Home Forums WWII How much variation in armor penetration?

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  • #101230
    Ivan Sorensen
    Ivan Sorensen
    Moderator

    So gun vs armor performance and math gets endlessly complex, since there are so many factors involved: Range, angle of impact, hardness (and brittleness) of armor, quality of shell, unexpected weak points in the armor plating, the whims of an uncaring universe and whether the gunner is feeling particularly lucky that morning.

    But as gamers, we’re usually pretty enterprising in taking all those factors and boiling them down to a +1 on a D6, so let’s talk about that:

    If we take a shell that, at a given range and at a given angle might be expected to penetrate 100mm of armor (for example), how much variation in penetration would be reasonable to factor into a game mechanic ?

    10%? 20%? Something else entirely?

    Nordic Weasel Games
    https://sites.google.com/site/nordicweaselgames/

    #101232
    grizzlymc
    grizzlymc
    Participant

    Almost anything, even a rifle bullet has a small chance of doing a mission kill on a tank and some large shots hitting a machine with paper thin armour will fail to destroy.

    How to model that is dependent on the scale of your game. At brigade or division level, I think its spearhead where a double six always kills and a double one always fails, it’s probably as goo a mechanism as any other. At platoon level, you might try a critical hit chart and subsume failure to destroy into a roll to hit.

    #101259
    John D Salt
    John D Salt
    Participant

    First I’m going to answer the question that was asked, then the one I think should have been asked.

    Mazonka & Shine, a favourite reference of mine because I like saying “Mazonka” (Oleg Mazonka and Denis Shine, “Methods and Models in Preparing Weapon-Target Interaction Data for Combat Simulations”, 20th International Congress on Modelling and Simulation, Adelaide, 1-6 Dec 2013) cite Cazzolato et al 2007 (a paper I haven’t yet found) suggesting that probability of penetration be varied by plus or minus 8% of the theoretical penetration.

    My own estimate, using some Russian figures for WW2 (Russian Battlefield) and modern (Fofanov’s armour pages) guns that gave P(20) and P(80) figures, is that, if we assume a Gaussian curve of penetration depths, WW2 guns have a standard deviation of about 6.3% of their P(50) penetration, and 125mm guns about twice that. If we wanted to model this using 1d6 rolled by the shooter and 1d6 rolled by the target, something like this would be about right for a WW2 gun:

    plus or minus 5 + or – 12% of nominal penetration
    plus or minus 4 + or – 9% of nominal penetration
    plus or minus 3 + or – 6% of nominal penetration
    plus or minus 2 + or – 4% of nominal penetration
    plus or minus 1 + or – 2% of nominal penetration

    Mathematically reasonably sound, but from the simulation modelling point of view almost certainly a complete waste of effort, because such pootling differences are likely to be totally dominated by other factors.

    The point here is that it is very unlikely, even in the most elaborately detailed wargame, that you would know exactly which plate is struck, and at what compound angle. Hal Hock’s “Tobruk”, mentioned recently in another thread, made the most extreme (and in my opinion pointless) effort in this direction, but even that did not bother to attempt to account for angle of strike. The variation of effective protection over the presented aspect of a tank is likely to vary considerably. Consider the following data extracted from Ronnie Shepherd’s AORG Memo C.20, “Characteristics of 29 tanks” (NA piece number WO 291/1231) giving the minimum and maximum effective armour thickness in mm over the frontal aspect:

    Tank            Min     Max
    ----------------------------
    PzKw III G	 30	 67
    PzKw IV G	 51	 51
    Stuart 6	 41	 63
    M24 Chaffee	 47.5	 70.5
    T41		 59	 70
    Sherman 5	 50	 93
    Sherman 5C	 50	 93
    PzKw III J	 50	112
    KV-85		 69	 94
    Valentine 5	 60	104
    Valentine 9	 60	104
    Cromwell 5 or 7	 60	117
    Sherman 2A	 93	 93
    Churchill 4	 85	113
    Comet		 71	128
    Tiger		104	116
    T-34/85		130	130
    Churchill 7	146	152
    Centurion 2	142	185
    Centurion 3	142	185
    Panther		146	195
    M26 Pershing	178	195
    M47 Patton	178	195
    Royal Tiger	214	321
    JS-3		244	333
    

