Weighing the Fog of War Part IV

There is another problem with the data in table 1 of [1]. The rates of fire are the same for all of the guns on each side, 2 rounds per minute for the British and 3 rounds per minute for the Germans. Which appear to correspond to the RoF figures quoted on NavWeaps for the British 12 and 13.5" guns and the German 11 and 12" guns.

If a ship waits for its previous salvo to land before firing the next with corrections at the battle ranges involved, rate of fire will be limited to something like 2 salvoes per minute. If instead full rate of fire is employed then the Blucher is firing 6 rounds per minute per gun (or salvoes per minute) and should dominate the hit and damage statistics.

My take on all of this is that the analysis is spoiled by the high effectiveness attributed to the Blucher's 21cm guns compared to the 12" guns on the British ships. This is partially compensated for by limiting Blucher's rate of fire. But even at its attenuated rate of fire I find Blucher will almost always eliminate all of an Invincible's turrets on the engaged side while sustaining only minor losses itself in a single ship on ship engagement under these rules.

References:

1. MacKay N, Price C, Wood J, Weighing the fog of war:Illustrating the power of Bayesian methods for historical analysis through the Battle of the Dogger Bank, Historical Methods 2016 49 (2)  pp80-91

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.

Weighing The Fog Of Battle, Part II

For the background to this post see the previous post "Weighing The Fog Of Battle, Part I" [1] where I discuss MacKay et al's paper  Weighing the fog of war:Illustrating the power of Bayesian methods for historical analysis through the Battle of the Dogger Bank [2].

What I want to discuss here is the part of their model (as I read it, to the best of my ability) that deals with gunfire exchange knocking out turrets. The relevant data, for HMS Invincible (Indomitable at Dogger Bank) and SMS Blucher, is shown in the table below. The number of turrets is the number able to fire on the beam, and no I do not count cross deck firing by the Invincibles. This may differ from that used in [2], but I think is more appropriate. I could also quibble about the rates of fire, possibly 1.5 and 4 rounds/min per gun might be more appropriate, but I will leave that for now.

		Prob of Hit	Resilience	Gun Effectivness	Gun RoF (rounds per min)	No Turrets	Ship RoF (rounds per min)
	Invincible	0.03	0.38	0.3	2	3	12
	Blucher	0.05	0.43	0.27	6	4	48

Given a hit, the probability of a turret being knocked out is Resilience of defender times the Gun Effectiveness of the attacker (I commented on the inappropriateness of this in the earlier post).

I have set up and run a simulation of a single ship engagement between Invincible and Blucher and after a maximum battle duration of 20 minutes at maximum rate of fire, in 86 of the 100 cases simulated Invincible is reduced to zero turrets on the engaged side with Blucher having an average of 3.8 turrets remaining on the engaged side. In the remaining cases at 20 minutes Invincible has an average of 1.2 and Blucher 3.3 turrets remaining. Which is decisively in Blucher's favour, and this result can almost solely be laid at the door of the different rates of fire and hit probabilities.

(even with reduced effectiveness and fewer guns, which for convenience I treat as 3 twin turrets rather than two twin and two singles, with a slightly lower rate of fire per gun Scharnhorst reduces Invincible to zero remaining turrets within 20 min in 46 of 100 cases simulated with average numbers of turrets remaining ~2 and ~3 in Scarnhorst's favour in the remaining cases).

If we factor in the small (but unspecified) chance of a hit being disabling a ship, Blucher also has an additional advantage due to its greater rate of fire.

References:
1. Larham R., Weighing The Fog Of Battle, Part I,  http://navalwargames.blogspot.co.uk/2017/08/weighing-fog-of-battle-part-i.html
2. MacKay N, Price C, Wood J, Weighing the fog of war:Illustrating the power of Bayesian methods for historical analysis through the Battle of the Dogger Bank, Historical Methods 2016 49 (2)  pp80-91