A Determination of the Wave Forms and Laws of Propagation and Dissipation of Ballistic Shock Waves

Abstract

Experiments to ascertain the wave forms and laws of propagation and dissipation of ballistic shock waves to large distances (80 yards) from the bullet trajectory are described. Calibers 0.30, 0.50, 20 mm, and 40 mm were studied. In every case an N-shaped wave profile was observed consisting of a sudden rise in pressure, the "head discontinuity," followed by an approximately linear decline to a pressure about equally far below atmospheric and then a second sudden return, the "tail discontinuity," to atmospheric pressure. The peak amplitudes of this disturbance are found to diminish about as the inverse • power of the miss-distance (perpendicular distance from the trajectory) while the period T' (measured between the discontinuous fronts) increases about as the ¬ power of the miss-distance for calibers 0.30, 0.50, and 20 mm. For 40-mm shells the amplitude decays a little faster, about as the inverse 0.9 power of miss-distance over the range studied. A theory taking account of the dissipation of the N-wave energy into heat is developed to explain the observed behavior. A method of measuring absolute N-wave amplitudes by observing the rate of change of period T' with propagation is described. The theory leads to an absolute relationship at large distances between distance, amplitude, and period in which no arbitrary constants appear. Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 131.215.225.9 On:

A Study of the Infrasonic Wave in the Atmosphere

“…As a shock wave propagates to higher altitudes, the increasing non-linear effect will cause the stretching of the wave and hence the lowering of frequency (Dumond et al 1946;Kinney, 1962). Such effect on the thermospheric waves has been clearly observed in the infrasonic signals from the Alaskan volcanoes (Wilson et al 1966;Wilson and Forbes, 1969), as well as from the supersonic flight of Concorde (Balachandran et al 1977;Donn, 1978).…”

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“…Friedrichs derived a scalar equation and carried the analysis for it. 1 Although the idea of N -waves was mentioned earlier, [10], Friedrichs computed the decay rate of t −1/2 of the shock and the width t 1/2 of the expansion wave. Here t represents the distance from the airfoil.…”

A Spectral Subtraction Based Algorithm for Real-time Noise Cancellation with Application to Gunshot Acoustics

“…Figure 2b also illustrates how the energy is transferred from the bullet to the shockwave. The average energy decreases as the shockwave propagates due to three main factors [1]: 1) increase in the mean radius x, the distance from the measured shockwave pulse to the bullet trajectory, also known as the miss-distance; 2) increase in the wave-length L; and 3) dissipation into heat. In between the two main shock waves there can also be secondary shockwaves which are commonly referred to as compression and expansion waves.…”

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