Predictive tests in water

[the Schwartz]

Upon seeing some of the tests performed and posted by other PF members, I hope that I can contribute something of value just as they have.

One of the more recent tests that I have run is posted below.

Winchester Bonded 9mm 147 gr. PDX1 JHP (S9MMPDB1)

Diameter: 0.5787 inch
Weight: 146.9 gr. (99.93% retained)
Velocity: 1,006 fps

Test Firearm: unmodified Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (~10 feet)
Test Barrier: 4 layers of 1-ounce cotton T-shirt fabric

29079

29080

Analysis:

Q-model
DoP: 13.710 inches
Wound Mass: 1.776 ounces
Wound Volume: 2.954 cubic inches

mTHOR
DoP: 13.300 inches
Wound Mass: 1.723 ounces
Wound Volume: 2.866 cubic inches

Probability of Incapacitation:
1st-shot P[I/H]: 69.95%
2nd-shot P[I/H]: 90.97%
3rd-shot P[I/H]: 97.29%
ΔE15 : -220.161 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
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)
ΔE15 = Amount of kinetic energy (in fpe) expended by the bullet from a penetration depth of 1 through 15 centimeters

The Winchester PDX1 bonded JHP design is the commercially-available version of the Winchester Ranger Bonded law enforcement product line.

In fact the Winchester Ranger Bonded test data found here-

http://winchesterle.com/SiteCollectionDocuments/pdf/Handgun%20Bullet%20Barrier%20Testing%20Protocol_20 16.pdf

-duplicates quite closely the water-test performance of the ammunition recorded in this test closely matching the terminal expansion of the Winchester Ranger Bonded 147-grain JHP with an average expanded diameter of 0.585" at 995 feet per second (with 100% weight retention) yielding a penetration depth of 14.10 inches and an average 1.75 ounces of wound mass. With a 1st-shot P[I/H] of 69.95%, the Winchester 9mm 147-grain PDX1 JHP is an excellent example of a well thought-out JHP design.

[TiroFijo]

Is there an accurate formula for estimating penetration and expanded diameter in gel vs water?

Does barrier performance with water traslates to gel?

I find the predicted % of incapacitation amusing, and the energy deposited in the first 15 cm anecdotal...

[Odin Bravo One]

Good to know how my bullets should perform if attacked by a bucket of water!!

[the Schwartz]

Is there an accurate formula for estimating penetration and expanded diameter in gel vs water?

Modifying the constants in the Poncelet equation, which assumes that the inertial pressure is a constant, times the Bernoulli flow pressure, ρV2, or alternatively, modifying the Recht equation appropriately, which assigns less intuitive representations of the three components of resisting force (those being inertial pressure which is a function of the wave velocity, U, mass density, ρ, and the speed of the projectile/target interface Vi), are both viable mathematical models. Duncan MacPherson elected to modify the Poncelet constants as he did, and preferring the Poncelet form over the Recht form myself, I also modified those constants albeit in a somewhat different manner. The Poncelet equation is quasi-empirical in that these constants must be determined experimentally and it assumes that the effect of surface friction upon the motion of the projectile is negligible, approximately 3%, as suggested by: Krafft JM. Surface Friction in Ballistic Penetration. J Appl Phys 1955; 26: 1248-1253. My preference for the Poncelet form comes from the fact that the Recht form, besides its tendency to slightly over-predict depth of penetration, is not tunable, within the statistical experimental design that I employed.

Furthermore, the late (and very much missed) Dr. Martin L. Fackler M.D., for whom the 'Fackler Box' is named, makes the unqualified statement that, "Shots into water cause bullets to expand as they do in gelatin or muscle" in his article, ''Simplified Bullet Effect Testing''. (page 21 of the Journal of the International Wound Ballistic Association Wound Ballistics Review, Fall 2001; Volume 5, Number 2)


Does barrier performance with water traslates to gel?

Yes.

Since the test projectile traverses the barrier prior to impinging upon the test medium, why not? When considering the passage of a projectile through clothing (and skin), this model-

https://ndiastorage.blob.core.usgovcloudapi.net/ndia/2005/garm/tuesday/hudgins.pdf

-does not consider ''post-barrier'' effects either. Given Dr. Fackler's position, which matches other research reaching that same conclusion, there is no reason to expect otherwise.

[TiroFijo]

Thanks Schwartz

I'm an engineer and understand and like math models myself, but I still don't think that water would accurately predict bullet behaviour, compared to say 10% gelatin. Sure Fackler said "Shots into water cause bullets to expand as they do in gelatin or muscle", but he didn't say "exactly as much as" or he would not had bothered to father and champion the 10% gelating tests.

[the Schwartz]

Thanks Schwartz

I'm an engineer and understand and like math models myself, but I still don't think that water would accurately predict bullet behaviour, compared to say 10% gelatin. Sure Fackler said "Shots into water cause bullets to expand as they do in gelatin or muscle", but he didn't say "exactly as much as" or he would not had bothered to father and champion the 10% gelating tests.


You're welcome. I understand and do appreciate your skepticism. :)

Besides my work, you might wish to look into MacPherson's book for a more technical explanation of the phenomena in Chapter 5 of Bullet Penetration under the section titled ''Tissue Simulant Requirements''.

Additionally, you might find very interesting, recent research by-

Bresson F., J Ducouret. Experimental study of the expansion dynamic of 9mm Parabellum hollow-point projectiles in ballistic gelatin. Forensic Science International 219 (2012) 113–118

-in which the authors conclude, that, ''the expansion law of the projectile is almost insensitive to small variation of the gelatin weight ratio", which varied from 0% (pure water) as well as 5%, 10% and 20% concentrations by weight.

[Odin Bravo One]

Never mind.

[the Schwartz]

Since TiroFijo asked some really good questions about the predictive ability and accuracy of these models (both here and via email), I think that it seems only fair that I share an example of the test data that I have relied upon in correlating these models to actual terminal performance in calibrated 10% ordnance gelatin with the SDE. I really do welcome and appreciate such healthy skepticism.

During development of these models, I asked John Ervin, of Brassfetcher.com, to conduct some testing for me involving several different brands and configurations of expanding and non-expanding ammunition.

In the gelatin test presented below, the Hornady 9mm 147-grain TAP-CQ XTP JHP was fired into calibrated 10% ordnance gelatin with the following results.


Firearm: 9mm Glock 19, 102mm barrel
Bare Gelatin: Nominal 10% concentration
Block Calibration: 3.10 ± 0.05 inches @ 585 ± 0.50 fps
Block Calibration Temperature: 36.90° ± 0.05 Fahrenheit
Block Core Temperature: 39.50° ± 0.05 Fahrenheit
Test Site Conditions: 66° Fahrenheit @ 44% relative humidity
Time Out of Refrigeration Prior to Shot Impact: 4 minutes
Range: 10 feet

29133
​
Average Expansion: 0.581 inch
Recovered Bullet Length: 0.494±0.0005"
Recovered Bullet Weight: 146.6 gr. (99.73% retained weight)
Impact Velocity: 992 fps
Maximum Penetration Depth: 13.70 ± 0.05 inches
Maximum Cavitation Depth : 10.80 ± 0.05 inches

Entering the average expansion, recovered weight, and the impact velocity from the test above into models gives the predictive yields of the models as seen below.
From this comparison, it can be seen how closely these models can predict/emulate the terminal performance of bullets in 10% gelatin.

Q-model
DoP: 13.436 inches
Wound Mass: 1.754 ounces
Wound Volume: 2.918 cubic inches

mTHOR
DoP: 13.032 inches
Wound Mass: 1.701 ounces
Wound Volume: 2.830 cubic inches

Probability of Incapacitation, 1st-shot and cumulative binomial P[I/H] values
1st-shot P[I/H]: 69.59%
2nd-shot P[I/H]: 90.75%
3rd-shot P[I/H]: 97.19%
ΔE15: -214.987 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire wound channel
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)
ΔE15 = Amount of kinetic energy (in fpe) expended by the bullet from a penetration depth of 1 through 15 centimeters

[HCM]

So you are comparing water to bare gel tests. However people aren’t homogeneous and the tests which most closely simulate what we see with bullets dug out of actual bodies is the four layer denim test. Regardless, bullets sometimes just do weird stuff in the real world.

Even if water does match gel results how much practical application is there ?

[the Schwartz]

So you are comparing water to bare gel tests. However people aren’t homogeneous and the tests which most closely simulate what we see with bullets dug out of actual bodies is the four layer denim test. Regardless, bullets sometimes just do weird stuff in the real world.

I agree. Sometimes bullets do indeed, 'do weird stuff'.

Of course, human beings are not homogeneous isotropic masses of ''stuff'' either, but that is not why gelatin and water are good tissue simulants. The reason that gelatin and water are good tissue simulants is that they are physically equivalent test mediums that duplicate the Bernoulli flow pressure, P = ρTV2, that drives the expansion of JHPs and the resistance (force) that decelerates bullets that occurs when bullets pass through flesh. According to the equation that describes the Bernoulli flow pressure, P = ρTV2, the hydraulic pressure produced at impact is a function of the mass density of the medium, ρT, and the impact velocity (V) of the bullet. Rearranging the Newton-LaPlace formula, C = √(K ÷ ρT), to solve for the mass density, ρT, of 10% gelatin and water, K ÷ C2 = ρT, it is not hard to see that both substances possess nearly identical densities and will therefore produce nearly identical pressures on any bullet that is traversing at the same velocity through either substance. 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 = ρTV2 = 999.972 kg/m3 x (381 m/s)2 = 145,156,935.5 N/m2

For 10% gelatin: Pressure = ρTV2 = 1,040 kg/m3 x (381 m/s)2 = 150,967,440.0 N/m2

-which means that there is a very small difference in Bernoulli flow pressure, 3.8% - 4.0%, produced by either medium upon our hypothetical JHP. With equal Bernoulli flow pressure, we get equal (or darned close to it) expansion.


Even if water does match gel results how much practical application is there ?

Quite a bit. Since the technical burden of maintaining laboratory control of the tissue simulant's properties is eliminated, or largely reduced. Since water produces dynamic forces on transient projectiles that are nearly identical to those produced by calibrated 10% ordnance gelatin, water is an excellent tissue simulant. Water is insensitive to ambient environmental conditions, requires no calibration in order to produce valid test results, and can be used with little difficulty and almost no expense. Ballistic tests conducted in calibrated ordnance gelatin require rigorous environmental control to ensure a valid test outcome. The ease of use and low cost of testing in water make it an attractive option for those individuals seeking a valid, yet cost-effective ballistic test medium.

This reduction in required technical control is why some experimenters are so attracted to the synthetic simulants, like Clear Ballistic Gel. Water, which is much, much less expensive than Clear Ballistic Gel, reproduces Bernoulli flow pressure that is nearly identical to that of 10% ordnance without the cost associated with Clear Ballistic Gel. Unfortunately, synthetic simulants, like Clear Ballistic Gel (ρT = 865 kg/m3), are unsuitable due to the fact that their mass densities, internal sonic velocity and bulk moduli do not match those of water or 10% ordnance gelatin. Once again, the constraints of the Newton-LaPlace formula, C = √(K ÷ ρT), determine the Bernoulli flow pressure, P = ρTV2, produced upon our hypothetical JHP by the test medium. If the mass density differs significantly (in the case of Clear Ballistic Gel, there is a -16.8% difference between CBG and 10% ordnance gelatin) then the test medium will produce dissimilar pressures that drive expansion. CBG, being one such example, demonstrates less expansion and greater penetration and fails BB validation/calibration as claimed by the manufacturer's website as shown in the video below.


https://www.youtube.com/watch?v=5pqPBnSYTIc

[Glenn E. Meyer]

This will be informative for the:

1. Can I shoot my Glock underwater
2. What round for giant squid
3. What should Aquaman carry for EDC as a bug for his trident.

Sorry.

[the Schwartz]

This will be informative for the:

1. Can I shoot my Glock underwater
2. What round for giant squid
3. What should Aquaman carry for EDC as a bug for his trident.

Sorry.

No need to apologize.

I thought it was hilarious!

Especially the point about the giant squid. :cool:

[the Schwartz]

HCM,

I failed to address this part of your post and wanted to confirm that the correlative data pool also contains data points involving various barriers.


So you are comparing water to bare gel tests.

Here is one such example:

Firearm: 9mm Glock 19, 102mm barrel
Barrier: 2 layers of 8-ounce denim
Gelatin: nominal 10% concentration
Block Calibration : 3.20 ± 0.05 inches @ 585 ± 0.50 fps
Block Calibration Temperature : 37.70° ± 0.05 Fahrenheit
Block Core Temperature : 40.10° ± 0.05 Fahrenheit
Test Site Conditions: 68° Fahrenheit @ 46% relative humidity
Time out of refrigeration prior to shot impact: 7 minutes
Range: 10 feet

29160

Average Expansion: 0.535 ± 0.0005 inch
Recovered Bullet Length: 0.526 ± 0.0005" inches
Recovered Bullet Weight: 147.5 ± 0.05 grains
Impact Velocity: 969 fps
Maximum Penetration Depth: 15.40 ± 0.05 inches
Maximum Cavitation Depth : 14.20 ± 0.05 inches

The comparison of the Q-model and mTHOR model's yields (specifically DoP) to the test above shows that these model's predictions are not affected by the presence of barriers.

Q-model
DoP: 15.986 inches
Wound Mass: 1.770 ounces
Wound Volume: 2.944 cubic inches

mTHOR
DoP: 15.198 inches
Wound Mass: 1.682 ounces
Wound Volume: 2.799 cubic inches

Probability of Incapacitation, 1st-shot and cumulative binomial P[I/H] values
1st-shot P[I/H]: 69.67%
2nd-shot P[I/H]: 89.55%
3rd-shot P[I/H]: 96.62%
ΔE15: -189.871 fpe

DoP = maximum equivalent depth of penetration in calibrated 10% ordnance gelatin
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire wound channel
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)
ΔE15 = Amount of kinetic energy (in fpe) expended by the bullet from a penetration depth of 1 through 15 centimeters

[scjbash]

Technical aspects and comparisons to gel aside (I'm unqualified to speak on it), trying to put a number on the probability of incapacitation is ridiculous.

[Unobtanium]

If we compare gel to people, why not water to gel? Water and gel have a whole lot more in common with people.

Gel simulates homogeneous, uninterrupted muscle. What person have you met that you can get 12" of penetration through homogeneous, uninterrupted muscle on without using a Serpa holster?

[the Schwartz]

Technical aspects and comparisons to gel aside (I'm unqualified to speak on it), trying to put a number on the probability of incapacitation is ridiculous.

There are numerous research sources that suggest that such modelling, based upon ΔE15 and P[I/H] (re: Sturdivan, Dziemian, etc.) or a similar concept referred to as ''ballistic dose'' (re: Sperrazza & Kokinakis), is valid.

Hopefully, you'll find the following links that I've attached to be interesting/informative-

http://www.dtic.mil/dtic/tr/fulltext/u2/a240295.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/a526125.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/359774.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/a058947.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/365619.pdf

[PNWTO]

Probability of Incapacitation, 1st-shot and cumulative binomial P[I/H] values
1st-shot P[I/H]: 69.67%
2nd-shot P[I/H]: 89.55%
3rd-shot P[I/H]: 96.62%
ΔE15: -189.871 fpe



DocGKR, care to weigh in?

[the Schwartz]

@DocGKR, care to weigh in?

For the sake of clarity, it should be noted that the logistic equation for determining the probability of incapacitation, P[I/H], being employed was developed Dziemian (1960), US Army Ballistic Research Laboratory at Aberdeen Proving Grounds;

P[I/H] = [1 + e -(-a + b(logΔE15))]-1

where-

a = 3.023
b = 1.651
e ≈ 2.718281828

-and the cumulative binomial distribution probability, ∑P[I/H], equation for successive shots is-

∑P[I/H] = 1 - (1 - P[I/H])n ; P(X > x)

where 'n' is the number of trials, or in this case, successive number of rounds striking a combatant in the torso.

This approach, amongst others, for determining P[I/H] can be found here:

http://www.dtic.mil/dtic/tr/fulltext/u2/a240295.pdf

[Wyoming Shooter]

This is fascinating stuff. Are commercial ammo producers using these models? Best, ELN.


There are numerous research sources that suggest that such modelling, based upon ΔE15 and P[I/H] (re: Sturdivan, Dziemian, etc.) or a similar concept referred to as ''ballistic dose'' (re: Sperrazza & Kokinakis), is valid.

Hopefully, you'll find the following links that I've attached to be interesting/informative-

http://www.dtic.mil/dtic/tr/fulltext/u2/a240295.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/a526125.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/359774.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/a058947.pdf

http://www.dtic.mil/dtic/tr/fulltext/u2/365619.pdf

[the Schwartz]

This is fascinating stuff. Are commercial ammo producers using these models? Best, ELN.

None that I am aware of at this time.

There are only two ways to determine ΔE15.

The first method is to fire a projectile into 10% ordnance gelatin while recording its flight through the test medium using high frame-rate recording to determine the projectile's velocity at the penetration depths of 1 and 15 centimeters. Using those two velocity values, ΔE15 (the rate of dissipation of KE from the penetration depth of 1 through 15 centimeters) can be computed for use in the logistic equation for determining the probability of incapacitation.

The second method is to model the projectile history through the Q-model to determine ΔE15 (the rate of dissipation of KE from the penetration depth of 1 through 15 centimeters) for use in the logistic equation. Of course, this means firing an expanding bullet into water for the purpose of obtaining the necessary test data (expanded average diameter, retained mass, impact velocity) so that the Q-model can be used to compute ΔE15. I should also note that Duncan MacPherson's bullet penetration model (it's also a Poncelet form) can also be used for this purpose with just a little algebraic rearrangement.

For most users, the complications and expense of using calibrated 10% ordnance gelatin are significant and being able to conduct such testing using water without the need of expensive high frame-rate recording equipment simplifies the process. Obviously, there are P-F members, like Tokarev, who do exceptionally good tests in gelatin, but the expense of a suitable high frame-rate camera (the $+100K Phantom comes to mind) is more than most are willing to bear.

[DocGKR]

"Are commercial ammo producers using these models?"

Let's hope they are not relying on the ARL type models, as these have some serious issues.

High speed video has a place, especially with some close range rifle testing, but it is generally NOT needed for most routine handgun, shotgun, and long range rifle testing, as proven by the LAIR, FBI BRF, JSWB-IPT, etc... testing.

[PNWTO]

Is there any data you are using that is GWTO-era?

[the Schwartz]

Let's hope they are not relying on the ARL type models, as these have some serious issues.


Would you be willing to provide a more detailed explanation regarding the issues that the ARL models suffer from?

I would really appreciate your insight on the topic and I am sure that others here would, too.

[Unobtanium]

*popcorn*
This is like Dr. Courtney all over again, but with an open mind, real data, and desire for dialogue. I hope to learn things.

[the Schwartz]

*popcorn*
This is like Dr. Courtney all over again, but with an open mind, real data, and desire for dialogue. I hope to learn things.


So do I. :)

If Doc can enlighten me (and everyone else here) as to the 'how' and the 'why' the BRL P[I/H] models are flawed, I will consider myself that much better off; although being a 'nerd' in the classic sense, all mathematical models, even flawed ones relating to P[I/H], will always fascinate me. I look forward to, and stand ready to, absorb his input.

Just the same, the two bullet penetration models (one based on the Poncelet form and the other upon the modified THOR power law) stand on solid ground (with superior ANOVAs) as they are correlated against nearly 900 data from 14 independent sources.

[Shawn Dodson]

Duncan MacPerson once observed, "Bullshit + mathematics = bullshit."

BRL formulae are overly-complicated bullshit applied to a simple problem.

Soft barrier materials, i.e., fabric, needs to be shored (placed) against the test medium to duplicate the conditions encountered by a penetrating handgun bullet that will produce the cookie-cutter effect to clog the hollowpoint cavity with a fabric plug.

[the Schwartz]

Duncan MacPerson once observed, "Bullshit + mathematics = bullshit."

BRL formulae are overly-complicated bullshit applied to a simple problem.

Soft barrier materials, i.e., fabric, needs to be shored (placed) against the test medium to duplicate the conditions encountered by a penetrating handgun bullet that will produce the cookie-cutter effect to clog the hollowpoint cavity with a fabric plug.

First, in reverse order, re: barrier materials; Yes, that is how I've always done it, materials are shored firmly against the test medium. That's easy enough to do with water cartons and the alternate method of testing with water-filled 1-gallon storage bags lined up in a PVC trough.


BRL formulae are overly-complicated bullshit applied to a simple problem.

And second: OK. How so? I am all ears. Well, I s'pose that it is more like ''I am all eyes'' what with having to read the typed words on my 'puter.

Specifics please.

[the Schwartz]

Another example of some of the independent data used to correlate the ever-so-slightly modified Poncelet form and the mTHOR model:

A one-ounce Brenneke USA Tactical Home Defense® (THD) 12-gauge slug was fired from a Remington 870 12-gauge shotgun into bare calibrated 10% ordnance gelatin which was validated by a .177-caliber BB at a depth of 8.89 centimeters.

The 430.8 gr. Brenneke Tactical Home Defense® (THD) slug (pictured below) struck the gelatin test block at a velocity of 1,256.6 feet per second, expanded to an average diameter of 0.888 inch and penetrated to a maximum depth of 17.75 inches.
The recovered weight of the 12-gauge Brenneke Tactical Home Defense® (THD) slug was 419.8 gr.
No significant fragmentation or loss of mass (a loss of 11 grains or 2.55% is noted) occurred.

29196

Comparing the gelatin-derived test data-

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 predictive yields of the Q-model and mTHOR model, it is easy to see that both models correlate well to the gelatin-derived test data.

Q-model
DoP: 17.520 inches
Wound Mass: 5.343 ounces
Wound Volume: 8.888 cubic inches

mTHOR
DoP: 19.029 inches
Wound Mass: 5.804 ounces
Wound Volume: 9.654 cubic inches

Probability of Incapacitation, 1st-shot and cumulative binomial P[I/H] values
1st-shot P[I/H]: 86.32%
2nd-shot P[I/H]: 98.13%
3rd-shot P[I/H]: 99.74%
ΔE15: -884.539 fpe

DoP = maximum equivalent depth of penetration in calibrated 10% ordnance gelatin
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire wound channel
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)
ΔE15 = Amount of kinetic energy (in fpe) expended by the bullet from a penetration depth of 1 through 15 centimeters

[the Schwartz]

Since so-called 'economy' ammunition appeals to my 'financially responsible' side (and yes, I have often been referred to as being a ''cheap-ass''), occasionally I get the desire to test such inexpensive fodder. Typically, I fire two or three test rounds without a barrier and against various types and weights of clothing so that my test sample is greater than '1'. The test of this ammunition through 'light clothing' will follow this one.

Test #1: Federal .45ACP 230-grain Hi-Shok JHP, standard pressure (C45D)

29203

Diameter: 0.7749 inch
Weight: 216.4 gr. (94.09% retained weight)
Velocity: 877 fps

Test Firearm: unmodified HK USP45 with a 4.41-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~78° Fahrenheit
Barrier: none

Frontal Expansion Face #1:

29199

Rear, test #1:

29200

The average expanded diameter of the Federal .45ACP 230-grain Hi-Shok JHP (C45D) test projectile was obtained by measuring the two maximum and minimum expansion face dimensions across the leading edge of the projectile's expansion face where the flow field separates from the edge of the test projectile. In this first of two tests of the Federal .45ACP 230-grain Hi-Shok JHP (C45D), the two minimum expansion dimensions of the test Federal .45ACP 230-grain Hi-Shok JHP were 0.763'' and 0.7605'' and the two maximum expansion dimensions were 0.790'' and 0.786''. The average expanded diameter was calculated at 0.774875''. Recovered length of this test round was measured as 0.441''. Weight measurements of the recovered test projectile (and its jacket) were obtained using an RCBS Model 505 magnetically-dampened reloading scale.

Predictive Analysis:

Q-model
DoP: 9.545 inches
Wound Mass: 2.217 ounces
Wound Volume: 3.687 cubic inches

mTHOR
DoP: 9.872 inches
Wound Mass: 2.293 ounces
Wound Volume: 3.814 cubic inches

Probability of Incapacitation:
1st-shot P[I/H]: 73.25%
2nd-shot P[I/H]: 92.85%
3rd-shot P[I/H]: 98.09%
ΔE15 : -276.233 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
P[I/H] = probability of incapacitation per random projectile strike to assailant's torso/abdomen: 30-second Assault modality, (Dziemian US Army BRL P[I/H] model)
ΔE15 = amount of kinetic energy, in fpe, expended by the bullet from a penetration depth of 1 through 15 centimeters

With an average predicted maximum penetration depth of 9.709 inches (the average of the Q-model and mTHOR model penetration depth predictions) and a 1st-shot P[I/H] of 73.25%, the Federal .45ACP 230-grain Hi-Shok JHP (C45D) demonstrates relatively shallow predicted penetration. In spite of this deficiency, the Federal .45ACP 230-grain Hi-Shok JHP (C45D) should be relatively effective given its predicted 1st-shot P[I/H] of 73.25%. A "double-tap' with ammunition, which comes as a highly recommended and technically-sound self-defense tactic gives this particular Federal .45ACP 230-grain Hi-Shok JHP (C45D) a 2nd-shot P[I/H] of 92.85%.