    If the location of the strike can make a difference of 20, 30, 40mm or more, piddling around with the odd millimetre of variation in penetration performance is neither here nor there. Eliminating duplicate entries for armour, and taking an average over the examples given, the minimum frontal protection is 27% less than the maximum. In some cases there is no variation; in others the min is less than half the max. If you wanted to be really rivet-counting, you might try to come up with a scheme whereby the armour protection classes of tanks reflect the degree of variability in armour thickness, instead of just the maximum or average thickness.

    This is before we make any accounting of the angle of strike, or the random factors mentioned in the Bovington “Fire and Movement” booklet such as a lug deflecting the shot to convert a certain failure into a penetration. I never tire of pointing out to people that rules accounting for armour penetration to the precision of a millimetre are silly, because armour plate was not even manufactured to that degree of precision in WW2. What’s more, I do not think people generally appreciate the degree of variation possible in the manufacturing quality of armour plate; it’s not easy stuff to mass-produce. As an example of this, a test shoot on a captive Tiger in Tunisia (reported in NA piece number WO 185/118, “DDG/FV(D) Armour plate experiments”) found that the left-side hull plate was of very poor quality, and easily penetrated by all sorts of projectiles way beyond their expected effective range.

    Add to this the point made by grizzlymc above that penetration does not equate to killing the target, and I would suggest that it is only sensible to allow a considerable degree of variation in results. Tanks can be penetrated without being killed, especially by small stuff, and tanks can be killed without being penetrated — German tanks of WW2 were notable both for poor-quality welds and designs that exposed weld runs to attack, and it doesn’t much matter if a plate has not been penetrated of the thing has been knocked off.

    All the best,

    John.

    [Note: I tried to give the links to the Russian pages from which my penetration data was drawn, but the forum software seems not to want to post them.]

    #101264
    irishserb
    irishserb
    Participant

    Okay, John is going to roll his eyes if he reads this (probably everybody will).

    My home brew roles are designed for very low level gaming.  For armor v. armor resolution, I have pared down the shooting process as follows; shooter determines range, finds his base percentage chance to hit and base penetration at the given range for the type of penetrator he is firing, the target gives a silhouette modifier (for moving or still), and a penalty is applied if the shooter is moving.   The modified chance to hit or less is rolled on % dice.  If the round hits, a second percentage determines what part of the silhouette of the target is hit (there can be up to 5 different areas on each face of each vehicle with different armor values (for each of three different types of penetrators)).  If the penetration is greater than the armor value for the part of the tank hit for the type of round being fired, the armor is penetrated.  If track is hit, the vehicle is immobile.

    In larger games a penetration is a kill.  In smaller games, if the armor thickness is less than 5 percent more than the penetration of the round, or if a penetration occurs by no more than 5% of the difference, a d10 is rolled against a chart which yields a kill, immobile, can’t shoot, no effect result.

    Now, when I started working on this, I took into consideration relative variations in elevation and positions in the horizontal plain, and found that it added in a lot of stuff to keep track of, but resulted in remarkably little variation in the results.  I’ve also studied and tinkered with endless other variables, and really spent a ridiculous amount of time studying how bullets engage armor over the years.  I just decided to ignore most stuff, and go with that listed above.

