Hydrostatic Shock - Physics of Ballistic Pressure Waves

Physics of Ballistic Pressure Waves

A number of papers describe the physics of ballistic pressure waves created when a high-speed projectile enters a viscous medium. These results show that ballistic impacts produce pressure waves that propagate at close to the speed of sound.

Lee et al. present an analytical model showing that unreflected ballistic pressure waves are well approximated by an exponential decay, which is similar to blast pressure waves. Lee et al. note the importance of the energy transfer:

As would be expected, an accurate estimation of the kinetic energy loss by a projectile is always important in determining the ballistic waves.

— Lee, Longoria, and Wilson

The rigorous calculations of Lee et al. require knowing the drag coefficient and frontal area of the penetrating projectile at every instant of the penetration. Since this is not generally possible with expanding handgun bullets, Courtney and Courtney developed a model for estimating the peak pressure waves of handgun bullets from the impact energy and penetration depth in ballistic gelatin. This model agrees with the more rigorous approach of Lee et al. for projectiles where they can both be applied. For expanding handgun bullets, the peak pressure wave magnitude is proportional to the bullet’s kinetic energy divided by the penetration depth.