Predictive tests in water

[the Schwartz]

You have clearly put a lot of time into your work in this area. My impression from your writing is that like most people who enjoy math, physics or engineering you probably take the time to find sources, read them in their entirety and understand the author's intent. This helps you evaluate the proper weight which should be placed on data given the underlying methodologies, sample size, etc.

Many of the visitors to this site will arrive at a post in a thread based on a keyword search and will not take the time to read the entire thread in context. For such a user looking to evaluate the different ammunition options at their local Wal-Mart, they may find your very well written post below. They will see an apparently knowledgeable source endorsing the specific round, if they don't read the entire thread and find your separate disclaimer on the Dziemian US Army BRL P[I/H] model they may accept those statistics as authoritative.

This could cause one of your readers to choose ammunition that may not be optimal in their application, for example CCW holders who often walk on or adjacent to streets in some areas may need ammunition which is more likely to provide adequate penetration after penetrating sheet metal or auto glass. Worse yet, your post and their own confirmation bias may cause our user to reinforce unrealistic and potentially fatal expectations about the effects of poorly placed handgun rounds into an attacker's torso or abdominal area.

I am not criticizing your intent, your effort, nor your well written posts, but I would consider omitting the BRL data or adding a very clear disclaimer to your posts on each round in consideration of the lay reader.

Thank you for the thoughtful, and very helpful, post. I am always looking to improve the 'lay' reader's experience with regard to the topic.

One of the reasons that I wrote Quantitative Ammunition Selection in the manner that I did—that is, avoiding technical terminology, or when its use was unavoidable, defining it in easy-to-understand terms—was to provide access to penetration equations to the ordinary average guy (like me) much as the late Stephen Hawking did with his seminal book, A Brief History of Time. Realizing that not everyone can solve partial derivatives or integrate by substitution in their heads, I elected to present the modified Poncelet and THOR power law, in Quantitative Ammunition Selection as closed form equations with step-by-step examples laid out much like those found in mathematics textbooks. I was struck that folks like Ronald Jones (Jones RL. Water Testing .38 Special +P Hollow Points. Wound Ballistics Rev 1997;3(1): 13 - 16) were relegated to relying upon charts instead of using the equations themselves; closed forms make that possible and being able to avail oneself of that ability means that one gains a certain autonomy, not to mention accuracy, by being able to compute results rather than having to depend on someone else to do it for them.

I am sure that I could include a brief disclaimer in each post for the lay audience. Thanks for the suggestion.

The purpose of computing is insight, not numbers. —Richard Hamming

[Ed L]

While I respect Dr. Roberts' opinions tremendously, and on many subjects, I also find the time-frame of terminal ballistic science in the period spanning the 1960s through the late-1990s to be both fascinating and historically noteworthy. Perhaps that is why I am so transfixed by these statistical constructs; they show where we were then, how the mistakes that were made came to be and why they took so long to correct. After all, Santayana, credited with the famous and often paraphrased aphorism, ''Those who cannot remember the past are condemned to repeat it'', was right.

Why forget what went wrong, why it was wrong or that it even existed?

So why include wrong information or predictions or invalid formulas?

Why include predictions of probability of incapacitation that are almost 60 years old and do not reflect real life?

Let's look at the formula you are citing:

P_[I/H] = probability of incapacitation per random munition strike to combatant's torso/abdomen: Assault, 30-second time-frame (US Army BRL P_[I/H] model, Dziemian, 1960)

This is a forumula that is almost 60 years old that has no reflection on actual shootings.

Also, you can't compare a hit to the abdomen with a hit to the heart, which this formula holds as equal. Second, people vary in their own reactions due to a variety of factory such as mindset, physical differences, drugs and other substances, exact placement, etc.

and some of the results of this formula:

Cumulative Binomial Expected Probability of Incapacitation
1st-shot P_[I/H]: 74.93%
2nd-shot P_[I/H]: 93.72%
3rd-shot P_[I/H]: 98.42%

The above has no bearing on reality.

[the Schwartz]

[PNWTO]

I also find the time-frame of terminal ballistic science in the period spanning the 1960s through the late-1990s to be both fascinating and historically noteworthy.

But that testing from decades ago has little relevancy to the much better work that organizations and people like @DocGKR have been doing. Honestly I don't see the point of something like QAS when Doc has done the hard work for us. Even then the suggestion of cultivating a warrior mindset is probably (definitely) the most important.

Finally, trying to predict Probability of Incapacitation is simply silly and not grounded in reality at all.

[the Schwartz]

Ammunition designs―even the 'premium' designs―are not static and unchanging. Manufacturers are constantly altering (sometimes in some not-so-minor ways) those designs. Until testing is conducted, there is no way for the end-user to know how the ammunition will perform unless, of course, one is willing to wait for the manufacturer to do so once a new iteration has been produced. Not everyone has the facilities, or can afford the expense and/or the technical burdens, to conduct testing in calibrated 10% ordnance gelatin. The mathematical models found in Quantitative Ammunition Selection allow end-users to test their ammunition in water (a valid, documented tissue simulant) and make that determination for themselves by removing certain technical obstacles (but not all of them) and the expense of doing so.

