In the paper titled "Unifying warfighting functions in mathematical modelling: combat, manoeuvre, and C2," authors Ryan Ahern, Mathew Zuparic, Keeley Hoek, and Alexander Kalloniatis explore the outcomes of warfare beyond the traditional focus on quantity and quality of combatant force elements. They argue that effective Command and Control (C2), which allows for maneuverability and adaptation across force elements, can enable smaller or weaker forces to overcome adversaries with greater resources and firepower. To support their argument, the authors combine two mathematical models: the classic Lanchester combat model and the Kuramoto-Sakaguchi model for phase oscillators on a network. This combination results in a flexible Networked-Lanchester-C2 representation of force-on-force military engagement. By unifying three key warfighting functions - fires, maneuverability, and C2 - into a single mathematical model, the authors aim to provide a comprehensive understanding of military engagements. The paper presents three illustrative use cases to demonstrate how this reduced model characterizes global effects in the full system. The authors find that even with inhomogeneous forces, an appropriate balance between internal organizational coupling, resource maneuverability, and weaker lethality can allow a force to adapt strategically and overcome initially stronger adversaries. Overall, this research contributes to our understanding of warfare by highlighting the importance of effective Command and Control in achieving successful outcomes on the battlefield. The mathematical model developed by the authors offers insights into how smaller or weaker forces can leverage their capabilities to gain an advantage over more powerful opponents. The findings have implications for military strategy development as well as decision-making processes. The paper has been accepted by the Journal of Operational Research Society.
The paper talks about what happens in a war besides just how many soldiers there are. It says that having good leaders and being able to control your forces well can help smaller or weaker armies win against bigger ones. The authors made a math model that combines different things like fighting, moving, and controlling forces to understand how wars work. They used the model to show how smaller armies can beat bigger ones by being smart and adaptable. They also said that having good leaders is really important for winning battles. The math model they made can help military leaders make better plans and decisions."
Definitions
- Warfare: fighting in a war
- Combatant force elements: the soldiers and weapons in an army
- Command and Control (C2): being able to give orders and control your forces well
- Adversaries: enemies or opponents
- Lanchester combat model: a math model that helps understand how battles work
- Kuramoto-Sakaguchi model: another math model used with the Lanchester combat model
- Force-on-force military engagement: when two armies fight each other directly
- Unifying fires, maneuverability, and C2: combining different aspects of warfare like shooting, moving, and controlling forces into one understanding
- Mathematical model: using numbers and equations to understand something
- Organizational coupling: how well different parts of an army work together
- Resource maneuverability: being able to use resources effectively
- Lethality: how deadly or dangerous something is
Unifying Warfighting Functions in Mathematical Modelling: Combat, Manoeuvre, and C2
Military engagements have traditionally been studied from the perspective of quantity and quality of combatant force elements. However, a new research paper by Ryan Ahern, Mathew Zuparic, Keeley Hoek, and Alexander Kalloniatis suggests that effective Command and Control (C2) can enable smaller or weaker forces to overcome adversaries with greater resources and firepower. The paper titled “Unifying warfighting functions in mathematical modelling: combat, manoeuvre, and C2” has been accepted by the Journal of Operational Research Society.
The Networked-Lanchester-C2 Model
To support their argument about the importance of effective command and control in warfare outcomes, the authors combine two mathematical models: the classic Lanchester combat model which is used to describe how opposing forces interact over time; and the Kuramoto-Sakaguchi model for phase oscillators on a network which is used to represent internal organization within each force element. This combination results in a flexible Networked-Lanchester-C2 representation of force-on-force military engagement. By unifying three key warfighting functions - fires (combat), maneuverability (manoeuvre), and C2 - into a single mathematical model, the authors aim to provide a comprehensive understanding of military engagements.
Illustrative Use Cases
The paper presents three illustrative use cases to demonstrate how this reduced model characterizes global effects in the full system. In one example scenario involving two homogeneous forces with equal lethality but different levels of maneuverability capability due to differences in resource availability; it was found that an appropriate balance between internal organizational coupling (network structure) could allow one force to adapt strategically while overcoming initially stronger opponents despite its weaker lethality score.
In another example involving inhomogeneous forces with unequal lethality scores but similar maneuverability capabilities; it was found that even when facing an adversary with greater firepower capabilities; an appropriate balance between resource maneuverability (network connectivity) could still allow one force to gain an advantage over more powerful opponents through strategic adaptation enabled by effective Command & Control processes.
Implications for Military Strategy Development
Overall this research contributes to our understanding of warfare by highlighting the importance of effective Command & Control processes as well as resource allocation strategies for achieving successful outcomes on battlefields where resources are limited or unevenly distributed among combatants. The findings have implications for military strategy development as well as decision making processes related to resource allocation during times of conflict or crisis situations where every second counts towards victory or defeat on battlefields around world today.
The outcomes of warfare have rarely only been characterised by the quantity and quality of individual combatant force elements. The ability to manoeuvre and adapt across force elements through effective Command and Control (C2) can allow smaller or weaker forces to overcome an adversary with greater resource and fire-power. In this paper, we combine the classic Lanchester combat model with the Kuramoto-Sakaguchi model for phase oscillators on a network to create a flexible Networked-Lanchester-C2 representation of force-on-force military engagement. The mathematical model thus unifies three of the military warfighting `functions': fires, manoeuvre and C2. We consider three illustrative use-cases, and show that an analytical treatment of a reduced model characterises global effects in the full system. For inhomogeneous forces we observe that with appropriate balance between internal organisational coupling, resource manoeuvrability and even weaker lethality the force can be adaptive to overcome an initially stronger adversary.
