Article ID: CBB663989105

An unpublished manuscript of John von Neumann on shock waves in boostered detonations: historical context and mathematical analysis (2021)


We report on an unpublished and previously unknown manuscript of John von Neumann and contextualize it within the development of the theory of shock waves and detonations during the nineteenth and twentieth centuries. Von Neumann studies bombs comprising a primary explosive charge along with explosive booster material. His goal is to calculate the minimal amount of booster needed to create a sustainable detonation, presumably because booster material is often more expensive and more volatile. In service of this goal, he formulates and analyzes a partial differential equation-based model describing a moving shock wave at the interface of detonated and undetonated material. We provide a complete transcription of von Neumann’s work and give our own accompanying explanations and analyses, including the correction of two small errors in his calculations. Today, detonations are typically modeled using a combination of experimental results and numerical simulations particular to the shape and materials of the explosive, as the complex three dimensional dynamics of detonations are analytically intractable. Although von Neumann’s manuscript will not revolutionize our modern understanding of detonations, the document is a valuable historical record of the state of hydrodynamics research during and after World War II.

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Authors & Contributors
Galison, Peter Louis
Aspray, William F.
Fortun, Michael A.
Hales, Peter Bacon
Easlea, Brian
Mackensie, Donald
Endeavour: Review of the Progress of Science
Journal of the History of Dentistry
Acta Historiae Rerum Naturalium necnon Technicarum
Historiographia Linguistica: International Journal for the History of the Language Sciences
Public Interest Report
Gender and History
Steerforth Press
Duke University Press
Science and war; science and the military
World War II
Operations research
Military technology
Von Neumann, John
Groves, Leslie R.
Stouffer, Samuel Andrew
Goudsmit, Samuel Abraham
Kármán, Theodor von
Szilard, Leo
Time Periods
20th century
20th century, early
United States
Great Britain
United States Marine Corps
Great Britain. Royal Air Force

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