150th Motor Rifle Division And Much Much More Military Power Related-III

So, the question is: do Osipov-Lanchester Equations work in real life? Not quite. This, inevitably, creates another question: why bother then with studying these equations? The answer is simple--to understand highly non-linear dynamics of a war and to get both tactical and operational (and, in the end, strategic) sense of opposing forces' ratios which become an absolute must when planning and fighting a battle. These equations give us an entrance into the world of both quantitative and qualitative considerations for opposing forces, which is later described by Salvo Model, which can sometimes get fairly complicated, not too bad, though.  

So, let's conduct some mental experiment--let's model a simplest battle from the point of view of non-military and non-mathematical average Joe, or Ivan, or Hans or what have you. Say we have two opposing forces A and B. Both forces are an exact match in terms of their weapons and skills, except for their numbers. Let's assume that force A has 1000 riflemen while force B has 750. These forces begin to shoot at each other and the intuitive, and very civilian, conclusion would be that by the time these forces A and B stop shooting at each-other, force A will have 1000-750=250 riflemen left after completely annihilating force B. After all, force A is simply larger (more numerous) than force B. Well, this is very wrong. This is not how it will happen. A way more realistic calculation will be done with the system of differential equations which you already saw in the previous post and we will simplify them even more by getting rid off those fancy Alpha and Betta which are merely numerical coefficients we will talk about later: 
                              

As you can see, we simplified these equations to merely reflect the changes in the numbers of both sides over time. Term dt merely stands for change in time: say our imaginary hostile forces started to shoot at 13:00 and stopped at 14:00, so dt=14:00-13:00=1 hour. dA and dB merely mean change (in our case this will be decrease in numbers) in respective forces. Thus, dA/dt and dB/dt are merely changes in respective forces over time or rates of losses. Now comes this tricky (not really, but still) moment--how are we going to calculate what's left of more numerical force A after it annihilates force B, and here our civilian non-mathematical intuition does not fail us--under all other conditions being equal (memorize this statement really well!!!), force A will eliminate force B, because it has numerical superiority. Here is how--all this is basic math: let us bring both equations in system to a single "floor": 
                      

As you may have already noticed, we are solving these equations in general, without plugging in our numbers yet. We also understand our initial conditions (and constrains) that once B is annihilated A stops sustaining casualties. So, let us simplify these equations even more, for people who are scared of math, by rewriting what these fancy dA and dB really are. They are nothing more than the difference between the numbers of respective forces before (start) and after (end) the battle, in our particular problem. In reality, we are the ones who choose the time period in which to see what those differences are. Thus:       

 

By now some of you may have guessed already that our dB will be 750 (or -750, depending on how you view your equations), which means only one thing--everyone in force B will be either killed or taken out of action. As you can see, I am being very deliberate and tedious in explaining these transformations and this is for only one reason--we have to integrate both sides of both equations. This is how simplest differential equations with separable variables are solved. Some of you probably will recall now what anti-derivative is. So, let me make things somewhat easier here. We already know from the bottom equation in the system that in the end B force will reduce (or, rather, will be reduced by A) itself from 750 riflemen to 0. But laws of mathematics do not allow us to simply write this number in the left side of this equation, it still has to look like this. I deliberately eliminated any mention of limits of integration to make it look simpler:                         

     

I know, I know, believe me I am trying desperately to make this as simple as possible for those who are intimidated a bit by all this math mambo-jumbo. But since we are dealing here with integrals and some abstract variables we have to remember that integration is a finding of anti-derivative and anti-derivative for a simple variable X (or A, or B or whatever letter you want to use) is always:                                       

         

So, the solution to our system of equations will look like this and we will call it Equation - I : 
                       

But, since we are back into simple math in Equation-I you may easily see that after all simplifications our equation becomes this, Equation-II:   
                        

This equation is in the foundation of what became known as Quadratic Law and we are about to demonstrate it. So, let's start plugging in our available data into this equation. We know that our B start=750, we also know that our B end=0, our A start is 1000 and A end is unknown and we will call it X. Look now at what our equation has become--yes, simplest quadratic equation:     
                      

   

