Lanchester models and the Battle of Britain

Ian Johnson, Niall MacKay

Research output: Contribution to journalArticlepeer-review


We fit deterministic generalized Lanchester models to daily sortie and loss data from the Battle of Britain. The best fit for the period 14th August - 30th October 1940 is $Bsim G^1.2,Gsim G^0.9$, where $B$ and $G$ are RAF Fighter Command and Luftwaffe sortie numbers, and $delta B$ and $delta G$ daily loss numbers, respectively. The data naturally divide into two phases, with losses as a proportion of overall sortie numbers much reduced after 15th September. Fits were generally better for the first phase than for the second, and for British losses than for German; in every case the dependence on $G$ is stronger than that on $B$. Days with higher sortie numbers on average favoured the Luftwaffe, while the loss-ratio was not significantly dependent on the force ratio.
Original languageEnglish
Pages (from-to)210-222
Number of pages13
JournalNaval Research Logistics
Issue number3
Early online date16 Dec 2008
Publication statusPublished - 1 Nov 2011

Bibliographical note

This paper is now compulsory reading on the course OA/MV 4655, Joint Combat Modeling, at the US Naval Postgraduate School, Montery, and was the subject of a guest lecture there by NJM in July 2011. The NPS is America's national security research university, with about 2500 students, mostly mid-career officers, on 2-year master's programmes. MOVES, the `Modeling, Virtual Environments and Simulation' institute, teaches `defense modeling and simulation ... in support of all the services and our allies.'


  • Applied Mathematics
  • Lanchaster equations
  • military modeling
  • air power

Cite this