Weighing the Fog Of Battle Part III

I have been running some models of gun fire and armour penetration for the guns on the Invincibles, Blucher and the Scharnhorst (and the 9.2"/47 Mk X as used on the RN armoured cruiser HMS Good Hope) as a matter of interest.

What I find is that the British 12"/45 Mk X can penetrate the 18cm armour of the German armoured cruisers (turrets), and Blucher at virtually any range. The 9.2"/47 Mk X can penetrate this armour at ~9km (the NavWeaps page on this gun would seem to imply this should be more like 6.2-6.3km?). The Blucher's guns appear not to be able to penetrate the 6" armour on Invincible outside ~7.3km, and those on Scharnhorst outside ~5.8km (possibly contradicted by events at Coronel, where one of Good Hope's 9.2" mounts (6" armour) was knocked out within 5 min of von Spee's ACs opening fire at ~12km).

These penetration figures are all for normal impact, so overestimate what could be achieved in battle and ignore poor shell design (at least for the RN) early in WW1. But the general conclusion that Blucher was very vulnerable to armour penetration by the British battlecruiser's 12" guns, while the Invincibles were relatively well armoured against attack by the Bluchers 21cm guns is probably valid.

I should add the caveat that these figures are derived by integrating the differential equations of projectile motion with drag characteristics only valid in a hand waving sense, and using the Krupp all purpose formula (set up for "typical" APC against KC ) for armour penetration. Also my penetration figures for the 9.2" and the 21cm guns appear to be inconsistent with some published figures and results at Coronel. I also suspect the penetration model is for better projectile design and better armour than in use in 1914-15.