    I think that in most cases, penetration is more predictable than many gamers would like to believe.  And most have no clue how great the range of possible variables is.   In my case, I needed a little detail to make my system believable to me, and I have included what makes me content.  As far as the tedium of resolving shots goes, within the rules, you gain a feel for what is likely to hit or not.  Probably something like 80 percent of the shots taken in games are either very likely or very unlikely to hit, so we so just roll dice, and if  the result  is close, we crunch the numbers, otherwise we simply declare hit or miss, role the location, most of the time know if it is a penetration or track without looking at the numbers.  Most shots are resolved in 1.5 to 3 seconds.

    Regarding the original question, most of my games involve a large enough number of vehicles, that I don’t consider the variation in penetration.  In games with a couple platoons of vehicles, I may apply variable effect when the difference between penetration and armor is 5 percent of the difference or less.   In these games, the shooter often doesn’t know the result of the effect, and it is not uncommon for people to re-shoot dead or non-threatening tanks.

    #101279
    Darkest Star Games
    Darkest Star Games
    Participant

    In these games, the shooter often doesn’t know the result of the effect, and it is not uncommon for people to re-shoot dead or non-threatening tanks.

    This needs to happen more often, IMO.  If you don’t see the crew bail or if it doesn’t brew up, then shoot it again!

     

    Honestly, I wouldn’t worry about percentage differences unless you feel it will be something that will really add value to the game or displays an overwhelming historical outcome.  Did all tanks that were made a Plant X have armor that varied a great deal in quality?  Then the rule would make sense.  But, if the armor is of the same basic quality, or there is no big difference in the armor covering a certain aspect then it shouldn’t matter much.

    "I saw this in a cartoon once, but I'm pretty sure I can do it..."

    #101310

    If you are hitting a plate at 90 degrees there should be very little, if any, variation.  If you are hitting a sloped plate,  most are sloped at least 45 degrees, there will be a fair bit of variation.   A shot that hits a sloped plate will effectively be penetrating more armor than if it hit the plate flat.  On top of that, the shot will tend to slide and redirect making sloped armor even more effective.  How much or how little is up to you to decide.  I am much more in favor of simple games that mimic these effects than those where you make calculations to get the exact penetration value.

    One story that comes to mind occurred between a Panther and a Sherman during the battle of the bulge.  A Panther (several really) took up position on a ridge where they spotted a Sherman near a village on a lower position about 1000 yards away.  The panther fired a round and it bounced off the Sherman’s frontal hull armor.  It fired a second round and also bounced but the shot may have gone through the Sherman’s barrel with a very lucky hit.  The third shot penetrated the frontal armor of the hull and destroyed the tank.  Three hits and the first two did not penetrate despite the height advantage which would have somewhat negated the sloped armor advantage of the Sherman.

     

    John

    "Nearly all men can stand adversity, but if you want to test a man's character, give him power."

    --Abraham Lincoln

    #101315
    grizzlymc
    grizzlymc
    Participant

    After 40 years of abstraction and rivets, for mid to late WWII, Charles Grant’s Battle produces results for tank v tank which are as good as any.

    Roll to hit 4-6 short, 5-6 med, 6 long
    Roll two dice to destroy, add to guns strike value if >target’s defence value, target kod
    SV=penetration in cm, DV=armour in cm +5.

    We toyed with using multi sided dice for penetration:
    >50mm 2XD4
    >80mm 2XD6
    >105mm 2XD8
    >130mm 2XD10

    • This reply was modified 2 months ago by grizzlymc grizzlymc.
    #101391
    John D Salt
    John D Salt
    Participant

    Okay, John is going to roll his eyes if he reads this (probably everybody will).

    Not quite sure why you think I should do that — as described, your scheme seems to do more or less what I was calling for, that is, paying attention to the difference between plates that could be hit, rather than the less significant variation in thickness penetrated by a given shot.

    If the round hits, a second percentage determines what part of the silhouette of the target is hit (there can be up to 5 different areas on each face of each vehicle with different armor values (for each of three different types of penetrators)).

    How do you determine the areas hittable and their thicknesses? This seems to me as if it might require a fair amount of poring over scale drawings of AFVs — always assuming it’s something more sophisticated that 1 = track, 2 = lower hull, 3 or 4 = upper hull, 5 or 6 = turret or superstructure.

