Why They Are Nervous. Short Excurse Into the Modern War. Part 1.

Patrick Armstrong thinks that they simply ran out of options in terms of color revolutions and he justifiably mentions this: 

Former successes – in recent times, Ukraine twice, Georgia – are becoming failures: Hong Kong, Venezuela and Belarus. The targets have learned how to counter the attacks.

Read the whole thing--it is excellent, as is usual for Armstrong. Then, there is a good piece by Tim Kirby on current US foreign policy, which he calls "surprising" because it is, in many important respects, repeats that of the Trump Admin. As Kirby astutely concludes:

In this sense, it could be that ultimately, both Biden and Trump were tasked with managing a crumbling global empire, trying to keep the sinking ship afloat as long as possible waiting for something to change. Thus, their reactions to events and plans could look similar because of the similar causes that underlie them, even if the spirit behind the actions are radically different. Like it or not NATO may just be obsolete, Afghanistan may have just been too expensive, China may just be too powerful. The reactions to these situations could wind up being similar out of necessity or a lack of options. Both Trump and Biden faced these same realities.

And then, there is this, which brings us to the main point: 

German Defense Minister Annegret Kramp-Karrenbauer has been one of the most active backers of NATO's new master plan to counter Russia in case a military conflict breaks out between the sides. The strategy, which was agreed on Thursday, envisages the military alliance’s troops fighting Russian forces in the Baltic region and across the Black Sea, while also calling for non-conventional warfare, including nuclear weapons, cyber-attacks, and space military technology, to be employed.

Here is THE main point, as any Western politico with degree in political "science" (or politics), she cannot have a faintest idea what she supports or doesn't whenever it relates to any issue of warfare. And I mean zero, zilch--you cannot, you simply cannot, explain even in the most comprehensive briefings to any person with degree in "politics" and experiences with running basic fiscal-political "protocols" of the West's regional and national election pipelines, how tactical translates into operational, and how operational translates into strategic and, essentially, into the political level when war is involved. You could do this in 1914 and 1945, you still could do it in 1955, however barely, and then "something" happened--it became very hard, and by mid-1960s it all became an alien language to the main shakers and movers of Western politics--people whose only skill in life is how to re-elect oneself or how to navigate regional and national bureaucracies. Don't take it from me, take it from the US armed forces general with Ph.D in physics. These two pages written by a man who knows what he is talking about should be made mandatory for reading by 100% politicos and by about 99% of the  so called military "experts". 

In other words, no contemporary Western politician can have any sound idea on matters which, actually, are the main drivers behind global affairs, because they do not understand modern warfare. They cannot, you need a solid math, physics, engineering and tactical-operational experience as an officer to be able to grasp a profound connection between foreign policies of nations and the global power balance. Latiff laments that "serious scholarly books are written about war and its consequences, but the vast majority ignores them." Tell me about it. Can you imagine trying to explain to Rachel Maddow or this Germany's "defense minister" how the Probability Theory and Theory of Operations applies to modern politics in the times of hyper-sonic weapons, netcentric warfare, AI elements and over-the-horizon surveillance and anti-satellite weapons. Good luck with that, I heard some "political science" courses even include such things, of course, as Game Theory and... and... here is John Mearsheimer of University of Chicago and, allegedly, "realist" teaches this course:

Seminar on Nuclear Weapons and International Politics. 100 Units. The aim of this course is to examine how nuclear weapons have affected the conduct of international relations. Special attention will be paid to subjects like: 1) nuclear deterrence, 2) the causes of nuclear proliferation, 3) the consequences of nuclear proliferation, 4) strategies for employing nuclear weapons, 4) the role of nuclear weapons in the Cold War, 5) how nuclear weapons will affect relations among the great powers in the emerging multipolar world, and 6) whether there has been a "nuclear revolution."    

