Thursday, January 15, 2015

Challenges to the Continuing Evolution of Terminal Ballistic Testing: A Mathematical Solution for Equivalence

Literally pounds of recovered bullets have been labeled and cataloged for model data and future reference.

Early on in my adoption of Clear Ballistics Gel as my ballistics testing media of choice, I realized that it wasn't an exact substitute for 10% ordnance gelatin. On the other hand, it offers the advantages of visibility, re-use, and stability at all temperatures. Since I conduct and publish a large volume of tests and test outside in all types of weather, Clear Ballistics Gel was a good fit for my budget and testing constraints.

I can't thank Charles Schwartz enough for all the time and effort he's invested in me, as well as his model development. He's been great to work with and a wealth of knowledge on both the art and science of terminal ballistics testing.  Working together, Charles and I embarked on a multi-year project to determine if it was possible to create a "conversion factor" to bring the Clear Ballistics test results in line with test results observed in 10% ordnance gelatin.  Charles has graciously submitted the following article to detail the results of our work.

On Friday, November 29th, 2013, Bruce published my first guest blog on the continuing evolution of terminal ballistic testing especially as it relates to alternative test mediums like physically associating gels (PAGs). As that technology continues to mature, significant challenges have arisen, the most important being that of equivalence of PAG test mediums to other terminal ballistic test mediums—namely the present testing standard of calibrated ten percent concentration ordnance gelatin.

Near the end of that article that I wrote:

As illustrated above, one of the benefits of using the QAS model is that it can be used to confirm a test result or, in the case of a test bullet exiting the test medium unexpectedly, to “save” the test by using the available data (impact velocity, retained mass, average expanded diameter) to predict the terminal performance of the otherwise “compromised” test event. Since I wish to substantiate this opinion further than I have in this article, I am extremely interested in conducting a detailed statistical analysis of Clear Ballistics Gel test data in order to determine just how closely the QAS bullet penetration model correlates to actual terminal ballistic behavior in that test medium. I hope to share the results of that analysis later.

Well, that analysis is now complete and I have to say that I am pleasantly surprised and quite pleased with the results. Of course, since I do not conduct terminal ballistic testing using Clear Ballistics Gel, none of this would have ever been possible without Bruce’s diligent testing and evaluation and his meticulous attention to detail.

To begin with, a brief review of the material properties of Clear Ballistics Gel and how they influence terminal ballistic performance is in order. Clear Ballistics Gel is a synthetic gel composed of a paraffinic oil and a blend of elastomers that has a density of 0.850 gram per cubic centimeter. Because the density of Clear Ballistics Gel is somewhat lower than calibrated ten percent ordnance gelatin, it calibrates using a 5.2-grain, 0.177”-caliber BB at 591 ± 13 feet per second, with slightly deeper penetration than what is seen in the biologically-derived ten percent ordnance gelatin so widely accepted and used in the terminal ballistics research community, international militaries, and our major ammunition manufacturers. What this means is that JHP bullets fired into Clear Ballistics Gel tend to expand a little less and produce slightly greater penetration than they would in calibrated ten percent ordnance gelatin. This is because the forces that drive expansion and ultimately dictate how far a bullet will penetrate are primarily dependent upon the dynamic pressure produced upon the bullet’s impact with Clear Ballistics Gel.

Dynamic pressure is a function of the impact velocity of the bullet and the density of the medium being struck and penetrated by the bullet. When used to compare the respective dynamic pressures produced by Clear Ballistic Gel, whose density is 0.850 gram per cubic centimeter, and ten percent ordnance gelatin, whose density is 1.040 gram per cubic centimeter, the equation for dynamic pressure, P = ½ρv2, shows that Clear Ballistic Gel should produce 18 - 20 percent less dynamic pressure than ten percent ordnance gelatin at any given impact velocity. The significance of this is that terminal ballistic test results obtained in Clear Ballistic Gel and calibrated ten percent ordnance gelatin are not directly comparable to one another.


The mathematical model found in Quantitative Ammunition Selection makes it possible to directly compare terminal ballistic test results obtained in Clear Ballistic Gel and calibrated ten percent ordnance gelatin. By setting the QAS model parameters for the ultimate tensile strength, σ, and density, ρ, of calibrated ordnance gelatin, and using the impact velocity, average recovered expanded diameter, and recovered bullet weight of a bullet fired into Clear Ballistic Gel, it is possible to “convert” those results obtained in Clear Ballistic Gel into equivalent penetration depth—and wound mass—as they would have occurred if the bullet had been tested in calibrated ten percent ordnance gelatin. It is also possible, using the QAS model, to predict and confirm projectile penetration depth—and wound mass—in Clear Ballistic Gel by setting the QAS model parameters for the ultimate tensile strength, σ, and density, ρ, to ρ = 0.850 gram per cubic centimeter and σ = 135 Newtons per square centimeter.


