Comments on the 2026 Defence Investment Plan (?)

The BBC item on the DIP:

£63bn for nuclear deterrent

Money is being earmarked for the UK's continuous-at-sea nuclear deterrent, and the warheads and infrastructure that supports it. 

The plan includes buying F35A combat aircraft modified to carry relatively small nuclear bombs to allow Britain to play a part in Nato's European Nuclear Plan. But these aircraft will not be delivered during this decade. 

Russia already possesses large numbers of smaller, tactical nuclear weapons while Britain has none. 

 

These will be US supplied aircraft, and US nuclear weapons. It will constitute a system not under UK sovereign control. US nuclear weapons allocated to NATO cannot be used without US permission and given the current US administrations ambivalence to responding to article 5 requests for NATO support, by a member state. Even if the next US administration favours observing its treaty obligations we cannot rely on the US electorate installing another rogue  administration down the line.

If the UK is to retain nuclear weapons they must be under full UK control (much like the French weapons). This implies replacing Trident with missiles serviced (and preferably manufactured) in the UK, and warheads not burdened under ITAR restrictions.

Also the "strategic goal": "Use investment in defence to drive growth, creating jobs and driving investment across the country" is not served adequately by procuring F35A's or US tactical nuclear weapons.

Just a reminder to write about the SeaHake Mod4 ER and/or Poseidon.

 The SeaHake Mod4 ER (DM2A4 ER) seems to have fallen out of the worlds awareness in the last few years (since I retired). The Russian Poseidon nuclear powered UWW has been in the news more recently but seems more a propaganda exercise than a viable weapon.

 Must write something about v-long range underwater weapons when I get the chance.

Zero Sum Games & Nuclear War?

 In a recent article in the Guardian on a wargame conducted recently to investigate tension between Russia and Finland a reference  was given to a paper by Roger Mason [1]. This paper was all pretty standard stuff on the history of wargaming, but we have this at the start of the section covering the Cold War:

The cold war offered strategists, political leaders, and wargamers a new set of  problems. The challenge was the new age of nuclear weapons where strategic warfare might truly be a global zero-sum game.

This left me wondering exactly what did the author think or intend this "zero-sum game" phrase to mean in this context?

Lets look at the definition of a Zero Sum Game, here from Wikipedia:

Zero-sum game is a mathematical representation in game theory and economic theory of a situation that involves two sides, where the result is an advantage for one side and an equivalent loss for the other.^[1] In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.^[2]

 What would a zero-sum pay-off matrix for strategic nuclear war look like!? There seems to be a couple (or more) possiblities behind this quote: 

1. I don't understand what the author is getting at,

 or (more likely)
2. The author does not know what a zero-sum gave is, and is using the phrase because it makes him sound smart.

References

Mason, Roger, Wargaming: Its  history and  future, The International Journal of Intelligence, Security, and Public Affairs, V20, 2 pp 77-101, 2018.

Kinematics Countermeasures to Anti-Torpedo Torpedoes.

Back in 2019 at the Undersea Defence Technology (UDT)  conference (in Stockholm) I attended a talk on the Netherlands' navy introduction of Anti-Torpedo Torpedoes (ATTs), and asked a question "Have you considered the effect of Counter Countermeasures (CCM) on the effectiveness of the ATT". The presenter, knowing who I was (as I had just delivered a paper on using machine learning to optimise torpedo homing algorithms, the day before), replied that he would leave that to me.

On returning home I put together a paper on kinematic CCMs to ATTs, based entirely on open source material, and in my own time, in a week or so for the 2020 UDT conference.

Unfortunately, I developed medical problem (Oct 2019) that led to me giving notice of my retirement, and would have made me reluctant to travel for the next UDT conference, and the conference was cancelled anyway (early 2020?) due to the outbreak of a pandemic. So the paper was never delivered.

I have now posted it to my research gate account: PDF of paper is here.

