Complicated stuff:
75mm KwK vs. Sherman 63mm glacis plate at 2,000 yards:
At 2,000 yards the incoming shell will have a trajectory of 15-20 degrees off horizontal. This reduces the effective slope of the Sherman’s glacis plate to 58-63 degrees. While the effective armor with an at best 58 degree slope included is still good at 74mm, it is now within the penetrating capabilities of the KwK 40. The 63mm plate is also relatively thin. This means that overmatched rounds will often crush the armor regardless of its theoretical sloped thickness. Theoretically, the higher the muzzle velocity, the more penetration any kind of AP round would have, all other variables remaining constant. In real WWII tank combat, however, other important variables intervened, such as the thickness to diameter (T/d) coefficient, which means that the higher the diameter of any given round relative to the thickness of the armor it is going to strike, the better the probability of achieving penetration. Furthermore, if the diameter of the shell overmatches the thickness of the armor plate, the protection given by the slope of the armor plate diminishes proportionally to the increase in the overmatch of the armor piercing round diameter or, in other words, to the increase in this T/d overmatch. So, when a KwK 40 shell hit the Sherman’s glacis plate, the 75 mm diameter of the shell overmatched the 63mm glacis plate by so much that it made little difference that the Sherman’s glacis was sloped at an angle of 58 degrees from vertical.
"Armor obliquity effects decrease as the shot diameter overmatches plate thickness in part because there is a smaller cylindrical surface area of the displaced slug of armor which can cling to the surrounding plate. If the volume which the shot displaces has lots of area to cling to the parent plate, it resists penetration better than if that same volume is spread out into a disc with relatively small area where it joins the undisturbed armor. Plate greatly overmatching shot involves the projectile digging its own tunnel, as it were, through the thick interior of the plate. It was found experimentally that the regions in the center of the plate produced the bulk of the resistance to penetration, while the outer regions, near front and rear surfaces, presented minimal resistance because they are unsupported. Thus, an overmatched plate will be forced to rely on tensile stresses within the displaced disc, and will tend to break out in front of the attacking projectile, regardless of whether the edges cling to the parent material or not. Plate obliquity works in defeating projectiles partly because it turns and deflects the projectile before it begins digging in. If there is insufficient material where the side of the nose contacts the plate, stresses will travel all the way through the plate and break out the unsupported back surface. The plate will fail instantaneously rather than gradually".
So the PzKpfw IV Ausf. H’s KwK 40 L/48 had a good chance of destroying an M4A3(76)W Sherman at ranges beyond 2,000 yards.
Now, let’s see if the reverse is true as well; will the Sherman be able to kill the Panzer at 2,000 yards?
The answer is: Very, vey unlikely, and the reason is twofold.
First, while the 76mm M1 was a very good gun, its ammunition was deficient. The theoretical penetration of 93mm at 90 degrees at 2,000 yards was only theoretical against German face-hardened armor. The noses of US AP ammunition turned out to be excessively soft. When these projectiles impacted armor which matched or exceeded the projectile diameter, the projectile would shatter and fail. At 80mm the Panzer’s armor overmatched the Sherman’s poor ammunition.
Secondly, the Panzer’s armor was of superior quality to the Sherman’s. As a general rule, BHN (Brinell Hardness Index) effects, shot shatter, and slope effects are related to the ratio between shot diameter and plate thickness. The relationship is complex, but a larger shell hitting relatively thinner plate will usually have the advantage, but the reverse is also true; a thicker plate will usually have the advantage over a smaller shell, regardless of the theoretical penetration. There is an optimum BHN level for every shot vs. plate confrontation, usually in the 260-300 BHN range for WWII situations. Below that, the armor is too soft and resists poorly, above that, the armor is too hard and therefore too brittle.
However the Germans took a lesson from the Japanese sword smiths of old and created rolled face-hardened armor plates using heat treatment techniques reminiscent of those used making Samurai swords. Hard tempered steel increases the armor’s ability to shatter incoming shells, but it is also brittle and may itself shatter. The Germans used heat tempering to gradually increase the hardness of the face of the plate while the core and back face of the plate remained soft and able to support the brittle hard face to prevent it from shattering. Rolled armor is also ballistically superior to cast armor due to the compaction and consolidation of grain structure which occurs during rolling. Today similar techniques are used to make “bullet resistant” glass.
The ideal armor is extremely tough and fairly hard at its outer surface, with two goals:
1. Reflecting enough energy back into the incoming shell to cause it to shatter or deform, thereby diffusing its kinetic energy (if square-on to the outer face) or deflect and carry off most of its energy (if at an angle to the outer face).
2. Maintaining as close to a perfectly stiff outer surface on the armor as possible during the extremely dynamic energy flow following impact, so that the incoming energy is spread over as large an area of the outer face of the armor as possible, to maximize the volume of metal behind the impact area into which the energy shock wave is transmitted.
Ideal armor is quite ductile for a significant depth from its inner face, so that a shock wave arriving from the outer face is dissipated to the greatest possible extent in deformation, so as to avoid spalling or fragmentation. Even if the inner face reaches its melting point during deformation, a minimum amount of molten metal will be ejected inward, and hopefully at low velocity. If the melting point is reached during spalling, on the other hand, relatively massive pieces of molten metal can be projected at high velocity, which is very undesirable. Even for minor impacts that do not cause inner-face melting, spalling is very likely to cause damage. If complete fragmentation occurs, catastrophic damage can be caused by the fragments and by passage of some or all of the incoming shell through the armor.
The reason that simple penetration figures are meaningless is that the best plate armor, can deliver a much greater degree of this kind of ideal performance. Simple, crude WWII castings on the other hand, were homogeneous all the way through at best, and were uncontrolled and variable in counterproductive ways in other cases. Very good plate armor may deliver three or four times the performance, inch for inch, of the best possible homogeneous casting.
The use of rolled armor is also the reason why German tanks look so angular and boxy compared to the mostly cast-steel allied tanks.
So in conclusion I stand by my previous statement:
"No, even the 76mm Sherman simply wasn’t a match for late-war PzKpfw IV’s. The IV had superior front armor and a gun that could kill a Sherman front-quarter at more than 2000 yards. In return the Sherman would have to close to 500-1000 yards to kill a IV with a front-quarter shot."
A combination of higher quality armor, the physics of overmatching that were not really understood at the time, better ammunition, better optics and a smaller silhouette made the PzKpfw IV Ausf. H a distinctly superior tank. There were more than one reason why allied tankers invariably reported every German tank as being a Tiger. It wasn’t just the looks.
I also want to address this claim:
“The specialty (and rare) APCR tungsten shot of both guns would be able to engage each other (just) at ranges of less than 2000 yards. 98mm at 30 degrees at 1800 yards for the Shermans "HVAP" vs 77mm at 1500 yards at 30 degrees for the Mark IVs APCR "Pzgr 40". However neither tank would possess many of those rounds, and in all likelyhood, especially for the Germans in 1944-45, none.”
While the western allies didn’t introduce HVAP rounds until mid 1944 the Germans had been using Hartkern (tungsten APCR) rounds since 1940, and about 25% of Germany’s production of AP tank/anti-tank shells were APCR. Germany used APCR rounds more extensively than any other nation, to the point of arming their anti-tank aircraft with hartkern firing cannons (Ju 87G, Ju 88 and Hs 129 primary). When the Germans ran out of tungsten in 1944 they used hardened steel and mild iron as core material. Not as effective as tungsten, but still better than a solid shot.
