Math Lesson/ why the 45 ACP is still Big Medicine

To state the obvious arrogantly, the purpose of the martial projectiles is to put a hole in their target.  Of course, as a hunter, soldier for life, and a practitioner in the defensive arts, this is important to me.  I spend a great deal of time trying to understanding the dynamics associated with martial projectiles, and to this end, embarked on this project.

I do not wish to speak about “stopping power” but that well-worn subject has been given new life and a new narrative with the FBI testing that pronounced the 9mm the best option for their federal agents.  In terms of stopping power, people have different views that populate differing beliefs, and that is fine with me.  A shooter should feel justified in carrying whatever one carries- and the shooter ultimately is the primary weapon system.  I have had this in the front of my brain when I have carried a 9mm into harm’s way, and I have done so often.

The thesis of this essay, calls upon the science- the math specifically, to shed some light upon the subject; if there is a difference in how handgun bullets cause critical wounding, and to what extent.  In doing so, we focus on the hole that a handgun bullet makes when it enters whatever it is supposed to, penetrates to the depth that it is going to penetrate- the permanent cavity- and make comparisons afterwards.

The prime of my assumptions is the projectile that causes the largest upset or the largest cavity, in terms of wound volume, would tend to generate the most effectiveness on a hit anywhere other than inside the brain, understanding that the brain is an instant stop regardless of the projectile’s dimension.  This sounds right to me, the more stuff broken means that you have broken….well, more stuff. So the first assumption that I am making is that the larger the wound volume- or the whole of the hole, the better the projectile will “stop.”

To explain more thoroughly- think of a drill bit that is .355 inches, drilled in wood to a depth of 18 inches.  What is the volume of the wood shavings that were displaced as we drilled this hole?  If somehow that drill bit expanded to .5 inch would the volume of material displaced from said hole be larger?  Of course it would.

My first, simple and instantly applicable gradient for an evaluation of this type is expanded diameter of bullet times penetration equals a numerical grade.   Simple, yet relatively unscientific method, and not totally mathematically sound in which to judge capability of the bullet involved, as it is two dimensional and linear.  Its value is to establish a gradient and a useful report card and a method for a basis for comparison that is easily calculated “in the field” ; while purposely edging this gradient towards those bullets that penetrate, which receive preferential treatment using this as a grading system.

As stated, a 45 caliber bullet that penetrates 18 inches generates a value of 810 (45 x 18=810). For the purposes of my evaluation, 810 (or 8.1, or 81) becomes the minimum acceptable standard- knowing that a 45 ACP hardball will penetrate 18 inches, actually more- every time.   Every other bullet of smaller caliber needs to expand to at least .45 inches and penetrate 18 inches to qualify as acceptable(or at least as good as GI hardball)- so this is fair enough basis for comparison.  If the bullet does not penetrate 18 inches, it needs to expand to a value to replicate the wounding potential of 810 to be qualified. Within the sample, the majority of the service grade ammunition did this without issues, regardless of caliber.  Generally stated, modern hollow point ammunition fired from a hand held firearm in 9mm, 357 Magnum, 357 Sig, 40 SW, 10mm Auto and 45 ACP will outperform 45 ACP  GI hardball using this evaluation system.  (38 Special will not.)

Penetration value should be credited no greater than 18, or the evaluation criterion becomes outwardly and irreversibly skewed.  If a bullet penetrated 20 inches, 24 inches, 36 or whatever, it would still only get credit in the formulary for 18, elsewise a 9mm hardball bullet that penetrates 36 inches would outperform every defensive hollow-point on the list.  Realistically, a bullet that does penetrate over 18 inches in fabric coated gelatin, will likely over-penetrate a human body, but this is something that the reader must determine if this impacts his choice, and change his or her tactics accordingly. For the purposes of this essay, 18 represents the optimum.  Adjust accordingly if your research indicates that this is too little, or too much.