This paper did not go through the full BAE (my employer at the time) vetting procedure (which it would have needed, as if I had delivered it at UDT I would do so as a representative of BAE), but as it was written on my time, and using open sources and I no longer represent BAE in any capacity, it should be OK to release it now. But note this does not necessarily reflect the views of BAE systems, doubly so as I don't know what their current view of ATT CCM are.

Errors in naval history books

I have recently been working on a talk about the Western Approaches Tactical Unit (WATU). The two main books that talk about WATU are references 1 and 2. Both of these contain errors which one would have expected the research for these to have caught.

Examples are calling HMS Prince of Wales, which Gilbert Rodgers, the head of WATU visited while it was fitting out, as a battle cruiser, giving the gun calibre of Spitfire guns a value that never existed. Possibly worse is not mentioning operation Drum Beat as the cause of the second U-boat Happy Time.

 As a result of a question when I was presenting this talk, I had to consult reference 3. Here the author failed to convert between metres per second, knots and mph. Having piqued my curiosity I looked at other parts that i know about (ATTs) and found errors there. Also I am left with a feeling that research for (3) was largely confined to Wikipedia.

All this leaves with the impression that these books are written by "journalists" with no real background interest in naval history. Just as well these books were all borrowed rather than purchased.

References

1. Mark Williams, Captain Gilbert Roberts, and the Anti-U-Boat School, Cassell, 1979

2. Simon Parkin, A Game of Birds and Wolves, Sceptre, 2020
3. Roger Branfill-Cook, Torpedo, Seaforth Publishing, 2014

Initial thoughts on ATTs for use against Russia's super torpedo Poseidon/Status-6/Kanyon

Poseidon[1] allegedly has practically unlimited endurance, a maximum speed ~70kts and a maximum operating depth of ~1000m. Some scaling arguments indicate that a maximum speed closer to 55kts may be likely.

I have addressed the speed requirements for ATTs against conventional torpedoes before, a few posts ago [2], which do not apply if the target is Russia's new "super" torpedo.

Presumably an ATT for use against Poseidon will have to be deployed from an aircraft. Now while at high speed Poseidon should be easily detectable and trackable there is no guarantee of being able to deploy the ATT for a near head-on attack. In which case a higher speed will be needed and so the $3/2$ rule may well be appropriate in this case. As the quoted maximum speed and in H.I. Sutton's article  is 70kts the 3/2-rule  puts the ATT maximum speed requirement up at 105kts which will present some interesting engineering challenges.. This may well raise issues about detectability of the target using sonar from the ATT. 

What other options are there for hard-kill counters to Poseidon are depth charges, mines, ...?

Some further thoughts: 
1. What endurance would be required of an ATT for this role? This would be determined by how close to Poseidon's position and track axis the ATT could be deployed. being dropped at ~1000m from the threat and close to the track would require a relatively modest endurance, while being dropped at greater distance might require a prohibitive endurance from a high speed weapon. Maybe a multi-speed  ATT would be useful?
2. What speed profile would Poseidon employ? How long would it operate close to its maximum speed?     Could it be attacked while at a lower speed?
3. Would it be better to attack/eliminate its launch vessel?
4. In the case of an airdropped ATT there would be no restriction on the ATT heading back towards the launch vessel, so if we have a high enough speed and sufficient endurance, tail chases are acceptable.

References:

1. Sutton, H. I., Russia’s New ‘Poseidon’ Super-Weapon: What You Need To Know, Naval News, 2022
   https://www.navalnews.com/naval-news/2022/03/russias-new-poseidon-super-weapon-what-you-need-to-know/
2. Larham, R., Maximum Design Speed of Homing Torpedoes. Naval Wargames and related stuff, Blog.
   https://navalwargames.blogspot.com/2021/09/maximum-design-speed-of-homing-torpedoes.html

HMS Queen Elizabeth nammed after the late Queen, after all!