***It should also be noted that while the gilding metal jacket did separate from the fully expanded lead core, it was found lying right next to the expanded lead core (about ½ of an inch away) in the test water column meaning that the jacket remained with the lead core throughout the entirety of the penetration event. For that reason, the gilding metal jacket's remaining mass (~22.6 grains) was included in the recovered weight of the Federal .45ACP 230-grain Hi-Shok JHP for the purpose of computing the predictive analysis of this water test.


While I am thinking of the BRL P[I/H] model (e.g.: Dziemian, 1960) and the yields that I have used in prior posts in this thread, I'd also like to take the time to clarify the position that I hold regarding the use and implications of the P[I/H] metric and all of the equations associated with that metric. I am very thick-skinned and I simply do not take myself, or any version of these P[I/H] models, so seriously that I would ever take offense towards anyone expressing their opinion, opposing or in favor of, the use and yields of these P[I/H] models. The P[I/H] models, produced by Sturdivan and Bruchey, Dziemian et. al., and Kokinakis and Sperrazza, are not of my creation and, as a result, I an unable to take offense from view points that find fault or disagree with the implications of these types of P[I/H] models. I include the yields of these P[I/H] models simply because I enjoy such algorithms for what they are in my own very 'nerdy' perspective....a lot of fun: statistical experimental design, analytical mathematics. With this thought, I welcome any well-reasoned opinion on this matter and any other topic.

On the other hand, if anyone questions the bullet penetration models of my own creation, I reserve the right to run around my office, knocking my desk and chair over, pulling out what little hair I have left all while yelling, "No, no, no, no, no!....I am not listening!....no, no, no, no, no!'' :D

[the Schwartz]

OK, as promised, here is the second test of the Federal .45ACP 230-grain Hi-Shok JHP against 'light clothing'...

Test #2: Federal .45ACP 230-grain Hi-Shok JHP, standard pressure (C45D)

29209

Diameter: 0.7889 inch
Weight: 221.8 gr. (96.43% retained weight)
Velocity: 891 fps

Test Firearm: unmodified HK USP45 with a 4.41-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~78° Fahrenheit
Barrier: 4 layers of 1-ounce cotton T-shirt fabric

Frontal Expansion Face #2:

29210

Rear, test #2:

29211

The average expanded diameter of the Federal .45ACP 230-grain Hi-Shok JHP (C45D) the test projectile, which was fired through light clothing in this test, was obtained by measuring the two maximum and two minimum expansion face dimensions across the leading edge of the expansion face where the flow field separates from the edge of the test projectile. In this second of two tests of the Federal .45ACP 230-grain Hi-Shok JHP (C45D), the two minimum expansion dimensions of the second test Federal .45ACP 230-grain Hi-Shok JHP were measured at 0.784'' and 0.786'' and the two maximum expansion dimensions were measured at 0.7875'' and 0.798''. The average expanded diameter was computed at 0.788875''. Recovered length of this test round was measured as 0.404''. Weight measurements of the recovered test projectile were obtained using an RCBS Model 505 magnetically-dampened reloading scale. No evidence of jacket/core separation was observed.

Analysis:

Q-model
DoP: 9.509 inches
Wound Mass: 2.289 ounces
Wound Volume: 3.807 cubic inches

mTHOR
DoP: 9.878 inches
Wound Mass: 2.378 ounces
Wound Volume: 3.955 cubic inches

Probability of Incapacitation:
1st-shot P[I/H]: 74.07%
2nd-shot P[I/H]: 93.28%
3rd-shot P[I/H]: 98.26%
ΔE15 : -292.893 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
P[I/H] = probability of incapacitation per random projectile strike to assailant's torso/abdomen: 30-second Assault modality, (Dziemian US Army BRL P[I/H] model)
ΔE15 = amount of kinetic energy, in fpe, expended by the bullet from a penetration depth of 1 through 15 centimeters

With an average predicted maximum penetration depth of 9.694 inches (the average of the Q-model and mTHOR model penetration depth predictions) and a 1st-shot P[I/H] of 74.07%, the Federal .45ACP 230-grain Hi-Shok JHP (C45D) demonstrates relatively shallow predicted penetration. Even though both test shots suggest the tendency of this JHP design towards shallow penetration depth for this ammunition, I suggest that it should still serve reasonably well in the role of a self-defense round in typically encountered environs.

[the Schwartz]

Winchester USA 9mm 115 gr. JHP (USA9JHP)

Average Recovered Diameter: 0.551 inch
Recovered Weight: 115 gr.
Impact Velocity: 1,172 fps

Test Firearm: unmodified Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~75° Fahrenheit
Barrier: 1 layer of 1.67-ounce (heavy-weight) cotton T-shirt fabric

Frontal Expansion Face:
29242

Predictive Analysis:

Q-model
DoP: 13.174 inches
Wound Mass: 1.547 ounces
Wound Volume: 2.573 cubic inches

mTHOR
DoP: 12.859 inches
Wound Mass: 1.510 ounces
Wound Volume: 2.512 cubic inches

Probability of Incapacitation:
1st shot P[I/H]: 71.51%
2nd shot P[I/H]: 91.88%
3rd shot P[I/H]: 97.69%
ΔE15 : -244.620 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
P[I/H] = probability of incapacitation per random projectile strike to assailant's torso/abdomen: 30-second Assault modality, (Dziemian US Army BRL P[I/H] model)
ΔE15 = amount of kinetic energy, in fpe, expended by the bullet from a penetration depth of 1 through 15 centimeters

I include a test of this Winchester USA 9mm 115 gr. JHP simply because it performs surprisingly well. With an average predicted penetration depth of 13.017 inches, it produces just enough predicted penetration to meet the 12-inch penetration minimum requirement suggested by the F.B.I. test protocol and produces approximately 1.529 ounces (or 43.346 grams) of damaged tissue over that same distance. Although my personal preference does run towards higher sectional density options regardless of the caliber being used, this is an option that I would carry under most conditions without concern. I do have a small supply laid up against 'bad days', which says a lot about what I think of this load.

[the Schwartz]

Winchester USA .45ACP 230-grain JHP (USA45JHP)

Expanded Diameter: 0.735 inch
Recovered Weight: 229.2 gr. (99.65% retained weight)
Impact Velocity: 865 fps

Test Firearm: unmodified HK USP45 with a 4.41-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~75° Fahrenheit
Barrier: 2 layers of 1.67-ounce T-shirt fabric

29279

29280

Predictive Analysis:

Q-model
DoP: 11.269 inches
Wound Mass: 2.355 ounces
Wound Volume: 3.917 cubic inches

mTHOR
DoP: 11.504 inches
Wound Mass: 2.404 ounces
Wound Volume: 3.999 cubic inches

Probability of Incapacitation:
1st-shot P[I/H]: 72.75%
2nd-shot P[I/H]: 92.57%
3rd-shot P[I/H]: 97.98%
ΔE15 : -266.493 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
P[I/H] = probability of incapacitation per random projectile strike to assailant's torso/abdomen: 30-second Assault modality, (Dziemian US Army BRL P[I/H] model)
ΔE15 = amount of kinetic energy, in fpe, expended by the bullet from a penetration depth of 1 through 15 centimeters

The average predicted penetration of 11.387 inches for the Winchester USA .45ACP 230-grain JHP, which used to be part of Winchester's Super-X® ammunition line, is just shy of the F.B.I. test protocol recommended minimum penetration depth of 12 inches. Expanding robustly upon impact to ~1.625x its initial diameter and with terminal penetration approaching 12 inches, this JHP is capable of destroying nearly 2.4 ounces of soft tissue per strike with the entirety of that damage occurring within the typical human body assuming that the expanded Winchester USA .45ACP 230-grain JHP remains within an assailant's body. Weight measurements of the recovered test projectile were obtained using an RCBS Model 505 magnetically-dampened reloading scale. The test projectile's jacket and core remained together throughout the entire penetration event.

[the Schwartz]

While surfing the 'net this afternoon, I stumbled across a Shooting Times article written by Allan Jones in 2011-

http://www.shootingtimes.com/ammo/ammunition_st_crimelabtests_200807/

-that contained a table with a small amount of exit velocity data for .38 Special LRN, LSWC and JHP projectiles after passing through a 15 centimeter-long block of 20% concentration ordnance gelatin.

Since none of the expansion values for the JHPs were included in the article or the table, I was limited to a 'quick-and-dirty' comparison limited to the LRN (2) and LSWC (2) data in order to examine how the Q-model predictions (which are included on the table in red) for the 15-centimeter exit velocities compares with Jones' test data:

29293

I really wish that Jones would have recorded the expansion dimensions for the JHPs and used 10% ordnance gelatin instead of the 20% gelatin, but there is little that I can do about that. Fortunately, the Q-model allows for the use/substitution of the correct material properties (mass density, strength) of 20% gelatin.

For such a small sample (n = 4), the results are encouraging.

[Wayne Dobbs]

While surfing the 'net this afternoon, I stumbled across a Shooting Times article written by Allan Jones in 2011-

http://www.shootingtimes.com/ammo/ammunition_st_crimelabtests_200807/

-that contained a table with a small amount of exit velocity data for .38 Special LRN, LSWC and JHP projectiles after passing through a 15 centimeter-long block of 20% concentration ordnance gelatin.

Since none of the expansion values for the JHPs were included in the article or the table, I was limited to a 'quick-and-dirty' comparison limited to the LRN (2) and LSWC (2) data in order to examine how the Q-model predictions (which are included on the table in red) for the 15-centimeter exit velocities compares with Jones' test data:

29293

I really wish that Jones would have recorded the expansion dimensions for the JHPs and used 10% ordnance gelatin instead of the 20% gelatin, but there is little that I can do about that. Fortunately, the Q-model allows for the use/substitution of the correct material properties (mass density, strength) of 20% gelatin.

For such a small sample (n = 4), the results are encouraging.

I knew Allan Jones when he was at the Dallas County Crime Lab (more properly, the Southwest Institute of Forensic Sciences - SWIFS) and was in frequent contact with him back in the late 70s and the 80s. His research was eye opening for those days and it led to the understanding of how adequate penetration and decent expansion of service ammo was so important. His findings directly contradicted the effectiveness of the lightweight JHPs, finding they didn't penetrate far enough in very common non-frontal shots present in police work. The area provided lots of OIS data to confirm his findings and SWIFS even published a list of recommended loads, much like DocGKR has done for years.

Allan now writes a monthly column in Shooting Times on various ballistic topics that's always a good read.

[Sigfan26]

Winchester USA .45ACP 230-grain JHP (USA45JHP)

Expanded Diameter: 0.735 inch
Recovered Weight: 229.2 gr. (99.65% retained weight)
Impact Velocity: 865 fps

Test Firearm: unmodified HK USP45 with a 4.41-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~75° Fahrenheit
Barrier: 2 layers of 1.67-ounce T-shirt fabric

29279

29280

Predictive Analysis:

Q-model
DoP: 11.269 inches
Wound Mass: 2.355 ounces
Wound Volume: 3.917 cubic inches

mTHOR
DoP: 11.504 inches
Wound Mass: 2.404 ounces
Wound Volume: 3.999 cubic inches

Probability of Incapacitation:
1st-shot P[I/H]: 72.75%
2nd-shot P[I/H]: 92.57%
3rd-shot P[I/H]: 97.98%
ΔE15 : -266.493 fpe

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
P[I/H] = probability of incapacitation per random projectile strike to assailant's torso/abdomen: 30-second Assault modality, (Dziemian US Army BRL P[I/H] model)
ΔE15 = amount of kinetic energy, in fpe, expended by the bullet from a penetration depth of 1 through 15 centimeters

The average predicted penetration of 11.387 inches for the Winchester USA .45ACP 230-grain JHP, which used to be part of Winchester's Super-X[emoji768] ammunition line, is just shy of the F.B.I. test protocol recommended minimum penetration depth of 12 inches. Expanding robustly upon impact to ~1.625x its initial diameter and with terminal penetration approaching 12 inches, this JHP is capable of destroying nearly 2.4 ounces of soft tissue per strike with the entirety of that damage occurring within the typical human body assuming that the expanded Winchester USA .45ACP 230-grain JHP remains within an assailant's body. Weight measurements of the recovered test projectile were obtained using an RCBS Model 505 magnetically-dampened reloading scale. The test projectile's jacket and core remained together throughout the entire penetration event.

Can you post some data on the loads on DocGKR’s list?


Sent from my iPhone using Tapatalk

[the Schwartz]

I knew Allan Jones when he was at the Dallas County Crime Lab (more properly, the Southwest Institute of Forensic Sciences - SWIFS) and was in frequent contact with him back in the late 70s and the 80s. His research was eye opening for those days and it led to the understanding of how adequate penetration and decent expansion of service ammo was so important. His findings directly contradicted the effectiveness of the lightweight JHPs, finding they didn't penetrate far enough in very common non-frontal shots present in police work. The area provided lots of OIS data to confirm his findings and SWIFS even published a list of recommended loads, much like DocGKR has done for years.

Allan now writes a monthly column in Shooting Times on various ballistic topics that's always a good read.

I have read quite a few of Jones' articles (mostly these last few days) and like his work a lot. Seems as if he was tapped into the BRL P[I/H] models, too. In fact, one of his latest articles on dangerous game bullets (March 2017) brought back a memory from early September 2002 when I was on safari in Tanzania for the first time which probably marks the genesis of my obsession with all things 'terminal ballistic'. After downing several trophies (without relying on my PH for any assistance) over the course of my first week on the savanna, we got into a lengthy discussion one evening as we sat by the fire pit about the benefits/advantages of monolithics (my point was that they 'up-calibered' the rifle due to their performance) and I debated that with the ammunition that I was using in my medium rifle (a Winchester 70 'Stainless Classic' chambered in .30-06 and loaded with the then-relatively-new 180-grain FailSafes) that I could bring down a cape buffalo authoritatively and that the bullets, if fired through the length of the animal (head-to-tail or tail-to-head), would pass through and exit even a sizeable dugga boy.

The following morning, as I brought my Winchester 70 'Stainless Classic' chambered in .375 H&H to go out for the second of two cape buffalo, he sent me back to my tent to retrieve my .30-06. I returned with it, confused, and asked why he had had me get my .30-06 knowing full-well that we were going out after buffalo that morning. My PH indicated that he'd obtained permission (I have no idea how he was able to do that) from the conservation enforcement officer accompanying us to use the .30-06 to settle the debate. To make keep a long story as mercifully short as possible, after we made a little wager (though I'll not say for how much) on whether or not the Winchester .30-06 180-grain FailSafes would completely penetrate a cape buffalo lengthwise, with me asserting that they would and my PH insisting that they would not do so, we hit the mopane in the concession area and ultimately we were able to ''engineer'' a shot, at a range of about 75 yards, that allowed me to make the 3 shots necessary to settle it once and for all. Three rounds, all of which found their marks, and about 90 seconds later, the buffalo was down for keeps and we had two 'data points' which proved me wrong (not for the first time I might add!) that allowed us to recover two expanded Winchester .30-06 180-grain FailSafe HPs from the interior wall (ribs) of the ascending ribs behind the buffalo's brisket. I did break out an inexpensive tape measure that I used to measure penetration depth of both rounds and made a note of the penetration depth while the (extremely patient) skinners and trackers went about the business of field dressing and preparing the buffalo for transport back to camp.

Here are a few images taken right afterwards:

29298

29299

29300

The two recovered (expanded) .30-06 180-grain FailSafes lost a significant portion of their noses and measured:

#1
Average Recovered Diameter: 0.405''
Recovered Weight: 149.9 grains (83.28% retained weight)
Estimated Impact Velocity: ~2,550 fps
Actual Penetration Depth: 47.5 ± 0.50 inches

Q-model Penetration Depth Prediction: 49.066 inches

#2
Average Recovered Diameter: 0.407''
Recovered Weight: 148.1 grains (82.28% retained weight)
Estimated Impact Velocity: ~2,550 fps
Actual Penetration Depth: 49.0 ± 0.50 inches

Q-model Penetration Depth Prediction: 47.97 inches

Using the estimated velocity of 2,550 fps for the 75-yard range at which those shots were taken, it is pleasing to see (at least to me) that the Q-model does a good job even beyond its design limitation of 1,650 fps.

Without realizing it then, this-

29301

-is the picture of that same cape buffalo that would eventually adorn the cover of the book.

[the Schwartz]

Can you post some data on the loads on DocGKR’s list?


Sent from my iPhone using Tapatalk



Sure. I have some free time in the next few weeks and should be able to sneak a few tests in.

Since I do not own pistols in .40 S&W I don't have the immediate ability to run water tests in that caliber, but I can run a few test shots in 9mm and .45ACP.

What are you interested in seeing? I'll try to scare up something along the lines of what you wish to see.

[Sigfan26]

Sure. I have some free time in the next few weeks and should be able to sneak a few tests in.

Since I do not own pistols in .40 S&W I don't have the immediate ability to run water tests in that caliber, but I can run a few test shots in 9mm and .45ACP.

What are you interested in seeing? I'll try to scare up something along the lines of what you wish to see.

Any of them, really.

[the Schwartz]

Here is another example of how the Q-model and mTHOR model correlate with not only converting water test data into predicted terminal ballistic performance in 10% ordnance gelatin, but also how they correlate with actual 10% gelatin test data like this:


https://youtu.be/jmQFzw11QxY

Comparing the gelatin-derived test data-

12 Gauge Remington ''Slugger'', 2¾" 1-ounce rifled slug (#20300) vs. 10% gelatin (Brassfetcher)
Expanded Diameter = 1.168 inch
Projectile Mass = 437.5 grains
Impact Velocity = 1,595 fps
Distance to target = 10 feet

Maximum Penetration Depth = 12.50 inches

-to the predictive yields of the Q-model and mTHOR model, it is easy to see how both models correlate to independent gelatin-derived test data.

29321

Q-model
DoP: 11.543 inches
Wound Mass: 6.091 ounces
Wound Volume: 10.131 cubic inches

mTHOR
DoP: 13.676 inches
Wound Mass: 7.216 ounces
Wound Volume: 12.003 cubic inches

Cumulative Probability of Incapacitation, 1st-shot and cumulative binomial P[I/H] values
1st-shot P[I/H]: 91.36%
2nd-shot P[I/H]: 99.25%
3rd-shot P[I/H]: 99.94%
ΔE15: -1,816.617 fpe

DoP = maximum equivalent depth of penetration in calibrated 10% ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire wound channel
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)
ΔE15 = Amount of kinetic energy (in fpe) expended by the bullet from a penetration depth of 1 through 15 centimeters

[DocGKR]

I apologize for the tardy response--with the new Residents starting on 01 July, a high intensity time consuming work effort doing "dentistry" at the hospital 12-18 hours per day the past few months (such as the procedure illustrated below), and a variety of other factors going on which have required close attention to my family, I have had very little free time to devote to outside pursuits.

In the next couple of posts, I will try to offer the ground work for how we have come to the current state in wound ballistic understanding.

Note that the text and commentary in the following posts below remain my intellectual property.

[DocGKR]

WOUND BALLISTIC TEST METHODOLOGY:

KOCHER, LaGARDE, & EARLY MEDICAL RESEARCH:
Since the advent of armed conflict eons ago, combatants have attempted to discover methods to measure wounding effects and find ways to increase the lethality of their weapons. The history of attempting scientifically based wound ballistic research begins with Dr. Theodore Kocher’s work and Dr. LaGarde/COL Thompson’s studies in the late 1800’s, along with those by DeLorme, Bircher, Stevenson, Longmore, and Makins. The efficacy of the concepts elucidated by these early wound ballistic researchers was proven on the far flung battlefields of British colonial campaigns, the Spanish-American War, the Russian-Japanese and Turkish-Balkan conflicts, and during the carnage of World War One. Unfortunately following WWI and for much of the 20th century wound ballistics entered into a metaphorical dark age, where the majority of research was marred by erroneous emphasis on kinetic energy “deposit”, a failure to fully comprehend the physiologic and anatomic effects of temporary stretch in relation to permanent crush during a projectile’s path through tissue, the use of tissue simulants that had no correlation with living tissue, and an over-reliance on flawed computer models.

KE & P(I/H):
Through the 1950’s and 1960’s, U.S. Army estimates of bullet lethality were obtained by firing projectiles into 20% ordnance gelatin, measuring the kinetic energy (KE) deposited in the tissue simulant, and then relating the “deposited” KE to some previously determined empirical relationship between KE and the probability of incapacitation, given a hit P(I/H). The KE theory postulated that the energy deposit measured in the first 15 cm of 20% gelatin correlated linearly with the volume of damage that would be found in 20.5 cm of tissue penetration. This methodology used by Aberdeen Ballistic Research Lab (BRL) and the Biophysics Laboratory of Edgewood Arsenal was completely flawed for numerous reasons, including the fact that kinetic energy is not a wounding mechanism, KE does not reflect anatomic and physiological damage from penetrating projectiles, and the probability of a hit is a training function, not a wound ballistics issue.

RII/COMPUTERMAN:
The Relative Incapacitation Index (RII) developed by the National Institute of Justice Law Enforcement Assistance Administration in 1973, was an attempt to determine which handgun bullets would have the greatest wounding effect and would incapacitate a human most reliably. Using a overly simplistic “computer man” model of human anatomy, RII erroneously assumed that the size of the temporary cavity produced by a given handgun bullet in ordnance gelatin is directly proportional to the wounding effect and incapacitation produced by that bullet in a human. The study recommended lightweight, high velocity bullets with rapid expansion in tissue and frangible, pre-fragmented bullets, such as the Glaser Safety Slug, as producing the greatest wounding effect and most reliable incapacitation in humans. The RII completely ignored the size and depth of the permanent cavity, the tissue which is actually destroyed by the bullet. Since many tissues in the human body are elastic, they absorb the stretch and tissue displacement produced by temporary cavitation with minimal damage.

Lightweight, high velocity handgun bullets which rapidly expand in tissue have decreased penetration depth compared to heavier, slower, less deformed bullets and cannot consistently reach the major organs and blood vessels in the torso, especially from transverse and oblique angles. Frangible handgun bullets designed to fragment on impact, like the Glaser and MagSafe, produce large shallow wounds, have extremely limited tissue penetration depth, and cannot consistently reach the major organs and blood vessels in the torso, especially from transverse and oblique angles. In addition, they cannot defeat commonly encountered intermediate obstacles.

Shallow penetrating, lightweight, high velocity, rapidly expanding bullets and frangible, pre-fragmented bullets were recommended because of the widespread fear of handgun bullet over-penetration, in other words, a bullet which completely passes through the body, exits the other side, and continues on to potentially endanger innocent bystanders. This feared hazard has been greatly exaggerated. The skin on the exit side of the body is tough, resilient, and flexible, and can have the same resistance to bullet passage as four inches (10 cm) of muscle. This often results in bullets ending their path just under the skin at the anticipated exit point rather than over-penetrating as might be expected. In addition, those few bullets which over-penetrate after hitting the target are not any more dangerous to innocent bystanders than the overwhelming majority of bullets fired by law enforcement personnel which miss the intended target all together. According to Special Agent Urey Patrick, formerly Assistant Chief of the FBI Firearms Training Unit:

"Choosing a bullet because of relatively shallow penetration will seriously compromise weapon effectiveness and needlessly endanger the lives of law enforcement officers using it. No law enforcement officer has lost his life because a bullet over-penetrated his adversary, and virtually none has ever been sued for hitting an innocent bystander through an adversary. On the other hand, tragically large numbers of officers have been killed because their bullets did not penetrate deeply enough."

The RII was seriously flawed and its recommendations erroneous. Deeper penetrating bullets have proven to be far superior to shallow penetrating bullets in LE OIS incidents since they have sufficient penetration to consistently reach the major organs and blood vessels in the torso, even from transverse and oblique angles and through intermediate obstacles.

EKE/AKE:
An outgrowth of the earlier KE theory, the Expected Kinetic Energy (EKE) model was developed by the U.S. military in 1975 to assess bullet lethality; in 1977 this new EKE model became the U.S. recommended method for the NATO small arms trials and also established it as the official Army Model. The EKE model estimated P(I/H) by correlating the weighted sum of experimentally determined, incremental kinetic energy deposits in 20% gelatin with existing estimates of P(I/H) from animal experiments. Note--although the notation “P(I/H)” was and is used in the literature, the meaning assigned was expected value of incapacitation given a hit; the preferred modern notation is E(I/H), expected level of incapacitation, in order to avoid the widespread misunderstanding that “P(I/H)” is a probability of incapacitation. EKE was later renamed AKE (ARRADCOM Kinetic Energy) and remains a current Army and NATO standard.

To compute the AKE of a particular projectile, ARL obtained the velocity decay curve by shooting into a 38 cm long block of 20% gelatin. The event is recorded with high seed cameras and the velocity versus distance kinetic energy decay curve is extracted by analyzing the camera footage on a frame by frame basis--this is called “dynamic” gel testing. From this decay curve, ARL can derive the energy deposit function within the gelatin medium. This function is then fed into a complex algorithm to calculate the expected level of incapacitation given a hit, or E (I/H). The AKE method for bullets is based upon summing the incremental kinetic energy lost in the gel block multiplied by the probability the projectile is still in the body at the same depth of penetration in the body component (thorax, abdomen, etc…) being evaluated. These probabilities have been generated for the whole body and for a number of specified major body components. The probabilities were estimated from horizontal shots on a number of shot-lines at different angles around a standing male body. This weighted value, AKE, is then inserted into an empirical correlation to predict a level of incapacitation given a hit. It is important to note that current dynamic testing (AKE and E(I/H)) actually measures the energy lost by the projectile, and NOT the damage done by that energy.

