Probably one of the most agonizing moments in armor miniature games comes when a hit has been scored and the time comes to compare the penetration capability of the shell with the armor it struck. It is at this juncture of the game that, much to bewilderment of many players, life or death for the poor tanks and armored cars becomes quite literally a matter of millimeters (1/25th of an inch). As an example, you're playing a game with TANK CHARTS (or just about any other rule system that compares shell AP to armor thickness). A PzKw IIId has just landed a 37mm round on the front upper hull of a Somua, at 275 meters range. According to the armor mechanics of the ruleset, the 500 meter range penetration figure for the 37mm L/45 gun is used as the guns' "punching power" (a real lightweight, by the way), which cross references to 39mm of armor penetration. Since the Somua has 40mm of hull armor at the point where the shot landed, no damage has been caused due to the effect of one silly little millimeter of armor. In just about all rule systems of this type, the effectiveness of guns is reciuced to a "hit or miss" affair based on whether the precise amount of armor carried by the target can be equaled. This is not only somewhat illogical due to a number of other factors that have been left out of the analysis (angle of impact, use of 500 meter range although hit at 275 meters, etc.), but also implies that penetration data can be figured out with the precision of a moonshot, which it obviously can't. Each round will probably differ by a tiny bit in penetration, and in the Somua- PzKw IIId case, an increase of 2.5% in penetration would have succeeded. Having suffered through a multitude of "hair-splitting" victories or defeats that hung on one millimeter of armor in our France, '40 games, our group decided to work out a procedure that would take account of many of the factors that play an important role in determining whether a shell penetrates. TABLE I -- GENERAL AP EFFECTS Shell Penetration AP Ratio armor thickness Maximum Die Roll Score for "Kill" (2d6 dice) 0.0-0.8 2 0.8-0.9 3 0.9 - .95 4 .95 - 1.05 7 1.05- 1.10 7 1.10-1.20 8 1.20-1.30 9 1.30-1.50 10 1.50 + 11 Shot Size and Characteristics Under41mm; add "+1" to roll Non-explosive; add "+1" to roll Immobilization Effect Rolling the highest kill score results in an immobilization of thetarget vehicle Take the case where the 500 meter penetration figure is exactly equal to the armor it hit. If the range is between 250 and 500 meters, the shell penetration can range from 10-15% higher depending upon where in the range interval the shot was made. A 250 meter range increment is used for playability, since a million arguments would ensue if tape measurements came down to the nearest 1/4 inch. There is also a small chance that the round will have a little more speed so one might except a +10-20% greater penetration. [1] Negative Side On the negative side, most frontal shot definitions allow frontal hits to land at thirty degree angles to the target facing, which increases the effective armor thickness by 12- 25% (depending upon whose data one uses) due to the ballistic effects of angled hits on effective armor thickness for penetration. Once again, shell variations from the average case are just as likely as to be decreases as increases, which can cancel out some of the bonus we previously considered. For our analysis we utilized the results from a 1948 U.S. Army Technical Manual (TM-1917) that provided highly detailed accounts of proving ground tests of shell penetration. An analysis of the effect of angle on penetration indicated that 30 degree obliquities (a really fancy word) increased armor resistance by about 25%, more than what the traditional 1/COSINE forumla would predict (about 12%). [2] This infers that not only does armor effective thickness increase rather rapidly with angle as one deviates from the target facing, but angle effects can overcome the effects of reduced range within an interval as the angle of incidence of the hit increases (a 20 degree angle increases armor by roughly 15%). In view of the proceeding, it was decided to use a method somewhat similar to the CROSS OF