I think Mr Courtney, IIRC, is currently studying this very subject matter at MIT. I think he's well qualified to do so, maybe one of the most qualified. If I'm wrong about him studying at MIT, my apologies. But that school turns out the best muscle brains in the world and I've read some of his threads. He knows his subject matter on ballistics better than nearly any other poster I've read on THR. He is certainly more scientific than any gun rag analysis of anything I've read.
BTW folks - charts without axis labels drops your grade by one point, B's for everyone.
jeepmor
My PhD is in Physics from MIT. I am currently a Physics Professor and Director of the Forensic Science Program at Western Carolina University. My research is conducted as a part of the Ballistics Testing Group. I hope to have a web site functional through the university by the end of the fall semester.
However, qualifications alone do not guarantee perfect understanding of the literature. I may well have misunderstood or misrepresented the work I cited. It is not uncommon for a scientist to misunderstand the work of another. I've made a private request of the author for clarification.
Looking back at my citation, I realize that there is ambiguity regarding what part of the assertions are contained explicitly in the reference, and what part of the assertions are ideas from our research group. Let me clarify.
Nice correlation, but there is room for improvement. The pressure wave does indeed cause wounding beyond the expanded bullet diameter early in the wound channel. This contributes to what Peters calls "prompt damage." See
Peters "A Mathematical-Physical Model of Wound Ballistics". J. Trauma
(China) 6 (Suppl): 303, 1990.
However, at some point in the penetration as the bullet transfers energy more slowly, the pressure wave decreases below the damage threshold of the tissue, and the direct crush mechanism dominates. I believe that an even more accurate correlation is possible by modeling the wound volume as a combination of these two effects. The non-trivial part is understanding the transition from the depths dominated by pressure wave contributions to wound volume to the depths dominated by the direct crush mechanism.
The main reason for the citation is the definition of prompt damage as "Compression, shearing, and stretching of tissue in the immediate vicinity of the projectile." "This damage occurs . . . typically on the order of 10 microseconds" which is much faster than formation of the full temporary cavity.
My assertion that "The pressure wave does indeed cause wounding beyond the expanded bullet diameter early in the wound channel." is the result of our work and is not asserted directly in the referenced article. However, I believe it can be reasonably inferred from Equation 7 on page 311.
This equation says that the cross sectional area of the prompt damage is proportional to the retarding force (dE/dx) and inversely proportional to the rupture modulus. Since there is nothing in the equation limiting the cross sectional area of the prompt damage to the cross sectional area of the bullet, it is easy to see that there must be some combination of retarding force, drag coefficient, and velocity for which the cross sectional area of the prompt damage exceeds the cross sectional area of the bullet.
This action at a distance (damage without direct crush) is conveyed by the outward propagating pressure disturbance which we call the pressure wave, which is also proportional to the retarding force, (dE/dx), as described in my earlier post, _The Physics of the Ballistic Pressure Wave_.
Lets throw some sample numbers to give a concrete example. The damage threshold for tissue can be expressed in PSI, and one number in the literature is around 600 PSI. However, we know that this can vary depending on the strain rate, so let's be conservative and double our damage threshold to 1200 PSI. To make the numbers easy consider a projectile which has a maximum rate of energy loss of 100 ft-lbs in 1 inch of penetration. This results in an instantaneous retarding force of 1200 pounds. Consequently, the expected cross sectional area of prompt damage at this point is 1 square inch. If the hole has a circular cross section, then the diameter of the local prompt damage is 1.13", which is considerably larger than the tissue that could be directly crushed by most bullets.
The assertions of the last paragraph which begins,
However, at some point in the penetration as the bullet transfers energy more slowly, the pressure wave decreases below the damage threshold of the tissue, and the direct crush mechanism dominates.
are my own and I do not believe are explicitly stated in the reference.
There is also some important discussion on page 314 of the reference demonstrating the basis for concluding that the wounding under consideration is "prompt damage" rather than the result of temporary cavitation.
Michael Courtney