Unfortunately, like its KE predecessor, as well as the RII/COMPUTERMAN, EKE/AKE methodology has numerous flaws, including a continued reliance on kinetic energy deposit as a measure of wounding rather than assessing potential physiologic and anatomic damage potential, an overly simplistic and inaccurate COMPUTERMAN anatomic and physiological model that does not account for different tissue types along a shot-line through the body, an inability for the COMPUTERMAN model to assess shot-lines other than standing and account for intervening body sections, projectiles that in reality have quite distinct terminal performance end up have their reported performance blurred to “just about the same” as all other projectiles when the expected levels of incapacitation are computed using the erroneous COMPUTERMAN model, an overemphasis on temporary stretch effects over permanent crush injuries, an inability to assess the synergistic effects of fragmenting projectiles, and ignoring the requirement that projectiles must have adequate penetration to reach critical anatomic structures deep within the body from any angle and despite intervening objects. AKE also fails to account for projectile total penetration, yaw effects, and bullet fragmentation. Finally, the dynamic AKE method requires expensive test measurement equipment and extensive data reduction and analysis.

LAIR, FACKLER, & IWBA:
A renaissance in wound ballistics began in the 1980’s at the Letterman Army Institute of Research (LAIR) Wound Ballistics Laboratory under the direction of COL Martin Fackler. The researchers at LAIR shot multiple projectile types at varying velocities into 50-100 kg hogs as well as various tissue simulants in order to discover which tissue simulant most closely correlated with living muscle tissue. The final determination was that 10% Type A, 250 bloom Pharmagel (250A ordnance gelatin) at 4 degrees Centigrade was the tissue simulant that most closely correlated with living muscle tissue. Gelatin must have approximately the same density as the tissue it is simulating; both 10% and 20% gelatin can fulfill this requirement, but they do so at different temperatures. However, the traditionally used warmer 20% gelatin was determined to result in overexpansion of projectiles and excessive velocity retardation compared to the cooler 10% gelatin that more accurately replicated the damage pattern seen in living tissue. Other advantages of 10% compared to 20% ordnance gelatin is the decreased cost, simpler fabrication, and easier storage. Rather than relying on high speed motion picture analysis of gel block impacts and calculated KE loss, Dr. Fackler’s research at LAIR measured the actual damage the projectile did to the gelatin block by assessing the radial cracks and fissures in the gelatin--this is referred to as “static” gel testing. Compared to the dynamic method, static testing is extremely cost effective and does not require as much time, equipment, or infrastructure to conduct.

Dr. Fackler’s seminal work emphasized the anatomical and physiological effects of penetrating projectiles and clearly described the primary wounding mechanisms of tissue crush and stretch. His efforts also illuminated the effects of bullet upset--including yaw, fragmentation, and expansion in modifying wounding effects. Dr. Fackler also emphasizing the critical importance of adequate projectile penetration depth to ensure disruption of the major organs and blood vessels in the torso from any angle and through excessive adipose tissue, hypertrophied muscle, or intervening anatomic structures, such as a raised arm. The medical research at LAIR also debunked and decried the frequent overemphasis on kinetic energy, high velocity, occult pressure waves, and faulty computer modeling when attempting to analyze projectile terminal effects in the human body. Obviously, these research results lead to a significant degree of conflict and animosity between the medical researchers at LAIR and the ordnance engineers at Aberdeen, Edgewood, and Picatinny.

Following his retirement from the military in 1991 and the closing of LAIR, Dr. Fackler founded the International Wound Ballistics Association (IWBA) to continue his research and data dissemination; IWBA put out a quarterly journal of research papers for the next decade. Some of the IWBA’s greatest contributions were in correlating lab testing and LE OIS incident forensic data to validate the accuracy of 10% gelatin as a tissue simulant in shots to living human torsos, developing the 4 layer denim test to assess the ability of handgun JHP projectiles to resist plugging with clothing materials and robustly expand, describing the terminal performance variability of the SMK OTM commonly used by LE and military snipers, recommending heavier 5.56 mm projectiles, exposing exotic ammunition vendors making exaggerated, fraudulent claims, as well as arguing for better body armor testing standards than the flawed NIJ methodology.

FBI BRF:
In the wake of the FBI Miami shooting in 1986, the FBI launched an ambitious program to improve the state of LE wound ballistics. The FBI solicited input from individuals in the military, law enforcement, medical, engineering, and forensic communities who were widely respected for their wound ballistic expertise; with this guidance, the FBI Ballistic Research Facility at the FBI Academy in Quantico, VA was established. Round table wound ballistic seminars were held by the FBI in 1987 and 1993. Like the researchers at LAIR, the FBI rejected the flawed “computer man” modeling, calculations based on kinetic energy, and exaggerated temporary stretch effects in favor of an anatomic and physiologic damaged based “static” analysis using 10% ordnance gelatin testing. Most importantly, the FBI BRF quantified adequate penetration depth for duty projectiles as being between 12 and 18 inches and established standardized intermediate barrier testing. In addition, the FBI BRF has documented the advantages gained in transitioning from handgun caliber sub-machine guns to rifle caliber carbines, such as the 5.56 mm M4, for LE entry and patrol use, emphasized the procurement of ammunition capable of defeating intermediate barriers with minimal reduction in terminal effectiveness (i.e. “barrier blind), and designed and implementing the most comprehensive and innovative body armor assessment protocol in existence. The FBI BRF shares their expertise and testing acumen with U.S. military SOF organizations needing mission essential, time-sensitive, accurate, precise, real-world relevant wound ballistic data that is unavailable via the expensive, time consuming, bureaucracy laden conventional military testing establishment. The FBI BRF provides crucial input regarding innovative new munitions developed to meet SOF warfighting needs, especially since the onset of anti-terrorist combat operations in the wake of 9/11/01.

COMPUTERMAN/ORCA:
U.S. Army Research Laboratory’s Survivability Lethality Analysis Directorate’s (ARL/SLAD) Operational Requirement-based Casualty Assessment (ORCA) computer modeling system was initiated in 1992 and has continued to the present. The COMPUTERMAN model of the human body is composed of a large number of horizontal cross-sections in which all tissues (muscles, organs, bones, blood vessels, and nerves) are dimensioned in detail. The limbs can be articulated to some degree (positions that cannot be created include arms or legs crossing in front of the body). Shot-lines through COMPUTERMAN are constrained to be straight lines between entry and exit points. A particular trajectory in the body is computed from the parameters of the fragment; and the determination of the resulting incapacitation is made from the hole size made in the various tissues encountered. COMPUTERMAN makes estimates of level of incapacitation based on the levels of functioning present in the four limbs at specified time intervals after wounding and on their importance to specific missions.

ORCA attempts to be a more comprehensive model for estimating incapacitation from a number of classes of body injury. ORCA does include a far wider range of injury mechanisms, extends the measure of incapacitation beyond the four limbs, and uses a more detailed model of the human body. Unfortunately, ORCA still contains as its ballistic insult subroutine, a refined version of the flawed COMPUTERMAN, because of this, the current ballistic wounding model is the same as COMPUTERMAN. The ORCA model proposes several metrics that attempt to evaluate the impairment caused by injuries to the body, for example, the Weighted Task Average Impairment (WTAI) metric provides the supposed percent reduction of impaired tasks relevant to a specific activity or job. Another metric, the Job Impairment (JI) is used to determine if an average human can successfully perform the totality of tasks that in aggregate constitute a specific job, for example infantry rifleman, vehicle crewman, helicopter pilot, etc... ORCA is compromised by a strong reliance on adaptation of previously flawed COMPUTERMAN models & EKE/AKE methodology, a failure to fully appreciate the infinite variety of stochastic variables inherent in trying to predict the potential incapacitation of a human, and an excessive averaging of measurements leading to loss of data fidelity (with too many fuzzy data points and gross averaging of physiological responses, a hit from a .22LR begins to look similar to a hit from a .338 Lap Mag).

JSWB-IPT:
The U.S. Joint Service Wound Ballistic Integrated Product Team (JSWB-IPT) was founded in 2002 following increasing complaints about the poor performance of issue 5.56 mm ammunition in CQB by U.S. SOF units engaged in OEF (Operation Enduring Freedom) combat operations. Feedback from the field suggested there was a larger performance differential between small-arms systems than predicted by the Army’s standard AKE and ORCA models of terminal performance evaluation; specifically, many combat AAR’s suggested that AKE/ORCA predicted better terminal performance from issued 5.56 mm ammunition than actually occurred in real-world combat engagements. To attempt to sort through these issues, the JSWB-IPT brought together experts from numerous communities, including "military users, law enforcement, trauma surgeons, aero ballisticians, weapon and munitions engineers, and other scientific specialists". Over the next 4 years researchers with the JSWB-IPT made more than 10,000 gelatin test shots at 4-6, 100, and 300 meters using eight calibers in 53 different combinations of cartridges and weapons at a cost of $6 million.

Differences between those organizations using static vs. dynamic methodologies soon became fractious. USSOCOM, NSWC Crane, the USMC, Department of Homeland Security (DHS), the FBI BRF, and almost all other U.S. LE agencies utilized some form of static testing in 10% gelatin. Alternatively, historical Army testing, current ARL testing, the U.S. Secret Service, and much of NATO utilized dynamic test methods in 20% gelatin. Beyond the gelatin mix ratio controversy, ARL took issue with the use of static damage based metrics to evaluate projectile performance and insisted the dynamic method was the only official Army “lethality” model, despite its failure to fully reflect actual combat derived wound ballistic findings. In contrast, military organizations and LE agencies with strong, scientifically based ammunition terminal performance testing programs have conducted reviews of their shooting incidents with much the same results as those originally reported by Gene Wolberg of San Diego PD in the IWBA proceedings--that there is an extremely strong correlation between properly conducted and interpreted 10% ordnance gelatin static laboratory studies and the anatomic and physiological effects of projectiles in actual human shooting incidents. Likewise, the last several years of OCONUS military operations have provided a tremendous amount of combat derived terminal performance information. When the JSWB-IPT analyzed this information in aggregate, the test protocol that was found to most closely correlate with actual shooting results and became the agreed upon JSWB-IPT “standard” evolved from the one first developed by Dr. Fackler at LAIR in the 1980’s, promoted by the IWBA in the 1990’s, and used by most reputable wound ballistic researchers, as noted above--static 10% gel testing.

Somehow in the 6 weeks between 12 April 2006 when the 331 page JSWB-IPT final report draft copy was submitted to U.S. Army higher command levels for review and 23 May 2006 when the JSWB-IPT results were publicly unveiled by the Army, the paper had shrunk to a mere 19 pages, the JSWB-IPT major findings were erased from the document, and the tenor of the report was utterly altered…

Partly in response to the truncated JSWB-IPT results and dissatisfaction with the U.S. Army’s continued use of the flawed ORCA computer modeling, the PM of USMC Infantry Weapons instituted a Phase I ammunition study using FBI BRF testing methodology. The use of the FBI protocols allowed the testing to proceed rapidly and cost efficiently. The Marine Phase I ammunition study dated 11 August 2006, contrasted U.S. military issue 5.56 mm ammunition with FBI 5.56 mm barrier blind ammunition, as well as the 6.5G and 6.8 SPC intermediate calibers. In this testing, the 6.8 mm 115 gr OTM performed best, followed by the FBI 5.56 mm 62 gr bonded JSP and 6.5G 120 gr OTM; none of the military issue 5.56 mm ammunition performed as well, especially when assessing intermediate barrier capability and initial upset depths. This further conformed the results discovered by the JSWB-IPT.

[DocGKR]

TISSUE SIMULANTS:

Currently, a variety of equally important methodologies are used for terminal performance testing, including actual shooting incident reconstruction, forensic evidence analysis, and post-mortem data and/or surgical findings; properly conducted ethical animal test results; and laboratory testing--this includes the use of tissue simulants proven to have correlation with living tissue. All of these areas provide important information. As noted earlier, the tissue simulant that has proven to most closely correlate with living muscle tissue is Type 250A ordnance gelatin at 4 deg C.

Other simulants fail to provide accurate replication of various facets of projectile terminal performance that occur in shots to living human tissue. Cadaver tissue lacks elasticity, tends to be disrupted by pressures that would simply push living tissue aside, and demonstrates exaggerated projectile effects leading to far more extensive damage than that produced in living tissue. Animal testing in cattle uses living tissue, but normal anatomic and physiological differences between individual animals leads to substantial differences in terminal effects; in addition, there are substantial differences in animal anatomy compared to human, animal testing is quite expensive and time consuming, and accurate data collection and comparison is difficult. 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. Inelastic simulants such as clay, duxseal, and soap can provide good estimates of penetration depth and bullet upset, but exaggerate stretch effects from the temporary cavity. Perma-gel and other synthetic polymer simulants can provide a reasonable result for bullet penetration and expansion, but under-represent bullet yaw, fragmentation, and stretch effects. Computer modeling may one day provide the best opportunity to study projectile effects outside the human body, however to date, the current models are overly-simplistic, use too many excessively averaged assumptions of anatomic and physiological factors, and fail to fully and accurately represent the complex dynamics of the interaction between living tissue and penetrating projectiles.

[DocGKR]

LETHALITY & INCAPACITATION vs. TERMINAL EFFECTIVENESS & DAMAGE:

The nebulous term "Lethality" is inappropriate and misleading and should ideally be banned from all discussions of terminal performance. What if an enemy combatant is hit with a projectile and immediately ceases hostile actions, but is not killed? If “Lethality” is the measured and defined metric, then the projectile has failed, because the opponent did not receive a lethal wound, although in actuality the projectile was extremely effective in stopping hostilities. Similarly, if an opponent is fatally shot, but manages to wipe out an entire squad of friendly personnel before succumbing to their wound, the projectile demonstrated 100% “Lethality”, but was utterly ineffective at stopping the enemy from continuing their attack. The phrase "Terminal Effectiveness" is far more accurate and appropriate than “Lethality”, as the death of an enemy combatant is then only one possible consequence instead of a stated intent and defined requirement for success.

Likewise, “Incapacitation” is something that is impossible to accurately calculate or predict. Physiological damage potential is the only factor that can be accurately measured and it is the only metric that has been shown to have any correlation with field results in actual shooting incidents, based on law enforcement autopsy findings, as well as historical and ongoing combat trauma results. In other words a “Damage” based metric has relevance to and accurately reflects the real world, while other measures of "Lethality" and "Incapacitation" are elaborate fantasy games of mathematical calculations and engineering statistics that fail to truly reflect the fact that in the gritty realm of face-to-face combat, incapacitating the enemy is about rapidly inflicting sufficient physiological DAMAGE to the enemy’s critical anatomic structures in order to stop that opponent from continuing to be a lethal threat. Thus, valid wound ballistic testing procedures measure DAMAGE.

The words of a U.S. Marine Corps Battalion Commander with extensive combat experience are telling:

“With damage based measures we are showing the end-users a picture of a gel block with a big hole through it and saying "Imagine that is a human, wouldn't that hurt." With dynamic based measures we are saying "Trust my math".

The damage based metric defines the potential of the round, under specific circumstances, given a single engagement. Measuring “incapacitation” seems to focus more on the statistical likelihood the target is still functioning at the conclusion of an engagement. In my own simple mind I am hesitant to place too much confidence in level of incapacitation for the following reasons:

1. It's too squishy - The measure is based on someone's guess as to a percentage of the time the target will choose to stop doing what he is doing because of a particular engagement. Everything is averaged; average target with average motivation, average hit placement, average effect on target. If down the road we redefine any of these average values the result is completely different. However if we shoot a gel block with a particular round today and say "Damn, that's a big hole", we don't introduce a bunch of changeable values and the result is roughly repeatable.

2. It gives an illusion of precision and scientific rigor that is just that; illusory - I don't mean to call in to question any of the rigor applied in the process of achieving the result. I trust fully that in dynamic modeling those who are doing it are correct in how they apply the statistical magic to arrive at the result, but the assignment of values to what does or does not equate to incapacitation are just as much of a guess as they are in the static method.

3. Accepting Level of Incapacitation is the first step down the road towards accepting the comparison of systems by "stowed kills" and "unit lethality". - Assessing the effect of a particular system on unit lethality over the course of a engagement or series of engagement has some place in evaluating small arms, but it must always take a back seat to evaluating the system based on it's performance in a single shot and what costs you accept to get that result (weight, maneuverability, range, etc). I understand if you are going to run a couple of million iterations through a computer model, it is necessary to look at it from the perspective of percentage incapacitation, unit lethality, etc. But the danger is someday looking at two systems - A has a 10% chance of killing my target in a single engagement, B has a 1% chance of killing my target in a single engagement. I can only carry 50 rounds of A, but I can carry 1,000 rounds of B. If I compare "stowed kills" I am carrying 5 kills with A, and 10 kills with B, so B must be better. Yet when I walk around the corner and there is a single bad guy waiting there who wants to kill me, I would rather be carrying system A.”

As noted by one of the JSWB-IPT researchers, the number of variables in combat is nearly infinite and terminal ballistic performance has a tremendous deviation surrounding the average result--anything can happen on any given day. Nonetheless, when an end-user experiences a terminal performance result in combat that is far different from the average effect he was told to expect by wound ballistic modeling, he no longer trusts the math. When using models like WTAI that overly average terminal performance and physiological factors, simplistic ideas such as “stowed kills” begin to pre-dominate and the predicted “average effectiveness” for most small arms systems appear similar. Note--the Stowed Kills (SK) metric has been used for both small and large caliber weapon systems; it is, essentially, a balance of the “killing potential” of the system against the weight of the system. Due to the modeling flaws when averaging “lethality” metrics, the SK philosophy ultimately favors weapon systems with the lightest weight and largest ammunition load, even if their actual terminal performance in combat proves less than desirable. Unfortunately, such modeling failures often leads to individual incidents were combat personnel find their weapons systems fail to meet their needs in specific engagements. Damage-based metrics like the static gel testing are highly attractive to end-user personnel because of the immediate relation they can make between their weapon system and what they can expect it to do to enemy combatants. The young Corporal kicking in a door in hostile village cares little about complex calculations, theoretical computer modeling, or physiological averages--his only desire is that his rifle can accurately, reliably, and rapidly deliver projectiles that will rapidly create enough physiological damage to rapidly stop the AK47 or PKM wielding terrorist he might have to engage once inside the structure.

[the Schwartz]

Outstanding! Thank you for the fascinating and incredibly comprehensive response, Doc. :)

That looks to be quite a procedure and I hope that the result was what you had hoped for your patient.

I just finished reading your posts and will have to take some time to absorb all of it. I truly do appreciate the time that you've taken from your schedule to address the questions that I have asked earlier in this thread regarding the P[I/H] and E[I/H] models and related models like the AKE/ORCA.

As stated earlier in post 29 of this thread:


While I am thinking of the BRL P[I/H] model (e.g.: Dziemian, 1960) and the yields that I have used in prior posts in this thread, I'd also like to take the time to clarify the position that I hold regarding the use and implications of the P[I/H] metric and all of the equations associated with that metric. I am very thick-skinned and I simply do not take myself, or any version of these P[I/H] models, so seriously that I would ever take offense towards anyone expressing their opinion, opposing or in favor of, the use and yields of these P[I/H] models. The P[I/H] models, produced by Sturdivan and Bruchey, Dziemian et. al., and Kokinakis and Sperrazza, are not of my creation and, as a result, I am unable to take offense from view points that find fault or disagree with the implications of these types of P[I/H] models. I include the yields of these P[I/H] models simply because I enjoy such algorithms for what they are in my own very 'nerdy' perspective....a lot of fun: statistical experimental design, analytical mathematics. With this thought, I welcome any well-reasoned opinion on this matter and any other topic.

Obviously, I 'get' it-


2. It gives an illusion of precision and scientific rigor that is just that; illusory - I don't mean to call in to question any of the rigor applied in the process of achieving the result. I trust fully that in dynamic modeling those who are doing it are correct in how they apply the statistical magic to arrive at the result, but the assignment of values to what does or does not equate to incapacitation are just as much of a guess as they are in the static method.

-so if you wish for me to exclude the P[I/H] metrics from further water test analyses, I can, and will, do so.

I note that in Chapter 7 of Bullet Penetration, (pp. 122 - 125) MacPherson discusses the use of water as a valid tissue simulant (Fackler ML. Handgun Performance Review. Intl Def Rev 1988; 21(5) pp. 555 - 557) citing on page 123, that, "The near identical expansion of bullets in water, tissue, or realistic soft solid tissue simulants is known to be true from experiment". This statement to me seems to suggest that Dr. Fackler's article, Fackler ML. Simplified Bullet Effect Testing. Wound Ballistics Rev 2001;5(2): 21 - 24 and articles preceding Dr. Fackler's article such as, Jones RL. Water Testing .38 Special +P Hollow Points. Wound Ballistics Rev 1997;3(1): 13 - 16, where Jones uses the Poncelet form as modified by Duncan MacPherson in Bullet Penetration to predict the maximum penetration depth ('Table 3' on page 16 of Wound Ballistics Rev 1997;3(1)) of those 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, where Duncan MacPherson discusses at length the dynamic similtude of water and seems to conclude that water is suitable terminal ballistic test medium. I also note that Jones did not use MacPherson's equations in his article, as he states on page 14 that, ''The penetration of each of the rounds tested was estimated using Figures 10-6 and 10-7 as described on page 251 of "Bullet Penetration" by Duncan MacPherson", and that those test data that fell outside of the range of the figures were computed by MacPherson at some later time.

My understanding, which may or may not be an accurate one, is that Duncan MacPherson has correlated his modified Poncelet form found in Bullet Penetration against some 400+ 10% ordnance gelatin test data, finding the use of water as a tissue simulant to be an acceptable methodology. Presently, the modified Poncelet form, as well as the modified THOR equation, which is a power law (in which the determining exponent was fitted to the proprietary body of 10% ordnance gelatin test data), found in Quantitative Ammunition Selection are correlated against nearly 900 independently-sourced (proprietary) 10% ordnance gelatin test data, a few of which I have referred to in this thread.

[TiroFijo]

Thanks a lot Doc!
You have managed to distillate A LOT of very useful (and not easy to obtain) information in those three posts.

[the Schwartz]

Can you post some data on the loads on DocGKR’s list?

Sent from my iPhone using Tapatalk

With the proviso that anyone reading this accepts Dr. Roberts' expert opinion found in these links-

https://pistol-forum.com/showthread.php?32530-Predictive-tests-in-water&p=776761&viewfull=1#post776761

https://pistol-forum.com/showthread.php?32530-Predictive-tests-in-water&p=776763&viewfull=1#post776763

https://pistol-forum.com/showthread.php?32530-Predictive-tests-in-water&p=776765&viewfull=1#post776765

-as the authoritative and final word on the validity of the BRL P[I/H] models, I will include the yields of the BRL P[I/H] model (Dziemian et al) for those interested in them. The presentation of the BRL P[I/H] model's yield is not an endorsement of its accuracy or its validity, that matter having been settled conclusively by Dr. Roberts' expert opinion (which I have the highest regard for) as expressed in the posts linked above. I include the yields of the BRL P[I/H] model below, not because I accept the P[I/H] model as being unconditionally and absolutely valid, but rather because I find it to be an interesting artifact and entertaining diversion. As I have stated before, I am not ''tied'' to these P[I/H] models in any way,rather in my own very 'nerdy' perspective, I think that they are simply a lot of fun to mess with.

The following was a water test of the Winchester Ranger-T 230-grain +P JHP (RA45TP) which was conducted a couple of years ago.

29356

Winchester Ranger-T 230-grain +P JHP (RA45TP)

Expanded Diameter: 0.668 inch
Recovered Weight: 229.7 gr. (99.87% retained weight)
Impact Velocity: 992 fps

Test Firearm: Springfield XD with a 5.00-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~81° Fahrenheit
Barrier: 2 layers of 8-ounce denim

Q-model
DoP: 15.433 inches
Wound Mass: 2.664 ounces
Wound Volume: 4.431 cubic inches

mTHOR model
DoP: 15.447 inches
Wound Mass: 2.666 ounces
Wound Volume: 4.435 cubic inches

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%
ΔE15: -312.013 fpe

For those curious as to how the Q-model's and mTHOR model's yields compare to how Duncan MacPherson's penetration model would evaluate these water test results, much as was done 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 in his article to predict the maximum penetration depths of several .38 Special +P hollow point bullets that he fired into water, those yields are provided here:

MacPherson model
DoP: 15.864 inches
Wound Mass: 2.395 ounces
Wound Volume: 3.984 cubic inches


Of course, I encourage everyone to draw their own conclusions. :)

[Ed L]

DocGKR, Thanks for taking the time to post all of that given your current situation. Your posts were amazing, especially the one quoted here as they apply to the "Cumulative Binomial Expected Probability of Incapacitation," which I don't see as having any logical or valid basis.