[Ed L]

But that testing from decades ago has little relevancy to the much better work that organizations and people like @DocGKR have been doing. Honestly I don't see the point of something like QAS when Doc has done the hard work for us. Even then the suggestion of cultivating a warrior mindset is probably (definitely) the most important.

Finally, trying to predict Probability of Incapacitation is simply silly and not grounded in reality at all.

Exactly. There is nothing wrong with testing them in water and showing the comparative results, even though calibrated gelatin is much better.

However, as PNWTO wrote, trying to predict the Probability of Incapacitation is absurd. Did the person who came up with that theory stand by with a stopwatch and watch hundreds of people shot with various bullets and time the results? There are too many variables among people and shootings to come up with that number. Even if it were true, someone could do a lot of damage in 30 seconds before incapacitation sets in.

I remember in the 1980s and 1990s when gunwriters marshal and Sannow came up with what proved to be bogus one-shot stop numbers that were claiming that certain rounds had a 95% chance of producing a one-shot stop in shootings that they had on record. There were a few issues.

First their records were BS and did not match any of the policy agencies that they attributed them to.

Second, by their own admission, any shootings with more than one shot fired were discarded from their records. This means that they were excluding all failures of one or more shots to shot someone.

But the result was many people were buying ammo based on their bogus figures with the expectation that the ammo would produce a one-shot stop if it someone in the chest an unrealistically large percentage of the times.

[the Schwartz]

Speer .327 Federal Magnum 115-grain Gold Dot JHP (23914)



Expanded Diameter: 0.547 inch
Recovered Weight: 114.2 gr. (99.30% retained weight)
Impact Velocity: 1,381 fps

Test Firearm: Taurus 327 revolver with a 2.50-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H₂O @ ~83° Fahrenheit
Barrier: 2 layers of 8-ounce denim

Q-model
DoP: 14.618 inches
Wound Mass: 1.692 ounces
Wound Volume: 2.814 cubic inches

mTHOR model
DoP: 14.630 inches
Wound Mass: 1.693 ounces
Wound Volume: 2.816 cubic inches

Cumulative Binomial Expected Probability of Incapacitation*
1st-shot P_[I/H]: 75.77%
2nd-shot P_[I/H]: 94.13%
3rd-shot P_[I/H]: 98.58%
ΔE₁₅: -332.300 fpe

*Disclaimer: The yields of the BRL P_[I/H] model (Dziemian et. al., 1960) are included here for those who have an historical interest in them and the way that these models' yields were computed. The yields of the BRL P_[I/H] model included here are not unconditionally and absolutely valid, but presented here simply because I find SDE methods like the BRL P_[I/H] model to be an interesting artifact and an entertaining diversion.

[arcfide]

I think the P(I/H) models have been dealt with adequately in this thread. However, I'd like some specific expert opinion from @DocGKR and anyone else on the specific claim from Schwartz about the correlative validity of the Q-model and mTHOR model on penetration depth.

DocGKR has said in this thread that water is useful for determining maximum expansion characteristics, but that penetration depth in water is different than penetration depth in gel. However, it appears that Schwarz has made a strong claim that the above models enable one to accurately correlate water test results to gel tests. To me this is a big deal. Traditionally, according to prevailing wisdom, water tests have been good for seeing how projectiles might expand, but in most testing, DocGKR's included here, the emphasis is first on penetration depth, and then secondly on expansion, and then only after these two are other considerations such as permanent cavity and time to upset considered. This made water testing fun, but ultimately not particularly useful to "spot check" ammunition on a local basis where full testing cannot be conducted, since there was no way to adequately correct for penetration depth. This made something like Clear Gel a better choice for those who couldn't do full gel testing.

However, if water testing can in fact result in accurately correlated penetration *and* expansion estimates, that's enough correlating data to make it useful as a casual test medium to spot check one's own ammo, as well as simply testing ammo for the fun of it.

To me, that's the whole point here. The P(I/H) stuff is just an amusing tangent, and basically irrelevant. What I want to know Is whether this Q-model and mTHOR model are actually valid predictors, because if they are, that is really neat.

[DocGKR]

Post 42 above, states: "Water is a good simulant to show maximum projectile upset, but penetration is 1.6-2 times deeper than in tissue and stretch effects are not visible."

[the Schwartz]

I think the P(I/H) models have been dealt with adequately in this thread. However, I'd like some specific expert opinion from @DocGKR and anyone else on the specific claim from Schwartz about the correlative validity of the Q-model and mTHOR model on penetration depth.

DocGKR has said in this thread that water is useful for determining maximum expansion characteristics, but that penetration depth in water is different than penetration depth in gel. However, it appears that Schwarz has made a strong claim that the above models enable one to accurately correlate water test results to gel tests. To me this is a big deal. Traditionally, according to prevailing wisdom, water tests have been good for seeing how projectiles might expand, but in most testing, DocGKR's included here, the emphasis is first on penetration depth, and then secondly on expansion, and then only after these two are other considerations such as permanent cavity and time to upset considered. This made water testing fun, but ultimately not particularly useful to "spot check" ammunition on a local basis where full testing cannot be conducted, since there was no way to adequately correct for penetration depth. This made something like Clear Gel a better choice for those who couldn't do full gel testing.

