# Tactical Size Unit as Distribution in a Data Farming Environment

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## Abstract

**:**

## 1. Introduction

## 2. The Platoon as Entity in Simulation Models

#### 2.1. Conceptual Model of an Infantry Platoon

#### 2.2. Computational Model

#### 2.2.1. Markov Model for Strength Distributions

#### 2.2.2. Model for Areal Distribution of the Unit

^{2}area. In order to handle an agent with, for example, 30 single soldiers spread over a large area, some kind of inner model is needed in order to answer simulation questions like: What is the distance between target and shooter, and what are the areas where equal hit probabilities can be expected with indirect fire?

#### 2.2.3. Model for Indirect Fire

_{impact}(x, y) is the probability that the round detonates at (x, y) and P

_{kill|impact}(x, y) is the probability that the target element is killed if a round detonates at (x, y) (see Figure 6). P

_{impact}(x, y) is the value of the probability density function of the bivariate normal distribution at (x, y).

#### 2.2.4. Optimal Target Selection of Calculation Points

## 3. Testing and Validation of the Model in a Data Farming Environment

#### 3.1. Some Simulated Cases with the Sandis Software

#### 3.2. Verification and Validation of the Model

## 4. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References and Notes

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**Figure 1.**An example of a group from the Finnish Defence Forces Combatant Guide [9].

**Figure 2.**A simplified state machine for soldiers at the platoon level [4], in which a soldier’s state changes over time. The unit has effective firing strength (distribution) and effective strength (distribution).

**Figure 3.**The states in the Markov model represent the number of soldiers in the unit. The right hand figure illustrate the model presented in this paper, in which all transitions are in possible during each time step, except those where the unit strength would increase.

**Figure 4.**The strength distributions for 27 soldiers unit after three artillery strikes when only one nine-man unit was under fire. Both expected value and deviation are different, thus illustrating the need for time-dependent inner model for platoon level agent.

**Figure 6.**The basics of artillery kill probability calculation. Reproduce with permission from [4].

**Figure 7.**Cross-sectional schematic of fragment zones of an exploding artillery shell. The fragment zones are modelled as spherical zones. Reproduce with permission from [17].

**Figure 8.**A cookie-cutter damage model and an exponent decay model for artillery effectiveness. The exponential model is much more accurate than cookie-cutter model, but both are worse than physical model used in Sandis. Reproduce with permission from [4].

**Figure 9.**A calculation point can shoot many target calculation points. A multi-step algorithm using weapon effect models is used to get a metric for target selection, which is used to minimize the shooters’ own casualties. Reproduce with permission from [15].

**Figure 10.**The historical battle map by Keinonen [23] and representation in Sandis with platoon size units. The Finnish platoons are scattered over a larger area, shown by the larger circles.

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**MDPI and ACS Style**

Lappi, E.; Åkesson, B.
Tactical Size Unit as Distribution in a Data Farming Environment. *Axioms* **2016**, *5*, 7.
https://doi.org/10.3390/axioms5010007

**AMA Style**

Lappi E, Åkesson B.
Tactical Size Unit as Distribution in a Data Farming Environment. *Axioms*. 2016; 5(1):7.
https://doi.org/10.3390/axioms5010007

**Chicago/Turabian Style**

Lappi, Esa, and Bernt Åkesson.
2016. "Tactical Size Unit as Distribution in a Data Farming Environment" *Axioms* 5, no. 1: 7.
https://doi.org/10.3390/axioms5010007