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Testing Self-Defense Ammunition
By Charles Schwartz
April 27^{th}, 2016
Considering how much ammunition has evolved over the last 150 years, the number of different approaches taken to predict accurately what effect a bullet will have when it hits a person (or a game animal) is testament to the tremendous attraction of that objective. After all, if no one was really interested in assessing the terminal effect of bullets, then nobody would bother trying to model it, either physically or mathematically. Instead, explaining and modeling terminal ballistic behavior is arguably the most debated topic in the field of self-defense and ammunition selection and for good reason. We carry and use these tools called firearms that launch a bullet against game animals for food, and as a means of protection against dangerous animals and hostile human beings intent on causing us, and perhaps our loved ones, severe physical injury or death. Relying upon these tools as we do, it is only natural that we should ask, “How well will my chosen self-defense ammunition do its job?”
Setting aside purely anecdotal accounts, we are left with scientific experimentation and collecting and analyzing combat and hunting data for meaningful information that would allow us to predict what a bullet does when it hits an animal or a human being and how effective a bullet is. From these sources, we can then model, and hopefully predict with some degree of reasonable confidence, how a bullet behaves in its terminal phase of flight. Of course, the first attempts to do so were limited by a lack of technical and scientific knowledge. Those who tried to model and predict terminal ballistic performance had to make do with what they had. Some attempts made in the first few decades of the 20^{th} century relied upon battlefield reports as their basis. Others relied upon data taken from shooting various species of livestock. The resulting models, from Hatcher’s RSP (Relative Stopping Power) to the TKO (Taylor Knock Out), and others too numerous to mention here, have been used to evaluate and predict the potential performance of ammunition in both human beings and animals, however they give results that are only relative, very simplistic, numerical rankings of cartridges against one another.
While these models do provide some answers, the answers they provide are not directly comparable to the answers given by other models because the answers lack dimensional definition. For example, one model might give a certain type of projectile a rating of ‘54’ and another model might give another type of projectile a rating of ‘73’. It is truly an example of comparing ‘apples to oranges’ because neither model clarifies what the ratings of ‘54’ or ‘73’ actually mean. Certainly ‘73’ is numerically greater than ‘54’, but ‘73’ and ‘54’ of what? Clearly, the way to eliminate this problem is to use a model that produces its results in real units of measurement so that their performance may be compared against one another. That option now exists.
When I wrote Quantitative Ammunition Selection, I did so seeking to achieve two very important objectives. The first objective was to produce a book written in simple everyday language that an ordinary average guy, just like me, could understand. The second objective was to put within reach of ordinary average guys, a technically valid test procedure and a mathematical bullet penetration model that produces answers in real, honest-to-goodness units of measurement like inches, ounces, and feet per second that would do away with the “apples to oranges” conundrum of dimensionally vague modeling. As fate would have it, I ended up with two mathematical models that alleviate that problem.
The first model, found in Chapter 3 of Quantitative Ammunition Selection, is a modified Poncelet penetration equation that uses test data from bullets fired into water to predict how far that same bullet would have penetrated into calibrated 10% ordnance gelatin or soft tissue, how much ordnance gelatin or soft tissue it would have damaged, and if it exits ordnance gelatin or soft tissue, at what speed it would exit. These predictions have the units of measurement of centimeters, grams, and meters per second, respectively. The second, supplementary model, found in Chapter 9, is a radically modified version of the THOR armor penetration algorithm that originated within the US Army’s Ballistic Research Laboratory (BRL) at Aberdeen Proving Grounds in the late 1950s.
Just like the primary quantitative model, the supplementary model produces predictions of a bullet’s performance during the terminal ballistic phase in terms of inches of penetration, ounces of tissue damage, and exit velocities expressed in feet per second. All that is needed to use either model is the test bullet’s impact velocity, its average expanded diameter, and its retained weight after being fired into water. Chapters 4 and 9 provide several step-by-step examples of how to ‘plug’ those values into each of the penetration equations to get results that are not only dimensional, but also directly comparable to one another regardless of the caliber or the bullet being used. Both models, when compared against more than 800 points of independent ordnance gelatin test data, show excellent agreement with that data with correlations of r = +0.94 for the primary quantitative model and r= +0.95 for the supplementary mTHOR model.
Another benefit of such a dimensionally based approach is that its ability to calculate the loss of kinetic energy with respect to instantaneous penetration depth permits the prediction of a bullet’s probability of incapacitation, symbolically defined as P[I/H], per bullet hit to an assailant’s center of mass (COM). This is something that, until this approach became available, was beyond the reach of the ordinary average guy interested in finding out what his self-defense ammunition is really capable of. There are three mathematical incapacitation probability models. The first two BRL incapacitation probability models, one by Dziemian (1960) and the other by Sturdivan and Bruchey (1968), rely upon the incremental kinetic energy expenditure of a projectile from a penetration depth of 1 to 15 centimeters, or ΔE15, which must be obtained using the Q-model. The third BRL incapacitation probability model, by Kokinakis and Sperrazza (1965), relies upon the total kinetic energy of the projectile, referred to as “ballistic dose” in their model, and as such does not require the use of the Q-model to produce an estimate of incapacitation probability. All three incapacitation probability models are correlated against thousands of points of WDMET (Wound Data Munitions Effectiveness Team) wound data collected during the Vietnam War.