 In the First Sea Lord's tribute to the late Queen, he admits (2:40 in the twitter video) that the aircraft carrier HMS Queen Elizabeth was named after her (previous claims seem to have said she did not want a ship named after her, and that the QE was named after QE1 like the previous QE)

https://twitter.com/i/status/1568879644786442241

US Naval War College Videos

 There are some YouTube videos about the US Naval War College (a home of naval wargaming):

1. How Does the US Navy Run Wargames? - A Guided Tour of the US Naval War College Wargaming Facilities

2. Historical Naval Wargaming Kit Demo (US Naval War College Museum)

3. How Did Wargaming Shape the War in the Pacific? (US vs Japan)

<<More links to follow, I'm sure>>

Maximum Design Speed of Homing Torpedoes.

Introduction 
One sees in many places maximum speeds quoted for various torpedoes. My concern here is primarily with the Wikipedia article [3] on the Spearfish torpedo, or rather with the article's sources for the quoted speed of 80kts. It should also be noted that other sources, which I no longer have access to, IIRC claim SF was tracked at AUTEC (Atlantic Undersea Test and Evaluation Center, Andros Island, Bahamas) at 90kts (Friedman's book on weapon systems 1992 [1]. I will say something about this later.). 

A rule of thumb often applied when designing homing torpedoes is that the maximum speed should be ~1.5 times the maximum speed of the target.

Derivation of the Energy Optimality of 3/2 Rule for a Tailchase
Notation: Weapon speed \(v_w\), target speed \(v_t\), initial range \(d_0\).

Assumptions: The drag on the weapon goes as \(v_w^2\) (high Reynolds number, and also assuming changing weapon incidence with speed does not bugger this dependence up too much), the weapon is faster than the target (\(v_w>v_t\) )

\[\text{Drag}=kv_w^2\]\[\text{Power}=kv_w^3\]\[\text{Time to Intercept}=\frac{d_0}{v_w-v_t}\]

\[\text{Distance to Intercept for Tail Chase}=\frac{d_0v_w}{v_w-v_t}\]

\[\text{Energy to Intercept}=E=\frac{kd_0v_w^3}{v_w-v_t}=\frac{Kv_w^3}{v_w-v_t}\]

The speed for a minimum energy for tail chase intercept is found when \(\frac{dE}{dv_w}=0\):

\[\frac{dE}{dv_w}=\frac{3Kv_w^2}{v_w-v_t}-\frac{Kv_w^3}{(v_w-v_t)^2}=0\]

Which after rearrangement gives \(v_w=\frac{3}{2}v_t\).

Now when SF was designed the bogyman was the Soviet Project 705 (Alpha) class submarine, which had a maximum speed variously reported from 40 to 45kts. In which case one would expect the maximum speed of SF to be based on this (if achivable) and be ~60 to 67.5kts. As an aside the only reliable information in the open press seems to be an item in the NYT [2] quoting the claimed underwater speed report for the NST7525 Engineering Test Vehicle (ETV) of 80mph (70kts). At the time though it was reported in a number of places, presumably sourced from a Marconi press release. The figure we normally saw in the technical press was for 70kts, which somebody presumably converted and rounded to 80mph for the "popular" press. A plausible explanation for the claimed 80kt speed for SF may be the confusion between mph and kts, the NYT report being 80mph.

Disinformation of AUTEC Tracking Quote
Now the claim that SF was tracked at 90kts [1] can be dismissed as disinformation. When tracking a source the source speed estimate has an error, which can be large when there is little tracking history but should reduce as the history builds up. So it is entirely possible that a source could, initially, be "tracked" at a speed very different from its actual speed, and if this is remarkable enough for it to be reported.

We can also do a plausibility check on such a speed. Suppose that the power source of a torpedo can produce the power to drive the weapon at such a speed. Also suppose that the propulsive range of the weapon at say ~30kts is ~50km (which seem to be typical-ish firgures one sees for torpedo low speed and range). Then as the energy required to go a fixed distance goes as \(v^3\) the propulsive endurance will fall to <2km at 90kts (assuming no loss of efficiency in the propulsion system, and no endurance used up prior to going to 90kts at a lower speed). If however the low speed were 24kts for a range of 50km, then the range at 90kts is <1km, and at 70kts is ~2km. How useful these ranges would be, at these speeds, I don't know.