LETHALITY & INCAPACITATION vs. TERMINAL EFFECTIVENESS & DAMAGE:

The nebulous term "Lethality" is inappropriate and misleading and should ideally be banned from all discussions of terminal performance. What if an enemy combatant is hit with a projectile and immediately ceases hostile actions, but is not killed? If “Lethality” is the measured and defined metric, then the projectile has failed, because the opponent did not receive a lethal wound, although in actuality the projectile was extremely effective in stopping hostilities. Similarly, if an opponent is fatally shot, but manages to wipe out an entire squad of friendly personnel before succumbing to their wound, the projectile demonstrated 100% “Lethality”, but was utterly ineffective at stopping the enemy from continuing their attack. The phrase "Terminal Effectiveness" is far more accurate and appropriate than “Lethality”, as the death of an enemy combatant is then only one possible consequence instead of a stated intent and defined requirement for success.

Likewise, “Incapacitation” is something that is impossible to accurately calculate or predict. Physiological damage potential is the only factor that can be accurately measured and it is the only metric that has been shown to have any correlation with field results in actual shooting incidents, based on law enforcement autopsy findings, as well as historical and ongoing combat trauma results. In other words a “Damage” based metric has relevance to and accurately reflects the real world, while other measures of "Lethality" and "Incapacitation" are elaborate fantasy games of mathematical calculations and engineering statistics that fail to truly reflect the fact that in the gritty realm of face-to-face combat, incapacitating the enemy is about rapidly inflicting sufficient physiological DAMAGE to the enemy’s critical anatomic structures in order to stop that opponent from continuing to be a lethal threat. Thus, valid wound ballistic testing procedures measure DAMAGE.

The words of a U.S. Marine Corps Battalion Commander with extensive combat experience are telling:

“With damage based measures we are showing the end-users a picture of a gel block with a big hole through it and saying "Imagine that is a human, wouldn't that hurt." With dynamic based measures we are saying "Trust my math".

The damage based metric defines the potential of the round, under specific circumstances, given a single engagement. Measuring “incapacitation” seems to focus more on the statistical likelihood the target is still functioning at the conclusion of an engagement. In my own simple mind I am hesitant to place too much confidence in level of incapacitation for the following reasons:

1. It's too squishy - The measure is based on someone's guess as to a percentage of the time the target will choose to stop doing what he is doing because of a particular engagement. Everything is averaged; average target with average motivation, average hit placement, average effect on target. If down the road we redefine any of these average values the result is completely different. However if we shoot a gel block with a particular round today and say "Damn, that's a big hole", we don't introduce a bunch of changeable values and the result is roughly repeatable.

2. It gives an illusion of precision and scientific rigor that is just that; illusory - I don't mean to call in to question any of the rigor applied in the process of achieving the result. I trust fully that in dynamic modeling those who are doing it are correct in how they apply the statistical magic to arrive at the result, but the assignment of values to what does or does not equate to incapacitation are just as much of a guess as they are in the static method.

3. Accepting Level of Incapacitation is the first step down the road towards accepting the comparison of systems by "stowed kills" and "unit lethality". - Assessing the effect of a particular system on unit lethality over the course of a engagement or series of engagement has some place in evaluating small arms, but it must always take a back seat to evaluating the system based on it's performance in a single shot and what costs you accept to get that result (weight, maneuverability, range, etc). I understand if you are going to run a couple of million iterations through a computer model, it is necessary to look at it from the perspective of percentage incapacitation, unit lethality, etc. But the danger is someday looking at two systems - A has a 10% chance of killing my target in a single engagement, B has a 1% chance of killing my target in a single engagement. I can only carry 50 rounds of A, but I can carry 1,000 rounds of B. If I compare "stowed kills" I am carrying 5 kills with A, and 10 kills with B, so B must be better. Yet when I walk around the corner and there is a single bad guy waiting there who wants to kill me, I would rather be carrying system A.”

As noted by one of the JSWB-IPT researchers, the number of variables in combat is nearly infinite and terminal ballistic performance has a tremendous deviation surrounding the average result--anything can happen on any given day. Nonetheless, when an end-user experiences a terminal performance result in combat that is far different from the average effect he was told to expect by wound ballistic modeling, he no longer trusts the math. When using models like WTAI that overly average terminal performance and physiological factors, simplistic ideas such as “stowed kills” begin to pre-dominate and the predicted “average effectiveness” for most small arms systems appear similar. Note--the Stowed Kills (SK) metric has been used for both small and large caliber weapon systems; it is, essentially, a balance of the “killing potential” of the system against the weight of the system. Due to the modeling flaws when averaging “lethality” metrics, the SK philosophy ultimately favors weapon systems with the lightest weight and largest ammunition load, even if their actual terminal performance in combat proves less than desirable. Unfortunately, such modeling failures often leads to individual incidents were combat personnel find their weapons systems fail to meet their needs in specific engagements. Damage-based metrics like the static gel testing are highly attractive to end-user personnel because of the immediate relation they can make between their weapon system and what they can expect it to do to enemy combatants. The young Corporal kicking in a door in hostile village cares little about complex calculations, theoretical computer modeling, or physiological averages--his only desire is that his rifle can accurately, reliably, and rapidly deliver projectiles that will rapidly create enough physiological damage to rapidly stop the AK47 or PKM wielding terrorist he might have to engage once inside the structure.

[Ed L]

the Schwartz,

First, I have to compliment you on the time and effort you have put into this. I really mean it. It must take you a lot of time and work.


However, I don't believe that any "Cumulative Binomial Expected Probability of incapacitation" number can be valid for the reasons that DocGKR elaborated on, as well as other reasons, so I don't see the point to include them.

[the Schwartz]

the Schwartz,

First, I have to compliment you on the time and effort you have put into this. I really mean it. It must take you a lot of time and work.

Thanks, Ed. Your compliment is greatly appreciated. I am sure that you've probably heard the sentiment, ''If you enjoy what you do, you'll never work another day in your life''. I have been blessed enough to live that reality for the majority of my life and doing tests like this, along with predictive modeling, is my 'fun' if you haven't figured that out already (although I'd be willing to bet that you have).


A friendly criticism, I don't believe that any "Cumulative Binomial Expected Probability of incapacitation" number can be valid, so I don't see the point to include them.

I do appreciate the criticism you've offered. Enjoying statistical analyses as much as I do, even those constructs that are dated/obsolete/imperfect/flawed or just flat out 'wrong', I believe that there is significant insight to be gained by examining them for what they are, for the purposes that they are/were intended to serve and by whom they were crafted. As stated earlier, I am not ''tied'' to any of these P models in any way, nor do I get ''wrapped around the axle'' over criticisms of them. I think that these P[I/H] models are a lot of fun to investigate, as they reflect how an entire institution conceived, and thought about, the science of terminal ballistics 'back in the day'. That is why, along with my proviso earlier in this thread-

https://pistol-forum.com/showthread.php?32530-Predictive-tests-in-water&p=777093&viewfull=1#post777093

- ''[I]....that anyone reading this accepts Dr. Roberts' expert opinion as the authoritative and final word on the validity of the BRL P[I/H] models, I will include the yields of the BRL P[I/H] model (Dziemian et al) for those interested in them. The presentation of the BRL P[I/H] model's yield is not an endorsement of its accuracy or its validity, that matter having been settled conclusively by Dr. Roberts' expert opinion (which I have the highest regard for) as expressed in the posts linked above. I include the yields of the BRL P[I/H] model below, not because I accept the P[I/H] model as being unconditionally and absolutely valid, but rather because I find it to be an interesting artifact and entertaining diversion. As I have stated before, I am not ''tied'' to these P[I/H] models in any way, rather in my own very 'nerdy' perspective, I think that they are simply a lot of fun to mess with.''

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?

[John10-19]

Concern was already covered, post can be removed.

[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]

29365

[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)

29384

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―

29424

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 = ½ρTV2 = ½ x 999.972 kg/m3 x (381 m/s)2 = 72,578,467.75 N/m2

For 10% gelatin: Pressure = ½ρTV2 = 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.

[the Schwartz]

In carrying on with the line of thought in post #60, the Q-model is also useful in predicting instantaneous velocities (at any point of the bullet's travel through the target) as well as exit velocities where the bullet passes through and exits a target of finite depth.

In post #33, I explored the small amount of data contained within Allan Jones' 2011 Shooting Times article-


While surfing the 'net this afternoon, I stumbled across a Shooting Times article written by Allan Jones in 2011-

http://www.shootingtimes.com/ammo/ammunition_st_crimelabtests_200807/

-that contained a table with a small amount of exit velocity data for .38 Special LRN, LSWC and JHP projectiles after passing through a 15 centimeter-long block of 20% concentration ordnance gelatin.

Since none of the expansion values for the JHPs were included in the article or the table, I was limited to a 'quick-and-dirty' comparison limited to the LRN (2) and LSWC (2) data in order to examine how the Q-model predictions (which are included on the table in red) for the 15-centimeter exit velocities compares with Jones' test data:

29441

I really wish that Jones would have recorded the expansion dimensions for the JHPs and used 10% ordnance gelatin instead of the 20% gelatin, but there is little that I can do about that. Fortunately, the Q-model allows for the use/substitution of the correct material properties (mass density, strength) of 20% gelatin.

For such a small sample (n = 4), the results are encouraging.

Using the correct mass density of the target, ρT, and target yield strength, σT, for 20% concentration ordnance gelatin, the Q-model did quite well in its predictions.

The ANOVA of this very small population is―

n = 4
r = 0.9613
r² = 0.9241
Stan Dev(Y) = 53.9475 fps
Stan Dev(Rx) = 75.1261 fps
95% confidence = 73.622 fps
Standard prediction error = 25.3454 fps
T-test (paired data) = 0.0856
F-test = 0.6002

―and looking at the table it can be seen that the Q-model does predict residual (or 'exit') velocities with promising accuracy even in 20% concentration ordnance gelatin.

[the Schwartz]

Admiring very much how Doc conducts his tests with sample sizes of n = 5 for each protocol, I also try to follow the same idea since a test sample of n = >1 means that any anomalous behavior attributable to a single (perhaps flawed or 'out-of-spec') bullet can be screened out.

In this case, I have included test data for three tests conducted on the Federal Classic Hi-Shok 9mm 115 gr. JHP (9BP). With an average predicted maximum penetration depth of just 8.973 inches, the Federal Classic Hi-Shok 9mm 115 gr. JHP is a round that I would consider employing only under very restrictive engagement conditions (e.g.: requiring very shallow penetration characteristics).

Test #1 of 3: Federal Classic Hi-Shok 9mm 115 gr. JHP (9BP)

29553

29554

Average Expanded Diameter: 0.665 inch
Recovered Weight: 112.2 gr. (97.57% retained weight)
Impact Velocity: 1,268 fps

Test Firearm: Stock Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~72° Fahrenheit
Barrier: 2 layers of 8-ounce denim

Predictive Analysis:

Q-model
DoP: 8.840 inches
Wound Mass: 1.512 ounces
Wound Volume: 2.515 cubic inches

mTHOR
DoP: 9.130 inches
Wound Mass: 1.562 ounces
Wound Volume: 2.598 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel
__________________________________________________ _________________

Test #2 of 3: Federal Classic Hi-Shok 9mm 115 gr. JHP (9BP), fired into water

29553

29555

Average Expanded Diameter: 0.661 inch
Recovered Weight: 113.3 gr. (98.52% retained weight)
Impact Velocity: 1,204 fps

Test Firearm: Stock Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~72° Fahrenheit
Barrier: 2 layers of 8-ounce denim

Predictive Analysis:

Q-model
DoP: 8.764 inches
Wound Mass: 1.481 ounces
Wound Volume: 2.464 cubic inches

mTHOR
DoP: 8.981 inches
Wound Mass: 1.518 ounces
Wound Volume: 2.524 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel
__________________________________________________ _________________

Test #3 of 3: Federal Classic Hi-Shok 9mm 115 gr. JHP (9BP)

29553

29557

Average Expanded Diameter: 0.636 inch
Recovered Weight: 109.7 gr. (95.39% retained weight)
Impact Velocity: 1,156 fps

Test Firearm: Stock Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ ~72° Fahrenheit
Barrier: 2 layers of 1.66-ounce pure cotton T-shirt fabric

Predictive Analysis:

Q-model
DoP: 9.008 inches
Wound Mass: 1.409 ounces
Wound Volume: 2.344 cubic inches

mTHOR
DoP: 9.114 inches
Wound Mass: 1.426 ounces
Wound Volume: 2.372 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

[arcfide]

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."

I did read that, but the claim being made here is not that the penetration in water is the same as in gel, but rather than the data collected from testing in water can be used to predict gel penetration levels to a high level of accuracy and at a level of precision greater than the 1.6-2 times range given by the penetration shown in the water. It appears to me that the models shown here do not rely at all on the penetration in water to predict the penetration in gel, but rather utilize as their variables the impact velocity, expanded diameter, initial projectile weight, and retained projectile weight.

It is this claim that it is possible to reasonably precisely predict penetration depth in gel without the use or reliance on the uncorrelated penetration in water, relying instead on values that are more reliably measured and correlated, that most interests me.

Schwarz, I know that you have said that you have 890+ sample data points for this test, and I greatly appreciate the ANOVA results. I have a few more questions about that though. I assume, hopefully, that these are all the data points, and that no cherry-picking or removal of outliers has been done? The other question, which I don't recall you answering, is how these data points are distributed across different manufacturers, weights, bullet designs, temperatures, &c. It's less convincing if most of these data points came from a relatively small sample size of different types of projectiles in a small range of velocities. If, on the other hand, you did something like 10 rounds for each individual cartridge loading, and thus tested 89+ different rounds of substantially different design and loading, then that would be more compelling I think, especially if they covered a wide enough range of calibers, including .22 and .44 magnum and everything in between.

If I understand you right, these models will only work for bullets designed for straight line expansion without tumbling and little to no fragmentation, yes? Would they, for instance, accurately predict penetration for Liberty 50gr 9mm +P for instance (impact velocity: 2000fps, 0.37" diameter, 27gr retained weight)? Sorry, I haven't read through your formulae carefully enough to plug in the numbers myself yet. What about for tipped rounds that include polymer tips, such as Critical Defense, Critical Duty, or Speer G2 rounds? Does this model scale to the velocities and bullet weight combinations found in non-fragmenting, non-tumbling rifle rounds, such as the 50gr TSX Black Hills and the 64gr BSB from Nosler or the 52gr Federal FBI round? Where does the model break down? Is there an upper or lower velocity, weight, or expansion threshold at which the predictive power of the models begins to break down?

[DocGKR]

Note that the Fed 115gr JHP projectile in the test above demonstrates rather inconsistent performance when shot into validated 10% ordnance gel...

Also, the standard is 4 layers of denim, not 2.

[arcfide]

Winchester Bonded 9mm 147 gr. PDX1 JHP (S9MMPDB1)

Diameter: 0.5787 inch
Weight: 146.9 gr. (99.93% retained)
Velocity: 1,006 fps

…

Q-model
DoP: 13.710 inches
Wound Mass: 1.776 ounces
Wound Volume: 2.954 cubic inches

…

In fact the Winchester Ranger Bonded test data found here-

http://winchesterle.com/SiteCollectionDocuments/pdf/Handgun%20Bullet%20Barrier%20Testing%20Protocol_20 16.pdf

-duplicates quite closely the water-test performance of the ammunition recorded in this test closely matching the terminal expansion of the Winchester Ranger Bonded 147-grain JHP with an average expanded diameter of 0.585" at 995 feet per second (with 100% weight retention) yielding a penetration depth of 14.10 inches

I'd just like to point out that while the correlation is pretty good with the data in the Winchester PDF, that same round tested again by DocGKR here, does not correlate as well:

https://pistol-forum.com/showthread.php?20650-9-mm-147-gr-duty-load-testing

What strikes me as interesting here is that you were doing a 4L test, though it appears not a 4LD test. In your case, the expansion that you saw from water was close to what the Winchester folks are putting in their PDF, but it is *not* close to what Doc got in his expansion tests (0.52" BG and 0.46" 4LD IIRC). If you re-run your models with these other values, does your model still predict the penetration that was seen in Doc's Gel tests?

This brings up a question about your tests. Water seems likely to have the potential to over-estimate the amount of expansion, particularly for some barrier tests, potentially. If that is the case, does your model rely on the assumption that the expansion seen in water will be the same as that seen in gel? If the bullet design is such that in water it expands slightly more than in gel, will it under-estimate the degree of penetration? Can you correct for this behavior if that is the case, under the assumption that you will not know what the expected expansion size is for gel tests?

[arcfide]

Note that the Fed 115gr JHP projectile in the test above demonstrates rather inconsistent performance when shot into validated 10% ordnance gel...

That brings up another question. I think it was mentioned before that the differences between a 3" and 4" barrel were relatively the same as the amount of variation seen between different lots of ammunition. However, I don't recall a precise statistical measure being given on the actual variation seen between different lots of ammo.

For a model like this, it would be important to know the relative expected variation between different lots of ammunition in order to determine how well these models perform. Do you happen to have such information or a rough guestimate of it?

[the Schwartz]

Note that the Fed 115gr JHP projectile in the test above demonstrates rather inconsistent performance when shot into validated 10% ordnance gel...

Also, the standard is 4 layers of denim, not 2.

That the Federal Hi-Shok 9mm 115 gr. JHP behaved in similar fashion in 10% gelatin is not surprising. The extreme spread of 112 fps in impact velocity amongst just these three test rounds was rather disconcerting. As much as I like the IWBA mechanical failure test of 4 layers of (16-ounce per square yard) denim, sometimes I do vary the barrier (occasionally using no barrier) material and composition. While I do see the IWBA mechanical test as being the critical failure standard to meet, there are other barriers that I like to assess as well.

[the Schwartz]

I did read that, but the claim being made here is not that the penetration in water is the same as in gel, but rather than the data collected from testing in water can be used to predict gel penetration levels to a high level of accuracy and at a level of precision greater than the 1.6-2 times range given by the penetration shown in the water. It appears to me that the models shown here do not rely at all on the penetration in water to predict the penetration in gel, but rather utilize as their variables the impact velocity, expanded diameter, initial projectile weight, and retained projectile weight.

It is this claim that it is possible to reasonably precisely predict penetration depth in gel without the use or reliance on the uncorrelated penetration in water, relying instead on values that are more reliably measured and correlated, that most interests me.

You are correct. Since water does not support shear, the depth of penetration between the two mediums will indeed differ. Numerical conversion values aside, the equations themselves serve as 'conversion values'. Remember that since water and 10% ordnance gelatin posses the same physical properties (internal sonic velocities, bulk moduli, and mass densities) described by the Newton-LaPlace formula, that both materials (water and 10% gelatin) will produce expansive (that drive the expansion within a JHP cavity) and resistant (or decelerative) forces equal in magnitude to one another upon bullets (of the same design) at a given velocity.


Schwarz, I know that you have said that you have 890+ sample data points for this test, and I greatly appreciate the ANOVA results. I have a few more questions about that though. I assume, hopefully, that these are all the data points, and that no cherry-picking or removal of outliers has been done? The other question, which I don't recall you answering, is how these data points are distributed across different manufacturers, weights, bullet designs, temperatures, &c. It's less convincing if most of these data points came from a relatively small sample size of different types of projectiles in a small range of velocities. If, on the other hand, you did something like 10 rounds for each individual cartridge loading, and thus tested 89+ different rounds of substantially different design and loading, then that would be more compelling I think, especially if they covered a wide enough range of calibers, including .22 and .44 magnum and everything in between.

If I understand you right, these models will only work for bullets designed for straight line expansion without tumbling and little to no fragmentation, yes? Would they, for instance, accurately predict penetration for Liberty 50gr 9mm +P for instance (impact velocity: 2000fps, 0.37" diameter, 27gr retained weight)? Sorry, I haven't read through your formulae carefully enough to plug in the numbers myself yet. What about for tipped rounds that include polymer tips, such as Critical Defense, Critical Duty, or Speer G2 rounds? Does this model scale to the velocities and bullet weight combinations found in non-fragmenting, non-tumbling rifle rounds, such as the 50gr TSX Black Hills and the 64gr BSB from Nosler or the 52gr Federal FBI round? Where does the model break down? Is there an upper or lower velocity, weight, or expansion threshold at which the predictive power of the models begins to break down?

I have amassed as much usable data as I can and have not discarded outliers. As I stated earlier, collecting data has become sort of a weird never-ending hobby at this point. In order to satisfy the criteria for usable data, the paired correlative population must be composed of data that contains the complete penetration track of the projectile in question so that it can be paired to the equations' (both Q-model and mTHOR) predictions (if I cannot obtain a full 'start-to-stop' penetration track, then I have nothing to correlate the models' yields against); it must have no appreciable yawing/tumbling or other gross instability and the projectile must not shatter or fragment to such an extent that a primary residual body/core cannot be defined. Bullet mass within the population is distributed broadly across the entire spectrum of bullet weights in the service-pistol calibers and where the above (stringent) conditions are met, by rifle-caliber data. Much of the data that I have amassed originates from laboratory/research providers that I have retained at my own expense (e.g.: John Ervin, Brassfetcher.com), some of which are included in posts in this thread while some of it comes from other sources that some of our members may, or may not, be familiar with.

Once impact velocities start to exceed 1,650 fps, things start to get a bit fuzzy for models like these and worsen as data (tests) being evaluated move farther from that 'speed limit'. You are also correct in your understanding that these models (that is the Q-model, mTHOR and MacPherson's model which is also a Poncelet form) rely upon projectiles that exhibit straight line expansion without tumbling or yawing, however fragmentation may be accounted for by using the retained mass of the bullet in computations. There are cases where some of the more ''unconventional'' designs―such as the G2 Labs RIP or the Liberty Civil Defense―can be modeled by treating the remaining right cylinder (which is left behind after the initial loss of mass occurs in the first 4 to 6 inches of travel) as a (rather short) wadcutter, but when we get into the total post-impact disintegration of a projectile these models simply cannot handle that.

Because the population (n = 891) is composed of matched correlative pairs, there is no real need to run a full ANOVA since the Student's T-test and the F-test will serve as the most direct (and adequate) means of comparing the models' predictions against the population. For those unfamiliar with these measures, the simplest way to think of them is to consider the Student's T-test as a way of determining how well the model(s) explains the population (on a decimal scale with 1.00 being the maximum value). ANOVAs use F-tests to statistically test the equality of means, so it is easiest to think of F-tests as a way of determining if the average of the group composed of the models' yields is equal to that of the correlative population's average. What the F-test actually does is retrun the two-tailed probability that the variances of both grouos are not significantly different from one another.

I have (at the risk of becoming repetitious) included the ANOVAs for all three models as they perform against the same population (n = 891) so that you can see how they perform―

The Q-model ANOVA is:
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

The mTHOR ANOVA is:
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

The MacPherson model ANOVA is:
n = 891
r = 0.950518
r² = 0.903484
95% confidence = ±0.369254 inch
99% confidence = ±0.485282 inch
T-test = 0.938199
F-test = 0.0000577

[the Schwartz]

What strikes me as interesting here is that you were doing a 4L test, though it appears not a 4LD test. In your case, the expansion that you saw from water was close to what the Winchester folks are putting in their PDF, but it is *not* close to what Doc got in his expansion tests (0.52" BG and 0.46" 4LD IIRC). If you re-run your models with these other values, does your model still predict the penetration that was seen in Doc's Gel tests?

I make this comparison I would also note that the use of 'averaged' data for making comparisons like this carries with it the introduction of significant predictive error. That is to say, that the velocity for each test shot could, and probably does vary significantly in velocity by several tens of feet per second and the differences in the way that measured diameters (which is kind of an 'art' in itself) are also assessed may produce inaccurate comparisons. I am sure that Doc's work is fine, but the individual projectile velocity―not to mention the individual recovered masses and actual diameters―of each test is not being used here so these factors do need to be taken into consideration as well. So, with that thought in mind, here you go―

9 mm Win 147 gr RA9B BG: Pen = 15.5", RD = 0.52”, RL = 0.44”, RW = 146.9 gr, V = 992 fps (the Q-model's prediction is 17.222 inches, mTHOR predicts 16.302 inches)

9 mm Win 147 gr RA9B 4LD: Pen = 19.4”, RD = 0.46”, RL = 0.49”, RW = 146.6 gr, V = 992 fps (the Q-model's prediction is 22.552 inches, mTHOR predicts 20.790 inches)


This brings up a question about your tests. Water seems likely to have the potential to over-estimate the amount of expansion, particularly for some barrier tests, potentially. If that is the case, does your model rely on the assumption that the expansion seen in water will be the same as that seen in gel? If the bullet design is such that in water it expands slightly more than in gel, will it under-estimate the degree of penetration? Can you correct for this behavior if that is the case, under the assumption that you will not know what the expected expansion size is for gel tests?

Water does over-drive expansion slightly, but only by a small amount, so results in water, given that both water and 10% gelatin have very close respective internal sonic velocities, bulk moduli, and mass densities, are very close to those seen in actual 10% gelatin. Correction necessary due to the differences in the physical properties of both mediums is possible though the utilization of the correct ρ and σ functions in the Q-model.