The issue here is not that Mearsheimer can hold those seminars, it is the fact that despite him being a graduate of the USMA at West-Point, class of 1970, he hardly qualifies for any serious  military input because his record of "conclusions" regarding the only country which can wipe the US off the map, Russia, in the last decade demonstrates his complete detachment from the geopolitical reality in so far as the global balance of power and technological revolution goes. Which his latest disastrous and empty treatise proves without a shade of a doubt. A nauseating meandering dabbling into the pile of contemporary Western political and foreign relations theories none of which ever predicted anything. Not to mention the fact that few in the West really know how things work precisely because the only thing they know is how to obfuscate facts to fit narratives. We are not like that, we have some clue and there is no reason to produce a pile of BS for the sake of own academic sinecure, no matter how risible this doctrine-mongering is. In 99% of the cases it is preposterous. 

Now, that we have re-established the fact that Western politicos do not have a clue beyond general political, primarily media-driven, issues and that they can like or dislike anything related to warfare only based on how they are briefed and are told by people with a clue, let's explain now how even knowledge of basic facts of say Search Theory, ASW and physics and math of the modern warfare, namely Salvo model (missile exchange) gives us immediately an exceptionally clear glimpse of this capricious animal of strategy. You see, you need to know not only what to do, you need to know HOW things work and, especially, WHY they work. No course in history, political "science" or social sciences, supported by studying the statistics of GIGO (Garbage In-Garbage Out) can answer this. 

Enter delivery systems and Washburn's classic equation for the so called Random Search in case the "flaming" datum (in our case the position of the submarine) is obtained because... how about the sub launches its anti-shipping missiles and gives itself away. Here we have to review two scenarios. 

a) the war breaks out with a very short escalation (threatening period) phase which sees a "moderate" ASW/Patrol aircraft presence in the area;

b) the breakout of hostilities is preceded by a fairly lengthy escalation (threatening period) phase which sees gradual but fairly fast increase of the ASW forces in the area. 

As you may have guessed it already, we are viewing possible (hopefully, impossible) conflict between NATO and Russia. Assume that in both scenarios you have this operational situation--it is not "strategic" yet, it will become soon. 

The five red circles (circumferences, really) are theoretical positions (done to be best of my ability to a real scale) of Russian Navy's SSGNs all carrying both 3M22 Zircon and 3M14 Kalibrs with P-800 Onyx. The range of roughly 950 kilometers (red circumferences) is given for 3M22. The area of each such circle is roughly 2,000,000 square kilometers (which is about the area of Greenland) and submarines, of course, are located at the centers of those circles. Small blue circumferences, however, in each of the circle are not related to subs, they merely show the scale (of around 50 kilometers) of the range of detection and main caliber gun battles between battleships of the closing period of WW II and they are there for comparison. 

The blue line which splits in two with the arrows at the ends are general routes of the US convoys to deliver reinforcements to NATO allies in case of the war getting (let's assume) into the more-or-less protracted mode, for now without nuclear weapons and the US navy is forced to fight yet another "Battle of the Atlantic". The straight green dashed line and two green rectangles (absolutely NOT to scale) are coverage at the ranges and hours on station (that is conducting some sort of ASW search) by a single P-8 Poseidon. As you might expect, the United States can fast increase the number of the ASW/Patrol aircraft in the area and we will talk about this too, but at this stage ANY scenario, even seemingly most realistic, is viewed ONLY for given the frame of reference, which Western decision-makers lack completely. What also has to be understood--those circumferences and rectangles they are not static, in real life they move, sometimes very actively, especially against the background of such advances in submarine quieting which allows dramatically increase "silent" velocities while being able to use acoustic detection capabilities without much interference. We discount here weather and hydrology factors for now. 

So, enter flaming datum formula. You can see the thesis by the officer of Chilean Navy Alberto Soto for Master of Science Degree in Operational Research (he had Bachelor of Science in Weapons Engineering) in US Naval Post-Graduate School, under the guidance of Dr. Washburn (page. 24, just in case). 

