During my study of naval armor protection, I uncovered a number of sets of data that I analyzed in depth. These are on a number of topics directly related to, but not actually changing, the formulae I give to determine penetration of face-hardened and homogeneous, ductile armors by armor-piercing projectile impacts. The following is a compilation of these formulae, data tables, and related information so that they can be used to develop rules for ascertaining ship damage when hit by gun projectiles and aircraft bombs of various types.

All formulae are in English units with plate and backing material thicknesses, lengths, and projectile diameters in inches unless they are clearly stated to be in dimensionless multiples of projectile diameter ("calibers"); velocities in feet/second; angles in degrees; and weights in pounds.

Both the Impact Obliquity "Ob" and the Exit Angle "Ex" of the projectile are measured along the line of flight of the projectile's center of mass (ignoring any yaw, which will be taken into account in other ways, as stated below) and are measured from the imaginary line sticking out of the armor plate face at the center of the initial impact site at right-angles (the "normal" line) - Ob is measured from this line extending out of the plate toward the projectile just as the projectile impacts on the plate face, pivoting at the surface of the plate to the center of mass of the projectile, and Ex is measured from the extension of this same line out the plate back (slid sideways if needed to the center of the exit hole of the projectile in the plate back) to the center of mass of the projectile portion of the projectile or all of its penetrating its pieces, if it broke up during penetration, immediately after it has exited the plate back, pivoting on the back surface of the plate, both angles being the smallest angles that connects the normal line to the applicable center-of-mass point.

Plate quality factors and other metallurgical properties of iron and steel plates given below, if not explicitly called out differently, are taken from my "Table of Metallurgical Properties of Naval Armor and Construction Materials" dated 3 May 1998, hereafter called merely the "TABLE."

A. Homogeneous, Ductile Iron or Steel Plates

For soft, ductile, homogeneous iron and steel plates, penetrating a laminated array where the plates are stacked together in contact and bolted or welded or riveted in place is harder than penetrating the array if the plates were spaced far apart - that is, penetrated separately - and hit in succession at normal (Ob = 0°) by a high-velocity, perfect, unbreakable, non-deforming, monobloc shot projectile with a pointed nose and no yaw angle, but easier than if the plates were formed of a single solid plate of a quality that was the weighted average of all of the plates in the laminated array, because the plates at the back do support the plates nearer the face somewhat, but the plates can bend and slide independently of each other to some extent, reducing the strength of the array compared to that single thick plate. The following approximation formula works very well sometimes and less well at other times, but it is at least as good as any other that I know of and gives reasonably accurate results most of the time. While there is a trend to get better results if the first plate(s) in the laminated array are the most resistant (strongest metal and/or thickest) at normal obliquity than if the array is rearranged so that the weaker plate(s) are hit first, due to a multiplicative effect on total resistance as the later plate(s) buttress the first plate(s) hit, this trend is not obvious for oblique impact and seems to depend on projectile nose shape (blunter noses show this effect more than long, pointed noses). I am thus not including any such laminated array arrangement order effects in this approximation formulae set.

1. First, apply the Average Plate Quality Factor QA to each plate in the array as found in the TABLE by simply multiplying the plate's actual thickness T at the center of the impact site in the face of each plate hit by the QA for that plate's homogeneous armor type, resulting in a

   TeN = Teffective(N) = [QA(N)][T(N)]

   for the Nth plate in the laminated array. This gives the value of TeN as though it was for a plate of standard armor of QA = 1.00. Note that any effects due to a low (under 25%) Percent Elongation in the penetration formula will be handled by simply assuming that the Percent Elongation of the complete final array is that of the first (N=1) plate in the array, regardless of the Percent Elongation values of any plates deeper into the array - this tends to make the first plate the most important, which takes the comments in the preceding paragraph somewhat into account without special logic.

2. Second, add the plate effective thicknesses up as a simple summation Tsum

   Tsum = Te1 + Te2 + ... + TeN

   for an array of N plates. This is the thickness of a solid plate of QA = 1.00 material.

3. Third, add the plates as though they were spaced well apart in parallel and then hit in succession at normal by a non-deforming, unbreakable, monobloc shot projectile with a pointed nose and no yaw using the DeMarre Nickel-Steel Armor Penetration Formula to barely penetrate all of the plates (Navy Ballistic Limit on last plate, TeN, just reached after projectile is slowed down by previous plates). This gives a thickness Tspaced found by the formula

   Tspaced = (Te1^1.4 + Te2^1.4 + ... + TeN^1.4)^0.71429

   for an array of N plates. This is the thickness of a solid plate of QA = 1.00 material.

4. Fourth, split the difference between Tsum and Tspaced to get the final effective thickness Tlam for the entire N-plate laminated array

   Tlam = (Tsum + Tspaced)/2

B. Face-Hardened Armor with Wood, Cement, and/or Metal Backing

For face-hardened armor using my computer program FACEHARD, I simply add the effective thickness of the face-hardened plate using the PENETRATION QUALITY FACTOR "QA" - actual plate thickness at the center of the impact site times QA - in my TABLE for that face-hardened armor to (1) the thickness of wood backing Twood (any kind of wood) divided by 100; (2) the thickness of cement/composition material backing Tcement divided by 25; and/or (3) half of the effective thickness of any iron or steel backing plate Tmetal, determined as follows:

1. Multiply the thickness of each metal backing plate TbN that is laminated together by the following quality factor Qback to determine its effective thickness for this calculation TbeN, where N is the Nth plate in the stacked plate array.

   TbeN = (Qback)(TbN)

2. If a laminated array of backing plates (N > 1), use the homogeneous, ductile armor laminated array formula with TbeN in place of TeN, to get the final effective metal plate backing thickness Tback. If only one metal backing plate, simply use Tbe as Tback.

3. Multiply the face-hardened plate's actual thickness TFH by its penetration resistance quality factor QA in the TABLE to get its effective thickness in terms of standard armor with QA = 1.00 and its face thickness, TeFH

   TeFH = (QA)(TFH)

4. Sum up the thickness of cement/composition material backing divided by 25 and the thickness of wood backing (any kind of wood) divided by 100 and the Tback value divided by 2 (only resists the plug ejection and does not resist the breaking of the face-hardened plate's face) and the TeFH value to get the final TFHplate thickness to use in calculating the plate resistance to penetration (this value is NOT to be used in determining plate-induced projectile damage, which ignores all backing and uses the armor's damage-causing quality factor QD, which may or may not equal QA, depending on the plate type)

   TFHplate = (Tcement)/25 + (Twood)/100 + (Tback)/2 + TeFH

   This simple summation is just about as accurate for our purposes as any more complex formulae for a face-hardened armor plate.

All projectiles will have their windscreen, if any, knocked off by an impact with any solid material (earth, rock, cement, metal), including those with a thin "hood" (German "Grundring") attached merely to allow the windscreen-retaining threads to be cut into its base ring rather than the hard, brittle projectile nose, such as U.S. Navy "Special" Common projectiles, introduced after WWI. The windscreen is also knocked off on the ocean surface for the following unusual projectile designs:

1. Japanese 15.5-46cm (6.1-18.1") Type 88 (1928) and Type 91 (1931) "diving" AP and APC projectiles designed for smooth water entry and more-or-less horizontal nose-first underwater motion for a long distance to allow hits below the armored belt of a target. These projectiles have break-away "cap heads," which are contoured solid uncapped-projectile nose tips or capped-projectile AP cap tips with diameters of about 0.69 caliber - half of the cross-sectional area of the projectile body - at their base that have a flat base fitting flush with the projectile's tapered, truncated, flat-ended lower nose or lower AP cap and are held on only by the windscreen threads, which are especially weakened to ensure that the threads break on water impact, separating the windscreen, cap head, and projectile body into three separate parts. These cap heads are instantly knocked off at impacts over 45° obliquity, but remain attached at 45° or less obliquity during penetration of the plate tearing off the windscreen - though the cap heads, if not destroyed by the impact, fly free afterward since nothing is holding them to the projectile noses any more - so as to act as regular, bluntly-pointed projectile noses or AP cap tips at low obliquity for optimum penetration performance against medium and heavy armor.

2. German WWII 20.3-40.6cm (8-16") "Panzersprenggranat mit Kappe" (German Navy name) or "Panzergranat mit Kappe" (German Army name) (abbreviated "Psgr.m.K.") L/4,4 (total length of projectile in calibers, 4.4 here) and late-WWII 15cm (5.91") Psgr.m.K. L/4,6 hard-capped post-1930 APC projectiles with aluminum windscreens (instead of the usual sheet steel), which snap off at their threads on the ocean surface due to their brittleness. Use of weak, brittle aluminum eliminated any possible stress on the AP cap during oblique armor impact, that sometimes, though very rarely, reduced the efficiency of the AP cap by partially prying it free from the projectile nose at a bad solder joint as the windscreen was torn off. (Nobody else ever used aluminum windscreens, but all U.S. and British naval APC projectiles manufactured since some time prior to WWI reinforced their AP cap solder attachment method by bending several evenly-spaced spots along the soft lower edge of their caps into matching shallow pits in the projectiles' lower nose to make sure that they stayed on when the windscreen was torn off (all German and post-1930 Japanese Type 91 projectile AP caps were held on by solder only), so the Germans were not imagining this problem.)

The AP cap and hood themselves will always be knocked off of the projectile by an impact with any face-hardened or high-hardness plate (over circa 400 Brinell) or with a homogeneous, ductile iron or steel plate whose actual thickness is 0.0805 times the projectile's nominal caliber (diameter plus windage) and has a 50/50 chance of being so knocked off if the plate is 0.08 times that diameter. Under the plate thicknesses given above, nothing happens (spaced plates do not add up). Note that the plate quality has no effect and if a laminated homogeneous, ductile iron or steel array is hit, the array is calculated using the laminated plate formulae as in section 2.A., above, but with QA = 1.00 used for all of the plates, regardless of type.

Note also that metal bulkheads and decks are not uniform in thickness all the way across, but have bracing beams and/or ribs to which they are attached (riveted, bolted, welded) and where they butt up against other plates, they may overlap or have reinforcement straps or doubling plates added to strengthen the joints. Thus, up to 20% of a homogeneous, ductile construction or armor plate, especially near its edges, may be actually up to 50-100% thicker in effect than the nominal plate thickness at the center of the plate (the thicker the plate, the less of an increase this usually gives). This can counter any weakening of the metal to penetration at its edges (this weakening does not apply to decapping), which can decrease plate quality by up to 15%, though the resistance increase needed to counter this is somewhat different in face-hardened armor than in homogeneous, ductile armor, as will be discussed below in more detail.

When hit by an AP or base-fuzed Common/SAP projectile (or even an HE projectile if it does not detonate instantly on impact), an armor plate may not be as resistant to penetration near its edges as it is in the center unless the edges are adequately buttressed by adjacent armor plates to which the impacted plate is joined by either having the edge of the other plate support the hit plate by being overlapped by the hit plate or tightly locked to it by keying or other method that prevents independent plate motion and by being strong enough to have some significant reinforcement ability, as defined below. This reduction in resistance is only for direct impact penetration resistance, and is not a reduction in resistance to fragment penetration and not a reduction in effective plate thickness for decapping or fuze activation calculations.

This reduction in plate edge resistance when not adequately buttressed applies to both homogeneous and face-hardened armors (to both the penetration resistance (QA) and the damage-causing ability (QD) equally in the latter armor type) hit so that some point on the edge of the impact site comes within 1.5 calibers of the plate edge (usually the closest edge of the initial impact site or, if the projectile hits at an oblique impact and skids, the edge of the far end of the gouge in the plate). By "edge" is meant that part of the impact region on the plate surface that has been directly touched by the projectile itself, not just a wide dent or dish in the plate beyond this region. The drop in an unreinforced plate's resistance from its tabulated QA-value, termed "Qloss" from now on, will be zero when the projectile's closest side barely reaches the 1.5-caliber point from the closest edge and linearly increases to a maximum "Qlossmax" of 15% when the projectile body touches that edge of the plate or extends beyond that edge (any further loss in resistance due to the projectile skidding past the plate's edge during an oblique impact or only having part of its nose hit the plate at low obliquity because the impact overlaps more than one plate is a separate consideration and is not discussed here). For example, a projectile that hits so that its edge is only 1 caliber from an unsupported plate edge would cause the hit plate to suffer a loss of resistance of Qloss = (1.5 - 1)(15%)/1.5 = (0.3333)(15%) = 5% of its quality factor at the plate center; that is, QA(used) = QA(table) - Qloss = (1 - 0.05)QA(table) = (0.95)QA(table). This is a rather modest drop in strength because I am being conservative in my analysis of such impacts and this reduction is enough to handle almost every case that I have of such impacts. If face-hardened armor is being hit, the reduction only applies to the face-hardened plate itself - the backing materials are added to the reduced strength armor plate for this impact in their regular manner with no quality losses.

What it takes to buttress a plate enough to prevent this reduction is not as easily quantified, but I have estimated the following (these simple formulae match my existing data points):

1. If the support plate at the edge that is keyed to or overlapping the back of the impacted plate is at an angle of 45° or greater to the face of the impacted plate at that edge (call it angle "X"), so that the edge of the support plate must be crushed/folded backward rather than merely bent back sideways, then the support plate will give full support to the impacted plate (giving Qloss = 0) if it has an effective thickness against penetration "Tfs" of at least Tfs = (0.3)(Te), where "Te" is the effective thickness of the impacted plate. Both Te and Tfs are found by applying the QA-value for each plate to get its individual effective thickness against penetration and, if either of the plates are laminated, calculating the laminated plate's effective penetration resistance using the regular laminated armor logic for that kind of metal, since laminated materials can have each layer bend separately, reducing the support provided, regardless of the kinds of iron or steel that the support plate or impacted plate are.

2. If the angle X = 0° (plates are parallel), then the support plate must be solidly attached to the impacted plate by keying, by butt welding, or by overlapping behind the impacted plate with welding or riveting or bolting, locking them tightly together, and its minimum thickness for full support is Tfs = (0.75)(Te), including the laminated plate calculations mentioned in (1), above. Strapping or doubling plates backed up by a ship's supporting rib or bracing structure that are riveted or bolted or welded to the back of the impacted plate if it is of homogeneous, ductile steel will be adequate in this calculation, as they resist the bending back of the impacted plate's edge just like a butt-welded parallel plate.