[the Schwartz]

Test: .40 S&W 165 gr. Speer Gold Dot JHP

29622

29623

Diameter: 0.684 inch
Weight: 164.4 gr. (99.64% retained)
Velocity: 1,127 fps

Test Firearm: Steyr M40-A1 with a 4.00-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ 79°F
Barrier: 4 layers of denim

Predictive Analysis:

Q-model
DoP: 11.404 inches
Wound Mass: 2.064 ounces
Wound Volume: 3.433 cubic inches

mTHOR
DoP: 11.588 inches
Wound Mass: 2.097 ounces
Wound Volume: 3.488 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel




Taking a moment to address one of the significant benefits of conducting terminal ballistic tests in water―that there is no need to calibrate/validate the test medium since its mass density (which effects the inertial drag component) and viscosity (which effects the frictional component of drag) do not differ appreciably over the range of temperatures normally encountered during testing. Viscous drag force, which increases linearly with the speed of the projectile through the fluid flow field, and in the case of water (which is a Newtonian fluid) where viscosity is independent of the shear rate, means that no calibration/validation of the test medium is necessary. So long as the water being used for terminal ballistic testing is not boiling (which would introduce pockets of lower density water vapor thereby reducing its average mass density, not to mention being problematic to work with) or frozen (making it a solid), at any reasonable temperature, which I would propose as being >0°C (>32°F, and at liquidus) ― 60°C (140°F), the mass density and viscosity of water fluctuates only by a very small amount. Across the range of expected temperatures at which water may be used as a test medium, the mass density of water fluctuates ±0.00833 g/cc and the dynamic viscosity of water has a range of just ±0.663 centipoise.

Mass Density of Water from >0°C (32°F) ― 60°C (140°F)
0°C (32°F) ―― 0.99987 g/cc
10°C (50°F) ―― 0.99973 g/cc
20°C (68°F) ―― 0.99823 g/cc
30°C (86°F) ―― 0.99568 g/cc
40°C (104°F) ―― 0.99225 g/cc
50°C (122°F) ―― 0.98806 g/cc
60°C (140°F) ―― 0.98321 g/cc

Dynamic Viscosity of Water from >0°C (32°F) ― 60°C (140°F)
0°C (32°F) ―― 1.7916 centipoise
10°C (50°F) ―― 1.3076 centipoise
20°C (68°F) ―― 1.0005 centipoise
30°C (86°F) ―― 0.7970 centipoise
40°C (104°F) ―― 0.6539 centipoise
50°C (122°F) ―― 0.5474 centipoise
60°C (140°F) ―― 0.4656 centipoise

[SiriusBlunder]

Test: .40 S&W 165 gr. Speer Gold Dot JHP

<snip>

Q-model
DoP: 11.404 inches
Wound Mass: 2.064 ounces
Wound Volume: 3.433 cubic inches

mTHOR
DoP: 11.588 inches
Wound Mass: 2.097 ounces
Wound Volume: 3.488 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

<snip>


On this round in 4LD testing, manufacturer data is:

Penetration: 17.55"
Expansion: .583"

http://www.le.vistaoutdoor.com/wound_ballistics/load_comparison/load_comparison.aspx

One test from Doc I found shows:

.40 S&W Speer 165 gr Gold Dot JHP; ave vel=1092 fps (S&W 4006); gel cal=10cm@578fps
BG: pen=15.0" RD=0.63", RL=0.37", RW=165.2gr
4LD: pen=16.5", RD=0.55", RL=0.51", RW=165.4gr

https://www.m4carbine.net/showthread.php?26026-Test-Double-Tap-155-gr-Gold-Dot-vs-Speer-165-gr-Gold-Dot

However, you are predicting about 11.5 inches of penetration?

[the Schwartz]

On this round in 4LD testing, manufacturer data is:

Penetration: 17.55"
Expansion: .583"

http://www.le.vistaoutdoor.com/wound_ballistics/load_comparison/load_comparison.aspx

One test from Doc I found shows:

.40 S&W Speer 165 gr Gold Dot JHP; ave vel=1092 fps (S&W 4006); gel cal=10cm@578fps
BG: pen=15.0" RD=0.63", RL=0.37", RW=165.2gr
4LD: pen=16.5", RD=0.55", RL=0.51", RW=165.4gr

https://www.m4carbine.net/showthread.php?26026-Test-Double-Tap-155-gr-Gold-Dot-vs-Speer-165-gr-Gold-Dot

However, you are predicting about 11.5 inches of penetration?

Good question, DMWINCLE.

With the test data that I have―

Diameter: 0.684 inch
Weight: 164.4 gr. (99.64% retained)
Velocity: 1,127 fps

Test Firearm: Steyr M40-A1 with a 4.00-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ 79°F
Barrier: 4 layers of denim

―in which a Speer .40 S&W 165-grain Gold Dot expands to an average diameter of 0.684 inch (which presents 0.3675 in2 of frontal presentation area as opposed to the listed JHP that expanded to 0.583 inch with a frontal presentation area of just 0.2669 in2), while retaining 164.4 grains of its initial mass with an impact velocity of 1,127 fps, that is correct. A JHP of the same mass and similar velocity exhibiting greater expansion will not penetrate as far as a JHP with a smaller expanded diameter (the 'averaged' data that you present).

In this case, all three models (the Q-model, the mTHOR model and the MacPherson bullet penetration model) using the test data supplied above agree with one another

Diameter: 0.684 inch
Weight: 164.4 gr. (99.64% retained)
Velocity: 1,127 fps

Test Firearm: Steyr M40-A1 with a 4.00-inch barrel
Test Range: 3 meters (~10 feet)
Test Medium: H2O @ 79°F
Barrier: 4 layers of denim

Q-model
DoP: 11.404 inches
Wound Mass: 2.064 ounces
Wound Volume: 3.433 cubic inches

mTHOR
DoP: 11.588 inches
Wound Mass: 2.097 ounces
Wound Volume: 3.488 cubic inches

MacPherson
DoP: 11.160 inches (10.160 ― 12.160 inches)
Wound Mass: 1.841 ounces
Wound Volume: 3.061 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

JHPs of the same manufacturing source and construction can, and often do, expand to significantly different diameters even under the same test conditions. Differences in impact velocities―sometimes in excess of 100 fps―amongst the test rounds, individual material irregularities that arise during the manufacturing process (in each bullet), etc.....these factors, and more, all contribute to such (unpredictable) behavior.

[the Schwartz]

Federal Classic .40 S&W 155 grain Hi-Shok JHP

29666

29663

29664

Average Diameter: 0.533 inch
Recovered Weight: 154.4 gr. (99.61% retained)
Impact Velocity: 1,123 fps

Test Firearm: unmodified Steyr M40-A1; 4.00-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 82°F
Barrier: 4 layers of denim

Predictive Analysis:

Q-model
DoP: 18.541 inches
Wound Mass: 2.037 ounces
Wound Volume: 3.389 cubic inches

mTHOR
DoP: 17.877 inches
Wound Mass: 1.964 ounces
Wound Volume: 3.267 cubic inches

DoP = maximum equivalent depth of penetration in calibrated 10% ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

[the Schwartz]

Winchester .40 S&W 180-grain PDX1 JHP (S40SWPDB1)

29798

Average Diameter: 0.609 inch
Recovered Weight: 179.9 gr. (99.94% retained)
Impact Velocity: 1,081 fps

Test Firearm: Steyr M40-A1 with a 4.00-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 78°F
Barrier: 4 layers of denim

Q-model
DoP: 15.712 inches
Wound Mass: 2.254 ounces
Wound Volume: 3.749 cubic inches

mTHOR
DoP: 15.511 inches
Wound Mass: 2.225 ounces
Wound Volume: 3.702 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

[the Schwartz]

Winchester .45ACP 230-grain PDX1 JHP (S45PDB)

29937

Average Diameter: 0.680 inch
Recovered Weight: 229.7 gr. (99.87% retained)
Impact Velocity: 889 fps

Test Firearm: Springfield XD with a 5.00-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 80° Fahrenheit
Barrier: 4 layers of denim

Predictive Analysis:

Q-model
DoP: 13.726 inches
Wound Mass: 2.455 ounces
Wound Volume: 4.083 cubic inches

mTHOR
DoP: 13.745 inches
Wound Mass: 2.458 ounces
Wound Volume: 4.089 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

Both penetration models are in tight agreement with one another regarding predicted maximum penetration depth, wound mass and permanent cavity volume. The PDX1 is a bonded design that has its roots in the bonded Ranger line up. I have never seen a PDX1 not expand to a 'picture perfect' mushroom either in water or in 10% gelatin. The consistency of this design always impresses me.

[the Schwartz]

Winchester Ranger 9mm 147 gr. SXT JHP (RA9T)

30071

30072

Average Diameter: 0.4975 inch
Recovered Weight: 141.4 grains (96.19% retained weight)
Recovered Length: 0.470 inch
Impact Velocity: 1,085 fps

Test Firearm: stock Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 82° Fahrenheit
Barrier: 4 layers of denim

Predictive Analysis:

Q-model
DoP: 19.353 inches
Wound Mass: 1.853 ounces
Wound Volume: 3.082 cubic inches

mTHOR
DoP: 18.319 inches
Wound Mass: 1.754 ounces
Wound Volume: 2.917 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

Expansion of this round against 4LD, which was 1.404 times caliber, left a little to be desired and resulted in an average predicted maximum penetration depth of 18.836 inches. Average predicted permanent wound mass is 1.804 ounces (about 51.14 grams).

[the Schwartz]

Test #1: Speer 9mm 124-grain Gold Dot JHP, standard pressure (23618)

Diameter: 0.523 inch
Weight: 123.5 gr. (99.60% retained)
Velocity: 1,160 fps

Test Firearm: stock Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 84° Fahrenheit
Barrier: 4 layers of denim

Frontal Expansion Face #1:
30457

Rear, test #1:
30458

The average expanded diameter of all test projectiles was obtained by measuring the three maximum and minimum expansion face dimensions across the leading edge of the expansion face where the flow field separates from the edge of the test projectile. In this particular case, the minimum dimensions were 0.448'', 0.458'' and 0.4575'' and the maximum dimensions were 0.589'', 0.5975'', and 0.589'' for an average expanded diameter of 0.532''. Recovered length was measured at 0.375''.

Maximum dimensions:
30459

Minimum dimensions:
30460

Predictive Analysis:

Q-model
DoP: 15.770 inches
Wound Mass: 1.668 ounces
Wound Volume: 2.775 cubic inches

mTHOR
DoP: 15.212 inches
Wound Mass: 1.609 ounces
Wound Volume: 2.677 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel


As usual, the Speer Gold Dot JHP shows why it has such a fine reputation. The Speer 9mm 124-grain Gold Dot JHP (23618) definitely qualifies as a superior selection even in its standard pressure loading. No evidence of jacket/core separation was noted and the test round held on to the vast majority of its initial 124-grain weight while producing a predicted average penetration depth of 15.491 inches falling well into the Quantitative Ammunition Selection terminal penetration range recommendation of 14 — 18 inches of depth while producing gentle recoil that is likely to enhance accuracy when rapid, multiple shots are required to stop a life-threatening assault.

One of the alternatives to using a Fackler Box (mine is a 6' length of 8''-diameter PVC drainage pipe cut lengthwise to make a trough which is loaded with 1-gallon freezer storage bags filled with water) is using one-half gallon paper board beverage cartons to contain the water test medium for projectile evaluation. Care should be taken to ensure that the sensor ports remain free of obstruction by the paper towles, otherwise no velocity reading will occur.

Note the paper shop towels covering the chronograph. As the instrumental distance to the target face is only three feet, it is not unusual for water to be thrown into the chronograph's interior. Since employing this measure, I have yet to lose a chronograph due to water entering the electronics.

30461

Typically, 'service-caliber' JHPs (regardless of caliber) rarely penetrate more than 5 or 6 cartons before coming to rest. Usually, I set up 10 — 12 cartons in the event that a JHP fails to expand so that the test specimen can be recovered for photographing, but this is not an absolute necessity unless one wants to ensure that a failed JHP doesn't ''get away''.

Of course, once the test bullet has been fired (and hopefully remains within the carefully arranged/aligned cartons) and recovered, it must be weighed, measured for maximum and minimum expansion diameters, and the impact velocity recorded for entry into the penetration equations found in Quantitative Ammunition Selection.

For those interested in further reading about this test method, I highly recommend the late Dr. Fackler's article, Fackler ML. Simplified Bullet Effect Testing. Wound Ballistics Rev 2001;5(2): 21 - 24 and those articles preceding Dr. Fackler's article such as, Jones RL. Water Testing .38 Special +P Hollow Points. Wound Ballistics Rev 1997;3(1): 13 - 16, where Jones uses the Poncelet form as modified by Duncan MacPherson in Bullet Penetration to predict the maximum penetration depth ('Table 3' on page 16 of Wound Ballistics Rev 1997;3(1)) of those 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, where Duncan MacPherson discusses at length the dynamic similtude of water and concludes that water is suitable terminal ballistic test medium.

[the Schwartz]

Test #2: Speer 9mm 124-grain Gold Dot JHP, standard pressure (23618)

Diameter: 0.525 inch
Weight: 124 gr. (100% retained)
Velocity: 1,134 fps

Test Firearm: unmodified Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 84° Fahrenheit
Barrier: 4 layers of 1-ounce cotton T-shirt fabric

Frontal Expansion Face #2:
30592

Lateral detail, #2:
30593

Rear, test #2:
30594

The average expanded diameter of all test projectiles was obtained by measuring the three maximum and minimum expansion face dimensions across the leading edge of the expansion face where the flow field separates from the edge of the test projectile. In this particular case, the minimum dimensions were 0.456'', 0.458'' and 0.4505'' and the maximum dimensions were 0.591'', 0.599'', and 0.596'' for an average expanded diameter of 0.525''. Recovered length was measured at 0.381''.

Analysis:

Q-model
DoP: 15.488 inches
Wound Mass: 1.651 ounces
Wound Volume: 2.746 cubic inches

mTHOR
DoP: 14.905 inches
Wound Mass: 1.589 ounces
Wound Volume: 2.643 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

With an average predicted maximum penetration depth of 15.197 inches and very consistent expansion through four layers of 16-ounce denim, the Speer 9mm 124-grain Gold Dot is good for approximately 1.62 ounces of damaged soft tissue equivalence.

[the Schwartz]

Test #3: Speer 9mm 124-grain Gold Dot JHP, standard pressure (23618)

Diameter: 0.559 inch
Weight: 124 gr. (100% retained)
Velocity: 1,171 fps

Test Firearm: unmodified Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 84° Fahrenheit
Barrier: 4 layers of 1-ounce cotton T-shirt fabric

Frontal Expansion Face #3:
30695

Rear, test #3:
30696

The average expanded diameter of each test projectile was obtained by measuring the three maximum and minimum expansion face dimensions across the leading edge of the expansion face where the flow field separates from the edge of the test projectile. In this third test, the minimum expansion dimensions of the test Speer 9mm 124-grain Gold Dot JHP were 0.465'', 0.483'' and 0.471'' and the maximum expansion dimensions were 0.631'', 0.6355'', and 0.6695''. The average expanded diameter was calculated at 0.559'' and the final recovered length of the test round was measured at 0.367''.

Predictive Analysis:

Q-model
DoP: 13.754 inches
Wound Mass: 1.662 ounces
Wound Volume: 2.765 cubic inches

mTHOR
DoP: 13.463 inches
Wound Mass: 1.627 ounces
Wound Volume: 2.707 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

Test averages across all barriers in this test series are―

Average Recovered Diameter: 0.5357 inch (1.509x caliber)
Average Recovered Weight: 123.83 gr. (99.84% retained)
Average Recovered Length: 0.3743 inch
Average Impact Velocity: 1,155 fps

Average Predicted Penetration Depth: 14.773 inches
Average Predicted Wound Mass: 1.634 ounces
Average Predicted Wound Volume: 2.719 cubic inches

[the Schwartz]

Winchester USA 9mm 147 gr. JHP (USA9JHP2)

Diameter: 0.5827 inch
Weight: 147 gr. (100% retained)
Velocity: 972.2 fps
Recovered Length: 0.441 inch

Test Firearm: unmodified Glock 17 with a 4.49-inch barrel
Test Range: 3 meters (≈10 feet)
Test Medium: H2O @ 78° Fahrenheit
Barrier: 4 layers of 1-ounce cotton T-shirt fabric

31878

Predictive Analysis:

Q-model
DoP: 13.206 inches
Wound Mass: 1.734 ounces
Wound Volume: 2.885 cubic inches

mTHOR
DoP: 12.799 inches
Wound Mass: 1.681 ounces
Wound Volume: 2.796 cubic inches

DoP = maximum equivalent depth of penetration in calibrated ordnance gelatin (or soft tissue)
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel
Wound Volume = volume of the entire permanent wound channel

While the Winchester USA 9mm 147 gr. JHP is an 'economy' load, its expansion to 1.65x initial caliber with an average predicted maximum penetration depth of 13.00 inches is surprisingly good. I believe that this projectile was once offered under the "Super X'' product line and is also the ammunition which was used to successfully correlate the terminal behavior of bullets in gelatin and human soft tissues in this article...

http://ar15.com/ammo/project/fackler_articles/winchester_9mm.pdf

...written by Eugene Wolberg, a Senior Firarms Criminologist for the San Diego Police Department Crime Lab.

[the Schwartz]

Hornady .45 ACP 230 gr. XTP JHP +P (9096)

Test Firearm: unmodified HK USP .45ACP with a 4.41'' barrel
Barrier: 4 layers of 8-ounce cotton denim
Range: 21 feet
Test Medium: water @ 70° F

32482


32483

Average Diameter: 0.5947 inch
Recovered Weight: 229.6 grains (99.83% retained weight)
Impact Velocity: 922 fps
Recovered Length: 0.495 inch

32484

Predictive Analysis:

Q-model
DoP: 19.007 inches
Wound Mass: 2.600 ounces
Wound Volume: 4.325 cubic inches

mTHOR
DoP: 18.545 inches
Wound Mass: 2.524 ounces
Wound Volume: 4.199 cubic inches


While the average predicted maximum penetration depth of this test ammunition is just a bit 'deep' at 18.776 inches (average predicted wound mass is 2.562 ounces), if this round were to exit a 12-inch deep human torso, its exit velocity would be on the order of 300 ― 325 fps which, due to being unstable after exiting a human body, is unlikely to produce a lethal injury in the event of an unintentional strike upon a down-range bystander.

[0ddl0t]

Diameter: 0.5787 inch
Weight: 146.9 gr. (99.93% retained)
Velocity: 1,006 fps

...

Analysis:

Q-model
DoP: 13.710 inches
Wound Mass: 1.776 ounces
Wound Volume: 2.954 cubic inches

mTHOR
DoP: 13.300 inches
Wound Mass: 1.723 ounces
Wound Volume: 2.866 cubic inches


Doesn't this methodology assume all projectiles have the same coefficient of drag? How do your formulae stand up to non standard projectiles like:

tumbling fmj like 5.7 or Fort Scott
unusual expansion shapes like Lehigh Extreme expansion
fluted bullets like from underwood or polycase
?

[the Schwartz]

Doesn't this methodology assume all projectiles have the same coefficient of drag?

No. Each projectile configuration in both the Q-model and mTHOR model has its own specific coefficient.


How do your formulae stand up to non standard projectiles like:

tumbling fmj like 5.7 or Fort Scott
unusual expansion shapes like Lehigh Extreme expansion
fluted bullets like from underwood or polycase?

Within the limitations of closed-form equations like the modified Poncelet forms—proposed (respectively) by myself and MacPherson—and the mTHOR model; yes, they stand up quite well to the fluted and "non-standard" shapes. This thread is replete with examples of how well these relatively simple models (mine and MacPherson's) agree with and are confirmed by test data obtained in 10% ordnance gelatin.

Against 891 data, an 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 for the fitted mTHOR power law:

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

Coefficients do exist for projectile configurations having cruciform/fluted noses; many of them are proprietary.

It is simply not possible to model projectiles that do not remain in a "nose-forward" attitude and "tumble" and/or reduce themselves to fragments using simple closed-form equations. Modeling "tumbling" projectiles and fragmentation (especially approaching complete disintegration) would require the use of numerical software (like LS-DYNA) modeling 10% ordnance gelatin as an isotropic, elastic-plastic material with linear strain-hardening and a cubic polynomial relationship (equation of state) between the hydrodynamic pressure and the gelatin's change in mass density. It is assumed that 10% gelatin would obey the von Mises yield criterion. Constitutive relations would need to supplement the polynomial EoS relating to internal sonic velocity, mass density and bulk modulus.

[0ddl0t]

Is the measured penetration in water so meaningless it can be discarded? Are there often instances in which properly expanded projectile A travels farther in water than projectile B, yet where B travels farther in gel than A?

[the Schwartz]

Is the measured penetration in water so meaningless it can be discarded? Are there often instances in which properly expanded projectile A travels farther in water than projectile B, yet where B travels farther in gel than A?

Yes (to your first question) and sometimes, but not usually (to your second question).

While there are certainly simple "conversion factors" such as those suggested in Fackler ML. Simplified Bullet Effect Testing. Wound Ballistics Rev. 2001;5(2): 21-24, the practice of using over-simplified numerical conversion factors carries with it the risk of significant error. Dr. Fackler goes as far as to offer a cautionary comment to this approach (on page 21) in the cited article stating that, "Most bullets will penetrate about 1.5 times as far in water as in standard 10% ordnance gelatin: some penetrate even farther." I suspect that Dr. Fackler was fully aware of the potential short-comings of employing such a simplistic approach.

Of course, such simple penetration equations like the modified Poncelet penetration equations in common use do not require these values, but bulk modulus (k), mass density (ρ), and internal speed of sound (c) as related to one another by the Newton-Laplace equation do have very much to do with the terminal ballistic behavior of projectiles in 10% ordnance gelatin—especially when using FEM software (LS-DYNA).

[0ddl0t]

Thanks. I'm having a hard time wrapping my head around the precision of the estimation given so few input variables.

I mean this:


the fitted mTHOR power law:

n = 891
95% confidence = ±0.364299 inch
99% confidence = ±0.478770 inch


suggests the following result is one of only ~9 gel tests that fell outside the 99% confidence interval for mTHOR...



29424

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

...

mTHOR
DoP: 19.029 inches

[the Schwartz]

Thanks. I'm having a hard time wrapping my head around the precision of the estimation given so few input variables.

Sometimes, I do, too.

Both equations do extraordinarily well within their design limits.

MacPherson's bullet penetration model also does quite well when compared against the same data set:

n = 891
r = 0.950263
r² = 0.902999
95% confidence = ±0.367783 inch
99% confidence = ±0.483348 inch
T-test = 0.922177
F-test = 5.8x10-5

[the Schwartz]

Wanting a compact EDC option for this summer, one of my former partners, a retired Supervisory U.S. Customs Agent, recently purchased a brand new Ruger MAX-9 in 9mm Luger. We evaluated the performance of the Hornady 9mm 115-grain FTX® Critical Defense® JHP (#90250) projectile using water as a test medium.

In the interest of clarity, two test protocols were conducted. The first test protocol was without an intermediate barrier to establish a minimum performance baseline. If the outcome produced by the first test protocol was successful then a second test protocol consisting of firing the test ammunition through the IWBA standard barrier consisting of 4 layers of 16-ounce denim (a simple mechanical failure test) would be conducted.

Here are the results of those two tests:

Walter, my son and ever-faithful lab assistant, handled the experimental set up and pulled the trigger on the first test protocol.

Here he is holding the recovered projectile from that test—

74221

Hornady 9x19mm 115 gr. FTX Critical Defense (#90250)

Date: 15th June 2021
Temperature: 75°F
Relative Humidity: 42%

Test Firearm: unmodified Ruger MAX-9, 9mm Luger
Barrel Length: 3.20 inches
Barrier: None
Test Medium: H₂O @ 68°F
Range: 21 feet

Average Expanded Diameter: 0.5379 ± 0.0005 inch
Recovered Weight: 114.1 grains
Recovered Length: 0.387 inch
Impact Velocity: 1,007 fps

74222


74223


Predictive Analysis:

Q-model
DoP: 12.53 inches
Permanent Wound Mass: 1.40 ounces
Wound Cavity Volume: 2.33 cubic inches


mTHOR algorithm
DoP: 11.97 inches
Permanent Wound Mass: 1.34 ounces
Wound Cavity Volume: 2.23 cubic inches


For the sake of comparison, the McPherson WTI bullet penetration model was also used to predict maximum terminal penetration depth and total permanent wound mass. The predictive yield from the McPherson WTI bullet penetration model was a DoP of 12.38’’ having a total permanent wound mass of 1.16 oz.

The Hornady 9mm 115-grain FTX® Critical Defense® JHP successfully passed this test protocol.

The Hornady 9mm 115-grain FTX® Critical Defense® JHP was then evaluated against the second test protocol.

