Applying Lanchester's linear law to model the Ardennes campaign

Abstract

Abstract:In modern warfare, many believe the decisive factor in winning a battle is seizing the right moment to shift from defense to attack, or vice versa. This paper attempts to bring that perspective to Lanchester's differential equations of warfare, and continues the application of Lanchester's linear law to the analysis of the World War II battle of Ardennes, as reported in earlier issues of Naval Research Logistics by Bracken and by Fricker. A new variable, shift time, accounting for the timing of the shift between defense and attack is explicitly included in our version of the model, and it helps obtain improved goodness of fit to historical data.

Approximations and empirics for stochastic war equations

“…The Allied force wages war in a superior manner compared with the German force. This is in agreement with Bracken [1] and Chen and Chu [3], but differs from Dupuy [6], discussed below for tank warfare. It is of interest to assess how the "scatter" or fluctuations in available empirics fare with respect to the standard deviations in the approximations, where we set Cov(N 1t 0 , The high combat effectiveness 1 (t) ϭ 7.655 ϫ 10…”

“…8 With firepower scores and weights 20, 5, 40, 1 for tanks, APCs, artillery, manpower, 9 applying the "least square fit" technique (Appendix B), the optimal combat effectiveness coefficients for the 33-day Campaign are ( 1 (t), 2 (t)) ϭ (5.38 ϫ 10 Ϫ9 , 8.22 ϫ 10 Ϫ9 ). These sizes are of the same order of magnitude as those of Bracken [1], Chen and Chu [3], and Fricker [7]. 10 Simulations (not included due to space constraints) reveal that the fit between the model and the empirics is not equally satisfactory throughout the Campaign.…”

“…8 Std L (N it ) should for exhaustive presentation be added and subtracted from the accumulative expected value ϪE L (N it ), which would require additional graphs believed to be intuitive. 9 The weights are derived from standard U.S. Army Concepts Analysis Agency practices, as utilized by Bracken [1], Chen and Chu [3], Fricker [7]. Fricker [7, p. 16] attaches weight 30 to air power.…”

“…Fourth, demonstrating closure of approximated solutions is more straightforward for linear warfare than for other forms of warfare. 3 Fifth, although the issue is not settled, linear warfare appears often to be descriptive of real warfare.…”