IRON approach (kill probabilities represented by dice roll scores), but heavily dependent on an analysis of shell penetration versus armor, damage tendencies of rounds, and the factors that were identified above. After much experimentation, Table I was prepared as the basis for our system: To explain the charts' subtleties, the AP Ratio signifies the ability of a given round to overcome the effects of angle on armor thickness and still equal or exceed the value needed for a penetration. As the ratio goes up, the shells should penetrate greater percentages of the time, leading up to a 97% chance by rounds that "overpenetrate" more than 50% (damage is dependent on the "overkill," to a degree, since a round with a lot of power left after entering a tank will probably do more in the way of significant damage than a shell that just made it through and fragmented on the way). The ratios less than 1 introduce an idea that is fairly interesting, since rounds that theoretically should fail to penetrate have the ability to do some major damage. In the case of ratios from 0.0 to .95, the main effect of hits will be to immobilize the target, which is probably a track hit that separates the treads from the wheels (even a 20mm round has a chance of detracking a Tiger II, although here it is less than 3%). From .95 to 1.05, we're dealing with shells that theoretically are right around the value needed to penetrate, and the real difference between them is small (.95 of 40mm is 38mm, the case where the shell failed to penetrate by 2mm in a strict comparison). This range takes into account the often "hairy" case where one fails or succeeds based on a millimeter by millimeter analysis, and it introduces some "reasonableness" into the results. Although these ratios are straddling the number needed to pierce the basic armor thickness, any angle at all on the hit will likely deflect the hit, and they are going to penetrate (if they do) with a low lethality, so the "kill" probability is only 28% (roll 5 or less with two die). In addition, of the 28% of rounds that do some worthwhile damage, about half will only immobilize the target, which corresponds to the case where hits get into the turret or hull with a minimum of kinetic energy left to generate useful mayhem. Special Modifiers The special modifiers at the bottom of the chart are there to introduce certain shell characteristics into the results, based on shell size and internal make-up. For instance, rounds up to 40mm in diameter generally weighed about 1.0 to 1.5 pounds, compared to the 4-5 pound range exhabited by 47-57mm shells (the 88mm shell is quite a bit larger. [3] Owing to the mass of the rounds, one would expect the heavier and larger shells to do more damage after getting into a tank owing to more bits of metal blowing about, and more explosive power when they explode (many AP rounds had primers and HE charges for added killing power). While it could penetrate quite a bit of armor, the 2 pounder round was solid, which decreases its effect somewhat due to the lack of a follow-up explosion inside the penetrated tank. Thus, its lethality suffers penalties with regard to shell size and explosive power, allowing some penetrated targets to roll along unperturbed after being hit by 2pdr rounds. Having prepared a basic system that relates shell penetration and size effects with damage potential, one then has to apply it to target armor in order to prepare scores that can be used in games. The problem of developing vehicle specific kill scores was then solved by copying down the armor and weapon penetration data from a popular set of armor miniature rules (TANK CHARTS), and comparing the AP Ratios to the die scores previously decided upon. Example As an example of the process, the French 47mm gun could blast through 45mm of armor at 500 meters (an average range in our games), and a common target was the German PzKw IIId (which had 32mm frontal armor). With 45mm of penetration and a 32mm thick target, the AP Ratio is 1.41, which corresponds to a kill score of 10 (83% chance of a "kill," 9% for an immobilization). This procedure was then carried out for every gun and major armor plate for the vehicles