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A continuous flow model of infantry behavior, based on conservation ofindividuals and tracking of subunit identity, has been developed in sufficientdetail that it can now be applied to a realistic simulation of a historicalbattle. Pickett's charge during the 1863 Battle of Gettysburg, Pennsylvania inthe U.S. Civil War was chosen as an initial application of the model. Thisscenario is a good test of the current mathematical model because many modernmilitary tactics were employed, in a context where the action took place onfoot or horseback, and the historical map and troop numbers are available.Compared to a discrete agent model, the flow model was found to better capturethe interaction of the forces with the terrain and each other. A brigade-levelsimulation, faithful to the details of the historical events, was performed.The main source of asymmetry in the numbers of casualties was found to be theinability of the Confederate forces to use effective ranged fire while theywere moving. Comparison of simulations with and without terrain effects showedthat they slow the pace of battle and favor the defenders, exposing theattackers to heavy ranged fire for an extended period. A statistical analysisof possible outcomes for an ensemble of 1000 randomized perturbations of thebaseline brigade-level scenario was carried out. Consistent with historicalevents, it was found that only 6 percent of the scenarios resulted in anoutcome that could be considered a Confederate victory.

Continuous Flow Model of a Historical Battle: A Fresh Look at Pickett's charge