If 810 is acceptable, 1200 or better should generate a premium level of performance and consideration- and I have assigned this grade as the more elite of the loadings available.  Again, this was fairly arbitrary- just a chalk line draw on the wall to codify what excellence should look like, report card wise. A fairly small percentage of loads did obtain such a score. To qualify, this bullet would have to penetrate 18 inches and expanded to 67 caliber or so (1206).  Likewise, if it expanded to 75 caliber and penetrated 16 inches (1200)- .8 inch expansion and 15 inches of penetration, 1.00 and penetrated 12 inches- and so on.  Even though the A grades require the bullet to expand, and do so tremendously- the simplified method of evaluation certainly still does emphasize penetration over expansion. This is a rough estimate of volume, and although as I have stated previously it is not precisely correct mathematically; as it is both linear and two dimensional, it’s still not a poor way to measure the potential of a bullet, or consistency from test to test.

The source data available was that data that I was able to find out online, and is widely available thanks to the good folks at Google. The 3 resources provided data for 4 separate tests, for the main testing of the 9, 40, 10, 45- test 1-3 of ballistic gelatin with a layered fabric barrier of some stripe, the final being bare gelatin.  These tests can be found from gelatin tests conducted from Lucky Gunner (test 1), Ammotogo (test 2), and Rangehot (test 3 and 4). For the 38, and 357 mag, a different testing sequence was used.    The Immediate analysis revealed the following based upon the simplified metric or 810 a passing score, and 1200+ being an A grade.

The newer designs for all calibers did the best, especially the Federal HST and the Winchester Ranger.  The Remington Golden Saber did fairly well, but the Federal Hydra Shok did very poorly throughout the calibers, as did the PMC Starfire, and conventional branded standard hollow points of design greater than 15 years old.

In large measure, the larger the caliber, the better the cartridge did on the testing.  While some of the 35 caliber bullets expanded very well- it was clear that they would have to be stressed greatly to do so.  High velocity rounds did not seem to make that much of a difference, and did so only in isolated cases.  Other observations from the calibers tested:

93 loads sampled from the 45 ACP, 100% of them met the 810 standard, with 19% (18 loads) that exceeded the 1200 threshold.

75 loads sampled from the 40 SW,  88% (66) met the standard, and 9%  (7) surpassed it.

113 loads sampled from the 9mm, 75% (85) met the standard, and 3% (4) loads surpassed it. All four loads that exceeded the 1200 standard did so only in one test, and two were just barely over the 810 standard in the others test, two others were below it.  This inconsistency brings some question to the testing protocol or the testing format, materials used, etc- or the 9mm itself.

42 loads from the 10mm, the tale of the tape was 95% (40) met the 810 standard, 16% (7) exceeded 1200.

9 loads from the 357 Sig, all passed, none exceeded. One test from the 357 Sig, provided by Luckygunner.

55 loads from the 38 special, 16% (9) passed the 810 standard, none exceeded. The 38 Special was evaluated using the Lucky Gunner test one as the data from the 2” barrel, test two was the 4 inch barrel, and test 3 was the ammotogo test.

64 loads from the 357 magnum, 75% (48) passed, 1.5% (1) load exceeded. The 357 testing schedule was identical to the 38 Specials.

20 loads from the 380 ACP, none of them came close to the 810 standard. One test from the 380 ACP, provided by Luckygunner.

The best loads from the testing using this scale, are depicted below.

If one is satisfied with the simplified gradient, then they may stop reading here.  I didn’t happen to be, and elected to be more mathematically responsible and correct by attempting to gauge the measure the   volume of the wound, and of course, the greater the volume, presumably the better the bullet would wound. The formula to measure the volume of a cylinder is: Pi x Radius squared (Expansion measurement) x depth in inches (not to exceed 18), gives one cubic inches, or if converted to metric of cubic centimeters.

While the FBI, the rank and file enthusiast, and I- all regard penetration as the primary consideration in respect to wound effectiveness, if we evaluate volume measurement, the results support expansion as being at least on equal terms, if not more important- than penetration.  I think if the optimum depth of expansion is determined to be 18” for grade, as we have here, penetration has certainly been given its full measure of credit despite of this bias.