3. If the plates are of an intermediate angle under 45° but over 0°, then the minimum plate thickness to provide adequate support of the impacted plate edge is linearly proportional to the angle "X." That is, the minimum full support plate thickness (giving Qloss = 0) is

   Tfs = (Te)[0.75 - (X/45)(0.75-0.3)]

   = (Te)[0.75 - (X/45)(0.45)]

   For example, if X = 35°, this gives

   Tfs = (0.4)(Te)

   Support plates angled the other way - tilted in front of the plate hit (concave joint with a negative X) - are considered just like parallel plates (X = 0°) and subject to the same restrictions as to minimum attachment requirements.

4. If the support plate is under the value calculated in (1), (2), or (3), above, then the loss of support is linearly related to the shortfall in effective thickness.

   1. For a homogeneous, ductile armor plate, the support due to the buttressing plate only goes to zero when the thickness of the buttressing plate goes to zero, since the support is only against bending of the impacted plate's edge and any support at all will help reduce this. For example, in the Tfs = (0.4)(Te) case used in (3), above, if the buttressing plate at X = 35° were only (0.1)(Te) thick, then the loss of strength at the plate edge would be

      Qlossmax = (0.4-0.1)(15%)/0.4

      = (3/4)(15%)

      = 11.25%

      so that the linear drop in the impacted plate's resistance (Qloss) as the projectile gets closer and closer to the impacted plate's edge would now run between Qloss = 0 when the closest the projectile gets to that supported edge is 1.5 caliber to Qloss = Qlossmax = 11.25%, instead of 15%, when the projectile touches the impacted plate's edge.

   2. For a face-hardened armor plate, the support due to the buttressing plate goes to zero when the buttressing plate thickness drops to 35% of the impacted plate's effective thickness for a parallel plate or to zero thickness at 45°, with a linear change from one to the other as the angle "X" increases. This is because the buttressing plate also absorbs impact shock that will crack the plate's hard, brittle face layer and such a thin plate will not be able to absorb enough of the energy to make a difference unless it is also acting as a buttress to hold the impacted plate edge from bending. In the X = 35° example in (3), above, if the impacted plate were a face-hardened plate, then the support plate thickness for zero support "Tzs" (giving Qloss = Qlossmax) would be calculated as

      Tzs = (Te)(0.35)(45 - X)/45

      = (Te)(0.00778)(45 - X)

      = (Te)(0.00778)(10)

      = (0.0778)(Te)

      = 7.78% of Te

      If the support plate was (0.1)(Te) thick and, as calculated in (a), above, Tfs = (0.4)(Te) (that is, when Qloss = 0), then

      Qlossmax = (0.4 - 0.1)(15%)/(0.4 - 0.0778)

      = (0.3/0.3922)(15%)

      = (0.7649)(15%)

      = 11.47%

      at the impacted plate's edge, which is slightly more than the homogeneous, ductile plate example in (a), above, as required.

5. The maximum drop in plate resistance Qlossmax can never be greater than 15% from being too close to an unsupported edge (drops from two edges at a corner do not add or multiply together).

6. This calculation does not affect the value at any other edge of the impacted plate, which may be supported in a different manner by a different plate or not supported at all. If the projectile gets within the weakening edge region of two or more separate edges, calculate each edge separately and choose the worst case (biggest loss in quality) to apply to the impact resistance calculation for that hit.

The minimum homogeneous, ductile iron or steel plate thickness necessary to set off the base fuze or internal impact fuze (used in some German and Japanese Common projectiles) by inertia at the impact on that plate varies with impact obliquity. My data is from U.S. Navy WWII tests of 5" and 16" base-fuzed Common and AP projectiles and U.S. WWII Mark 17 to Mark 21 Base Detonating Fuzes, which were rather complex "Chinese puzzle" designs to improve safety and reliability at oblique impact, and may not represent other base or internal fuze types, but I have little data on any other designs. Face-hardened armor will always set off a base fuze on impact at any obliquity due to the very hard impact shock, unless the fuze is rendered "blind" by impact damage or mechanical/design defect.

Some fuzes, including the U.S. base fuzes given here and most intricate WWII British base fuzes (both nations considered safety to a higher degree than anyone else, to my knowledge), cannot be set off by hitting multiple thinner spaced plates in rapid succession, but most other designs can be so set off (for example, most U.S. Navy WWI base fuzes through the early-WWII Mark 23 Base Detonating Fuze, most British WWI base fuzes, and most German and Japanese WWI and WWII base fuzes).

Plate quality, as with decapping, does not seem to matter, so always assume QA = 1.00 when computing the effective thickness of a single solid homogeneous, ductile plate or laminated plate array for both decapping and fuze activation calculations. See section 2.A. for details in calculating a laminated plate array's effective single-plate effective thickness (using QA = 1.00 here).

The minimum homogeneous, ductile plate effective thickness to set off a base or internal fuze, "Tfuze," due to impact inertia is found by the following formula for the U.S. fuzes mentioned above:

Tfuze = (Tfzmin)(D){(1 + COS[{2}Ob1])/2 + (0.4537)SIN^5.7019(Ob1)}

Many early base fuzes were designed for normal or near-normal obliquity, as were the projectile themselves, and had a lot of duds if they hit at any significant obliquity since the firing pin would be thrown sideways hard enough to either prevent it from moving forward properly or to tilt it so that it did not fit into the small hole in front of the primer pellet, in either case rendering the fuze blind even if it was in perfect working order during the impact. This seems to be a particular problem with the "Semple" Base Fuzes used in U.S. Army and Navy AP and Common projectiles for much of the early 20th Century, which had the firing pin sticking like a sharp finger out of an offset "fist" of metal that was locked in a tilted position prior to firing the gun, but which was unlocked by the firing shock and then pivoted due to the spinning projectile's centrifical force so that the firing pin pointed directly down the axis of the projectile inside the fuze and would strike the primer pellet when the latter, held in the front of a weighted cylinder that was also unlocked and free to move toward the firing pin after firing, was thrown forward by a near-normal-obliquity impact. However, the unlocked firing pin was only held fixed by the centrifical force and could still pivot freely. Therefore, at armor impact at a medium-to-high obliquity the projectile could pivot sharply as it dug into or ricochetted from the plate and leave the firing pin cocked off at an angle inside the fuze when the primer pellet tried to impale itself on the pin, blinding the projectile. The U.S. Navy late-1930's Mark 23 Base Detonating Fuze and, to even a more rigorous standard, the later Mark 17 through Mark 21 Base Detonating Fuzes were designed to keep the fuze's internal pieces aligned no matter what the impact obliquity, with the Mark 23 design still allowing two-thinner-plate (Tfzmin=0.05) operation, while the latter fuzes required a harder blow - single-thick-plate (Tfzmin=0.07) operation - to move the interlocking fuze parts into their final armed and activated position.

Attempts to get very high obliquity (over 70°) "graze" sensitivity in inertially-activated (base and internal) fuzes met with spotty success and I do not know of any such fuze that could be trusted to activate if the projectile ricochetted from the impacted surface (including the surface of the ocean), though a penetration would give a much longer and more reliable force on the projectile and make its chance of functioning much higher, though still not certain at such a high obliquity.

As an aside, the very unusual, but ultimately unsuccessful, U.S. Navy late-1930's Mark 23 Base Detonating Fuze (BDF) for major-caliber projectiles 6" and up had some very advanced features. However, it could not be reliably mass produced and was removed from service in 1941 and 1942, being replaced by the Mark 21 Base Detonating Fuze. The 0.033-second-delay Mark 21 BDF - and, I assume, the very similar short-delay (0.01-second) or non-delay (0.003-second) HC/Common-projectile Mark 17 through Mark 20 BDF designs - was much safer and more reliable when new, but it had its own problems with corrosion of its intricate internal parts from fumes from the projectile's Explosive "D" filler that limited it to a reliable shelf-life of six months until a Bakelite plastic outer coating was developed in mid-1943 to seal the fumes out, solving the shelf-life problem from then on in new or remanufactured AP, HC, and Common projectiles - though the HC projectiles usually used a nose fuze and therefore usually would not have noticed any problem from the slower-acting base fuze, whether it worked or not.

The Mark 23 BDF was internally backward from most fuzes in that the firing pin was mounted to the rear-facing end of a freely-moving (once released after firing the gun) weighted disk that was lightly held in place by an anti-creep spring on its firing pin face and a heavy spring on the other face. When the projectile hit its target, the disk would be thrown toward the projectile nose, away from the primer, compressing the heavy spring. Only when the projectile either stopped moving or passed entirely through the plate hit would the deceleration cease and the spring be able to throw the disk and firing pin backwards and thus cause the firing pin to hit the fixed primer pellet, detonating it. It also explains why several thin plate hits in rapid succession could cock the heavy spring in stages to get it to work. Prior to firing the gun, several small ball bearings were locked into the space between the primer and firing pin and only got out of the way after the set-back of the gun firing pulled locking pins and allowed the bearings to be flung sideways by the projectile's spin out of the path of the now-freely-moving weighted firing pin when the heavy spring threw it backward into the primer. Note that this spring-action design had the interesting property that it would also act as a super-long fuze delay during an underwater trajectory because the water would provide the deceleration force to keep the heavy spring cocked until the projectile either slowed to a stop, tumbled sideways, or hit the target below its armor belt and passed into the target. Ironically, because base fuzes were almost always designed sensitive enough to be set off on water impact, the U.S. Mark 23 BDF is the fuze design that the Japanese post-WWI Type 88 and Type 91 "diving" AP projectiles needed, but did not have, since it allowed a standard, rather short, black powder delay (0.025-0.035 second) instead of the actual super-long delays (0.08-0.4 second) used with those Japanese projectiles. Their existing BDF's turned them, in effect, into inert, solid-shot rounds that passed out the far side of the ship before exploding if direct hits on the target ship were made against anything but heavy armor. The U.S. Mark 23 BDF design, if perfected, would have solved this problem.

The Mark 23 BDF had another unique feature: A variable black powder time delay that automatically adjusted itself (when it worked right) to the size of the target by measuring the force of deceleration of the projectile on the plate which set it off. The less the deceleration, the lighter the armor and, it was assumed, the smaller the target ship (or the smaller the protected area hit on a larger ship), so the shorter the black powder time delay should be. The method for doing this was to have a hollow needle-like tube sticking out of the front center of a weighted disk (totally separate from the weighted firing pin) that would be released to move on the gun firing and would be thrown forward on impact, imbedding its tip into the tiny compressed black powder delay pellet. The heavier the armor hit, the stronger and/or longer the deceleration and the deeper the tube imbedded itself. The primer's blast would pass into the tube, out of its tip, and then burn the black powder starting from there backwards down the length of the tube along its outside. The deeper the tube buried itself, the longer the burn on the outside of the tube must be to reach back to the ring-shaped opening surrounding the tube base, at which point the flame would set off the sensitive detonator, which would then instantly set off the two small, but extremely powerful, tetryl booster charges that acted like needle-shaped rocket blasts into the Explosive "D" main filler on either side of the fuze, detonating it. Pellet delay times of from 0.01 (thin armor) to 0.025 second (thick armor) from the instant that the firing pin set off the primer could be achieved (in addition to the circa 0.003-second fixed inertial delay from the instant that the impact deceleration ceased, releasing the cocked firing-pin spring to function, until the primer exploded when the firing pin hit it). This part of the fuze was the most unreliable in mass-produced fuzes and was replaced by a fixed 0.025-second delay (non-moving tube pushed in to its maximum depth when the fuze was manufactured) in 1941, which was used until the fuzes were finally replaced by the safer, more reliable Mark 21 BDF when manufacturing of this latter fuze had ramped up to meet the demand in late 1942. The Mark 21 used a fixed 0.033-second total (black powder plus inertial) delay (average value with some variation from fuze to fuze) and used the same kind of 100% redundant, two-piece, rocket-nozzle-shaped tetryl booster design.

U.S. Navy WWII High Capacity (HC) projectiles ("High Explosive" (HE) projectiles in British terminology and "Sprenggrenat mit Kopfzunder" ("Spgr.m.Kz." or "HE Shell with Head Fuze") in German terminology) had a unique design. Most included a Mark 17 , 18, 19, or 20 BDF with a short (0.01-second black powder plus inertial) delay or no (0.003-second inertial) delay, to be used against lightly-armored or unarmored ships (destroyers and merchant ships) or against moderately-protected (dug-in) shore bombardment targets when none of the various nose fuzes were applicable and a hardened, solid steel nose plug was retained. U.S. Navy HC projectiles were shipped with the nose plug screwed on and a nose fuze, if used, was inserted in its place as needed before a battle by hand aboard ship - except for 1943 and later "AA Common" HC-type projectiles with VT ("Variable Time," proximity, or radar influence) fuzes for smaller anti-aircraft guns, which had permanent VT nose fuzes installed, each VT fuze with an internal impact fuze that doubled as an Auxiliary Detonating Fuze (see below), and in many cases no other fuze, usually because the large (remember, tiny vaccuum tubes!) VT fuze took up so much space that other fuzes were removed to allow adequate explosive filler weight. The multi-purpose HC projectile's optional nose fuzes were (1) Point Detonating Fuzes (British "Direct Action" fuzes), (2) Mechanical Time Fuzes (set just before firing and armed on firing; no old Powder Time Fuzes were used by the U.S. Navy in WWII, to my knowledge), or, after mid-1943 as just mentioned, (3) VT Fuzes - the last primarily for AA use, but also used in large HC projectiles for shore bombardment against exposed "soft" shore targets (men, trucks, etc.) for air bursts near the ground in place of the time fuze. All of these fuzes would detonate instantly on impact with water, earth, rock, concrete, or metal plate due to impact shock (few specially-hardened nose fuzes were used by naval guns, though some army weapons had them for use against protected targets like pill boxes).

Another unique feature of U.S. Navy WWII HC projectiles with optional multiple nose fuzes was the addition of a unique, to my knowledge, Auxiliary Detonating Fuze (ADF) permanently installed in the nose between the nose fuze (or steel nose plug) and the large booster/exploder/magazine/gaine. The ADF was like the lower end of an instantaneous impact nose fuze, with its own firing pin and primer/detonator, armed only when the projectile was spinning rapidly after firing, which had the detonator of the regular nose fuze above it blast into an opening in the ADF's top to slam the ADF's firing pin into its own primer/detonator and, hence, to set off the booster and the main 6-8% filler charge of Explosive "D". Unless physically compressed during projectile impact with thick-enough solid metal plate (see below), this fuze had no means to set itself off; it was supposed to act merely as a backup safety feature to prevent projectile detonation if the nose fuze went off if the projectile was somehow dropped on its nose from a height in the barbette/ammunition handling room or turret/gun mount prior to firing. If no nose fuze was present, it was supposed to remain inert on impact and it did remain inert on any impact with water, earth, rock, or concrete, allowing the projectile's BDF to function as designed. As with a BDF, an ADF could not be removed aboard ship.

