Customer Reviews

Aircraft in Warfare: The Dawn of the Fourth Arm

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Personally I was interested only in a particular part of this book, namely Lanchester's battle model. It goes like this. There is a battle between two armies, one with A soldiers and one with B soldiers. Each army has a constant efficiency coefficient (determined by weaponry, training, etc.): a side A soldier takes out a enemies per unit time while a side B soldier takes out b enemies per unit time. The battle is then described by the differential equations dA/dt=-bB and dB/dt=-aA. Dividing the first by the second gives aAda = bBdb, which we integrate to get aA^2-bB^2=constant. (Lanchester avoids mentioning integration and uses a direct infinitesimal argument.) The sign of this constant determines the outcome of the battle, since if, for example, there are side A troops still standing when B reaches zero then the constant must be positive (indeed we see that the number of side A troops surviving the battle can be calculated by setting B=0 and solving for A). Also, the fact that the strength of an army is proportional to the square of its size has an important strategical implication: never divide your forces. For example, assuming equal efficiency a=b=1, an army of 5000 could handle an army of 7000 split into two, 5000^2=4000^2+3000^2, but if the 5000 army faced the full 7000 army at once it would be destroyed after having killed only about 2100 enemies, 7000^2-5000^2=4900^2.

This historical book (1917) documents revolutionary insight for its time into how to make effective use of aircraft in warfare. Although hardware capabilities and operational tactics have changed over the years, many observations about the strategic importance of aircraft are still valid today. The "Lanchester Equations" for battlefield attrition are based on a model that damage between opposing forces occurs primarily along lines of contact rather than in depth, which was representative of warfare when the book was written. Modeling combat using differential equations continues to be an aspect for theater level simulations in modern warfare. The analysis in the book represents a considerable improvement over the prevailing views at the time concerning the limited importance of aircraft in warfare.

This is a reprint of the 1916 book by the inventor of the Lanchester equations. Here Lanchester advances his N-Square Law, which has become what we now refer to as Lanchester Equations. The interest of the book is its historical value, as better presentations are to be found elsewhere. There are other interesting portions of the book beyond the mathematics, such as "aeroplane versus dirigible." The book's value is as a historical record of both the advent of military aviation and military operations research.