The effective mass of the penetrator is a sum of the actual core’s mass and some extra mass that pushes on it, until the moment it enters the target to a depth greater than its length. If the penetration process is finished before then, the effective mass of the penetrator, and therefore its penetration, is simply the sum of both parts.
In most situations of interest here the tungsten subcaliber shell is penetrating thickness of armor much greater than that, therefore the effect will be cosiderably smaller.
Since we are comparing two projectiles of the same Diameter attacking the same target, the variables D, T and K are equal and will cancel out resulting in this equation:
Let’s look at a schematic of the 3.7cm PzGr.40, since its most similar to the soviet 45mm APCR of which I dont have a detailed schematic:
Spoiler
so, if we take the m_p variable to equal 83g, then the mass ratio in the equation will equal 0.62 and the ballistic limit of the full shell against a target of thickness less that the core’s length, will be ~79% of that of a naked core.
Against a reasonably thicker target the effect might be about half of that, or ~10% increase in ballistic limit.
Applying this adjustment to the 45mm APCR limit we get 840 * 1.1 = 924m/s BL for a naked core. Using this as reference to estimate the BL for the .40cal core in the US testwe get 2970fps, very close to the actual obtained limits of 2990fps and 3040fps.
My gut feeling tells me: Because nobody, especially the Germans, will accept a ±10% dimensional tolerance spread on manufacturing of anything this important.
I see. Then probably an error based on the fact that 5 easily turns into 6 based on the fact they are so close toghether and can easily be misidentified in print.
Makes little sense to produce both 15x58 and 16x58mm cores.
Nah that sounds unlikely. Theres some German manual on the usuage of the tungsten ammo and it says it only provided better arrmor penetration up to 150m.
The bullet has a less aerodyanmic flat base design copared to the the AP round, probably to save weight. But that reduces the effective range.
So for a tank it seems rather impractical. Most AT gun shields just provide some protection from fragmentation or maybe SMG rounds.
I guess if you give every rifleman and machine gunner a bunch of rounds, you just end up with a lot of tungsten ammo.
The 15mm x 58mm Core is 135gm±4. with a 0.1mm diameter tolerance. So there could be some variability. The 37mm APCR rounds the US captured were 57.4 mm - 58mm long, and 15mm - 15.6mm diameter.
Good news all: I calculated the penetration of both extremes, a 15mm - 135g core and a 16mm dia 155g core and the penetration differs between them by only 1 mm.
Apparently if all the extra mass is concentrated on the sides of the projectile, its extra kinetic energy is compensated by the fact that it needs to make a bigger hole through the armour.
Edit: Btw, my bad, previously I took the diameter value for the 37mm APCR from the soviet document from my memory, but the actual document gives the diameters of the 37mm and 50mm german APCR as 16mm and 20mm respectively.
I have a theory: prehaps, the early 37mm cores had 16mm dia, but as I have just shown, reducing it to 15mm does not markedly decrease its penetration. Perhaps at some point the cores were slimmed down a bit to conserve tungsten?
