Browsing Brock University Publications & Manuscripts by Subject "Lanchester equations"
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Effects of lethality on naval combat modelsIn the context of both discrete time salvo models and continuous time Lanchester models we examine the effect on naval combat of lethality: that is, the relative balance between the offensive and defensive attributes of the units involved. We define three distinct levels of lethality and describe the distinguishing features of combat for each level. We discuss the implications of these characteristics for naval decision-makers; in particular, we show that the usefulness of the intuitive concept "more is better" varies greatly depending on the lethality level.
Refighting Pickett’s Charge: mathematical modeling of the Civil War battlefieldObjective. We model Pickett’s Charge at the Battle of Gettysburg to see whether the Confederates could have achieved victory by committing more infantry, executing a better barrage, or facing a weaker defense. Methods. Our mathematical modeling is based on Lanchester equations, calibrated using historical army strengths. We weight the Union artillery and infantry two different ways using two sources of data, and so have four versions of the model. Results. The models estimate that a successful Confederate charge would have required at least 1 to 3 additional brigades. An improved artillery barrage would have reduced these needs by about 1 brigade. A weaker Union defense could have allowed the charge to succeed as executed. Conclusions. The Confederates plausibly had enough troops to take the Union position and alter the battle’s outcome, but likely too few to further exploit such a success.