Note that the forward, super-firing (#2) turret explosion during the Vietnam War aboard USS NEWPORT NEWS occurred because somehow both the Mechanical Time Nose Fuze AND the ADF armed themselves when an 8" HC projectile being used for shore bombardment was rammed into the center gun of the turret and the time fuze somehow started running and ran down in the barrel prior to firing, setting both itself and the ADF off, which detonated both the projectile and propellant powder case in the breech, blowing up the gun and setting off a huge propellent fire (only a single brass cartridge case in the barbette did not burn and it was crushed so badly that removing it was a task right out of a WWII "bomb squad" movie!) that killed everyone in the turret and barbette (the magazine isolation systems worked perfectly, as they had in all other U.S. warships since 1900, to my knowledge). This seems to me to have been an act of sabotage, since the likelihood of both fuzes in one projectile malfunctioning simultaneously in such a strange and deadly manner (as opposed to the usual result of rendering the projectile a dud) is so small as to be almost impossible to imagine.

As mentioned, when used in an HC projectile with the steel nose plug in place, the ADF was supposed to remain inert and allow the BDF to set off the projectile. However, WWII tests discovered that a homogeneous, ductile iron or steel plate of any kind that was 0.075 caliber or more in thickness at any obliquity would set off the ADF due to impact shock, rendering the projectile's BDF useless in this case. Thus, at low obliquity there was only a very small difference between the iron or steel ship construction or armor plate needed to set off the BDF and that needed to set off the ADF, so the BDF would be of limited use when these projectiles were used with steel nose plugs against ship targets because the ADF would instantly detonate the projectile first against most plates thick enough to set off the BDF. At higher obliquity impacts, which are of course more likely, the difference in the required plate thicknesses to set off the BDF compared to that needed to set off the ADF was greater, but against a large ship target with a thick construction steel hull, bulkheads, or decks, even if unarmored, there was a good chance of the ADF instantly setting off the projectile and eliminating any kind of delay action from the BDF. Since neither the ADF or the BDF could be removed aboard ship, this problem had no solution. (To get around this problem, a modified 8" HC projectile with its ADF removed and a steel nose plug permanently installed was developed during WWII as an extra-powerful Common projectile for use against unarmored ships, but I do not know to what ships it was issued.)

A. Introduction

When a projectile has a delay between the impact on the plate and the explosion of its filler, even if the delay is rather small, the projectile will act like a solid shot (albeit a sometimes rather weak one) during the initial stages of penetration where it is making the hole and beginning to pass through the plate (assuming it is hitting at a high enough velocity to do so). Even a non-delay base fuze has about 0.003-second inertial delay, which means that the projectile would move 3 feet if its average velocity during the penetration was 1000 feet/second (say, 1500 feet/second on impact and 500 feet/second after penetrating). For a small projectile, this is a complete penetration; for a medium-sized projectile, this is a partial penetration with most of the projectile through the plate; and for a large projectile, this is a partial penetration with the upper end of the projectile through the plate. This delay could be caused by using a black powder or nitro-cellulose filler and/or a black powder booster (which acts like a huge delay element, but which was capable of detonating Lyddite and exploding a black powder filler and was so used before, during, and, in a few cases, after WWI) or using a special delay element in a hardened nose fuze (rare, but not unheard of, especially against land fortifications) with a detonating booster and filler.

If the projectile has a nose fuze, a detonating booster, and a detonating filler, as did U.S. HC projectiles, British HE projectiles, and German Spgr.m.Kz. projectiles, hitting a solid homogeneous, ductile iron or steel plate will result in the projectile detonating almost instantly, with rather a reduced dependence on the striking velocity until that velocity gets rather high, because the projectile will move a rather small distance before the filler detonates and essentially removes most of the projectile's mass sideways in a very short time compared to the forward speed of the projectile.

For want of any other data, I will assume that the laminated plate formula for armor penetration by AP projectiles also works for nose-fuzed, instantaneously-detonating projectiles. See section 2.A. for details.

I am also assuming that the nose-fuzed projectiles discussed here have fillers 6.5% of the total projectile weight or larger of TNT or the equivalent of another detonating explosive and the filler is set off in a complete, "high-order" detonation instantly (as close as possible to this ideal) by the nose fuze. Even if the nose fuze is not an impact fuze, if it is crushed on impact, it will usually act as one. The U.S. ADF does have some effect here, as will be discussed below.

There are two kinds of penetration involved with a projectile when it explodes. First, the penetration that the projectile body achieves through a plate that it hits, which may be by its kinetic energy or by its explosive force or both. In this case for our purposes here, the projectile is in contact with or very close to the plate when it explodes. Second, the thickness of iron or steel plating that a projectile's fragments projected more-or-less sideways by the explosion of its filler can penetrate at some given distance from the projectile side, front, or rear surface. The projectile may be very far from the plate hit by the fragment. I will arbitrarily cut off the possible penetration of plates at 1,000 calibers radially measured from the projectile surface, since by then any heavy fragments that are still moving will have been ejected upward at a steep angle (I am ignoring high-altitude air bursts here!) and have curved down and will only hit something directly under them, which will usually be the ocean or ground in most cases, unless something is unfortunate enough to be in the way.

When a projectile explodes, the base plug region usually stays in one piece and is slowed down considerably by the blast pressure against its front surface, though it can still do some damage due to its weight when it falls down. However, it has very little penetrative power, so any damage it causes will be within the same space as the projectile, close to the projectile, and usually underneath the point where the projectile exploded. The base plug also tends to block blast and fragments from directly reaching an object behind the projectile (blocks a 90° cone centered on the projectile centerline), so damage here is reduced somewhat.

The nose pieces of an exploded projectile act differently depending on how large the filler cavity is and whether the projectile nose is solid or has a large hole for a nose fuze and whether the filler detonates or merely explodes (the latter due to poor fuze/booster operation - malfunction or a hard-to-detonate filler with an inadequate booster (TNT filler and a Lyddite booster, for example) - or to a black powder or guncotton filler that does not detonate). A detonation, even a partial one, will usually break up the projectile body around it into many small pieces, though the thick nose of a base-fuzed, small-to-medium-sized filler (under 6.5% detonating filler), Common/SAP or AP projectile will usually remain in one piece, with some large chunks flying forward in a ring around the central heavy nose piece. Typically, the solid nose piece of an AP projectile is roughly 33% of the projectile's body weight prior to the detonation and this drops to 25% for a Common/SAP projectile (see below for details). The more complete the detonation of a projectile, the faster the middle-body fragments move sideways, but, for a given explosive type, shell casing thickness, and shell casing material, the fragment size and number stay roughly the same. An HE/HC projectile with the explosive cavity extending almost all the way to the tip of the nose will break up its nose to the very tip of the cavity, leaving only the nose fuze and perhaps a ring of projectile nose metal intact after the explosion, with virtually no significant penetration capability due to its light weight (the fuze is hollow and has many small internal pieces of sometimes light-weight materials with empty spaces around them to allow them to move during arming and firing). Other than damaging close-by unprotected equipment or causing personnel casualties, the nose piece of an HE/HC projectile is of no consequence as far as damaging the target is concerned - the base plug is more dangerous!

A non-detonating explosion will result in the projectile merely breaking apart with much less blast effect and much larger and fewer fragments, though throwing many more flaming filler pieces that can start fires, with the heavy nose being even larger than with a detonation of a base-fuzed Common/SAP or AP projectile and the sideways-moving middle-body pieces going so slowly that the forward motion of the projectile will usually make the fragments form a dense cone moving forward along the original path of the projectile just before the explosion and only slowly spreading sideways. For example, pre-WWI British Common, Pointed, Capped (CPC) base-fuzed projectiles had about a 10% black powder filler - consider them as very light-case Semi-Armor Piercing (SAP) designs with a very long, very thin-walled, middle and lower body - usually formed cones of rather large, relatively slowly-moving, fragments about 60° wide centered on the direction of motion of the projectiles' noses even when the projectiles exploded in their most powerful manner and had not been slowed much by the plates setting off their fuzes, with this cone getting narrower if the fuze/booster did not function properly or if the filler casing was cracked open by the impact that set off the fuze, which reduces the power of the explosion noticeably and greatly reduces the sideways velocity of the fragments formed. Note that the breakage of the projectile body has much less of an effect on a detonating - that is, a self-propagating, shock-wave-induced, super-fast-burning explosion - explosive unless the filler is physically torn apart into separate pieces before detonation occurs. These cones get wider if the projectiles were slowed down appreciably by the impacts, but not much wider, since any really heavy armor would break up these light-case projectiles prior to their filler exploding and thus drastically reduce their explosive force, narrowing the fragment cones considerably.

B. Definition of Target Damage

When a projectile explodes, the damage that it does to the target changes significantly. Prior to the explosion, the projectile merely causes punching damage by its own body (intact or in pieces due to breakup on a armor or construction plate previously hit) and, sometimes, by fragments knocked out of the objects that it hits as it moves through the target. These impacts can cause sparks and fires or set off sensitive shipboard explosives, but these are rather low-probability events over most of the internal volume of the typical warship target - letting in water due to punching a hole below the waterline is more likely with a solid-shot-type, non-exploding projectile. Also, almost all of the damage is caused in a narrow, though possibly very deep, tunnel made through the target and very near to the projectile's path, with only farther-afield damage being caused by ricochetting fragments or by indirect effects like cutting electrical cables or pipes that are used by more distant parts of the target.

When the projectile's filler charge explodes, however, this immediately widens the zone of damage due to the blast wave (atmospheric over-pressure), heat, shock (concussion), and fragments of the projectile. How the damage occurs depends on the type of projectile (which determines the distribution of the explosive and metal casing mass within the projectile body), the size of the projectile, the percentage of it that is explosive, what kind of explosive (can it detonate and, if so, how powerful is it relative to an equal weight of the standard explosive TNT?), how well the fuze/booster combination performed in attempting to explode the filler in its most destructive possible manner (including if any previous projectile damage may have compromised this explosion), where the explosion occurred in the target, in what direction the projectile body's long axis was facing when the projectile exploded, where the objects to be damaged are positioned relative to the projectile body axis, how far they are away from the projectile, how vulnerable are the objects to be damaged to fragment impact and blast-induced heat and concussion, and what intermediate materials (deck or bulkhead plates and other pieces of equipment) are between the projectile and the objects to be damaged.

Some portions of the nose of the projectile will continue forward, usually in one large piece, if not stopped by a bulkhead or deck, ranging from up to 33% (detonating filler) or 38% (non-detonating filler) of the projectile's pre-explosion body weight (the entire nose portion) for small-cavity AP projectiles, 25% (detonating) or 30% (non-detonating) for medium-sized cavity Common/SAP projectiles, and down to only 2% (any filler) of the projectile for very light-case, large-filler HE/HC-type nose-fuzed projectiles (only the nose fuze/nose plug and the projectile's ring-shaped nose portion screwed to it), even if a steel nose plug and base fuze are used in these last projectiles. For a base-fuzed Common/SAP or AP projectile, this nose piece can be considered exactly like an AP solid shot projectile of original projectile diameter, but of reduced weight, moving at the same velocity as it had just prior to the explosion of its filler. For a nose-fuzed projectile, this remaining nose piece has almost no real penetrative power due to its small size and light weight (the fuze is hollow with considerable room for its internal pieces to move around during arming and firing and the hardened nose plug is matched to the nose fuze weight), so it usually only can cause some minor damage as a medium-sized projectile fragment bouncing around inside the space where the projectile exploded (it is a rather minor player in the damage to the target). For Common/SAP and AP projectiles, some medium-sized chunks of the upper projectile body will also be thrown forward forming a ring around the central heavy nose piece and moving at an equal speed and these can cause some additional damage to the target in a narrow cone centered around the path of the central nose piece, though they will be stopped by or made to ricochet off of any truly heavy bulkhead or deck in their path due to their irregular shape and rather light weight (much like the nose piece of the HE/HC projectile, but heavier since they are solid iron or steel) - see discussion below about a black-powder-filled, base-fuzed projectile's fragments for more details on this ring of medium-sized pieces.

If the projectile filler explodes, but does not detonate (either partially or completely), most of its body behind the heavy nose piece will form into a moderate number of medium-sized chunks and can tear a rather deep cone-shaped hole through the target if not stopped by the aforementioned bulkheads and decks; this cone will typically be on an arc of about 60° width centered on the central heavy nose piece for a maximum power black powder filler explosion in a projectile moving at a moderate post-impact velocity (circa 1000 feet/second), with a slower velocity (which would widen the cone) not being possible since these old black-powder-filled projectiles would break up on any really heavy armor that slowed them down very much. A reduced-power explosion of a black powder or guncotton filler (both non-detonating) due to projectile damage or a malfunctioning fuze/booster will narrow this cone by reducing the sideways velocity of the fragments considerably. Note that even the smallest middle-body pieces of a black-powder- or guncotton-filled projectile are still rather large and moving rather slowly compared to fragments from a detonation, though faster than the larger, heavier body pieces, so they will form most of the outer edge of the 60° arc, but have rather little penetrative power through any armored bulkheads and decks (a large percentage of them will tear up a large, deeply-piercing volume in the target if not stopped, however, since air resistance has rather little effect on such large pieces compared to its effects on the tiny, fast-moving middle-body pieces from a detonating projectile).

The base of the projectile will usually be stopped or slowed by the blast pressure on its forward surface and merely become a large, slow-moving fragment that can damage objects nearby, especially under, the explosion, but cannot penetrate any decks or bulkheads to increase the volume of damage it might do.

If the projectile filler detonates, however, even if it is not a complete, maximum-power ("high order") detonation, the projectile body immediately around the filler cavity to the side will shatter into tiny pieces under the concussion and be ejected sideways at a high velocity; the larger the filler, the thinner the casing surrounding the filler, reducing the total mass of these middle-body fragments, but the faster these fragments will be moving - the more thoroughly the filler detonates, the higher this velocity will be for a given filler weight - and the more concussive/faster-burning/"brisant" the detonating filler explosive is, the smaller they will be, on the average, so they can tear up a ring-shaped region nearby the explosion surrounding the projectile middle body (actually tilted forward in a cone if the projectile is moving forward, but the tilt is rather small due to the very high sideways speed of the projectile fragments). Air resistance will slow such small fragments down rapidly and they cannot penetrate very much deck or bulkhead plating because of their small size and because they are irregularly shaped and stressed by the highly-concussive filler blast so that they tend to break up into even smaller pieces during punching through any metal plate and they will usually punch out a "shadow" piece (plug) from the plate like a cookie cutter, which drastically lowers the remaining velocity of the fragment and usually precludes the fragment penetrating more than one bulkhead or deck plate, confining most of the damage to a much smaller, though wider, total volume than with the heavier pieces of a black-powder- or guncotton-filled projectile if not stopped by an armored bulkhead or deck. The larger, slower non-detonating projectile fragments cause less damage to the side of their conical path of destruction and have less penetrative power through the FIRST plate in their way than the high-speed fragments from a detonating projectile, but they can penetrate a SECOND or even a THIRD unarmored plate in their path much more easily due to their retention of their original mass (they tend to remain intact after hitting a bulkhead or deck, whether they penetrate or not) and more of their original velocity after a bulkhead or deck impact.