From here you can easily establish that the value of X, that is the number of remaining riflemen in the force A after they annihilate whole force B will be a square root of 1,000,000-562,500=437,500 which is approximately 661 riflemen. That is 2.5 times more than linear approach would suggest. I hope those lively colors in equations helped all of you to keep focus on what matters here. So, the implications of this simple quadratic law are immense. In fact,  all those Alphas and Bettas which are, in this particular case, coefficients of combat efficiency enter the fray. You may get a somewhat expanded form of these equations which introduce combat efficiency here and here (pay attention to page 8):

Consider this simple problem: we know that combat efficiency of the machine gunner equals combat efficiency of 36 riflemen. How many machine gunners will we need to completely substitute 1000 riflemen. No, it is not 1000 divided by 36, it is 1000 divided by the square root of 36 which is 6. 1000/6 gives us about 167 machine gunners. That means that combat strength of a fighting force is calculated by multiplication of combat efficiency of a single unit (rifleman, squad, platoon etc.) by the square of numerical strength. In layman's lingo it means one very important thing: the more numbers you have (let alone when you have numbers more effective than that of your enemy), the more disproportionate will be the distribution of losses in your favor. Indeed, recalculate this same problem but now 2,000 against 750. You will lose roughly 146 of your riflemen, that is 1854 of your troops will survive the battle. These simple calculations lead us to a very fundamental conclusion which is one of the main principles of war:

         PRINCIPLE OF CONCENTRATION OF FORCE 

This principle also has a very famous application in everyday life in famous formula from physics: P=F/A. Pressure equals applied force divided by area. The larger is a force and the smaller is an area--the larger is a pressure. This is what went into the foundation of the Blitzkrieg and its famous schwerpunkt (focal point) principle, where a massive force, locally more numerous than that of the enemy, was concentrated on a small segment of the front thus applying and immense pressure on the enemy defense, eventually breaking the front and going on the exploitation which was a death knell to a broken enemy. For anyone who ever even remotely dealt with the issues of military technology, combat training or combat, let alone studied military history not from propaganda outlets, the arguments which Shlykov used in his article do not sound convincing at all. Basic operations research can give some fairly accurate answers. 

To Be Continued...... 

          

150th Motor Rifle Division And Much Much More Military Power Related-II

So, let us review some of the fundamental ideas which Vitaly Shlykov advocated for Russia's "military reform" which, in the end, resulted in a disaster that required urgent intervention of....drum roll...none other than President Vladimir Putin, that is a man, whose appointment of Anatoly Serdyukov to the Defense Minister position precipitated that disaster in the first place. But first, we need to point out positions where Vitaly Shlykov was correct. 

1. He, certainly, was correct about the necessity to reform Soviet Armed Forces, which were massive and, effectively, existed in overkill mode insofar as the numbers go. Yet, while correctly pointing out in his What Killed Soviet Union. The General Staff And Economy the fact of Soviet military and intelligence failure to correctly estimate (by inflating) NATO's military potential, Shlykov went overkill the other way--he "informed" Gorbachov that Soviet General Staff overestimated NATO's mobilization potential 50 to 100 times. 

2.  Well....that's about it. 

Yes, those were the times of Perestroika (correctly dubbed Catastroika by Alexander Zinovyev) and ascendance of highly idealistic, if not altogether naive and uncritical to the point of folly, views of the combined West and Vitaly Shlykov's ideas on war and military reflected it fully. In fact, they influenced them in the most harmful way possible. Here I need to make a confession. It was then, late 1980s when I also, together with very many of my peers, exercised the idea of possible re-formatting of the geopolitical order after the collapse of the communist ideology into some sort of a cooperative environment in which reformed USSR would take its proper place and fears and hostilities of the Cold War would be the thing of the past.  But that was me, at that time senior lieutenant of Soviet Armed Forces, who still thought that surely the Colonel of GRU must know more than me about the war. Boy, was I wrong. By 1992, two years after I left the service for health reasons and scarred by the events related to Nagorny Karabakh, there was nothing left of the Soviet Union, Warsaw Pact and former Soviet Armed Forces were in the process of disintegration. It was also the time of mindless economic, military and political so called reforms (in reality, annihilation of anything perceived as Soviet) which would bring upon peoples of Russia a suffering and humiliation not seen since the first days of the Great Patriotic War. This would become the time when history would be taken away from Russian people. 