I had to make two command decisions when I was looking at the expansion dynamic- the first is that I did not give any consideration towards disruption generated from a temporary wound cavity, as it is common perception or misperception that all pistol bullets are moving slowly enough that they do not wound measurably in that way.  I think the fans of the 357 magnum, 357 Sig, and the 10mm automatic may have lost out here in some small degree, as my belief structure tells me that those rounds may be capable of a stretch cavity- but I don’t have anything scientific to prove this. Actually, this belief is generated by policemen, agents, and troopers that have used these rounds, and claim through their experience that something is magical about them, stopping power wise.

The second part that was not considered was the rapidity of expansion from fired caliber to the completely expanded bullet.  If a 40 SW expands to 65 caliber, I have dismissed consideration relative to this expansion as it developed. That is to say, the bullet entered the gel at 40, and by 4 inches of penetration had expanded to 65, so there was a point in this process that this bullet was 41 caliber, 42, 43, all the way to 65, and remained 65 caliber from 4 inches in to 18.  Trying to measure the cavitation when it was 41, 42, 43, etc becomes too complicated for analysis, and assigning a random depth of 4 inches seems less scientific and just arbitrary.  Instead, I am applying that bullet as a 65 caliber bullet for the entire depth of its recorded penetration value, giving greatly expanded bullets a fairly modest edge.   Fair? I don’t know, but figure that it may wash with the temporary wound cavity not being considered either.  If you’d like to factor in that expansion curve, history, whatever- feel free, but I am confident that this control measure still applies the proper amount of scientific rigor.

Ok, back to cavitation volume.  The formula is  -Pi x expansion Radius squared x Depth in inches (not to exceed 18), gives one a volume measurement of inches cubed, or if converted to metric CM3.  The acceptable “floor” load of a 45 caliber bullet penetrating 18 inches, (810) drills a hole that displaces or “crushes” 2.86 cubic inches, or roughly 47cm3 (46.867).

A selected load can be below the 810 pass/fail standard, and still disrupt more than 3 cubic inches of matter if expansion is large enough.  The 10mm Hornady 155 XTP load ( 8 inches of penetration, expanded caliber at 70) is indicative of this, as it failed- miserably- the diameter x depth scale (560)- but did displace more material than GI hardball, and managed a passing grade with the displacement formulary (50.43cm3).

If the floor is 47 cm3, the optimum is assigned as 120 cm3 displaced- slightly less than 3 times the 45 GI hardball standard- and slightly more than four times the displacement of a 9mm GI hardball of 28.3 cm3.  Under the simplified formulary stated earlier( expanded caliber x penetration in inches) , the larger calibers did generally better, and by some margin, although the leaders were not exclusive to one caliber, and all generated some competition. Actually measuring the mathematical cavitation- the mid bores were not competitive.  The best performing 9mm load did not meet the 120 Cm3 standard. Many that reached the mark with the simplified gradient fell from grace as well.  Listed below are the best performers from the testing.

The cavitation for the very first load, the 230 Ranger at 185cm3 of displacement, is exceptional and awesome.  6.6X the 9mm GI ball cavitation, and nearly 4X as much cavitation as the 45 GI hardball. This load did so in 14.5” of penetration.  Understanding that expansion numbers can be difficult to repeat- but this performance in this instance is noteworthy.  Drives higher consideration choice wise as the Ranger Load repeated higher degrees of performance through the different testing.

Likewise with the HST offering.  The consistency cannot be accidental.

All told, I think that larger calibers need to be considered again in contrast with the current 9mm narrative.  Imagine that the bad guy is coming through your door, and you will have the time to put a single- one and only one- handgun bullet center of mass, and you can have in our hand any of the calibers that we have talked about.  Knowing what the larger caliber does in terms of displacement and cavitation, would you intentionally choose the 9mm?