Comparison of Models of Cruiser Staying Power Against Torpedo Hits

In an earlier post I mentioned the SpringSharp measure of staying power for Derfflinger and Barham. In addition to the quantity of gunnery hits SpringSharp [1] gives a number of torpedo hits (presumably mean or median number to sink). Now I don't know what model underlies this number, but I do have another model where the probability of sinking is given for RN cruisers against the TPBE (thousand pound bomb equivalent) of torpedo hits. So if we set SpringSharp up to represent a particular RN cruiser we could compare the number of torpedo hits given by SpringSharp with that given by the model in [2].


Choosing Leander as the reference ship and setting up SpingSharp with its particulars we find the SS rates it at 1.2 torpedoes (presumably for 50% probability of sinking). Now looking up a 9000 ton full load cruiser on figure 4 of [2] we find that the TPBE for 50% chance of sinking is ~1.6, which is about ~1.3 equivalent 21" torpedo hits. This seems pretty good agreement, repeating the same for Edinburgh SpringSharp gives 1.9 and [2] gives ~2.2 TPBE which is ~1.8 equivalent 21" torpedo hits.


References
1. SpringSharp warship rough design software, http://www.springsharp.com/
2. Larham R., Historical Data in Modelling Warship Battle Damage Survival Probability, 2nd IMA Conference on Mathematics in Defence, October 2011, link to copy on Academia.edu

Prime Minister's Excellent Grasp of Naval Metaphor

I think it is nice to know that the Prime Minister has a good grasp of nautical metaphor as shown by this quote for the Telegraph web site:

“I think it is important that you try to go on holiday, but if you need to come back, you drop everything,” he said. “The captain of the ship should be at the helm.”

If the Captain is at the helm who the hell is in command? I think he probably means that the captain should be on the bridge, but what would I know?

To quote Wikipedia:

"In the merchant marine, the person at the helm is usually an able seaman, particularly during ship arrivals, departures, and while maneuvering in restricted waters or other conditions requiring precise steering. An ordinary seaman is commonly restricted to steering in open waters. Moreover, military ships may have a seaman or quartermaster at the helm."

Or perhaps he has a better grasp of the metaphor involved than I give him credit for and the British "Ship of State" has shrunk to a mere "Boat of State" where we may expect the captain to take the helm?  ...or he may have a classical education and be thinking of an ancient Greek warship where I am informed that the captain did take the steering oar.

Either way he seems eminently qualified to be the "Ruler of the Queen's Navy"

Dunnigan on Fire Control, Comments on Chapter 10 of The Fletcher Pratt Book, Pt III

The next major section in chapter 10 of [1] is a quote from Dunnigan [2] on fire control.

Dunnigan points out that the FPWR employ a form of ladder about the estimated range to model the dispersion in the fall of shot, which is uncontentious enough. He then goes on to tell us that with a ladder the shells would almost certainly bracket the target on the first broadside. Now my memory may be starting to fail but I seem to recall that finding and keeping the range in the Fletcher-Pratt game was not easy, which is confirmed by the accounts of players in earlier chapters of the book [1]. This in my case at least with ship models over-scale compared to the floor scale. From this we can probably conclude that Dunnigan never played the FPWR.

Dunnigan then moves on to observe that a ladder system was used only by the Germans at Jutland, the RN employed a slower method to find the range but employed better fire control systems so would be potentially more accurate in the long run [3](the inherent statistical errors of range finder range, and systematic differences between geometric, gun and rangefinder ranges even after calibration mean that the rangefinder range is/was not sufficiently accurate to allow their use without modification from observation of fall of shot [3]). The lack of adequate facilities at Rosyth for gunnery practice ensured that the main body of the Battlecruiser Fleet's gunnery was crap despite having superior gunnery control systems. The criticism of the gunnery system of the FPWR on the grounds that it is only (a bit) like that of one of the protagonists at Jutland is absurd. First because it is even less like the systems employed by the cruisers and destroyers at Jutland, and by anyone at any later date. The gunnery system is a game mechanism not a model of the systems on a particular day, which should be represented by special mods for the particular game for that day (by modifying the ladder size depending on the number of salvos fired at a particular target and/or adding random ranging errors to one or both sides opening salvos at a target, or ...).