    From the reference to different kinds of penetrators (what’s the third?) I imagine you are dealing with the “modern” period rather than WW2, and I think things do tend to be more clear-cut when plates are mostly either MBT frontal plates or fairly feeble, guns are mostly MBT main guns or auto-cannon, and HEAT can usually penetrate anything. I would be quite surprised about angle not mattering at all, but I doubt it’s as important as in WW2, when “Kleeblatter” or “clover-leaf” diagrams showed very strong differences in vulnerability with aspect — and tactics were to some extent based on this. Of course the problem with this is that, unless you have a very fine-grained time scale indeed, a moving tank will probably dispplay several different angles to a shooter during the course of a single turn.

    One story that comes to mind occurred between a Panther and a Sherman during the battle of the bulge.

    Got a source for that? Note that the idea of a height advantage nullifying the advantage of sloped armour is such a negligible consideration that you should probably be thinking about rules for cold affecting muzzle velocity and armour brittleness long before worrying about that. The slope on which the target tank is standing probably has a much greater influence on the angle of impact than any height advantage.

    After 40 years of abstraction and rivets, for mid to late WWII, Charles Grant’s Battle produces results for tank v tank which are as good as any.

    Roll to hit 4-6 short, 5-6 med, 6 long
    Roll two dice to destroy, add to guns strike value if >target’s defence value, target kod
    SV=penetration in cm, DV=armour in cm +5.

    I loved “Battle!” because it was the first book I had read that showed the reasoning behind a set of rules being the way they are — which many books still don’t. While there were some odd omissions (direct HE fire, for one) the rules positively encouraged tweaking, and I have seen all sorts of “modified Charles Grant” games being played and enjoyed years and years after “Battle!” came out. Still, he used 2d6 to hit for anti-tank shooting, and his armour scale was not so finely divided as 10mm a point (athough MMP’s re-issue of Hal Hock’s “Tobruk” seems to use this scale).

    The question of how much variation there should be in armour penetration in a set of wargames rules is, I suppose, linked to the question of how one determines the banding for armour classes. The absolute minimum (as used, among others, by the WRG Infantry Action rules) is a Goldilocks three-level scale, “light”, “medium” and “heavy”. Most people would I think want at least a five-point (augmented Goldilocks) scale. The original WRG WW2 amrour and infantry rules used six armour classes; the latest use eight.

    As far as I can see there are three ways of constructing an armour scale. Yes, I have a spreadsheet for constructng armour scales, of course I have a spreadsheet for constructing armour scales.

    The most obvious method is to go up in even steps of effective thickness. 25mm (a metric inch) is quite a nice interval; recalling that Charles Grant had the Sherman’s armour value set at 14, we might have something like this:

    D.V.    From    To
    11	0	12	Half tracks
    12	13	37	Pz II A-D, Hellcat, Pz 38(t), Pz III D-G
    13	38	62	T-70, M3 Stuart, Chaffee, Pz IIIJ, M5 Stuart
    14	63	87	Valentine, Pz III L-N, T-34 m40-m41, Cromwell, StuG IIIG, Sherman
    15	88	112	T-34 m42-43, T-34/85, Tiger
    16	113	137	
    17	138	162	Panther, IS-2
    18	163	187	Jadgpanther
    19	188	212	Elefant
    20	213	237	Tiger II
    21	238	262	Jadgtiger
    22	263	287	IS-3
    

    Alternatively, the banding might work exponentially. This one works by raising a number (8 less than the D.V.) to the power of 2.4, and gives a scale that, if you subtract ten from the Grant-style defence values, bears a close resemblance to the armour classes used in the latest WRG armour and infantry rules.