=========================================

Hornady 9x19mm 115 gr. FTX Critical Defense (#90250)

Date: 15th June 2021
Temperature: 75°F
Relative Humidity: 42%

Test Firearm: unmodified Ruger MAX-9, 9mm Luger
Barrel Length: 3.20 inches
Barrier: IWBA 4 layers of 16-ounce cotton denim
Test Medium: H₂O @ 68°F
Range: 21 feet

Average Expanded Diameter: 0.5216 ± 0.0005 inch (asymmetric)
Recovered Weight: 114.2 grains
Recovered Length: 0.649 inch
Impact Velocity: 1,005 fps

74226

74225

Predictive Analysis:

Q-model
DoP: 13.411 inches
Permanent Wound Mass: 1.411 ounces
Wound Cavity Volume: 2.347 cubic inches


mTHOR algorithm
DoP: 12.718 inches
Permanent Wound Mass: 1.338 ounces
Wound Cavity Volume: 2.226 cubic inches


Because the Hornady 9mm 115-grain FTX® Critical Defense® JHP failed to produce reliable, uniform expansion after passing through the IWBA standard barrier consisting of 4 layers of 16-ounce denim, my former partner rejected it as an option and decided to continue testing other candidate ammunition for his new EDC.

[the Schwartz]

While we had the test materials and set up available, we also ran the Norma 9x19mm 108-grain MHP (299740020) through the Ruger MAX-9 just to see how it would behave from a shorter-than-service-length (< 4'') barrel after passing through the IWBA standard barrier consisting of 4 layers of 16-ounce denim. Not surprisingly, there seems to be a lower velocity limit at which the Norma MHP will not expand.

Norma 9x19mm 108-grain MHP (299740020)

Date: 15th June 2021
Temperature: 75°F
Relative Humidity: 42%

Test Firearm: unmodified Ruger MAX-9, 9x19mm
Barrel Length: 3.20 inches
Barrier: 4 layers of 16-ounce cotton denim
Range: 21 feet
Test Medium: H₂O @ 68°F

Average Expanded Diameter: 0.355 ± 0.0005 inch
Recovered Weight: 108.4 grains
Recovered Length: 0.655 inch
Impact Velocity: 1,049 fps

74317


Predictive Analysis:

Q-model
DoP: 23.437 inches
Wound Mass: 0.960 ounces
Wound Cavity Volume: 1.597 cubic inches

mTHOR model
DoP: 23.320 inches
Wound Mass: 0.955 ounces
Wound Cavity Volume: 1.589 cubic inches


Testing of the Norma 9x19mm 108-grain MHP from the 3.20-inch barrel of the Ruger MAX-9 was halted after it failed to fully expand in the water test medium after passing through 4 layers of 16-ounce cotton denim. The nose of the bullet was only slightly deformed with two of the four skived expansion cavity wall sections pushed inward about 1.5 millimeters at impact displacing the other two skived expansion cavity wall sections outward about 1.5 millimeters. Predicted penetration depth, permanent wound mass, and wound cavity volumes of the test projectile were modeled as for an FMJRN while assuming that it would maintain nose-forward stable flight through the test medium.

[the Schwartz]

A few months ago, I purchased a box of Norma's latest offering, the Norma 9mm 108-grain Monolithic Hollow Point (MHP).

74430

Not only was I curious as to how fast Norma's new design would leave the 4.49-inch barrel of my EDC, an otherwise stock Glock 17 with Heinie target sights, I also wanted to see how it would perform after passing through the IWBA standard failure test of four layers of 16-ounce denim.

The velocity from my Glock 17's barrel is about 85 - 130 fps slower than Norma's advertised velocity of 1,312 fps but, in all fairness, Norma's advertised velocity is obtained from a 6-inch test barrel according to the information printed on the side of their product's box. With that thought in mind, the lower velocities that I obtained from my Glock 17's 1.5-inch shorter barrel appear to be what anyone could reasonably expect.

Here is the 1st IWBA 4LD test—

Norma 9x19mm 108-grain MHP (299740020)

Date: 15th June 2021
Temperature: 75°F
Relative Humidity: 42%

Test Firearm: unmodified Glock 17, 9x19mm
Barrel Length: 4.49 inches
Barrier: 4 layers of 16-ounce cotton denim
Range: 21 feet
Test Medium: H2O @ 68°F

Average Expanded Diameter: 0.6504 ± 0.0005 inch
Recovered Weight: 108.4 grains
Recovered Length: 0.393 inch
Impact Velocity: 1,183 fps

74432

74433

Predictive Analysis:

Q-model
DoP: 8.67 inches
Wound Mass: 1.42 ounces
Wound Cavity Volume: 2.36 cubic inches


mTHOR model
DoP: 8.76 inches
Wound Mass: 1.43 ounces
Wound Cavity Volume: 2.38 cubic inches

Simply for the sake of comparison, this water test data was also evaluated using the McPherson WTI model with the following results of DoP of 9.54 inches and a Wound Mass of 1.24 oz.

DoP = depth of penetration in inches

[the Schwartz]

Here is the 2nd IWBA 4LD test—


Norma 9x19mm 108-grain MHP (299740020)

Date: 15th June 2021
Temperature: 75°F
Relative Humidity: 42%

Test Firearm: unmodified Glock 17, 9x19mm
Barrel Length: 4.49 inches
Barrier: 4 layers of 16-ounce cotton denim, IWBA standard
Range: 21 feet
Test Medium: H2O @ 68°F

Average Expanded Diameter: 0.6529 ± 0.0005 inch
Recovered Weight: 108.5 grains
Recovered Length: 0.4035 inch
Impact Velocity: 1,227 fps

74435

74438

Predictive Analysis:

Q-model
DoP: 8.79 inches
Wound Mass: 1.45 ounces
Wound Cavity Volume: 2.41 cubic inches


mTHOR model
DoP: 8.94 inches
Wound Mass: 1.47 ounces
Wound Cavity Volume: 2.45 cubic inches


And once again, strictly for the sake of comparison, the McPherson WTI model gives us a DoP of 9.63 inches and a Wound Mass of 1.26 oz.

[the Schwartz]

Water test results follow for the Speer 9x19mm 124-grain Gold Dot +P JHP fired from the Ruger MAX-9.

Not unexpectedly, the velocity of this particular load matches very closely the average velocity of the standard pressure 9mm Gold Dot JHP (1,155 fps) as tested from the 4.49'' barrel of my Glock 17 in 2018. The higher pressure of the +P offering makes up for the 1.30 inch shorter barrel in effect bringing the terminal performance of a longer barrel to the Ruger MAX-9 subcompact pistol.

Speer 9x19mm 124 gr. Gold Dot +P JHP (23617)

Date: 20th July 2021
Temperature: 85°F
Relative Humidity: 47%

Test Firearm: unmodified Ruger MAX-9, 9x19mm
Barrel Length: 3.20 inches
Barrier: 4 layers of 16-ounce cotton denim, IWBA standard
Range: 21 feet
Test Medium: H2O @ 71°F

Average Expanded Diameter: 0.5529 ± 0.0005 inch
Recovered Weight: 125.2 grains
Impact Velocity: 1,164 fps

74985

Predictive Analysis:


Q-model
DoP: 14.18 inches
Wound Mass: 1.68 ounces
Wound Cavity Volume: 2.79 cubic inches


mTHOR model
DoP: 13.83 inches
Wound Mass: 1.64 ounces
Wound Cavity Volume: 2.72 cubic inches

Average predicted maximum penetration depth of 14.00 ± 0.15 inches with an average permanent wound cavity volume of 2.75 in³.

Comparison with the McPherson WTI model yields predictions of 13.70’’ penetration depth with a permanent wound mass of 1.38 oz.

[the Schwartz]

Sellier & Bellot 10mm 180 gr. JHP (SB10B)

Date: 25th July 2021
Temperature: 89°F
Relative Humidity: 66%

Test Firearm: Dan Wesson Razorback, 10mm
Barrel Length: 5.00 inches
Barrier: None
Range: 21 feet
Test Medium: H2O @ 82°F

Average Expanded Diameter: 0.7195 ± 0.0005 inch
Recovered Weight: 177.0 grains
Impact Velocity: 1,119 fps


75197


75198


Predictive Analysis:

Q-model
DoP: 10.93 inches
Wound Mass: 2.19 ounces
Wound Cavity Volume: 3.64 cubic inches

mTHOR model
DoP: 11.22 inches
Wound Mass: 2.25 ounces
Wound Cavity Volume: 3.74 cubic inches

With an average expanded diameter approaching ¾'', the sectional density of the Sellier & Bellot 10mm 180-grain JHP was redefined from a pre-impact sectional density of 0.1603 to 0.0488 at impact—a decrease of nearly 70%. Still, the test bullet is predicted to penetrate to an average maximum depth of 11.08 inches and produce a wound cavity volume of 3.70 ounces while retaining 98.33% of its pre-impact mass. I suspect that penetration would increase somewhat if this projectile was fired through an IWBA 4LD standard barrier test as JHP expansion tends to be mitigated by passage through four layers of 16-ounce denim.

[the Schwartz]

Hornady 5.7x28mm 40 gr. V-MAX JHP

Date: 25th July 2021
Temperature: 89°F
Relative Humidity: 66%

Test Firearm: Ruger-57™, 5.7x28mm
Barrel Length: 4.94 inches
Barrier: None
Range: 21 feet
Test Medium: H2O @ 82°F

Average Expanded Diameter: 0.2777 ± 0.0005 inch
Recovered Weight: 18.3 grains
Impact Velocity: 1,828 fps

75326

75327

Predictive Analysis:

Q-model
DoP: 11.68 inches
Wound Mass: 0.348 ounces
Wound Cavity Volume: 0.579 cubic inches

mTHOR model
DoP: 11.20 inches
Wound Mass: 0.334 ounces
Wound Cavity Volume: 0.555 cubic inches

DoP: Depth of Penetration

This water test was conducted using a Ruger-57™ pistol and a Hornady 5.7x28mm 40 gr. V-MAX JHP loaded over 5.0 grains of Alliant's Power Pistol. The 40-grain Hornady V-MAX bullet was fired into the water test medium with no barrier present. It expanded radically, shed its jacket, and fragmented losing 21.7 grains—or 54.25%—of its initial mass. Radical expansion, in which a bullet loses more than 10% of its mass through fragmentation, severely limits the maximum terminal penetration depth of a JHP. In this case, the Hornady 5.7x28mm 40 gr. V-MAX JHP would fall just shy of the 12-inch penetration minimum established by the F.B.I. test protocols by a little more than ½-inch on the average. In strong agreement with both the Q-model and mTHOR, the MacPherson WTI model predicts a maximum terminal penetration depth for this round of 11.15 inches with a corresponding wound mass of 0.273 ounces.

[the Schwartz]

Winchester Super-X .45 ACP 185 gr. Silvertip JHP (X45ASHP2)

Date: 25th July 2021
Temperature: 89°F
Relative Humidity: 66%

Test Firearm: Les Baer 1911A1, .45 ACP
Barrel Length: 5.00 inches
Barrier: 4 layers of 16-ounce cotton denim, IWBA standard
Range: 21 feet
Test Medium: H2O @ 82°F

Average Expanded Diameter: 0.8630 ± 0.0005 inch
Recovered Weight: 172.9 grains
Impact Velocity: 1,006 fps

75456

75457

Predictive Analysis:

Q-model
DoP: 6.62 inches
Wound Volume: 3.17 cubic inches
Wound Mass: 1.91 ounces

mTHOR model
DoP: 7.04 inches
Wound Volume: 3.37 cubic inches
Wound Mass: 2.03 ounces

DoP = maximum equivalent depth of penetration in 10% ordnance gelatin (or soft tissue)
Wound Volume = total weight of tissue damaged/destroyed within the entire wound channel
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel

The Winchester .45 ACP 185-grain Silvertip JHP, known for being a very fragile JHP design that expands very aggressively and tends to shed mass through fragmentation, didn't fail to live up to its reputation in this terminal ballistic water test. The averaged (Q-model and mTHOR model) predicted terminal penetration is very shallow at ≈6¾'' which becomes a concern if this round has to pass through an upraised forearm or bicep or an angled target presentation on the way to striking the COM of an assailant. Of course, terminal ballistic performance like this is exactly what lead the F.B.I. (and other U.S. law-enforcement agencies) to re-examine their ammunition selection after the events of 11th April 1986, and ultimately to the place we are now with service-caliber JHP designs that offer moderate expansion and consistent penetration that routinely meets the 12 - 18 inches of penetration depth recommended by the F.B.I. test protocols. For the sake of comparison, the McPherson WTI model predicts a maximum terminal penetration depth of 6.52’’ and a total wound mass of 1.88 oz.

[the Schwartz]

Federal Premium .45 ACP 230 gr. HST JHP (P45HST2)

Date: 25th July 2021
Temperature: 89°F
Relative Humidity: 66%

Test Firearm: unmodified HK45, .45 ACP
Barrel Length: 4.41 inches
Barrier: 16-ounce cotton denim, four layers, IWBA standard failure test
Range: 21 feet
Test Medium: H2O @ 82°F

Average Expanded Diameter: 0.7482 ± 0.0005 inch
Recovered Weight: 229.6 grains
Impact Velocity: 909 fps

75824

75825

Predictive Analysis:

Q-model
DoP: 11.25 inches
Wound Volume: 4.05 cubic inches
Wound Mass: 2.44 ounces

mTHOR model
DoP: 11.54 inches
Wound Volume: 4.16 cubic inches
Wound Mass: 2.50 ounces

DoP = predicted maximum depth of penetration in 10% ordnance gelatin (or soft tissue)
Wound Volume = total volume of the entire wound channel
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel

This water test was conducted using an unmodified Heckler & Koch HK45 pistol. Worth noting is that the Federal HST is an unbonded design evidenced by the lack of jacket adhesion to the lead alloy core (in the image of the reverse side of the expanded JHP). After passing through four layers of 16-ounce/yd² denim, the Federal 230-grain HST behaves as expected offering penetration approaching 12 inches with robust expansion and minimal lass of pre-impact mass. In comparison for this water test, the McPherson WTI model predicts a maximum terminal penetration depth of 11.69 ± 1.00’’ with a corresponding wound mass of 2.32 oz.

[Nephrology]

Hate to be that guy but it's H2O, not H2O

[the Schwartz]

Hate to be that guy but it's H2O, not H2O

Yes, I realize that. As you can see, I have correctly formatted H2O in several prior posts on this page and prior pages.

Being human and just as capable of error as any other, I must've hit the wrong format button when posting. I have no ability to edit the post now.

Perhaps you could help out rather than "being that guy"? ;)

ETA: I see that you took pity on me. Thanks! That was very kind of you!

I have to admit to having asked BBI to delete an entire thread not so long ago because I made an algebraic error (it was the ''Simple closed-form extensions of the Alekseevskii-Tate equation for rigid penetrators'' thread) that threw the whole thing sideways. So, rather than trying to explain to him what and how to correct the original post, I asked to give it the axe so I could try again.

[the Schwartz]

Federal 9mm 124-grain JHP +P HST (P9HST3)

Date: 25th July 2021
Temperature: 89°F
Relative Humidity: 66%

Test Firearm: unmodified Heckler & Koch P30SK; 9x19mm
Barrel Length: 3.30 inches
Barrier: 4 layers of 16-ounce cotton denim, IWBA standard barrier
Range: 21 feet
Test Medium: H2O @ 82°F

Average Expanded Diameter: 0.5599 ± 0.0005 inch
Recovered Weight: 124.1 grains
Impact Velocity: 1,188 fps

76095

76096

Predictive Analysis:

Q-model
DoP: 13.84 inches
Wound Volume: 2.79 cubic inches
Wound Mass: 1.68 ounces

mTHOR model
DoP: 13.57 inches
Wound Volume: 2.74 cubic inches
Wound Mass: 1.65 ounces

Not surprisingly, even from a very short barrel (3.3 inches), the Federal 9mm 124-grain JHP +P HST (P9HST3) performed well against the IWBA standard barrier of 4 layers of 16-ounce cotton denim.

DoP = maximum depth of penetration in 10% ordnance gelatin (or soft tissue)
Wound Volume = total volume of the entire wound channel
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel

[Lost River]

Yes, I realize that. As you can see, I have correctly formatted H2O in several prior posts on this page and prior pages.

Being human and just as capable of error as any other, I must've hit the wrong format button when posting. I have no ability to edit the post now.

Perhaps you could help out rather than "being that guy"? ;)

ETA: I see that you took pity on me. Thanks! That was very kind of you!

I have to admit to having asked BBI to delete an entire thread not so long ago because I made an algebraic error (it was the ''Simple closed-form extensions of the Alekseevskii-Tate equation for rigid penetrators'' thread) that threw the whole thing sideways. So, rather than trying to explain to him what and how to correct the original post, I asked to give it the axe so I could try again.

Open admissions of human error and corrections lend a sense of credibility in my book. Quite frankly, it is normal. It is part of the regular work process.

[the Schwartz]

Open admissions of human error and corrections lend a sense of credibility in my book. Quite frankly, it is normal. It is part of the regular work process.

“To make no mistakes is not in the power of man; but from their errors and mistakes the wise and good learn wisdom for the future.” ―Plutarch

[Glock17JHP]

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.


Sir, I read Duncan MacPherson's book all by myself, twice. Then I was able to figure out for myself how to use the information in that book to estimate ammo performance for my own personal needs. You see, I figured I should know what to expect from my own firearm/ammunition combination in case I should ever need to use it for self-defense. After doing the first tests with .38+P hollow points, I sent my data to Duncan MacPherson to see what he thought of it, and he encouraged me to submit it for publication in the IWBA's journal, the Wound Ballistics Review. My article was accepted for publication, including acceptance by the editor, Dr. Martin L. Fackler. I was published 3 times total; the other 2 times were for .380 ACP hollow points and .357 Magnum hollow points.

Prior to this, a question was posed by Dr. Fackler on problems with ballistic gelatin (WBR, Vol 2, No. 3, Pg. 3, Paragraph 2) that I was able to solve, and my answer was published in the following journal (WBR, Vol 2, No. 4, Page 5, last paragraph).

Also, I was asked to speak at the last IWBA Conference on my water-testing procedure and method, I gave papers that were requested for that, and they were accepted.

In closing, this all started because I was interested in wound ballistics for my own personal use, it expanded when Duncan MacPherson encouraged me to go beyond that, I was published 3 times, and eventually asked to speak at the IWBA Conference. And do you want to know the most interesting thing about all of this, sir? I am a high school graduate who never went to college. Imagine that!

-Ronald L Jones (IWBA full-member)

[the Schwartz]

In the interest of providing a clear understanding of what I stated in the post that you quoted only partially in your post (#102, 26th February 2022), I have restored the complete context surrounding the remarks that I made in post #51 (21st August 2018).






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.

Sir, I read Duncan MacPherson's book all by myself, twice. Then I was able to figure out for myself how to use the information in that book to estimate ammo performance for my own personal needs. You see, I figured I should know what to expect from my own firearm/ammunition combination in case I should ever need to use it for self-defense. After doing the first tests with .38+P hollow points, I sent my data to Duncan MacPherson to see what he thought of it, and he encouraged me to submit it for publication in the IWBA's journal, the Wound Ballistics Review. My article was accepted for publication, including acceptance by the editor, Dr. Martin L. Fackler. I was published 3 times total; the other 2 times were for .380 ACP hollow points and .357 Magnum hollow points.

Prior to this, a question was posed by Dr. Fackler on problems with ballistic gelatin (WBR, Vol 2, No. 3, Pg. 3, Paragraph 2) that I was able to solve, and my answer was published in the following journal (WBR, Vol 2, No. 4, Page 5, last paragraph).

Also, I was asked to speak at the last IWBA Conference on my water-testing procedure and method, I gave papers that were requested for that, and they were accepted.

In closing, this all started because I was interested in wound ballistics for my own personal use, it expanded when Duncan MacPherson encouraged me to go beyond that, I was published 3 times, and eventually asked to speak at the IWBA Conference. And do you want to know the most interesting thing about all of this, sir? I am a high school graduate who never went to college. Imagine that!

-Ronald L Jones (IWBA full-member)

On page 14 of "Jones RL. Water Testing .38 Special +P Hollow Points" in Wound Ballistics Rev. 1997;3(1): 13-16 under the section heading of ''Analysis and Conclusions'' you stated and I quote; ''The penetration of each of the rounds tested was estimated using Figures 10-6 and 10-7 as described on page 251 of "Bullet Penetration" by Duncan MacPherson. (Note: some of the data points fell beyond the boundaries of figures 10-6 and 10-7, and were calculated separately by Duncan MacPherson for the author.)'' That statement confirms that you were indeed relegated to relying upon the charts (specifically Figures 10-6 and 10-7 on pages 252 and 253, respectively) as opposed to performing the computations yourself.

I stand by my commentary above cited once again here—


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.

—simply because the information that I cited was factual, truthful, and accurate. As I stated on 21st August 2018, the purpose of writing Quantitative Ammunition Selection was to provide access to ordinary average guys (like us) to mathematical bullet penetration models that do not require ''some assembly before use'' or the use of small, blurry charts and graphs that cannot match the accuracy and assurance of a computed result. It is my aspiration that everyone should have the same sort of access and ability to benefit from these models that experts and professionals have.

In the event that you have taken exception to my commentary of 21st August 2018, I can assure you that no derision, disparagement, or disrespect was intended towards you (or anyone else for that matter) in the observation that I made in post #51.

[Glock17JHP]

In the event that you have taken exception to my commentary of 21st August 2018, I can assure you that no derision, disparagement, or disrespect was intended towards you (or anyone else for that matter) in the observation that I made in post #51.

Sir,

My response was not due to offense, it was sent to give you and everyone else here reading this the 'backstory' on myself. I was attempting to show that if one has a desire to pursue a subject, they should do whatever they can to accomplish that goal. My road took me from reading every gun magazine I could get my hands on, to figuring out how to contact Dr. Fackler who I read about in one of them. I talked with Dr. Fackler, and then he sent me a lot of information while he was at LAIR. When the IWBA started I was able to join as an associate member, and then I tried to figure out how to do my own ammunition testing. My journey eventually led me to using water since that was a lot easier than preparing and using properly calibrated ballistic gelatin.

The rest of my story is in my previous reply.

-Ron.

[the Schwartz]

Sir,

My response was not due to offense, it was sent to give you and everyone else here reading this the 'backstory' on myself. I was attempting to show that if one has a desire to pursue a subject, they should do whatever they can to accomplish that goal. My road took me from reading every gun magazine I could get my hands on, to figuring out how to contact Dr. Fackler who I read about in one of them. I talked with Dr. Fackler, and then he sent me a lot of information while he was at LAIR. When the IWBA started I was able to join as an associate member, and then I tried to figure out how to do my own ammunition testing. My journey eventually led me to using water since that was a lot easier than preparing and using properly calibrated ballistic gelatin.

The rest of my story is in my previous reply.

-Ron.

Got it, Ron. Thank you.

Once we accept the fact that terminal ballistic testing in water has certain limitations that can be resolved through mathematical modeling, it is probably one of the easiest mediums with which to work. The icing on the cake in this case is that if its temperature is kept between 20°C and 50°C, it can be thermally ''tuned'' to duplicate the shock Hugoniot of any imaginable human soft tissue.

BTW, if you have not gotten around to doing it for yourself, I would be happy to provide you an Excel computational spreadsheet that would free you from having to rely upon the small print and blurry graphs to determine maximum terminal penetration depth. Operation of the comp-sheet is simplicity itself. The comp-sheet is secured against unintentional corruption, just type in a few inputs and it gives you everything you want to a ridiculous degree of precision... maximum terminal penetration depth, wound cavity volume, and wound mass in both regimes (cavitation and non-cavitation).

Just shoot me a PM.

[Glock17JHP]

BTW, if you have not gotten around to doing it for yourself, I would be happy to provide you an Excel computational spreadsheet that would free you from having to rely upon the small print and blurry graphs to determine maximum terminal penetration depth. Operation of the comp-sheet is simplicity itself. The comp-sheet is secured against unintentional corruption, just type in a few inputs and it gives you everything you want to a ridiculous degree of precision... maximum terminal penetration depth, wound cavity volume, and wound mass in both regimes (cavitation and non-cavitation).

Just shoot me a PM.

Sir,

I'm good... thank you.

-Ron.

[the Schwartz]

OK, let's get this thread back on track.

I thought that it might be interesting to evaluate a subsonic heavy-for-caliber JHP intended for use in short barrels (< 3.5 inches) in water. Test barrier was the ever-popular IWBA 4LD denim barrier.

Expansion was excellent even though the velocity was somewhat less than I expected from a much longer barrel than intended for this round.

Predicted penetration is right in the middle of the 12 - 18 inch range specified by the F.B.I. test protocols.

Federal 9mm 150-grain HST 'Micro' JHP (P9HST5S)

Date: 20th July 2021
Temperature: 85°F
Relative Humidity: 47%

Test Firearm: unmodified Glock 17, 9x19mm
Barrel Length: 4.49 inches

Barrier: 16-ounce cotton denim, four layers
Range: 21 feet
Test Medium: H2O @ 71°F

Average Expanded Diameter: 0.5327 ± 0.0005 inch
Recovered Weight: 148.9 grains
Impact Velocity: 954.4 fps

87986

87987

Predictive Analysis:

Q-model
DoP: 16.127 inches
Wound Volume: 2.945 cubic inches
Wound Mass: 1.770 ounces

mTHOR model
DoP: 15.300 inches
Wound Volume: 2.794 cubic inches
Wound Mass: 1.679 ounces

DoP = maximum equivalent depth of penetration in 10% ordnance gelatin (or soft tissue)
Wound Volume = total volume of the entire wound channel
Wound Mass = total weight of tissue damaged/destroyed within the entire wound channel

[the Schwartz]

Yesterday, I had occasion to test the ''short barrel'' version of the Speer .45ACP 230-grain JHP from a Ruger American Compact pistol. The instrumental velocity of this particular load, 926.3 feet per second, was particularly impressive given the abbreviated length of the little Ruger's barrel. Performance was exceptional.