In a nutshell, a detonating filler will cause fragments that can tear up a nearby region completely around the projectile and send many fragments through a single medium-thickness deck or bulkhead, but rather few (including the heavy nose piece of a Common/SAP or AP projectile) capable of penetrating more than one bulkhead, so damage ends for the most part in the next space over from the one where the projectile detonated, assuming the decks or bulkheads are thin enough to be penetrated in the first place. A non-detonating filler creates fewer, heavier, much slower-moving fragments that move forward in a roughly-60°-wide cone, with much less damage to the sides of the projectile, but more ability to have its projectile fragments keep going through successive light bulkheads and thus spread the damage more deeply, if not more widely, into the target. Both fillers will cause fires from blast in the same space and in adjacent spaces where only one deck or bulkhead was pierced to reach that space (the higher temperature of the detonating explosive is rather short-lived as the filler is consumed compared to the weaker, lower-temperature, but long-duration and long-burning-filler-fragment-throwing, non-detonating explosive), but no blast or burning filler fragments will usually reach through more than one metal bulkhead or deck from the center of the explosion (unless the bulkheads are very thin and/or the explosion is very large). Only sparks from fragment impacts or electrical shorts or fragment impacts on explosive/flammable materials will cause any fires at a larger distance through a second (and any succeeding) bulkhead or deck that may be pierced by the heavier fragments.

The introduction of the delay-action base fuze with a detonating filler (block TNT) by the Germans (Krupp) and Austro-Hungarians (Skoda) in 1911 - which was proved successful during WWI even with the very primitive and unreliable base fuzes and boosters that they used - was "to get the best of both worlds" by placing the HE filler as near the ship's centerline as possible prior to setting off the filler, which allowed a deep, though very narrow, path of damage through the ship to that point and then a very complete pulverization of the hit space and any nearby spaces (since the projectile was already deep in the ship target, the lack of any penetrating ability of the tiny, high-velocity fragments and blast through more than one light bulkhead or deck was of little consequence; the projectile was already in the most vital area that it was likely to reach when it went off).

Note that air resistance does rapidly slow down the tiny fragments of a detonating projectile, but they are going so fast initially that they still have a long "reach" if not stopped by a bulkhead or deck and can cause damage and crew casualties to unprotected or lightly-protected areas facing the explosion even at up to a 1,000 calibers (about 667 feet for an 8" projectile with a detonating filler!), though the number of still-dangerous fragments per square foot drops off drastically as gravity pulls them down and the surface area of the affected region increases.

C. Projectile Types

The thicker the casing of the projectile, the more mass of metal is thrown and the smaller the explosive charge, so the result is that the sideways-thrown middle-body fragments from an exploding projectile are usually reduced to the same average size (depending on filler type, whether it detonated or not (partial or complete detonation are about the same for this factor), and projectile body metallurgy) and thus end up going at a reduced average velocity as the less energy available in a smaller filler is spread over a larger weight of casing material. This reduces the penetration ability and carrying distance of the fragments as projectile filler size goes down. The same reduction in average fragment velocity, but not in the number or size of the fragments, happens when a partial detonation occurs due to poor fuze/booster performance or projectile impact damage (the shock wave velocity of the given explosive is the same in either case and this determines the way the metal casing breaks up, with the bigger the detonation, the greater the acceleration of the fragments after they form).

This is a complicated situation, so I just divide gun projectiles into three categories (note that cavity size in Common/SAP and AP projectiles may be larger than filler weight implies due to cushioning material surrounding filler in some cases - TNT and Japanese Type 91 Explosive, for example):

Type	Percent of filler by weight
Large Cavity ("Bombardment," HE/HC, British WWI CPC, etc.)	6.0%
Common/SAP	3.51-5.99%
AP	1.4-3.5%

Note that what some nations call "Common" falls into what another nation calls "AP," and vice-versa, so the names used do not necessarily select which category the projectile falls into. To my knowledge nobody used less than 1.4% filler in a projectile designed to hit a target rather than do some kind of air burst ("shrapnel") and/or to merely spread some other filler around ("smoke" or "incendiary" (white phosphorus) or poison gas) - these tiny-explosive-filler, large-non-explosive-payload, very-weak-bodied projectiles will break open on virtually any solid impact with even a thin bulkhead or deck and have no penetrating power other than what some torn pieces retain due to their impact velocity.

These categories are further divided up into detonating and non-detonating fillers (a detonating filler can get a reduced rating to a smaller filler type and/or even to non-detonating, if its fuze or booster does not work right, the projectile body breaks open prior to fuze action, or the filler is sensitive and is set off by impact instead of fuze action).

Also, a filler can merely "deflagrate" (burn like a Roman Candle rather than explode) or even remain inert (dud) if the fuze and/or booster do not work properly or projectile damage is so bad that the filler is compromised considerably.

D. Penetration by Projectile Middle-Body Fragments at a Distance

Both German and U.S. WWII tests with indicate that the minimum thickness of "standard" WWII U.S. Special Treatment Steel (STS) or Class "B" armor required to completely stop sideways-thrown fragments from a TNT-filled projectile undergoing a complete high-order detonation is just over 0.08 caliber for AP projectiles, 0.095 caliber for Common/SAP projectiles, and 0.11 caliber for Large-Cavity (HE/HC/CPC) projectiles, as defined above. This assumes that the projectile is about 5 calibers from the plate and that the plate is not hit by the heavy nose piece or the few medium-sized pieces flying in a narrow cone around the nose piece.

If the projectile is closer than 5 calibers, the fragments are still being accelerated by the filler and the force of the blast will assist the fragments in penetrating. This is covered in the next section E. Contact Explosions.

If the projectile is over 5 calibers away from the plate hit by the fragments, the penetration will gradually decrease for the heavier fragments and more rapidly decrease for the lighter fragments.

Using a test of an over-6.5%-TNT-filled, 240-pound, WWII U.S. Army 8" nose-fuzed HE projectile standing on its base at the center of a bull's-eye pattern of various steel US Army RHA plates (similar to US Navy STS/Class "B" armor) throwing about 2,000 middle-body fragments (the "original mass" mentioned below) sideways and (only in an arc of about 10° up and down with most fragments in an even narrower 5-degree-up-and-down ring), we have the following Large-Cavity projectile results. Remember that the surface over which these fragments are spread is growing roughly linearly with the distance in this narrow ring at right angles to the projectile direction of motion (here at zero speed straight up), so the fragments per unit area are going down fast. Also, note that the forward motion of a projectile will cause the ring of fragments to move forward at that speed initially, but this is much lower than the initial sideways velocity of the fragments so the forward motion is small compared to the sideways speed of the fragments; additionally, as air resistance sets in, the forward motion drops even more at longer distances, making the fragment pattern a nearly-stationary expanding ring shape.

MIDDLE-BODY FRAGMENT PENETRATION VERSUS DISTANCE THROWN FOR A TYPICAL 8" HE SHELL

DISTANCE		REMAINING FRAGMENTS 1		PENETRATION FOR 50% OF REMAINING			PENETRATION FOR 10% OF REMAINING			PENETRATION FOR 1% OF REMAINING
CAL	FEET	NUMBER	%	NUMBER	T (CAL)	T (INCHES)	NUMBER	T (CAL)	T (INCHES)	NUMBER	T (CAL)	T (INCHES)
5	3.33	2000	100	1000	0.1100 2	0.880	200	0.110	0.880	20	0.110	0.880
20	13.33	1900	95	950	0.0213	0.170	190	0.093	0.744	19	0.106	0.848
50	33.33	1760	88	880	0.0158	0.126	176	0.075	0.600	17-18	0.100	0.800
100	66.67	1600	80	800	0.0113	0.090	160	0.057	0.456	16	0.091	0.728
500	333.33	1040	52	520	0.0011	0.0088	104	0.0186	0.148	10-11	0.0464	0.371
10003	666.67	800	40	400	0.0006	0.0048	80	0.012	0.096	8	0.023	0.184

• ^This is the fraction of the original 2000 fragments still in the air at the given range. For an SAP projectile use 3000 fragments (50% more) and for an AP projectile use 4000 fragments (100% more) due to their thicker middle bodies, on the average. All of the other NUMBER columns will go up in proportion.
• ^The 0.11-caliber thickness at 5-caliber-distance (0.88" for the HE shell used here) is the thickest armor plate that a fragment from a typical HE shell can penetrate due to inertia only (not being accelerated by the detonation blast wave behind it, as is true at under 5 calibers -- see Contact Explosions in Section E). At 5 calibers the fragments are so concentrated that the larger, more-penetrating fragments are tearing large holes in the plates and allowing virtually all fragments through. This is not true at longer distances. This 5-caliber-distance value is replaced by the 0.095-caliber maximum penetration for an SAP projectile (small amount of explosive accelerating more fragments) and by the 0.08-caliber maximum for an AP projectile (smallest amount of explosive and the most fragments formed). For the values at larger distances than 5 calibers in this table, multiply the thicknesses given by (0.095/0.11) = 0.864 x T (i.e., 0.0213-caliber thickness for the 20-caliber distance with 50% of fragments becomes 0.0213 x 0.864 = 0.0184 caliber) for an SAP projectile and by (0.08/0.11) = 0.727 x T (i.e., 0.0213 becomes 0.727 x 0.0213 = 0.0155) for an AP shell.
• ^This is the maximum distance that I calculate anything. Most fragments by now have very small penetrative ability and the number that still do are so small that they will be unlikely to hit anything important.

In a battle, the projectile will usually be oriented much more horizontally against a surface target, so the ring of fragments is moving directly upward and downward and to the sides. However, the only difference is where the fragments hit, since in a given direction radially from the shell, the target hit will see no real difference due to this, other than that fragments projected steeply upward will have their maximum distance reached shortened; small sideways-thrown fragments have little damage-causing ability once slowed down by air resistance, no matter how far they fall downward due to gravity. The larger fragments drop off in penetration quite slowly, with gravity causing them to hit the ground before air resistance slows them to a velocity where they cannot penetrate any significant plate thickness. At the longer distances, the remaining fragments are those that were projected upward and are thus flying a curved arc, further dropping their velocity by air drag.

There is a very small scaling effect, so to a first good approximation, these values will fit all size Large-Cavity projectiles when multiplied by the new projectile caliber in inches divided by 8 to get the new thicknesses penetrated in inches.

The larger fragments drop off in penetration quite slowly, with gravity causing them to hit the ground before air resistance slows them to a velocity where they cannot penetrate any significant plate thickness. There is a very small scaling effect, so to a first good approximation, these values will fit all size Large-Cavity projectiles when multiplied by the new projectile caliber in inches divided by 8 to get the new thicknesses penetrated in inches.

For example, the 38cm (14.96") Psgr.m.K. L/4,4 APC projectile used by KM BISMARCK can penetrate (0.156/0.11)(0.08)(14.96") = 1.36" of STS on contact or (0.08)(14.96") = 1.2" of STS at 5 calibers (6.23 feet) and would have a 1%/10%/50% (of the remaining projectiles fragments) STS plate penetration of 1.16"/1.01"/0.23" at 20 calibers (24.93 feet) and 1.09"/0.81"/0.17" at 50 calibers (62.33 feet), using the above HE projectile values for 0.11-caliber penetration (1.65") at 5-calibers distance reduced to 0.08 caliber (1.2", AP projectile value) at 5-calibers distance. Since HMS HOOD only had a single 1" HTS plate (equaling circa 0.8" STS) between its aft machinery room and its aft magazines, even at over 50 calibers distance (over 62.33 feet) a considerable number of fragments - dozens - from such a 38cm APC projectile penetrating into the aft machinery room and properly detonating could still punch through that bulkhead and allow blast effects and projectile fragment impacts to occur on propellant-filled 4" secondary ammunition cases, with a very good chance of them blowing up the secondary magazine and setting off the aft main magazine, as actually occurred. No "fluke" hits are needed to destroy HOOD from BISMARCK.

Test data for 10% black-powder-filled British WWI (and before) Common, Pointed, Capped (CPC) projectiles gives a maximum, full-power-explosion (British Navy "burst") velocity of the medium-sized middle-body fragments of circa 600 feet/second (most moving slower than this), which is much lower than the average of the many smaller fragments created by a Large-Cavity HE projectile detonation. In fact, this is about half of the expected remaining velocity after a near-normal complete penetration of a 0.25-caliber KC plate (the thickest that this projectile could penetrate at that obliquity and still remain intact afterwards) at the typical battle ranges, so the penetration ability of the pieces is much more dependent on the remaining velocity of the projectile after penetration than on the blast-induced velocity of the fragments. Calculating the remaining penetration of the fragments is not easy, so I have merely developed the following very crude system:

1. The sideways velocity of the fragments is proportional to the HE fragments, so a Large-Cavity projectile has 600 feet/second (best case), a Common/SAP projectile has 540 feet/second (using relative penetration ability (0.095 versus 0.11 for the Large-Cavity projectile) turned into a velocity ratio by using the DeMarre Nickel-Steel Penetration Formula - (600)(0.095/0.11)^0.71429 = 540 feet/second), and an AP projectile has 478 feet/second. If the projectile suffers damage that renders it "ineffective" then reduce the velocity by a large amount (cut it in half) if it can still explode, though reduce it to nothing if the filler merely deflagrates and the body breaks into a few big pieces (must be determined by projectile design factors not mentioned here).

2. Calculate the remaining velocity of the projectile after it penetrates the plate that sets off its fuze and any other plates it might pierce prior to it finally going off (inherent 0.025-0.075 second delay occurs with a black powder and, I assume, guncotton filler) and add the sideways velocity of fragments from (1), above, using the Pythagorean Rule

   Vfragments = (Vremaining² + Vsideways²)^0.5

3. Calculate using some homogeneous steel armor penetration formula the remaining normal-obliquity penetration of the intact projectile through STS using Vfragments instead of Vremaining and assuming that the projectile has suffered no damage. Multiply this by 0.15 and use it as the penetration ability (assume normal impact always) of the average fragment through any bulkhead or deck within the 60° arc directly in front of the projectile.