Throughout Dunnigan criticises FPWR essentially for being general rather than specific to Jutland, which to some extent is understandable since at the time he was preoccupied with the SPI Jutland game. However exactly the same sort of criticisms could be made if we focus on a particular naval engagement, and are irrelevant to a general set of rules, it is the gamers responsibility to introduce day specific features.

Dunnigan's comments about fire control at night go off at half cock because he confounds factoids related to Jutland with factoids from later in WW1 and from WW2. These can safely be ignored.

John Curry comments after the quoted text from [2] that Dunnigan whet on to criticise FPWR for not representing the fog of war adequately, which he points out was a misconception due to Dunnigan not having access to all of the FPWR as documented in the earlier chapters of [1].

Summary: The quoted text criticises FPWR for not being a detailed and/or accurate model of battleship and battlecruiser gunnery at the end of May 1916. This is a fair criticism in the sense that you can criticise an apple for not being a banana.



References
1. Curry, J., Fletcher Pratt Naval Wargame, the history of wargames project 2011
2. Dunnigan, J., Article in Strategy and Tactics, Vol1, 1967
3. Brooks, J., Dreadnought Gunnery at the Battle of Jutland: The Question of Fire Control, Routledge, 2005

Dunnigan on Protection, Comments on Chapter 10 of The Fletcher Pratt Book, Pt II

The next major section of chapter 10 of [1] is a quote from James Dunnigan from [2], the gist of this is that the points value of ships in the FPWR do not reflect the true staying power of the ships involved. Now I have no disagreement with this, as I have indicated elsewhere [3]. However it is his argument for this conclusion that is unjustified. Dunnigan claims that the discrepancy is due to the FPWR not accounting for differences in quantity and quality of ship protection. For instance he quotes the average percentage of displacement given over to armour in British and German battleships and battle cruisers in WW1 (he gives these as 35% vs 30% and 30% vs 26% which may be arguable I may come back to this). He also claims that the German armour was better arranged than that of the RN, I will not comment on this, it needs more justification than I have time for at present.

Dunnigan presents as examples Derfflinger, Barham and Lion which he claims have points values under the FPWR of 131,000, 142,000 and 104,000 points respectively. His comment on these is that we might conclude that the Derfflinger was less capable of taking damage than Barham with Lion not far behind. First lets dispose of the last remark; Lion is 27,000 points behind Derfflinger, or Lion is only capable of absorbing 79% of the damage that Derfflinger is capable of absorbing, this is not "not far behind" in these rules Lion has significantly less staying power than Derfflinger (and I may argue later that this difference is in fact excessive for exactly the same reason that I believe that FPWR over rate Barham with respect to Derfflinger). We may as well note here that the percentage of normal displacement devoted to armour in Derfflinger and Barham are about 33-34% and 32% respectively, which given the difference in other characteristics (like area to be armoured per unit displacement) and the uncertainty in what is counted as armour when different people calculate such percentages, are very closely comparable.

Under the FPWR Derfflinger has slightly less staying power (ability to absorb penetrating hit damage for a given loss of capability) than Barham (about 8%). In this Derfflinger is disadvantaged by thinner maximum armour thickness and smaller caliber armament and advantaged by greater speed. None of these should be influencing the ships staying power. I will discuss armour in particular (the arguments against the others are more obvious). As I have defined staying power the armour is obviously irrelevant since the definition refers to penetrating hits. Armour will have already have contributed to the ships survivability by preventing penetration of certain hits at certain ranges (and also accounting for other factors if we so wish) so has no place here (or at least no significant place). This leaves displacement as the only relevant factor in the FPWR ship formula. On ship displacement alone we find that Derfflinger has about 5% less staying power than Barham (and Lion is more or less equivalent to Derfflinger on this measure). I would probably favour a model where staying power were a monotonic function of the displacement devoted to the ship hull plus that devoted to auxiliary machinery but this data is difficult, but not impossible to come by, so I wont pursue this.

On displacement all three of the ships discussed by Dunnigan are closely comparable and this is what we should take as a baseline which we may modify if we feel strongly that one nationality build intrinsically more survivable ships than another. However caution is called for here since in the time frame of Dunnigan’s article Bismark was thought to be disproportionately well protected but current opinion is that its armour was poorly disposed and the Germans had not kept up with armour developments in the US and UK which resulted in inch for inch superior belt amour in US and RN ships (don't know about deck armour as this tended to be a different type from vertical armour).

