The attempt to simulate "average" tensile/shear/compressive strengths of muscle tissue has been through "calibration" of standard gel at 590 fps BB impact resulting in 3.35" penetration (however most of the "professional" gel tests that I have seen posted on the Internet have been performed in less viscous gel giving unrealistically favorable penetration performance) . As was made clear by interesting information revealed in an Australian fellow's Ph.D. dissertation I believe you provided a link to several months ago, there are other body "soft" tissues with greater strengths than muscle. This, of course, would exert greater non-inertial forces on a penetrating bullet and cause less penetration than penetration even in a properly "calibrated" 10% ordnance gel. These non-inertial forces -- which are not at all dependent on sonic velocity or bulk modulus of tissue or gel -- play a major role in bullet penetration and result, generally, in greater penetration in standard gel than in overall "soft" tissues in a body.
A gel expert explains
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Right, MacPherson -- but when an expanded JHP's velocity gets down to 400 ft/sec or so even 1/16" thick skin is able to stop it -- equivalent to some 4" penetration in standard ordnance gel. Surely, quite a few "soft" tissues have greater tensile/shear strength than skin.....
In his "Bullet Penetration" book MacPherson makes an attempt to address obvious mechanical differences between 10% standard ordnance gel and body tissues that affect bullet penetration. He lists them (p. 221): 1. Inhomogeneities in density, 2. Inhomogeneities in resistance to strain, 3. Viscous effects, and 4. Skin resistance. Bones have been left out, of course, because impact with bones, some with compressive strengths exceeding 15 kpsi have a tendency to stop an expanded JHP without further penetration (the notion that FBI auto glass test is indicative of JHP performance against bone in a body is flawed for a number of reasons).
What is particularly interesting is MacPherson's admission regarding "viscous effects": "The effective value of u (constant representing viscosity in his equations) may differ slightly in different types of soft tissue, but quantification of any viscosity differences would be an extremely difficult testing project." So, he simply assumed that different tissues do not have significantly different "viscous effects" (a term best reserved for gel not body tissues) because it would be "extremely difficult" to verify it. Well, the fellow in Australia in his Ph.D. dissertation (referenced in a previous post) -- did perform the "extremely difficult" testing and found, indeed, that there are significant differences in tensile strengths of body tissues. But I give MacPherson credit for writing the "Bullet Penetration" book nearly 30 years ago -- properly interpreted and "updated" it's still useful.
What is particularly interesting is MacPherson's admission regarding "viscous effects": "The effective value of u (constant representing viscosity in his equations) may differ slightly in different types of soft tissue, but quantification of any viscosity differences would be an extremely difficult testing project." So, he simply assumed that different tissues do not have significantly different "viscous effects" (a term best reserved for gel not body tissues) because it would be "extremely difficult" to verify it. Well, the fellow in Australia in his Ph.D. dissertation (referenced in a previous post) -- did perform the "extremely difficult" testing and found, indeed, that there are significant differences in tensile strengths of body tissues. But I give MacPherson credit for writing the "Bullet Penetration" book nearly 30 years ago -- properly interpreted and "updated" it's still useful.
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I do apologize for my directness, but this is simply not the case.
Bulk modulus (k), mass density (ρ), and internal speed of sound (c) are indeed relevant material properties that bear significantly upon the behavior of gelatin tissue simulants and how they represent the terminal behavior of projectiles and the respective suitability of candidate materials as soft tissue surrogates.
When FEM software—like LS-DYNA—is used to model projectile penetration in 10% ordnance gelatin, the constitutive relations for the shock Hugoniot are used to supplement the EoS with the material constants C₁ (bulk modulus), and C₂ and C₃ which are related to the internal speed of sound in 10% ordnance gelatin which is taken as being 1,520 m/s.ᵃ 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 whether one wants to admit it or not.
ᵃ J. Mech. Behavior of Bio-Med Matls 67 (2017) 40–50, Wen, Batra et. al.; Rifle Bullet Penetration into Ballistic Gelatin
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d2wing
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Excellent and informative video and right on point. Understand that they are not talking about hunting. They are talking about what works in gun fights. As in hunting, shot placement Trumps everything. Studies show that as long as you put the bullet in the correct place and it penetrates and expands the way you need the rest doesn't matter much. The key here it not like hunting. Shooting at someone who is shooting at you is nothing like hunting. You have to be able to concentrate on shot placement while seeking cover, your target moving and trying to kill you. There are several documented cases of multiple shooters in a small space shooting over 20 times and no one hit anybody. It takes lots of practice and training for most people to do this. I am speaking as a combat veteran. I have a 44 magnum and a 9 MM. If I was hunting a deer I would prefer a well placed shot with the .44, As a person who has been in an actual gunfight with other humans, I would take the 9 MM. I can shoot it way faster, getting on target and follow up shots are way quicker. Especially for multiple targets. I am pretty sure I can hit the guy in the heart or spine quicker than he can do that to me. You wouldn't believe how fast things happen and how much adrenaline is pumped into your system. The ability to concentrate and shot accurately is something I would only trust to someone who has done it. Talk and bravado don't count.