There has also been one other recent development. During a consultation that I participated in over the last 13 months, it became necessary for me to develop an equation for my own use that was based upon the exponential structure of an engineering equation that would permit the expedient prediction of projectile penetration in soft tissue surrogates with a high degree of accuracy. That equation, a highly modified and rather abbreviated version of the THOR armor penetration equation used to predict the penetration and retained weight of fragments and low-aspect (L/D < 3) projectiles after striking and perforating various metallic materials, was evaluated against Bruce’s Clear Ballistic Gel test data and found to produce accurate predictive results. Later, I also evaluated the modified THOR equation against the 777 points of calibrated ordnance gelatin test data that I have been continually amassing over the last three years from ten independent, published and unpublished sources, composed of various ammunition manufacturers, laboratories, and law-enforcement agencies. I found, with the addition of the correct exponential variables, that the modified THOR equation cold also produce accurate predictions for bullet penetration in calibrated ten percent ordnance gelatin. As a result of those evaluations, the modified THOR equation is now included in its very own chapter complete with examples, in the latest edition of Quantitative Ammunition Selection.

So, what were the results of the statistical analysis?

Over the last thirteen months, Bruce and I were able to assemble 103 data points taken from Bruce’s tests conducted in Clear Ballistic Gel. Of those 103 data, fourteen had to be discarded due to conditions (bullets that exited test blocks, bullets that tumbled during the penetration event, etc.) that were beyond our control. The remaining 89 data were then used to establish a correlative relationship with each model and to develop the following analytical perspective.

The analysis results for the QAS bullet penetration model and modified THOR equation are found in the table below:


Statistical analysis results for the QAS model in its “conversion” mode for translating test data obtained from Clear Ballistics Gel into their calibrated ten percent ordnance gelatin equivalent (QAS @ σ = 100, ρ = 1.040) are found in the second column of the table, results for the QAS model in its “predictive” mode for Clear Ballistics Gel test data (QAS @ σ = 135, ρ = 0.850) are found in the third column, results for the modified THOR equation used in its “confirmatory/predictive” mode for Clear Ballistics Gel test data are found in the fourth column, and results for the modified THOR equation used in its “confirmatory/predictive” mode for calibrated ten percent ordnance gelatin are found in the fifth column.

Despite the relatively small sample size for the Clear Ballistic Gel data, I am pleased by the outcome of this analysis. While I would like to have had at least one thousand test data against which to compare each model, practicality dictates that a sample population of that size would take a tremendous amount of time—not to mention money—to compile. What these results tell me is that the QAS bullet penetration model and the modified THOR equation can be used with high confidence in both the conversion of Clear Ballistic Gel results to equivalent yields in calibrated ordnance gelatin and in their respective “confirmatory/predictive” modes for both terminal ballistic test mediums.

So, in spite of the challenges to the continuing evolution of PAGs, there is an answer to the issue of incomparability of terminal ballistic test mediums—mathematical modeling.

As always, 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 ‘Home’ page for the format that you want.

—Charles Schwartz
  

4 comments:

  1. Great article - Thanks I also highly recommend Quantitative Ammunition Selection

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  2. For those of us who are math challenged, is there a simple table or cheat cheat or a working % to show the differences in testing in these two mediums?

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    Replies
    1. I'll ask Charles to reply to this question.

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  3. Anonymous,

    Generally speaking, bullet expansion in Clear Ballistics Gel is about 90-95 percent of that seen in calibrated 10% ordnance gelatin. Bullet penetration in Clear Ballistics Gel is about 5-10% greater than that seen in calibrated 10% ordnance gelatin. Recognizing that bullet penetration in either test medium is dictated by a complex balance of bullet weight and expansion, impact velocity, and the physical properties of the respective mediums, Bruce and I collaborated for over a year in order to ascertain the most valid procedure for converting penetration test data obtained from Clear Ballistics gel into a calibrated 10% ordnance gelatin “equivalent”.

    Unfortunately, there is no simple percentage or conversion table that can be used to convert penetration test data obtained in Clear Ballistics Gel into equivalent penetration in calibrated 10% ordnance gelatin. The only way to make such a conversion is through the use of the two mathematical models evaluated in this article.

    Kindest regards,

    Charles Schwartz

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