that fought in 1940 France, and the following chart was prepared: TABLE II -- FRANCE '40 AP EFFECTS FRENCH AND BRITISH WEAPONS Target 47mm 37mmL/33 37mmL/21 2 pounder PzKw 38t 11/11 9/9 4/4 9/9 PzKw 35t 11/11 9/10 4/10 9/9 PzKw IIId 10/10 7/7 3/3 9/9 PzKw IVd 10/11 7/10 2/48 9/9 PzKw IIb 10/11 7/10 2/10 9/9 Small Targets 11/11 10/10 10/10 9/9 TABLE II -- FRANCE '40 AP EFFECTS GERMAN WEAPONS target 47mmL/43 37mmL/45 75mmL/24 88mm 20mmL/55 Somua 4 10/5-10 2-4/2-4 5-10/9-10 11/11 2/2 H35 8-10/5-10 3-7/3-6 9-11/8-11 11/11 2/2 H39 7-10/5-10 3-7/3-6 8-11/8-11 11/11 2/2 Char B1 bis 42/5-3 2/2 5-3/8-3 11/11 2/2 Matilda I 3/3 2/2 4-5/4-5 11/11 2/2 Matilda II 2/2 2/2 2/2 11/11 2/2 A10 11/11 9/9 11/11 11/11 2/2 Small Targets 11/11 10/10 11/11 11/11 10/10 NOTES 1: Small Targets include MG Tanks, halfbacks, armored cars, and other vehicles with less than 20mm of armor 2: Number to left of slash is frontal armor, to the right is the flank and rear armor plate (roughly equivalent for our purposes) 3: Where two numbers are on one side of the slash, the first is the kill score against the turret, the second against the hull. Illustration To illustrate the use of the procedure, say a Somua has hit a PzKw IVd in the front at a range of 650 meters. From the chart, the unmodified kill score is a 10, which then is reduced by one due to the range and the shell size. Thus, rolling 2-8 (72%) will destroy the unlucky panzer and a roll of 9 (11 % chance) will stop the German tank in its tracks. Although this method pretty much incorporates the share of hits that will land on the tracks, the turret/hull split has yet to be determined. For simplicity, assume that one-third of the frontal hits will bounce up against the turret, and one-sixth of the flank hits (treat the rear like the front). Therefore roll one colored die with the regular die To Hit roll, with scores of 1 or 2 on frontal/ rear hits and 1 on flank hits indicating a turret hit (if hulldown, increase the range of rolls needed for a turret hit by three (1-5 for frontal, 1-4 for flank). Range Modifications A few words about the range modifications are in order since some results might be hard to rationalize. For instance, 700 meters was chosen as the limit beyond which a single modifier is used since very few hits (except by 88's) that mean anything will be made much beyond that range (37mm guns are fairly worthless much after 800 meters), and 88's don't decrease in killing power all that much. RANGE MODIFIERS Range Shell Diameter Add to Kill Roll 0-240m any -2 501-700m under 41 mm +2 501-700m over 41 mm +1 701m and beyond under 41 mm +3 701m and beyond over 41 mm +2 The -2 add-on within 240 meters will jack up kill numbers high enough so that PzKw II's will have a 17% chance of damaging Matilda's a seemingly illogical result if armor penetration is considered. Within 240 meters the chance of hitting tracks usually goes up as a generai rule (the effect of furls in the ground towards screening the lower reaches of a tank are minimized), and given the rate-of-fire of the mini-tanks of 1940, a track "kill" is a good possibility (half the kills with a score of "4" will be track tears). Armor penetration for small guns also goes up tremendously within 240 meters as compared to the 500 meter value used in the analysis, so a good-sized bonus is needed to "accurately" portray the increase in killing power at short range. To show how this method stacks up against a mathematical comparison of AP versus armor (where AP must equal or exceed armor for damage), the following chart was put together. The results were taken from TANK CHARTS: Range 37mmL/45 Penetration Somua Front Hull Armor %KO %Immobilize 0m. 54mm 40mm 33%(28%) 50%(15%) 230m 43mm 40mm 33%(28%) 50%(15%) 500m. 39mm 40mm 0% (9%) 0% (8%) 600m. 36mm 40mm 0% (3%) 0% (5%) To compare, the percentages given by our method are in parenthesis. Most of the differences in damage effects are due, in part, to the fact that 37mm rounds are highly penalized under our approach, while the armor miniatures ruleset treats 20mm rounds exactly the same as it does 47mm. In addition, most armor rules treat a through penetration of armor exactly the same as a partial