Now you can talk and pontificate all you want. I'll trust the experts. Not some person who talks ballistic in terms of momentum and 45-70's on the internet.
Another thing they explained is that there are different kinds of gelatin and they behave differently. The main point of test is to have a consistent medium to test bullets relative to each other. As stated in the video, they understand it is different than human tissue. Field results and studies show that there is a strong correlation . that is about all you can hope for. In humans the heart is also a nerve center. I have never heard of anyone doing anything but die when shot in the heart. Not waiting for bleed out and low percent head shots. To each his own. Like they said, if you are good with a .45 or other caliber go ahead use it.
Now you can talk and pontificate all you want. I'll trust the experts. Not some person who talks ballistic in terms of momentum and 45-70's on the internet.
Another thing they explained is that there are different kinds of gelatin and they behave differently. The main point of test is to have a consistent medium to test bullets relative to each other. As stated in the video, they understand it is different than human tissue. Field results and studies show that there is a strong correlation . that is about all you can hope for. In humans the heart is also a nerve center. I have never heard of anyone doing anything but die when shot in the heart. Not waiting for bleed out and low percent head shots. To each his own. Like they said, if you are good with a .45 or other caliber go ahead use it.
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I accept MacPherson's mathematical development, given in his "Bullet Penetration" book, as quite valid for predicting ordinary handgun bullet penetration in 10% ordnance gel (relevant topic here) -- and no one has refuted his peer-reviewed analysis. As pointed out to you previously, nowhere in his treatment of handgun bullet penetration does sonic velocity or bulk modulus enter into his bullet penetration equation as relevant variables -- although density certainly can be expressed in terms of bulk modulus and sonic velocity. As was also pointed out to you, the fact that two variables (sonic velocity and bulk modulus in this case) can define a function which is an important variable (density in this case is an important variable in bullet penetration equation) does not imply that those two variables themselves are important in bullet penetration. I also gave you an example where density, though defined as mass divided by unit volume, does not imply that either mass or volume of mass being penetrated by a bullet are relevant variables by themselves in bullet penetration equation. Bottom line: though density can be expressed in terms of sonic velocity and bulk modulus, neither of those two properties are relevant variables in handgun bullet penetration equation in gel.
What bullet velocity range is analyzed and, explicitly, what is the bullet penetration equation in the referenced article in terms of sonic velocity and bulk modulus outside of Newton-Lapalace equation for density? Now, granted, if bullet velocity is increased way beyond usable handgun velocities, then an entirely different mathematical treatment would be necessary -- but, again, that's not the relevant topic in this thread.
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You should be aware that Fackler is any but an expert on wound ballistics. He was a mortician with no ballistic training or knowledge that along with others hated the M-16, so he made up reports with many errors to push his unscientific opinions. Through self promotions he made money but some of what he says is wrong, some is outright lies.
There is no argument really; you brought up an irrelevant topic to try to justify your misunderstanding about relevant variables affecting handgun bullet penetration and then refuse to provide either an equation by anyone credible (not someone with just a b.s. in psychology) or even a range of relevant bullet velocities for that equation. How predictable...
The paper referenced may be fine for the analytical treatment of that particular topic, and you obviously are strongly disinclined to go beyond referencing it -- and that's just fine. However, as was made quite clear, MacPherson's bullet penetration analysis is acceptable to me, which is obviously at odds with your understanding, for discussion of the relevant topic here and that's just fine as well. Carry on.
Incidentally, as bullet velocity is increased above ordinary handgun velocities to rifle velocities -- bullet penetrations in water, gel, soft tissue, and even wetpack have greater similarity than penetrations in same at ordinary handgun velocities. As Einstein pointed out, velocity is a game changer for just about everything.
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Right. He expressed the fact that velocity is a game changer with differential manifolds and tensors.