    D.V.    From	To	
    11	0	20	Half-tracks, Pz IIA-D, Hellcat
    12	21	37	Pz 38(t), Pz III D-G
    13	38	60	T-70, M3 Stuart, Chaffee, Pz IIIJ, M5 Stuart
    14	61	90	Valentine, Pz III L-N, T-34 m40-m42, Cromwell, StuG IIIG, Sherman
    15	91	126	T-34 m43, T-34/85, Churchill, Tiger
    16	127	171	Panther, IS-2, Jadgpanther
    17	172	223	Elefant
    18	224	283	Tiger II, Jadgtiger, IS-3
    

    Also, one might multiply the thicknesses by a constant amount to obtain the next band. This scale is based on starting at 20mm, and multiplying successively by 1.4:

    D.V.    From	To	
    10	0	24	Half-tracks, Pz IIA-D, Hellcat
    11	25	33	Pz 38(t), Pz III D-G
    12	34	47	T-70, M3 Stuart, Chaffee
    13	48	65	Pz IIIJ, M5 Stuart, Valentine
    14	66	92	Pz III L-N, T-34 m40-m43, Cromwell, StuG IIIG, Sherman
    15	93	129	T-34/85, Churchill, Tiger
    16	130	180	Panther, IS-2, Jadgpanther
    17	181	252	Elefant, Tiger II
    18	253	354	Jadgtiger, IS-3
    

    I like this one best becuase it makes distinctions as fine as I think need making, and this slight extra discrimination at the lower end should make it good enough for early war as well as late war games.

    If using the original Charles Grant approach, then strike values need to be 7 lower than the defence value corresponding to the thickness they can penetrate. Equivalently, one can number the armour bands from 1, put the strike values on the same scale, and instead of resolving hits by having the attacker roll 2d6 and add it to the strike value, have each player roll 1d6, attacker rolling up and defender rolling down. If players trust each other sufficiently (and why not?) you could rule that the defender keeps their die roll a secret, and does not need to declare a destroyed tank as dead unless the defence value is beaten by 2 or more. This should promote the re-shooting of dead tanks that as been mentioned, which I think has the potential to influence a tank battle considerably — and it adds a bit of suspense, too.

    Charles Grant used his famous “tank stick”, with strike value deductions of -1 and -2 for angles over 30 or 60 degrees, but I think it easier to divide the area around a target tank into octants. Front, side, and rear defence values should be specified separately (+1 for the front and -1 for the back isn’t really good enough). If attacked from what a sailor would call the bow, use a D.V. equal to the average of the front and side armour, plus one (round up). If attacked from the quarter, use a D.V. equal to the average of the rear and side armour, plus one. This should give something of the effect of “Kleeblatter” without having to actually draw them out.

    Finally, I offer the following Charles-Grant-like roll-to-hit table, based on the observation in Biryukov & Melnikov’s “Anti-Tank Warfare” that anti-tank guns needed 1-2 shots to secure a hit at 300 metres, 8-10 shots at 1000 metres:

    Range (ins)	5	10	15	20	25	30	45	60
    Range (yds)	167	333	500	667	833	1000	1500	2000
    Range (m)	152	305	457	610	762	914	1371	1829
    								
    Roll to hit      5	 6	 7	 8	 9	10	11	12
    Hit chance	83%	72%	58%	42%	28%	17%	8%	3%
    

    Add one to the score needed for moving or hull-down targets.

    As grizzlymc says, Charles Grant can be made just as believable as rivet-counting rules, if not more so.

    All the best,

    John.

    #101393
    telzy amber
    telzy amber
    Participant

    bears a close resemblance to the armour classes used in the latest WRG armour and infantry rules.

    What, pray tell, is the latest WRG armour and infantry rules?

    #101395
    John D Salt
    John D Salt
    Participant

    bears a close resemblance to the armour classes used in the latest WRG armour and infantry rules.

    What, pray tell, is the latest WRG armour and infantry rules?

