[sultanbev]

Here we go, another essay 
A lot of wargames rules have got this wrong in the past, because they assume the difference between penetration and armour is a % chance of a KO.
There are so many variables that not having a separate dice roll for KO once you've penetrated wouldn't be doing it any justice whatsoever.
There are many photos of Shermans with 4-6 holes in their hull fronts ie the much vaunted PAK40s and 88s often needed multiple hits to kill tanks, even when each one penetrated. Doctrine for 88mm flak guns was to fire 2-3 shells at the target, regardless of outcomes, before moving onto the next target. And at 700m range or so.

Overmatch and Over penetration are two other factors to add in as well (more later...)

The reason it is often worked out wrong is because it is often assumed that kinetic energy (KE) is the onlyparameter in town, when momentum and moment of inertia are also factors.
There was a fiction that did the rounds for a bit in the 1980s that the T-74 (sic) was so good with it's 1650m/s 125mm FSAPDS round that even if it didn't penetrate our beloved Challengers, it would simply rip the turret right off.    Baloney of course.

KE does count for a lot, but after you've spent most of that penetrating armour, sheer momentum counts for more as far as I'm concerned. Momentum = mass x velocity compared to KE's mass x velocity x velocity. Put plainly a big lump of lead whizzing around inside your tank is going to do more damage than a small lump of lead. Although both can be lethal.
Shell mass is nearly always directly proportional to gun calibre (for full bore rounds like AP, APHE, APC, APCBC, HE) so you can simply derive a system, that once you do penetrate, regardless of how much higher your penetration is over the armour, the chance of KO is directly related to gun calibre. To add nuance, in my own rules, to reflect the moment of inertia bit, I compare the calibre to vehicle weight, it becoming increasingly harder to KO as the target gets heavier, and easier at lighter weights.

The classic example of the latter is the Tiger I. At 56t but with 11cm frontal armour, it was grossly under armoured, the Soviets got more armour on a 47t KV tank. The Matilda II was only 2cm less all round on half the weight. And yet, the Tiger I is reknown for being difficult to knock out. Basically, the Tiger 1 was over-engineered, but that gave it an inherent toughness not really brought out by it's armour values. Much in the same way that the C-47 was over-engineered and still in service around the world. The Centurion is another example - post war it was a tough tank, but in comparison to it's peers it was thinly armoured, on paper. In the Centurion's case it was because it was a large tank, with high internal volume.

What is overlooked is if you take two armour plates, both the same metallurgy and thickness, but one larger in area than the other, then fire 10 identical shells at each, the larger plate fails later than the smaller one. It's to do with the way the atoms transfer the energy of impact across the plate, before reaching the weld seams or structural supports. So a larger glascis plate that is penetrated, eg Centurion or Tiger II, is going to be tougher than a smaller plate eg T-55 hull or Is-3. The differences might be small in % terms, which is why I use a D20 kill system.


Complicating factors:
Overmatch.
For larger calibre guns, over 75mm I think, if the thickness of the plate is less than the diameter of the shell, then overmatch occurs, whereby, especially for angled armour, the shell basically crushes the armour, even if it can't in theory penetrate. So you don't necessarily knock the tank out, but it's left with a gaping ragged hole in the plate through which the next shell is gonna pass through. Time to bale out! Panthers hit frontally by 152mm guns on ISU-152 are an example of this.

Overpenetration.
This occurs where high velocity shells hit very thin armour. If the armour is so weak that it doesn't set the fuze off of your APHE round, the shell often passes right through, out the other side and just adds to the air conditioning, unless something vital is in the way, such as the engine or the gunner's arm. In my rules I rules this as any gun with 6cm penetration or greater hitting armour of 1cm passes straight through on a roll of 1-6 on the D20, even if in theory you might be on 3or more to kill. The classic example of this is Shermans against Type 95 in the Pacific islands.

High explosive ammo.
Not gonna go there too much, but in simple terms, HE rounds of 75mmL40 or more can penetrate armour 1-3cm thick. So against light armour 75mm or bigger HE can be treated as APHE with a much bigger bang inside the target. It goes without saying of course, HE fired at tanks that you cannot penetrate will always have a chance of doing some external damage, as well as a chance of doing nowt whatsoever.

Sub-calibre rounds.
APCR, HVAP, APDS, these tend to be about 25-60mm in diameter, perhaps 60% of the actual gun barrel calibre. For simplicity's sake, I say the extra velocity counteracts the decreased shell mass, so you can treat these rounds as the same their full bore bretheren for the purpose of actual knock out rolls.