Speer .45 ACP 230-grain Gold Dot JHP (23975GD)
Date: 3rd July 2023
Temperature: 90°F
Relative Humidity: 71%

Test Firearm: unmodified Ruger American Compact pistol, .45ACP
Barrel Length: 3.75 inches
Barrier: 4 layers of 16-ounce cotton denim; IWBA standard
Range: 10 feet
Test Medium: H2O @ 77°F

Front expansion face of test projectile:
106726

Rear aspect of test projectile:
106727

Average Expanded Diameter: 0.7270 ± 0.0005 inch
Recovered Weight: 228.6 grains
Impact Velocity: 926.3 fps

Predictive Analysis:

Q-model
DoP: 12.093 inches
Wound Mass: 2.479 ounces
Wound Cavity Volume: 4.112 cubic inches

m-THOR model
DoP: 12.337 inches
Wound Mass: 2.522 ounces
Wound Cavity Volume: 4.195 cubic inches


DoP = maximum equivalent depth of penetration in 10% ordnance gelatin (or soft tissue)
Wound Cavity Volume = total volume contained within the permanent wound channel
Wound Mass = total weight of tissue damaged/destroyed within the permanent wound channel

[Glock17JHP]

Yesterday, I had occasion to test the ''short barrel'' version of the Speer .45ACP 230-grain JHP from a Ruger American Compact pistol. The instrumental velocity of this particular load, 926.3 feet per second, was particularly impressive given the abbreviated length of the little Ruger's barrel. Performance was exceptional.

Speer .45 ACP 230-grain Gold Dot JHP (23975GD)
Date: 3rd July 2023
Temperature: 90°F
Relative Humidity: 71%

Test Firearm: unmodified Ruger American Compact pistol, .45ACP
Barrel Length: 3.75 inches
Barrier: 4 layers of 16-ounce cotton denim; IWBA standard
Range: 10 feet
Test Medium: H2O @ 77°F

Front expansion face of test projectile:
106726

Rear aspect of test projectile:
106727

Average Expanded Diameter: 0.7270 ± 0.0005 inch
Recovered Weight: 228.6 grains
Impact Velocity: 926.3 fps

Predictive Analysis:

Q-model
DoP: 12.093 inches
Wound Mass: 2.479 ounces
Wound Cavity Volume: 4.112 cubic inches

m-THOR model
DoP: 12.337 inches
Wound Mass: 2.522 ounces
Wound Cavity Volume: 4.195 cubic inches


DoP = maximum equivalent depth of penetration in 10% ordnance gelatin (or soft tissue)
Wound Cavity Volume = total volume contained within the permanent wound channel
Wound Mass = total weight of tissue damaged/destroyed within the permanent wound channel


That Speer Short Barrel load is listed at 820 fps from a 4-inch barrel on Speer's website. Your data is showing it more than 100 fps higher velocity from a barrel that is 1/4 of an inch shorter, and that has me puzzled.

[the Schwartz]

That Speer Short Barrel load is listed at 820 fps from a 4-inch barrel on Speer's website. Your data is showing it more than 100 fps higher velocity from a barrel that is 1/4 of an inch shorter, and that has me puzzled.

The chronograph used to obtain the test data (impact velocity) has been validated against a Lab Radar Doppler unit on numerous occasions and once—just recently—against a Garmin Xero C1: it has always demonstrated ±0.75% agreement with the other units. I have no reason to distrust the reading that the chronograph provided in this particular test.

[Glock17JHP]

The chronograph used to obtain the test data (impact velocity) has been validated against a Lab Radar Doppler unit on numerous occasions and once—just recently—against a Garmin Xero C1: it has always demonstrated ±0.75% agreement with the other units. I have no reason to distrust the reading that the chronograph provided in this particular test.

I would reject this load for my usage if that velocity is correct.

[Glock17JHP]

I have a Detonics Combat Master .45 ACP, which has a 3.5-inch barrel and is designed for standard velocity (830ish fps) 230 grain FMJ ammunition. I want to select a hollowpoint that will expand and also is as close as possible in bullet shape, weight and velocity to this standard ammunition. At this point, it's down to Speer Gold Dot Short Barrel 230 grain (23975GD) @820 fps in a 4-inch barrel, and Federal HST 230 grain (P45HST2) @890 fps in a 5-inch barrel. I am leaning toward the Federal HST.

[Ghost Dog]

I have a Detonics Combat Master .45 ACP, which has a 3.5-inch barrel and is designed for standard velocity (830ish fps) 230 grain FMJ ammunition. I want to select a hollowpoint that will expand and also is as close as possible in bullet shape, weight and velocity to this standard ammunition. At this point, it's down to Speer Gold Dot Short Barrel 230 grain (23975GD) @820 fps in a 4-inch barrel, and Federal HST 230 grain (P45HST2) @890 fps in a 5-inch barrel. I am leaning toward the Federal HST.


Not sure if you're basing just on Terminal performance or if you have already function checked...

Reliability, especially w something so old short and chopped is paramount...

While hst is my choice especially from so short a barrel...if those 2 aren't thoroughly reliable I'd try 185 Golden Saber for nose profile and ogive discussed in another thread and because such a short barrel just my 2 cents

[Ghost Dog]

Can you please help in simple Lay terms?

Is the wound volume simply Volume of a Cylinder by Penetration and Expansion numbers? Or is there some variable modifying off that or in the equation? I don't have a device handy to check right now. If different is there a simple formula to figure this out one can use or it's simple Volume of a cylinder?

While adequate Penetration desired being met then Expansion therefore Would Volume seems the most important and reliable every time;
It seems that velocity and ME are all but ignored nowadays, however, I'm curious if E15 is also ignored now and if so why?

It would seem Pen/Exp/Would Volume are the most important and reliable but E15 would then be wanted as sometimes but not always may lead to higher psychological reaction (given a snippet of what Dr Gokor wrote theoretically on .357 sig not only louder bang and perhaps flash, but I'm wondering if e15 may indeed matter?)

Also, didn't Secret Service do some study going w fast 9mm then 357 sig? Has anyone ever had access to this?

And while most that old thinking under appreciating the most important metrics of Pen/Exp/Wound Volume perhaps E15 is that extra thing not being considered?

Or has that been totally disregarded now and if so why?

Certainly .357mag/Sig seemed to have had quicker changing of behavior in bad guys than similar 9mm close equivalent JHPs/bullet weights and yet they shouldn't on paper when ignoring velocity/ME/E15.
Bigger bullet more wound volume is every time but is e15 the other metric being ignored?

Typing on small cell phone I hope my questions make some sense.

[Ghost Dog]

Is there a simple way to plug and play figure out the E15 for each load tested or if you have Organic Gel Data? Please explain how to do that I find you including that metric interesting and wonder what readings would discuss this?

[Glock17JHP]

Reliability, especially w something so old short and chopped is paramount...



My Detonics Combat Master functions flawlessly with standard 230 grain FMJ. So, it should be fine with any 230 grain JHP that has a good bullet shape and is close to 830 fps (or slightly higher) in a 5-inch barrel. Since I trust the Federal HST standard velocity load, expansion at a lower velocity is my main concern. Trying currently to estimate velocity from my 3.5-inch barrel based on 890 fps from a 5-inch barrel.

Maybe I to just need to do some testing...

[Half Moon]

My Detonics Combat Master functions flawlessly with standard 230 grain FMJ. So, it should be fine with any 230 grain JHP that has a good bullet shape and is close to 830 fps (or slightly higher) in a 5-inch barrel. Since I trust the Federal HST standard velocity load, expansion at a lower velocity is my main concern. Trying currently to estimate velocity from my 3.5-inch barrel based on 890 fps from a 5-inch barrel.

Maybe I to just need to do some testing...

FWIW, might help you get in the ballpark:

http://ballisticsbytheinch.com/45auto.html

http://ballisticsbytheinch.com/45auto2.html

Testing would be best though. A lot of variables that can cause variation model to model.

[Ghost Dog]

My Detonics Combat Master functions flawlessly with standard 230 grain FMJ. So, it should be fine with any 230 grain JHP that has a good bullet shape and is close to 830 fps (or slightly higher) in a 5-inch barrel. Since I trust the Federal HST standard velocity load, expansion at a lower velocity is my main concern. Trying currently to estimate velocity from my 3.5-inch barrel based on 890 fps from a 5-inch barrel.

Maybe I to just need to do some testing...

feeding reliability is by far the bigger concern for that.

In Organic Gel, I've seen 45 HST expand as low as 730fps from Revolvers, and often in 3.3" tests as well.

Again, known JHP hollow point shape and ogive for reliable feeding in finicky 1911's is Golden Saber. Since only a 3.5", 185 gr recommended for most reliable expansion.

If you have a bunch of HST function check...if not going to check a ton, then I strongly suggest trying 185 Golden Sabers...you may find the recoil less as well which nice for that small Detonics. There is also 185+p if wanted, or 185 bonded if desired though less expansion

FBI data
45 ACP 185 grain Remington Golden Saber JHP, 3/21/94:

Test Gun Barrel Length Velocity
Bare Gelatin

Clothed Gelatin

Penetration Expansion Penetration Expansion
S&W M645

5" 1037 fps BARE 14.40" 0.72" CLOTHED15.95" 0.68"

In 17ish% less Dense Clear Ballistics
You can see 185s still expand in 3.64" Kahr in Lucky Gunner Labs

[the Schwartz]

Can you please help in simple Lay terms?

I'll do the best that I can.


Is the wound volume simply Volume of a Cylinder by Penetration and Expansion numbers? Or is there some variable modifying off that or in the equation? I don't have a device handy to check right now. If different is there a simple formula to figure this out one can use or it's simple Volume of a cylinder?

Predicted cavity volume is computed by multiplying the square of the expanded bullet's cross-sectional radius, r2, times π (3.1415927), times the length, L, of the permanent cavity, times a projectile-specific configuration factor, Φ, or V = π·r2·L·Φ


While adequate Penetration desired being met then Expansion therefore Would Volume seems the most important and reliable every time;
It seems that velocity and ME are all but ignored nowadays, however, I'm curious if E15 is also ignored now and if so why?

It would seem Pen/Exp/Would Volume are the most important and reliable but E15 would then be wanted as sometimes but not always may lead to higher psychological reaction (given a snippet of what Dr Gokor wrote theoretically on .357 sig not only louder bang and perhaps flash, but I'm wondering if e15 may indeed matter?)

ΔE15 is the amount of kinetic energy that a given projectile expends as it traverses a penetration depth of 1 centimeter to 15 centimeters through soft tissue or 10% ordnance gelatin test medium. The ΔE15 parameter (in later research referred to as EKE or expected kinetic energy) is still in use by the US military today in the ballistic insult subroutine contained within the ORCA/MUVES-S2 SLV software that has been used successfully to match the capability of our small arms munitions to those of our adversaries' munitions over the last 50+ years. The ΔE15 parameter is still relevant and not being ignored.

Due to technical misunderstanding and confusion, some researchers have chosen to ignore or discount the use of the ΔE15 (or EKE) parameter mistaking it as a direct causal mechanism of tissue damage and incapacitation rather than as a correlative factor. If you wish to read the technical paper in which the ΔE15/EKE parameter is correctly discussed, I would refer you to, A Mathematical Model for Assessing Weapons Effects From Gelatin Penetration by Spheres (AD-770352); Sturdivan, LM; Edgewood Arsenal, SAREA-BL-BS, Aberdeen Proving Ground, MD, 21010, September, 1973.

Here is a very brief excerpt from that source explaining the concept in simple terms:

''The ideal evaluative procedure is one in which the gelatin penetration/retardation performance of a projectile could be predicted from its physical characteristics. Conversely, the same models which allow prediction of performance could be used to design projectiles possessing the desired terminal, soft-target effects within the constraints placed on the weapon system. An integral part of most weapons effectiveness analyses - and therefore the most common measure of antipersonnel effect - is the probability of incapacitating an infantry soldier, given a random hit, or P. It has recently been shown that P[I/H] is closely correlated to the expected kinetic energy deposit (EKE) in the "average" soldier struck at random by a particular projectile.''

The ΔE15/EKE parameter has no relationship to psychological effects; it is a physical measure of projectile kinetic energy expenditure.


And while most that old thinking under appreciating the most important metrics of Pen/Exp/Wound Volume perhaps E15 is that extra thing not being considered?

Or has that been totally disregarded now and if so why?

Certainly .357mag/Sig seemed to have had quicker changing of behavior in bad guys than similar 9mm close equivalent JHPs/bullet weights and yet they shouldn't on paper when ignoring velocity/ME/E15.
Bigger bullet more wound volume is every time but is e15 the other metric being ignored?


While I have included ΔE15/EKE calculations in past contributions, I have not done so for quite some time. The controversial nature of the methodology led to complaints, so I don't offer them here anymore; I still do so on other forums. If you need a ΔE15/EKE for a particular case, I can provide it to you via PM.


Is there a simple way to plug and play figure out the E15 for each load tested or if you have Organic Gel Data? Please explain how to do that I find you including that metric interesting and wonder what readings would discuss this?

Unfortunately, there is no 'easy button'.

In order to determine the ΔE15/EKE of a test projectile, you would need high frame rate videography of the test in 10% ordnance gelatin from which the test projectile's instantaneous velocity can be determined at both depths. Using that data, the test projectile's ΔE15/EKE could be computed.

The mathematical basis for this process is addressed in the technical paper referenced earlier in this post:

''The EKE from random hits on actual enemy soldiers cannot be measured: but EKE may be approximated by:

EKE = [I]∫oxmax F(x)P(x)dx

where F(x) is the retarding force on the projectile as a function of depth of penetration, x, into a 20% gelatin block, P(x) is the probability that the projectile would still be within the "average" soldier at depth x, given a random hit, and xmax is the maximum gelatin penetration depth of the projectile. F(x) is usually calculated from time-penetration data derived from high-speed movies of gelatin impacts. However, if the gelatin retardation could be predicted from a mathematical model, then the predicted F(x) could be used to calculate EKE. Since P(x) is already known, EKEs derived in this manner would require no firing. In fact, EKEs could be predicted for purely hypothetical projectiles.''

Any of the five existing mathematical bullet penetration models—the mTHOR algorithm (Schwartz, 2014), Q-model (Schwartz, 2012), WTI (MacPherson, 1995), UTSI (Peters, 1990), and US Army BRL (Sturdivan, 1973)—can be rearranged algebraically to perform the ΔE15/EKE calculation for both hypothetical and actual tests.

[Ghost Dog]

I'll do the best that I can.



Predicted cavity volume is computed by multiplying the square of the expanded bullet's cross-sectional radius, r2, times π (�3.1415927), times the length, L, of the permanent cavity, times a projectile-specific configuration factor, Φ, or V = π·r2·L·Φ



ΔE15 is the amount of kinetic energy that a given projectile expends as it traverses a penetration depth of 1 centimeter to 15 centimeters through soft tissue or 10% ordnance gelatin test medium. The ΔE15 parameter (in later research referred to as EKE or expected kinetic energy) is still in use by the US military today in the ballistic insult subroutine contained within the ORCA/MUVES-S2 SLV software that has been used successfully to match the capability of our small arms munitions to those of our adversaries' munitions over the last 50+ years. The ΔE15 parameter is still relevant and not being ignored.

Due to technical misunderstanding and confusion, some researchers have chosen to ignore or discount the use of the ΔE15 (or EKE) parameter mistaking it as a direct causal mechanism of tissue damage and incapacitation rather than as a correlative factor. If you wish to read the technical paper in which the ΔE15/EKE parameter is correctly discussed, I would refer you to, A Mathematical Model for Assessing Weapons Effects From Gelatin Penetration by Spheres (AD-770352); Sturdivan, LM; Edgewood Arsenal, SAREA-BL-BS, Aberdeen Proving Ground, MD, 21010, September, 1973.

Here is a very brief excerpt from that source explaining the concept in simple terms:


The ΔE15/EKE parameter has no relationship to psychological effects; it is a physical measure of projectile kinetic energy expenditure.



While I have included ΔE15/EKE calculations in past contributions, I have not done so for quite some time. The controversial nature of the methodology led to complaints, so I don't offer them here anymore; I still do so on other forums. If you need a ΔE15/EKE for a particular case, I can provide it to you via PM.



Unfortunately, there is no 'easy button'.

In order to determine the ΔE15/EKE of a test projectile, you would need high frame rate videography of the test in 10% ordnance gelatin from which the test projectile's instantaneous velocity can be determined at both depths. Using that data, the test projectile's ΔE15/EKE could be computed.

Barring that, any of the five existing mathematical bullet penetration models—mTHOR algorithm (Schwartz, 2014), Q-model (Schwartz, 2012), WTI (MacPherson, 1995), UTSI (Peters, 1990), and US Army BRL (Sturdivan, 1973)—can be rearranged algebraically to perform the ΔE15/EKE calculation for both hypothetical and actual tests.

The mathematical basis for this process is addressed in the technical paper referenced earlier in this post:


The five existing mathematical bullet penetration models can be used to perform these kinds of calculations.


First off, thank you for the response, though a lot here is difficult.

Delving into E15/EKE territory acknowledging that 1st and foremost PROPER PENETRATION must be present, then Expansion, and therefore Wound Volume causing blood loss.....

But wondering what part E15 MAY PERHAPS play (in combination with often being a louder cartridge, sometimes more flash, as well as a higher physical pressure wave blast of expanding gases at closer ranges hitting the subject) in someone realizing they have been shot, which many, but not all (such as dedicated attackers/Platt etc.) will than have psychological reaction causing behavioral changes (running away, keeling over, dropping to the ground as if hit by lightning, FIBS) ie .357 Sig/Mag vs 9mm often or common reactions and to some extent +p+ vs standard pressure reactions (let's say outside of CNS or Heart shots-obviously anything reaching cns or heart will be somewhere between somewhat to totally effective). Ie while a good hunter can certainly kill deer with a well placed 9mm, it's easier and considered more ethical, and illegal vs legal in many states to do so with similar diameter but faster velocity .357 magnum...the shot can be a little less well placed and still be ethically effective.

For my purposes all are pistol JHP's, so what does this mean "times a projectile-specific configuration factor", and would it change for each round or handgun caliber? Or can I plug and play expanded r2, Penetration in inches, times 3.1415927? What is this specific configuration factor or how to calculate that? Is a 9mm JHP starting diameter different than a .45 JHP for plugging into this equation to figure out wound volume? Or is JHP a constant configuration factor?


I see that in some of the early rounds you gave data for in this thread you gave E15/EKE but stopped because most think it is irrelevant. While the PI may be (for handgun calibers anyways and not rifles), I think E15/EKE may be relevant, at least sometimes. And I believe physiological relates to psychological but would like very much to get some numbers from you.

Do you have any e15 data you would share with me, in PM if desired on any 125 grain .357 Mag/.357 Sig, so I can compare to other calibers or perhaps 158 gr .357 Mag? Similarly, I would love to compare the e15 values for the hotter 155/165 gr .40 loads to 180 gr, and to other caliber grain weights as well. Also, any +p+ 9mm data, to compare to the few you gave e15 to earlier in the thread of standard pressure 9mm like WWB 115 and 147 whose performance is known. Any 124+p Data on a more modern design like Gold Dot or HST? I am curious what a difference in E15 say 9bple +p+ 115 gr was compared to standard pressure 9bp & if there is perhaps correlation there to the difference in real world OIS performance. Plus, wondering if these factors were why Secret Service went with +p+ 115 (Winchester) & then .357 Sig after their Super Secret Study (has anyone ever been granted access to this that is known)?

Your 147 gr WWB/USA water penetration of app 13" being similar to the avg 13" in Organic Gel and the avg 13" in app 41 bodies 27/28 published in study and I believe DrGkr said 14 more with similar results after that in IWBA (not through bone) is interesting.
So water testing expansion for PISTOL bullets or below 1700 fps is 95-99% correlation to Organic Gel though a bit great expansion typically?
Is Water Jug Penetration similarly around 95-99% correlation to Organic Gel Penetration once you divide by X (and this X be that 1.6 or 1.7 is different depending on which method?)
Thank you

[Glock17JHP]

feeding reliability is by far the bigger concern for that.

In Organic Gel, I've seen 45 HST expand as low as 730fps from Revolvers, and often in 3.3" tests as well.

Again, known JHP hollow point shape and ogive for reliable feeding in finicky 1911's is Golden Saber. Since only a 3.5", 185 gr recommended for most reliable expansion.

If you have a bunch of HST function check...if not going to check a ton, then I strongly suggest trying 185 Golden Sabers...you may find the recoil less as well which nice for that small Detonics. There is also 185+p if wanted, or 185 bonded if desired though less expansion

FBI data
45 ACP 185 grain Remington Golden Saber JHP, 3/21/94:

Test Gun Barrel Length Velocity
Bare Gelatin

Clothed Gelatin

Penetration Expansion Penetration Expansion
S&W M645

5" 1037 fps BARE 14.40" 0.72" CLOTHED15.95" 0.68"

In 17ish% less Dense Clear Ballistics
You can see 185s still expand in 3.64" Kahr in Lucky Gunner Labs

This post contains information that is helpful to me, but I intend to stick with a 230 grain bullet at standard pressures, since the Detonics is designed for that type of load.

[Glock17JHP]

FWIW, might help you get in the ballpark:

http://ballisticsbytheinch.com/45auto.html

http://ballisticsbytheinch.com/45auto2.html

Testing would be best though. A lot of variables that can cause variation model to model.

I really appreciate the 2 links, especially the 2nd one from 2015 ! ! !

[Glock17JHP]

In Organic Gel, I've seen 45 HST expand as low as 730fps from Revolvers, and often in 3.3" tests as well.



That specific information is very helpful, thank you ! ! !

[the Schwartz]

First off, thank you for the response, though a lot here is difficult.

You're welcome. Hopefully, I can help you get ''out of the weeds'' regarding the ΔE15/EKE parameter and what it means. There's a lot that you're attributing to the parameter that shouldn't be.


Delving into E15/EKE territory acknowledging that 1st and foremost PROPER PENETRATION must be present, then Expansion, and therefore Wound Volume causing blood loss.....

But wondering what part E15 MAY PERHAPS play (in combination with often being a louder cartridge, sometimes more flash, as well as a higher physical pressure wave blast of expanding gases at closer ranges hitting the subject) in someone realizing they have been shot, which many, but not all (such as dedicated attackers/Platt etc.) will than have psychological reaction causing behavioral changes (running away, keeling over, dropping to the ground as if hit by lightning, FIBS) ie .357 Sig/Mag vs 9mm often or common reactions and to some extent +p+ vs standard pressure reactions (let's say outside of CNS or Heart shots-obviously anything reaching cns or heart will be somewhere between somewhat to totally effective). Ie while a good hunter can certainly kill deer with a well placed 9mm, it's easier and considered more ethical, and illegal vs legal in many states to do so with similar diameter but faster velocity .357 magnum...the shot can be a little less well placed and still be ethically effective.

ΔE15 (or EKE) has nothing to do with a cartridge's muzzle signature (flash or blast), the action of propellant gases vented from the muzzle, or any psychological response of the subject struck by a projectile. The only thing that ΔE15 quantifies is the amount of kinetic energy that is lost by a projectile during its passage through soft tissue or ordnance gelatin from a depth of one centimeter to a depth of 15 centimeters. The amount of kinetic energy lost is expressed as a negative value (loss) in either joules or foot-pounds and must be determined either through the use of a physical model (that is, high frame rate video analysis of a bullet passing through ordnance gelatin) or by computation using any one of the five existing mathematical bullet penetration equations in conjunction with a water test (when necessary to induce projectile expansion).

Once ΔE15 has been determined, the value must then be applied to any of the three provisional incapacitation equations along with the appropriate coefficients (for 'a', 'b', and 'n') in order to calculate the probability of incapacitation or P[I].

1.) P[I] = [1 + e -(-a + b(logΔE15))]-1 (Dziemian, 1961)

2.) P[I] = 1 – e -a(mv[SUB]₀¹·⁵ - b)ⁿ (Sperrazza & Kokinakis, 1965)

3.) P[I] = 1 – e -a(ΔE15)ⁿ (Sturdivan & Bruchey, 1968)


For my purposes all are pistol JHP's, so what does this mean "times a projectile-specific configuration factor", and would it change for each round or handgun caliber? Or can I plug and play expanded r2, Penetration in inches, times 3.1415927? What is this specific configuration factor or how to calculate that? Is a 9mm JHP starting diameter different than a .45 JHP for plugging into this equation to figure out wound volume? Or is JHP a constant configuration factor?

Configuration factors are constant for expanded JHPs (regardless of diameter), FMJRNs, FMJFNs, WCs, SWCs, etc. They can be found in the literature cited for all of the mathematical models that I mentioned earlier. On the other hand, ΔE15 values are dependent upon the diameter, mass, impact velocity, drag coefficient of the specific test projectile as well as the density of the target medium and they vary accordingly with each individual test. Since ΔE15 is a value that is unique to each specific test, there is no ''one size fits all'' ΔE15 for any one given bullet mass, diameter, or configuration.