However, if water testing can in fact result in accurately correlated penetration *and* expansion estimates, that's enough correlating data to make it useful as a casual test medium to spot check one's own ammo, as well as simply testing ammo for the fun of it.

To me, that's the whole point here. The P(I/H) stuff is just an amusing tangent, and basically irrelevant. What I want to know Is whether this Q-model and mTHOR model are actually valid predictors, because if they are, that is really neat.

arcfide,

One need go no further than to review any one of the tests conducted in 10% ordnance gelatin posted in this thread to see how any of these models function as valid predictive instruments.

Comparing the manufacturer's gelatin-derived test data in this test, pictured below―



Average Expansion: 0.888 inch
Recovered Slug Weight: 419.8 grains (97.45% retained weight)
Impact Velocity: 1,256.6 fps
Maximum Penetration Depth: 17.75 inches

―to the predicted penetration depths of the Q-model, the mTHOR model, and to MacPherson's penetration model (which is also a modified Poncelet equation), it is easy to see that all of these models correlate well to the gelatin-derived test data. The Q-model prediction is bracketed by MacPherson's 'high' and 'low' predictions due to the way in which he elected to modify the Poncelet equation (which is a topic for another time). I am sure that you will also notice that the Q-model prediction is very close to that of MacPherson's lower predicted value and that the mTHOR model prediction is close to that of MacPherson's higher predicted value. This, too, also results from the way I elected to modify and fit the equations that I used. Neither MacPherson nor I did anything wrong; we just attacked the task from different angles. It is also worth noting that the prediction of maximum penetration depth from water tests has already been carried out in Jones RL. Water Testing .38 Special +P Hollow Points. Wound Ballistics Rev 1997;3(1): 13 - 16, where Jones uses the Poncelet form modified by Duncan MacPherson in Bullet Penetration to predict the maximum penetration depth (see 'Table 3' on page 16 of Wound Ballistics Rev 1997;3(1)) of those .38 Special projectiles that he fired into, and recovered from, water as suggested in Cotey, Jr. G. A Poor Man's Ballistics Lab. Rifle, March - April 1990; 22 (2) and the accompanying article, MacPherson D. The Dynamics of Tissue Simulation. Wound Ballistics Rev 1997;3( 1 ): 21 - 23. This is proven science.

Q-model
DoP: 17.520 inches

mTHOR
DoP: 19.029 inches

MacPherson's penetration model
DoP: 16.784 inches (without MacPherson's correction factor of 2 inches being added to that model's prediction)

or

DoP: 18.784 inches (with MacPherson's correction factor of 2 inches being added to that model's prediction)

Because the mass density, internal sonic velocity and bulk modulus of 10% ordnance gelatin and water are quite close to one another, they also produce the same Bernoulli flow pressure, ρV², which drives bullet expansion in both mediums and agrees with what Dr. Roberts points out here―

Post 42 above, states: "Water is a good simulant to show maximum projectile upset, but penetration is 1.6-2 times deeper than in tissue and stretch effects are not visible."

For example:

If we take a hypothetical JHP moving at 1,250 fps (381 mps) through water and 10% gelatin, we get the following pressure values that drive the expansion of our hypothetical JHP-

For water: Pressure = ½ρ_TV² = ½ x 999.972 kg/m³ x (381 m/s)² = 72,578,467.75 N/m²

For 10% gelatin: Pressure = ½ρ_TV² = ½ x 1,040 kg/m³ x (381 m/s)² = 75,483,270.0 N/m²

Because all of these material variables (that is, the mass densities, internal sonic velocities and bulk moduli; I can provide those values if need be and the Newton-LaPlace formula that describes their relationship to one another) are very nearly identical in both test mediums, then the prediction of a projectile's penetration depth using any of the three models is accomplished by obtaining values for the three regressors (average expanded diameter, initial/retained projectile mass, and impact velocity) and applying them to the modified Poncelet equation or the fitted mTHOR power law to obtain the predicted maximum penetration depth of the test projectile.

Obviously, I cannot, nor do I intend to, share 891 points of data here.

However as it stands right now, for the two model's predictive abilities against the same data (n = 891)―

The ANOVA for the Q-model has the following values:

n = 891
r = 0.940513
r² = 0.884564
95% confidence = ±0.345815 inch
99% confidence = ±0.454477 inch
T-test = 0.999962
F-test = 0.700256

―and―

The ANOVA for the fitted mTHOR power law has the following values:

n = 891
r = 0.948401
r² = 0.899465
95% confidence = ±0.364299 inch
99% confidence = ±0.478770 inch
T-test = 0.875151
F-test = 0.656238

I do continue to amass data over time which, even though it was never my intention, has become sort of a weird never-ending hobby at this point.....and I do realize that this test method may upset certain manufacturers of synthetic tissue simulants since testing in water is essentially 'free' whereas the use of PAGs (Physically Associating Gels), which are typically composed of elastomers plasticized by a paraffinic oil, can become quite expensive in addition to posing their own set of technical challenges due to their significantly lower mass densities.