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The full title of this work is "Weaponeering - Conventional Weapon System Effectiveness" by Morris Driels, who teaches at the USN Postgraduate School, and the cover of the edition I have in hand can be seen below.

9781563476655.jpg

 

The book aims to "describe and quantify the methods commonly used to predict the probably of successfully attacking ground targets using air-launched or ground-launched weapons", including "the various methodologies utilized in operational products used widely in the [US military]." Essentially, this boils down to a series of statistical methods to calculate Pk and Ph for various weapons and engagements. 

The author gave the book to my mother, who was a coworker of his at the time, and is of the opinion that Driels is not as smart as he perceives himself to be. But, hey, it's worth a review for friends.

I will unfortunately be quite busy in the next few days, but I have enough spare time tonight to begin a small review of a chapter. I aim to eventually get a full review of the piece done.

Our dear friends @Collimatrix and @N-L-M requested specifically chapter 15 covering mines, and chapter 16 covering target acquisition.

Chapter 15

Mines


The mine section covers both land mines and sea mines, and is split roughly in twain along these lines.

The land mine section begins with roughly a page of technical description of AT vs AP, M-Kill vs K-Kill, and lists common US FAmily of SCatterably Mines (FASCAM) systems. The section includes decent representative diagrams. The chapter then proceeds to discuss the specification and planning of minefields, beginning with the mean effective diameter of a mine. Driels discusses a simplified minefield method based on mine density, and then a detailed method.

The simplified method expresses the effectiveness of the minefield as a density value. Diels derives for the release of unitary mines from aircraft

NMines = Fractional coverage in range * fractional coverage in deflection * number of mines released per pass * reliability * number of passes

and for cluster type

NMines = FRange * FDefl * NDispensers * Reliability dispenser * NMines per Dispenser * Reliability Submunition * number of passes

and then exploits the evident geometry to express the Area and Frontal densities. Most useful is the table of suggested minefield densities for Area Denial Artillery Munition and Remote Anti-Armor Mine System, giving the Area and Linear densities required to Disrupt, Turn, Fix, and Block an opponent. 
RcrZ8Nw.jpg

Whereas the simplistic method expresses effectiveness as a density, the detailed model views the targets and mines individually, assuming the targets are driving directly through the minefield perpendicular to the width and that there is only one casualty and no sympathetic detonations per detonation. The model computes the expected number of targets destroyed by the minefield, beginning with the Mean Effective Diameter and the PEncounter based on distance from the mine. 

Driels derives the number of mines encountered which will be encountered, not avoided, and will engage the target. I can't be arsed to type the equations in full, so here you go.

HddZGB8.jpg

The section concludes with an example calculation using the detailed mine method. Overall, this shows the strengths and weaknesses of the book fairly well - it is a reasonable derivation of open-source statistical methods for predicting Pk and Ph and the number of sorties required, but US-specific and limited in scope and depth. 

The treatment of Sea Mines  begins by describing the various types and uses of said mines, importantly noting that they have both defensive and offensive uses, and that the presence of the threat of mines is equally important as the actual sinking which occurs. There are three classifications of sea mines, contact, influence, and controlled.

Shallow water mines are treated trivially, considering them equivalent to land mines with Blast Diameter in the place of MED, and assuming that the mines cannot be avoided.

Deep water mines are approached in a similar manner, with the desire to determine the number of mines needed to achieve the required probability of damage, and planning missions from there. Two features of sea mines must be considered, however - mine actuation by passing of the target, and mine damage to the target. The probability of activation is, unfortunately, dependent on the depth of the mine and distance, forming a series of stacked bowls as below.

IHgLhOR.jpg
The mean value of PActivation is the statistical expectation of the curve. Because I don't feel like screencapping another equation, the Width of Seaway where an actuation can occur is qualitatively merely the area under the actuation curve calculated for a specific mine and target combo.

The damage function is also of interest - because we require the mine to both actuate and damage the target, this limits our earlier area under the curve to that area integrated to the limits of the damage function. The selection of mine sensitivity plays a very large role in the effectiveness of our mines. A high setting will lead to many more actuations than damages, which can be indicated by the ratio of the actuation area and the damage area from earlier. Setting the actuation distance equal to the damage distance means that every actuation causes damage, but the probability of actuation is only around 42%. The compromise which selects some Areadamage / Areaactuation of around .8 to .93 is generally preferred. This gives us several useful terms -

PA+D = Reliability * Areadamage / Widthminefield . The probability that the first ship to transit a minefield is referred to as the threat, or

Threat T = 1 - (1 - PA+D)^NMines = 1 - (1 - Reliability * Areadamage / Widthminefield ) which can obviously be solved for NMines to get the desired number of mines for a desired threat level.

Anti-submarine mines are an interesting subset of deep sea mines, as they turn the problem from two-dimensions to three. Driels accounts for this by replacing the mine damage width with the mine damage area, to no one's surprise. Driels claims that the probability of actuation and damage is 

PA/D =  Damage Area / (Width * Depth of minefield). Despite my initial confusion, the reliability term safely reappears in the threat definition below.

T = 1 - (1 - (Reliability * Area damage)/(Width * Depth of minefield))^NMines, with a solution for number of mines for given threat level fairly easily taken out as before.

Lastly, there is a summary of topics for each chapter, though unfortunately they are qualitative descriptions. Including the final derived equations in this part would be a major benefit, but is overlooked. Ah well. They are quite good for review or refreshing the material.

As before, this is a relatively interesting if shallow engagement with the statistical methods to calculate Pk and Ph and the number of sorties required. Going more into detail regarding selecting Threat values or common (unclass) parameters would be interesting, but is lacking. Assuming I don't slack off tomorrow, I should have most or all of the Target Acquisition chapter covered.

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