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 3/4 power of the miss‐distance (perpendicular distance from the trajectory) while the period T′ (measured between the discontinuous fronts) increases about as the 1/4 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.