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

Weighing The Fog Of Battle, Part I

I recently attended the DSTL Symposium on Historical Analysis (of defence related topics). One of the talks was "Dogger Bank, Weighing the fog of war", based on [1] and summarised  in this article in Significance [2] and the slides from the DSTL presentation (which are not very informative). Unfortunately [1] is behind a paywall and so unless you know how to obtain copies of such papers without paying you are a bit stuck (I did request a copy form one of the authors on their Research Gate page but have had no response). There is also a longer version of the talk given to the Naval War College on YouTube. There is also a related paper [3] on Jutland which also looks interesting, but which I have not yet had time to procure or study, but expect I will get around to it in the near future.

As the paper deals with matters - Bayesian Statistics, Lanchester Like Models of Combat, Monte-Carlo Simulation, Operational Analysis, Naval History, ... - in which I have both a professional and personal interest I have acquired a copy of the original paper. The paper is quite interesting but I find it difficult to follow when describing the combat model (worrying since I am some sort of expert on this sort of stuff). Before I go any further I should say that I like the general idea of this type of analysis, and that I am inclined to agree with the conclusions in [1].

The basic model of combat is idealised to an exchange of fire one turret at a time (not sure what target selection, or turret scheduling rules are applied, presumably those that reproduce what happened in the actual battle - Tiger we are looking at you here. I suspect a next event type simulation with the next turret/gun ready to fire being the critical timing events is employed). But the ships are characterised by gun data: "Rate of fire", "Number of turrets", "Accuracy", "Effectiveness", and the ship itself by "Resilience", "Flash" and "Disablement".

"Accuracy" appears to be the hit probability (assumed independent shot-to-shot) and reflects the actual hit proportions observed at Dogger Bank and Jutland. The "Accuracy" is 3% for the Battle Cruiser Fleet, and 5% for the 1st Scouting Group which seems about right (I would have preferred two digits of precision here) and is consistent with my own models of naval gun fire at a gross level. 

Now we have the following enigmatic statement (Italic text added by current author for clarification.):

"The ship to fire then has certain probability of hitting its target "Accuracy"(Table 1); if a hit is achieved, the probability of damage is then computed. This probability is computed by multiplying two factors, which quantify respectively the effectiveness of the shell of the attacker "Effectiveness"  and that of the armor of the defender (1 D resilience) "Resilience" to arrive at a probability. Damage here means probability of affecting the Lanchestrian unit, the turret.

This I must assume contains a typo, the probability of damage must go up with "Effectiveness" and down with "Resilience". I assume what is meant is something like (there seems to be something wrong with our bloody LaTeX today):

\[ P(\rm{damage}|\rm{hit})= \frac{\rm{effectivness\ of\ attacking\ gun}}{\rm{reslilience\ of\ defending\ ship}}\]

or more generally, that there exists some increasing function mapping \([-\infty,\infty]\) to \([0,1]\) such that:

\[ P(\rm{damage}|\rm{hit})=f\left( \frac{\rm{effectivness\ of\ attacking\ gun}}{\rm{reslilience\ of\ defending\ ship}}\right)\]

However there is a problem here; According to MacKay et al [1] Campbell [4] tells us that at Jutland the probability of a hit causing the loss of a turret is ~12% independent of nationality or of the individual ship, and the product form rather than that above is set up to approximately give this. In addition there must be all sorts of caveats on Campbell's assessment, as I'm sure that at least he does not wish it to apply to medium calibre hits on battleships. Note there is an implicit assumption that a damage causing (penetrating?) large calibre hit (on a turret) will knock the turret out, not an unreasonable assumption. (The authors have just confirmed 2017-09-28, by email that there is indeed a typo they used \( (1-\rm{resilience}) \))

OK.. lets look at how this would look at the battle of the Falkland Islands. Invincible took about 12 hits from 21cm projectiles according to Massie[6]. These are the same mass as those from Blucher but at 87% of the muzzle velocity which reduces the effectiveness from Blucher's 0.27 to ~0.20*, so the probability of a hit knocking out a turret on Invincible goes from ~10.3% to ~7.7%. Then the number of turrets knocked out by 12 hits has a binomial distribution B(12,0.077), and the probability that no turrets were knocked out is ~38%. Not overwhelmingly in agreement with the actual result, but also not sufficiently in disagreement to raise any eyebrows.

Anyway this post is becoming over long and I will end it here with the statement that I do not believe the Blucher's 21cm guns had anything like the relatively effectiveness compared to 11", 12" or 13.5" guns proposed in [1]. Which of course calls into question how the effectiveness used are calculated.

I expect I will have more to say about this paper in subsequent posts.

*How the effectiveness is obtained is not clear, the reference [5] does not give a value (unless I am reading wrongly) but just formulae for calculating T/D, penetration normalised to projectile diameter. Now it might be that the article has changed since Mackay et al retrieved it, but probably not. It appears that the "Effectiveness" is close to being proportional to \( \frac{W V^2}{D^3}\), where \(W\) is the projectile mass, \(V\) the muzzle velocity and \( D \) the projectile diameter. Thus for geometrically similar projectiles the MoE is proportional to \(V^2\). I have used this relation in scaling the effectiveness of the East Asiatic Squadron's 21cm guns from that given in [1] for the Blucher's. I can see an argument for using a MoE  \(\propto \frac{W V^2}{D^2}\), that is proportional to the kinetic energy per unit area of the projectile cross section, but using this this would make no difference to the argument here.

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

2. MacKay N, Price C, Wood J, Dogger Bank:Weighing the fog of war, Significance 2017 14 (3) pp14-19
3. MacKay N, Price C, Wood J, Weight of Shell Must Tell: A Lanchestrian Reappraisal of the Battle of Jutland, History 2016 101 (347) pp536-563
4. Campbell, J., Jutland: An analysis of the fighting. Conway Maritime Press,  1986.
5. Okun, N. Major Historical Naval Armor Penetration Formulae.
http://www.navweaps.com/index_nathan/Hstfrmla. 2001
6. Massie R. K., Castles Of Steel: Britain, Germany and the Winning of The Great War at Sea , Jonathan Cape, 2004

Publicity Department In Time Warp, Put Artisan 3D on 1930's US Battleship?

Every day when firing up the web browser at work to check my time recordings I am presented with the company bumf page. At present this includes a piece on the Artisan 3D radar, and in particular an infographic on it:

As you can see if you examine under powerful magnification in the centre it appears to show a ship equipped with Artisan. I will save you the trouble of zooming the image, here is a blow up of the ship:

A Type 23?, QE Carrier?, UK Assault ship of some kind? No, I'm not sure exactly what ship is depicted but it is clearly a US Battleship in the 1930's. As far as I can tell the tripod mast and clipper bow are not consistent with any particular ship. With a tower bridge I would have plumped for a New Mexico, with a non-clipper bow a Nevada or Pennsylvania. maybe someone can narrow the field down?

However excellent a radar Artisan is (and I believe so having worked with the project for a short while) the publicity department and their infographic make us look ridiculous rather than inspired as the company ID in the lower right tries to imply.

An alternative explanation is that there is a hidden subtext in the infographic - BAE have built a time machine and sent a number of Artisan 3D's back to 1941 and fitted them to US battleships in an attempt to reverse the result of the Japanese attack on Pearl Harbour!

Another point of disinterest is the total lack of hits on this post, but if you are reading this that is no longer true. Of course it would still be of disinterest if you are me (or a bot)!?