As an aside we might look at the staying power calculations from a ship modelling tool like SpringSharp. This gives the mass of penetrating non-critical hits to sink for Derfflinger and Barham as 41,100 and 39,600 pounds respectively. Which reverses the order of the displacement ranking, but still leaves them closely comparable. The problem here is that I do not know how SpringSharp models staying power.

In conclusion we may say that if we ignore the poor quality of RN armour piercing shells and the instability of RN cordite and poor propellant handling hygiene the staying power of these three ships is comparable. But in battle Barham would be expected to prevail against Derfflinger because of its' heavier armament and thicker armour.  The result of a Lion/Derfflinger encounter is less clear, the weaker armour of Lion is countered by the weaker armament of Derfflinger (but my money would go on Derfflinger). In reality the outcome of encounters between these ships would depend on factors not accounted for here, specifically the poor explosive hygiene  and fire control on/in British battle cruisers at Jutland, and the poor quality of British shells (both of these were at least partially corrected after Jutland).


References

1. Curry, J., Fletcher Pratt Naval Wargame, the history of wargames project 2011
2. Dunnigan, J., Article in Strategy and Tactics, Vol1, 1967
3. Larham R. Fletcher Pratt Pt 4 (what I think is wrong with the FP Gunnery/Damage models), blog post on this blog:  http://navalwargames.blogspot.com/2011/07/fletcher-pratt-pt-4-what-i-think-is.html, 2011

Comments on Chapter 10 of The Fletcher Pratt Book, Pt I

Preamble
There are many points in Chapter 10 "The Fletcher Pratt Rules and Reality" of [1] where questionable claims are made. Before I start dissecting the chapter I should say that I am in general agreement with the thesis of the chapter that the Fletcher Pratt wargame Rules (FPWGR) are not a valid model of naval warfare for the 1914-1945 period, not even when restricted to surface actions. Some of my reasons for claiming this are reported in other posts in this blog, and other will be reported in future. However I also believe that there are ideas in the FPWGRs that are intrinsically interesting and potentially educational, these are reported (or will be) elsewhere. I should also state that Michael Vlahos's book Blue Sword [2] might clear up most of the questions about the influence of the FPWGRs on US Naval doctrine as it covers the history of wagaming at the Naval War College over the relevant period, however I have not yet located a copy at an affordable price so its analysis must wait for another occasion (if the History of Wargames Project could re-publish it I would be the first in the queue to buy a copy).

Phil Barker's Remarks and John Curry's Comments on Them
I wish to start in this post by discussing the very opening paragraphs. We start with a quote from an article by Phil Barker published in The Nugget in 2006:

This is one of thoe legendary systems that everyone has heard of but very few played with. Since the author is long dead, there is no chance of hurting his feelings and I can mention his rule set is credited in some USN circles with being responsible for many of the initial defeats in the Pacific in WW2. It would not have been a bad set for refighting Jutland (though in fine weather and unrestricted visibility), but its concentration on gunnery of the fighting line at extreme range and downplaying of the surface ship torpedo led to tactical mistakes made fatal by the Long Lance torpedo.

John Curry then observers that Phil is not a Naval expert but claims his anecdotal report carries weight because he is an older guy who has been involved in wargaming for a long time. This is an argument from authority (by proxy), that is hearsay carries weight because of the indirect authority of the reported. We can therefore discard this as evidence without further consideration. However I am not going to do that because John in the next paragraph points out the apparent value place on the game just before and during WW2 by the Naval War College and this is a documented report (Time Magazine 1939, but I think I would like to see the item myself).

Analysis of Removal of TT from US Heavy Cruisers
The doctrinal problem that we are discussing is the belief that cruisers (other than those intended to work with destroyers) would not engage in surface combat at ranges where torpedoes could be used, and therefore were more a liability than an asset on heavy (and large light) cruisers. The story told at [3] is that this belief was a result of wargaming studies conducted at the Naval War College. This may also have been because due to the low rate of fire of the 8" gun these cruisers were vulnerable at night and poor visibility to fast moving targets such as destroyers [4] (and also to the high rate of fire of 6" gun cruisers). Also, as [4] also claims, that during construction (of the Pensacola and Salt Lake City) it became evident that they would be able to accommodate director fire control. This presumably pushed the expected effective range up from ca 10000m to possibly in excess of 20000m (the range of their guns was in excess of 28000m). Looking at the photo of Pensacola as complete in[4] it is evident that she was completed with spotting tops but no DCT.