Unfortunately I can't paste in here my D20 damage chart to show you how it works, so I've manually pasted in a couple of lines
Here are the categories
target weight:               1-5t   6-10t   11-15t 16-20t    21-34t   35-40t   41-50t   51-59t   60-69t   71-100t
gun calibre:
Rifle                            12            13             18       18            20               22         23        24       25        26 (D20 to KO)
11-14.5mm
15-25mm
28mm sPzB41
30mm
35mm
37mm AP
2pdr AP
37-42mm
45-47mm
50-60mm
65mm
70-82mm                       5               6               8     8               10                 12           13              14            15                  16 (D20 to KO)
83-90mm
88mmL56-L71
94-100mm
102-115mm
117-126mm
127-134mm
135-145mm
146-155mm
158-160mm
162-175mm
176-190mm
193-205mm
210mm

So, towards some kind of formula:
it sort of works out at half the calibre in mm, that is the target weight at which you have 50% chance of kill. in the front. +/-5% per 5ton difference-ish.
So a 75mm gun, if it penetrates, has a 50% chance of KO against a tank of 37t, in the chart above that'd be all those 35-40t tanks. a 25t tank would be about 60%, a 41-50t tank 40%, a 51-59t would be 30%.
An Su-100 would have 50% chance of KOing a 50t tank, 40% chance of a 60t tank, 70% chance of a 30t tank.
A 25mm anti-tank gun would have 50% chance of KOing a 12t tank, 40% of a 22t tank, 30% of a 32t tank, 60% chance of a 2t tank.
And so on.
That's only a rough layout, my chart is a little more varied than that at the outliers, but if gives you ballpark figures which you can adjust up or down as you like, from which you could make a chart, perhaps reducing it to a D10 or 2D6 system. I wouldn't recommend a single D6, no probabilities in warfare are calculated in 16% intervals.

You could, for example, just divide targets into light, medium and heavy at 1-20t, 21-39t, 40t+

Modifiers that I use:
In the sides it's 15% better, in the rear 25%. I also have that if you roll over 20% more than required, it brews up the tank, if you roll 40% over, it blows up.
Also, if the armour equals the penetration, then I reduce the kill chance by 20%. HE that actually penetrates gets +20%. A natural 1 on the D20 is always a dud, 1-2 for HEAT rounds, and 1-3 for Panzerfausts. {It was shown after the war that 18% of Panzerfausts, and about 11% of Panzershreck rockets were duds due to slave labour sabotage}
One modifier I have but forget to use is a +10% for guns L60 and above, representing extra damage capability of higher velocity guns.

{Also, note I only use centimetres of armour, not to the exact mm. if you've ever touched the surface of tank, the finish is so rough that a +/-2mm variation would be quite normal, so quoting to the exact millimetre is a good way to induce phycosis.  I too use a 69mm penetration rounds up to 7cm. I also normalise everything to vertical armour, but that's a separate story.}

This D20 kill system I use has served me well for over 35 years, and no users have complained. By using 5% intervals (the D20) you can add in subtle modifiers for special weak/potent guns that don't throw the whole game balance. It gives that extra flavour of difference between different vehicle types. Some people like that kind of thing, some people don't, but I hope this all helps.

[Norm]

Very interesting - thanks for the detail.

[Lord Kermit of Birkenhead]

The only way to get anything like accurate figures is to find sets of range test figures. Even then there would be variations due to differences in propellant and even in the metallergy of the shot. The angle of impact will also play a part, causing skiding if it's very accute. There are formulae fior calculating the penetration, but they are only theroetical penettrations.

[fred.]

With delayed resolution this becomes even more complicated to manage in game. I like delayed resolution and we have used it on our Epic scale rules, and it works well. With that we have two types of hits, normal and big. Big hits negate the first armour save.

But how you apply this to WWII tank combat with all the factors that Mark outlines so well - when you only want to determine the effect of the hit later, I don't know. They only thought that comes to mind, is to have 6 bands of shooting capability (1 is small arms, 6 is 150mm) and put a small dice with that number next to the target for each hit from that capability band. But this will be hugely fiddly as you move vehicles around, and may be impractical if you are putting lots of hits on to a unit in a turn.

[Last Hussar]

No, actually simple.

Roll to hit.

If you hit you put a small die next to the tank, on the side it was hit showing Penetration value.

When that tank activates you resolve the penetration before it does anything.

That means if you get to activate 3 different tanks before the target they have to decide "Was One hit REALLY enough?"

[Duke Speedy of Leighton]

Like this?

Catch!

[holdfast]

Another reason why tanks had multiple holes in them was because any tanks that were identified were shot at. So 'dead' tanks were fired at in order to make sure that they were 'dead'. The photos were taken when it was safe for photographers, not necessarily immediately after the action.

[Lord Kermit of Birkenhead]

Quite right Holdfast, unless a tank was burning passing hostiles would pot off a couple of rounds to make sure.

[Gwydion]

One thing sultanbev:

' Momentum = mass x velocity compared to KE's mass x velocity x velocity. '

I presume you meant: KE - 1/2mv²

[steve_holmes_11]

One thing sultanbev:

' Momentum = mass x velocity compared to KE's mass x velocity x velocity. '

I presume you meant: KE - 1/2mv²

Kinetic energy is half mass times velocity squared - 100 lines after class!!