Aggregation, Disaggregation, and the 3:1 Rules in Ground Combat

by Paul K. Davis


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This report illustrates a number of basic principles about aggregation and disaggregation in combat modeling by working through the mathematics and phenomenology of a concrete example. In the example, simplified ground combat takes place in a number of sectors and subsectors within a theater. The author assumes that combat at some level of detail is dictated by the Lanchester square law then discusses whether an aggregate law, Lanchester or otherwise, applies at the next level up (that is, one with more aggregation and less detail). The answer depends on the ratios of several time scales related to information, decisions, maneuver, and the duration of a breakthrough battle. The author also discusses how the 3:1 rule does and does not apply at different levels of combat.

Table of Contents

  • Chapter One


  • Chapter Two

    The Microscopic Model: The Lanchester Square Law on Combat Sectors

  • Chapter Three

    Deriving Aggregate Models for Cases Without Reinforcement or Redeployment of Forces

  • Chapter Four

    Generalizing: Effects on Aggregation of Reinforcement and Maneuver

  • Chapter Five

    Implications for Temporary Disaggregation in Simulations, Including Distributed Interactive Simulation

  • Chapter Six

    Conclusions and Summary

  • Appendix A

    Lanchester Equations and Scoring Systems

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