( I no longer have access to [1] as I left my copy behind when I retired from BAE. If my memory is playing me false this could have been 80kts rather than 90, in which case it could be the source of the Wikipedia references claims?)

Speed Requirements for Anti-Torpedo Torpedoes
One might expect the above argument to also hold for ATTs, but it does not. If you are an ATT the last thing you want is to end up in a tail chase, you never want to be chasing a homing weapon back towards a friendly ship, among other reasons. 

The constraints on an ATT engagement mean that the ATT needs to be in a near head-on geometry when it starts its search and homing. To home stably from such a geometry requires that the ATT at least equal the speed of the target (or if you can ensure that the target is dead ahead of the ATT at acquisition then any speed will suffice for the ATT). A speed advantage over the target is highly desirable as it makes homing more robust, but if the target is capable of 60kts+ one is already near  practical sonar and propulsion limits. In such a case 90kts would be desirable but would be difficult engineering and costly, which has not stopped us in the past from at least studying the practicality of very high speed ATTs.

That it is desirable for an ATT to at least match the speed of its target suggests that high speed may be part of a torpedoes counter measure suite to ATTs.

References
1. Friedman, Norman, The Naval Institute Guide to World Naval Weapon Systems, 1992 edition.
2. A U.S.-British Torpedo Fight, New York Times, May 14th 1981.
3. Wikipedia contributors, Spearfish torpedo, Wikipedia,The Free Encyclopedia https://en.wikipedia.org/wiki/Spearfish_torpedo ,retrieved 2021-09-09.

A Game of Birds and Wolves II

 I have now finished "A Game of Birds and Wolves", I must say I am somewhat disappointed. It more of less finished in April 43 except for the what happened to the protagonists later. No account of WATUs activities for the remainder of the war in the Atlantic. As WATU was involved in developing tactics for use against German anti-escort (acoustic homing) torpedoes when these arrived later in 43 this is a significant omission.

I suppose this is a consequence of a world where journalists are attempting to write "a good story" disguised as history and see no point in continuing beyond where their point has been made, where they think things become uninteresting to their target audience or they become bored with the topic. 

In retrospect I am also suspicious about the origin of the title. As the author is trying to show the contribution of (young) women to the war effort, there is a suspicion in my mind that the "Birds" of the title is the (outdated) slang term for young women (and the wolves maybe the U-Boats if not a male dominated RN of the time)

Of lesser concern is my suspicion that that the author is not that familiar with the game of "Battleships" seeming to think it any vaguely hobby (as opposed to professional) naval game.

HMS Clyde (off South Georgia?)

 Another old painting of mine, HMS Clyde off South Georgia, Acrylic on board, ~175x225mm, 2017.

... and here is the related pencil sketch (on A5 pad):

A Game of Birds and Wolves

 I am currently reading Simon Parkin's A Game of Birds and Wolves which is largely about WATU (Western Approaches tactical Unit) which I have talked about in other postings  on this blog [1], [2]. This is a pretty interesting read (and I do recommend it), but has a somewhat jarring fault. Throughout there are minor errors when the author makes assumptions that those not familiar with naval history and related matters might make.

I think this is a generic problem of journalism. The reporting may be OK on those parts of the topic that the author has researched, but when the author strays beyond the researched what is written can be full of erroneous assumptions.

References
1. https://navalwargames.blogspot.com/2018/08/western-approaches-tactical-unit.html

2. https://navalwargames.blogspot.com/2020/03/naval-war-colledge-review-article-and.html

 Not much new to post here recently, so I thought I might post some of my ship paintings!

Ark Royal (R07) returning to Portsmouth in the fog, to decommission for the last time 2010.Acrylic on greyboard ~200x300mm.

