page_title: Gurney equations
section_title: Imploding cylinder
hierarchical_section_title: Gurney equations / Equations / Imploding cylinder
caption_attribution_description: English: Gurney equation ( ) diagram of explosives engineering imploding cylinder configuration - inner hollow cylindrical mass M, evenly detonated explosive charge C, and outer tamper N.
context_page_description: The Gurney equations are a set of mathematical formulas used in explosives engineering to relate how fast an explosive will accelerate an adjacent layer of metal or other material when the explosive detonates. This determines how fast fragments are released by military explosives, how quickly shaped charge explosives accelerate their liners inwards, and in other calculations such as explosive welding where explosives force two metal sheets together and bond them.
  The equations were first developed in the 1940s by Ronald Gurney
  and have been expanded on and added to significantly since that time. The original paper by Gurney analyzed the situation of an exploding shell or bomb, a mass of explosives surrounded by a solid shell. Other researchers have extended similar methods of analysis to other geometries. All of the equations derived based on Gurney's methods are collectively called "Gurney equations".
context_section_description: A hollow cylinder of explosive, initiated evenly around its surface, with an outer tamper and inner hollow shell which is then accelerated inwards ("imploded") rather than outwards is described by the following equations.
  Unlike other forms of the Gurney equation, implosion forms (cylindrical and spherical) must take into account the shape of the control volume of the detonating shell of explosives and the distribution of momentum and energy within the detonation product gases.  For cylindrical implosions, the geometry involved is simplified to include the inner and outer radii of the explosive charge, Rᵢ and Rₒ.
  While the imploding cylinder equations are fundamentally similar to the general equation for asymmetrical sandwiches, the geometry involved (volume and area within the explosive's hollow shell, and expanding shell of detonation product gases pushing inwards and out) is more complicated, as the equations demonstrate.
  The constant  was experimentally and analytically determined to be 1.0.
caption: Uniformly initiated cylindrical charge imploding an inner mass - cylinder shell explosive charge of mass C, outer tamper layer of mass N, and inner imploding cylindrical flyer shell of mass M, with inner explosive charge radius Ri and outer charge radius of Ro
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