Lanchester models and the battle of Britain

Abstract

Abstract: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 to 30th October 1940 is δB ∼ G 1.2 , δG ∼ G 0.9 , where B and G are RAF Fighter Command and Luftwaffe sortie numbers, and δB and δG are 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 favored the Luftwaffe, whereas the loss-ratio was not significantly dependent on the force ratio.

Refighting Pickett's Charge: Mathematical Modeling of the Civil War Battlefield*

“…For example, Weiss (1966) used them to look for patterns across 64 battles from the American Civil War. Other examples include Iwo Jima (Samz, 1972), Inchon-Seoul (Hartley and Helmbold, 1995), the Ardennes (Hung, Yang, and Deng, 2005), Kursk (Speight, 2011), the Battle of Britain (Johnson and MacKay, 2011), and the air war over North Vietnam (Horwood, MacKay, and Price, 2014). These studies mostly looked at aggregated strengths and casualties rather than those of a single tactical engagement.…”

Fight the power: Lanchester's laws of combat in human evolution

“…5 However, evidence for the Square Law at the level of battle outcomes is scant. Early support (Engel, 1954) was superseded by a more confused later picture, in which land, air and all-arms battle outcomes more typically approximate Linear Law results (among numerous papers see, for example, Fricker, 1998;Johnson and MacKay, 2011;Lucas and Turkes, 2004; a full bibliography is given by Wrigge et al (1995)). The underlying point is that Square Law conditions are not the norm, especially above what Turney-High called the "military horizon" (Turney-High, 1949), where the disadvantaged force can usually work to mitigate the effect.…”

“…Although there are variations in how the models are set up, and in real life there are many complicating factors (Adams & MestertonGibbons, 2003;Johnson & MacKay, 2011;MacKay, 2011), the underlying logic of Lanchester's Laws capture the essence of conflict processes irrespective of species or setting-"elementary principles", as Lanchester called them, "which underlie the whole science and practice of warfare in all its branches" (Lanchester, 1916, p. 39).…”

An integrated network/firepower operation model based on Lanchester equation

“…Therefore, with the development of the equipment for network and electronic attacking, it is necessary to study the simulation and the resource planning methods of the integrated combat of network attack, electronic attack, firepower and other different types of forces, so as to use the resources reasonably [2][3][4][5][6][7][8]. With the arrival of information war, the classical Lanchester equation is difficult to adapt to the modern information war and meet the demand of the war.…”