    “War games rules 1925-1950: wargames rules for all arms land warfare from platoon to battalion level”, Wargames Research Group, June 1988.

    All the best,

    John.

    #101404
    telzy amber
    telzy amber
    Participant

    War games rules 1925-1950: wargames rules for all arms land warfare from platoon to battalion level, Wargames Research Group, June 1988

    Certainly the latest from the esteemed Mr Barker. Ah the olden days

    #101431
    Not Connard Sage
    Not Connard Sage
    Participant

     

    bears a close resemblance to the armour classes used in the latest WRG armour and infantry rules.

    What, pray tell, is the latest WRG armour and infantry rules?

    “War games rules 1925-1950: wargames rules for all arms land warfare from platoon to battalion level”, Wargames Research Group, June 1988. All the best, John.

    Although the earlier set were better. Barker should have found a way of grafting the updated armour and gun classes on to them and left the basic mechanics well alone. Ditto the WRG modern warfare rules.

     

     

    "I go online sometimes, but everyone's spelling is really bad. It's... depressing."

    #101435
    irishserb
    irishserb
    Participant

    Regarding John’s questions/comments:

    I expected that method that I used for shot resolution on the table top, would strike you as overly tedious.

     

    For silhouettes, I either found drawings, or chased down or took photos of vehicles that were suitable to calculate the various faces making up each silhouette of each vehicle.  Where there are multiple surfaces/plates/thicknesses in a single area, say upper hull front, I usually take the value of the largest portion of the area in question.

    For curved/compound curved castings, I use a value from a point roughly 30% of the way from the CL of the vertical plane of the vehicle to the side, and half way up the area in question.  This yields an “average” value better than the minimum possible armor thickness, but not at the maximum extreme, and within a more probable zone to be hit by the average shot aimed at center of mass.  This zone excludes the area where deflections are more likely.

    For anomalous areas, on a face, where there is a significant portion of an area on the vehicle offering highly contrasting armor values, I will note on a card, that a special roll has to be made for the given vehicle, for example, if you hit the left side of the hull on a French Char B1, you will make an extra roll to see if you hit the large engine cooling inlet, which has a notably weaker armor value than the rest of the side plating.

    If you roll a hit on the target, which is resolved against and considered to be the entire silhouette, a hit on the hidden portion of a hull down vehicle yields a miss.

     

    The system is designed to span from the 1930s to the modern era, though I have stopped adding data much beyond 2005.  The third armor value is for resistance to HEP/HESH, which can deviate greatly from the pure kinetic value which composite, laminate, and spaced armor in the modern era.

    Resistance to HEAT rounds involves calculations based on average projectile velocities, average plasma jet burn rates, and as a percentage increase in armor value relative to angle of slope in 5 degree increments, based on average mid/Cold War HEAT round penetration.  While these compromises aren’t completely correct, they yield a fair relative representation of the performance of the most of the projectiles represented in the game.

     

    The game is set up such that the typical vehicle has up to five rounds available (assuming it had them in real life), 2x kinetic, 1-2X HEAT, 0-1x HEP/HESH, and 1x HE.  The shooter specifies what he is shooting, if other than the primary round, then resolves for it.  Depending on the scope of the game, in cases where a type of bullet is in short supply, the number of rounds available is noted per vehicle, and the shot is marked off as it is used.

    #101449
    telzy amber
    telzy amber
    Participant

    Although the earlier set were better. Barker should have found a way of grafting the updated armour and gun classes on to them and left the basic mechanics well alone. Ditto the WRG modern warfare rules.

    I quite agree. We played the first ww2 and the first and second modern sets a lot. I couldn’t understand the last modern set at all and I am considered fluent in Barkerese

    #102298
    John D Salt
    John D Salt
    Participant

    Regarding John’s questions/comments:
    I expected that method that I used for shot resolution on the table top, would strike you as overly tedious.

    If you were to do it with the endless series of dice rolls required in, say, Hal Hock’s “Tobruk” (AH), then yes; but by your own account you seem to have got the procedure pretty slick.

