  We report on an unpublished and previously unknown manuscript of John von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.