One of the major, if not the most important, premises, on which demolition of what used to be Soviet military was based was the idea that the victory over Wehrmacht in WW II was won by the enormous purely military losses and despite, not thanks, to Soviet highest military-political leadership. A popular "trupami zabrosali" (overwhelmed the enemy by throwing corpses at it) meme became extremely popular among "liberal" post-Soviet "intelligentsia" and all kinds of "fighters with bloody Soviet past". All kinds of revisionist crap, akin to incompetent propaganda BS by turncoat Victor Rezun (aka Suvorov) filled the void of military science. Indeed, the logic went, if USSR collapsed, together with ideology which supposedly held it together, then everything associated with it must be wrong. And it was then that the revision started. Vitaly Shlykov led the charge with his 1988 Mezhdunarodnaya Zhizn (International Life) famous article The Armor Is Strong (Bronya Krepka). 

"Посеянные в те годы семена «науки побеждать» числом, а не умением нашли благодатную почву в консерватизме советской военной мысли застойного Периода, наследие которого еще предстоит преодолеть. Броня крепка, стереотипы прочны, отходят от них иные с трудом".(c)

The seeds of the "science of winning" by numbers, not by the skill,  sown in those years (he means WWII period) found a fertile soil in conservatism of the Soviet military thought of the zastoi (stagnation), whose heritage we are yet to overcome. The Armor is strong, stereotypes are rigid and some people abandon them with difficulty. 

Shlykov went further in the same article and stated: 

Stalin and his immediate military surrounding always tried to hide from complex and incomprehensible for them variety of qualitative characteristics of the military might of states with different social structures behind the thick wall of numerical superiority over the enemy. (c)

I know, the hindsight is a 20/20 vision, especially considering the time when Shlykov's pieces were written, but it is impossible to ignore such absolutely sweeping generalizations from a man who inserted himself into the discussion on one of Russia's most important, existential, issues and who started to built his conclusions based on cliches which had very little to do with the realities of the Great Patriotic War. There is no denying that Red Army was sustaining abhorring losses at the start of the war. Wehrmacht losses inflicted by the Red Army at the end of the war were no less massive. Yes, the issue of large tank units is valid, the same as, to a certain degree, the issue of Red Army's prewar purges. But today, when most of the archives are opened, it becomes absolutely inconceivable to accuse Stalin, let alone Stavka in "hiding" from "qualitative" characteristics of military might when, in reality, if not for Stalin and his "military surrounding" the victory of the Soviet Union in the Great Patriotic War would have been inconceivable. 

Admitting almost miraculous survival and recovery of what essentially can be termed Stalin's (and Beria's, Vannikov's and many others) economy doesn't make one a Stalinist. In the end, it was this economy which provided not only quantity but the quality of weapons which ensured the final outcome. In the end, Soviet tanks as a force turned out to be simply better than German ones and so were, in the end, Lavochkin or Yakovlev fighters which were at least on par with what Luftwaffe could field and they were produced in quantities which ensured, from the skies of Kursk Battle and massive air campaign over Kuban, Soviet dominance in the air. Not without Allied help with US providing P-39 Cobras which were flown by none other than Pokryshkin and Rechkalov brothers--all, together with Ivan Kozhedub who flew Lavochkin aircraft, top Allied aces by far.  But the question here is why the issue of numbers even came up at all? By what means Vitaly Shlykov was going to fight the greatest and most advanced military force in history, fresh from its....drum roll....lightning victories over French and British Armies and subjugation of Europe? Here we are going to make a small detour to elaborate on some basic operational facts and they will involve a little bit of mathematics (rather, simplest calculus). Welcome to the world of Osipov-Lanchester differential equations.   

dA/dt = -βB

dB/dt = -αA

Well, as it is usually the case, the original 1915 essays by Russian mathematician M.P. Osipov "Estimation Of Victims Of War" went unnoticed in the West, but Lanchester's work in the same field did get noticed. Today Western world knows those equations as Lanchester Model or Laws, while truly educated people call it Osipov-Lanchester equations. Before I get accused of abstract approach to a war or playing "percentage" war ( I had exchange on this issue with incomparable Colonel Lang) I want to make a disclaimer--I am no military nerd who views the world through the prism of dry numbers. Far from it, I am keenly aware of a chaotic and too often very human nature of war in which command ability, heroism, sacrifice and skill are as, if not more, important as technological and operational dimensions of a war. 

To Be Continued...........

P.S. Do not run for cover yet. I will explain how this simple math works.