Calculus in Warfare
Calculus in Warfare
Introduction
Throughout the all of human history, one aspect truly stands out as definitive of human political interaction: war. From the story of Abraham militantly freeing his nephew Lot from the hands of a coalition of Mesopotamian kings to modern nuclear war threats between North Korea and the West, war has ever been one of the defining characteristics of human society and government. Furthermore, each society has specific ideas about war and how to effectively strategize so as to gain the greatest advantage. Recently though, a new system has arisen that has challenged traditional military thought. With the advancement of mathematics through these past few hundred years, some have propounded the theory that warfare and combat situations can be effectively modeled using calculus analytical techniques. While many different models and methods for various combat situations have been created, they are nevertheless extremely useful for more closely analyzing military strategy and creating more efficient methods to engage in warfare.
Lanchester Model
In the early 20th century, a man named Frederick W. Lanchester was engaged in a great deal of study in various kinds of mechanical engineering, especially aeronautical engineering. During his intensive study, he became convinced of the massive importance that aeronautics could play in modern warfare. In his book entitled Aircraft in Warfare: the Dawn of the Fourth Arm, Lanchester argued extensively for a military emphasis on aircraft and introduced his famous equations for modeling basic modern combat situations, which have since become known as the “Lanchester Power Equations” (“Frederick W. Lanchester?”). These equations serve as the basis for virtually every other calculus-based combat model created. Essentially, they state that the rate at which a force decrease per time can be approximated using the enemy force size and a constant expressing the fighting effectiveness of that
Introduction
Throughout the all of human history, one aspect truly stands out as definitive of human political interaction: war. From the story of Abraham militantly freeing his nephew Lot from the hands of a coalition of Mesopotamian kings to modern nuclear war threats between North Korea and the West, war has ever been one of the defining characteristics of human society and government. Furthermore, each society has specific ideas about war and how to effectively strategize so as to gain the greatest advantage. Recently though, a new system has arisen that has challenged traditional military thought. With the advancement of mathematics through these past few hundred years, some have propounded the theory that warfare and combat situations can be effectively modeled using calculus analytical techniques. While many different models and methods for various combat situations have been created, they are nevertheless extremely useful for more closely analyzing military strategy and creating more efficient methods to engage in warfare.
Lanchester Model
In the early 20th century, a man named Frederick W. Lanchester was engaged in a great deal of study in various kinds of mechanical engineering, especially aeronautical engineering. During his intensive study, he became convinced of the massive importance that aeronautics could play in modern warfare. In his book entitled Aircraft in Warfare: the Dawn of the Fourth Arm, Lanchester argued extensively for a military emphasis on aircraft and introduced his famous equations for modeling basic modern combat situations, which have since become known as the “Lanchester Power Equations” (“Frederick W. Lanchester?”). These equations serve as the basis for virtually every other calculus-based combat model created. Essentially, they state that the rate at which a force decrease per time can be approximated using the enemy force size and a constant expressing the fighting effectiveness of that
Cited: "Combat Models Extension: Guerrilla Warfare." Ncssm.edu. North Carolina School of Science and Mathematics, n.d. Web. 27 May 2013. . Czarnecki, Joseph. "’N-Squared Law’: An Examination of One of the Mathematical Theories behind the Dreadnought Battleship." NavWeaps.com. The Naval Technical Board, 17 Oct. 2010. Web. 20 June 2012. . Davis, Paul K. Aggregation, Disaggregation, and the 3:1 Rule in Ground Combat. Santa Monica: RAND Publications, 1995. Print. Hlywa, Ed. Salvo Model for Anti-Surface Warfare Study. WeaponsAnalysis.com. Weapons Analysis LLC, n.d. Web. 20 June 2013. . Lanchester, F. W. Aircraft in Warfare, the Dawn of the Fourth Arm,. London: Constable and Limited, 1916. Print. McGunnigle, John, Jr. An Exploratory Analysis in the Military Value of Information and Force. Thesis. Naval Postgraduate School, 1999. N.p.: n.p., n.d. Print. "The Battle of Trafalgar: A Stochastic Approach." Ncssm.edu. North Carolina School of Science and Mathematics, n.d. Web. 27 May 2013. . "Who Was Frederick W. Lanchester?" Informs.org. The Institute for Operations Research and the Management Sciences, n.d. Web. 22 June 2013. .