📂Dynamics

Simultaneous Firing Combat Model

Overview

If Lanchester’s Laws are a model describing the aspects of modern and contemporary warfare, the Salvo Combat Model specifically depicts large-scale naval battles among them. In naval warfare, the means of attack are often large and powerful, such as missiles, and conversely, there are missiles for intercepting these missiles, which is a difference.

Model¹

$$\begin{align*} \Delta A =& - { { 1 } \over { H_{A} } } \left( O_{B} B - D_{A} A \right) \\ \Delta B =& - { { 1 } \over { H_{B} } } \left( O_{A} A - D_{B} B \right) \end{align*}$$ However, the following limitations apply. $$0 \le - \Delta A \le A \\ 0 \le - \Delta B \le B$$

Variables

• $A(t)$: Represents the number of entities in group $A$ at time $t$.
• $B(t)$: Represents the number of entities in group $B$ at time $t$.

Parameters

• $H_{k}$: Represents the Staying Power of group $k$.
• $O_{k}$: Represents the Offensive Firepower of group $k$.
• $D_{k}$: Represents the Defensive Firepower of group $k$.

Explanation

It might seem odd to mention population dynamics when talking about the number of ships in a naval battle, but viewed abstractly, this model is fully sufficient as a population dynamics model. What differs it from other models is that it is expressed discretely, instead of using differential equations, and it considers very short moments compared to ecosystem models that consider long periods, which means it does not account for reinforcements and hence the following limitation. $$0 \le - \Delta A \le A \\ 0 \le - \Delta B \le B$$ This expresses in an equation that just because defensive firepower is high, no new ships arise, nor do ships sink simply because they are outnumbered.

Comparison with Lanchester Model

Compared to the Lanchester Model, the difference lies in whether or not it reflects defensive capabilities. In the equations, the act of defense is not merely armoring each entity but reflects launching intercept missiles, hence the defensive power is proportional to the size of the fleet.