Mathematical modelling of a mediaeval battle: the Battle of Agincourt, 1415
By Richard R. Clements and Roger L. Hughes
Mathematics and Computers in Simulation, Vol. 64 (2004)
Abstract: Recent developments in our ability to model mathematically the motion of crowds have led to some rather unusual applications. Here a continuum theory is used to model the Battle of Agincourt, a mediaeval battle between an English army on the one side and a combined French and Burgundian army on the other. The calculation reported here predicts that an instability of the front between the opposing armies would have developed. Such an instability is consistent with the mounds of fallen reported in the chronicles of the time but is surprisingly at variance with modern descriptions, which describe the fallen as forming a straight ‘wall’ running the length of the battleﬁeld. Interestingly, the study suggests that the battle was lost by the greater army, because of its excessive zeal for combat leading to sections of it pushing through the ranks of the weaker army only to be surrounded and isolated.
Introduction: There have been dramatic changes in the way in which the motion of a crowd is modelled in recent years. No longer is the motion of a crowd modelled as a continuum by the Navier–Stokes equations of fluid mechanics or as a collection of individuals by the equations of particle-dynamics. Equations of motion have been speciﬁcally developed for the purpose from general ‘rules’ of behaviour in psychological and sociological studies.
The present study aims at using a modern continuum theory that includes contact between individuals, to model the mediaeval Battle of Agincourt in 1415 at the start of the second stage of the Hundred Year War between England and France when the idea of nationalism was young. A well-documented mediaeval battle such as Agincourt is well suited to a study of the present form. Its details are neither highly obscured by history such as the battles in the Roman era, nor by smoke and complexity such as in the Napoleonic era. It is not complicated by the vastness of its scale as are the battles of the First and Second World Wars, nor the intricacies of individual behaviour in guerrilla warfare. A good general account of the Battle of Agincourt may be found in. The model developed here is extremely simple but, as will be shown, it has a predictive capacity that is capable of clarifying historical accounts.