The amount of armor a naval gun projectile can penetrate by sideways-blasted fragments from the middle body (not counting the heavy nose pieces or base plug) depends somewhat on the filler (detonating high explosive (HE) filler assumed; not black powder or guncotton) used and a lot on the percentage weight of explosive. For a first approximation, I simply use an "average" HE (circa TNT in power), rather than try to adjust for the individual type of filler (there were many), since for gun projectiles the explosive power usually only ranged from 0.9-1.4 (TNT = 1.0), with only the WWII "RDX" or "Cyclonite" filler mixtures being above 1.1 and they were not used except for US AA guns projectiles very much during WWII and very rarely against ships).
My MISCELLANEOUS FORMULAE artcle uses roughly 0.08 caliber as the maximum plate thickness of US WWII STS (or equivalent in another metal using its "effective" plate quality against penetration) for the small-fillerAP projectiles blowing up 5 calibers away to the projectiles' sides from the target that any of these sideways-mpoving fragments can penetrate (barring the rare fluke), 0.095 caliber STS for Common/SAP medium-size filler projectiles, and 0.11 caliber STS for large-filler ("Bombardment"/HE/HC/CPC) projectiles. Thus, at 5 calibers to the side, the 11.1" GRAF SPEE shells can penetrate 0.89" STS with its APC shell, 1.05" STS with its base-fuzed HE shell (SAP), and 1.22" STS with its nose-fuzed HE shell.
This linearly ramps up to 0.156 caliber of STS for the nose-fuzed HE shell in contact with the shell's middle side (1.73" for the 11.1" gun) ("zero caliber distance"), and, proportionally, 0.156 x (0.08/.11) = 0.113 caliber STS on contact for an AP round (1.26" for the 11.1" gun) and 0.156 x (0.095/0.11) = 0.135 caliber STS on contact for an SAP shell (1.5" for the 11.1" gun).
Going away from the target from the 5 caliber distance starting point, the penetration ability drops off with distance, with the heavier fragments having the least loss in penetration before they simply fall down to the ground/ocean surface rather than hit the target as distance increases (as expected), and the small fragments slowing down faster, reaching less and less distance and with less and less penetrating power for those that do make it to any given distance.
Even at 1000 calibers (11,100" or 925' or 308.33 yards for the 11.1" shells), some fragments can still penetrate, as follows:
(1) Only 40% of the original fragment weight thrown in a direction that could reach the target are still there. Those thrown in other directions of course do not matter and the conical spread of fragments reduces the hits per presented area of the target using the same inverse square law used with light and gravity. The rest thrown at the target were so small that air resistance essentially stopped them and they fell down with no real velocity (they could injure people, but that it about it).
(2) Of this 40% left, 62.5% of it (25% of the original weight portion thrown at the target) can still penetrate 0.0064 caliber STS (HE shell) (0.071" for the 11.1" gun), 0.095/0.11) x 0.0064 = 0.0055 caliber STS (SAP shell) (0.061" for the 11.1" gun), and (0.08/0.11) x 0.0064 = 0.0047 caliber STS (AP shell) (0.052" for the 11.1" gun).
(3) Similarly, a further 25% of the 40% (10% of the original weight thrown at the target) can penetrate, for HE/SAP/AP, resepctively, 0.012/0.01/0.009 caliber STS (0.133"/0.111"/0.1" for the 11.1" gun).
(4) A further 2.5% of the 40% (1% of the original weight thrown at the target) can still penetrate 0.023/0.02/0.017 caliber STS (0.255"/0.222"/0.189" for the 11.1" gun).
(5) The rest of the 40% that is still "in play" (100 - 62.5 - 25 - 2.5 = 10% of the 40% or 4% of the original thrown fragment weight at the target) fall in-between the three values given here -- none are below the 62.5% lowest-penetration value or above the 2.5% value (give them random penetration values in this range of possible penetration values).
In reality there would be a smooth spread in fragment penetration ability from the minimum given to the maximum given, but the above fractions, if used in a step-based Monte Carlo probability system, will usually give "good-enough" estimates of the chances of damaging the target.
Thus, even at 1000 calibers miss distance, if the GRAF SPEE had an 11.1" nose-fuzed HE shell hit near one of the British cruisers, there is some chance for up to 0.25" NCA plate (British STS equivalent) to be penetrated by a fragment or two. You of course have to work out how few fragments per unit area of that penetating power there were left, which is pretty thin, and how big the target ship's vulnerable area is, but it is possible, though rare, to hit something -Nathan Okun