    For anomalous areas, on a face, where there is a significant portion of an area on the vehicle offering highly contrasting armor values, I will note on a card, that a special roll has to be made for the given vehicle, for example, if you hit the left side of the hull on a French Char B1, you will make an extra roll to see if you hit the large engine cooling inlet, which has a notably weaker armor value than the rest of the side plating.

    It shouldn’t be — AIUI to pass through the grille a shot would have to go through two armoured slats each 28mm thick and sloped at 45 degrees, as against the 55mm hull sides at normal. I believe the story of the grille’s vulnerability srises from a single incident during the battle of Stonne when some PaK 36s got lucky.

    If you roll a hit on the target, which is resolved against and considered to be the entire silhouette, a hit on the hidden portion of a hull down vehicle yields a miss.

    Apart from its intuitive appeal, the nice thing about this mechanism is that it gives a very easy way of showing the different cover-busting properties of different ammunition natures. As Iraqi T-72s hiding behind “kill-me” berms found ot, something that will handsomely stop 120mm HEAT or HESH might not stop 120mm fin.

    Resistance to HEAT rounds involves calculations based on average projectile velocities, average plasma jet burn rates,[…]

    Mr. Picky points out that the HEAT jet is made of liner particles, plasma is not involved.

    Now, unable to resist the temptation to poke around with this sort of scheme, I seem to have written a short Python program to estimate the areas and effective thicknesses of the plates visible from front, side and rear of a couple of the more popular tanks. Taking the dimensions off googled drawings (mostly Russian) of armour schemes is a pain in the fundament, involving creating rectangles and triangles in LibreOffice Draw over the top if the piccy and summing their areas, so I am going to explore the possibilities 3-D printing files might have for that sort of thing.

    Still, using this partially-handraulic approach, I have run a quick experiment to compare the results from assuming plus-or-minus 8% wobble in penetrative performance (Mazonka and Shine) as compared to a simple greater-than comparison (i.e., if the expected penetration is greater than the effective thickness of the plate, it’s a projectile win, otherwise it’s a plate win).

    This involved considering the frontal aspect of the Sherman (75mm turret, with both kinds of glacis plate, with and without crew position applique) and T-34 (model 41 and T-34/85) under attack from projectiles with penetration performance increasing in steps of 5mm. Effective armour thickness was assumed to be 1/cos^1.32(angle) of the plate thickness. Going from the penetration performance that gave 0% chance of penetration to the one that gave 95%+, we get the following differences in percentage chance of penetration with and without the 8% wobble:

    Sweep from 45mm to 120mm pen, 56-deg glacis Sherman (16 cases):
    Identical, with and without crew position applique
    
    Sweep from 60mm to 120mm pen, 47-deg glacis Sherman (13 cases):
    % chance of pen with and without 8% wobble:
     85mm     02    01
     90mm     13    01
     95mm     25    35
    100mm     42    35
    105mm     60    35
    110mm     79    86
    115mm     97   100
    
    Sweep from 50mm to 170mm, T-34 m41 (25 cases):
    % chance of pen with and without 8% wobble:
     55mm     06    00
     60mm     16    15
     65mm     21    23
    ...
     85mm     28    23
     90mm     34    40
    ...
    105mm     45    40
    110mm     59    40
    115mm     74    91
    120mm     88    91
    
    Sweep from 80mm to 125mm, T-35/85 (10 cases):
    Identical
    

    For a total of 64 cases, only 16 showed any difference at all. As you can see from the differences above, even where there was a difference, it often didn’t matter much (the difference between 88% and 91% is wholly negligible when considered against the other sources of inaccuracy in the model).

    Executive summary: if (as in Irishserb’s approach) you are randomly selecting which plate is hit, it is probably not necessary to bother with the random shot-to-shot variation in penetration performance.

    All the best,

    John.

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