page_title: Gurney equations
section_title: Effective charge volume for small diameter charges
hierarchical_section_title: Gurney equations / Underlying physics / Effective charge volume for small diameter charges
caption_attribution_description: English: Gurney equations ( ) explosives engineering - effective mass of a thin charge.
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: The basic Gurney equations for flat sheets assume that the sheet of material is large diameter.
  Small explosive charges, where the explosive's diameter is not significantly larger than its thickness, have reduced effectiveness as gas and energy are lost to the sides.
  This loss is empirically modeled as reducing the effective explosive charge mass C to an effective value Ceff which is the volume of explosives contained within a 60° cone with its base on the explosives/flyer boundary.
  Putting a cylindrical tamper around the explosive charge reduces that side loss effectively, as analyzed by Benham.
caption: Effective charge mass for thin charges - a 60° cone
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