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

In 1995 the world saw the first edition of When Titans Clashed: How The Red Army Stopped Hitler by David Glantz and Jonathan House, both senior officers of US Army. With a single book these military historians rendered useless and inconsequential pretty much the whole army of Western historians such as Anthony Beavor who was left to write on Red Army "raping" 2 million, or 20 or 1.5 billion German women in 1945. A phenomenon of Glantz' and House's book was not in employing at that time the latest data from Soviet Archives and data provided in famous General Krivosheev's treatise Grif Sekretnosti Snyat (The Seal Of Secrecy Is Removed), later updated and reissued as Russia And USSR In The XX Century Wars, Armed Forces Losses. In the end, even before the book, despite Soviet, somewhat whitewashed, version of the events of the Great Patriotic War it was clear to many professionals that classic narrative of the First Period of that war, when Red Army was sustaining catastrophic losses can not be explained just by Stalin's purges of the Red Army or, what Shlykov called hiding "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)  
           

 
While one may or may not agree with Glantz' and House's conclusions (European "elites" of the time are directly culpable in precipitating WW II), there is no denial of the fact that they were able to struck a necessary balance between purely political and military narratives. They, in the end, correctly attributed initial failures of the Red Army to a much more comprehensive set of factors than some inability or purges. It is there, where Glantz and House make an extremely important statement, which is relevant to our discussion:       

Omitting here a newly revealed facts of, indeed, a possibility of military coup in the midst of Red Army's top brass, which precipitated  purges, taking this (framed in red) military constant to heart is what we will do here. Size does matter but only insofar as this size is effective and properly deployed--pure quantitative comparison does not work and it shouldn't. Argumentation based on comparison of sheer numbers of personnel and equipment of the Red Army and Wehrmacht prior to the start of hostilities in June 1941 without comprehensive analysis of their respective effectiveness is a waste of time. Obviously, it is possible to measure dyadic (that is mano o mano) technological advantage of one force over the other:             

From Stephen Biddle's Book

But, as you can see, mere addition of weighted averages of tanks and aircraft doesn't tell us much. In the end, Saddam's army had many tanks and not all of them were old, by far more important was the fact that all of them were monkey models. Overwhelming technological advantage of the US and coalition in both Gulf Wars was never in question.

I elaborated slightly on an extremely simplified form of Osipov-Lanchester model, where I removed numerical coefficients of combat effectiveness. Once those combat effectiveness numbers are introduced the picture changes dramatically. We must ask ourselves several important questions when trying, using an example of, say First Gulf War, to get a grasp of this combat effectiveness. Will start with a simple question:

Was US average soldier better than Saddam's average soldier in that war? The answer is evident--yes. US soldier was more educated, had more tactical acumen, was better trained than Saddam's soldier. By how much? That is yet to be discussed, but US average soldier's advantage over Saddam's soldier was also in the very military system which the US soldier was part of, that is the way US forces were not only armed but how they were deployed. It is possible to imagine this same war without overwhelming US (and allies) air superiority and, while paying much steeper price in KIAs and time, US Army would still have overcome Saddam's Army purely on a vast superiority, apart from quality of soldiers, of its Command, Control, Communications, Computers, Intelligence, Surveillance and Reconnaissance capabilities, known to all as C4ISR. It is a fusion of human and technological factors which defines the "betterness" or otherwise of a soldier. Now, going back to Great Patriotic War. The question of comparison of the average Red Army and Wehrmacht soldiers is not even a fair one. 

On the morning of 22 June, 1941 Wehrmacht was still fresh from its triumphant demolition of the best West European armies in a matter of weeks. The morale was extremely high, combat cohesion of units was high, many Wehrmacht soldiers and generals were battle tested and confident in their command. On 22 June of 1941, Wehrmacht was the best Army in the world history since Napoleon's Grandee Armee'. Wehrmacht in general, and its average soldier in particular, simply had an overwhelming advantage in this combat effectiveness department. Simple measure of a dyadic technological advantage (see illustration above) completely breaks down here when only quantities (slightly "enhanced" with the maturity of technology) are considered. Numbers still matter a great deal, but in the end, these are Alpha and Betta (reduced to a simple number very complex metrics) which are as important! But many in the "reformer's" club decided to merely list the numbers of tanks, aircraft and artillery pieces, where USSR had a noticeable advantage, as Shlykov did not on one occasion, to come to  conclusions, which almost cost Russian Armed Forces in 2000s their ability to fight a serious war. Remember, memorize this:

                                               dA/dt = -βB

                                   dB/dt = -αA

  

Alexey Isaev in one of his books on Great Patriotic War makes an excellent reference to Jack London's famous short story The Mexican. 

"It was not a fight. It was a slaughter, a massacre. Any audience, save a prize fighting one, would have exhausted its emotions in that first minute. Danny was certainly showing what he could do--a splendid exhibition. Such was the certainty of the audience, as well as its excitement and favoritism, that it failed to take notice that the Mexican still stayed on his feet. It forgot Rivera. It rarely saw him, so closely was he enveloped in Danny's man-eating attack. A minute of this went by, and two minutes. Then, in a separation, it caught a clear glimpse of the Mexican. His lip was cut, his nose was bleeding. As he turned and staggered into a clinch, the welts of oozing blood, from his contacts with the ropes, showed in red bars. across his back. But what the audience did not notice was that his chest was not heaving and that his eyes were coldly burning as ever. Too many aspiring champions, in the cruel welter of the training camps, had practiced this man-eating attack on him. He had learned to live through for a compensation of from half a dollar a go up to fifteen dollars a week--a hard school, and he was schooled hard.

Then happened the amazing thing. The whirling, blurring mix-up ceased suddenly. Rivera stood alone. Danny, the redoubtable Danny, lay on his back. His body quivered as consciousness strove to return to it. He had not staggered and sunk down, nor had he gone over in a long slumping fall. The right hook of Rivera had dropped him in midair with the abruptness of death. The referee shoved Rivera back with one hand, and stood over the fallen gladiator counting the seconds. It is the custom of prize-fighting audiences to cheer a clean knock-down blow. But this audience did not cheer. The thing had been too unexpected. It watched the toll of the seconds in tense silence, and through this silence the voice of Roberts rose exultantly: 

"I told you he was a two-handed fighter!"

 To be continued.....

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......