We can establish an indicative timescale for the wargaming that lead to these decisions by looking at the completion dates of the first four groups of US treaty cruisers. The Pensacolas were designed and completed with torpedo tubes, as was the succeeding Northampton class. The next class (Portland) had the torpedo tubes deleted in the course of design (I find this an ambiguous term, what we can say with certainty is that they completed without tubes), so presumably this is some time between the freezing of the design of the previous class and the completion of Indianapolis, the first of the Portlands to complete. This puts the date of the decision somewhere between 1929 and early 1932. Thus we can probably date the wargames to no later than 1931 and possibly as early as 1929.

Comparison of the Time Line of Removal of Cruise TT and that of the FPWRG
As we have seen NWC studies had concluded that US treaty cruisers would be vulnerable at night and in poor visibility to light forces and so as they would outrage them in better conditions they would not be used under these circumstances and so did not need torpedo tubes (may be a bit of interpretation on my part here, and it still sounds ludicrous to me but I have seen similar behaviour in modern times so.. ). These conclusions were drawn before 1933.

In [1] we discover that Fletcher Pratt claims to have written the first version of his rules in 1928, but not shared them with his friends until 1933. If this is accurate then I rest my case the FPWGR could not have been the rules used in the NWC games supporting the removal of TT from US heavy cruisers, and so the doctrinal errors were probably in place before the NWC ever saw the FPWGRs.

(The reader will note that unlike Phil Barker I have no qualms about possibly hurting peoples feelings, though will be upset when mine are hurt be someone pointing out the faults in my arguments, but that is war(gaming) for you :).

References
1. Curry, J., Fletcher Pratt Naval Wargame, the history of wargames project 2011
2. Vlahos, M., Blue Sword, Naval War College 1980.
3. CA-32 New Orleans, http://globalsecurity.org/military/systems/ship/ca-32.htm
4. Conway's, All the World's Fighting Ships 1922-1946, Conway Maritime Press 1980.

Test page for using MathJax for LaTeX on Blogger

There is a javascriptb block containing:

<script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript">
</script>

in the HTML source on this page which causes the rendering of LaTeX using MathJax the delimiters are slash( and slash) for inline maths and slash[ and slash] for display maths. (the slash is the \ character which if I used it would lead to confusion)

This is inline with tex \tex in square brackets delimiters [tex] 4\times \sin(x^2) [/tex] these are set up as alternate delimiters using the guidance on the MathJax site.

Some continuous text with inline maths \( \sin(x)^2 \) some more text. Now a display equation (in a bigger font!):

\[ \int_0^3 f(x)\; dx=7 \]

Now display maths between Tex \Tex delimiters:

[Tex]\int_1^2 g(x)\; dx =17 [/Tex]

The JavaScript block can be placed in the template html rather than at the top of each post.

(Looks like the Tex delimiters only display correctly on chrome! Better switch any posts over to delimiters that will work on any browser. Other sources indicate that the problem may well be with Internet Exploder rather than anything else)

Fletcher Pratt Pt 4 (what I think is wrong with the FP Gunnery/Damage models)

The basic model of damage from gunfire is attritional. Each hit contributes a number of points of damage (which is modulated by armour penetration ..) and the loss of fire power and speed of the ship is proportional to the fractional damage (the points damage received divided by the ships points value). This is a perfectly acceptable model if that is how you want to represent accumulated damage in the game (in my opinion it is not the most suitable model for gaming but that is another story)

In addition to the attritional damage if in the measuring up in the gunnery round a shell is deemed to have fallen on a gun position (assuming the ability to penetrate the local armour) that gun position is deemed knocked out. There are at least two problems with this, the first is that this means that the conditional probability of a gun position hit is the ratio of gun house plan area to deck area of the ship which may be OK-ish at long range but will be wrong at shorter ranges. Secondly it is inconsistent with the attritional model of ship damage effectivly double counting the guns when it comes to taking damage. In addition we could ask why we do not apply the same method to machinery spaces.