IDEAS home Printed from https://ideas.repec.org/a/sae/joudef/v23y2026i2p193-205.html

Estimating attrition coefficients for the Lanchester equations from small-unit combat models

Author

Listed:
  • Vikram Mittal

Abstract

The Lanchester equations are a valuable tool for analyzing attrition warfare and the impact of new technologies on the battlefield. However, uncertainties regarding the numerical values of attrition coefficients pose a challenge in accurately applying these equations. To address this, entity-based combat simulations focusing on small-unit operations can offer insights into calculating attrition coefficients and analyzing the effects of new technology on the battlefield. This study outlines the development of such entity-based simulations and the associated derivation of attrition coefficients from the results. One method involves using combat simulation to determine the combat multiplier factor associated with a new technology and multiplying the attrition coefficients accordingly. The second method involves basing the attrition coefficients solely on the results of the model. This paper explores each of these methods through two case studies, both of which use the Infantry Warrior Simulation (IWARS). The first case study examines the Battle of Mosul, analyzing the impact of drone technology on ISIS insurgents and the Iraqi army. The second case study investigates the influence of a more accurate rifle in a conflict involving rural and urban combat. It is important to note that these models provide approximations for attrition coefficients and are subject to inherent limitations. Nonetheless, they offer value by capturing the broader implications of integrating technological changes at the small-unit level.

Suggested Citation

  • Vikram Mittal, 2026. "Estimating attrition coefficients for the Lanchester equations from small-unit combat models," The Journal of Defense Modeling and Simulation, , vol. 23(2), pages 193-205, April.
    • Handle: RePEc:sae:joudef:v:23:y:2026:i:2:p:193-205
    DOI: 10.1177/15485129231210301
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/15485129231210301
    Download Restriction: no
    File URL: https://libkey.io/10.1177/15485129231210301?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kress, Moshe & Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Seidl, Andrea, 2018. "Lanchester model for three-way combat," European Journal of Operational Research, Elsevier, vol. 264(1), pages 46-54.
    2. Moshe Kress, 2020. "Lanchester Models for Irregular Warfare," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    3. S. J. Deitchman, 1962. "A Lanchester Model of Guerrilla Warfare," Operations Research, INFORMS, vol. 10(6), pages 818-827, December.
    4. Thomas W. Lucas & Turker Turkes, 2004. "Fitting Lanchester equations to the battles of Kursk and Ardennes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 95-116, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gerardo Minguela-Castro & Ruben Heradio & Carlos Cerrada, 2021. "Automated Support for Battle Operational–Strategic Decision-Making," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    2. Li, Meixuan Jade & Zhu, Cheng & Zhu, Xianqiang & Tse, Chi K., 2026. "Competitiveness of competing complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).
    3. Moshe Kress, 2020. "Lanchester Models for Irregular Warfare," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    4. Hausken, Kjell, 2024. "Fifty Years of Operations Research in Defense," European Journal of Operational Research, Elsevier, vol. 318(2), pages 355-368.
    5. Chad W. Seagren & Donald P. Gaver & Patricia A. Jacobs, 2019. "A stochastic air combat logistics decision model for Blue versus Red opposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 663-674, December.
    6. Adam T Biggs & Joseph A Hamilton & Rachel R Markwald, 2025. "Challenges of incorporating wounded personnel into small arms combat simulations," The Journal of Defense Modeling and Simulation, , vol. 22(2), pages 207-214, April.
    7. Adam T Biggs & Joseph A Hamilton & Rachel R Markwald, 2025. "Identifying appropriate scenario termination rules for squad-level simulations of warfighter lethality," The Journal of Defense Modeling and Simulation, , vol. 22(4), pages 521-528, October.
    8. Sergey Salishev, 2025. "The Narrow Corridor of Stable Solutions in an Extended Osipov--Lanchester Model with Constant Total Population," Papers 2512.18515, arXiv.org.
    9. Anelí Bongers & José L. Torres, 2021. "A bottleneck combat model: an application to the Battle of Thermopylae," Operational Research, Springer, vol. 21(4), pages 2859-2877, December.
    10. Timothy A. McLennan-Smith & Alexander C. Kalloniatis & Zlatko Jovanoski & Harvinder S. Sidhu & Dale O. Roberts & Simon Watt & Isaac N. Towers, 2021. "A Mathematical Model of Humanitarian Aid Agencies in Attritional Conflict Environments," Operations Research, INFORMS, vol. 69(6), pages 1696-1714, November.
    11. Graham V Weinberg, 2026. "Stochastic attrition modeling," The Journal of Defense Modeling and Simulation, , vol. 23(2), pages 245-253, April.
    12. Michael J. Armstrong, 2013. "The salvo combat model with area fire," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 652-660, December.
    13. C-Y Hung & G K Yang & P S Deng & T Tang & S-P Lan & P Chu, 2005. "Fitting Lanchester's square law to the Ardennes Campaign," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 942-946, August.
    14. Yuewen Liu & Juan Feng, 2021. "Does Money Talk? The Impact of Monetary Incentives on User-Generated Content Contributions," Information Systems Research, INFORMS, vol. 32(2), pages 394-409, June.
    15. Burton Lucy & Johnson Shane D. & Braithwaite Alex, 2017. "Potential uses of Numerical Simulation for the Modelling of Civil Conflict," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 23(1), pages 1-39, January.
    16. Moshe Kress & Roberto Szechtman, 2009. "Why Defeating Insurgencies Is Hard: The Effect of Intelligence in Counterinsurgency Operations---A Best-Case Scenario," Operations Research, INFORMS, vol. 57(3), pages 578-585, June.
    17. Nam H Nguyen & My A Vu & Anh N Ta & Dinh V Bui & Manh D Hy, 2022. "Optimizing fire allocation in a Network Centric Warfare-type model," The Journal of Defense Modeling and Simulation, , vol. 19(4), pages 691-701, October.
    18. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    19. Yuri M. Zhukov, 2014. "Theory of Indiscriminate Violence," Working Paper 365551, Harvard University OpenScholar.
    20. Shawn C. McKay & Alok Chaturvedi & Douglas E. Adams, 2011. "A process for anticipating and shaping adversarial behavior," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 255-280, April.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:joudef:v:23:y:2026:i:2:p:193-205. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.