Approximate Methods of Estimating Energy Spectra of Line Charges Fired under Water

An approximate method is discussed for estimating the energy spectrum of the shock‐wave pulse from an end‐detonated underwater explosive line charge of any weight and length, and at any angle of emission and range. This method requires only that the following quantities, which can be estimated, be known: (a) the impulse of an equivalent‐weight ”point“ charge at the same range; (b) the shock‐wave pulse‐time parameter; (c) the frequency function for an approximate waveform generated at the emission angle of interest. Calculated results of energy‐per‐unit‐area spectral density for several angles of emission are compared with experimental results for a 40‐g 5‐ft‐long charge at 40‐ft range and for a 2‐lb 10‐ft‐long charge at 80‐ft range. Also described is a method for scaling shock‐wave energy spectra measured for one set of experimental conditions to the spectra for another set of conditions particularly for cases in which quantities (b) and (c) cannot be readily determined. This method is illustrated for complex waveforms resulting from line charges initiated simultaneously at several equally spaced points.