4. Subtract the effective thickness of the bulkhead or deck plate hit (use the regular laminated-plate calculation for determining its effective thickness) from the penetration ability of the average fragment and, if there is any penetration ability left, use it to determine the penetration through the next plate in line by subtracting that plate's effective thickness from the remaining penetration ability and seeing if the remainder is greater than zero - if zero or negative, the fragment does not penetrate. Keep doing this until the fragment does not penetrate. (This linear method is due to the fragment cutting irregular plugs out of the plates hit, which subtract extra energy to push them out of the way on top of the energy needed to cut them out of the plate to penetrate it. Otherwise, a kinetic energy subtraction using the DeMarre Nickel-Steel Penetration Formula would have been used.)

Note that different high explosive filler types have different blast and fragmentation abilities. However, a more powerful explosive might accelerate the projectile fragments to higher velocities, but also break them into smaller, more numerous pieces, which will reduce penetration from the fragments, not increase it. Since I do not know most of this detail, I am not including it here. Blast pressure effects definitely depend on the explosive used, especially underwater blast from torpedoes and mines.

E. Contact Explosions

When a projectile explodes while pressing up against a plate, it transmits more of its blast effects into that plate, as well as trying to push the fragments through the plate more forcefully as they will not decelerate as rapidly with the explosive blast pressure on their rear side. The result is a larger hole and more fragments through the plate for a given plate thickness that is penetrable. Also, for impacts up to 45° obliquity, a instantaneous-nose-fuzed HE projectile's forward velocity will have some effect in that a higher velocity will bury the nose deeper into the plate prior to the filler detonating - the delay is very small in this case, so only a rather high impact velocity has an effect. In addition, the U.S. ADF has a definite effect in increasing the delay and hence the penetration in some cases for projectiles up to about 10" (25.4cm) in diameter. The ADF had no effect compared to similar German post-1930 Spgr.m.Kz. (as mentioned above, impact-nose-fuzed HE without an ADF) projectile tests (described in the German 1940 naval "Gunnery Bible" G.Kdos. 100 and related post-WWII U.S. Naval Technical Mission in Europe documents) when similar tests were performed with 12" (30.5cm) and larger WWII U.S. Navy HC projectiles using an ADF, but the ADF had a definite effect in tests with 3-8" (7.62-20.3cm) WWII U.S. Navy HC projectiles using an ADF. Note that these results for the ADF also include the case of the HC projectile with a steel nose plug if it hits a plate heavy enough to set off the ADF anyway, as previously described.

The definition of "penetration" is not sharp in this case, since a hole is blown through the plate and the size of the hole varies from merely a crack at the bottom of a dent in heavier plates - which has obviously minimal effect - to a large hole of caliber diameter or greater in thinner plates - which obviously can have major effects in the space behind the plate. The maximum STS plate thickness that will barely have a caliber-diameter hole blown in it by an instantaneously-nose-fuzed HE/HC projectile with a detonating filler is "Tphe." STS plates up to 20% thicker than the thicknesses Tphe calculated below - that is, 1.2 times Tphe - will be dented and cracked by the projectile, with a linear increase in hole size as the plate drops down to Tphe from (1.2)Tphe.

For a nose-fuzed HE projectile that detonates with its nose tip just touching the affected plate at any striking velocity (whether or not it is set off by a nose or base fuze), the orientation of the projectile has a minimal effect on the maximum thickness of the plate that can be penetrated by the projectile's fragments; only the small nose-tip fuze and the heavy base plug will provide any kind of shield from the blast and fragments of the explosion. If the same thing occurs with a Common/SAP or AP projectile, the heavy nose provides a major shielding effect from the blast and fragments in the forward 90° arc, though any plate in front of the nose will now have to stop a smaller, lighter, but equally-wide and equally-fast-moving spin-stabilized projectile made from the heavy nose (circa 25% of the original projectile body weight for Common/SAP projectiles and circa 33% for AP projectiles, as defined above) plus some medium-sized fragments ringing the nose piece. Thus, for Common/SAP and AP projectiles, the projectile must be hitting the plate at over 45° obliquity for the filler blast and filler-blast-created sideways-moving fragments to be considered in the penetration of that plate. Also, with a base- or internal-fuzed projectile, the projectile may explode at any time during its contact with the plate, which will obviously cause more damage if it has already torn open a hole or slot in the plate, while an instantaneous-nose-fuzed HE projectile will always explode before the projectile has moved more than a few inches, depending on the striking velocity and ADF, so no prior hole is made in the plate other than the dent/gouge made by the tip of the projectile's nose.

Restricting ourselves to instantaneous-nose-fuzed (not hardened for armor impact and with no special delay, which were options in a few special-purpose impact nose fuzes used in WWII), HE-booster (trinitrophenol or more powerful booster explosive; not black-powder), Large-Cavity HE/HC projectiles without an ADF (including time fuzes and VT fuzes, which will act as such fuzes on impact), we get from U.S. and German tests the HE Projectile Armor Penetration Formula (No ADF) for blowing a caliber-wide or larger hole in the plate:

Tphe(noADF) = (2.576 x 10^-20)(D)V^5.6084COS[2(Ob2 - 45°)] + (0.156)(D)

Note that the minimum plate thickness that will barely have a caliber-wide hole made in it even at zero striking velocity is 0.156 caliber of STS (1.25" for the 240-pound 8" HE projectile mentioned previously), with over 0.1872 caliber of STS (1.2 times 0.156 caliber, over 1.498" for the 8" HE projectile) needed to stop a through-crack in a dented STS plate. Note how little the striking velocity increases penetration until it nears the gun's muzzle velocity.

If the projectile has an ADF, but is otherwise identical, and is 10" or less in diameter, the following HE Projectile Armor Penetration Formula (ADF) gives a Tphe(ADF) value that replaces the above no ADF formula Tphe(noADF) value if and only if Tphe(ADF) is greater than Tphe(noADF); otherwise, always use Tphe(noADF):

Tphe(ADF) = [(0.00013333)(D)V + 0.033333]COS[2(Ob2 - 45°)]

This second formula is linear and from what I can figure out has to do with how deep the projectile nose can dig into the plate prior to detonating compared to the total length of the nose fuze and ADF. The ADF increases the delay by a more-or-less fixed amount and in a smaller projectile this allows a much lower striking velocity for the nose to dig into the plate deep enough prior to exploding so that the upper end of the main explosive cavity itself is touching the plate when the explosion occurs, allowing the main filler charge to assist directly in blowing open the hole, while for larger (over-10") HE/HC projectiles with an ADF, the much larger nose does not dig deep enough even with the added delay until the striking velocity increases considerably, eliminating this effect, so the projectile fragments must blow open the hole by themselves, though obviously assisted by the filler blast behind them. When the striking velocity increases high enough, however, all projectiles dig their noses into the plate far enough to get this added direct-blast bonus (which is why their penetration increases so rapidly at this point), merging the smaller ADF-equipped projectiles and all other nose-fuzed projectiles into the no ADF formula from that velocity on up. There is no scaling effect in the data that I have seen, so at under 45° obliquity, the two formulae merge for all applicable projectiles at a minimum striking velocity of 929 feet/second and at a maximum striking velocity of 2300 feet/second (with the ADF formula used between these values only if the projectile is 10" or less in diameter and has an ADF). These limits change with increasing obliquity over 45°. The 20% thicker plate that is dented and cracked also occurs with both of these formulae. Note that 2300 feet/second is above the standard muzzle velocity for most nose-fuzed HC projectiles used by the U.S. Navy in WWII, though not when a "super-charge" was used for added range or when some more-specialized designs, such as AA Common, were employed with an ADF.

The increase in penetration from a contact Large-Cavity HE projectile explosion compared to a 5-caliber-distance Non-Contact Explosion for a zero-velocity impact (see Section D, above) is 0.156-caliber (for example, 1.248" for a typical 8" HE shell) for all fragments, giving (0.156/.11) = 142%. (I assume that this value stays constant for most of the distance from 0 (touching the plate) to 0.499 calibers away due to the detonation blast wave behind the fragment preventing the fragments from slowing down in this close range and due to the fragments being so concentrated that the highest-penetration fragments tear large holes that allow virtually all other fragments through too. The hole in the thickest plate that can be penetrated is thus shaped roughly like a rectangle as wide as the projectile and as long as the projectile body from the base to just above where the tip of the explosive cavity ends -- almost the entire length of the shell for an HE shell, but somewhat less due to the smaller/shorter cavities in SAP and AP shells. At around 5 calibers distance, the high-velocity blast wave passes through the cloud of fragments and leaves them behind to move forward only by inertia, subject to gravity and air resistance, as discussed in Section D. The 5-caliber boundary between Contact and Non-Contact effects is of course somewhat "fuzzy", but for want of a better set of data, I assume that the boundary is sharp, with the 0.156-caliber maximum for an HE shell in the Contact region dropping suddenly to 0.11 caliber maximum in the Non-Contact region starting at 5 calibers exactly. The same is true for the SAP and AP projectiles, as adjusted here and in Section D.

The size of the hole in a plate from a Contact Explosion varies by how thin it is compared to the maximum thickness that will be holed, with the thinner the plate, the larger the hole, of course. Looking at various hits, I would use a "quick-and-dirty" rule of thumb for gun projectiles that the size of the hole in a single plate varies in a formula inversely with its thickness compared to the maximum. So a 12" diameter HE shell 4' long makes a large hole of 1' x 4' in the 0.156-caliber (0.872") STS plate due to fragmentation (blast would merely dent it and tear its edge supports) with this hole going up by Hole Width (right angles to projectile centerline) = 2 x D x 0.156/T(cal), so that a plate half as thick (0.436"/0.078 cal) as the 0.872"/0.156-cal maximum would make a hole that was 2 x 1' x 2 = 4' wide. The length of the hole along the projectile centerline would not increase very fast, about L(min) x (1 + 0.1 x 0.156/T(cal)), so that the Hole Length in this same case goes up to 4' x (1 + 0.2) = 4.8'. Note that if the plate gets thin enough for detonation blast to tear it open, then the hole size will increase in all directions very rapidly as it gets thinner; this would be around T = D/10 or so.

Note that aircraft bombs have MUCH larger filler weights than gun projectiles of the same nominal type. An HE bomb will have typically a 50% filler weight, for example, with SAP and AP bombs also significantly scaled up in filler weight. Thus, the thickness of the plates that blast damage will start to be a serious problem is significantly greater than with gun projectile explosions.

If we use this same percentage increase for a contact, over-45°-obliquity impact by the sideways-thrown, numerous, and fast-moving fragments of the middle body of an HE-filled Common/SAP and AP projectiles, then they can blow a hole through a (1.42)(0.095) = 0.135-caliber STS plate for the Common/SAP case and a (1.42)(0.08) = 0.113-caliber STS plate for an AP projectile, if they are in the process of penetrating or ricochetting from the plate at high obliquity when they detonate. These are the average minimums if the filler completely detonates high-order, even if the projectile has not damaged the plate prior to the detonation. However, if the projectile has torn open a hole in a thicker plate, the blast and fragments can of course possibly make the hole larger (having some effect up to perhaps a plate twice as thick from blast and fragments working alone). Also, a degraded explosion due to projectile damage or poor fuze and/or booster action or shock setting off the filler without the fuze or booster functioning will of course degrade the plate thickness holed from the fragments and blast alone by a proportional amount - this is a random effect, however.

If the in-contact projectile has a non-detonating explosion equal to a maximum-power black-powder "burst" for the given percentage weight of explosive, then the larger, slower-moving fragments will also penetrate, for want of any other data, the same 142% greater thickness on contact than the value calculated above for the 60° forward arc will be used, with the 60° forward arc value used for a 5-caliber distance or greater, rapidly changing from one to the other at the 5 caliber distance.

If the Common/SAP or AP projectile is imbedded into the plate deeply enough so that the plate surrounds the cavity when the filler explodes, regardless of the impact obliquity, the blast can split open brittle plates of rather large thicknesses, especially face-hardened plates that have just been holed by the projectile, which is now passing through the cracked, brittle face layer around the hole when it explodes. These explosions can break a plate in two and are quite spectacular at a proving ground, though much less important than a deep, delay-action hit through the hull armor in a real ship, which usually has internal protective bulkheads and decks and side-mounted fuel bunkers designed just to stop such outer hull effects from reaching the "vitals" of the ship.

A black-powder explosion is usually a rather low-blast-power (compared to an equal weight of a typical detonating explosive like TNT), long-duration effect, with considerable incendiary effect as the flaming fragments of not-quite-burned powder are thrown around. The projectile casing is only broken into a relatively few large, slow-moving fragments compared to an HE filler. The blast power of black powder is only about one-third that of TNT. However, when a black-powder-filled AP-capped AP/SAP-type shell hits a thick face-hardened plate and is in the process of penetrating it with its thick, hard nose and upper body passing through the plate still in an intact condition (the projectile may break up during this time, but if above the complete penetration velocity at a low obliquity, this will usually occur after the nose has punched through the plate), the very sharp deceleration on the hard face, where most of the plate's resistance occurs, will cause the black powder to be thrown forward and compressed to about half of its volume. This is because black powder, unlike HE fillers, is not a single solid mass, but is made up of many tiny grains of three separate materials (charcoal, sulfur, and potassium nitrate (saltpeter)) thoroughly mixed and tightly compressed. However, being separate grains, there exists a lot of empty space between them and even inside them, so the sudden enormous deceleration will squeeze these air gaps out and form a solid mass for a very short period of time. This motion will cause friction and heating everywhere throughout its mass and the black powder will begin to burn everywhere simultaneously under high pressure, which results in a "pseudo-detonation". If the black powder weight was three times the weight of an equivalent AP shell's HE filler weight -- British WWI CPC shell with its 10% black powder filler compared to the same gun's AP shell 3.3% Lyddite HE filler weight, for example -- the detonation of both fillers, now of similar power, inside a thick face-hardened plate as the shell is halfway through can cause the now-cracked plate to split in half, as was shown in a number of British test firings. Thus, it is critical to completely understand a sequence of events to see what the actual results will be, which may be quite different from what one might imagine prior to such analysis and actual tests.