Average number of detections with the time z(t):

I once elaborated on this formula which is applicable to the so called Random Search (which also is applicable to a Parallel Search) and there is literally nothing complex in this formula despite the integral sign. As we already established z(t) is a number of detections by whatever (ASW Helo, ASW/Patrol aircraft etc.). So: 

R--is a detection range of our "cookie cutter" sensor. You may ask what the hell a kitchen device has anything to do with submarine hunting. The answer is very simple--all cookie cutters have sharp and well defined edges which are unchanged. In real life, of course, the detection ranges of any sensor, be that radar, sonar or FLIR are subjects to change due to weather conditions, radio-permeability for radar, hydrology for sonar and as a result, for our theoretical calculations we have to assume that ranges do not change and are as sharp and well-defined as the edges of a cookie cutter. (Hint: ASW is the most complex and daunting task in naval warfare). One of my favorite sketches. 

Ranges, of course, vary--if radar range is influenced, among many other things, by the elevation of its antenna and under some conditions could either lose or gain up to 20-30% of its range and its "cookie cutter" shape is circle, the range of, say, MAD, Magnetic Anomaly Detector is a "strip" whose width is the double range and it is not that huge (which will matter later) and varies say between 500 meters to 2 kilometers. Let's assume that it is one kilometer for the ease of calculations, so, in this case MAD's range will be 1 kilometer x 2 = 2 kilometers. It is all simplified, of course.

V--of course is velocity because our sensors move: radar on ship moves with the speed of a ship and leaves behind itself a "strip" with the area of V x 2R, because any sensor looks on "both sides" thus doubling its range (see above about MAD's range). If our radar detection range on the ship is 40 kilometers and the ship moves with the speed of 20 kilometers per hour, that means in one hour it will "cover" the area of 40 x 2 x 20 x 1= 1, 600 square kilometers. If the double width (2R) of our MAD is 2 kilometers, then P-8 Poseidon, flying with speed of (roughly) 400 kilometers per hour, will cover the area of 2 x 400 = 800 square kilometers. 

This "scary" Pi x y(t)^2 is nothing more than the formula of the area of the circle you know from the middle school and it is nothing more than 3.14 x r^2, where our r in this case is an expanding radius of a search circle (with the center of datum) at any given time (t) which is velocity of submarine time time at any given moment starting from the moment Tau (a funny lower case letter at the lower limit of integration of our integral) and it is nothing more than the delay time, between the time of datum--the sub blows its own cover by a missile launch--and the moment helicopter or P-8 Poseidon (or P-3 Orion) arrives at the circle to start its search, or hunt. Say, the sub launched missiles and was detected (Flaming Datum) at noon, 12:00, Poseidon arrives at the expanding circle at 12:30, our tau (delay) thus is 0.5 hours. If the submarine was moving all this time with "let's save our asses" speed (velocity) of 20 kilometers per hour (roughly 12 knots) then the radius of the circle in which Poseidon will have to search is y(t) = 20 x 0.5 = 10 kilometers, thus the area of this circle is Pi x y(t)^2 = 3.14 x 10^2=3.14 x 100 =314 square kilometers.  

This is all tactics but it becomes a serious operation with enormous strategic ramifications once the search (hunt) starts because at this stage a truckload of factors begins to affect all this chaos and we get to see the numbers which today can make any serious American military professional feel very uncomfortable, because once the latest anti-shipping cruise missiles such as 3M22 or Onyx get involved, mathematics becomes insane and ASW operations begin to look daunting, to put it mildly. Because Probability of Detection (POD) of the enemy (Russian) submarine, which is calculated like this:   

Is the major reason behind many recent statements and actions on NATO's part, because it is difficult to fight a war, when you know that you will get defeated badly. But about this later. Waiting for your feedback if I need to continue with this, because real analysis has to have some numerical framework, which is also comprehensible to a well educated layman, who can do basic calculations. 

To Be Continued (maybe?)...

P.S. Someone may say that I gave John Mearsheimer a bad rap, I don't know how anyone who for the last 10 years was on record about "mediocre" Russian Armed Forces and who obviously lacks understanding of physics and mathematics of delivery systems, which ARE the foundation of a nuclear deterrence (anyone can make warhead today), can teach and hold any seminars on nuclear deterrence. Can he answer the question if Kinzhal is a deterrent?