Of the three P[I/H] models, the Kokinakis and Sperrazza P[I/H] model has been determined by the US Army BRL to closely match the performance of the “computer man’’ model used in the RII study (Relative Incapacitation Index) conducted in the mid-1980s where computer-generated “shots” were fired against a computer-generated numeric simulation of a human “phantom anatomy”. Of course, these three incapacitation probability models precede by three decades the efforts of two highly controversial, if not noteworthy, individuals who attempted to statistically model the probability of incapacitation using street combat data in 1992. Regardless of what one might think of the way in which Evan Marshall and Edwin Sanow gathered their data and the criteria against which they ranked it, their work attempts to achieve what I consider to be a very noble objective; to provide law enforcement officers and private citizens alike with the ability to determine what ammunition best suits their respective needs based upon its prior performance.
In order to use the mathematical bullet penetration models found in Quantitative Ammunition Selection, all that is needed is the test bullet’s impact velocity, average expanded diameter, and its recovered or final weight after being fired into water. Non-expanding bullets, such as FMJ (full metal jacket) bullets, do not require testing before being analyzed in the models because they (typically) do not change their diameters or weight during the penetration event. Expanding bullets, such as JHP (jacketed hollow point) bullets, must be tested for expansion and weight retention in water before evaluation in the models since they (hopefully) expand shortly after impact and may lose some weight during that process.
By way of example, let’s compare the terminal ballistic performance of two FMJs that are often the basis of heated debate and endless conjecture using both the primary and supplementary bullet penetration models; the .45ACP 230 gr. FMJ at 850 feet per second and the 9mm 115 gr. FMJ at 1,155 feet per second. Some people argue that the .45-caliber 230-grain FMJ is more effective at ending hostilities than the 9mm 115-grain FMJ, while others argue that there is little difference between the two.
As can be seen by the results found in Tables 1 and 2, both the primary and supplementary terminal ballistic models predict very similar maximum penetration depths and wound masses for the 9mm and .45ACP FMJ projectiles:
Table 1
Q-model | Penetration Depth | Wound mass | ΔE15 |
9mm 115 gr. FMJ | 26.19 inches | 1.073 oz. | 171.114 |
.45ACP 230 gr. FMJ | 25.38 inches | 1.681 oz. | 167.180 |
Table 2
mTHOR model | Penetration Depth | Wound mass |
9mm 115 gr. FMJ | 26.61 inches | 1.090 oz. |
.45ACP 230 gr. FMJ | 26.39 inches | 1.748 oz. |
According to Marshall and Sanow, the .45ACP 230 gr. FMJ and the 9mm 115 gr. FMJ have respective “one shot stop” (or OSS) probabilities of incapacitation of 62% and 70%. Using the Q-model to obtain an ΔE15 value for each FMJ for use in the Dziemian incapacitation probability model, the 9mm 115 gr. FMJ has a P[I/H] of 66.02% and the .45ACP 230 gr. FMJ has a P[I/H] of 65.64% lending credence to the position that there is little practical difference between the two.
Of course, these penetration models can also be used to predict the maximum penetration depth, the volume and mass of damaged tissue contained within the permanent wound cavity, and the exit velocity of an expanded JHP bullet from a block of 10% ordnance gelatin or even a part of the human body. For example, a Hornady 9mm 147-grain XTP JHP, loaded over 7.0 grains of Accurate No.7, was fired from a Glock 17 through a barrier composed of four layers of 16-ounce denim and into a series of plastic 1-gallon freezer bags filled with water.
The 147-grain XTP struck the denim test barrier and water test medium at a velocity of 1,047 feet per second, expanded to an average diameter of 0.555 inch, and retained 146.5 grains of its original weight.
Using the water test data in the Q-model and the mTHOR model to predict the test projectile’s equivalent performance in calibrated 10% ordnance gelatin, we can see in Table 3, that both models’ predictions closely agree that the 9mm 147-grain XTP JHP would have performed admirably:
Table 3
Penetration Depth | Wound mass | Wound volume | P[I/H] | |
Q-model | 15.27 inches | 1.82 ounces | 3.026 in³ | 70.47% |
mTHOR model | 14.85 inches | 1.77 ounces | 2.944 in³ |
The Q-model was used to predict the ΔE15 of the test projectile, which came to 227.911 foot·pounds of kinetic energy expended from a depth of 1 to 15 centimeters. Applying this value to the Dziemian equation for estimating the first shot probability of incapacitation (P[I/H]) for this round, we see that there is a 70.47% probability that it will incapacitate a human assailant (within 30 seconds) with a single COM hit. This is a significant improvement over the performance of the 9mm 115-grain FMJ at 1,155 feet per second which has a predicted first shot probability of incapacitation of 66.02%.
So, with a minor investment in terms of easy-to-find items—a few boxes of inexpensive one-gallon freezer bags and some building materials to construct a fixture to hold them in place once they are filled with water for testing—anyone with access to a range can easily answer the most important question of all, “How well will my chosen self-defense ammunition do its job?”
Quantitative Ammunition Selection is available domestically and internationally in hardcover, paperback, and eBook formats and may be purchased at www.quantitativeammunitionselection.com. Just select the appropriate link found on the lower third of the homepage for the format that you want.