When a projectile is damaged by an armor plate during penetration, the projectile can bend (offset), be compressed (upset), or break (pieces split off), in any combination. The damage can be to the projectile's nose, to its middle body, or to its base, in that order as to the importance to reducing the projectile's penetration ability through the plate causing the damage (though all three can have equally-degrading results when trying to penetrate a later plate after penetrating or ricochetting off of the plate causing the damage). Hardened noses and, in some cases, middle bodies do not bend if manufactured properly and can compress only to a limited extent, so they tend to suffer breakage when they are damaged. Softer middle bodies and bases - except for brittle chilled cast iron projectiles - are much more likely to bend or to suffer compression damage, though the grooves cut into them for the driving band(s) and the reduction in the weight of metal due to the hollow explosive-filled cavity cause breakage here too (the softening of these portions of the projectile is designed to minimize such breakage, with varying degrees of success).

At normal impact, the shock of hitting a heavy armor plate, especially "face-hardened" armor plates especially designed to do this, can cause shatter (sudden breakage of the nose into several pieces that can just include the nose, but usually destroys the entire projectile) as the nose is suddenly compressed, cracking at the sides of the nose as the shock wave formed in the nose reflects. An AP cap is designed to soak up this sideways-moving portion of the shock wave and blow outward like an over-filled balloon on impact to eliminate this cause of projectile shatter. It works quite well in this capacity as long as there is no gap between its inside surface and the surface of the projectile nose under it. Soft AP caps (wrought iron or, later through the end of WWI, soft steel) used by most nations prior to the end of WWI - except for the last versions of the APC projectiles developed by Krupp and Skoda in 1911 (the Krupp "Psgr.m.K. L/3,4" for example) and the post-Jutland 1918 British "Greenboy" APC projectiles with improved body and nose hardening and the new "Hadfield" hardened AP cap, as well as a new delay-action fuze patterned after the German L/3,4's base fuze and a new insensitive "Shellite" filler - begin to fail at just over 15° obliquity and never work at over 20° obliquity because they are peeled off of the nose due to the asymmetric forces and their elastic composition. Hard AP caps remain relatively undeformed under such stress and function at all obliquities where they hit the plate first (requiring wider caps for high obliquities than were used in many WWI APC projectiles), as well as gouging out a pit in the plate as the cap is destroyed, which seats the projectile nose like a center-punch seats a drill bit, eliminates much of the high-hardness plate material in front of the projectile, and reduces the plate thickness in front of the projectile. A couple of WWI face-hardened armors - U.S. pre-WWI Midvale Co. 'Midvale Non-Cemented' Class "A" armor and Austro-Hungarian Witkowitzer Company 'Krupp Cemented' armor - and most post-WWI face-hardened armors (except for Japanese Vickers Hardened Non-Cemented face-hardened armor used in the YAMATO Class battleships, which was purposely made as a slightly-improved, non-cemented version of the pre-WWI British Vickers Company 'Vickers Cemented' KC-type armor obtained when the Japanese bought the battle-cruiser IJN KONGO in 1912) seem to be able to remain unbroken due either to improved toughness (most such improved armor, including the Witkowitzer KC) or to an extra-thick face layer coupled to adequate minimum toughness (Midvale MNC) under the initial projectile impact shock when hit by a soft-capped projectile. The soft cap does not damage the plate significantly prior to being destroyed, unlike a hard AP cap, and the now-cap-less projectile nose is then crushed as it is squeezed between the still-uncracked plate face and the decelerating projectile body behind the nose, which gives identical results to the previously-mentioned shock-induced shatter, since both occur prior to the plate's face layer breaking, if it ever does. I call these improved face-hardened armors "SOFTSHAT" armors. Shatter of either sort causes a sudden increase in the effective thickness of any kind of face-hardened plate of 30% at normal obliquity, but it also impedes ricochet (the deflection of the nose, now in pieces, no longer pulls the rest of the projectile along with it) and gradually the benefit is lost, until at 55° obliquity or more for thick plates, shatter actually makes it easier for the projectile's pieces to penetrate than if it had not shattered.

Against relatively soft homogeneous, ductile naval armor, as used in thin plates, very thick WWII U.S. battleship vertical armor plates for conning towers and turret faces, and in armored decks, shatter, if it occurs (which is rather rare with a well-designed steel AP projectile, especially if it still has its AP cap attached on impact), has a much more complicated result depending on the plate thickness and obliquity, though at high obliquity shatter reduces the plate's resistance in a manner similar to face-hardened armor and for the same reason. Since shatter is relatively rare with steel projectiles when hitting non-face-hardened armor (chilled cast iron projectiles shatter on any steel plate if they do not have an AP cap, however), I am simply going to assume that the same rules used for thick face-hardened armor apply if it happens. My computer program FACEHARD can be used to show the effects of shatter versus no shatter on any given kind of projectile by removing the AP cap prior to impact and increasing the total projectile weight without the AP cap and windscreen to compensate, which will result in shatter of an "equivalent" uncapped projectile of otherwise the same design as the capped one.

Shatter eliminates other forms of nose damage (there is no longer a nose to damage) and most normal-impact body damage effects, though oblique-impact body damage effects and the any-obliquity compression-induced body collapse I call "upset body failure" in its most extreme form in lightly-built projectiles such as British anti-ship CPC (for relatively lightly-armored ship targets), German WWI "Sprenggranat mit Bodenzunder" (abreviated "Spgr.m.Bdz.") (uncapped, base-fuzed, large-cavity, CPC-like anti-ship projectiles) and U.S. WWI uncapped CPC-like "Bombardment" or "Class B'" shore bombardment projectiles, which I term "Light-Case" projectiles, can still occur, drastically lowering penetration ability through heavy armor (much like dropping a watermelon end-first on a concrete slab from a height with a metal bowl over its front end to keep that end intact, but letting the middle body "splash" sideways). Upset body failure occurs to some extent to most weaker forms of Common/SAP and AP projectiles, but once complete penetration is achieved by increasing the striking velocity high enough (the damage requires an extra velocity increase over a "perfect" projectile of otherwise identical design to allow penetration), this problem tends to go away due to the shorter time that the forces causing it have to make it happen. Shatter itself cannot be eliminated by increasing the striking velocity, since that merely increases the impact shock wave formed and makes the crushing of the nose against a SOFTSHAT plate occur that much faster.

Bending damage, which usually occurs at medium-to-high obliquity (25° or more), always reduces the ability to penetrate since it makes the hole required in the plate significantly larger (usually wider), which is not true for breakage damage, where part of the projectile may penetrate through any hole formed if the projectile pieces are small enough or the hole merely large enough to admit an unbent projectile that is shortened by its nose or base breaking off. Compression damage would act the same way, but if it gets too extreme, the sideways bulging of the affected portion will begin to crack so that the nose, if this is the affected portion, will shatter or undergo some other, less extreme, form of breakage or the body, if it is the affected portion, will collapse and break due to upset body failure, changing the damage to breakage, anyway.

General nose and body breakage that is severe enough to affect penetration will usually cause the projectile to be rendered "ineffective" due to splitting open of the explosive-filled cavity, though with small-cavity AP projectiles, nose damage might sometimes occur that does not reach down low enough to damage the cavity. Note that damage that renders the projectile "ineffective" may have no penetration-related effects, such as fuze damage or cracking of the lower projectile body due to the base of the projectile slamming up against the plate on ricochet or during penetration at an oblique angle where the projectile is deflected strongly from its original path in the process.

Average, typical, penetration-changing effects of projectile breakage-type damage on a hardened Common/SAP or AP projectile when it hits homogeneous, ductile armor are given in the following table, based on very extensive tests of WWI-era, soft-capped U.S. AP projectiles against STS or Class "B" armor of about half-caliber or more in thickness (thinner plates rarely damaged the projectiles at any obliquity, though the minimum plate thickness that could cause significant damage decreased steadily as obliquity increased). This table gives the average percentage change in the minimum striking velocity needed to get a complete penetration (the "base through" or U.S. "Navy Ballistic Limit" (NBL)) compared to an undamaged projectile of otherwise identical design. Note that the effects gradually increase with increasing obliquity, peak sharply at 45°, then rapidly decrease until at 61.6° obliquity the effects of the damage on penetration are nil, while above 61.6° obliquity, breakage actually improves the chance of penetration by impeding ricochet (nose damage is obviously a major part of this total damage effect), this improvement being considerable by 80° obliquity, where I stop my calculations. Note that not all of the projectile may make it through the plate when breakage occurs - I use 80% or more of the projectile's pieces, by weight, for defining the Navy BL when breakage occurs.

Table of Average Projectile Breakage Effects on Navy Ballistic Limit

Obliquity (°)	% NBL Change
0	3.84
5	4.44
10	5.56
15	7.22
20	9.56
25	11.94
30	14.44
35	17.56
40	22.22
45	30.56
50	18.89
55	10.00
60	2.22
61.6	0.00
65	-5.00
70	-11.94
75	-16.67
80	-20.20

These value vary from projectile design to projectile design, but they are typical of the results of heavily-constructed-projectile damage due to homogeneous, ductile armor penetration through the plate causing the damage. This table is NOT used for projectiles which suffer extensive bending or upsetting damage during penetration, such as post-1930 British Common/SAP and AP projectiles, which had hard noses, but very soft, ductile lower bodies and no hardening of the body in the sideways direction (centerline hardness and surface hardness were the same for most right-angle "salami slices" through the projectile, what is called "decremental hardening"), unlike WWII U.S. Navy AP and Common projectile "full sheath hardening," where the higher hardness on the surface reached much farther down the projectile side from the nose, while softening more rapidly along the centerline from the nose down (but never dropping to as low a level as the British projectiles), which acted as a hard "girdle" to prevent sideways forces from distorting the projectile's upper and middle body. These British projectiles must be covered separately.

If the projectile was not broken, then this NBL value would represent the minimum velocity that allowed any part of the projectile to pass through the plate (all or nothing). However, under several circumstances, especially with broken projectiles, the area behind the plate may be damaged or even destroyed when the projectile hits at below the NBL. For example, at above 45° the projectile will usually ricochet off of the plate if it does not penetrate all of the way through; decelerating to a stop and remaining stuck in the plate is rare because the projectile is in many cases moving at a velocity much greater than the minimum velocity to punch through the plate if the deflection effect on its nose - that tilts the projectile nose and, if the projectile is still in one pieces, the rest of the projectile to skip off and away from the plate face - was not working. An impact on homogeneous, ductile armor below the NBL at over 45° will in some cases tear a long, narrow hole in the plate during ricochet that is not wide enough to allow an intact projectile through, but will allow pieces of a broken projectile through, especially the lower body if the nose breaks off and the lower body continues to punch into the plate rather than be pulled away as the nose ricochets, which occurs with an intact projectile with nose and body still firmly attached to one another. Since the lower body of naval Common/SAP and AP gun projectiles contains most or all of the explosive charge and the base fuze, if it goes through the plate there is a good chance that some sort of explosion will occur behind the plate (it may not be a full-power, as-designed explosion of a completely "effective" projectile, but in many cases, such as turrets and conning towers, this is not going to make much difference!) and the armor protection has been defeated.

I call the velocity that allows a hole to be punched through the plate of roughly caliber size or greater, whether the projectile itself penetrates or not, the "Holing Ballistic Limit" (HBL) and it is very important to impacts against brittle face-hardened armor, where the armor material that used to be in the hole is punched out the plate back at high speed and acts as a second, rather large, solid shot projectile (intact or in pieces), or in homogeneous, ductile armor at high obliquity when the projectile breaks or it explodes prior to bouncing off (especially at very high obliquity where the canoe-shaped gouge and tear in the plate may be quite long and the base fuze delay short enough to explode the projectile before the projectile has moved far enough from the initial impact point to begin to be deflected away from the plate face). The sometimes even lower striking velocity that begins to crack the plate open entirely through from face surface to back surface is termed the "through crack" or, in the U.S. through the end of WWII, the "Army Ballistic Limit" (ABL) - for face-hardened armor, the ABL and HBL are virtually the same (all or nothing effect), but the ABL may be far lower than the HBL at high obliquity against homogeneous, ductile armor where a hair-line slot may be torn in the plate during ricochet that satisfies the definition of the ABL but has virtually no effect on decreasing the protection afforded by the plate against that impact. At low obliquity against homogeneous, ductile armor hit by a pointed-nose projectile, the ABL may also be much lower than the HBL - the NBL and HBL are usually quite close to one-another - but the heavy projectile nose plugs the hole and prevents any explosive effects from passing through the small hole in the plate when the plate is hit at between the ABL and HBL, so the ABL may have little meaning. If the projectile has a flat or at least very blunt nose, however, it may cut out a disk-shaped plug at the ABL in homogeneous, ductile armor that can cause some damage behind the armor even if the projectile does not penetrate itself - here, as in face-hardened armor, the ABL and the HBL are the same.

After WWII, the U.S. Army realized that the ABL in many cases did not mean much when determining if the weapon used had destroyed the target, so they changed this to the "Protection Ballistic Limit" (PBL) where a thin metal "witness" plate was placed behind the armor and some minimum level of damage must be inflicted on this witness plate before the armor could be considered "defeated" by the weapon. Usually the PBL is between the ABL and the HBL, but in plates hit by weapons that can break off pieces of the armor's back surface - by shock effects, for example - (including excessively brittle armors or plates held together by bolts and rivets that can be knocked off and fly around like bullets), the PBL may actually be lower than the ABL. In a large warship, the internal protective bulkheads, decks, and fuel-filled spaces in the side hull behind the main belt armor and beneath the outer deck armor require the NBL be reached and exceeded by some amount to be able to do major damage to the target's "vitals" (machinery spaces and powder magazines), but this is obviously not true when smaller spaces like turrets or conning towers or, in the Army, rather crowded spaces inside tanks and armored personnel carriers are hit. Defining the PBL is not always easy, since a hit in one place that does nothing may in another place, even on the same plate, cause the armor to bend enough to, say, jam a turret (for example, as happened to the French battleship JEAN BART at Casablanca when a 16" AP projectile fired by USS MASSACHUSETTS hit and ricochetted off right where the single operating 15" turret's lower side armor and barbette top edge met, jamming the two metal plates together so that a cutting torch was needed to eventually free the turret; if the hit had been even a couple of feet higher, the projectile would have done nothing as it bounced off, though a similar distance to one side would have meant a direct hit on the turret face plate and almost certainly the destruction of the hit half-turret - the turret was divided by a heavily-armored centerline longitudinal bulkhead and armored floor into two side-by-side two-gun half-turrets rotating together, a uniquely French design - if not the entire turret, if the projectile penetrated). Also, bad design practice - such as, say, placing the electric cables for the lights in the turret against an armor plate (you cannot load the guns in the dark!) - can play a key role in the PBL, which makes it even harder to define. Luck is a major factor here - good armor and supporting structure design practice (do not have anything important close to the back surface of an armor plate!) can minimize, but never eliminate, the effects of such "fluke" hits.