I see that in some of the early rounds you gave data for in this thread you gave E15/EKE but stopped because most think it is irrelevant. While the PI may be (for handgun calibers anyways and not rifles), I think E15/EKE may be relevant, at least sometimes. And I believe physiological relates to psychological but would like very much to get some numbers from you.

Do you have any e15 data you would share with me, in PM if desired on any 125 grain .357 Mag/.357 Sig, so I can compare to other calibers or perhaps 158 gr .357 Mag? Similarly, I would love to compare the e15 values for the hotter 155/165 gr .40 loads to 180 gr, and to other caliber grain weights as well. Also, any +p+ 9mm data, to compare to the few you gave e15 to earlier in the thread of standard pressure 9mm like WWB 115 and 147 whose performance is known. Any 124+p Data on a more modern design like Gold Dot or HST? I am curious what a difference in E15 say 9bple +p+ 115 gr was compared to standard pressure 9bp & if there is perhaps correlation there to the difference in real world OIS performance. Plus, wondering if these factors were why Secret Service went with +p+ 115 (Winchester) & then .357 Sig after their Super Secret Study (has anyone ever been granted access to this that is known)?

In this thread, there are examples of standard pressure and +P loads in the calibers that you mention. Even amongst those few, ΔE15 values must be determined independently of one another and must, once again, be obtained using the rearranged mathematical bullet penetration equation of your choice. As far as your statement, ''And I believe physiological relates to psychological but would like very much to get some numbers from you''...there is no number that that I can provide to you that could ever quantify such a relationship if it existed in the first place.

If there is a specific ΔE15 value that you would like for me to provide you with, I can do so via PM if you can provide the variables needed—I can help with that,too.


Your 147 gr WWB/USA water penetration of app 13" being similar to the avg 13" in Organic Gel and the avg 13" in app 41 bodies 27/28 published in study and I believe DrGkr said 14 more with similar results after that in IWBA (not through bone) is interesting.
So water testing expansion for PISTOL bullets or below 1700 fps is 95-99% correlation to Organic Gel though a bit great expansion typically?
Is Water Jug Penetration similarly around 95-99% correlation to Organic Gel Penetration once you divide by X (and this X be that 1.6 or 1.7 is different depending on which method?)
Thank you

In the case of water testing, since liquids (water) cannot support a shear force whereas solids (e.g.: 10% ordnance gelatin or soft tissue) can, the penetration depth of a projectile in water must be ''converted'' to its equivalent depth of penetration in 10% ordnance gelatin or soft tissue through the use of a mathematical bullet penetration model. All of the five bullet penetration models are capable of doing so with high correlation to actual gelatin test data and excellent accuracy. The only values that are needed to use these equations are the bullet's drag coefficient, density of the test/target medium, post-impact diameter, post impact mass, and its velocity at impact. I advise against the use of plastic beverage containers in testing because the polymers used in their construction introduce strength effects into the experiment that can skew test results significantly. The best options for testing in water are sealable polyethylene 1-gallon freezer/storage bags or the ½-gallon paperboard cartons used most commonly for milk and orange juice.

In reference to 1.5x ''conversion'' factor proposed by Dr Fackler (that you seem to be referring to) on page 21 of the Fall 2001 issue of the IWBA Journal of Wound Ballistic Review: 5;2, Dr Fackler points out the limitation of using a simple linear conversion value by making it clear that there is some inherent inaccuracy in its use—''Most bullets will penetrate about 1.5 times as farther in water as in standard 10% ordnance gelatin: some penetrate even farther.'' More to the point, simple linear conversion values do not consider the influence of physical effects of drag, test medium density and strength, bullet diameter, mass, and/or velocity upon the maximum terminal penetration depth of a bullet.

The employment of mathematical bullet penetration equations—all of which consider the effect of drag, test medium density and strength, bullet diameter, mass, and velocity in their respective forms—greatly reduces the error in such predictions often to within a small fraction of an inch. While water does slightly over-drive projectile expansion, its effect upon the accuracy of these equation's predictions is minimal.

[Ghost Dog]

Hello Sir,
It was only early on in the thread that you included the E15 EKE data..

With the .327 Gold Dot and the 230+P is where a fairly large increase of EKE is present or the larger negative number

What I am really curious to see is any data on 125 gr .357 Mag or .357 Sig, 155 or 165 gr .40 increase over 180s, or if some 185+P's EKE is greater than standard pressure 230's...or say how much difference +p+ like 9bple is over standard pressure 9bp?

Can you please provide me any E15/EKE numbers of these faster rounds please?

I expect some of these pass -350 or get close to it...especially the 125 gr .357s and faster 155/165 gr 40s....which is quite a bit difference than say a standard pressure 115 or 124 gr 9mm.

While they lighter for caliber rounds generally may have less lead to spread, a bit less expanded diameter then their heavy for caliber counterparts, and therefore less Tissue Crush/Would Volume

...It seems to be that these faster rounds that I am guessing had more EKE, in real world OIS/DGU often had very successful effect, at least when there were no intermediate barriers present nor was it a side lateral shot through the arm first. While in shots through the later criteria, often present in the LE context, 15" of Penetration may be ideal.

However in the former more frontal shots that didn't require going through a barrier or arm first 11" of Penetration, huge expansion, large EKE & all energy being deposited inside the body may may have mostly worked great especially before better bullet technology and may still work great for the None LE situations .

I'm hypothesizing that something in-between, 13" of Penetration, larger expansion, larger Wound Volume before being stuck in the skin on the back or exiting, More EKE and more Energy in the body....

May be more ideal MORE OFTEN then then rounds with less expansion & 15-18" of Penetration (other than for those dealing with vehicles more often/state police etc.)

IE while Gold Dot, or perhaps Critical Duty may be better for Law Enforcement depending on the job duties
HST seems to be the best for Civilians overall
But 125 gr SJHP .357 Magnum, then to a lesser effect 9ple or other 115+p+, later .357 Sig 125 gr seemed to have worked great in most cases and with the two former...it wasn't huge penetration or huge expansion compared to others (or heavier for caliber 158s and 147's)
EKE seems to me to be this other thing that may matter...at least most of the time...

[Ghost Dog]

Whether you set you Penetration Parameter minimum at 11" or 12" or 13"

It would be nice if in different Calibers, and averages of say 5 rounds of the various bullet weights Light/Medium/Heavy were done in 9/40/45, and .327/.357 Magnum & .357 Sig whatever data is available...

Mr. Schwartz can you please Average 3 or 5 rounds by bullet weights and provide, even if in PM, the Would Volume and EKE please?

To see on average which bullet weights give the largest 1. Wound Volume & 2. Most EKE

It seems Heavy for Caliber is often the recommended, but perhaps that was with older Cup N Core bullets to ensure adequate penetration.

Is a Faster Medium weight for caliber perhaps better, at least with higher tech bullets that barely fragment?

And whey did extremely fast but light for caliber bullets...often work, at least in frontal non barrier shots?

If wound volume is fairly close, is one with more EKE desired? I'd like this data if possible.

IE I have tended towards 124+ over 147 in general and more specifically HST if available (though out of all 147s it seems HST seems the best out of all barrel lengths)
180 (HST) over 165, though I wonder if Wound Volume is similar, and wonder if the 165 (or even old 155 if you can find it) had more EKE?

I'm also curious if 185+P give similar enough Wound Volume, but more EKE, then 230 grain which by having more lead to spread greater expansion is it therefore a much greater Wound Volume or is it actually fairly close?

[Glock17JHP]

To me, "heavy for caliber" is better so that there is more bullet material to convert into greater expansion while also helping to keep penetration depth good through increased mass. Once a good penetration depth is achieved, then expansion increases can be achieved through more bullet material/mass. Remember that energy is not a reliable component of wounding effectiveness, a projectile has to physically disrupt structures to be reliably effective.

[the Schwartz]

Whether you set you Penetration Parameter minimum at 11" or 12" or 13"

It would be nice if in different Calibers, and averages of say 5 rounds of the various bullet weights Light/Medium/Heavy were done in 9/40/45, and .327/.357 Magnum & .357 Sig whatever data is available...

Mr. Schwartz can you please Average 3 or 5 rounds by bullet weights and provide, even if in PM, the Would Volume and EKE please?

To see on average which bullet weights give the largest 1. Wound Volume & 2. Most EKE

It seems Heavy for Caliber is often the recommended, but perhaps that was with older Cup N Core bullets to ensure adequate penetration.

Is a Faster Medium weight for caliber perhaps better, at least with higher tech bullets that barely fragment?

And whey did extremely fast but light for caliber bullets...often work, at least in frontal non barrier shots?

If wound volume is fairly close, is one with more EKE desired? I'd like this data if possible.

IE I have tended towards 124+ over 147 in general and more specifically HST if available (though out of all 147s it seems HST seems the best out of all barrel lengths)
180 (HST) over 165, though I wonder if Wound Volume is similar, and wonder if the 165 (or even old 155 if you can find it) had more EKE?

I'm also curious if 185+P give similar enough Wound Volume, but more EKE, then 230 grain which by having more lead to spread greater expansion is it therefore a much greater Wound Volume or is it actually fairly close?

Using manufacturer's 10% ordnance gelatin test data, I'll attempt to provide some reference points for you.

116886
ΔE15 = -320.13 fpe

116887
ΔE15 = -295.25 fpe

116888
ΔE15 = -335.23 fpe

116889
ΔE15 = -325.25 fpe

116890
ΔE15 = -415.56 fpe

I hope that this post answers some of the questions that you've asked.

[Ghost Dog]

Thank you, I will have to compare tomorrow to some of the rounds you gave earlier in the thread. Ie looking for 124+P HST vs 147 HST (and would love the eke on 9bple or other 115+p+ to compare), and 185 say Gold Dot vs 230 gold dot.

Thank you again, sorry to ask for more but is there any chance of providing the E15/EKE for 147 HST, 230 Gold Dot, 230 HST, and any 115+p+ as a comparison (Winchester gave their data on the Ranger, though I don't believe Federal ever did)? That would help me understand some things.

I do know many here like heavy for caliber, yet a lot of depts issue 124+P mostly Gold Dots I assume, or 135+p Critical Duty, though I wonder if more departments have gone to 147 HST, if that is cheaper than the gold dots, and also now penetrates farther since double cannelure added?

Just would like to have that data on different bullet weights, again if adequate penetration is reached (which 9bple doesn't penetrate very far but was very successful in most cases all over for a long time)

It seems the .45 crowd just sticks to 230, but shorter than 4-4.25" barrels the only 230 I see expand at low threshold is HST. For short barrels I do think many would be served better with 185s, and perhaps lower recoil in the smaller lighter 45 carried by AARP members... :)

I wish I knew how to figure E15/EKE from published data, is it a fairly easy formula to apply if you know bullet weight and velocity, as well as penetration and expansion?

On charts I have seen, am I correct that almost always with a pistol jhp you are looking at a bit over half of ME is lost by the 15cm mark? (That's probably the same for 5.56 too depending on bullet type, say a 193 that yaws and frags, but maybe not larger over .30 rifles & I know that is very dependent on projectile type?)

How much of a wider wound is there torn flesh the first few inches...say in a deer hit with a .357 hit at 1500 fps from 4-6" Revolver vs one hit with a 1200 fps by .355 9mm Pistol where legal to do so?

From high speed footage, is that what would be shown in Organic Gel and taken into consideration when calculating Wound Volume? So it's not just the r2 and depth, but also some actual tearing the first few inches of the wound adding to wound volume? I know we are not talking rifles, but there is a difference in the first few inches of the wound that adds to overall wound volume in those formulas, if seen in the gel on high speed cameras?

In both pistols, and rifle calibers I've heard many prefer that short neck for either expansion or Yaw (heavier 75-77 grain yaws later but that is still around lung penetration depth I believe when that happens hence effective and probably a sideways keyhole large exit out BGs back is my guess is what has been found though I don't know if that is true?)


That .357 Sig HST I have to assume will generally have VERY good effectiveness, where as the gold dot is likely better dealing with vehicles, but I know of two instances that .357 LE Gold Dot had ACTUAL Overpenetration of the BG. There was a Personal Defense Gold Dot that I believe had more like around 13" of Penetration.

Similarly I think it was the .45+p Ranger T that had a large EKE number you provided early in the thread.

It's hard for me to think that a round that gives adequate 1. Penetration for the task/duty 2. Expansion 3. Wound Volume that then higher EKE wouldn't be desired.

[Velo Dog]

How much of a wider wound is there torn flesh the first few inches...say in a deer hit with a .357 hit at 1500 fps from 4-6" Revolver vs one hit with a 1200 fps by .355 9mm Pistol where legal to do so?

Although they don't directly answer your questions, you might find these links interesting and somewhat relevant...

https://brassfetcher.com/Wounding%20Theories/Velocity%20of%20Radial%20Expansion.html

https://www.ballisticstudies.com/Knowledgebase/.357+Magnum.html

"As a general guide to performance, the .357 can produce quite spectacular kills at impact velocities of 2000fps and faster using hollow point projectiles.

At impact velocities of 2000 to 1600fps, game hit with a fast expanding hollow point tend to react in a drunken manner, often attempting to run but not generally making too much ground before succumbing quickly to blood loss.

Between 1600 and 1300fps, dead runs may be longer but wounding is still somewhat disproportionate to caliber. Again, bullet weights must be matched to the job at hand. If the bullet is too heavy, it may not meet enough resistance to render a wide wound at low velocities. If the bullet is too light, it may not have enough energy to render a deep and broad wound on larger bodied animals.

At impact velocities of 1200fps and below, bullet expansion may be fully evident, yet wounding can be narrow (proportionate to the expanded caliber of the bullet) and blood trails poor. At these velocities and in the absence of any major hydraulic force, the .357 is reliant on mechanical wounding, the size of the wound being directly proportionate to the diameter of the expanded bullet."

[Ghost Dog]

Although they don't directly answer your questions, you might find these links interesting and somewhat relevant...

https://brassfetcher.com/Wounding%20Theories/Velocity%20of%20Radial%20Expansion.html

https://www.ballisticstudies.com/Knowledgebase/.357+Magnum.html

"As a general guide to performance, the .357 can produce quite spectacular kills at impact velocities of 2000fps and faster using hollow point projectiles.

At impact velocities of 2000 to 1600fps, game hit with a fast expanding hollow point tend to react in a drunken manner, often attempting to run but not generally making too much ground before succumbing quickly to blood loss.

Between 1600 and 1300fps, dead runs may be longer but wounding is still somewhat disproportionate to caliber. Again, bullet weights must be matched to the job at hand. If the bullet is too heavy, it may not meet enough resistance to render a wide wound at low velocities. If the bullet is too light, it may not have enough energy to render a deep and broad wound on larger bodied animals.

At impact velocities of 1200fps and below, bullet expansion may be fully evident, yet wounding can be narrow (proportionate to the expanded caliber of the bullet) and blood trails poor. At these velocities and in the absence of any major hydraulic force, the .357 is reliant on mechanical wounding, the size of the wound being directly proportionate to the diameter of the expanded bullet."

Thank you very very much for this!

[DocGKR]

I have never been impressed with ΔE15/EKE or P[I], as they are pretty inaccurate as a measure of wounding effects in living tissue.

[the Schwartz]

I wish I knew how to figure E15/EKE from published data, is it a fairly easy formula to apply if you know bullet weight and velocity, as well as penetration and expansion?

Yes, it is fairly easy, so long as one has the ability to rearrange algebraically any of the five existing bullet penetration equations to solve for instantaneous projectile velocity; the only parameters that one needs to have available is the projectile's expanded diameter, mass, and impact velocity.

Rearranged correctly, any of the five bullet penetration equations can also be manipulated to solve for deceleration history (ΔV/ΔT), ballistic limit (V50), residual velocity (VR), instantaneous kinetic energy with respect to projectile position (F = ΔE/Δx) which is also known as the ''Work-Energy theorem'', and other relevant terminal ballistic performance metrics such as time with respect to projectile position (ΔT/Δx).

Each of the five existing bullet penetration equations will require a unique solution for these functions since they differ (mathematically) from one another.

[Ghost Dog]

I have never been impressed with ΔE15/EKE or P[I], as they are pretty inaccurate as a measure of wounding effects in living tissue.

Thank you for re-joining this thread. I appreciate your time.

I'm aware that #1 is adequate penetration for the expected situations or job description
#2 Expansion
I thought this gave you the amount of Tissue physically Crushed based on Dr Martin Fackler, but maybe I am wrong in figuring out Wound Volume ...is that only by high speed camera so it's not just r2 x penetration distance?

Given that having far greater priority to anything that doesn't penetrate deeply enough, wouldn't higher EKE be desired as long as adequate penetration? Obviously, Sub 11" penetration & Incapacitation Index shallow BS isn't good.

It seems to me that anything of at least 115 gr, or 125 gr at over 1300 fps , and better at 1450 fps seemed to work exceptional well from all reports I have ever heard ie 9bple, 125 gr Magnum/Sig why do you think this so? Isn't the initial wound the first few inches a bit wider in those velocity bullets Given Pen and Exp, doesn't it seem something closer to 475+ ft lbs seem to do more than 350 ft lbs or is it all just physical crush in your opinion? And the reports from the hunter that claims to have killed 8k+ animals on .357 in the 1300-1600 fps range seems to say there is a bit extra there, and certainly in the 1600-2100 fps from lever guns....Dick Fairburn says he trained with Dr. Fackler some and he is big on a .357 levergun for home/ranch defense with 125 gr xtp. He is also a big fan of .40/.45 over 9mm. Perhaps isn't the higher physiological sensation bad guys recognizing that they have been shot more likely to have a psychological reaction? I read your comments about .357 sig Loud bang and Flash perhaps having some psychological effect.

I believe you were originally a fan of .45...and I believe you liked HST, you've acknowledge .40 is really good if you are dealing in and around vehicles a lot (I assume Gold Dot would be the desired one for that, though I have lurked LE here saying everyone was very happy with 180 HST performance), and I believe you are now set on 147 HST is that so and if so from all barrel lengths? What are you carry choices and in which calibers? Always prefer the heavier for caliber? I don't know if you are still working LE part time or deputy etc or just carrying in a civilian context?

How often did Duty Caliber size JHPs under penetration and stop short of reaching vital organs in real world data you got? What about 115 gr was this or major bone deflection more of an issue with lighter for caliber 115 vs 124+p or 147 which penetrated straight line better? What about .32/380 FMJ vs JHP real world can you touch on that a bit more, how often did under penetration or major bone deflection changing path happen in this mouse caliber vs .38 & larger...I have read everything on here and other forums you have put out like .38 over .380... Thoughts on so many on here liking .32 H&R Magnum?

Final question for now, did you or anyone ever get to Read whatever study the Secret Service supposedly did? The 115+p+ Ranger they selected was a pretty shallow penetrator, & then they went to better .357 Sig.

Thank you very much,

[Ghost Dog]

Yes, it is fairly easy, so long as one has the ability to rearrange algebraically any of the five existing bullet penetration equations to solve for instantaneous projectile velocity; the only parameters that one needs to have available is the projectile's expanded diameter, mass, and impact velocity.

Rearranged correctly, any of the five bullet penetration equations can also be manipulated to solve for deceleration history (ΔV/ΔT), ballistic limit (V50), residual velocity (VR), instantaneous kinetic energy with respect to projectile position (F = ΔE/Δx) which is also known as the ''Work-Energy theorem'', and other relevant terminal ballistic performance metrics such as time with respect to projectile position (ΔT/Δx).

Each of the five existing bullet penetration equations will require a unique solution for these functions since they differ (mathematically) from one another.

Thank you

Where is the easiest or free place to learn these formulas? Or are they in your book? Being able to figure out EKE from like Vista or Hornady's published data is of interest to me

[Glock17JHP]

Suggest reading DocGKR's "sticky"" titled: "Basic Wound Ballistic Terminal Performance Facts"...

[the Schwartz]

Thank you

Where is the easiest or free place to learn these formulas? Or are they in your book? Being able to figure out EKE from like Vista or Hornady's published data is of interest to me

All five bullet penetration equations are available—some at no cost—while others will require a purchase.

1.) A Mathematical Model for Assessing Weapons Effects From Gelatin Penetration by Spheres (AD-770352); Sturdivan, LM; Edgewood Arsenal, SAREA-BL-BS, Aberdeen Proving Ground, MD, 21010, September, (1973)

Available here as a PDF: https://apps.dtic.mil/sti/tr/pdf/AD0770352.pdf

This particular bullet penetration model is a Resal's form equation. Algebraic manipulation may prove challenging to those unaccustomed to the form.

2.) A Mathematical-Physical Model of Wound Ballistics; Peters, CE; J Trauma (China), 6(2), Supplement: 303 - 318; (1990) University of Tennessee Space Institute, Tullahoma, TN, 37388

Peters' model is a Poncelet form equation. It also can be used to represent the temporary cavity using ''disc-energy trading'' by the integration of volumes using the method of disks in calculus. This mathematical method represents the temporary cavity as a series of disks with each separate disc diameter closely approximating the temporary cavity at a given penetration depth.

I cannot locate a link online for the PDF. I do have a copy of the technical paper if you'd like.

3.) Bullet Penetration: Modeling the Dynamics and the Incapacitation Resulting from Wound Trauma, MacPherson, D; 1995 and 2005

MacPherson's WTI model is also a Poncelet form.

Available here: https://www.amazon.com/Bullet-Penetration-Modeling-Incapacitation-Resulting/dp/0964357712

4. & 5.) Quantitative Ammunition Selection; Schwartz, C; (2012, 2014)

The Q-model is a Poncelet form. The mTHOR equation is a modified power law derived of a 1950's armor penetration equation.

Available at Barnes & Noble, Books-A-Million, Amazon, etc.

Once you decide upon an approach, you can use any of these models to investigate anything from deceleration (ΔV/ΔT), ballistic limit (V50), residual velocity (VR), instantaneous kinetic energy with respect to projectile position (F = ΔE/Δx) and even ΔE15 (EKE). Any exploration of the mathematical incapacitation models discussed here—

https://pistol-forum.com/showthread.php?32530-Predictive-tests-in-water&p=1566571&viewfull=1#post1566571

—will require the use of the correct respective 'a', 'b', and 'n', coefficients. The coefficients for the first two mathematical incapacitation models (Dziemian, 1961; Sperrazza & Kokinakis, 1965) are widely available. The coefficients for the Sturdivan mathematical incapacitation model remain classified so I cannot release them.

=====

Finally, using the approach described by Alekseevskii (1966) and Tate (1967) which assumes a steady-state flow stress field in a gelatin target ahead of the projectile and setting 'm' as the slope of the intact yield strength/pressure curve (where m = ¾) of the target material, solution of the transcendental equation for 'a' is—

[1 + (ρTU² ÷ YT) · √(KT - ρTa²U²)] = YT · [1 + (ρTa²U² ÷ 2GT) · √(KT - ρTU²)]

a = √[(2√3GT) ÷ (2σyT + ½mρTU²)]

—where 'a' must then be utilized in the computation of RT —

RT = (7 ÷ 3) · LN(a) · σyT

σyT = yield strength of the gelatin target material (350 kPa)

U = √(ρT ÷ ρP)

At any point along a bullet's path of travel, once the instantaneous velocity of the bullet is computed using any of the five bullet penetration equations above, the diameter of the penetration cavity, ØCAVITY, produced by the passage of the projectile through the target is—

ØCAVITY = ØPROJECTILE · √[(½ρPV2 ÷ RT) · ((V - U) ÷ U)]

[the Schwartz]

An interesting application of AT (Alekseevskii-Tate) hydrodynamic model is that the diameter of a projectile's temporary cavity in 10% ordnance gelatin can be predicted using the approach described below by Alekseevskii (1966) and Tate (1967) which assumes a steady-state flow stress field in a gelatin target ahead of the projectile and setting 'm' as the slope of the intact yield strength/pressure curve (where m = ¾) of the target material, solution of the transcendental equation for 'a' is—

[1 + (ρTU² ÷ YT) · √(KT - ρTa²U²)] = YT · [1 + (ρTa²U² ÷ 2GT) · √(KT - ρTU²)]

a = √[(2√3GT) ÷ (2σyT + ½mρTU²)]

—where 'a' must then be utilized in the computation of RT —

RT = (7 ÷ 3) · LN(a) · σyT

σyT = yield strength of the gelatin target material (350 kPa)

U = √(ρT ÷ ρP)

At any point along a bullet's path of travel, once the instantaneous velocity of the bullet is computed using any of the five bullet penetration equations above, the diameter of the penetration cavity, ØCAVITY, produced by the passage of the projectile through the target is—

ØCAVITY = ØPROJECTILE · √[(½ρPV2 ÷ RT) · ((V - U) ÷ U)]

For example, several years ago we conducted tests where 45 ACP 230-grain FMJ bullets were fired into calibrated 10% ordnance gelatin under high frame rate videography.

In this still image taken from a video in which a 0.451'' 230-grain FMJ was fired at 648 fps into 10% ordnance gelatin—

117466

—the diameter of the temporary cavity was determined to be 1.65 ± 0.05 inches.

Using the equation above, predicted diameter of the temporary cavity was 1.75 inches.