Naval War Colledge Review Article and the Western Approaches Tactical Unit WATU

It is some time since I posted anything naval wargames related, as I have been otehrwise engaged recently. But I was browsing the latest issue of the Naval War College Review recently when I came accross an article [1] tangentially related to naval wargaming as it was using the Western Approaches Tactical Unit as an example.

I have mentioned WATU in a previous post https://navalwargames.blogspot.com/2018/08/western-approaches-tactical-unit.html where there is a link to a pretty good paper from the Military Operation Research Soc.

In Sloans paper he discusses WATUs analysis of U-boat apprach and attach tactics against convoys.

[1] Sloan, G., The Royal Navy and Organizational Learning—The Western Approaches Tactical Unit and the Battle of the Atlantic, https://digital-commons.usnwc.edu/nwc-review/vol72/iss4/9/

I have turned off comments here due to spam comments. I do not have the time to delete these so comments will only be enabled when there is a new post.

A message to the spammers: Fuck-off you moron/s, nobody wants to click on your links

ECM BrainBuster August 2019

ECM BrainBuster

It's bonus time again at ACME Software!

In one small group, the six employees receive the following amounts: £3000, £3200, £3600, £3800, £4000, and one fortunate employee £6200.

The group comprises one engineer acting as manager, Team A with two employees and Team B with three.

One team receives a total bonus of exactly twice the amount as the other team.

Which bonuses are awarded to the manager, Team A and Team B? And can you demonstrate if/why your answer is the only possible solution

There are \(\frac{6!}{3!2!}=60\) possible ways of dividing the bonuses up between a team of two and a team of  three and a singleton. So all the solutions could be found by exhaustive search.

But first we observe that if the team of three bonus total is twice that of the team of two then that team's bonus must be greater than \( £18000\), which is not possible. So the team of 2 bonus is twice that of the team of 3.

Suppose the team of two's bonuses include the \(£6200\) then the team of threes bonus must exceed \(£18400\), which is not possible. A similar argument can be applied to show that the team of two's bonuses cannot include the \(£4000\) bonus, as this would imply that the team of threes bonus total would have to be \(£14000\) or more, but this can only be done if their bonuses include both \(£6200\) and \(£4000\). Which leaves 6 possibilities for Team A's bonuses, which are shown in this table:

We can also observe that we cannot make more than \(£12000\) with the sum of three of the bonusues unless we include the \(£6200\) among the three. Then we can by inspection find the only combination of bonuses for Team B that meet the specificationof the problem, shown in this table:

(The middle column is the third column minus \(£6200\), and the only way that Teanm B can satisfy the required conditions is shown in the last three columns.)

So the Managers bonus is \(£4000\), The Team A bonuses are \(£3000,\ £3600\) and Team B bonuses are \(£6200,\ £3800,\ £3200\) .

Gnu-Octave (very)crude exhaustive search code:

more off 

BB=[3000,3200,3600,3800,4000,6200];
rv1=[];rv2=[];
for idx=1:factorial(6)-1
    SumA=BB(1)+BB(2);
    SumB=BB(3)+BB(4)+BB(5); 

    if SumA*2==SumB
       rv1=[rv1;BB];
    endif
    if SumA==2*SumB
       rv2=[rv2;BB];
    endif 

    BB=Next(BB); 

endfor
rv1
rv2

Where the function Next() gives the next permutation (in lexicographic order) of the input permutation.

This gives the same result as above (though with every valid permutation)

Western Approaches Tactical Unit

I have come across reference to the Western Aproaches tactical Unit and their use of wargaming before (it seems to appear in the Cruel sea, but I would have to go and check that to be sure), but it does seem to be getting more coverage these days. The most recent thing I have seen is Lindybeige's  YouTube video  on the unit. This is quite good but not being an expert on naval affairs Lloyd makes a number of errors. Better yet if less entertainingis the recent MORS (Military Operations Research Society) paper on WATU which is available here.

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