When a projectile bends or compresses excessively on impact due to a soft nose and/or body structure (usually designed to reduce breakage that would render the projectile "ineffective" as an explosive device after the impact), the effects on penetration ability can be considerable and when they occur, they do not help penetration at high obliquity as nose breakage does, since a bent projectile is still in one piece and will glance off the plate even easier than a rigid-body projectile will if the soft body deforms itself to the shape of the gouge it is making in the plate. Usually plate thickness and obliquity interact to determine if the projectile is going to be deformed significantly or not, creating a rather complex formula to ascertain the results of such deformation. Note that the results of the formula can never make it easier to penetrate the plate, so if the formula gives such a result, then the projectile has not deformed and the effects of the formula are to be ignored.

The following formula is used in the German document G.Kdos. 100 for calculating the effects of obliquity and plate thickness on intact penetration ability into homogeneous, ductile armor (Krupp Wh armor in that document) and on both intact and broken penetration through face-hardened armor (Krupp KC n/A armor in that document). I derived the formula and the constants used by plotting the changes that plate thickness and obliquity had on the projectile's tabulated penetration ability compared to undeformed penetration at normal obliquity by the same projectile against each of the plates (the Krupp Post-1930 Universal Penetration Formula given in my article "Historical Naval Armor Penetration Formulae" was used for normal impact in the German document, with a "C" quality factor given separately for each plate against each projectile - two "C" values for KC n/A against broken and intact penetrations, respectively). I am certain that the tabulated penetrations in G.Kdos. 100 were derived from actual test results and are therefore good data, once one realizes the limitations as to when the formula is applicable and when it is not. I used the same formula, but derived my own constants from tests of other, non-German projectile tests, when I thought that these other projectiles were similar enough to the German designs to allow the formula to be used - for example, this was definitely not true for U.S. "fully-sheath-hardened" WWII AP and Common projectiles when hitting face-hardened armor; they required a different kind of formula for damage effects.

The formula is a multiplier of the projectile's penetration (and, for face-hardened armor, separate damage resistance) quality factor to increase the minimum striking velocity to satisfy the definition of penetration being used. Here, when applied in G.Kdos. 100 to homogeneous, ductile armor, penetration implied intact "effective" penetration. In real life, base slap can prevent effective penetration even if the projectile is otherwise unaffected by the impact, so usually a higher striking velocity is needed to reduce deflection during penetration to the point where lower body damage ceases. However, in badly deforming projectiles a single-valued increase rule (such as the 25% increase in striking velocity at over 45° used with more rigid projectiles) does not work, requiring a progressively higher velocity increase above the NBL as obliquity and plate thickness or both go up. This puts homogeneous, ductile armor on the same footing as face-hardened armor in this regard, though the minimum plate thickness needed to cause damage is higher for a homogeneous, ductile plate in many cases.

The general formula for progressive reduction in penetration ability for progressively-deforming projectiles as impact obliquity and/or plate thickness increases is:

QPused = (QPtable)[1 + (Ob3)(Cqtbl) - (Aqtbl)(Teff/D)(Ob3^Bqtbl) - (LC)(Teff - Tmin)/D]

Tmin/D = 1.75; QPtable =1.00; Aqtbl, Bqtbl, and Cqtbl are 0.004017, 1.46971, and 0.0198476; LC = 0.5; QA = 1.00 for US WWII STS/Class "B" armor (the standard homogeneous armor that I use), so Teff = Tactual and Teff/D = Tactual/D.

Thus, for the British WWII APC shells, we get:

QPused = 1.00 x [1 + (OB3 x 0.0198476) - {0.004017 x Tactual/D x (OB3 ^ 1.46971)} - 0.5 x (Tactual - 1.75)/D]

where:

The LC term (0.5 x ...) is set to zero unless Tactual > Tmin, since it is an extra deformation term that really does not apply to thick-bodied AP projectiles, even the deformable WWII British AP shells unless they hit very thick armor (it is primarily for typical SAP and similar weak-bodied shells with a low Tmin).

For example, with an 18" US Navy WWII Class "B" turret face plate, a 1590-lb 14" British Mark IB NT "K" APC projectile has a Tactual/D = 1.286, which is less than 1.75, so the LC term disappears. At 30°, we get:

QPused = 1 + 30 x 0.0198476 - 0.004017 x 1.286 x (30 ^ 1.46971) = 1 + 0.595428 - 0.0051659 x 148.23129 = 1.595428 - 0.76575 = 0.8297

At 45°, we get:

QPused = 1 + 45 x 0.0198476 - 0.004017 x 1.286 x (45 ^ 1.46971) = 1 + 0.893142 - 0.0051659 x 268.99423 = 1.893142 - 1.3896 = 0.5035

Against 7.25" US Navy WWII Class "B" armor turret roof plates at 55° (OB3 = 45), that shell gives:

QPused = 1 + 45 x 0.0198476 - 0.004017 x 0.51786 x (45 ^ 1.46971) = 1 + 0.893142 - 0.00208023 x 268.99423 = 1.893142 - 0.5596 > 1.00, so 1.00 used.

The QPused for the British shell is its regular QPtable = 1.00 value, which gives an NBL at 55° of 1886 ft/sec in HCWCALC Revision 2 (I did not use the Cap Edge Effect (answered "N" to that question in HCWCALC) due to the rounded contour of the Hadfield AP Cap face of that British shell, unlike the sharp outer corner of the US Navy Standard WWII AP Cap's 50° half-angle conical face (AP Cap Selection #1 in HCWCALC)). Also, the British AP Cap had a face hardness of over 600 Brinell, so I said "Y" to that question in HCWCALC. This velocity was well above the highest British projectile test velocity used in this evaluation of 1679 ft/sec, so the British shell ricocheted off with only a 4"-deep canoe-shaped gouge in the plate even with its QP unchanged, while the US very-blunt- oval-nosed, slightly softer-capped (c. 555 Brinell face) 1500-lb 14" Mark 16 MOD 8 AP shell, using a standard US Navy WWII AP Cap shape with that sharp edge corner, punched entirely through with only some base damage. From this and other data, I estimate that the oval-nosed WWII US AP shells get about a 12.5% reduction in the NBL at 55°, decreasing to zero benefit at 30° and at 70° in a smooth, though not symmetric, bell-shaped curve in either direction (the blunt nose does not penetrate thick armor at low obliquity quite as well as a point, though the loss is small so I ignore it, and as obliquity goes up above 55°, the center of the blunt nose never gets involved until later and later in the penetration process as a long, canoe-shaped gouge is made in the thinner plates, so the nose bluntness has less and less of a benefit there too). However, the Cap Edge Effect also gives a 12% drop in NBL (countered by a small rise in NBL due to the windscreen being crumpled up on impact) over a wide range of obliquities due to the cap edge cutting a notch in the face and peeling up a section of the plate's face like a wood plane, which masks the projectile's actual nose shape here during the initial impact where most of the benefits of either nose shape or cap design occur. The NBL is calculated at 1712 ft/sec using HCWCALC results, including both the Cap Edge Effect and the Windscreen adjustment, which is close to the actual test value (average of two impacts, one ricochet at 1685 ft/sec and one penetration at 1750 ft/sec) of 1700-1720 ft/sec. Perfect match between HCWCALC and an actual test! Also note how important the Cap Edge Effect is when it comes into play, giving virtually any pointed or oval-nosed AP projectile the capability to penetrate at a wide range of oblique angles as if it had an optimized blunt nose shape.

As mentioned, QPused can never exceed QPtable; if the formula says it does, simply use QPtable as is instead. Note that only the LC (for "Light Case" weak-bodied projectiles) term has any effect at normal obliquity and it does only when Teff is greater than Tmin (if not, ignore this term in the formula). This is because most well-designed projectiles are rather strong against forces coming directly down their length with no sideways component. In fact, most post-1900 naval AP projectiles have LC close to zero and/or a high value for Tmin, as is indicated by the results for the more rigid-body AP projectiles described in this section and in section 8, below.

QPused defined above for the projectile increases the NBL as QPused itself decreases, so it DIVIDES the tabulated value of the Plate Quality Factor "QA" for the armor type hit to get the Combined Projectile-Vs-Plate Quality Factor "Qtotal" = QA/QPused, which is only used for that plate hit by that projectile at that obliquity and at that striking velocity (not for any other conditions!!).

Each projectile that has this formula applied to it for any given ballistic limit must have the values of Aqtbl, Bqtbl, Cqtbl, LC, and Tmin specified for that ballistic limit against the particular type of armor (face-hardened or homogeneous,ductile). Note that only the Aqtbl/Bqtbl term is not linear and it increases rapidly with increasing obliquity Ob3, though even it is linear with increasing plate thickness for a given fixed obliquity value. This forms a "fan" of straight-line QPused values below Tmin if QPused is graphed versus plate thickness Teff with Ob3 given in, say, 5° increments. Above Tmin, the QPused lines will curve toward zero as Teff increases, since the LC term affects all QPused values for all Ob3 values.

As an example, in post-WWII U.S. Naval Proving Ground tests the late-WWII 1595-pound (723.5kg) British 14" (35.56cm) 'K' APC projectile (British official designation "Shell, Breach-Loading, Armour-Piercing with Cap, 14-Inch, Heavy, K, Mark IB Night Tracer") was found to have relatively poor performance at 55° obliquity against U.S. 7.25" (184.2mm) (T/D = 0.518) Class "B" turret roof armor, merely making a 4"-deep (101.6mm) gouge where the U.S. 1500-pound (680.4kg), hard-capped, oval-nosed 14" Mark 16 Mod 8 AP projectile was penetrating completely (partially due to the more pointed British projectile nose and partially due to the British projectile bending on impact like a banana so its nose was tilted farther away from the normal than the middle and lower body). Against new U.S. 13.5" (342.9mm) Class "B" plate (T/D = 0.964) at 30° obliquity, both the U.S. and British projectiles were virtually identical in penetration ability, while against new U.S. 13.5" Class "A" plates, the British projectile was slightly better than the U.S. projectile (due to a harder AP cap), but against U.S. 17.3" (439.4mm) Class "A" (T/D = 1.236) and 18" (457.2mm) Class "B" (T/D = 1.286) barbette and turret face plates, respectively, at 30° obliquity, all British 14" projectiles merely made deep dents in the plates, broke their noses off, and bent into bananas again - though they usually remained in effective bursting condition afterward - at striking velocities where the above U.S. 14" projectile was punching completely through, though with extensive lower body damage, to be sure, indicating that the British projectiles had a grossly over-soft body under such extreme impact conditions and the U.S. projectile's lower body was perhaps a little too hard (though this brittle base may have been a condition that the U.S. Navy had to live with if minimum penetration velocity was to be achieved, given the level of expertise in metallurgy at the time). The British seem to have taken the concepts of the "Treaty" battleship and their poor projectile performance during Jutland in WWI rather too much to heart, not only in restricting their ship's displacement, but even in the ability of their weapons to handle heavier armor than what they considered the maximum that such ships could carry (incorrectly, as the USS NORTH CAROLINA, USS WASHINGTON, and the U.S. SOUTH DAKOTA Class battleships' extremely thick barbette, turret, and conning tower armor showed), while simultaneously demanding reliable post-impact explosive effectiveness even when it interfered with armor penetration ability.

For these British projectiles against homogeneous, ductile armor, which I assume are typical of post-1930 British APC projectiles of 14", 15" (381mm), and 16" (406.4mm) size (15" mid-WWII "Cardonald" APC projectiles were supposed to be better, but I have no hard test results to ascertain by how much), I will assume that (Tmin/D) is 1.75 caliber (as with the 3" M79 standard AP projectile) and LC is 0.5 (the same as used by my FACEHARD program for CPC-type "Light Case" projectiles against standard face-hardened armor) - this eliminates most armor from consideration at normal obliquity (the Tmin value would be much lower for most non-U.S. SAP, SAPC, and base-fuzed Common (British WWII CPBC, for example) projectiles). I also assume that the British WWII Ministry of War Homogeneous Armor Penetration Formula, developed from tests of the 1.96-pound (0.889kg) British 1.5648" (39.75mm) "2-pounder" Armor-Piercing Monobloc Shot anti-tank projectile used at the start of WWII and scaled models thereof up to 45° obliquity against British WWII Non-Cemented Armor (NCA), gives a good indication of the ratios of the NBL at various obliquities and plate thicknesses compared to the normal obliquity NBL against the same plate. The values for the NBL calculated by this formula and from the U.S. Naval Proving Ground formulae derived from tests of the 15-pound (6.804kg) U.S. Army WWII 3" (76.2mm) M79 AP Monobloc Shot projectile, which was similar to the British projectile, being slightly heavier for its size and with a slightly more pointed nose, are very close for a 3" scale model of the British projectile weighing the same as the U.S. 3" projectile fired against caliber-thickness NCA at normal obliquity - this test gives an average NBL only 1.39% lower than the U.S. 3" projectile hitting average U.S. Navy WWII caliber-thickness STS armor at normal obliquity! The match is not as good for very large projectiles, but the ratios of oblique-to-normal NBL seem to be consistant with other data on British projectiles, so I am using this ratio applied to the U.S. 3"-M79-projectile-based formulae set to calculate the QPused value for British Navy WWII major-caliber APC projectiles (14", 15", and 16"), assuming that they are roughly equal to U.S. Navy WWII major-caliber APC projectiles (12" (304.8mm), 14", and 16") against plates up to caliber thickness and up to 30° obliquity, which matches actual test results done just after WWII at the U.S. NPG, as mentioned above.

