The Gurney Formula: Variations on a Theme by Lagrange
NAVAL ORDNANCE LAB WHITE OAK MD
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The Gurney formula for predicting the velocity of fragments from bombs and artillery shells is shown to be modelled after the interior ballistic problem of Lagrange. Though the model differs significantly from the real situation for the interaction of a detonating charge with the metal case, the resulting simple equation gives a fairly good prediction of mean fragment velocity. It is shown that the accuracy of the prediction can be improved by altering one constant term in the equation. Experimental results on the velocity of fragments and on the velocity of expansion of metal cylinders are analyzed. A new set of Gurney constants is given for the ten most frequently used explosives for both the original formula and the proposed modified form. Precautions which must be taken in defining the Gurney constant and in applying the equation are discussed.