penetration, while we've differentiated between clean penetrations (where the round easily pierced the plate due to an abundance of "zing") and minimal breakthroughs (where the round hardly manages to get inside the vehicle). While there are a number of factors that would seem to indicate that our approach is superior to other rules, it should be noted that so much of this material is subjective and based on personal guesses, and that it is impossible to say "this is right, and that is wrong." TANK CHARTS, despite widely disparate results, is just as "correct" insofar as it is consistent with the designers' view of what is important and is likely to occur, which just points out the tremendous subjectivity of rule design. Owing to our interest in allowing rounds to cause damage even if their penetration is 1 or 2 millimeters short, we've chosen to take a different approach which must of necessity create different results. Players wishing to use the AFV Kill Scores provided in this article can add them to their usual games (although it's somewhat unusual to play 1940 scenarios given the appeal of Barbarossa and Normandy), using the hit process their normal rules provide but substituting the Kill Scores for the AP/armor comparisons. If nothing else, these rules add some unusual considerations into the damage determinations used in our armor gaming, and gives the nitpicker types something to study and improve upon. TABLE IIl -- FRANCE '40 DATA Gun 500 meter Penetration Tank Front Armor Side Armor Turret Hull Turret Hull 20L/55 25mm PzKw IIb 30mm 31mm 17mm 15mm 37L/45 39mm (tank gun) German 42mm AT gun & 38t weapon 'Czech*' PzKw IId 32mm 32mm 36mm 30mm PzKw 35t 26mm 27mm 16mm 16mm PzKw38t 25mm 25mm 25mm 25mm PzKw IVd 32mm 32mm 24mm 20mm PzJg I 15mm 15mm 15mm 15mm H35 45mm 35mm 50mm 37mm 37L/33 36mm H39 49mm 35mm 50mm 37mm 75L/24 57mm Somua S35 56mm 40mm 51mm 39mm 47L/P43 52mm Char B1 bis 56mm 66mm 51mm 60mm 37L/21 23mm - 47L/34 45mm - * The higher penetration for the Czech gun is due to the solid AP rounds heavier weight due to the absence of any expensive charge. Source: TANK CHARTS armor ruleset. CHAR B1 BIS Special Notes The Char B1 had an engine grill on the left flank of the vehicle that formed a sort of "Achilles Heel," and enabled the German 37mm anti-tank guns to disable the tank. This weak spot can be modeled by increasing the flank Kill Score by "2" whenever a hit is made on the left side armor (the left as one is sitting on the rear of the AFV facing the front). In addition, the 75mm gun carried by this tank only fired high explosive rounds (HE), which could severely damage the lightly armored vehicles it was up against. The lethality of the 75mm HE can be incorporated by treating its kill score as a "6" against all target vehicles (the problem is mostly in hitting targets, since the 75mm gun was "fixed," in the literal sense, and useless against moving targets). Treating rolls of 5 and 6 as immobilizations. As a bit of general clarification, immobilization of a tanks' turret (as opposed to hull immobilization, which wipes out the movement capability) not only eliminates the target's turret weapons, but may wipe out the turret crew (roll one die, with 1-3 killing the turret crew and leading to a bailout of the rest of the crew). Hull immobilizations stand a fair chance of causing a crew bailout, so roll the one die and 1-2 scatters the entire crew. EDITOR'S NOTES by Rod Burr [1] 1. A variation of + or - 10- 15% is plausible due to munitions quality and other factors. [2] 2. To a large degree this reflects glancing/deflection, as well as the geometric effects represented by 1/cosine. [3] 3. I would use under 70mm rather than 41mm. There is a much more dramatic change here than between 37mm and 50mm. The bursting charges for German APHE rounds are: Charge Weight 37mm 13 gm 6830 gm 50mm/L42 16.4 gm 20600 gm 75mm/L48 82 gm 68000 gm Note: Round weight is a function of the diameter cubed (diameter x diameter x diameter) for shells of the same shape when comparing guns of significantly different lengths in calibers, a conversion factor of the ratio of the calibers should be included. 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