Double Naught Spy
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Water indeed has similar bulk modulus to soft tissue as well as to 10% ordnance gel and similar internal sonic velocity as well, yet handgun bullet penetrations in water and 10% ordnance gel (and soft tissue) are vastly different, on the order of twice as great in water than in gel (all bullet parameters being equal). Now, increase bullet speed substantially above typical handgun speeds and that penetration difference begins to lessen. Yes, indeed, modeling terminal ballistic performance in fluids/liquids to achieve dynamic equivalence with soft tissue requires more than matching density -- it requires matching viscous forces in fluids/liquids to shear/tensile/compressive forces in "soft" tissues.
You put game changer in quotes, it was not a quote from Einstein but is a fact that velocity alters perception of space, time, mass -- just about everything.
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That was my point. Einstein would NEVER have referred to velocity as a "game changer," particularly as he saw all factors having their specific roles.
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Since the cited paper is not behind a pay-wall and is easily retrieved in less than 2 minutes' surfing on the 'net, I am sure that you can locate it for your own reference. Caution though, it is very technical. Earlier, in my haste, I did not make clear that the material constant C₁ (bulk modulus, k) that is used to supplement the EoS (that means equation of state) was expressed in the cited paper as C₁ = ρc² which is....wait for it.....the Newton-Laplace equation, c = √(k/ρ) , which is algebraically re-arranged so that C₁ is 10% ordnance gelatin bulk density (k).
MacPherson's modification of the Poncelet form and his analysis are certainly not at odds with my understanding. Technically comprehensive research far beyond MacPherson does exist on the topic.
There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. —William Shakespeare, Hamlet to Horatio (1.5.167-8)
Certainly there are more rigorous ways to analyze bullet penetration in gel than MacPherson's approach; however, adequacy of his approach has been established for virtually all practical purposes. Your position is indeed at odds with his approach since you maintain that density and density alone (aside from viscous forces that are not dependent on internal sonic velocity or bulk modulus) is not adequate to account for bullet penetration in gel.
QUANTITATIVE AMMUNITION SELECTION presents an accessible mathematical model that allows armed professionals and lawfully-armed citizens to use water as a valid tissue simulant to evaluate the terminal ballistic performance of self-defense ammunition.
Using a projectile's average recovered diameter, weight, and impact velocity to predict its penetration depth and the mass of permanently damaged tissue within the permanent wound cavity, the quantitative model produces a tangible measure of any projectile's terminal performance, permitting an accurate and direct comparison of all types of self-defense ammunition.
The model produces results equivalent to those obtained in tests employing calibrated ten percent ordnance gelatin as a tissue simulant without the associated technical and logistic difficulties.
With a little familiarization, the model's equations can generate accurate results in less than three minutes using only a hand-held scientific calculator.
I didn't state Einstein ever used "game changer" to describe the importance of velocity -- in virtually everything that's perceptible. Now, I said "game changer" to make it simple to understand the importance of velocity (instead of using Lorentz's contractions, differential manifolds and tensors that Einstein used).
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It is interesting that you offer this observation—
—as it matches very closely the perspective expressed in this peer review:
Of course, you are right. Both modified Poncelet forms (as proposed by MacPherson and Schwartz) are quite adequate for virtually all practical purposes.
—as it matches very closely the perspective expressed in this peer review:
Of course, you are right. Both modified Poncelet forms (as proposed by MacPherson and Schwartz) are quite adequate for virtually all practical purposes.
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And considering how much deviation from standard 10% gel there is in overwhelming majority of even "professional" tests that I have seen on the Internet (without "calibration" information), less than absolute rigor in MacPherson's approach is entirely tolerable. In academic circles anything can be made more rigorous than practically necessary just because it can be "challenging."
The problem with equating penetration in standard 10% gel and soft tissue is matching known viscous forces in gel to unknown shear/tensile/compressive forces in tissue and that is really not possible, meaning an unknown discrepancy is inevitable leading to necessity of a "correction" factor to account for the likely difference.
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With rare exception, if professional testing in 10% gelatin is desired, it will have to obtained through a paid professional source, like Brassfetcher.com (who is a member here) who is a Mechanical Engineer and more than capable of producing valid, quality data.
Some decent manufacturer test data does exist, but it is scarcer than hen's teeth.
One such example (with calibration BBs shown in each block) is this one, done by Brenneke USA:
Brenneke's 12-gauge Tactical Home Defense® (THD) test data in bare 10% gelatin is V = 1,256.6 fps, RD = 0.888”, RW = 419.8 gr., PEN = 17.75 inches
Using Brenneke's gel test data, both modified Poncelet forms give the following confirming penetration values:
MacPherson bullet penetration model: PEN = 16.78 inches
Schwartz bullet penetration model: PEN = 17.52 inches
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