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.