Using the British formula to calculate the ratio of NBL at 30° for the 14" British WWII APC projectile to their normal (0°) NBL against a 1.00 caliber (14") and a 1.28571 caliber (18") NCA plate and this same ratio at 45° against the 18" NCA plate, I used the ratio to calculate the reduction in QPused from QPtable = 1.00 (for this projectile against thin STS plate at normal) by setting QPused = 1.00 for 14" STS armor hit at 30° (as found in the actual tests compared to U.S. 14" AP projectiles), and found that QPused for the 18" plate was only 0.82988 at 30° and only 0.50391 at 45° (which matches the rather poor performance of the British projectiles against 18" U.S. Class "B" armor at 30° actually found in the same tests). With those three data points (the actual 14" plate results and the two 18" plate calculated results), I calculated Aqtbl, Bqtbl, and Cqtbl to be 0.004017, 1.46971, and 0.0198476, respectively, for the QPused formula applied to all British WWII BB-size APC projectiles - remember, QPused is set to QPtable if QPused is found to be greater than QPtable from this formula, since deformation damage will NEVER improve penetration ability, unlike projectile breakage over 45° obliquity sometimes can. For example, when applied to the 7.25" Class "B" turret roof plate hit at 55° obliquity in that same post-WWII US and British 14" AP shell comparative test series done at NPG/Dahlgren in 1947, the British 1590-lb 14" projectile had its QP unchanged by the formula (it was above 1.00, which negates the formula result) and the calculated 1886 ft/sec NBL from my HCWCALC homogeneous armor penetration computer program (this shell's nose shape was not much different from the standard WWII US Army 76mm M79 AP Shot used as the nose shape for HCWCALC), applying the appropriate AP Cap shape and hardness values (a rounded-face-contour Hadfield AP Cap design with no sharp edge to the face so the Cap Edge Effect (see below) does not occur; AP Cap face hardness over 600 Brinell; and a pointed nose preventing the Intact Cap Effect -- a dislodged AP Cap riding a rounded projectile nose through the plate tilted at an angle that makes penetration more difficult) was well above the highest test velocity of 1679 ft/sec, so the British shell ricocheted off with only a 4"-deep gouge in the plate and was broken up when its lower body slapped the plate face and bent and then broke as the nose ricocheted upward. At the about the same striking energy, with a ricochet at 1685 ft/sec and a complete penetration at 1750 ft/sec, we have an estimated NBL of 1700-1720 ft/sec, for the US Navy very-blunt-oval-nosed, slightly-softer-capped (c. 555 Brinell maximum) 1500-lb 14" Mark 16 MOD 8 AP shell. The US projectile's AP Cap had a sharp edge to its conical, rounded-tip face, allowing the Cap Edge Effect to occur (cutting a deep notch in the plate face which folds the armor upward and reduces the required striking velocity to penetrate by, for the US AP Cap shape, about 12%); the cap face was below 600 Brinell; and the shell had a very blunt oval nose with no point, allowing the Intact Cap Effect to occur, if so calculated. The NBL was identical to the actual calculated NBL, using my HCWCALC program, of 1712 ft/sec, with only some base damage that would not have stopped the shell from destroying the inside of the hypothetical turret even if the shell was a dud. Most of the agreement between the actual test NBL and the HCWCALC NBL is due to the Cap Edge Effect (which occurs over a wide range of impact obliquities), since the thick cap was masking the actual projectile nose shape. Without the Cap Edge Effect, as seen in the British results with an otherwise similar projectile, but a rounded AP Cap shape, you get a much poorer result whenever the effect could occur. NOTE: The very blunt nose of the US shell was to give a better oblique impact penetration ability in those cases where the AP Cap was stripped off by a thinly-armored weather deck plate so that the shell hit the primary armored deck bare-nosed, which, as the results with the British shell show, a pointed nose, even when covered by a rather blunt AP Cap, may give poor results.

By the way, the "K" in the name for the British 14" projectiles stands for a form of dye bag use that was adopted from the French Navy after the British obtained some French projectiles after the loss at Dunkerque in 1940, though the technique was not fully adopted by the British until circa late-1942 or early-1943, to my knowledge.

The post-WWI U.S. and Japanese Navies used small dye bags in the projectile windscreens that mixed with water forced into the windscreen on ocean impact (due to the break-away "cap head" design for the Japanese Type 88 and Type 91 AP/APC projectiles and due to special pop-out windows and plugs cut into the U.S. AP and "Special" Common projectile windscreens) and colored the large pillar-like splashes made by the projectiles. This was used in good visibility in daytime to tell the shots from one set of guns from another, if more than one were firing at the same target, and thus improve fire-control updates. The French and, later, the British realized that this had two problems: It was only useful in daytime with good visibility (night or bad weather defeated this system) and it did not record direct hits on the target unless there was a spectacular and immediate post-impact effect, such as a fire or explosion on the target (and direct hits were the best indication of good shooting, of course!).

The French post-WWI design was simple: Take an impact nose fuze and booster charge from an HE projectile, strengthen the windscreen somewhat, and mount the fuze/booster at the tip of the windscreen, with an especially large dye bag inside the windscreen. When the projectile hit the water or hit the target, day or night, the nose fuze would instantly set off the booster, which was powerful enough to blow open the windscreen, causing a bright colored flash and puff of colored smoke. (Thus the windscreen and dye bag weights and any other effects should really not be counted in determining armor penetration, since they did not last long enough to have any effect whatsoever.) This was by far a better system than that used by anyone else for this purpose (though eventually made obsolete by improved radar). Just why the British called this "K" I do not know, though it probably relates to the name the French used for this dye bag system ("Night Tracer" is a burning flare set into the projectile base fuze).

Projectiles are made out of iron and steel and thus are just as susceptible to damage as the iron and steel armor plates that they hit (see section 7, above). Elongated, spin-stabilized projectiles hitting nose-first are strongest when they hit a plate at right-angles where the forces are directly and symmetrically down the centerline of the projectile. As obliquity increases the forces become more and more asymmetric and subject the projectile to more and more sideways stresses that vary from point to point down the projectile length, with the forces peaking at around 45° obliquity and then gradually reducing in magnitude as the projectile skids sideways on the plate and takes a longer and longer time to either penetrate or ricochet off. However, the impacts at over 45° may increase base damage considerably as the projectile slams its base against the plate face either when it is digging into the plate to penetrate or when it is rotating its nose away from the plate surface to bounce off; this damage also gradually increases with obliquity from normal (0°), but it peaks at closer to 60° obliquity and rapidly decreases from there as the rotation of the projectile is reduced during ricochet or the projectile punches through the plate sideways or only slightly nose-first (only thin plates can be penetrated at any reasonable striking velocity at such extremely high obliquities, anyway).

For the purposes of this section, when a projectile suffers damage by satisfying the requirements for that projectile under the given impact conditions, the projectile will have both a modified penetration ability as defined in section 7 on the average, and, unless specifically stated otherwise, a loss of projectile explosive "effectiveness" which reduces or entirely prevents the explosive filler from acting in its "as-designed" manner (when no damage has occurred). The loss in effectiveness may merely mean that the projectile's fuze has been broken and the projectile rendered "blind" with no other damage to the lower body surrounding the explosive-filled cavity (meaning that nose damage is the sole cause of the change of the projectile's penetration ability) or it may mean that the projectile has broken up into several pieces or it may mean something in-between. This is somewhat a random variation, though distinct trends for certain projectile types (even for certain models of a given type) usually are evident, as specified in section 7.

The "Table of the Effects of Impact Obliquity on Minimum Plate Thickness To Damage Common/SAP and AP Projectiles" gives the change in the minimum plate thickness of standard U.S. Navy WWII Special Treatment Steel (STS) or Class "B" armor - or the equivalent effective thickness of other homogeneous, ductile iron or steel materials after applying the armor type's quality factor to the actual plate thickness and after applying the laminated plate formula if the material is laminated - needed to damage a given projectile compared to the thickness at normal obliquity to cause the damage. The damage is assumed to be BREAKAGE damage, not deformation damage as described previously for the soft-bodied British WWII APC projectiles. There are two columns: Column 1 is for hard, brittle projectiles that suffer more damage on oblique impact (that is, they are designed with near-normal impact as their main priority) and they usually will require a thicker plate at normal, but thinner plates at high obliquity, to damage them (ignoring shatter for the moment); while Column 2 is for projectiles with more ductile middle and lower bodies designed with some oblique-impact post-impact effectiveness in mind and they may or may not be as strong as those in Column 1 at normal impact, but they are much better at resisting damage at oblique impact, so thicker plates - as a fraction of the plate thickness needed to damage the projectile at normal - are needed at oblique impact to get damage comparable to the projectiles of Column 1 at any given obliquity. That is, if two projectiles, one using Column 1 and the other using Column 2, have the same minimum plate thickness to damage them at normal, the Column 1 projectile will be damaged by plates that get progressively thinner and thinner compared to the plates needed to damage the Column 2 projectile as obliquity increases. Column 1 plate thickness reaches its minimum at 65° obliquity and Column 2 plate thickness reaches its minimum at 70° obliquity - the thickness remains constant up to 80° where all penetration calculations stop (above 80° penetration becomes essentially impossible and projectile damage can be considered to decrease to zero, other than loss of the projectile's windscreen, if any, as the projectile barely skims across the plate surface, leaving a shallow dent as it ricochets off at nearly full impact velocity).

Table of the Effects of Impact Obliquity on Minimum Plate Thickness To Damage Common/SAP and AP Projectiles

Obliquity (°)	Angle
	Narrow	Wide
0	1.000	1.000
5	0.917	0.946
10	0.828	0.877
15	0.745	0.815
20	0.662	0.754
25	0.580	0.692
30	0.503	0.631
35	0.427	0.569
40	0.357	0.515
45	0.293	0.462
50	0.236	0.415
55	0.197	0.377
60	0.178	0.354
65	0.172	0.348
70+	0.172	0.346

The plate thickness at normal that equals the 1.000 value at the top of the applicable column must be specified for each projectile in addition to the column (NARROW ANGLE or WIDE ANGLE) that the particular projectile is to use. Body damage for determining the projectile's post-impact explosive "effectiveness" (ignored if the projectile has no explosive filler) and nose damage for determining penetration ability changes would each have its own normal-obliquity thickness value, usually different, but sometimes the same These of course vary with design details of the projectile and must be included as part of any tabular listing of the properties of the projectile along with its identifying nomenclature, projectile type, size, weight, nose shape parameters, fuze type, filler weight, filler type, AP cap type, AP cap weight, muzzle velocity, etc.

The data in the above table for Column 1 is from tests of the U.S. Army 3" M79 projectile mentioned above, which had no AP cap, hood, windscreen, or explosive cavity, and which had a tangent ogive nose shape with a Radius of Ogive (also called "Caliber Radius Head" or "CRH") of 1.667 caliber (5" here); that is, a sharply pointed nose contour made from a single arc of a circle of 5" radius with the center of the circle at the level where the cylindrical projectile side joins the nose, so that there is no crease or shoulder at the joint. For this projectile, the minimum normal-obliquity STS plate thickness to cause nose damage as defined above (= 1.000) was roughly 1.75 caliber or 5.14" (130.6mm) (body damage is ignored here because the projectile has no explosive filler). Interestingly enough, this column more-or-less matches the German Krupp APC projectile armor-penetration specification for impacts against KC a/A (WWI) or KC n/A (WWII) face-hardened armor, which specified a half-caliber-thickness KC plate at 30 obliquity and a caliber-thickness KC plate at normal obliquity must be penetrated in "effective bursting condition" at the NBL (somewhat less than U.S. Navy WWII APC projectile requirements but very advanced in 1911 when they were introduced with the then-new Krupp "Psgr.m.K. L/3,4" APC projectile design).

For Column 2, the test projectiles were the U.S. Navy WWII 105-pound (47.63kg) 6" (152.4mm) Mark 27 and Mark 33 "Special" Common projectiles, which include large windscreens with punch-out plugs; small dye bags to color the water rammed through the windscreen openings after the plugs had been knocked out by an ocean impact; soft-steel, soldered-on hoods to cut the threads to screw on the windscreen; rather small 2.1-2.3% Explosive "D" filler charges (similar to the weight used in most foreign naval AP projectiles), and Mark 21 Base Detonating Fuzes (originally, a Mark 23 BDF). They had tangent ogive noses that varied with model (Mod Number) from 1.51-1.97 caliber (9.06-11.82") radii of ogive. These projectiles had a normal-obliquity minimum STS plate thickness to cause both nose and body damage as defined above (= 1.000) of roughly 1.3 caliber or 7.8" (19.81cm). Not as good as the M79 AP projectile at normal, but pretty good for an SAP/Common projectile, especially at oblique impact!

If the projectile fails to completely penetrate the plate (rebounds backward or remains stuck in the plate at up to 45° obliquity or ricochets at a higher obliquity up to 80°), it will suffer more damage over-all due to the forces on the projectile lasting longer and/or occurring over a larger portion of the projectile from nose to base, rather than just on the nose and upper body, which were usually the hardest and strongest portion of the projectile. As with the other effects of oblique impact, the change in minimum plate thickness for projectile damage for non-penetrating impacts is greatest at an obliquity of 45° and gradually goes back toward the applicable table value as obliquity increases over 45°. This minimum thickness reduction for a given projectile can be approximated by the following formula (not used for impacts with Ob over 80°):

MINIMUM THICKNESS(No Penetration) = (TABLE THICKNESS){0.9 - (0.3)SIN[2(Ob)]}

Note that the worse case at 45° gives a change in minimum damage-causing thickness to the point where it is only 60% of the table value (0.176 or 0.277 for NARROW or WIDE, respectively), while at normal the reduction is only to 90% (0.9 for all projectiles) and at 80° it is only to 79.7% of the table value (0.137 or 0.276 for NARROW or WIDE, respectively). This minimum thickness calculation applies separately to body and nose damage, but need be only done once to get the multiplier, since projectiles use the same column in the table for both nose and body damage (I do not have enough information to separate the two in most cases as to which column to use for which damage, so I will not attempt to do so).

If a projectile subject to this section's damage rules penetrates a plate that causes damage at the modified NBL (see section 7) at up to 45° obliquity with an excess striking velocity of 10% over the modified NBL, nose damage and, as a result, any other damage, will cease to occur (projectile effectiveness and the remaining velocity calculations will revert to an undamaged projectile situation using the unmodified NBL instead of the modified NBL since damage is no longer happening), due to the very short time for the impact forces to act on the nose. This same 10% increase over the modified NBL will eliminate nose damage at over 45° obliquity, which will eliminate the penetration-modifying effects of the damage (that is, the remaining velocity calculation will now revert to an undamaged projectile calculation), but the increase must be by 25% at over 45° obliquity to eliminate lower body damage due to the twisting of the body and "base slap" of the lower body and base against the plate during penetration (that is, return the projectile to "effective" status after the impact).

If the projectile undergoes shatter due to the impact being above its shatter velocity for the given plate type and obliquity angle (uncapped chilled cast iron projectiles against any steel plate or uncapped steel projectiles at very high velocity against some harder forms of homogeneous, ductile armor, especially at oblique impact), no amount of velocity increase will eliminate the shatter. However, this is rarely a consideration with steel naval projectiles against homogeneous, ductile naval armor due to their rather low muzzle velocities compared to army anti-tank gun projectiles.

This article is copyrighted 1998-2018 by Nathan Okun and is reproduced on NavWeaps.com with permission.

10 December 1998 - Baseline
18 January 2011 - Corrected typographical errors
21 February 2018 - In Section 7, corrected formula for QPused, added information on British 14" projectile performance and fixed typographical errors
17 April 2018 - In Section 6, redid Fragment Penetration table and added note regarding SAP projectiles, in Section 7 redid explanations